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1 Crystal Structures of Principal Ceramic Materials Bruce G. Hyde, John G. Thompson, and Ray L. Withers
Research School of Chemistry, The Australian National University, Canberra, Australia
List of Symbols and Abbreviations 1.1 Introduction 1.2 Simple Structures 1.2.1 Bl, NaCl Type (cF8) 1.2.2 Cl, Fluorite Type (cF12) 1.2.3 A4, Diamond or Silicon Type (cF8); B3, SiC, BN, etc. Type (cF8); and A9, Graphite Type (hP4) 1.2.4 B h , Tungsten Monocarbide, WC (hP2) 1.2.5 C32, A1B2 Type (hP3) 1.2.6 D5 l 5 Corundum or oc-Alumina, A12O3 (hR10) 1.2.7 C16, Fe 2 B = CuAl2 Type (til2) 1.3 More Complex Structures 1.3.1 C43, ZrO 2 , Baddeleyite Type (mP12) 1.3.2 D2 1? Calcium Hexaboride, CaB 6 (cP7) 1.3.3 E2 1? Cubic Perovskites, ABX3 (cP5) 1.3.4 D0 l x , Cementite, Fe 3 C Type (oP16); Fe 5 C 2 (mC28); Fe 7 C 3 etc. [Cr 7 C 3 = D10 i ; Th 7 Fe 3 = D102]; B27, FeB (oP8); CrB (oC8); D7 b , Ta 3 B 4 (oI14); oc-MoB (til6) 1.3.5 H l l 9 Spinel, MgAl 2 O 4 (cF56) 1.3.6 Hexagonal Barium Ferrite Structures Related to the Magnetoplumbite (PbO • 6Fe 2 O 3 ) Type (hP66) 1.3.7 (3-Alumina (hP58) 1.3.8 HI3/SI3, P-Si3N4, and the (3'-Sialons (hP14) 1.3.9 Other (AIN-Related) Sialons 1.3.10 H5 7 , Apatite-Type Nitride Silicates of the Rare Earths (hP42); and the D8 8 , Mn 5 Si 3 Type (hP16) 1.4 High-Temperature Superconductors 1.4.1 The "1:2:3" Compound Ln 1 Ba 2 Cu 3 O 7 _ 5 [Ln = Y or Rare Earth(s)] 1.4.2 LnBa 2 Cu 4 O 8 1.4.3 (La, M) 2 CuO 4 (M = Sr, Ba) 1.4.4 The T1-, Bi- or Pb-Containing Families: (i) M 1 Ca w _ 1 M 2 Cu M O 2n + 3 (1
3 5 5 5 6 7 9 9 10 10 12 12 14 14
16 18 21 23 23 24 25 27 28 29 30 31 31 32
2 1.6 1.6.1 1.6.2 1.6.3 1.6.4 1.6.5 1.7 1.8 1.9
1 Crystal Structures of Principal Ceramic Materials Ferroelectrics Pyrochlores, A2B2X6Z (cF88) Perovskites, ABX3 LiNbO 3 Types Aurivillius Structures "Tetragonal Tungsten Bronze (TTB)"-Type Structures Solid Electrolytes Notes References
35 35 37 38 38 39 40 41 43
List of Symbols and Abbreviations
3
List of Symbols and Abbreviations a, b, c lattice parameters a, A, c lattice vectors a, b, c symbols for positions in c.p., anion-layer, stacking sequences A, A', B, M, M', Me atomic species, cations cll9 c22, c 3 3 elastic constants d second-nearest neighbour distance K bulk modulus I b o n d length Ln rare earth element (or yttrium) m(R, H) number of layers in the repeat unit of a (rhombohedral, hexagonal) c.p. stacking sequence M prototype structure: B a F e 1 2 O 1 9 p(O 2 ) partial pressure of oxygen Ps spontaneous polarisation Rt, Rwp crystallographic reliability parameters Ro length of bond of unit valence S prototype structure: spinel-type Me 2 Fe 4 O 8 ASf fusion entropy AStr entropy change at a (solid electrolyte) transition AStot total entropy change (here ASf + AStr) T, 7* tetrahedrally coordinated cations Tc critical temperature (of a superconductor) Ttr transition temperature v bond valence vid ideal bond valence x, x m a x variable, maximum stoichiometric proportion (in a formula) x, y9 z atom parameters X, XZ,Zf atomic species, anions Y prototype structure: I ^ M ^ F e ^ C ^ Z number of formula units per unit cell a, (3, y 5 a
symbols for positions in c.p., cation-layer, stacking sequences small variation in stoichiometric proportion (in a formula) specific conductivity
b.c.c. c c.c.p. c.e. c.p. C.N. f.c. f.c.c. F
body-centered cubic cubic cubic-close-packed cubic eutaxy close-packed coordination number face-centered (all) face-centered cubic face centered (lattice symbol)
4
h H h.c.p. h.e. m o oh P PSZ R R.T. s.g. t TTB VC
1 Crystal Structures of Principal Ceramic Materials
hexagonal hexagonal (lattice symbol) hexagonal-close-packed hexagonal eutaxy monoclinic orthorhombic ortho-hexagonal primitive (lattice symbol) partly-stabilised zirconia rhombohedral (lattice symbol) room temperature space group tetragonal tetragonal tungsten bronze Villars and Calvert reference
1.2 Simple Structures
1.1 Introduction The description of each structure includes (in the title) the Strukturbericht symbol and the Pearson symbol. The latter states, in order, the crystal system (c = cubic, h = hexagonal, etc.), the lattice symbol (P = primitive, F = [all] face centered, R = rhombohedral, etc.), and the number of atoms in the crystallographic unit cell so described. The text is usually preceded by the crystallographic data: symmetry, space group (s.g.), and space group number (in the International Tables of Crystallography, Vol. 1 or A), number of formula units per unit cell (Z), (sometimes) the unit cell parameters and, finally, the Wyckoff positions for the atoms in the unit cell together with the values of the parameters for the atoms. In the past, structural descriptions of inorganic materials such as oxides have, almost exclusively, emphasised the anions, often in terms of a more-or-less regular anion array (e.g., "close-packing") into the interstices of which the cations are inserted. It is time that rigid adherence to this convention was abandoned, for it is clear that the inverse description - anions in the interstices of a more-or-less regular cation array - is at least equally applicable (and in many instances more revealing). In this chapter we will therefore use any method of describing a structure which provides insight into its geometry. The separation into "simple" and "more complex" structures is, of course, rather arbitrary.
1.2 Simple Structures 1.2.1 Bl, NaCl Type (cF8) Cubic, s.g. Fm3m, No. 225; Z = 4: M in 4 (a) 000 + f.a, X in 4(b) lA lA lA +f.c.
This is perhaps the simplest and best known of structure types. Cations and anions both lie at the nodes of (separate) f.c.c. lattices, displaced from each other by a< Vi lA V2y (Fig. 1-1 a). It follows that the structure is unchanged if the M and X atoms (lattices) are interchanged, i.e. this structure is its own antitype. M occupies all the octahedral interstices in a cubic eutactic array of X, and vice versa, so that both atoms have regular octahedral coordination (CAT. = 6; Figs. 1-1 b, c), and each octahedron shares each of its edges with an adjacent octahedron (twelve of them; cf. Figs. 1-1 c, d). The eutactic layers (parallel to {111} planes of the f.c.c. unit cell) of M and X alternate along the stacking direction, <111>, the layer sequence being • • • aybocc pay * • •.1 This is a "one-parameter structure": a single parameter, usually taken as the f.c.c. unit cell edge, a, specifies it completely. Once fixed, all the remaining parameters are determined, e.g., bond length, /(Na-Cl) = a/2, secondnearest neighbour distances, d(Na...Na) = / Many binary compounds have this structure: alkaline earth and other monoxides (MgO, CaO); mono-nitrides of the lanthanides and actinides as well as those of the transition metals, e.g., CrN, NbN, TaN (high-pressure form), TiN, VN, and ZrN; and transition metal mono-borides and -carbides, e.g., TiB, TiC, VC, etc. (These last are often non-stoichiometric, carbon deficient.) Many ternary, quaternary, etc. compounds and alloys are also reported to be isostructural: they must be disordered (because there are only two crystallographically distinct sites in the structure), or ordered and of lower symmetry, possibly with an enlarged unit cell. Villars and Calvert (1985) (VC) list 374 examples, only a minority of which are binaries with MX
1 Crystal Structures of Principal Ceramic Materials
(a)
(d)
(b)
(c)
a
Figure 1-1. (a) The B1 structure of sodium chloride. The unit cell is outlined; large circles are Na, small ones are Cl (but they can be vice versa), (b) Bonds in the NaCl structure, cf. (a), (c) The cations at the corners and faces of the unit cell of NaCl in (a) and their anion coordination polyhedra. (d) The NaCl structure projected on (100) of the orthohexagonal unit cell (Z = 6; outlined with broken black line). This is equivalent to (T 01) of the f.c.c. cell (Z = 4), (10 T) of the primitive rhombohedral cell (the projection of which is outlined with a broken white line), and (001) of the body-centered tetragonal cell (Z = 2; outlined with a continuous white line), and (1120) of the hexagonal cell (Z = 3). The matrices are, respectively, h-±oK(l 10/110/0 01); r - » M l T 0 / 0 1 I / l l l ) ; / - > r , (0 Y2 Vi/Yz 0 Vi/V2 XA 0); and
/ -• t,
(l/20
V2/010/
-YiOVi) and *-•/, (101/010/101).
stoichiometry. (But not all of them exist, e.g., most of the listed rare earth monoxides, LnO are really nitrides or oxy-nitrides.) 1.2.2 Cl, Fluorite Type (cF12) Cubic, s.g. Fm3m, No. 225; Z = 4: M in 4(a) 000 + f.c, X in 8(c): + (% % Vj + Lc. This is also a one-parameter structure: it consists of two interpenetrating arrays which are, in the case of CaF 2 itself, a cubic eutactic ("cubic close packed", c.c.p.) array of Ca plus a primitive cubic array of F (Fig. 1-2 a). Usually (Fig. l-2b) it is described as consisting of {M}X8 cubes sharing each edge with an adjacent cube but, equally
accurately, it can be described as X atoms in all the available tetrahedral interstices (two per M atom) of a cubic eutactic or "close-packed" array of M, i.e., {X} M 4 tetrahedra sharing each edge with an adjacent tetrahedron (Fig. l-2c). For this latter description the sequence of eutactic layers is ...cab ape bya cab ape bya cab ape bya... (Note that while the labels of the anion layers correspond to c.c.p., their array is not of that form because the inter-layer spacings are inappropriate.) Examples of materials with this structure include some lanthanide and actinide dioxides (e.g., CeO 2 , ThO 2 , UO 2 , PuO 2 )
1.2 Simple Structures
as well as ZrO 2 (at very high temperature; or "stabilised" - usually by CaO or Y 2 O 3 , and therefore oxygen deficient); but no metal nitrides; a boride and carbide, Be2B and Be2C; and silicides such as CoSi 2 , Mg2Si. VC list over 100 isostructural compounds but, again, only a minority are MX2 (or M2X); and their list is not complete.
O
6
j
(a)
(c)
Figure 1-2. (a) A unit cell of fluorite, CaF2: large circles are Ca, small ones are F. (b) The structure of CaF 2 depicted as {Ca} F 8 cubes: each cube shares each of its edges with another cube, (c) The structure of CaF 2 depicted as {F}Ca4 tetrahedra (F not shown; they center the tetrahedra): each tetrahedron shares each edge with another tetrahedron.
1.2.3 A4, Diamond or Silicon (cF8); B3, SiC, BN, etc. Type (cF8); and A9, Graphite Type (hP4) Diamond-Cubic, s.g. Fd3rn, No. 227, Z = 8; a = 3.567 A; F = (000, OViVi, !/20 V2, lA Y2 0) + C in 8(a): (000, % % %). [With the alternative origin (3m instead of 43m), the atom parameters are ± (% Vs Vs) rather than (000, % % %).] Diamond is, of course, the hardest, least compressible substance known. (Its bulk modulus, K = 5.42 x l O ^ N m " 2 = 5.42 Mbar: cf. corundum, K = 2.4 Mbar; silicon, K = 1.0 Mbar; graphite, K = 0.33 Mbar.) But it is a high-pressure polymorph, not stable under ambient conditions; the stable form is graphite. Si, oc-Ge and a-Sn are isostructural. It is a rather simple (one-parameter) structure, based on the perfectly regular tetrahedral arrangement of first nearest neighbour atoms around each carbon atom (Figs. 1-3 a and b). The structure is often said to be very empty (as Figs. l-3b and c suggest) but, as its extreme incompressibility implies, this is quite untrue - as is shown by Fig. l-3d, in which the C atoms are given their van der Waals radii. There is overlap of van der Waals spheres, not only for first- and second-nearest neighbours, but for third-nearest neighbours also! 2 If alternate atoms in the 4-connected net are of different chemical species, the 8 (a) sites ofFd3m (000, VA VA VA) split into two 4-fold sets in F43m: 4(a) (000) and 4 (c) (VA % VA). We then get the following structure type. SiC-Cubic, s.g. F43m, No. 216, Z = 4; a = 4.359 A; all atoms in F =(000, 0 Vi Vi, V*0lA, lA 14 0) + Si in 4(a): (000); C in 4(c): (VA VA VA) (or vice versa). This is the B3 structure of the sphalerite ("cubic zinc sulfide" or "zinc blende") type; and of one of the (very many) poly-
1 Crystal Structures of Principal Ceramic Materials
(a)
(b)
(c)
morphs of silicon carbide, SiC ("carborundum").3 In terms of eutactic layers, it is •••aabpcyaab(3cya--- or, equivalently, •••apbycaapbycaa---. [The other SiC polymorphs are "polytypes": stacking variants which are basal plane {(lll) c u b i c / (0001)hexagonal} intergrowths of the cubic form with the 2-layer hexagonal form, which is called the "hexagonal zinc sulfide" or "wurtzite" type B4 polymorph (cf. Sec. 1.3.9, below). A rare form of diamond, lonsdaleite, also has this simple hexagonal structure.] The B3 structure corresponds to Fig. 1-3, but with alternate atoms of e.g., Zn and S: Fig. 1-3 a then corresponds to {Zn} S4 (or {S} Zn 4 } tetrahedra. Another refractory material isostructural with B3-type ZnS, and which is also extremely hard and incompressible, is cubic boron nitride.4 (A high-pressure polymorph; the stable form at one atmosphere is a layer structure (B12) - different from, but more like, graphite.) Graphite has a simple layer structure ("two-" not "three-dimensional"). The layers are well-separated, and each carbon atom is bonded to only three first-nearest neighbours (Fig. 1-4). The crystallographic data are as follows:
(d) Figure 1-3. The structure of diamond, (a) As {C} C 4 tetrahedra; (b) showing C-C bonds (the unit cell is outlined in both of these; and they are clinographic projections), (c) Shows a "ball and stick" model of a small diamond crystal, with "dangling bonds" tied off by H atoms, (d) Shows exactly the same structure as (c), but now the atoms are depicted as their van der Waals spheres: note how the "empty structure" in (c) has now become very crowded.
Figure 1-4. The structure of graphite in clinographic projection, approximately on (1 00)oh = (1120) hex . The unit cell is outlined. The two fine vertical lines indicate the ... abab... layer stacking sequence.
1.2 Simple Structures
Hexagonal, s.g. P63/mmc, No. 194, Z = 4; a = 2.461, c = 6.709 A; C in 2(a): ± (00 %); C in 2(d): + (2/3 lA %). [There may still be some doubt about the exact z parameters, and therefore the s.g., but the errors are Az< 0.004 (Donohue, 1974).] This is "hexagonal graphite": the stacking sequence of the 6 3 layers of C atoms is • • a b a b a - - . There is a rarer rhombohedral form with the sequence •••abcabca---.
1.2.4 B h , Tungsten Monocarbide, WC(hP2)
Hexagonal, s.g. P6m2, No. 187; Z = l: for WC, a = 2.906, c = 2.837 A (c/a = 0.976); W in I (a): 000, C in l(d): lA 2A lA. This is a very simple structure (only one atom of each type per unit cell) which consists of a primitive hexagonal array of tungsten atoms with a carbon atom occupying alternate W6 trigonal prisms. There are, of course, many ways of doing that: in this structure the arrangement which prevails produces columns of {C} W6 prisms sharing triangular faces; the columns being united by edge-sharing between adjacent prisms in a basal plane layer, Fig. 1-5. It is, obviously, its own antistructure (with {W}C6 prisms); and is to be contrasted with the NiAs, B8b type, in which triangular prisms {As}Ni6 share only edges so that the {Ni}As6 polyhedra are trigonal anti-prisms, i.e., octahedra. Ignoring the difference between W and C, the stacking of (0001) layers of atoms is that in h.c.p., but the c/a ratio is very different, 0.976 compared with y/S/3 = 1.633. It seems highly likely that there is W-W as well as W - C bonding: the distances /(W-W) = 2.837 A (2x), 2.906 A (6x) in this structure are comparable with those in b.c.c. Wmetal-2.741 A(8 x), 3.165 A(6 x).
Figure 1-5. The structure of WC, approximately on (1120), showing {C} W 6 trigonal prisms; c axis vertical.
[The distances / (C-C) = / (W-W) are much too long for C-C bonding.] Some transition-metal borides, carbides, nitrides and phosphides are isostructural (VC lists about 20), but others are Bl type (cf. Sec. 1.2.1). 1.2.5 C32, A1B2 Type (hP3)
Hexagonal, s.g. P6/mmm, No. 191; Z = 1: for A1B2, a = 3.009, c = 3.262 A (c/a = 1.084); Al in l(a): 000, B in 2(d): ±( 1 /3 2 /3 Vl).
This, also very simple, structure consists of a primitive hexagonal array of Al atoms, with every trigonal prism site (of which there are two per Al atom) occupied by a B atom. The result is 6 3 nets of B atoms sandwiched between 3 6 nets of Al atoms, i.e., {B}A16 trigonal prisms and {A1}B12 hexagonal prisms. The structure of A1B2 is shown in Fig. 1-6; it may be regarded as a "filled-up" WC type. Undoubtedly the B atoms are bonded to each other, as are the Al atoms; and there is also Al-B bonding. The bond lengths are: /(B-B) = 1.74 A in the (0001) plane, C.N. = 3 (cf., an average of 1.81 A in elemental, tetragonal-50 boron, C.N. = 5), Z(Al-Al) = 3.0lA (6x), 3.26 A (2x) [cf., 2.86 A (12 x) in Al metal], and /(Al-B) = 2.38 A. ZrBe2 and HfBe2 are isostructural, as are a number of transition metal (including lanthanide and actinide) di-borides and di-
10
1 Crystal Structures of Principal Ceramic Materials
The structure is shown in two projections in Figs. 1-7 a and b. These exhibit the well known facts about this structure:
Figure 1-6. ine structure oi /\1B2 projected on (0001). Large circles are Al at height z/c = 0, small ones are B at z/c —1/2. {B}A16 trigonal prisms are shown; and the hexagonal unit cell is outlined in white.
silicides; a total of about 40 different compounds. (There are also many isostructural intermetallic alloys; VC list about 250 examples.) Some of the compounds listed as C32 are "non-stoichiometric": these must be disordered, or (undetected) superstructures. [Geometrically at least, B8b (Ni2ln) type structures should also be included. (VC list 120 of these.) Although usually described as a "filled-up" NiAs type, i.e., h.c.p. As with all octahedra and trigonal bipyramids occupied by Ni, they are superstructures of the C32 type: if the latter is MX 2 , the former is X(MX) (O'Keeffe and Hyde, 1991). Both families cover the same wide range of c/a ratios - from ~ 1 to ~2.5!] 1.2.6 D5 1 9 Corundum or a-Alumina, A1 2 O 3 (hR10)
Rhombohedral, s.g. R3c, No. 167; Z = 2 for the rhombohedral cell, but Z = 6 for the hexagonal cell (which we will use): for A12O3, a = 4.754 [4.7602], c = 12.99 [12.9933] A (c/a = 2.730); Al in 12 (c): ±(0 0z, OOVi+z) with z = 0.35228 [0.35216]); O in 18(e): ±(x0 1 / 4 , Ox1/*, xx*A) with x = 0.3064 [0.30624], both + rhombohedral centering: (0,0,0, lA,2A,2A, 2 /3, lA9 XA) X-ray data: Ishizawa et al. (1980); [neutron data: Lewis et al. (1982)].
(i) That the anions are arranged in slightly deformed hexagonal eutaxy ("close packing"); (ii) that, in those terms, it is a "6-layer structure"; (iii)that there is very obvious cationcation repulsion along c, due to the closeness of approach of the two Al atoms in each pair of face-shared {A1}O6 octahedra. It results in Al-O bonds of two rather different lengths: three short (1.852 A) and three long (1.972 A), a difference of 6%. This distortion may also be regarded as a consequence of the conflict (in Al^O^) between regular octahedral coordination of Al by O ({Al} O6) and regular tetrahedral coordination of O by Al ({O} Al4), i.e., a consequence of second-nearest neighbour repulsions - anion-anion in the first case and cation-cation in the second. In this case the former appear to be greater than the latter, for their range of secondnearest neighbour distances is much less. Since this is a 6-layer structure, if the anions were in perfect hexagonal eutaxy c/a would be 6 x , / % / ^ 3 = ^ 8 = 2.828, The observed value is 0.965 x ^S. There are a few isostructural transitionmetal sesquioxides and sesquisulfides. (And there are several "aluminas", with various prefixes from the Greek alphabet. Most of them are ill-defined, but cf. P-alumina, Sec. 1.3.7.) 1.2.7 C16, Fe 2 B = CuAl 2 Type (tI12)
Fe 2 B-tetragonal, s.g. 74/racm, No. 140, Z = 4; a = 5.110, c = 4.249 A; atoms at (000, lA Vi V2) + Fe in 8(/z): ± (x lA + x 0, V2+XXO) with x = 0.1649; B in 4(a): ±(00%).
1.2 Simple Structures
11
(a)
(b) O
O
O
c
oh
(b) Figure 1-7. (a) The structure of a-Al 2 O 3 projected on (000 l)h. It has a 6-layer repeat, but only two layers are shown. Large circles are Al, small ones are O atoms. The broken black line outlines the ortho-hexagonal unit cell (with two circles at the origin). The two hexagons (full and broken white lines) are units of the two cation layers - 6 3 nets: the obvious displacement vector between them, when repeated, generates all the other layers. Atom heights are given in units of
Figure 1-8. (a) The {B} Fe 8 coordination polyhedron in Fe2B - a square antiprism. (b) The tetragonal structure of Fe2B projected on (001). Small dark circles are B at z/c= ± %, large open circles'are Fe at z/c = 0, yA. (It is a 2-layer structure.)
In this structure the smaller atom (B in Fe2B) has coordination number 8. The coordination polyhedron is a (not perfectly regular) square antiprism, Fig. 1-8 a (very similar to the bi-capped prism; a small distortion transforms one into the other). These square antiprisms share square faces to form columns parallel to e, and edges to produce the 3-dimensional structure, Fig. 1-8 b. A number of borides [M2B, with M = Co, Fe, Mn, Mo, Ni and W, or even two sorts of (disordered) metal atoms] and a few carbides, silicides and phosphides are iso-structural [also many intermetallic alloys - a total of ~ 120 compounds in VC: see also Havinga et al. (1972)].
c/100; they reveal the puckering of cation and anion layers. The latter are in distorted hexagonal eutaxy ("close-packing"), (b) The structure of a-Al 2 O 3 projected on (11 20) of the hexagonal cell, (100) of the ortho-hexagonal cell. Again, large circles are Al, small ones are O atoms. The broken black line outlines the ortho-hexagonal unit cell (with two circles at the origin). Anion heights are given in units of aoh/100, cations are at 0 (open circles) and a/2 (filled circles).
12
1 Crystal Structures of Principal Ceramic Materials
1.3 More Complex Structures 1.3.1 C43, ZrO 2 , Baddeleyite Type (mP12) Monoclinic, s.g. P2Jc9 No. 14; Z = 4:
all atoms in 4(e): ±(xyz, x y+Vi Vi—z): atom parameters in Table 1-1. Although baddeleyite (the name of the mineral zirconia) is, chemically, a binary compound, crystallographically it is a ternary: atoms occupy three crystallographic distinct sets of sites. Most of the few isostructural compounds are, in fact,
chemical ternaries (Table 1-1). ZrO 2 has several polymorphs (cf., Sec. 1.7, below); the three with well-determined structures are: this (monoclinic) one (m), which is the stable form up to ~1100°C; a tetragonal one (t), stable up to ~2300°C; and a cubic, Cl type (c) stable only at the highest temperatures. Topologically, they have virtually the same structure; transformations between them are therefore "martensitic"; in principle, coherent.5 Consequently, this structure is frequently described as a distorted fluorite
Table 1-1. MX2 compounds with the C43 (baddeleyite) structure. Unit cell parameters
Atom parameters
a(k)
b(k)
c(k)
P
Atom
x/a
y/b
z/c
R (%)
1. HfO 2 a
5.1170
5.1754
5.2915
99.216°
4.970
5.033
5.193
100.23°
3. ScOF c
5.167
5.147
5.248
99.70°
4. ScOF d
5.1673
5.1466
5.2475
99.70
5. TaON b
4.968
5.037
5.185
99.56°
6. TaON e
4.9581
5.0267
5.1752
99.64
7. ZrO 2 f
5.169
5.232
5.341
99.25°
8. ZrO 2 8
5.145
5.2075
5.3107
99.23°
9. ZrO 2 h
5.1505
5.2116
5.3173
99.23°
0.2755 0.0742 0.4487 0.2911 0.0636 0.4402 0.30785 0.0563 0.4565 0.3073 0.057 0.4574 0.2912 0.065 0.443 0.292 0.064 0.445 0.2758 0.069 0.451 0.2758 0.070 0.442 0.2754 0.0700 0.4496
0.0397 0.332 0.758 0.0472 0.3244 0.7546 0.02656 0.3243 0.7531 0.0267 0.3254 0.7525 0.0440 0.333 0.753 0.046 0.324 0.757 0.0404 0.342 0.758 0.0411 0.336 0.755 0.0395 0.3317 0.7569
0.2080 0.347 0.480 0.2151 0.3476 0.4782 0.21256 0.3426 0.4879 0.2129 0.343 0.490 0.2150 0.344 0.482 0.213 0.345 0.481 0.2089 0.345 0.479 0.2082 0.341 0.479 0.2083 0.3447 0.4792
?
2. NbON b
Hf O(l) O(2) Nb O N Sc F O Sc F O Ta O N Ta O N Zr O(l) O(2) Zr O(l) O(2) Zr O(l) O(2)
a
3.1
3.0
7.6
8.4
12.9
12.5
?
4.7 (jR w )
Hann et al. (1985); b Weishaupt and Strahle (1977); c Vlasse et al. (1979); d Holmberg (1966); e Armytage and Fender (1974);f McCullough and Trueblood (1959); g Smith and Newkirk (1965); h Howard et al. (1988).
1.3 More Complex Structures
13
(Cl) type; the three edges of the unit cells are very similar in length - about 5.0 to 5.2 A for all the compounds with first-row anions (Table 1-1). But the monoclinic angle, /?^100°, is a measure of the quite considerable distortion of the fluorite type - a shear of the cubic Cl cell by -10°. But this is only a part of it: the structure of ScOF, shown in Fig. 1-9, reveals the ~10° offset/shear (0° in Cl), and also the alternating large and small intervals between (10 0) layers of cations (which are equally spaced in Cl, Fig. 1-10).6 As in Cl, the oxygen atoms occupy tetrahedral sites in the cation array, {O} Sc4 [{O(2)}Zr4 in ZrO 2 ]; but the fluorines are 3-coordinate, {F}Sc3 [{O(l)}Zr 3 in Figure 1-10. The structure of fluorite, CaF 2 . Cf. Fig. 1-9.
Figure 1-9. The baddeleyite/C43 type structure of ScOF projected on (010); large circles are Sc, small ones are O (heavy rings) or F (lighter rings). The structure is depicted as layers of edge-shared {O} Sc4 tetrahedra with intervening layers of 3-coordinate fluorine, {F}Sc3. Within the shaded layers, filled/ open circles are cations at y/b « 0.5/0, anions at y/b « 0.75/0.25: between them the F atoms are at heights given (in units of c/100). The tetrahedral layers occur in Cl type (Figs. 1-2, 1-10) but, in C43, adjacent layers are offset by the ~ 10° shear (see text). Some of the F-Sc bonds are shown in the lower left by full lines (with bond lengths in A). The broken lines are F • • F contacts: longer = 2.58, 3.81 A; shorter = 2.78 A (2 x).
ZrO 2 ], although not quite at the centers of the Sc3 triangles.7 The cations are therefore 7-coordinate, {Sc}O4F3 [{Zr} O(2) 4 O(l) 3 in ZrO 2 ]. The cation coordination polyhedron may be variously described - as a cube (Cl) with one face replaced by a triangle, or as a monocapped trigonal prism: either way it is a rather irregular figure. It is interesting to compare the anion nets in the two structures, Cl and C43. In the former, for example, the {100} nets are all 4 4 , of course; and accurately planar. The (100) nets for the latter (ScOF) are shown in Fig. 1-11; they are slightly puckered, but the big change is that the transformation (from {O} Zr 4 in the former to {F} Sc3 in the latter) changes alternate 4 4 nets to 32.4.3.4. We chose to depict the structure of ScOF (rather than ZrO 2 ) because it seems to be the best determined. Except for the third solution of ZrO 2 , number 9 in Table 1-1
14
1 Crystal Structures of Principal Ceramic Materials
o
o
sion of the latter: it has twice as many O(l) sites as O(l) atoms. 1.3.2 D2 15 Calcium Hexaboride, CaB6 (cP7)
o Figure 1-11. The anion layers in baddeleyite-type ScOF parallel to (100): large, open circles are F atoms at x/a^0; small ones are O atoms at x/awl/2. (Heights are given in units of a/100.) The former lie on slightly deformed 32.4.3.4 nets, and the latter on slightly deformed 4 4 nets (outlined with full and broken lines respectively).
[a powder neutron (Rietveld) solution], the R factors are not as low as one would like (and expect). But there seems little reason to doubt that the structures are correct.8 Several orthorhombic polymorphs of zirconia have also been reported recently, although we will not discuss them here. Those with well-authenticated structures are a high-pressure one, s.g. Pbca (with a doubled a-axis; prepared at 600 °C and 60kbar; Ohtaka et al, 1990), and a lowtemperature one, s.g. Pbc21 (prepared by cooling to 30 K; Kisi et al., 1989): both may be (and were) "quenched" to ambient conditions, at which neutron powder-diffraction data were collected. [The latter is one of 5 co-existing phases in partly-stabilised zirconia (PSZ) containing ~10mol% MgO: the stoichiometry of the orthorhombic phase is not given.] A third orthorhombic polymorph, s.g. Pbcm [structure determined by X-ray diffraction at high pressure in a diamond-anvil cell (Kudoh et al., 1986)], may be a disordered or twinned ver-
Cubic, s.g. Pm3m, No. 221, Z = l, a = 4.145 A, Ca in l(a): 000; B in 6(/): ±(x00, 0x0, OOx) with x = 0.207. In this example the bonding between the smaller atoms is very pronounced: they form octahedra, which are united by additional bonds: another (natural) "composite structure" (cf., Sec. 1.2.5), with a primitive cubic array of Ca interpenetrating a similar array of B 6 octahedra. Bond lengths are /(B-B) = 1.72 A (5 x), within and between the B 6 octahedra [cf., an average of 1.81 A (6x) in (elemental) tetragonal-50 boron, and 1.75-1.85 A (6 and 7 x) in rhombohedral-12 boron (Donohue, 1974)]. For the metal array, /(Ca-Ca) = 4.15 A (6 x) [compared with 3.95 A (12 x) in f.c.c. Ca metal]. These values are consistent with B-B, Ca-Ca and Ca-B bonding. Formally, the structure may be regarded as deriving from the simple B2 = CsCl type by replacing the non-metals by B 6 octahedra, see Fig. 1-12 a. The coordination number of Ca by B is 24(!), and the coordination polyhedron is approximately a truncated cube (Fig. l-12b). Iso-structural compounds include hexaborides of the other alkaline earth metals, the lanthanides, Y, Th, K and even Si (as well as some ternary borides) - a total of about 50 examples according to VC. 1.3.3 E219 Cubic Perovskites, ABX3 (cP5) Cubic, s.g. Pm3m, No. 221, Z = l; A in l(a): 000; B in l(fc): Vi Vi XA\ X in 3(c): OViVi, Y2OV2, YiYiO.
In this structure the B atoms are in 6-coordination (octahedral) and the A atoms are in 12-coordination (cuboctahedral). But
1.3 More Complex Structures
o
o
15
o
o
(b) Figure 1-12. (a) The cubic structure of CaB 6 . Small circles are B atoms, larges ones are Ca. (Empty) B 6 octahedra are shaded, and the B-B bonds between them shown as heavy lines, (b) The {Ca} B 24 coordination polyhedron in CaB 6 .
it is unfortunately named, for "perovskite" is the mineral CaTiO 3 which, contrary to the original determination, does not in fact have this structure (except above 900 °C). Under ambient conditions it is distorted, from the cubic "aristotype" to an orthorhombic "hettotype"; although the latter differs only slightly from the cubic form (which is the structure of SrTiO 3 at R.T.) by a small topological distortion. The cubic parent, shown in Fig. 1-13, can and does yield several topologically distorted derivatives of various symmetries, i.e. hettotypes, of which the orthorhombic variety is only one. However, we will not pursue
Figure 1-13. The E2 l 5 cubic "perovskite"-type structure (as originally, but incorrectly reported for CaTiO3) projected on (a) (001), (b) (110), and (c) in clinographic projection. The largest circles are A atoms (Ca), the smallest are X(O), and the medium sized ones are B (Ti); in (a) and (b), open at x/a = 0, shaded at x/a= V2. {Ti}O6 octahedra are drawn.
this matter here: reference may be made to several available treatments of this crystallographically interesting question (e.g., Megaw, 1973; Glazer, 1972; O'Keeffe and Hyde, 1977). The basis of this apparent complexity is very simple - the cubic structure is
16
1 Crystal Structures of Principal Ceramic Materials
"overdetermined". Even if only the bond lengths l(A-X\ l(B-X) (or bond valences) have to be satisfied, which means two parameters, this is strictly not possible for it is a "one-parameter structure": all atoms are in special positions, and hence the sole adjustable variable is the unit cell edge, a. This dilemma for the structure was first discussed in terms of a "tolerance factor", the departure from the ideal ratio
Q = l(A-X)/l(B-X)
= (aA/2)/(a/2) = Jl
which, for unconstrained bonds, is likely to be the case for any A, B or X. In the simplest terms: (i) if the ratio g > y/2, B is "too small": it may "rattle" in its {B} X6 octahedron, and hence go "off-center" - an obvious source of ferroelectric behaviour (cf., Sec. 1.6 below); (ii) if the ratio g < ^/2, A is "too small": and the BX3 framework of corner-connected {B}X6 octahedra "collapses" (by concerted tilts of the octahedra) to shorten some of the A-X bonds, and improve the bond valence sum at A. (An inevitable consequence is a reduction in the coordination number of A byX) While best known as an oxide structure (JST = O), Villars and Calvert (1985) list about 140 different anti-structure compounds ABX3 (all cubic) in which X and A are metal atoms and B is boron, carbon, or nitrogen etc. - i.e., refractory alloys.9 This range is greatly extended if one includes the hettotypes and those related compounds in which, especially, the B sites are unoccupied. The classic example is cementite, Fe 3 C, to be discussed next: it is the orthorhombic hettotype AnBX3 (• represents a vacant site) with A = C, B empty and X = Fe. (Contrast AlFe3C, or AlCFe3, with A = A1,B = C and C = Fe.)
1.3.4 D 0 n , Cementite, Fe3C Type (oP16); Fe 5 C 2 (mC28); Fe 7 C 3 etc. [Cr7C3 = D1019 Th7Fe3 = D102]; B27, FeB (oP8); CrB (oC8); D7 b , Ta3B4 (oI14); a-MoB Cementite-orthorhombic, s.g. Pnma, No. 62, Z = 4: for Fe 2 . 7 Mn 0 . 3 C 10 , a = 5.0598, £ = 6.7462, c = 4.5074 A; (Fe,Mn)(l) in 4(c): ±{x % z, Vi + x % Vi-z) with x = 0.0367, z = 0.8402; (Fe,Mn)(2) in 8(d):
±(xyz,
Vi+x lA—y Vi—z, x Vi—yz,
Vi + xy Vi-z) with x = 0.1816, j/ = 0.066, z = 0.3374; C in 4(c): with x = 0.877, z = 0.444 (Fasiska and Jeffrey, 1965). This very elegant structure, shown in Fig. 1-14, is that of several borides, carbides, silicides and phosphides (and many intermetallic compounds too: VC lists 137 examples). It contains carbon in trigonal prismatic coordination (as does WC, Sec. 1.2.4), and is the anti-type of YF3 and other metal trihalides. {C} Fe 6 prisms share edges to form zigzag strings parallel to a, and then corners to form sheets in the ac plane. These sheets are stacked along b (and joined through bonds from C to capping atoms on two square faces of each prism). Elsewhere it has been shown that the Fe array is quite accurately derived by reflection twinning [on (010)FC3C = (1120)h.e.] of h.c.p. Fe, i.e., of the high-pressure form of iron, s-Fe (Hyde and Andersson, 1989). The trigonal prisms in the mirror planes (all occupied by C) are automatically produced by this operation, but the twin lamellae are very narrow - only 3 atoms wide (• • •, 3,3,3,3, • • •). Nevertheless, variation in the lamella width (still keeping all trigonal prisms filled by C, or similar, atoms) generates related structures, e.g.: (i) alternate lamellae two and three atoms wide (• • •, 3,2,3,2, • • •) = M3X • M2X = Pd 5 B 2 type = x-Fe 5 C 2 , Mn 5 C 2 (and,
1.3 More Complex Structures
17
Figure 1-14. The structure of (Fe0 9 Mn 0 i)3C projected on (010). Large circles are Fe, small ones are C atoms (heights in units of 6/100). The {C} Fe 6 trigonal prisms are shown on the left and the (empty) Fe 6 octahedra on the right. The former are obviously capped by Fe atoms in adjacent sheets of prisms (bonds not drawn); and the latter show the Fe array to be h.c.p. twinned on (010)Fe3C = (l 122) h c p .
again, many intermetallic alloys): such asymmetric "twinned" structures are monoclinic; (ii) all lamellae two atoms thick (• • •, 2,2,2,2, • • •) = M2X: this hypothetical structure is unknown: one might have expected it to be the structure of Fe2B, but this is not so (cf., Sec. 1.2.7 above); (iii) all lamellae one atom thick ( • • • , l , l , l , l , - ) = MX = FeB t ype = MB (with M = Hf, Mn, Co, Ti), MSi (M = Ti, Zr, Hf; Ce, Dy, Er, Gd, Ho, La, Pr, Nd, Sm, Tb; Th, U, Pu) (and, again, many intermetallic alloys). %-Fe5C2-monoclinic, s.g. C2/c9 No. 15, Z = 4; a = 11.562, b = 4.5727, c = 5.0595 A, P = 97.74°; atoms in (000, Vi Vi 0) + Fe(l) in 4(e): ±{0y %) with y = 0.5723; Fe(2) in 8(/): ±(xyz, xyz+Vi) with x = 0.0957, y = 0.0879, z = 0.4184; Fe(3) in 8(/): with x = 0.2174, y = 0.5837, z = 0.3060; C in 8(/): with x = 0.115, y = 0.303, z = 0.084 (Jack and Wild, 1966). FeB-orthorhombic, s.g. Pnrna, No. 62, Z = 4; a = 5.495, b = 2.946, c = 4.053; Fe
in 4(c): ± ( x % z , V2 % Vi-z) with x = 0.180, z = 0.125; B in 4(c): with x = 0.036, z = 0.61 (Bjurstrom, 1933 a, b). The structures of Pd 5 B 2 and FeB are shown in Figs. 1-15 and 1-16 (the latter in the common, alternative unit cell setting, Pbnm). The same reflection operation on hexagonal eutaxy, when carried out cyclically, again generates trigonal prisms in the mirror planes (now 27i/3 radians apart) and can produce the (obviously now hexagonal) structure of Ru 7 B 3 (Hyde and Andersson, 1989). Yet another carbide of iron, Fe 7 C 3 , is very similar but is orthorhombic (Mn 7 C 3 is isostructural). Cr 7 C 3 is also similar, but has a hexagonal unit cell with a = 2xaRujB3. For details of these last, complex structures the reader should refer to Roualt etal. (1970). The structure of Ru 7 B 3 is shown in Fig. 1-17. CrB-orthorhombic, s.g. Crncm, No. 63; a = 2.969, b = 7.858, c = 2.932 A; Cr in 4(c): ± (0 y %, V* Y2+y %) with y = 0.146; B in 4(c): with y = 0.440 (Kiessling, 1949). In FeB, rods of A1B2 type appear (Fig. 1-16). The same rods appear in the CrB
18
1 Crystal Structures of Principal Ceramic Materials X
Figure 1-15. The monoclinic structure of Pd 5 B 2 projected on (010). Only half of the {B} Pd 6 trigonal prisms are drawn (cf. Fig. 1-14). The finer broken line delineates the (0001) layers in the (twinned) h.c.p. array of Pd atoms (cf. the Pd 6 octahedron in the "3" band on the right: the "2" band is too narrow for an octahedron to be drawn).
structure, Fig. 1-18, but now they are joined (by sharing of triangular faces between the trigonal prisms) to form "walls" of A1B2 type (cf. Fig. 1-6). The walls are stacked side by side, and appear to be unconnected: in fact they are joined by the Cr atoms in one wall "capping" the {B}Cr6 prisms in the adjacent walls. There are numerous examples of iso-structural metal borides, aluminides, silicides and germanides (as well as intermetallics): Villars and Calvert (1985) list 165 examples. There are many types of trigonal prism structures with stoichiometry MX; and even more are based on the same sorts of structural units, but with different stoichiometry. For example, Ta 3 B 4 is similar to CrB but the "walls" are of double thickness; V5B6 consists of alternate walls of CrB and Ta 3 B 4 types, i.e. 2VB • V 3 B 4 = V 5 B 6 ; p-MoB is CrB type, but in oc-MoB alternate walls have been rotated by 90°; and so on. The possibilities are numerous.
[Many more examples are dealt with elsewhere, and in more detail (Hyde and Andersson, 1989).] In almost every case there are many iso-structural compounds (Villars and Calvert, 1985). In the last few of these structures (FeB, CrB, Ta 3 B 4 , V 5 B 6 , oc-MoB: where the ratio M/X is not very high) face-sharing between trigonal prisms means that the X atoms are rather close together; so close in fact, that there must be X-X bonding: zig-zag rows of B^ in FeB and CrB, edge-shared hexagons (Bg)^ in Ta 3 B 4 etc. (cf. A1B2, Sec. 1.2.5). Thus, in a sense, these are again natural "composite materials", with M-M bonding in the M array, X-X bonding in the X array, and M-X bonding between the two interpenetrating arrays. 1.3.5 Hl 1 9 Spinel, MgAl2O4 (cF56) Cubic, s.g. Fd3m, No. 227, Z = 8; a = 8.080 A; (origin at 3m), atoms at (000,
1.3 More Complex Structures
19
(a:
This well known structure is usually described as "cubic-close-packed" oxygens with Al in half the octahedral interstices and Mg in one eighth of the tetrahedral interstices. In fact, the anion array is a distortion of the ideal (which would have x = y4). Drawings of the structure are usually projections on to a cube face, but this makes it very difficult to "see", as the repeat is four layers of polyhedra deep. But, for a structure with a f.c.c. unit cell there is always a smaller, body-centered-tetragonal unit cell of half the volume (related to the cubic one by the matrix V2V2O/ Figure 1-16. The structure of FeB projected on (a) -V2 lA0/ 001). The latter has a conve(100)PbnmiE(001)Pnmfl, (b) (001)Pbnm^(010)Pnmfl. The nient projection axis, [010] (or the equivasheets of {B} Fe 6 trigonal prisms (again, only one half of the prisms are drawn) are like those in the previous lent [10 0]) with a repeat only two two figures, but now they share ("square") faces to polyhedra deep; this is used to depict the form rods of A1B2 type (Sec. 1.2.5). [If the open or structure in Fig. 1 -19 a.1 * filled circles in the trigonal prisms in part (b) are The spinel structure consists of rods of ignored, this diagram serves equally well for a single layer of trigonal prisms in Figs. 1-14, 15.] edge-sharing octahedra: those parallel to at are drawn in the figure; the equivalent ones parallel to bt are not, but appear as the two l tunnels centered by Al atoms. The octahe0 y2 Vi9 ViOYi, A y2O) + Mg in 8(a): l l l dra in adjacent rods are joined by further ±(Vs Vs Vs); Al in 16(d): A A A, V* VA VA9 VA VI %, Vi Vi Vi; O in 32(e): edge-sharing, creating cages in which isolated {Mg} O 4 tetrahedra are fixed by ±(xxx, xlA—xlA—x, VA—XXVA—X, sharing corners with {A1}O6 octahedra. VA-X VA-X X) with x = 0.262.
1 Crystal Structures of Principal Ceramic Materials
20
o o Figure 1-17. The structure of Ru 7 B 3 projected on (0001) of its hexagonal unit cell: the Ru atoms (larger circles) form trigonal prisms centered by the B atoms. It may be described as cyclically twinned Fe3C type. {At [00z] there are columns of empty, face-sharing Ru6 octahedra, and at ±[lA 2A z] columns of corner-shared Ru5 trigonal bipyramids = face-shared pairs of Ru 4 tetrahedra. Both these features are characteristic of h.c.p.}
o---
i o| ;j U
4
•o—
i
I?
•
H IO
.L1• 0 - - -
lol
'I'll .J
(a) Figure 1-18. The structure of CrB projected on (a) (100), (b) (001) of its orthorhombic cell. The {B} Cr6 prisms share "square" faces (as in FeB, Fig. 1-16) but now triangular faces also.
An alternative description (O'Keeffe and Hyde, 1985) notes that all the cations are in special positions (fixed parameters), and form an MgAl2 array identical to the MgCu 2 array in the alloy MgCu 2 (C15 type): all the oxygens are in {O}MgAl3 tetrahedra. It is still not an easy structure
to "see" in a drawing as the coordination polyhedron in C15 is an {Mg}Al12 truncated tetrahedron. Alternatively it may be described as C15 type, with Al in place of Cu and {Mg} O 4 tetrahedra in place of Mg: a drawing (of the complete structure) based on this alter-
1.3 More Complex Structures
±27
native is given in Fig. 1-19 b. It shows {Mg} O 4 tetrahedra in the tunnels in a C9like array of empty, corner-connected Al4 tetrahedra. (The interstices of the C9-like array are the Al 12 truncated tetrahedra.) 1.3.6 Hexagonal Barium Ferrite Structures Related to the Magnetoplumbite (PbO-6Fe 2 O 3 ) Type (hP66) BaFe 12 O 19 -Hexagonal, s.g. P63/mmc, No. 194, Z = 2; a = 5.893, c = 23.194 A; Ba
21
Figure 1-19. (a) The structure of spinel, MgAl 2 O 4 projected on (010) of the tetragonal unit cell. The largest circles represent Mg, the smallest O, and the intermediate ones Al: open at y/b = 0, filled at y/b = Vi, shaded at y/b= ± lA. Some of the oxygens have their heights (close, but not equal to + lA) shown in units of 6/100. Just over a (tetragonal) unit cell is drawn, and outlined as a broken white line, (b) An alternative description of spinel in a similar projection: {Mg} O 4 tetrahedra occur in (empty) truncated tetrahedra, Al 12 . These latter are not drawn, but are defined by the C9-like array of corner-connected Al4 tetrahedra (which are drawn, and are also empty). (The Al4 array is identical to that shown in perspective in the bottom part of Fig. 1-36, Sec. 1.6.1.)
in 2(c): ±( 1 / 3 2A %); Fe(l) in 2(a): 000, 00 V2; Fe(2) in 4(e): ±(00z, 00 V2+z) with z = 0.2561 (half occupancy); Fe(3) in 4(/): ±( 1 / 3 2/3 z, 'A 2A lA-z) with z= -0.0272; Fe(4) in 4(/): with z = -0.1902; Fe(5) in
12(fc): ±(x2xz,2xxz, xxz, x2xyi+z9 l l 2x x /2+z, x x /i+z) with x = 0.1687, z = 0.1083; O(l) in 4(e): with z = 0.1501; O(2) in 4(/): with z = 0.0546; O(3) in 6(/z): ±(x 2x %, 2x x %, x x %) with x = 0.816; O(4) in 12(fe): x = 0.8447, z = 0.0522; O(5) in 12(fc): with x = 0.4967, z = 0.1495 (Townes etal, 1967).
22
1 Crystal Structures of Principal Ceramic Materials
This ferrimagnetic substance has a 10 layer structure partly based on that of spinel, with Fe in both octahedral and tetrahedral sites; it is shown in Fig. 1-20. It is a eutactic array of O plus Ba atoms, the 3 6 layers being four of O 4 alternating with one of BaO 3 (i.e., Ba "in an O site"). The stacking sequence is complex: (/*3c2)2. The spinel part is an infinite slice, three layers of polyhedra thick (4 layers of O: hech\ parallel to (111) of the spinel cubic unit cell Fef4tFet4etO24. This alternates with 2-layer thick, h.c.p. slices [3 layers of (Ba)O: • • • hhh---] which contain, at the mirror plane, Fe in trigonal bipyramidal coordination ({Fe}O5) and Ba in "twinned cuboctahedral" coordination ({Ba}O12)~ Ba 2 Fe 4 ct Fe 2 bp O 14 . [Note that Fe has 3 different coordinations: {Fe}O4 tetrahedra, {Fe}O5 trigonal bipyramids 12 and {Fe}O6 octahedra.] For this 10-layer eutactic structure the ideal c/a = 10 x ^ 2 / 3 / ^ 3 = 4.714 (a = y/3 x ah c p ): cf. the actual c/a = 3.936 = 0.835 x the ideal. The c-axis, i.e., is somewhat reduced - as is apparent from the shape of some of the octahedra in Fig. 1-20. This substance is just one member of a large family of structures based on 3 prototypes: S = spinel-type magnetite, Fe 3 O 4 ; structural unit = Me 2 Fe 4 O 8 ; M = BaFe 12 O 19 ; Y =Ba 2 Me 2 Fe 1 2 O 2 2 . Layers of each of two types may intergrow to produce sub-families, the two main ones being: (i) SMn, 5 members known with n = 0 to oo; the first is magnetite (spinel type Fe 3 O 4 ) and the last is M itself. Other members include (ft = 2, Me = Fe) BaFe 18 O 27 , which has thicker slices of spinel, being (/i3c4)2 instead of (h3c2)2 (Braun, 1952).
h c c h h h c c h h h c c h
Figure 1-20. The structure of magneto-plumbite-like M-BaFe 12 O 19 projected on (100) of the ortho-hexagonal cell = (l 120) of the hexagonal cell. Largest circles are Ba, smallest are O, intermediate ones are Fe; open at y/aoh = 0, filled at y/aoh= V2, shaded at y/aoh~ ± y*- T n e u m t cen< is outlined with a broken, black line. Parts of the tetragonal unit cells in the spinel parts (cf. Fig. 1-19 a) are delineated by broken white lines. (0001) layers of oxygen (and BaO3) are appropriately labelled h or c, depending on whether they are in an h.c.p. or a c.c.p. relation to their neighbouring layers. The Fe(2) sites (broken circles) occur in closelyspaced pairs, and are half-occupied; Fe (2) is therefore off-centre in a trigonal bipyramid of oxygens, but no bonds or coordination polyhedra are drawn. Fe(l), Fe(3) and Fe(5) are in octahedral coordination in the spinel layers, and Fe (4) in octahedra in the intervening layers (forming face-shared pairs). Apart from some of the {Fe(5)}O6 octahedra (cf. Fig. 1-19, spinel); these octahedra are drawn. Ba is in a "twinned cuboctahedron" (no polyhedra or bonds drawn).
1.3 More Complex Structures
23
(ii) MnYm, a very large family, some members of which have very long c-axes, e.g., M 4 7 33 = My 6 M7 1 0 M7 7 M7 1 0 = = Ba 7 0 Me 6 6 Fe 4 4 4 O 8 0 2 with c = 1577 A! (Kohn and Eckart, 1965 a, b; van Landuyt et al., 1974.)
1.3.7 P-Alumina (hP58)
Na 2 O-llAl 2 O 3 -Hexagonal, s.g. P6 3 / mmc, No. 194, Z = 1; a = 5.5962, c = 22.526 A; Na in 2(d): ±(14 2/3 3/4); Al(l) in 2(a): 000, 00 54; Al(2) in 4(/): ±(y 3 2/3z, 14 2/3 Vi-z) with z = 0.0248; Al(3) in 4(/): with z = 0.1753; Al(4) in 12 (fc): ± ( x 2 x z , 2xxz, xxz, xlxVi+z, ixxVi+z, x x V2+z) with x = 0.1665, z = 0.6060; O(l) in 2(c): ± (14 2/3 %); O(2) in 4(e): ± (0 0 z, 0 0 14+z) with z = 0.1421; O(3) in 4(/): with z = 0.5540; O(4) in 12(fc): with x = 0.1624, z = 0.0496; O(5) in 12(fc): with x = 0.5016, z = 0.1464 (Flesche, 1968). This structure too is based on spinel twinned by reflection in (0001), see Fig. 1-21: in fact, most of the structure is spinel type. Since it too is a 10-layer structure of eutactic oxygens, but with a doubled aaxis, the ideal c/a = v / 2 / 3 x 10/2-4.083, compared with the observed 4.025; i.e., 98.6% of, and therefore rather close to, the ideal. The given solution of the structure may be slightly idealised - there is some doubt about the degree of occupancy of the Na and O sites in the h layers. This is connected with the ready mobility of Na [in the (0001) plane], and its ready exchangeability: it is a solid electrolyte. It is reported that there are > 2 N a atoms per unit cell (e.g., Peters et al., 1971). There are related structures: P'-alumina, "M 2 O-7.22A1 2 O 3 "; (3"-alumina, "M 2 O • 5.34A12O3" (M = Na,K); P'", "Na 2 O •
Figure 1-21. The structure of P-alumina, Na 2 Al 22 O 34 , projected on (100) of the ortho-hexagonal cell [ = (1120) of the hexagonal cell]. Large circles are Na, small ones are O, and intermediate ones are Al; open at x/a = 0, filled at x/a= V2, shaded at x/a& ± lA. The unit cell is outlined with a broken, black line. Na 2 O 2 layers parallel to (0001) are labelled h (they are 63/incomplete 3 6 , in an h.c.p. relation to adjacent O layers); O 4 layers are c type. The vertical lines at the right indicate the thickness of the spinel type layers. These are drawn as in Fig. 1-19 a: rods of edge-sharing {A1}O6 octahedra parallel to the projection axis are not drawn. Broken white lines are the outline of parts of the tetragonal unit cells of spinel (again as in Fig. 1-19). The Na atoms are in 9-coordination (a tall tricapped trigonal prism) not drawn.
4MgO- 15A12O3", etc. (Yamaguchi and Suzuki, 1968; Bettmann and Terner, 1971). 1.3.8 HI3/SI3, P-Si3N4, and the p'-Sialons (hP14) P-Si 3 N 4 -Hexagonal, s.g. P63/m, No. 176, Z = 2\ a -7.6018, c = 2.9066 A; Si in
24
1 Crystal Structures of Principal Ceramic Materials
6{h): ±{xyV*\ yx-ylA;
y—xxlA) with
x = 0.1773, y = 0J677; N(l) in 2(c): ±(y 3 2/3 %); N(2) in 6(/z): with x = 0.3337, y -0.0323 (Billy et al., 1983). This is the more symmetrical of the two polymorphs of silicon nitride. Figure 1-22 shows that it consists of a corner-connected array of {Si}N4 tetrahedra: each tetrahedron shares every corner with two neighbours, so that the N atoms are 3-coordinate, i.e., iv Si 3 iii N 4 . [Phenacite, BeSi2O4 is a superstructure of this, with (ordered) Be2Si in place of Si 3 , and O in place of N.] The "P'-sialons" are isostructural with (3-Si3N4, but there is a coupled substitution of (A1 3+ O 2 ~) + in place of some (Si 4+ N 3 ~) + . The solid solution range is remarkably wide (0 to - 7 0 % at 1750°C; - 3 3 % at 1450°C), the reason undoubtedly being the similarity in bond lengths the ideal values are Z(Si-N) = 1.77 A and /(Al-O) = 1.76 A for bond valences of, respectively, 4A and 3A, i-e., 1.00 and 0.75 (Jack, 1978). [He also pointed out that, for the opposite reason, the solid solution range in this quaternary system was very narrow in the alternative direction - along the AlN-SiO 2 join, the ideal bond lengths
Figure 1-22. A clinographic projection of the hexagonal structure of p-Si3N4, approx. on (0001). Large circles are Si, small ones are N; a unit cell is outlined.
now being very different: /(Si-O) = 1.62 A and /(Al-N) = 1.90 A for the same bond valences.] 1.3.9 Other (AIN-Related) Sialons
At compositions between the p'-sialons and A1N there is a family of structures, also with tetrahedral coordination, {M}X 4 , but now based on eutactic arrays ("closepacking") of cations: their general formula is Mn Xn +1, where n is an integer 4 < n < 9 (Jack, 1978). Their structures, based on that of A1N (B4, wurtzite type, hexagonal, Fig. 1-23) are rhombohedral (R) or hexagonal (H). As with the SiC polytypes, for a
Figure 1-23. The structure of B 4-, wurtzite-type A1N in clinographic projection, approx. on (100) of the ortho-hexagonal cell (outlined) [equivalent to (1120) of the hexagonal cell].
hexagonal cell with m(0001)(=3 6 ) layers in the repeat unit, m(R) = 3p and m(H) = 2p (with the latter taking preference; p an integer), e.g., 8 H, 15 R, but 12 H. (These last symbols are identical to the Ramsdell notation for polytypes.) Stoichiometries, unit cell parameters and symbols are given in Table 1-2. Note that with decreasing A1N content, to a small extent, a decreases (by 4.0%), c/m increases (by 15%), and Q therefore also increases. The decrease of a obviously reflects the difference in Si-N and Al-N bond lengths. The increase of c/m has a different cause: the increase in the stoichiometric ratio, R, down the table means an
25
1.3 More Complex Structures
Table 1-2. AIN-related sialons. Stoichiometry Composition A1N = Si3N4 • ooAIN Si 3 N 4 -6AlN Si3N4 • 6A1N Si3N4 • 4A1N Si 3 N 4 -3AlN Si 3 N 4 -2AlN Si3N4 • 1A1N
Unit cell axes (A) R = X/M
Symbol
a
c
1/1 10/9 10/9 8/7 7/6 5/6 5/4
2H 2H 27 R 21 R 12H 15R 8H
3.114 3.079 3.059 3.048 3.029 3.010 2.988
4.986 5.30 71.98 57.19 32.91 41.81 23.02
increase in the number of occupied tetrahedral interstices in the eutactic array of cations. In A1N only half the available tetrahedral sites are occupied, the filled sites being arranged so that {X} M 4 tetrahedra share only corners (Fig. 1 -23). Filling more tetrahedral sites means that there must now be some edge-sharing also 13 ; but this is restricted to a minimum number of layers (evenly spaced in a fully ordered structure) - in which all tetrahedral sites are occupied. The proportion of these completely filled layers is clearly 1/n, and their stoichiometry is MX2. Thus, the overall stoichiometry of the crystal is (n-l)MX • MX2 = MnXn+l9 as stated earlier. The MX2 layers are Cl, fluorite type (cf. Sec. 1.2.2, above), and so the sialon structures are ordered inter growths of Cl +B4 type basal layers. A similar situation obtains in the system A1N +A1 4 C 3 ; but now it is the anions (not the cations) that are eutactic, and the cations that occupy the tetrahedra between them (Jeffrey and Wu, 1963; 1966). 1.3.10 H5 7 , Apatite-Type Nitride Silicates of the Rare Earths (hP42); and the D8 8 , Mn5Si3 Type (hP16) The apatite structure is well known and widespread, if difficult to appreciate be-
Average layer Ratio spacing (A) Q = (c 2/ci)/{jn -\J AJ c/m
2.49 2.65 2.67 2.72 2.74 2.79 2.88
5)
0.98 1.05 1.07 1.09 1.11 1.13 1.18
cause it is rather complex. Apatite is a mineral (and a constituent of bones and teeth), C a 5 ( P O 4 ) 3 X where X = OH,F, Cl, etc. for hydroxy-, fluoro-, chlor-apatite, etc. Although sometimes slightly distorted, its space group symmetry is usually P63/m. It is important in the context of ceramics because isostructural materials appear in sialon-related systems (Jack, 1978): these are Ln 5 (SiO 4 ) 3 • N, with Ln = any rare earth (or Y). (There are also other silicate analogues in the system, cf. Jack, loc. cit) With a few exceptions most such "N-apatites" have been identified and characterised only by X-ray powder diffraction; and, with the formula written that way, it is tempting to expect them to have N in the unique position at (OOz). But this seems not to be the case: indeed, in these compounds even the space group is of somewhat lower symmetry than P63/m (the mirror plane is absent - but "only just"). An example - solved by single-crystal X-ray diffraction - is the following: Sm 5 Si 3 O 12 N-hexagonal, s.g. P6 3 , No. 173, Z = 2; a = 9.517, c = 6.981 A; Sm(l) in
6{c): xyz, yx—yz, y—xxz, xyVz + z, yy-x V2 + z,x—yx Vi+z;with* = 0.2411, y = 0.0089, z = 0.0030; Sm (2) in 2 (b): lA 2A z, 2 A Vs lA+z9 with z = 0.250; Sm(3) in 2(b): with z = 0.7501; Si in 6(c): with x = 0.3998, y = 0.0278, z = 0.4953; O(l) in 2(a): OOz,
26
1 Crystal Structures of Principal Ceramic Materials
0 0 Vi+z, with z= -0.023; O(2) in 6(c): with x = 0.601, y = 0.128, z = 0.486; O(3) in 6(c): with x = 0.247, 3; = 0.329, z = 0.184; O(4) in 6(c): with x = 0.358, y = 0.101, z = 0.308; (O 0 5 N 0 5) in 6(c): with x = -0.168, y = 0.513, z = 0'.001 (Gaude et al., 1975). From the calculated values of the bond valence sums, i.e., the apparent valence at each atom, even this structure solution seems to be somewhat less than perfect: the O/N disorder is probably more widespread among the anion sites. (Jack (1978) expresses the "N-apatite" phase of yttrium as Y5[Si(O,N)4]3(O,N).) But any errors are more in O,N occupancies than in atom parameters. The structure, shown in Fig. 1-24, is not easy to describe, especially in conventional terms (cf. Wells, 1984). To avoid confusion, in this figure we have drawn the coordinating anion polyhedron for only one pf each of the three cations: Sm(l) is at the center of an irregular, mono-capped octahedron (CAT. = 7). Sm(2) and Sm(3) are symmetry-
O
Figure 1-24. The structure of Sm5SiO12N projected on (0001). Large circles are Sm, medium ones are Si: open at z/c^0, filled at z/c& V2, shaded at z/czz ± %. The smallest circles are the anions: heavily ringed at z/c &0 and Yi, open at z/c «0, filled at z/c « Vi, lightly shaded at z/c = 0.18 and 0.31 (i.e., 1/4±0.067), heavily shaded at z/e = 0.68 and 0.81 (i.e., 3/4±0.067). One of each of the {Sm(l)}X7 monocapped octahedra, {Sm(2,3)}X9 tricapped "trigonal prisms" and {Si}X4 tetrahedra are drawn.
equivalent in s.g. P63/m, and almost so here in P6 3 , so we do not distinguish them: hence, both are at the centers of tri-capped figures which are close to trigonal prisms, but somewhat distorted towards antiprisms (octahedra) (C.N. = 6 + 3); Si is at the center of a fairly regular tetrahedron angles [L(XSiX) = 100° to 114°]. Clearly
Figure 1-25. (a) The Sm5Si3 (cation-only) part of the structure in Fig. 1-24; same symbols. At the origin there are columns of face-sharing Sm(l) 6 octahedra (as in h.c.p.). These are capped on every edge: those parallel to (0001) by Si atoms (forming Sm2Si triangles - shaded at z/c = 0, broken outlines only at those not parallel to (0001) by Sm(2,3) z/c=y2); atoms at z/c=±*/4 [forming Sm(l)2Sm(2,3) triangles]. The decorated columns are united by each Sm(2,3) atom being common to three columns. (b) The structure of Sm5Si3 projected on (0001); symbols as in Figs. 1-24 and 1-25 a (except that atom heights are now exactly 0, V2, ± lA, instead of approximately so: but the differences are very small, < c/100, and mostly very much less. [Note that, apart from a change of scale, (a) and (b) are identical.]
1.4 High-Temperature Superconductors
27
z[Sm(l)] = z[O(l)]}. The {X}Sm3Si tetrahedra are not regular; nor would they be expected to be: Si-O bonds are much shorter than Sm-O bonds [/(Si-O) = 1.62-1.67 A compared with /(Sm-O) = 2.39-2.93 A], and non-bonded distances
1.4 High-Temperature Superconductors Figure 1-26. The structure of Sm 5 Si 3 O 12 N as anionstuffed Sm5Si3; symbols as before. Four {X}Sm3Si tetrahedral bond sets are drawn, and those in the {X} Sm3 triangles at 1 Oz. (On the left, one Sm3 "capping" triangle has been omitted so that the bonds may be seen more clearly.)
the anion array is far from regular; we therefore turn to the cation array. It is shown in Fig. 1-25 a. While still not simple, it does have the merit of being rather regular: and the Ln 5 Si 3 part of all these rare-earth nitride-apatites is a trivially-small distortion of the D8 8 (sometimes called D8b) structure - Mn 5 Si 3 type. Furthermore, the corresponding (anionfree, rare-earth silicides) Ln 5 Si 3 all have the Mn 5 Si 3 structure: that of Sm5Si3 is shown in Fig. 1-25 b. 1 4 Obviously, therefore, the structures of the N-apatites Ln 5 Si 3 O 12 N may be described as "anion-stuffed Lrc5Si3s".15 Figure 1-26 shows the samarium N-apatite in this way: the bonds are drawn from one of each of the five crystallographic-distinct anions to their surrounding cations (in the center left of the drawing): all except the "unique anion" (the one at OOz) are in tetrahedra, {X} Sm3Si; the exception is in 3-coordination, {O(l)}Sm 3 . (According to the crystal data given above, the last has bond angles Z_(SmXSm) = 119.4°: it is almost inconceivable that this should not be 120° {and therefore that
Oxide superconductors were known before the 1970s, but their Tcs were low compared with those of alloys with the A15/ Cr3Si-type structure (Fig. 1-27), for which the highest Tc was 23.2 K for Nb 3 Ge. 1 6 Cr 3 Si-cubic, s.g. Pm3rc, No. 223, Z = 2; a = 4.556 A; Si in 2(a): 000, lA V* !4; Cr in 6(c): ± ( % 0 V2, lA %0, 0 y2 %). Two oxides with T C ^12K were then discovered: Li1_JCTi2 + x O 4 with the Hl 1 ? spinel structure (Fig. 1-19) and x^0.2 (Johnson et al., 1973), and Ba(Pb1_JCBiJC)O3 with a slightly distorted E2i (cubic) perovskite structure (Fig. 1-13) and x^0.27 (Sleight et al., 1975). In the latter, Tc could be raised to 30 K by replacing Ba by K (Cava et al., 1988). But, since Bednorz and Miiller (1986), dramatic modern developments involving ternary (and higher) copper oxides with perovskite and perovskite-related structures have raised the maximum Tc to well over 100 K. 17 As we shall see below, the common element in the structures of the new materials appears to be a two-dimensional sheet of corner-connected {Cu}On polyhedra. In principle, of course, the stoichiometry of any metal oxide depends on ambient conditions - in particular, for example, x in MOX varies with temperature and oxygen pressure. In practice changes may be vesti-
28
(a)
1 Crystal Structures of Principal Ceramic Materials
in 1 (a): 0 0 0; Cu(2) in 2(q): ±(0 0 0.3557); O(l) in l(e): 0 Vi 0; O(2) in 2(s): ±( 1 / 2 0 0.3775); O(3) in 2(r): ±(0 Vi 0.3786); O(4) in 2{q): ±(0 0 0.1582) (Johnston et al., 1987). YBa 2 Cu 3 O 6 -Tetragonal, s.g. PAjmmm, No. 123, Z = l; a = b = 3.8577(2), c = 11.8274(8) = 3x3.9427 A; Y in l(d):
c
V2 V2 l/2; Ba in 2(h): ±{XA V* 0.1954); Cu(l)
(b)
•%•••<•
Figure 1-27. (a) The A15 structure of Cr3Si. Larger circles are Cr and smaller ones are Si, the latter in a b.c.c. array. Two {Si}Cr12 coordination polyhedra are drawn: they are slightly deformed regular icosahedra. (In fact, their vertices are alternate ones on a perfectly regular truncated cube.) (b) 1 x 2 x 2 units cells of Cr3Si; here the structure is depicted as a primitive cubic packing of infinite rectilinear rods of equidistant Cr atoms, with the Si atoms in the interstices.
gially small but, in the case of these superconductors the variations - even when they are small - are still highly significant, not least for their effect on Tc.18 1.4.1 The " 1 : 2 : 3" Compound L/f 1 Ba 2 Cu 3 O 7 _d [Ln = Y or Rare Earth(s)]
YBa 2 Cu 3 O 7 -Orthorhombic, s.g. Pmmm, No. 47, Z = 1; a = 3.8240(2), b = 3.8879(2), c = 11.6901(8) = 3x3.8967 A; Y in l(/i): Vi lA l/2; Ba in 2(t): ±(V2 lA 0.1854); Cu(l)
in 1 (a): 0 0 0; Cu(2) in 2(g): ±(0 0 0.3608); [O(l) in 2(/): 0 V2 0, lA 0 0, occupancy « 0]; O(2) in 4(i): ±(0 V2 0.3795, V2 0 0.3795); O(3) in 2(g): ±(0 0 0.1528) (Johnston et al, 1987). LftBa2Cu3O7_(5 was the first compound with Tc > 90 K (Wu et al, 1987); it is a superstructure of perovskite, ABX3, with a small orthorhombic distortion when 8 < — 0.5. Due to the ordering of Ln and Ba on the A sites it has a tripled c axis; and the loss of two O atoms from the (3 x) formula unit converts the three {B} X6 octahedra to two {Cu} O 5 square pyramids (half-octahedra) and one {Cu}O4 square, Fig. 1-28.
CuO
Figure 1-28. The structure of YBa 2 Cu 3 O 7 in clinographic projection, approx. on (100). Large circles are Ba and Y; small ones are O atoms; open at x/a = 0, filled at x/a= V2. On the left the structure is depicted as {Cu(2)}O5 square pyramids and {Cu(l)}O 4 squares, and the Ba-O bonds (9 x) and Y-O bonds (8 x) are drawn. On the right only some Cu-O bonds are drawn; and the atomic layers are labelled with their stoichiometry.
1.4 High-Temperature Superconductors
o°
Figure 1-29. The structure of YBa 2 Cu 3 O 6 in the same projection as Fig. 1-28. On the left are shown the {Cu(2)}O5 pyramids, O-Cu(l)-O linear groups and La-O and Y-O bonds; on the right, the atomic layers. Circles represent the same atoms as in Fig. 1-28.
[3xABX3 = A3B3X9
AAf2B3X9
29
V2 0 V2; Ba in 4(h): ±(V2 0z) with z = 0.3654; Cu(l) in 4(g): ±(00z) with z = 0.2126; Cu(2) in 4(0): with z = 0.0614; O(l) in 4for): with z = 0.1452; O(2) in 4(h): with z = 0.0522; O(3) in 4{g): with z = 0.4475; O(4) in 4(0): with z = 0.2812 Kaldis et al., 1989). This substance has a Tc« 80 K. Its structure (Fig. 1-30) is closely related to that of YBa 2 Cu 3 O 7 : the difference is that the former contains double (edge-shared) instead of single chains of corner-shared {Cu} O 4 squares. Surprisingly, no significant variability in oxygen content has been reported.
-2X
AA'2B3X1] The stoichiometry implies one positive hole per formula unit, i.e. some Cu(2) 3+ or O 1 " - the source of the superconductivity. The oxygen content of this phase is a function of p(O 2 ) and T; with change in these parameters it varies readily between (5 = 0 and 1, even at lowish temperature (down to about 200 °C or less). Thus it readily loses oxygen to form YBa 2 Cu 3 O 6 a very similar structure (Fig. 1-29), but with slightly higher symmetry. The coordination number of Cu(l) has now fallen from C.N. = 4 (square planar, characteristic of Cu 2 + ) to C.N. = 2 (linear, characteristic of Cu 1+ ). This is consistent with Cu (2)2 + and O 2 " (i.e., no positive holes), so that the reduced phase is a semiconductor which has lost its capacity for superconductivity. 1.4.2 L/iBa 2 Cu 4 O 8 Orthorhombic, s.g. Ammm (non-standard, cba setting of Cmmm), No. 65, Z = 2; at 165 K: a = 3.8399, b = 3.8719, c = 27.2105 A; all atoms at (000, 0 V2 72) + Y in 2(c):
CuO,
Figure 1-30. The structure of YBa 2 Cu 4 O 8 projected on approx. (100) of the unit cell (setting Ammm). Large circles are Y (shaded) and Ba (open), small ones are O and intermediate ones Cu. On the left are shown the (Cu(l)} O 4 squares and {Cu(2)} O 5 square pyramids; on the right some of the bonds. [Y is 8-coordinated with bond lengths 2.39 A (4 x) and 2.40 A (4x): Ba is 10-coordinated with bond lengths from 2.74 A to 2.99 A.] Atomic layers parallel to (001) are labelled according to their composition.
30
1 Crystal Structures of Principal Ceramic Materials
Y 2 Ba 4 Cu 7 O 15 is also known: it is a lamellar intergrowth of the two previous superconductors: Y 2 Ba 4 Cu 7 O 15 = YBa 2 Cu 3 O 7 + YBa 2 Cu 4 O 8 . 1.4.3 (La,M)2CuO4 (M=Sr,Ba) (La,Ba) 2 CuO 4 -Orthorhombic, s.g. Pccn, No. 56, Z = 4; a = 5.378, b = 5.371,
c = 13.234 A; La in i(e): ±{xyz, Vi-x Yi-y z, Vi+x y V2—z9 x Y2+y Vi—z) with x = 0.0032, y = 0.0032, z = 0.3610; Cu in 4(a): (000, !/2 V2 0, 0 Vi Vi, Vi 0 y2); O(l) in 4(d): ± ( % 3/4z, % 3/4 J/2+z) with z - 0.0004; O (2) in 4 (c): ± (% % z, % % Vi+z) with z = 0.0112; O(3) in S(e): with x = 0.0143, y = 0.4872, z = 0.3165 (Structure Reports, 1987). This was the first of the new, "ceramic" superconductors, reported by Bednorz and Miiller (1986). Its structure is shown in Fig. 1-31: apart from the tilting and the obvious Jahn-Teller distortion of the {Cu}O 6 octahedra (giving two long and four short bonds, characteristic of Cu 2+ ), it is one of a well known family of structures - the so-called Ruddlesden-Popper phases (Ruddlesden and Popper, 1958) - in fact the simplest one, isostructural with K 2 NiF 4 and Sr 2 TiO 4 . This (RuddlesdenPopper) family is usually and conveniently described as intergrowths of the B1 (NaCl) and perovskite types; the various members have different numbers of perovskite layers between unit (100)B1 layers (which are only two atoms thick), i.e., AX • nABX3. In the present instance, due to the tilting of the octahedra (alternately in opposite directions) the a and b axes are ~ y/l times those of YBa 2 Cu 3 O 7 _ a . The analogues of higher members of the Ruddlesden-Popper series are also known as superconductors. Their Tcs increase with increasing thickness of the perovskite part.
Figure 1-31. On the left, the structure of (La,Ba)2CuO4 in clinographic projection on (010). Largest circles are (La,Ba), medium circles are Cu, smallest ones are O. [Metal atoms (only) at y/b&0 and y/b&Vi are distinguished by being open or shaded, respectively.] The unit cell is outlined; {Cu}O6 octahedra are drawn (elongated by the Jahn-Teller distortion); and, for one La atom only (lower right) the La-O bonds are drawn. On the right, the structure is projected on (110) - for direct comparison with related figures and shows the bonds and layers as before. (In the latter, the unit cell is Jl x Jl x 1 x that on the left - in order that the projection corresponds with those in the bond diagrams for the other oxide superconductors. For the same reason not all atoms in the new cell are drawn.)
Formally, and assuming an exact stoichiometry and all oxygens to be divalent, O 2 ", = (1 -x) • La 2 CuO 4 + x • Ba 2 CuO
i.e., the substitution of Ba for La produces (or encourages) the oxidation of some Cu2 + to Cu 3 + : L a 3 + + C u 2 + - » B a 2 + + C u 3 + . But, as with YBa 2 Cu 3 O 7 _ 5 , it is now known that these compounds are capable of non-stoichiometry or variation in oxygen content: small amounts of excess oxygen can be accommodated, even in pure La 2 CuO 4 (although it is not yet certain
1.4 High-Temperature Superconductors
exactly how or where: it appears to be between the pairs of Bl layers)19. This has the same effect as doping with Ba: formally, some Cu 2 + is converted to Cu 3 + (or O2~ to O~); i.e., positive holes appear in the conduction band. One consequence of converting Cu2 + to Cu3 + is the elimination of the Jahn-Teller effect, which means that the apical oxygens in the {Cu} O 6 octahedra move closer to the Cu atom (and, presumably, the other four oxygens also move). This effect, not shown in Fig. 1-31, is believed to be closely associated with the superconductivity, here and in all the other cuprate superconductors (above and below); i.e, the operational part of the structure is the {Cu} O 6 octahedra (or, in some cases, the {Cu} O 5 square pyramids or half-octahedra).
31
CuO,
CuO, CuO, CuO,
CuO,
Figure 1-32. The structure of Tl 1 Ca 2 Ba 2 Cu 3 O 9 in clinographic projection, approx. on (010). In order of decreasing size, the circles represent Ba, Ca, Tl, Cu and O atoms, respectively; open at y/b = 0, shaded at y/b= lA. A unit cell is outlined, and the stoichiometries of the various (001) layers indicated.
1.4.4 The T1-, Bi- or Pb-Containing Families: (i) M1Can_1M'2CunO2n + 3
(l
creases: hence, n = 2 has no such CuO 2 layer and, in n = 1, the two (now adjacent) layers of {Cu}O5 half-octahedra have TlBa 2 Ca 2 Cu 3 O 9 -average symmetry tefused to form a single layer of {Cu} O 6 octragonal, s.g. PA/mmm, No. 123, Z = l; a = b = 3.853, c = 15.913A; Tl in 4(/) 20 : tahedra, as in the M2 family member with n = l, Tl 2 Ba 2 CuO 6 , shown in Fig. 1-33. ±(x00, 0x0) with x-0.085; Ba in 2(/i): (Cf. next section.) ±( 1 / 2 Viz) with z = 0.1729; Cu(l) in 1(6): 00 V2; Cu(2) in 2{g): ±(00z) with Tc increases with n up to a maximum of z = 0.2991; Cain2(fc):withz = 0.3953;O(l) ~ 125 K at n = 3, after which it falls again. in 2(e): OViVi, ViOVi; O(2) in 4(0: Compounds with M = Bi are unknown in ±(0Viz, ViOz) with z = 0.3019; O(3) in this family. 2{g): with z = 0.1277; O(4) in l(c): lA lA0 For more information on these families (Subramanian et al., 1988). of structures see, for example, Goodenough and Manthiram (1990). The structure of Tl 1 Ca 2 Ba 2 Cu 3 O 9 is shown in Fig. 1-32: it is the n = 3 member of the family M = Tl, M' = Ba, for which all 1.4.5 The Tl~, Bi- or Pb-Containing 5 members are known. As n increases the Families: (ii) M2Caw_1M^CuttO2w + 4 structure changes incrementally by in(l
32
1 Crystal Structures of Principal Ceramic Materials
For M = Bi, M = Sr,n = 1,2 and 3 are stable. Unlike the Tl compounds, these cleave easily - presumably due to the lone pairs of electrons on Bi3 + in the intervening space between the BiO layers. In both these families of structures the upper and lower parts of the figures remain constant: M 1 M 2 CuO 5 (Fig. 1-32), and M 2 M 2 CuO 6 (Fig. 1-33). And, in both groups of structures (Sees. 1.4.4 and 1.4.5), as in those discussed earlier, additional oxygen may be incorporated - exactly how is still not certain; in the Bi cases it appears to be in the space between the BiO layers. It is this which is believed to be responsible for a long-period modulation along b that is usually observed. It, of course, results in some "Cu 2+ -» Cu 3 + ". There is also a susFigure 1-33. The structure of Tl 2 Ba 2 CuO 6 in clinopicion that not all the Tl sites are occupied graphic projection; circle sizes as in Fig. 1-32. Compare in these structures. (The major Tl species is with Figs. 1-28 to 32. Tl 3 + .) Again, it appears that the {Cu}O 5 pyramids are the seat of the superconducCmca)2\ No. 64, Z = 4; a = 5.4967, tivity. b = 5.4651, c = 23.246 A; all atoms at Hence, these structures are more com(000, 0 V2 l/2) + Tl in 8(/): ± (x 0 z, plex than we have so far indicated: they are Vi-xViz) with x = 0, z = 0.2018; Ba in incommensurately modulated, and their 8(/): with x = 0, z = 0.5822; Cu in 4(a): complete solution in these terms has yet to 000, y20l/2;O(l)inS(e): ±(% %z, Vi 3Az) be achieved. with z = 0; O(2) in 8(/): with x = 0, z = 0.1161; O(3) in 8(/): with x = 0.045, z = 0.2887 (Parise et al., 1988). Also previously reported as being tetrag1.5 Sillimanite, Al 2 SiO 5 (oP32); onal, s.g. /4/mmm (cf. TlBa 2 Ca 2 Cu 3 O 9 above), the Tl 2 Ba 2 CuO 6 structure (n = 1) and Mullite, was later found to be orthorhombic. The differences in atom positions in the two These are alumino-silicate, high-temperas.g.s are very small, and again restricted to ture refractories with closely-related structhe T1O layers, which now occur in pairs. tures. It is difficult to distinguish them by These layers are now seen to be distorted their properties, and is probably most easfrom Bl type: the bond lengths in the ily done by means of their lattice parame{T1}O6 octahedron are 1.99, 2.03, 2.51, ters (note that, csillimanite « 2 x cmullitc). Silli2.75(2 x) and 3.00 A. It is the orthorhommanite is an important mineral, and the bic form which is shown in Fig. 1-33. complications of its obvious relation to mullite have kept mineralogists busy for a For M = Tl, M' = Ba, all 5 members are long time (even though mullite is a rare known: Tc increases with n up to a maximineral). But details of the structure and mum of ~ 125 K at n = 3.
1.5 Sillimanite, AI 2 Si0 5 (oP32); and Mullite,
phase relationships of mullite are still not completely resolved. Sillimanite-orthorhombic, s.g. Pbnrn22, No. 62, Z = 4; a = 7.4883 [7.4856], fe = 7.6808 [7.6738], c = 5.7774 [5.7698] A; Al(l) in 4(a): 000, ViOO, lA ViO, 72 % Vi; Al(2) in 4(c): ±(xy%, 1 4 - x Vi+y %) with x = 0.1417 [0.1419], y = 0.3449 [0.3447]; Si in 4(c): with x = 0.8467 [0.8465], y = 0.6598 [0.6596]; O(l) (or OA) in 4(c): with x = 0.6395 [0.6401], y = 0.5906 [0.5922]; O(2) (or OB) in 4(c): with x = 0.3569 [0.3576], y = 0.4341 [0.4352]; O (3) (or O c ) in 4 (c): with x = 0.5237 [0.5247], j / = -0.0015 [-0.0008]; O(4) (or OD) in 8(d): ±(xyz, Vi+x V2— y 14+z; xyVi— z; !/2— x Vi+yz) with x = 0.1252 [0.1248], y = 0.2230 [0.2237], z = 0.5145][0.5164] at 25°C (Winter and Ghose, 1979); [Burnham, 1963]. Although it occurs naturally, sillimanite is the high-temperature polymorph of Al 2 SiO 5 . (The stable room-temperature variety is andalusite; kyanite is a high-pressure form.) Its structure is shown in Fig. 134: it reveals, in projection, [001] chains of edge-sharing {A1(1)}O6 octahedra at the unit cell corners and center, and these are connected by [001] chains of cornershared {T}O 4 tetrahedra. In each chain T = Si and Al(2), in strict alternation. The tetrahedral chains are also corner-connected [via O(3) = O C atoms] into ("bow-tie") pairs in such a way that there are only Al-O-Si bridges (and no Al-O-Al or Si-O-Si). We note, in passing, that the cationcation distances along c are unusually short: d[Al(l) • • • Al(l)] = c/2 = 2.889 A, d[Al(2) • • • Si] = 2.890 A.23 This is consistent with the crystal being less compressible in this direction; c 33 = 3.88 Mbar, compared with c±1 = 2.82 and c22 = 2.32 Mbar; cation repulsions are strongest along c. Compared with sillimanite, mullite is alumina-rich: it has a (temperature-depen-
33
Figure 1-34. The Al2SiO5-sillimanite structure projected on (001) (setting Pbnm). Large circles are Si (heavily ringed) and Al, open at z/c = O and V2, lightly shaded at lA, heavily shaded at 3A; small circles are O, open at 0 + 0.01 and V2 ±0.01, light or heavy shading at lA or 3A respectively. Only half of the polyhedra are drawn: they almost completely obscure the other half. The O (3) = O c atoms are those close to the centres of the unit cell edges.
dent) composition range nAl 2 O 3 • SiO2, 131
A12O3, which means that one oxygen is lost for every two cations substituted. Mullite, x = 0.4 (i.e., composition 2 A12O3 • SiO2), A
34
1 Crystal Structures of Principal Ceramic Materials
thorhombic, s.g. Pbam, No. 55, Z = 1; a = 7.5785(6), b = 7.6817(7), c = 2.8864(3) A; 1.0 x Al in 2 (a): 000; [O.56(2)A1 + 0.25(2)Si, Z = 0.81xT] in 4(/i): ±{xylA, V2 + x l A - y lA) with x = 0.14901(2), y=0.34026(2); [0.13(2)Al + 0.06(2)Si, Z = 0.19 x T*] in 4(ft): with x = 0.26247(9), y = 0.20529(9); 1.0 x O(l) = O AB in 4(ft): with x = 0.3590(1), y = 0.4218(1); 0.39(1) x O(2) = O c in 2(d): 0 lA lA, y2 0 Vi; 0.19(1) x O(3) = O* in 4(fc): with x = 0.4498(4), y = 0.0505(4); 1.0 x O(4)
= ODin4(#): ±(xy09 lA + x lA -yO) with
x = 0.1273, y = 0.2186(l) (Angel and Prewitt, 1986). [Occupancies of the various sites are given (recall that this is an average structure); and the equivalent nomenclature (O A , O B , etc.) is that for the sillimanite structure.] The structure derives from that of sillimanite in the following way. Oxygen is lost from an O c position, which leaves two T atoms 3-coordinated. These T atoms then move (in opposite directions, to T*, Fig. 1-35) to acquire a fourth coordinating oxygen each; the latter - previously 2-coordinated O c atoms - now become 3-coordinate "O*" atoms, {Og}T*T 2 . 24 [As a result of these changes, Og and all its surrounding atoms will be shifted slightly from their original (sillimanite) positions: the surroundings of O* will tend towards 3-fold symmetry. Figure 1-35 i.e., is schematic] This occurs at many positions in the crystal; the exact concentration depending on the value of n or x in the above formulae. Each O c which is lost generates two O£ so that, unless oxygens other than O c are involved, a maximum of lA of the O c s can be removed in this way; and, since there are 2 O c atoms in the (small, mullite) unit cell, x < 2A. This suggests that the maximum substitution of Si by Al is 67% in 4A12O3 • SiO2 (cf. xmax = 59%, nmax = 3.16, above). Cameron (1977) suggested that the
Figure 1-35. Schematic description of the transformation of an element of sillimanite (approx. 2 x Fig. 1-34) to an element of mullite. An oxygen atom, O c has been lost from the centre of the figure (heavily shaded square); two T atoms have jumped into T* sites (see arrows) in order to restore their tetrahedral coordination by O, hence 2 {T } O 4 - ^ 2 { T } O 3 > 2(T*}O 4 . (These last tetrahedra are heavily outlined in the figure.)
limit could conceivably be higher than he observed, perhaps even 100% (then corresponding, structurally and compositionally, to I-A1 2 O 3 ). The distribution of these [{Og} T* T2] centers is far from random, for it is well known that, in addition to the Bragg reflections due to the underlying "average structure", diffraction patterns from mullites also exhibit relatively sharp, incommensurate satellite reflections and closely-related diffuse intensity distribution (see, for example, Welberry and Withers, 1990). The structure is incommensurately modulated
1.6 Ferroelectrics
- parallel to a for x < 0.5, plus an increasing c component for x>0.5. The periodicity is also composition dependent, ~ 9 to 15 A. The distribution can therefore be best described in terms of a probability wave for occupation of the O c sites; which is hardly surprising when one considers the elastic strain that must be generated at each center. The most detailed studies of the "average" and incommensurately modulated structures are by Angel and Prewitt (1986, 1987) and Angel, McMullan and Prewitt (1992). Details are beyond our scope here; they include information on atomic shifts (sillimanite -• mullite), and the likelihood that the cations around OJ are largely (probably entirely) Al, i.e., in {Og} T2 T*9
35
ing means all atom coordinates are (000, 01/21/2, y2Ol/29 ViViO) plus Y( = A) in 16(d): lA Yi !4, lA lA lA, lA Vi %, % lA lA; T\{ = B) in 16(c): 000, 0 % Vi, ViOVi, 1 1 /4 /40; O(l) ( = X) in 48(/): ±{XVB1A9 VBXVS, VSVSX, 'A-XYSVS,
ViVi-xVi,
Vs Vs lA-x) with x-0.0788; O(2)( = Z) in 8 (ft): 3/83/83/8, 5 /8 5 / 8 5 / 8 (Becker and Will, 1970). Although only 2 parameters are needed to describe it [a and x(X)\ it is obviously a complex structure since it has a large unit cell containing 88 atoms. It may be simply described as two separate, interpenetrating structures; see Fig. 1-36. The first is an array of corner-connected (cation-centered)
1.6 Ferroelectrics Of the known ceramic ferroelectric materials the principal structure types are (i) pyrochlore, (ii) perovskite, (iii) LiNbO 3 , (iv) "Aurivillus phases", (v) "tungsten bronzes". We consider these next. 1.6.1 Pyrochlores, A 2B2X6Z (c¥88) This is a very large group of compounds (although not, of course, listed by VC because it is not found for intermetallic phases; but cf. below). Many are refractory, and some are ferroelectric. [Pyrochlore itself is a complex mineral, (Na,Ca)2(Nb,Ti)2(O,F)7. The family may also be named after the mineral atopite, (Na,Ca,Mn)2Sb2(O,OH,F)7.] To illustrate the structure we use that of Y 2 Ti 2 O 7 , in which oxygen occupies both the X and Z sites. Y 2 Ti 2 O 7 -pyrochlore-cubic, s.g. Fd3m, No. 227, Z = 8; a = 10.090 A; face center-
Figure 1-36. The two interpenetrating parts that comprise the complete structure of pyrochlore-type Y 2 Ti 2 O 7 : above, the B2X6 array of corner-connected {Ti} O(l) 6 octahedra; below, the A2Z array of cornerconnected {O(2)}Y4 tetrahedra, (In the complete structure the unit cells - outlined in the two parts of the drawing - coincide.)
36
1 Crystal Structures of Principal Ceramic Materials
{Ti}O(l) 6 octahedra, each octahedron sharing each of its corners with another octahedron, Tiv2iO^ = 2BX3. The second is a high-symmetry, C9-like array (anti to the "ideal" high-cristobalite structure) of corner-connected (ara'on-centered) {O (2)} Y 4 tetrahedra, stoichiometry Y2nOlv = A 2 Z. The rectilinear chains of tetrahedra in the second part run in <110> directions, and occupy the tunnels in the octahedral array. Together, the two parts comprise the whole
structure: 2BX3+A2Z = A2B2X6Z.
The
yttrium atoms are at the centers of the hexagonal "windows" in the octahedral array so that, as well as being coordinated to 2O(2) atoms, they are also coordinated by 6O(l) atoms in the form of a puckered hexagon. This {Y}O8 coordination polyhedron is close to a cube. The structure is often described as a reduced fluorite-derivative [4MX2— X-^ 4MX1.15 = M4X1 (with M = A0.5B0.5)]. This is best realised when one notices what is, perhaps, the most striking single fact about the structure: in spite of the different sizes of the two cations, together they form a perfect c.c.p. array. (Note that both cations are in special positions.) Because of the A, B ordering it is a 2 x 2 x 2 superstructure of the simple f.c.c. unit cell of c.c.p. The A array seen in the lower part of Fig. 1-36 (the spheres at the corners of the tetrahedra) is half of a complete c.c.p. array: the B array, identical to that of A but shifted by
type (in which all these tetrahedra are, of course, identical) all the tetrahedra are occupied by anions (cf. Sec. 1.2.2 above); in pyrochlore the first are occupied by Z = O (2), the last by X = O (1), and the second sort (B4) are empty. Hence the stoichiometry A2B2X6Z.25 Two further points may be made: (i) The X atoms are not likely to be at the centers of the A2B2 tetrahedra, because the A-X bonds and B-X bonds are unlikely to be of the same length. It is the ratio of these two bond lengths that determines the atom parameter x (X). (ii) Their sum could then determine the unit cell parameter, a, but that leaves no adjustable parameter to allow the A-X bonds to attain their optimum length: hence all three sorts of bonds may have non-optimum values. In Y 2 Ti 2 O 7 the bond strength sum at O(2) = Z is high and that at O(1) = X a little low (2.52 and 1.94 respectively): hence the two Y-O(2) bonds are rather short, 2.18 A (corresponding to v = 0.63 instead of the ideal vid. = 0.5), while the six bonds Y-O(l) are rather long, 2.48 A (corresponding to i; = 0.28 instead of the ideal vid = 0.33). This suggests that the former are compressed. The Ti-O bonds (Z=1.95A) are close to ideal: i? = 0.69 compared with i;id = 0.67. In these comparisons one sees that the structure is a compromise. (Some pyrochlores are of lower than cubic symmetry, e.g. rhombohedral. Such a distortion is the only way in which the bond lengths can be adjusted to more optimum values.) In other pyrochlores, the number of A, and particularly the number of Z, atoms may vary. Indeed, some have no Z ("defect pyrochlores") while others have small tetrahedra of atoms (Z4) in place of Z, etc.26 From this sort of variability arises a num-
37
1.6 Ferroelectrics Table 1-3. Pyrochlore-related structures. Wyckoff positions in Fd3m Substance Y 2 Ti 2 O 7 Sb 2 O 3 AgSbO3 M 3 Ti 3 O W 3 Fe 3 C Co 2 W 4 C
a (A) 10.090 11.152 10.32 -11.3 11.087 11.21
A = 16(d)
B=16(c)
X = 48(/)
x(X)
(Na,Ca) — Sb Ma Fe(l) W(l)
(Nb,Ti) _ Ag O C
O(l) O
0.0788 0.0613 0.040 0.060 0.073 0.070
c
o
Ti W W(2)
O(2) — — _ —
Z' = 32(e)
x(Y)
Sb Ma Fe(2) Co
0.2397 0.290 0.295 0.300
a
M = Co, Cu, Fe, Mn or Ni. VC list 54 different substances with these last three structure types (cF 112), mainly carbides, nitrides and oxides.
ber of closely-related structures, and particularly anti-structures (cations and anions interchanged), although this is often not apparent from their stoichiometric formulae. A few examples will suffice, see Table 1-3. (Some of them are important refractories.) 1.6.2 Perovskites, ABX3 The ideal cubic perovskite structure has already been discussed (Sec. 1.3.3); and it was mentioned that distortions to lower symmetry were common and, in particular, were associated with the ferroelectric property. [References were given there to discussions of the nature of these topological distortions. Megaw (1957) treated them (and other structure types) in the context of ferroelectricity, but see also Newnham (1975).] BaTiO 3 -tetragonal, s.g. P4mm, No. 99, Z = l;a = 3.9923, c = 4.0349 A (Wittels and Sherill), 1957, c/a = 1.0107; Ba in l(a): OOz, with z = 0; Ti in 1(6): ViViz, with z=Vi+ 0.014; O(l) in l(b): with z = 0-0.023; O(2) in 2(c): ViOz, 0 Viz, with z = Vi-0.014 (Frazer et al., 1955). [There are four variable atom parameters - z for each of the four types of atom - only three can be independent, so z(Ba) is set arbitrarily to zero.]
BaTiO 3 is a classic example, with the simplest sort of atom shifts leading to electric dipoles - all parallel to z (and small). The room-temperature, ferroelectric form (shown in Fig. 1-37) is tetragonal, but only slightly distorted from cubic: c/a^ 1.01, bond lengths are /(TiO-O) = 1.86, 2.00(4 x) and 2.17 A, and J(Ba-O) = 2.80, 2.83 and 2.88 A (each 4 x). Above the Curie temperature (120 °C) it is cubic. NaNbO 3 , KNbO 3 and PbTiO 3 are similar examples in which the dipoles are parallel; and there are many other examples, with different symmetries due to atom shifts in other directions. For example, below 0°C BaTiO3 becomes or-
Figure 1-37. The structure of tetragonal BaTiO3 projected on (010). Large, medium and small circles are, respectively, Ba, Ti and O (open at y/b = 0, filled at y/b = lA). Note the very small shifts of the atoms from the cubic perovskite type (cf. data in text).
38
1 Crystal Structures of Principal Ceramic Materials
thorhombic, Amm2\ with atom shifts parallel to <110> of the cubic subcell, and a new unit cell of doubled volume (approx. yfl x y/l x 1 x the cubic subcell). Below 90 °C it becomes rhombohedral (but "only slightly": the cubic cell angle changes by only 8'), Rim (Z = l). This structure is of the LiNbO 3 type (see below). If, as in PbZrO 3 for example, the atom shifts are anti-parallel, then the crystals are anti-ferroelectric. 1.6.3 LiNbO3 Types These are a subset of the previous section, for LiNbO 3 is a rhombohedrally-distorted perovskite, customarily described as collapsed by rotating all the {Nb} O 6 octahedra around axes through their centers and parallel to ±<111> of the cubic subcell. This topological distortion would result in the calcite (CaCO^GOi) structure, with Li in triangular, {Li}O3 coordination. In fact, the Li atoms jump from these faces of O 6 octahedra into the octahedra themselves. (Above 1200 °C, the paraelectric form of LiNbO 3 does have the GO! structure; but this is just an average - the Li atoms are jumping between the two octahedra that share the face in which their average position is located.) The result is a corundumlike structure (cf. Sec. 1.2.6) with Li, Nb in octahedral coordination, but ordered. As with a-Al 2 O 3 , the anion array is distorted h.c.p. (the 12 closest anion-anion distances vary between 2.73 and 3.35 A; c/a = 2.693, cf. 2.730 for corundum), and the cations in adjacent, face-sharing octahedra repel each other along c - in this case d (Li... Nb) = 0.219 xc (ideal = 0.166xc for h.c.p.; d(Al... Al) = 0.205 x c for a-Al2O3). Consequently, again (as with corundum) each cation has three shorter and three longer bonds to oxygen: /(Li-O) = 2.05, 2.25 A, Z(Nb-O) = 1.88, 2.13 A; cf. I(A1-O) = 1.85,
1.97 A. It is these shifts from the ideal positions, different for the two cations in LiNbO 3 , which produces the dipoles. 1.6.4 Aurivillius Structures
The large family of Aurivillius phases, with general formula Bi 2 O 2 • An_1BnO3n + 1 (n an integer), may be regarded as lamellar intergrowths of layers of perovskite with (pseudo-)tetragonal Bi 2 O 2 layers [of the type which occur in PbFCl-type BiOF or, parallel to (100), in Cl/fluorite type] (Aurivillius, 1949 a, b; 1950).27 Many of them are ferroelectric, but the largest spontaneous polarisations, Ps9 are observed when A is also Bi, e.g., Bi 4 Ti 3 O 12 ( = Bi 2 O 2 • Bi 2 Ti 3 O 10 , n = 3; Rae etal., 1990), Bi 3 TiNbO 9 [ = Bi 2 O 2 Bi(TiNb)O7, n = 2; Thompson etal., 1991] and the n = \ members, Bi 2 WO 6 (Rae et al., 1991) and y-Bi 2 MoO 6 (Theobald et al., 1984). Bi 4 Ti 3 O 12 -monoclinic, s.g. Pa (alternative setting of Pc), No. 7, Z = 2; a = 5.450, b = 5.4059, c = 16.6406 A, j? = 99.4°; all atoms in 2 (a): x y z, x 4- Yi y z. The parameters for the 19 crystallographically distinct atoms (each one in the formula) may be derived from those given in the reference (Rae et al., 1990) by the matrix 101/010/ 002 (also, shift their origin by [0 YAO]). The "parent", high-symmetry structure of Bi 4 Ti 3 O 12 has tetragonal symmetry, s.g. lA/mmm (Z = l) 2 8 , which is related to the real (monoclinic, Z = 2) structure, shown in Fig. 1-38, by the matrix ViOO/- Yi YiO/ 102. This is reduced to the observed monoclinic symmetry (at R.T.) by quite large shifts of the atoms [Rae et al. (1990) identify 4 independent, condensed soft modes plus 3 other, induced components!].29 In the high-symmetry parent, the coordination numbers are 12, 6 and 5 or 6 (in equal quantities) for Bi, Ti and O, and the
1.6 Ferroelectrics
39
{Ti}O6 octahedra are regular. In the actual structure, the (not very well defined) coordination numbers have been reduced to 6 (3 x) and 8 for the four Bi atoms, and 5, 4 ( 7 x ) and 3 ( 4 x ) for the twelve O atoms; the coordination number, C.N. (Ti), remains at 6, but there is now a range of bond lengths, 1.73
These too are perovskite related: the BX3 framework in the latter is easily transformed to the BX3 framework in the former by concerted rotation of columns 2 x 2 octahedra in cross-section, see Fig. 1-39 (Bursill and Hyde, 1972; Hyde and O'Keeffe, 1973).30 The resulting framework (also BX3, usually with B = Ti, Nb, Ta and/or W) contains three different types of interstices analogous to those for the A atoms in perovskite; in the ideal, high-symmetry structure these are (per unit cell, 10BX3) two of type ^4(1) (square in crossection - cuboctahedra, as in perovskite itself), four of type A (2) (pentagonal in crossection) and four more of type ^4(3) (triangular in crossection - a tricapped trigonal prism, or a pair of faceshared octahedra, depending on the axial ratio c/a).31 If all these sites were filled (which is unlikely), the stoichiometry would 32 therefore be A(l)2A(2)4A(3)4B10X30. In Na 2 _ 2 x Ba 4 + x Nb 1 0 O 3 0 ^Na 2 Ba 4 • Nb10O30(Jamieson et al., 1969), ^(1) 2 = ^ a o . 8 7 o " a o . 0 6 5 Qo.065)2 >
A(2)4.=
Ba4,
^4 (3) 4 = CU [i.e., all the smallest ('triangular' tunnel) sites are empty], 2?lo = Nbio and X 3 0 = O 3 0 ; the appropriate types of
Figure 1-38. The structure Bi 4 Ti 3 O 12 . Large, medium and small circles are Bi, Ti and O, respectively. The broken lines outline the monoclinic (Pa) unit cell; the fine lines outline the pseudo-tetragonal (I4/mmm, but with an arbitrary origin) unit cell of the "parent" structure. On the left it is shown as {Ti} O 6 octahedra and {O}Bi4 tetrahedra; the octahedra are radically tilted, but the perovskite-like nature remains clear. On the right, all the anions (and coordination polyhedra) are omitted so that we see only the Bi4Ti3 cation array: note its regularity compared with that of the anion array. Tetragonal [pseudo-b.c.c/CsCl] unit cells are drawn: the top and bottom halves are, of course, in antiphase due to the pairs of adjacent Bi layers (the stoichiometry being A4B3 and not AB).
'A' sites are occupied by large cations. A minor complication is that these structures have a doubled c-axis. (We give no data; too much is required - the structure has 19 crystallographically distinct atomic sites!)
40
1 Crystal Structures of Principal Ceramic Materials
(a)
Figure 1-39. A mechanism for transforming the BX3 array of corner-connected {B}X6 octahedra from that in (a) perovskite type to that in (b) TTB. It involves rotating (about the projection axis) the emphasised columns of four octahedra. A (2) sites, shown as filled circles in (b), correspond to the open circles in (a).
1.7 Solid Electrolytes Also called "fast ion" or "superionic" conductors, terms which are misleading and therefore better avoided: they are good (ionic) conductors, with specific conductivities similar to those of molten salts, but not "superconductors"; and this property appears to be associated with high concentrations of mobile ions rather than high velocities. Their specific conductivity a is of the order of l - 1 0 Q ~ 1 m ~ 1 , which is at
least 3 orders of magnitude higher than that of other solid ionic conductors. The solid electrolyte state occurs at a temperature above that of an order-disorder transition (which, thermally, may be sharp or diffuse): it affects only one of the atom arrays in the crystal, i.e. either the anions or the cations. (If it affects all the atoms in the crystal then it is the melting process, with which we are not concerned here.) Some transitions are sharp (first order), e.g., (i) p--Kx-AgI (at 146 °C), in which the iodine array transforms from h.c.p. (P-AgI is B4/wurtzite type) to b.c.c. and, so it appears, the cation array becomes "molten"33; and (ii) low- -*high-chalcocite (Cu2S; at 100 °C), in which the anion array is now almost unchanged h.c.p. Further examples (and their transition temperatures) include Ag2S (179 °C), Ag3SI (235 °C), MAg 4 I 5 (M = K, Rb, NH 4 , etc. (~_140°C), Cu halides (-400-500°C), SrBr2 (644 °C), BaCl2 (920 °C), LuF 3 (954 °C), YF 3 (1074 °C), etc. Other transitions are diffuse, with no change in the array of immobile ions; examples include all the fluorite and anti-fluorite (e.g., Na2S) type structures, in which the disorder occurs in, respectively, the anion and cation arrays - i.e., the atoms in tetrahedral coordination. These (gradual) transitions are termed "higher order" or, after the shape of their curves of specific heat vs. temperature, "lambda" type. The received wisdom is that there are many more sites available for the mobile species than there are atoms to fill them, e.g., for a-Agl there are 42 possible sites in the unit cell containing only 2Ag atoms. (In a sense this is a truism.) But there is striking thermodynamic evidence that is relevant. For the straightforward melting of a solid 34 there is a pleasing simplicity in val-
1.8 Notes
ues of the entropy of fusion, ASf: per mole of atoms its value is 13.8-14.2 J m o l " 1 K 1 for the rare gases and ~ 11.5-14.0 J m o r 1 ! ^ 1 for the alkali halides (9.211.3 Jmol" 1 K " 1 for the c.p. metals) - let us take an average of 13Jmol~ 1 K~ 1 . Now, for the solid electrolytes we have mentioned, the values are ASf = 5.7,4.2, 6.3, 3.8, 4.4, 5.2 and 4.9 Jmol"* K " 1 for Agl, Ag2S, CuBr, SrBr2, BaCl2, LuF 3 and YF 3 respectively: for fluorite-type PbF 2 , CaF 2 , UO 2 , K 2 S and for LaF 3 the values are 5.3, 5.8, 8.1, 4.5 and 7.1 J m o l ^ K " 1 respectively. All the solid electrolyte values are anomalously low, by about 50% or so. However, there is a significant entropy change, AStr, at the solid electrolyte transition and, if this is added to the entropy of fusion one gets, for the first sequence of compounds (AStr is not as readily available for diffuse transitions), ASf + AStr = AStot = 12.9, 7.3, 10.8, 8.2, 9.2, 10.3 and 10.9 J mol ~x K ~ * - much more respectable values! This suggests that part (roughly a half) of each compound already "melted" at Ttr - consistent with the idea that the mobile ions are a melt in the framework of the immobile ones [cf. O'Keeffe and Hyde (1976) and Ubbelohde (1965)].35 Most of the materials mentioned so far are hardly ceramics, but they do serve to show that compounds of especially Ag and Cu (with large anions like S) are common solid electrolytes. Their interest is precisely that they behave this way at lowish temperatures (which are more convenient for studying the solid electrolyte state). But, it should be remarked, the fluorite-type dioxides and all fiuorite-related structures ("defect fluorites") also become solid electrolytes (at a few hundred to > 1 000 °C); anion-deficient ones particularly stabilised zirconias (Sec. 1.3.1) are widely used: and anion-excess ones such as zirconia "stabilised" with Nb 2 O 5 or Ta 2 O 5 (compounds
41
not yet widely used and therefore not discussed here, although they are of great structural interest). These all have in common the stable c.c.p. cation array. Other oxide, ceramic, solid-electrolyte materials include the pyrochlores (also with a c.c.p. cation array; Sec. 1.6.1) and P-aluminas [in which the mobile species is the low-valence cation, e.g., Na (sometimes Ag); Sec. 1.3.7]. Fluorides such as YF 3 (anti-structure of the Fe 3 C type) and LaF 3 (which is not very different in structure) are possibly useful electrolytes for high-temperature cells.
1.8 Notes 1 Note the convention, roman letters for anions, greek letters for cations (although, in this case the distinction is irrelevant since the structure and antistructure are identical). The equal spacing of the letters shows that the cations are midway between the anion layers, and vice versa. Because they occupy octahedral interstices in the array, atoms must have a position indicated by a letter different from those on either side (and of the other font), i.e., a between b and c, p between a and c, etc. Tetrahedral sites lie at one quarter of the distance between eutactic layers, and therefore correspond to the spaces between greek and roman letters in the present sequence, cf. the B 3 structure, below. They must be represented by a letter identical to that of the furthest adjacent layer, but of different font (cf. tetrahedral structures, below). We would prefer the term "eutactic" to (the usual) "close-packed" because it describes the geometry without implications about distance. For example, in the B1 type both anion and cation arrays have the same ("eutactic") geometry, but (logically) not more than one of the two is likely to be "close-packed". However, the latter term is now entrenched. 2 At 2.54 A (12 x), the second-nearest-neighbour distances in diamond are extremely short, and it has been suggested that it is this rather than strongly-directional bonding that is reponsible for its hardness and incompressibility. Third-nearest neighbours are not much more distant, 2.95 A (12 x). Cf. the van der Waals radius for carbon is 1.60 A (which may be compared with the inter-layer separation of 3.35 A in graphite), and its non-bonded radius (at which overlap repulsion is very high, ~ 15 kJ mol" 1 ) is 1.25 A (O'Keeffe and Hyde, 1981). 3 SiC is also extremely hard and incompressible, due to the short, second-nearest-neighbour, Si-Si distances, <2(Si • • • Si) = ajjl = 3.08 A. [When {Si}X4 tetrahedra are corner-connected, i.e. the Si atoms are
42
1 Crystal Structures of Principal Ceramic Materials
bonded via a single bridging atom (Si-X-Si), in this circumstance only exceptionally (cf. Sect. 1.3.8, pSi3N4 below) is d(Si • • • Si) < 3.06 A (O'Keeffe and Hyde, 1978).] 4 This too has very short second-nearest-neighbour distances; in this case J(B-B) = 2.56 A. It is therefore not surprising that it too is a high-pressure polymorph. 5 The nature of the transformations is important in the use of "stabilised zirconia" as a ceramic. 6 It is this shear which is partly responsible for the catastrophic shattering of ZrO 2 crystals/specimens when they are cooled from high temperatures: at about 1000 °C the structure transforms - with a large shape change, and a 5% volume increase - from the tetragonal polymorph (rather close to Cl) to the monoclinic form. 7 The asymmetry clearly results from the short d(F--F) = 2.5&k (cf. Fig. 1-9) and an obviously short d(O • • • F) = 2.56 A. The latter also displaces the O atoms from the centers of their Sc4 tetrahedra. 8 This relatively low precision is surprising when one considers the technical and commercial importance of zirconia, and the enormous amount of structural work that has been done on it and its "stabilised" modifications. 9 Other examples include the suboxides M3M'O, with M = Ca, Sr or Ba, and M' = Sn or Pb; all cubic, s.g. Pm3m. Especially intriguing is Ba 3 PbO, i.e. PbOBa3 = ABX3 (Widera and Schafer, 1980), which may be compared with BaPbO 3 = ABX3 in Sec. 1.6. The latter is a very slightly distorted (orthorhombic, y/2 x ^/2 x 2) perovskite type, originally reported as cubic. 10 This is stable under ambient conditions; Fe 3 C is not, it is metastable and therefore not suitable for single-crystal structure determination. 11 It is strange that this projection is not used, as it is exactly that used in the conventional drawings of the next two structure types - which are spinel intergrowths. 12 This Fe is off-center in its polyhedron: two close, half-occupied sites occur - shown by broken circles in Fig. 1-20. This site-splitting is probably an artefact from a twinned crystal. 13 A reminder about the topology of eutaxy ("closepacking"): (i) There is one octahedral and two tetrahedral interstices per "close-packed" atom. (ii) In the space between a pair of eutactic (36) layers, the octahedra share faces with the tetrahedra, while the octahedra share edges with each other and the tetrahedra share edges with their nearest neighbours but corners with their next-nearest neighbours. (iii) Across a eutactic layer, the arrangement of the two layers of interstices are different for c.e. and for h.e.: (a) c.e., i.e., either side of a c layer: octahedra share edges with each other, and faces with tetrahedra; tetrahedra share edges and corners with each other.
(b) h.e., i.e., either side of an h layer: octahedra share faces with each other, as to tetrahedra. 14 No accurate, single-crystal solution seems to be available for any Ln5Si3. Approximate atom parameters are available for Y5Si3, and are consistent with those for Mn 5 Si 3 . Figure 1-31 b has therefore been constructed using the unit cell parameters for Sm5Si3 and the more precise atom parameters for Mn 5 Si 3 : (i) Sm5Si3-hexagonal, s.g. P63/mcm, No. 193, Z = 2; a = 8.56, c = 6.45 A (c/a = 0.754); X-ray powder data (Gladyshevskii and Kripyakevich, 1965 a, b). (ii) Y5Si3-s.g. details as in (i); a = 8.403, c = 6.303 A (c/a = 0.750); Y(l) in 4(d): ±(lA 2A 0, Y3 2A lA)\ Y(2) in 6fe): ±(x0 lA, 0x %, xx 3A) with x = 0.25; Si in 6(g): with x = 0.61 (Parthe, 1960). (iii) Mn 5 Si 3 -s.g. details as in (i); a = 6.910, c = 4.814 A (c/a = 0.6967); Mn(l) in 4(d): ±(lA 2A0, l 2 A A V2); Mn(2) in 6{g): ±{x0 %, Ox %, xx3A) with x = 0.2356; Si in 6(g): with x = 0.599 (Aronsson, 1960). 15 The addition of 13 anions to Sm5Si3 causes some increase in the volume of the unit cell: a increases by 11% and c by 8%; c/a increases by 2.7%. 16 It may be relevant (in the context of ceramics) to point out that this structure type was originally known as the "p-tungsten" structure. Subsequently it transpired that this material was not tungsten but a sub-oxide, W 3 O. 17 The rapid rise to ~ 9 0 K (i.e., above the normal boiling point of liquid nitrogen) for YBa 2 Cu 3 O 7 in 1987 was a significant development because, previously, (expensive) liquid helium (or hydrogen) was needed to attain temperatures below Tc. 18 It should perhaps be recalled that Tc is not the sole figure of merit for a superconductor. 19 La 2 NiO 4 behaves similarly, yielding La 2 NiO 4+(5 . 20 The Tl site occupancy is lA, i.e., Tl atoms appear to be randomly distributed over the four equivalent / sites [0.33 A from the center of gravity at \{a): 000]. This suggests that the true symmetry is lower than tetragonal, although no evidence for this could be found. The average, 1 (a) position is used in Fig. 1-32. 21 This continual use of non-standard settings is simply to maintain equivalent axial directions for the unit cells of all these superconductors - an aid in comparing their structures. 22 A non-standard setting of Pnma, beloved by mineralogists. We retain it here in order to correspond with the standard setting of the space group for mullite, Pbam, considered next (which is exactly the sort of justification usually put forward for Pbnm). 23 The normal distance for corner-connected {T} O 4 tetrahedra is d(Si • • • Si) = 3.06 A, d(Al • • • Al) = 3.24 A and d(Al - • • Si) = 3.15 A (O'Keeffe and Hyde, 1978; 1981). Cf. d[Al(l)---Al(2)] =
1.9 References
d(A\ -• - Al)<2.70 A. This is confirmed experimentally by Welberry and Withers (1990) and Angel et al. (1990). 25 All the octahedra in the A2B2 array are A3B3; and they are all unoccupied. 26 The {Z} AA tetrahedron then becomes a {Z'4} A4 tetrahedron. The latter is a "stella quadrangula" - a tetrahedron (Zf4) capped on each face by another atom (A); i.e., a central Z'4 tetrahedron sharing each face with an AZ'2 tetrahedron. 27 Removal of the oxygen between the two Bi layers produces the structures of the Ruddlesden-Popper phases (cf. Sec. 1.4.3, above). 28 This is the para-electric, presumably high-temperature, form. 29 In spite of a great deal of earlier work, it appears that it is only now that the true symmetry and accurate details have been determined for this (and similar) structures. 30 This is not just formal geometry; faults corresponding to this rotation operation and its inverse have frequently been observed in electron microscope studies of appropriate chemical systems, e.g., WO 3 + Nb 2 O 5 . Perhaps the first report was by Allpress (1972). The A (2) sites are penta-capped pentagonal prisms: these are, of course, larger than the cuboctahedra (= "tetra-capped tetragonal prisms") from which they were derived, and hence can accommodate larger cations. This, presumably, is the underlying cause for the transformation of the octahedral framework (Fig. 1-39). 31 The total number of such tunnels is, of course, identical to that in the perovskite parent 10BX3 in the unit cell implies 10 A-typQ sites in perovskite. In the transformation, 8 of these "squares" are converted - half to pentagons and half to triangles. 32 Jamieson et al. (1969) use 041)2042)4C4(Bl)2(fl2)8O3O. 33 The conductivity of Agl actually drops slightly when it melts! 34 I.e., where there are no prior order-disorder transitions in the solid state. 35 But there may be philosophical questions about the nature of a liquid: until recently, at least, the most successful theories of liquids were "quasi-crystalline" (e.g., Ubbelohde, loc. cit)!
1.9 References Allpress, I G. (1972), in: Solid State Chemistry (Proceedings of the 5th Materials Research Symposium at Gaithersburg, Maryland, October 1971): Roth, R. S., Schneider, S. J. (Eds.). Washington: N.B.S., pp. 104-109. Angel, R. I , Prewitt, C. T. (1986), Amer. Mineral 71, 1476-1482. Angel, R. X, Prewitt, C. T. (1987), Ada Cryst. B43, 116-126.
43
Angel, R. X, McMullan, R. K., Prewitt, C. T. (1992), Amer. Mineral., in press. Armytage, D., Fender, B. E. F. (1974), Acta Cryst. B30, 809-812. Aronsson, B. (1960), Acta Chem. Scand. 14, 14141418. Aurivillius, B. (1949a), Arkiv Kemi 1, 463-480. Aurivillius, B. (1949b), Arkiv Kemi 1, 499-512. Aurivillius, B. (1950), Arkiv Kemi 2, 519-527. Becker, W.-X, Will, G. (1970), Z. Kristallogr. 131, 278-288. Bednorz, T. G., Miiller, K. A. (1986), Z. Phys. B64, 189-193. Bettmann, M., Terner, L. L. (1971), Inorg. Chem. 10, 1442-1446. Billy, M., Labbe, X-C, Selvaraj, A., Roult, G. (1983), Mater. Res. Bull. 18, 921-934. Bjurstrom, T. (1933 a), Arkiv Kemi Mineral. Geol. 11 A, 12. Bjurstrom, T. (1933 b), Structure Reports 3, 12-13, 619. Braun, P. B. (1952), Nature 170, 708. Brown, I. D., Altermatt, D. (1985), Acta Cryst. B41, 244-247. Burnham, C. W. (1963), Z. Kristallogr. 118, 127-148. Bursill, L. A., Hyde, B. G. (1972), Nature 240, 122124. Cameron, W. E. (1977), Amer. Mineral. 62, 747-755. Cava, R. X, Batlogg, B., Ktajewski, X X, Farrow, R., Rupp, L. W, White A. E., Short, K., Peck, W F, Kometani, T. (1988), Nature 332, 814-816. Donohue, X (1974), The Structures of the Elements. New York: Wiley. Fasiska, E. X, Jeffrey, G. A. (1965), Acta Cryst. 19, 463
-Alrl.
Felsche, X (1968), Z. Kristallogr. 127, 94-100. Frazer, B. C , Danner, H. R., Pepinsky, R. (1955), Phys. Rev. 100, 745-746. Gaude, X, L'Haridon, P., Hamon, C , Marchand, R., Laurent, Y (1975), Bull Soc.fr. Mineral. Crist. 98, 214-217. Gladyshevskii, E. I., Kripyakevich, P. I. (1965 a), Izv. Akad. Nauk, SSSR, Neorg. Mater. 1, 702-705. Gladyshevskii, E. L, Kripyakevich, P.I. (1965 b), Chem. Abs. 63, 10789d. Glazer, A. M. (1972), Acta Cryst. B28, 3384-3392. Goodenough, X B., Manthiram, A. (1990), J. Solid State Chem. 88, 115-139. Hann, R. E., Suitch, P. R., Pentecost, X L. (1985), /. Amer. Ceram. Soc. 68, C285-C286. Havinga, E. E., Damsma, H., Hokkeling, P., Kanis, XM. (1972), reviewed in: Structure Reports 38A, 5-6. Holmberg, B. (1966), Acta Chem. Scand. 20, 10821088. Howard, C. X, Hill, R. X, Reichert, B. E. (1988), Acta Cryst. B44, 116-120. Hyde, B. G., Andersson, S. (1989), Inorganic Crystal Structures. New York: Wiley.
44
1 Crystal Structures of Principal Ceramic Materials
Hyde, B. G., O'Keeffe, M. (1973), Acta Cryst. A 29, 243-248. International Tables of Crystallography, Vol. 1 (1969). Birmingham: Kynoch Press or A (1983). Dordrecht: Reidel. Ishizawa, N., Miyata, T., Minato, I., Marumo, R, Iwai, S. (1980), Acta Cryst. B36, 228-230. Jack, K. H. (1978), Mater. Res. Bull. 13, 13271333. Jack, K. H., Wild, S. (1966), Nature 212, 248-250. Jamieson, P. B., Abrahams, S. C , Bernstein, J. L. (1969), /. Chem. Phys. 50, 4352-4363. Jeffrey, G. A., Wu, V. Y. (1963), Acta Cryst. 16, 559566. Jeffrey, G. A., Wu, V. Y. (1966), Acta Cryst. 20, 538547. Johnston, D. C , Prakash, H., Zachariasen, W. H., Viswanathan, R. (1973), Mater. Res. Bull. 8, 111784. Johnston, D. C , Jacobson, A. X, Newsam, J. M., Lewandowski, J. T., Goshorn, D. P., Xie, D., Yelon, W B. (1987), Chemistry of High Tc Superconducting Oxides (ACS Symp. Ser., 351). Washington: American Chemical Society, p. 136. Kaldis, E., Fischer, P., Hewat, A. W, Hewat, E. A., Karpinski, X, Rusiecki, S. (1989), Physica C 159, 668-680. Kiessling, R. (1949), Acta Chem. Scand. 3, 595-602. Kisi, E. H., Howard, C. X, Hill, R. X (1989), J. Amer. Ceram. Soc. 72, 1757-1760. Kohn, J. A., Eckart, D. W. (1965 a), Amer. Miner. 50, 1371-1380. Kohn, X A., Eckart, D. W. (1965b), J. Appl. Phys. 36, 1171-1172. Kudoh, Y, Takeda, H., Arashi, H. (1986), Phys. Chem. Minerals 13, 233-237. Lewis, X, Schwarzenbach, D., Flack, H. D. (1982), Acta Cryst. A38, 733-739. McCullough, X D., Trueblood, K. N. (1959), Acta Cryst. 12, 507-511. Megaw, H. (1957), Ferroelectricity in Crystals. London: Methuen. Megaw, H. (1973), Crystal Structures: A Working Approach. Philadelphia: Saunders. Newnham, R. E. (1975), Structure-Property Relations. Berlin: Springer-Verlag. Ohtaka, O., Yamanaka, X, Kume, S., Hara, N., Asano, H., Izumi, F. (1990), Proc. Japan Acad. B66, 193-196. O'Keeffe, M., Hyde, B. G. (1976), Phil. Mag. 33, 219-224. O'Keeffe, M., Hyde, B. G. (1977), Acta Cryst. B33, 3802-3813. O'Keeffe, M., Hyde, B. G. (1978), Acta Cryst. B34, 27-32. O'Keeffe, M., Hyde, B. G. (1981), Structure and Bonding in Crystals, Vol. 1. New York: Academic Press, pp. 227-254.
O'Keeffe, M., Hyde, B. G. (1985), Structure and Bonding 61, 11-144. O'Keeffe, M., Hyde, B. G. (1992), Acta Chem. Scand., in press. Parise, I B . , Gopalakrishnan, X, Subramanian, M. A., Sleight, A. W. (1988), /. Solid State Chem. 76, 432-436. Parthe, E. (1960), Acta Cryst. 13, 868-871. Peters, C. R., Bettmann, M., Moore, X W, Glick, M. D. (1971), Acta Cryst. B27, 1826-1834. Rae, A. D., Thompson, X G., Withers, R. L., Willis, A. C. (1990), Acta Cryst. B46, 474-487. Rae, A. D., Thompson, X G., Withers, R. L. (1991), Acta Cryst. B47, 870-881. Roualt, A., Herpin, P., Fruchart, R. (1970), Ann. Chim. 5, 461-470; and refs. therein. Ruddlesden, S. N., Popper, P. (1958), Acta Cryst. 11, 54-55. Sleight, A. W, Gillson, X L., Bierstedt, P. E. (1975), Solid State Commun. i 7, 27-28. Smith, D. K., Newkirk, H. W. (1965), Acta Cryst. 18, 983-991. Structure Reports (1987), 54 A, 195. Subramanian, M. A., Parise, X B., Calabrese, X C , Torardi, C. C , Gopalakrishnan, X, Sleight, A. W (1988), /. Solid State Chem. 77, 192-195. Theobald, F , Laarif, A., Hewat, A. W. (1984), Ferroelectrics 56, 219-237. Thompson, X G., Rae, A. D., Withers, R. L., Craig, D. C. (1991), Acta Cryst. B47, 174-180. Townes, W D., Fang, X H., Oerrotta, A. X (1967), Z. Kristallogr. 125, 437-449. Ubbelohde, A. R. (1965), Melting and Crystal Structure. Oxford: Clarendon Press. Van Landuyt, X, Amelinckx, S., Kohn, X A., Eckart, D. W. (1974), J Solid State Chem. 9, 103-119. Villars, P., Calvert, L. D. (1985), Pearson's Handbook of Crystallographic Data for Intermetallic Phases. Metals Park: American Society for Metals. Vlasse, M., Saux, M., Echegut, P., Villeneuve, G. (1979), Mater. Res. Bull. 14, 807-812. Weishaupt, M., Strahle, X (1977), Zeit. anorg. allgem. Chem. 429, 261-269. Welberry, T. R., Withers, R. L. (1990), Phys. Chem. Minerals 17, 117-124. Wells, A. F. (1984), Structural Inorganic Chemistry, 5th edn. Oxford: Clarendon Press, p. 645. Widera, A., Schafer, H. (1980), Mater. Res. Bull. 15, 1805-1809. Winter, X K., Ghose, S. (1979), Amer. Mineral 64, 573-586. Wittels, M. C , Sherrill, E A. (1957), J. Appl. Phys. 28, 606-609. Wu, M. K., Ashburn, X R., Torng, C. X, Hor, P. H., Meng, R. C , Gao, L., Huang, Z. X, Wang, Y. Q., Chu, C. W. (1987), Phys. Rev. Lett. 58, 908. Yamaguchi, G., Suzuki, K. (1968), Bull. Chem. Soc. Japan 41, 93-99.
1.9 References
General Reading Aronsson, B., Lundstrom, T., Rundqvist, S. (1965), Borides, Silicides and Phosphides. London: Methuen. Bevan, D. J. M. (1973), in: Comprehensive Inorganic Chemistry, Vol. 4. Oxford: Pergamon, pp. 453540. O'Keeffe, M. (1989), Structure and Bonding 71, 161190. Perez-Mato, J. M., Zufliga, F. X, Madariaga, G. (1992) (Eds.), Methods of Structural Analysis of Modulated Structures and Quasicrystals. Singapore: World Scientific.
45
Schubert, K. (1864), Kristallstrukturen zweikomponentiger Phasen. Berlin: Springer-Verlag. Wadsley, A. D. (1964), in: Non-stoichiometric Compounds: Mandelcorn, L. (Ed.). New York: Academic Press. Wyckoff, R.W. G. (1963), Crystal Structures, 2nd edn., Vol. 1. New York: Interscience. Wyckoff, R.W. G. (1964), Crystal Structures, 2nd edn., Vol. 2. New York: Interscience. Wyckoff, R. W G. (1965), Crystal Structures, 2nd edn., Vol. 3. New York: Interscience. Wyckoff, R. W. G. (1968), Crystal Structures, 2nd edn., Vol. 4. New York: Interscience.
2 Oxide Ceramics James D. Cawley Department of Materials Science and Engineering, Case Western Reserve University, Cleveland, OH, U.S.A. William E. Lee Department of Engineering Materials, University of Sheffield, Sheffield, U.K.
List of 2.1 2.2 2.2.1 2.2.1.1 2.2.1.2 2.2.1.3 2.2.2 2.2.2.1 2.2.2.2 2.2.2.3 2.2.3 2.2.3.1 2.2.3.2 2.2.3.3 2.2.4 2.2.4.1 2.2.4.2 2.2.4.3
Symbols and Abbreviations Introduction Silicate Ceramics Phyllosilicates Crystal Structure Mineral Sources Characteristic Properties Fluxes Crystal Structure Mineral Sources Characteristic Properties Fillers Crystal Structure Mineral Sources Characteristic Properties Triaxial Formulations Clay-Quartz-Feldspar Clay-Alumina-Feldspar, Clay-Zircon-Feldspar Pyrophyllite- and Talc-Based Formulations, Clay-Wollastonite-Nepheline Syenite 2.2.5 Summary and Analogies in Single Phase Ceramics 2.3 MgO, Magnesia, Periclase 2.3.1 Crystal Structure , 2.3.2 Mineral Sources and Production 2.3.3 Properties 2.3.3.1 Single-Crystal MgO 2.3.3.2 Refractory Fabrication and Microstructure 2.4 A12O3, Alumina, Sapphire, Corundum 2.4.1 Crystallography 2.4.2 Mineral Sources and Chemical Synthesis 2.4.2.1 Fused and Tabular Refractory Grades Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.
49 50 51 51 52 56 59 63 64 64 65 66 66 68 69 69 70 71 72 73 74 74 74 75 75 77 85 85 87 91
48
2.4.2.2 2.4.2.3 2.4.3 2.4.3.1 2.4.3.2 2.4.3.3 2.4.3.4 2.5 2.5.1 2.5.2 2.5.3 2.5.3.1 2.5.3.2 2.5.3.3 2.5.3.4 2.5.4 2.5.4.1 2.5.4.2 2.5.4.3 2.6 2.7
2 Oxide Ceramics
Abrasives Fibers Ceramic Fabrication and Microstructural Evolution Bulk Single Crystal Alumina Solid State Sintering Liquid Phase Sintering Microstructures of Commercial Aluminas and Relation to Properties Zirconia Mineral Sources and Powder Production Crystal Structure, Polymorphism and Physical Properties of Single Crystal ZrO 2 Ceramic Fabrication and Microstructural Control of Binary Zirconia Alloys ZrO 2 -MgO ZrO 2 -CaO ZrO 2 -Y 2 O 3 ZrO 2 -CeO 2 Properties and Applications of Selected Zirconia Ceramics Mg-PSZ Y-TZP ZTA Composites Summary References
92 92 94 94 95 97 98 101 102 103 104 105 106 108 110 110 110 Ill 113 114 114
List of Symbols and Abbreviations
List of Symbols and Abbreviations c/a C/S T I
ratio of crystal lattice parameters calcia to silica ratio fracture toughness melting temperature wavelength
BOS CMC CMS DS EFG f.c.c. i LHFZ LPS MOR PLZT PSZ RT SEM TEM TZP V XRD YAG ZTA
basic oxygen steelmaking ceramic matrix composites monticellite directionally solidified edge defined film-fed growth face-centered cubic interstitial laser-heated float zone liquid phase sintered modulus of rupture lead lanthanum zirconate titanate partially stabilized zirconia room temperature scanning electron microscopy transmission electron microscopy tetragonal zirconia polycrystals vacancy X-ray diffraction yttrium aluminum garnet zirconia toughened alumina
49
50
2 Oxide Ceramics
2.1 Introduction The world production of industrial ceramics was about $ 73 billion (U.S.) in 1991. This is broken down into broad categories in Table 2-1. The field of oxide glasses constitutes more than half of the world dollar volume. This important field is covered in Volume 9 of this Series. The remaining categories of industrial ceramics are broken down further in Table 2-2 which reveals several important points. Firstly, worldwide ceramics production is overwhelmingly concerned with oxide materials. Nonoxides dominate categories such as engineering ceramics, but they are a small percentage of current production. While nonoxides do find niche applications in areas such as electronics and refractories both of these areas are currently dominated by oxides. Secondly, both single oxides and multicomponent/multiphase formulations are important. Structure - processing - property relations in complex (and often nonequilibrium) "triaxial" formulations are important to understand in their own right and because many of the principles originally derived in this context are equally applicable to what are nominally single oxides. Lastly, the applications of oxide ceramics depend on an array of different properties: electrical
Table 2-1. US dollar volume of industrial ceramics (Based on data from the August 1991 issue of Ceramic Industry, Business News Publishing Co., Solon, OH). Types Glass Advanced ceramics Porcelain enamel Whitewares Refractories
Billion US dollars 56% 19% 10% 8% 7%
41.5 13.6 7.4 6.1 4.9
Table 2-2. Breakdown of crystalline ceramics US dollar volume (Based on data from the August 1991 issue of Ceramic Industry, Business News Publishing Co., Solon, OH). Billion US dollars
Types Advanced ceramics capacitors, electronic substrates and packages other electroceramics electrical porcelain engineering ceramics optical fibers other
48% 17% 12% 9% 9% 4%
6.5 2.3 1.6 1.2 1.2 0.6
Whitewares floor/wall tile sanitaryware dinnerware/fine china artware food service ware other
39% 33% 17% 5% 3% 3%
2.4 2.0 1.0 0.3 0.2 0.2
Refractories bricks and shapes bulk refractories insulating fibers other
63% 30% 3% 4%
3.0 1.4 0.1 0.2
Porcelain enamels appliances sanitaryware other
85% 12% 3%
6.3 0.9 0.2
properties (either as passive components, e.g. alumina substrates and electrical porcelains, or as active components, e.g. zinc oxide - a semiconducting oxide used in the fabrication of varistors); thermal properties (ceramic fiber insulation and refractories); corrosion resistance (refractories, whitewares); mechanical properties (structural ceramics such as zirconia toughened oxides, and structural clay products); optical properties (hard porcelain and electro-optical ceramics, such as LiNbO 3 , PLZTs); and magnetic (both permanent and electromagnets from ferrites). Although it has been popular to distin-
2.2 Silicate Ceramics
guish between "traditional" and "advanced" ceramics, it is evident from the above list that the properties which are available and the nature of the structureproperty relations do not observe such an arbitrary classification scheme and it is not attempted here. This chapter presents structure-properties relationships in silicate ceramics as a class, then separate sections are devoted to magnesia, alumina, and zirconia. The effect of both crystal structure and microstructure on properties is discussed.
2,2 Silicate Ceramics Silicate ceramics are often classified as "clay-based" ceramics. This is misleading since it is uncommon for an industrial ceramic to be simply fired clay and often these formulations do not contain clay, but minerals which are closely related to, but distinct from, clays. The system is rendered more ambiguous by the fact that the term "clay" can refer either to a rock (i.e., a collection of minerals) or a specific mineral. A more formal description of this commercially important class of ceramics is "triaxial formulations". The three main ingredients in a triaxial formulation may be written: a phyllosilicate; a flux; and a filler. Frequently, this is written: clay, feldspar and flint (quartz) as formulations based on these constituents are the most common. In addition to the three main ingredients, a number of minor ingredients are often included. These may be fugitive phases such as organic binders or minor amounts of additional inorganics. A well designed ceramic "body" has to satisfy fairly restrictive criteria at three separate stages of manufacture. Rheology of
51
particulate systems is the key to a successful forming step, mass transport is central to densification and physical properties (such as thermal expansion) determine whether or not the fired ceramic is amenable to post-densification processing. The principles which govern such "body design" are related to both crystal structure and microstructure. This is true for both the green ceramic and the fired material. 2.2.1 Phyllosilicates The phyllosilicates are a class of minerals (Klein and Hurlbut, 1985). The name, derived from the Greek word phyllon, meaning leaf, refers to characteristic properties of natural mineral deposits which are a direct consequence of the fact that all of the crystal structures in this class are based on combinations of sheets of Si 2 O 5 and either gibbsite, A1(OH)3, or brucite, Mg(OH) 2 , type sheets. Of the six major classes or clay minerals, five fall into the classification of phyllosilicates. These are kaolinite, smectite, illite, chlorite, and vermiculite. The last major class, sepiolite (or equivalently attapulgite or meerschaum), is classified as a lath-form structure (Grim, 1962). The study of the structure and properties of phyllosilicates has a long history, but remains an active field of research, though perhaps more so by mineralogists than ceramists. The information presented in Sees. 2.2.1-2.2.3 summarizes material available in a number of excellent textbooks (Brownell, 1976; Grim, 1962; Grimshaw, 1971; Klein and Hurlbut, 1985; McColm, 1983; Norton, 1976; Singer and Singer, 1963; Van Olphen, 1977; Worrell, 1986), specific citations are given for material which is difficult to locate or outside the scope of these references.
52
2 Oxide Ceramics
2.2.1.1 Crystal Structure
In considering the structure of these materials it is convenient to analyze the arrangement of so-called coordination polyhedra. Such a polyhedron is defined as a regular arrangement of anions, either oxygens or hydroxyls, which encloses a site that may or may not be occupied by a cation. The two most important polyhedra are the tetrahedron, typically occupied by a silicon ion, and the octahedron, typically occupied by either aluminum or magnesium. Both of these basic polyhedra can be defined as subunits of layers comprised of two sheets based on a hexagonally close packed net, see Fig. 2-1 a. In considering the stacking of such nets it is conventional to define three types of sites termed A, B and C. The A sites are defined by the atoms in the first layer and are arbitrary. A second complete hexagonal net could be placed in either of two equivalent, but distinct positions termed B or C, see Fig.
2-1 b. As evident in this figure, for an A-B stack there are tetrahedral sites midway between the plane of A atoms and B atoms which are directly beneath each of the atoms in the B sites. In addition, octahedral sites, in the same plane as the tetrahedral sites, are located under each of the C sites. Both the tetrahedral and octahedral sites are depicted in Figs. 2-1 c and 2-1 d. It is only the octahedra which are occupied in the brucite or gibbsite layers and therefore these are generally termed octahedral layers, regardless of the nature of the cation(s) present within the interstices. One of the characteristics of these materials is that chemical bonds, mixed ionic/ covalent, only occur within the two-dimensional sheets. This results from the fact that the anions in the simple hydroxides are all hydroxyls, OH~, which have a valence of negative one. Within an infinite two-sheet layer all of the anions are shared by three octahedra, see Fig. 2-2, and since there are six anions associated with each octahedron (recall that an octahedron has eight faces,
QQQUO ,CXX_XJ ZJ
c)
Figure 2-1. (a) Hexagonally close packed network of hard sphere atoms, (b) Identification of the A-, B- and C-type sites. The A-type sites are represented by crosses and lie in the plane which contains the centers of the atoms. The B-type are indicated by squares (triangular sites pointing to top of page) and the C-type by diamonds; both lie in a plane parallel to that containing the A-type sites but vertically displaced by a distance of ^ 2 / 3 times the center-to-center distance of the atoms, (c) Population of the B-type sites (or equivalently the C-type sites) by a second layer of atoms to form tetrahedral and octahedral interstices. The tetrahedral interstice is located directly underneath a B-type site and the octahedral interstice is located under the C-type site, (d) Tetrahedral and octahedral coordination polyhedra.
2.2 Silicate Ceramics
Shared Vertex
Figure 2-2. Illustration of an octahedral sheet drawn using coordination polyhedra illustrating that the corner of each polyhedron (which is occupied by an oxygen atom) is shared between three octahedra.
but only six vertices) the anions associated with each octahedron will accept an average of two valence electrons. In brucite all of the octahedra are occupied by divalent ions, Mg 2 + , whereas in gibbsite only two of every three octahedra are occupied by the trivalent Al3 + . Thus in both cases three octahedra contain cations capable of supplying a total of six valence electrons; or an average of two per octahedron. This pattern of occupancy has led to structures involving brucite type layers to be referred to as trioctahedral and those involving gibbsite as dioctahedral. Bonding in the third dimension, between the layers, involves only secondary, or physical, bonding. In all of the phyllosilicates, silicate layers are attached to the brucite or gibbsite layers. The basic unit in the Si 2 O 5 layer is the SiO 4 tetrahedron, arranged in a two-dimensional infinite layer. The tetrahedra are connected within this layer to form hexagonal rings in which one face on each tetrahedron lies in a common plane. The arrangement of the tetrahedra may also be described in terms of the stacking of hexagonal nets. In this case the base net is perforated, i.e., one-sixth of the oxygens are re-
53
moved from the net, but the oxygens that remain retain the hexagonal packing arrangement, i.e. they all reside in A sites (see Fig. 2-3). The second sheet is constructed by placing oxygens on each of the triangles present in the first as illustrated in Figs. 2-4 a and 2-4 b. This results in one-half of the oxygens sitting in B sites and one-half sitting in C sites, as illustrated in Fig. 2-4 a. Assuming ideal packing and hard sphere atoms, the distance between the apical oxygens is 2/^/3 times the oxygen-oxygen distance in the base sheet. Since the oxygens at the base of the tetrahedra are shared between two tetrahedra, each tetrahedron is associated with 1 silicon and 2.5 oxygen ions so that the chemical formula for these layers is Si 2 O 5 which has a net valence of negative two. For obvious reasons, these are known as tetrahedral layers. (In contrast to the "octahedral" layer which contains both octahedral and tetrahedral sites, the tetrahedral layer contains only tetrahedral sites.) The phyllosilicates can be conceptualized in terms of joining tetrahedral and octahedral layers. The process of joining
Figure 2-3. Schematic illustration of the "perforated" hexagonally closed packed net that makes up the base of the tetrahedral sheet with A-, B-, and C-type sites illustrated using the same notation as in Fig. 2-1.
54
2 Oxide Ceramics Dioctahedral
Figure 2-4. Completion of the tetrahedral layer through a population of both B-type and C-type sites to form a hexagonal array of tetrahedral interstices.
these layers may be thought of as bringing together the tetrahedral and octahedral layers and replacing hexagonal rings of hydroxyls on the surface of the octahedra with apical oxygens from the tetrahedra (the anion-anion distance in the tetrahedral layer is slightly larger than in the octahedral sheet so that the hexagonal rings mesh with small strains which become important in determining particle shapes). The net effect is that two-thirds of the hydroxyls are replaced on the surface to which the tetrahedral layer is attached. Figure 2-5 illustrates the two families of phyllosilicates using schematic projections of idealized crystal structures. Kaolinite and antigorite are so-called 1:1 structures involving an asymmetric arrangement of
Figure 2-5. Schematic illustration of the two families of phyllosilicates made up by stacking the tetrahedral and octahedral sheets (after Klein and Hurlbut, 1985).
one tetrahedral (silicate) and one octahedral layer (gibbsite for the former and brucite for the latter). Pyrophyllite and talc are 2:1 structures which are symmetric assemblies of two tetrahedral layers attached to opposite faces of a single octahedral sheet. It is convenient to write the chemical formulae for these minerals to reflect the structure. Gibbsite may be written A12(OH)6. Using this as a reference and comparing to kaolinite written as Al2(Si2O5)(OH)4 immediately indicates
2.2 Silicate Ceramics
that one silicate layer is present and that one third of the hydroxyls have been replaced by the apical oxygens from the silicate layer. Further when pyrophyllite is written Al2(Si2O5)2(OH)2 it is evident that two silicate layers are involved and that two-thirds of the hydroxyls have been replaced. Analogous formulae may be written for antigorite and talc; Mg3(Si2O5)(OH)4 and Mg 3 (Si 2 O 5 ) 2 (OH) 2 . Micas differ qualitatively from the preceding structures. In these materials, some of the aluminum is present in both octahedral and tetrahedral sites. This is often described as aluminum substituting for silicon in the tetrahedral layer. In alkaline micas, one quarter of the tetrahedral sites are occupied by aluminum whereas in alkaline earth micas, one half of the tetrahedral sites are substituted. This substitution of the trivalent aluminum for the tetravalent silicon leaves each layer with a net charge that is compensated by the presence of cations between the layers as illustrated in Fig. 2-5. Thus, in micas there is an ionic component to bonding between sheets. The formula for muscovite may be written KA12(A1O 5 Si 15 O 5 ) 2 (OH) 2 indicating the relative proportion of aluminum in each type of site: (the Al outside the parentheses is located in the normal octahedral site, whereas the Al within the parentheses is located in a tetrahedral site) and that the interlayer cation is potassium. The trioctahedral equivalent is phlogopite KMg 3 (Al 0 . 5 Si 1 . 5 O 5 ) 2 (OH) 2 . In this material the octahedral sites are occupied by magnesium ions and all of the aluminum is in tetrahedral coordination. The calcerous micas margarite and xanthophyllite, CaAl2(AlSiO5)2(OH)2 and CaAl2(AlSiO5)2(OH)2 respectively, are often termed brittle micas because the strength of the ionic bonds between sheets is sufficient to prevent easy cleavage.
55
Other mineral classes important to ceramics can be derived from substitution into the 2:1 structures. The smectites result from a partial substitution in either or both the tetrahedral and octahedral layers. The most abundant smectite, montmorillonite, is characterized by a small degree of substitution in the octahedral sheet by a divalent species such as Mg or Fe (and possibly some smaller degree of substitution in the tetrahedral layer). As in the case of micas, this produces sheets with a net charge and this charge is also accommodated by interlayer cations, but with a difference. In micas the interlayer separation is independent of the environment and the nature of the compensating ions is fixed whereas the interlayer separation in montmorillonites is strongly influenced by the environment, in particular the presence of water or other polar molecules, and in some circumstances the interlayer cations may be readily exchanged. This is not true of micas. Illites are also based on substitutions into the pyrophyllite structure and are often referred to as hydrous micas. These materials involve substitution of aluminum into the tetrahedral layer, but the degree of substitution is small compared to micas. As a result, these minerals generally contain less alkali or alkaline earth ions and more combined water than the corresponding mica. Chlorites are trioctahedral phyllosilicates again consisting of substituted layers, but with a distinct mechanism for maintaining electroneutrality. Chlorites are mixed-layer materials containing both brucite and talc layers. Both layers are aluminum substituted. In the talc layers aluminum is substituted into one-quarter of the tetrahedral sites producing a net negative charge. Within the brucite layer aluminum substitutes for one-third of the magnesium in octahedral sites. The chlor-
56
2 Oxide Ceramics
ite structure is made up by alternating substituted talc and brucite layers. Vermiculites are often described by analogy to chlorites and montmorillonites. They consist of similar aluminum substituted talc layers, but charge compensation occurs via hydrated magnesium interlayer ions rather than substituted brucite sheets. 2.2.1.2 Mineral Sources
The production of phyllosilicates in general, and clays in particular, is part of a geochemical cycle which involves both subtractive and additive processes (Millot, 1978; Velde, 1985). The cycle is illustrated in Fig. 2-6, and may be broken down into five stages: 1) rocks are continually brought to the earth's surface as a result of
3. Transport, Sedimentation
Figure 2-6. The geological cycle which produces clay minerals consists of five stages: (1) rocks are brought to the surface through the tectonic processes; (2) rocks are broken down both mechanically and chemically to form clay minerals (residual china clays or kaolins are mined from this condition); (3) some fragments are transported through the action of wind and water (forming deposits of ball clays); (4) clay minerals are deposited and begin to undergo diagenesis (forming flint fireclays); (5) metamorphic changes occur to complete the cycle (after Millot, 1978).
folding, faulting, and volcanic eruption; 2) the minerals in the rocks are altered at or near the surface due to weathering; 3) some fraction of these minerals are transported by the action of, for example, wind or water; 4) these minerals are eventually deposited, buried and; 5) are gradually transformed into sedimentary then metamorphic rocks to complete the cycle. Although the time scale associated with this geological cycle is rather long compared to the life span of any living creature, understanding it, principally stages 2, 3, and 4, helps to explain the characteristics of the clays which are mined and exploited in the ceramic industry. One fortunate consequence of this cycle in that the phyllosilicates are typically located near to the surface of the earth where they are readily mined. The parent rocks which are brought to the surface are typically granite (a mixture of feldspar, mica and quartz) and basalt (principally hornblende, pyroxene and olivine). Weathering acts to alter these materials both mechanically and chemically. The mechanical alteration is fragmentation to produce a very fine particulate which presents a large specific surface area to the environment. The chief chemical effect is to leach cations from the minerals and in effect to progress from the bottom of Fig. 2-6 towards the top. The hydrolysis is generally accepted to replace cations in the following order: Na, K, Ca, Mg, Fe, Si and Al. The terminus of such leaching, which is most likely to be achieved in hot wet environments, is bauxite; a mixture of aluminum hydrates with some siliceous and ferrous contamination. The kaolinization of a feldspar (the latter is discussed more fully in Sec. 2.2.2) is often provided as an example. The overall chemical reaction may be written in terms of orthoclase, KAlSi 3 O 8 , reacting with water
2.2 Silicate Ceramics
and carbon dioxide, i.e. 2KAlSi 3 O 8 CO 2 2H 2 O -+ Al2(Si2O5)(OH)4 + 4SiO 2 + K 2 CO 3 . In reality (Keller, 1982), kaolinite originates via a variety of weathering processes acting on a variety of parent materials. Robertson and Eggleton (1991) employed high resolution transmission electron microscopy to analyze the formation of kaolinite and halloysite in partially and completely weathered soil samples. Evidence was presented for the topotactic conversion of muscovite to kaolinite. Figure 2-7 indicates the conversion of one layer of the mica by proton exchange 10 to 20 nm ahead of the stripping off of one silicate layer to convert the 2:1 phyllosilicate to 1:1. One implication of such a mechanism is that accessory minerals, such as mica, are likely to be intimately mixed with, and therefore difficult to separate from, the clay. Other phyllosilicates are believed to form as a result of similar processes. A brief outline of some parent materials and weathering products is given in Table 2-3.
57
The term clay (as opposed to clay mineral) refers to a rock (i.e., a consolidated or unconsolidated solid mineral matter) and is defined as "... a group of natural mineral aggregates consisting essentially of hydrous aluminum silicates which become plastic when sufficiently wetted, rigid when dried en masse, and vitrified (made glasslike) when heated to a sufficiently high temperature" (O'Bannon, 1984). The constituents of the clay and its properties depend on its age in the geological cycle. For example, there are a variety of clays based on the kaolinite mineral. China clay (or kaolin) is a residual clay formed by the weathering of granite. The term residual refers to the fact that the clay resides in the same physical location as the parent material and therefore lies at step 2 in the geochemical cycle. This clay is typically the result of hypogenic weathering processes and is therefore often found in deep deposits which contain a number of accessory minerals, such as quartz as well as unconverted feldspar and mica. The kaolinite mineral itself is typically of rather high purity and therefore gives a white fir-
®- interlayer cation H= proton
Figure 2-7. Schematic illustrating the topotactic conversion of muscovite mica to kaolinite through leaching of the interlayer cation followed by stripping of one tetrahedral layer as proposed by Robertson and Eggleton (1991).
58
2 Oxide Ceramics
Table 2-3. The composition of igneous rocks and their breakdown products (Worrall, 1986). Mineral
Approximate formula
Approximate % present Granite
Basalt
Probable decomposition products
Orthoclase
KAlSi3O8
70
10
Anorthite
CaAl2Si2O8
70
10
SiO2
25
—
Unchanged
(Na,K) 2 (Fe ,Mg) (Fe 3 + ,Al) 4 Al 2 Si 6 O 22 (OH) 2
—
90
Pyroxene
(Mg,Fe)SiO3
—
90
Olivine
(Mg,Fe)2SiO4
—
90
Kaolinite or montmorillonite, limonite, haematite, CaCO 3 , MgCO 3 , colloidal silica Colloidal silica, limonite, haematite, MgCO3 As for pyroxene
KAl 3 Si 3 O 10 (OH) 2 K(Mg,Fe)3Si3AlO10(OH)2
5 5
— —
Quartz Hornblende
Muscovite Biotite
2+
ing body. Separation of the kaolinite from the accessory minerals relies on the difference in particle size. The clay is often hydraulically mined, i.e., a water jet is used to extract the material from the ground, the suspension of minerals is simply allowed to stand undisturbed in ponds to allow the coarse accessory mineral to settle under the influence of gravity. The resultant clay is typically of high purity, but relatively coarse particle size (1-10 jim) for a clay. Ball clays, so named because they were originally mined by cutting out large blocks or balls, are secondary clays. They have been transported, usually by water, from the point of origin, i.e. they sit at stage 3 of the geochemical cycle. The act of transporting the clay serves to classify it by size; only the finest particles (<0.1 |im) are able to be swept large distances from the origi-
Kaolinite, colloidal silica, K 2 CO 3 Kaolinite, colloidal silica, CaCO 3
Probably unchanged Kaolinite or montmorillonite, iron oxides, colloidal silica, MgCO 3 , K 2 CO 3
nal source. This process also tends to classify any accessory minerals so that separation is more difficult than with residual clays since both the clay and the accessory minerals are of nearly the same size and density. (It is sometimes possible to use a magnetic field to remove some iron bearing minerals). Common accessory minerals are illites and micas which being 2:1 structures yield clays which have a higher silica to alumina ratio than china clays. One noted feature of these clays is that they contain a relatively high proportion of low rank organic material, primarily the result of deposition onto vegetation. Fireclays occur in stage 4 of the geochemical cycle and may be subdivided into plastic fireclays, shales, and flint fireclay. These categories are of roughly increasing age and degree of compaction. The clay
2.2 Silicate Ceramics
Kaolinite I."-; •'••:] Halloysite
Halloysite spiral
59
stacked with a 0.7 nm spacing. Upon hydration, the interspacing increases by 40% to 1.0 nm and it is believed that the concomitant weakening of the bonding between adjacent layers allows curling to occur. More refractory grades may also contain diaspore, AIO(OH) and thus offer a lower silica to alumina ratio than china clays. The organic matter associated with these clays usually is in the form of coal. Other phyllosilicates such as talc (also referred to as steatite), pyrophyllite and mica are also mined from natural deposits. 2.2.1.3 Characteristic Properties
Figure 2-8. Illustration of the formation of halloysite tubes due to hydrolysis of kaolinite as proposed by Robertson and Eggleton (1991).
mineral in many fireclays is halloysite rather than kaolinite. Halloysite has the same basic chemical formula as kaolinite, but is hydrated. Keller (1982) presented evidence suggesting that halloysite is formed by hydration of kaolinite. This is consistent with the fact that fireclays are located further into the geochemical clay cycle. The process involves the peeling of hydrated halloysite from a kaolinite plate and is schematically illustrated in Fig. 2-8. This mechanism leads directly to the tubeshaped particles characteristic of halloysite. The driving force for curling is the misfit strain associated between the silicate and gibbsite layers mentioned in Sec. 22.1 A. In kaolinite, curling is prevented by the presence of a large number of layers
Three types of properties will be considered here: particle (crystallite) size and shape; interaction with water; and transformation upon firing. Most of the gibbsite and brucite used in the ceramic industry is synthetic, resulting from either the Bayer process in the case of gibbsite or the sea-water magnesia process in the case of brucite. The particle size and size distribution may therefore be controlled in the precipitation step of these processes, as discussed in Sees. 2.3.2 and 2.4.2, and are not determined by natural processes. All phyllosilicates have weak interlayer bonding. This has a direct effect on the morphology and size of the crystallites which make up the mined aggregates. All tend to form flat platey particles of relatively high aspect ratio. In natural deposits crystallites are often agglomerated. Grinding and slaking (soaking in water) are processes used to reduce the size of the aggregates. Grinding is a straightforward process. It is, however, very inefficient and energy intensive (Shinohara, 1991). Furthermore, there is a lower limit to the particle size which can be obtained by grinding (Kendall, 1978).
60
2 Oxide Ceramics
Talc and pyrophyllite are both characterized by being soft unctuous (having a greasy feel) materials. This is a straightforward manifestation of the symmetric, and therefore nonpolar, layer structure. Successive layers are only held together with van der Waals bonds which are easily disrupted. These materials are easily mined and ground to relatively fine particle sizes. The 1:1 clay minerals are polar and therefore have stronger interlayer bonds. They are often found as well crystallized particles on the order of tens of microns in diameter. As a result of classification the kaolinite particles found in ball clays are considerably finer. Figure 2-9 compares the particle size distribution of a residual china clay and a ball clay. Depending on the age of the clay and the degree of compaction it will be more or less susceptible to "slaking" (Keller, 1982). Free slaking clays spontaneously disintegrate in water to yield particles on the order of the crystallite size; china clays and ball clays are examples. Clays which are resistant to slaking must be ground to reduce the aggregate size to the desired level, flint fire clays are typical of this class.
0.05 0.1
0.5
1
5
10
Particle Diameter 4(//m)
Figure 2-9. Typical particle size distributions for (a) ball clay and (b) china clay or kaolin. The finer average particle size of the ball clay is the result of natural particle size classification during transport (after Dinsdale, 1986).
Illites are very finely divided in the natural state with average particle sizes on the order of 0.05 jim, similar to the kaolinite in ball clays. The most finely divided natural clays are the smectites; thin platey crystals which, when in aqueous suspension, may be one formula unit thick and 0.01 to 2.0 jim in diameter. Vermiculites and chlorites are platey mica-like particles which may be readily observed under the optical microscope. Micas occur naturally in two forms: sheet mica (on the order of 10 cm in diameter) or flake mica. The former may be stamped or punched and used in its natural form whereas the latter is typically ground to yield a desired particle size distribution. The interaction with water is one of the unique features of clay minerals. Ceramic forming operations depend on the development of plasticity, the ability to be deformed without fracture, upon the addition of water. The degree of plasticity is a complicated function of the average particle size, the shape of the particle size distribution as well as the nature of the interparticle forces. In general, the minerals mica, talc, pyrophyllite, vermiculite and chlorite do not develop substantial plasticity through the addition of water alone. A wide range of plasticity is observed for kaolinitic clays; coarse china clays are often dilatant whereas fine grained ball clays may be highly plastic. The plasticity of ball clays arises from the combination of small particle size and the presence of an appreciable quantity of low rank organic material. The smectite clays exhibit the highest degree of plasticity. This is ascribed to the fact that the interlayer bonding in these minerals is weak allowing spontaneous division into extremely thin platelets. The plasticity of smectites is also augmented by the fact that the interlayer cations are "exchangable". When smectites are in contact with water the water
2.2 Silicate Ceramics
molecules penetrate in between the layers giving rise to a large, two fold, increase in the interlayer spacing. In the swollen condition, the cations which are adsorbed onto the surface of the tetrahedral sheets are accessible. It is possible, using salt solutions, to change the type of compensating ion. For example, a sodium montmorillonite, written Na0.33(Mg0.33Al1>67)(Si2O5)2(OH)2, can be converted to a calcium montmorillonite, Ca 0 . 17 (Mg 0 . 33 Al 1 . 67 )(Si 2 O 5 ) 2 (OH) 2 , through room temperature ion exchange in solution. The plasticity of the smectites is strongly affected by such exchange with sodium yielding a much higher degree of plasticity. Neither pyrophyllite (on which the smectites are based) nor the dioctahedral analogues talc and vermiculite exhibit swelling. A complete explanation for this difference is lacking (Van Olphen, 1977), but, as an aside, it is noted that the properties of the montmorillonites determined by crystal structure offer unique flexibility in processing. Sugahara et al. (1984,1988) developed processing schemes for P-SiAlON and aluminum silicon carbide using montmorillonite clay. The montmorillonite was first treated with a hexylammonium hydrochloride solution to exchange the interlayer alkali ions with hexylammonium which burn out during firing. After washing and drying, it was immersed in acrylonitrile monomer and allowed to stand for sufficient time to allow the monomer to penetrate between the layers after which polymerization was induced. The result was an extremely homogeneous distribution of a carbon source (polyacrylonitrile or PAN). Heating in a nitrogen bearing atmosphere caused carbothermic reduction of the silicate layer to form silicon nitride which interdiffused with the gibbsite layer to produce SiAlON. The ability to form an intimate mixture, an intercala-
61
tion compound, of the reactants leads to a significantly more efficient conversion than mechanical mixtures of carbon black and clay. More recently, Seron et al. (1992) have shown that the efficiency of carbon retention is increased if acriflavine ammonium cations are used. This is a direct result of ionic bonds which form between the Cl 3 N 3 Hi 3 f ions and the substituted sheets in the montmorillonite. Montmorillonite clays are also widely used as suspension aids, for example in ceramic glazes. Although a very different application from that discussed in the preceding paragraph, it is also based on the tendency of the clay to spontaneously dissociate when suspended in water. In this case, the colloidal nature of the montmorillonite produces a situation known as "hindered settling" which retards the settling rate of the coarser particles. The effect of heat on the phyllosilicates is also intimately dependent on the details of the structure. The first process which occurs during heating is the removal of physically bound water followed by dehydroxylation, or the removal of chemically bound water. In the case of halloysite the dehydration occurs around 50 °C. Dehydration results in a collapse of the interlayer spacing (from 1.0 nm to 0.7 nm) and a significant change in the degree of plasticity. Since it occurs at such a low temperature, the degree of hydration often changes during transport or storage. From an engineering point of view the material is therefore subject to uncontrolled variations which is a disadvantage. Similarly, heating vermiculites causes the dehydration of the interlayer magnesium ions, but at a higher temperature, 110°C. If heated rapidly the explosive conversion of the interlayer water to steam results in exfoliation, or separation of individual layers, yielding a volume expansion up to 100 times. Such
62
2 Oxide Ceramics
behavior is exploited in, for example, the manufacture of thermal insulating refractories. At higher temperatures, the structure of the phyllosilicates breaks down. In the case of the dioctahedral materials mullite, Al 6 Si 2 O 13 , is usually one of the decomposition products whereas enstatite, MgSiO 3 , is usually formed from trioctahedral materials. In both cases decomposition usually involves the rejection of silica. The processes occurring upon firing kaolinite clay have been the subject of extensive investigation ever since the work of LeChatelier (1887). However, it was not until the work of Brindley and Nakahira (1957,1959) that the reaction sequence was essentially understood. Recently, Brown etal. (1985) and MacKenzie et al. (1985) have characterized the details of the threestage reaction sequence outlined below. The combined water in the clay is driven off at about 500 °C (dehydroxylation) and metakaolin is formed. Stage I Al 2 Si 2 O 5 (OH) 4 kaolinite 500 °C
metakaolin + 2H 2 O
Stage II metakaolin 970
°c
3A1 2 O 3
Al 6 Si 2 O 1 3
3SiO 2
defect spinel
alumina-rich mullite
glass
Stage III defect spinel -f silica glass 1125°C 2Al 6 Si 2 O 13 + SiO2 mullite
cristobalite
The metakaolin structure is essentially glassy consisting of anhydrous regions of distorted Al-O tetrahedra containing about 12% randomly-distributed, isolated, residual hydroxyls associated with A l - O
configurations of regular octahedral and tetrahedral symmetry. Decomposition of the metakaolin by removal of the final residual hydroxyl radicals at 970 °C triggers the separation of amorphous free silica and formation of both poorly crystalline mullite and a phase with a cubic, defective spinel, crystal structure similar to y-Al 2 O 3 . The mullite and spinel form in tandem, the former originating in the vicinity of Al-O units of regular symmetry. There is some disagreement as to whether the spinel phase formed is actually y-Al 2 O 3 or a defective spinel containing A12O3 and SiO 2 . The nuclear magnetic resonance studies of MacKenzie et al. (1985) suggest the former while the transmission electron microscopy study of Srikrishna etal. (1990) suggest the spinel has a 3Al 2 O 3 -2SiO 2 mullite composition. The spinel crystallites are about 10-50 nm diameter at 1020°C. Initially the mullite forms as alumina-rich but at higher temperatures it gains silica to approach the 3 A12O3 • 2SiO 2 composition. On further heating above 1125°C, the spinel phase is converted to mullite by reaction with some of the amorphous silica, the balance of which eventually becomes cristobalite (discussed in Sec. 2.2.3.1) if held at high temperature for sufficient time. The end products of firing the mineral kaolinite are mullite and silica. Natural clays often have impurities which yield a mixture of mullite crystals and a multicomponent siliceous glass. The temperature at which natural clays are fired depends closely on its alumina and flux content. Higher firing temperatures are required for clays with greater alumina and less flux. The decomposition of pyrophyllite also has a long history and is the subject of recent investigations (MacKenzie et al.,
2.2 Silicate Ceramics
63
1986). This material also undergoes a series of reactions upon heating ultimately forming mullite and cristobalite. The ratio of cristobalite to mullite is higher for pyrophyllite since it is a 2:1 structure. Although cristobalite forms during the decomposition of phase pure kaolinite or pyrophyllite, the final form of the liberated silica in a triaxial formulation is influenced by the presence of alkali and alkaline earths as is discussed in Sec. 2.2.2. Although they are unambiguously phyllosilicates, micas which contain relatively high concentrations of alkali ions are better classified as fluxes in the context of industrial ceramic manufacture. 2.2.2 Fluxes A flux is defined as "any substance which promotes the fusion and flow of a ceramic or glass mixture when subjected to heat" (O'Bannon, 1984). For silicate ceramics, fluxes are generally compounds which contain alkali or alkaline earth elements (although anionic fluxes such as fluorine are used in some applications). Fluxes are often described as breaking up the network structure of a glass. The classic (and highly schematic) illustrations of the effect of fluxes on the structure of silicate glasses are presented in Fig. 2-10. Figure 2-10 a and b represent the structural difference between a crystal and glass of the same composition. In the glass structure the coordination polyhedra are preserved (i.e., short range order is preserved), but the connectivity between the tetrahedra becomes randomized. The effect of fluxes on the structure of the glass is illustrated in Fig. 2-10c. The addition of the flux, for example Na 2 O, produces what are termed nonbridging oxygens decreasing the degree of connectivity of the structure (analogous to decreasing the molecular
Figure 2-10. Schematic illustration of (a) a crystal and (b) the corresponding glass. Although the long range order is lost in the structure of the glass the local order (i.e. tetrahedra) and the connectivity (two tetrahedra per vertex) are preserved. The addition of a flux decreases the connectivity of the structure as shown in (c).
weight of a polymer melt). The most commonly employed fluxes contain alkali; alkaline earth elements are less commonly used. The most widely employed mineral sources of fluxing elements are feldspars and feldspathoids. The general chemical formula for feldspars (Griffen, 1992) may be written MT 4 O 8 where M is either sodium, potassium, or calcium (less commonly, barium
64
2 Oxide Ceramics
and ammonium) and T represents either aluminum or silicon. The significance of the symbol T is that both the aluminum and the silicon are in tetrahedral coordination within the crystal structures of these minerals. As in the case of micas, aluminum in tetrahedral coordination must be charge compensated. In the case of the sodium and potassium feldspars compensation is available for one aluminum per formula unit, NaAlSi 3 O 8 and KAlSi 3 O 8 respectively, whereas calcium provides compensation for two aluminums per unit cell, CaAl 2 Si 2 O 8 . All of these minerals can exist in more than one polymorph. In the case of the albite, NaAlSi 3 O 8 , and anorthite, CaAl 2 Si 2 O 8 , these are simply distinguished by the modifier low- or high-. However, potash feldspar, KAlSi 3 O 8 , is referred to either as orthoclase or microcline depending on the structure. Although microcline is the stable phase at room temperature and is the most commonly occurring mineral, the term orthoclase is more frequently encountered in the ceramics literature. An alternate flux somewhat higher in sodium and potassium is the mineral nepheline, sometimes reported as Na 2 Al 2 Si 2 O 8 and alternately as (Na 3 K)Al 4 Si 4 O 16 . Lithium is also used as a flux. Due to its relatively high cost, it finds application only where it offers unique properties. When substituted for sodium or potassium, lithium increases the elastic modulus, increases the surface tension, and increases the hardness (Taylor and Bull, 1986; De Guire and Brown, 1984) of a silicate glass. Many lithium chemicals, such as lithium chloride or carbonate are highly processed, but the principal mineral sources of lithium are spodumene and petalite. Spodumene, LiAlSi 2 O 4 , is somewhat richer in lithium than petalite, LiAlSi 4 O 6 .
2.2.2.1 Crystal Structure During the early stages of processing fluxing agents are generally molten and on cooling often form a glass. Therefore, the crystal structure of the flux is not directly related to the properties of the final ceramic, unless the glass is intentionally crystallized during the final stages of processing. The distinguishing characteristic of the feldspar structure is the existence of four membered rings of tetrahedra (Griffen, 1992). The minerals nepheline and petalite are tectosilicates, i.e., they have a crystal structure based on the silica polymorph tridymite (the tridymite structure is discussed in Sec. 2.2.3.1). Spodumene is classified as pyroxene, which is a chain silicate. In chain silicates SiO4 tetrahedra are linked, i.e., share corners, in only one direction, in contrast to the two dimensional linking in sheet silicates. 2.2.2.2 Mineral Sources
Feldspars rarely occur in nature as pure minerals. Since albite and anorthite form a complete solid solution series, they occur in nature as alloys. Even though orthoclase and albite form only limited solid solutions, deposits of orthoclase always contain some albite. The rock nepheline syenite is a mixture of orthoclase, albite, and nepheline with minor impurities. Typical compositions of mined materials (somewhat arbitrarily termed soda and potash feldspars) are compared to mineral compositions in Table 2-4. These materials are typically ground to a relatively coarse powder, on the order of 70 to 100 jam, for use in ceramic (or glass) manufacture.
65
2.2 Silicate Ceramics
Table 2-4. Chemical composition of fluxes (Dinsdale, 1986). Oxide (%)
Minerals
Raw materials
Feldspars Orthoclase K2O Na 2 O A12O3 SiO2 K 2 O + Na 2 O
Albite
Nepheline
11.82 19.44 78.74 11.82
21.81 35.89 42.30 21.81
16.92 18.31 64.76 16.92
2.2.2.3 Characteristic Properties
The tendency to form a glass is strongly correlated to the viscosity of a melt. In general, molten feldspars are rather viscous which is ascribed to the existence of polymerized silicon-aluminum-oxygen tetrahedra in the liquid (Barth, 1969). Despite lower melting points, the alkali feldspars produce much more viscous liquids than anorthite. In the case of albite this is inter-
Potash feldspar
Soda feldspar
Cornish stone
Nephelinesyenite
11.9 2.8 19.0 65.8 14.7
2.2 8.0 19.9 67.2 10.2
4.6 3.7 12.0 76.0 8.3
9.8 7.4 24.0 57.0 17.2
preted as evidence for a higher degree of polymerization in the melt. In the case of orthoclase it is due to the formation of leucite, KAlSi 2 O 6 , crystals. In all cases glasses are produced under the cooling rates normally encountered in ceramic processing. As indicated in the phase diagram, Fig. 2-11, albite melts at the lower temperature than orthoclase, but the addition of anorthite increases the melting temperature of
CaAI 2 Si 2 O 8 (lime feldspar)
1348 ± 5°
NaAISi 3 O 8 (soda feldspar)
1078 ± 3°
KAISi 3 O 8 (potash feldspar)
Figure 2-11. Pseud oternary phase diagram of the feldspars anorthitealbite-orthoclase.
66
2 Oxide Ceramics
soda feldspar while decreasing that of the potash feldspar (down to a minimum at about 22% anorthite). Similarly a 50%: 50% mixture of albite and orthoclase melts at a lower temperature than either end member. Often mixtures of fluxes are employed in order to take advantage of eutectic melting. Lithium bearing minerals are often very effective fluxes when used in conjunction with feldspar since such combinations form deep eutectics.
a)
2.2.3 Fillers
Most fillers used in silicate ceramics do not undergo irreversible changes during processing. As a result, the fillers may be accurately regarded as the dispersed phase in an engineering composite. The properties of the resultant ceramic, therefore, are strongly influenced by the properties and relative volume fraction of the filler. The most commonly employed filler is silica (either as quartz or cristobalite), but other materials which are used as fillers include alumina, mullite (often in the form of calcined clay-alumina mixtures), wollastonite, and zircon. 2.2.3.1 Crystal Structure
From a naive point of view silica, SiO 2 , is the simplest of the silicates. It is, however, a remarkably complex material. There are six acknowledged equilibrium polymorphs of silica depending on temperature and pressure. In silicate ceramics, the crystalline forms of interest are quartz, tridymite, and cristobalite. In addition to equilibrium structures there are metastable modifications of each of these three. Further, vitreous (or fused) silica glass has properties which differ significantly from crystalline silica.
b) Figure 2-12. (a) The perforated hexagonal net of tetrahedra that may be stacked to make the tridymite and cristobalite crystal structures in which the apices of alternate tetrahedra point in opposite directions, (b) The B-type layer which may be alternately stacked on the A-type layer, shown in (a), to represent the high temperature polymorph of tridymite. Note that a Btype layer in this structure may be obtained by a simple translation of the A-type layer.
Although they are framework silicates (ionic/covalent bonding in all three dimensions), both the tridymite and cristobalite structures can be built from hexagonal nets of tetrahedra. However, in contrast to the phyllosilicates, the apical oxygens of adjacent tetrahedra point in opposite directions as illustrated in Fig. 2-12 a. The two structures differ in a manner analogous to f.c.c. and h.c.p. metals. Figure 2-12 illustrates the A-B stacking sequence of SiO 4 tetrahedra which leads to tridymite and Fig. 2-13 shows the latter two steps in the A - B - C stacking sequence corresponding
2.2 Silicate Ceramics
7 X
7
b) Figure 2-13. The stacking sequence of hexagonal nets of tetrahedra leading to the high temperature polymorph of cristobalite. (a) A two layer stack of A- and B-type layers. Note in this structure that a 180° rotation is required in addition to a translation to obtain a B-type layer from an A-type. (b) A three layer stack of A-, B-, and C-type layers which contains the unit cell for cristobalite and onto which another A-type layer could be joined.
67
to cristobalite. In both illustrations, the addition of another layer leads to a repetition of the original layer. The quartz structure is markedly different from tridymite or cristobalite. Rather than being described in terms of the stacking of sheets, quartz is described (Griffen, 1992) in terms of a double helixes of tetrahedra as illustrated in Fig. 2-14. Each of these phases is stable over a defined temperature range at atmospheric pressure. In addition to the structures illustrated in Figs. 2-12, 2-13 and 2-14, there are lower symmetry derivative structures which may be viewed as distortions of the high temperature phases. Thus the commonly cited polymorphs of silica are: oc- and (3-quartz; high, middle, and low tridymite; and high and low cristobalite. Polymorphic transitions become an important consideration during thermal processing of a ceramic containing silica. A summary of the transitions between polymorphs in silica is presented in Fig. 2-15. The crystal structures of wollastonite, CaSiO 3 , fosterite, Mg 2 SiO 4 , and zircon, ZrSiO 4 , are complicated. In all cases, the silicon is in tetrahedral coordination. In wollastonite, the tetrahedra are linked in infinite one dimensional chains which are
Figure 2-14. The structure of quartz, which may be viewed in terms of double helices of tetrahedra. In this figure the projection is on a plane perpendicular to the axis of the helix and the orientation of the tetrahedra is such that they project onto this plane as squares.
2 Oxide Ceramics
68
Polymorphic Forms of Crystalline Silica at Normal Pressures High quartz
Reconstructive \ N 867°c
Reconstructive u. . nign tridymite ^ 1 4 7 0 o C
Displacive
160°C Displacive 573°C
u'nh cristobalite
|h
vll Middle tridymite
Displacive 200-270°C
Displacive I h 105°C vll
Low quartz
Low tridymite
Low cristobalite
linked together by calcium ions in irregular octahedral coordination (Klein and Hurlbut, 1985). In zircon the tetrahedra are all separated and share edges with a ZrO 8 triangular dodecahedron to form a 3-D connected structure (Griffen, 1992). The crystal structures of alumina and mullite are discussed in Chapter 1 of this Volume. 2.2.3.2 Mineral Sources
Silica is present in a number of forms (Worrall, 1986; Klein and Hurlbut, 1985). Quartz is the most common polymorph; sources include sand, sandstone, ganister, quartzite, and flint. Sands are a widely occurring and familiar material, commercial deposits are characterized by being of sufficient volume and high purity. Sandstone is a sedimentary rock which is easily ground to the crystallite size. Quartzite is a metamorphic rock derived from sandstone characterized by interlocking grains which result from solution and reprecipitation reactions. Ganister is a form of quartzite commonly located along coal seams and is typically contaminated with clay minerals. Flint is an accessory mineral found in chalk (CaCO3) deposits and is referred to
Figure 2-15. Summary of the polymorphic transformations of silica.
as a cryptocrystalline quartz (i.e., the individual crystals are too small to be resolved under an optical microscope). Both tridymite and cristobalite occur naturally, but are limited to volcanic extrusions. They are both common constituents in fired ceramics as a result of effectively irreversible reconstructive transformations. Diatomaceous earth (or diatomite) is an unusual form of silica. It is a sedimentary rock composed of the fossilized skeletons of the diatoms. The result is a highly siliceous mineral with very low bulk density and high specific surface area which is not abrasive. This material finds application in the fabrication of insulating refractories. Wollastonite is a metamorphic rock which has recently become an important mineral in ceramics. It is a soft mineral which is mined and may be crushed to reduce the particle size down to the crystallites which are acicular reflecting the chain silicate crystal structure (Klein and Hurlbut, 1985). Zircon is mined from mineral sand deposits throughout the world (Adams, 1989). Alumina is a synthetic material. The preparation of alumina is discussed further in Sec. 2.4.2.
2.2 Silicate Ceramics
2.2.3.3 Characteristic Properties
The overriding characteristic of silica fillers is their unique thermal strain. There are, in general, two distinct contributions to thermal strain, thermal expansion (as a result of the anharmonicity of the pair potential) and phase or polymorph changes. Both are dependent on the particular form of silica which is used. It is important to distinguish between reconstructive and displacive transformations. The former require bond breaking and a rearrangement of the connectivity between tetrahedra whereas the latter may be viewed as the result of bond bending leaving the topology unchanged. The transformations between the basic structures (quartz, tridymite, and cristobalite) are necessarily reconstructive. Therefore, they are relatively slow and thermally activated. Some conversion of quartz to cristobalite may occur during anneals at high temperature, but the reverse transformation will not occur simply because the kinetics of transformation are extremely slow in the temperature regime in which, say, quartz is thermodynamically stable. For whitewares the duration of firing is usually too short for reconstructive transformations to be significant, although this may not the case for silica refractories which are typically fired above 1400 °C. Significant conversion to tridymite and cristobalite may also occur during service at high temperature, and the presence of a lime flux will enhance the rate of conversion. In sharp contrast, the displacive transitions within a polymorph cannot be suppressed and are extremely rapid. The details of the displacive transformations remain an area of active research and, in fact, speculation (Griffen, 1992). However, the key consequence of interest in ceramic processing is the dimensional changes which
69
occur during the oc- to f$-quartz, low- to high-tridymite, and low- to high-cristobalite transformations. The molar volume of quartz is a smooth function of temperature except for the phase transformation which occurs at 573 °C which causes a sudden change in volume on the order of one percent. Interestingly, high quartz exhibits a negative thermal expansion coefficient. Tridymite exhibits a smaller displacive volume change at 105 °C, but also exhibits negative expansion above 575 °C. In the case of cristobalite the transformation occurs at a low temperature, about 215 °C, and the volume change is roughly three percent, that is, significantly larger than in the case of the other two polymorphs. The thermal expansion of other fillers is also an important property. Over the temperature range of interest zircon, mullite, wollastonite, and alumina are all considered to have low thermal expansion coefficients, in the range 4.5 to 8.8xl0~ 6 /°C respectively. Conversely, fosterite is used as a filler for specific applications because it has a high thermal expansion, but exhibits no phase transformation. Other characteristics of fillers which are important are index of refraction, to achieve translucency, as well as the dielectric constant and loss tangent, for low loss electrical insulators. 2.2.4 Triaxial Formulations
There are a sizable number of commercially important triaxial compositions. Design of a specific system is nearly always the result of a compromise between demands related to processing and a desired set of properties. The processing of most oxide ceramics (excepting glass) is based on powder technology. One characteristic of powder processing is that the geometrical information
70
2 Oxide Ceramics
is stored independent of densification and microstructural development. There are three basic steps in the process: i) a powder mixture, sometimes suspended in a liquid, is formed into the desired shape, ii) the shaped powder compact is subjected to heat, and iii) the fired component is often glazed. The structure of the raw materials, the chemical reactions which occur during firing and the final microstructure all impact important properties. Phelps (1976) and Lehman et al. (1984) have pointed out that complete characterization of a triaxial formulation requires specification of: average chemical composition; percentages of individual mineral phases; particle size distribution; colloidal content; and amount of organics. Nevertheless there are general families which serve to illustrate the influence of each material. 2.2.4.1 Clay-Quartz-Feldspar
There are many variations within this general category. The term triaxial is somewhat misleading in this case since it is conventional to distinguish between the amount of ball clay and china clay and therefore four independent variables are required to completely specify the composition. Increasing the relative amount of ball clay generally improves the plasticity as well as the green strength, but often leads to discoloration as a result of contamination by iron-bearing accessory minerals. Therefore applications where green strength is at a premium, and color is of less importance, employ larger amounts of ball clay. One example where ball clays are heavily used is high tension insulators (Norton, 1976). These are extruded as large cylinders, perhaps 0.5 m in diameter and 1.5 m in length and then machined in the green state to form the ribs; green strength is crucial. Fine china represents the oppo-
site end of the spectrum where aesthetics take priority. China clays are used in these formulations, because they are nearly phase pure (unlike ball clays) and do not occur as iron bearing solid solutions (as do the smectites and illites). The maturation of a triaxial formulation during thermal treatment is a complex process and is not understandable from the equilibrium viewpoint. In many triaxial formulations the filler may be regarded as chemically nonreactive. Usually this is the result of sluggish kinetics rather than thermodynamic equilibrium. The decomposing clay forms mullite and rejects silica which combines with feldspar (and other fluxes) to form a glass. The quartz filler undergoes a displacive polymorph transition during heating, undergoes some conversion to cristobalite or tridymite and dissolves slowly in the glass. The final microstructure of the fired ceramic contains unaltered filler (in fact, the "unaltered" filler has experienced displacive phase transformations during both heating and cooling), glass, and mullite. Therefore, the fired whiteware is, in essence, a glass matrix composite containing two different types of particulate and typical mixing rules apply to the properties. The extent of glass formation affects properties such as dimensional stability and degree of densification. In systems which require high dimensional stability such as structural clay products (i.e., large ceramic pipes and tiles) the extent of glass formation is kept to a minimum (Brownell, 1976). In contrast, dental porcelains must fuse at low temperatures to be compatible with metal substructures and therefore may contain in excess of 80% feldspars. The physical properties of the glass are of obvious importance to the performance of the fired ceramic. One method for controlling the properties of the glass, such as
2.2 Silicate Ceramics
strength and thermal expansion coefficient is through the control of the potassium to sodium ratio in the feldspars. The index of refraction of the glass, on the other hand, is insensitive to this ratio; glasses derived from orthoclase, albite and nepheline syenite all have indices very near to 1.5 (Kingery et al., 1976). This is closely matched by a silica filler regardless of polymorph (the indices of quartz, tridymite and cristobalite are 1.55, 1.47, and 1.49 respectively). Mullite has a somewhat higher index, 1.64, but most of the light which is scattered results from residual porosity and material fired to low porosity is translucent. The role of the quartz is to increase the effective thermal expansion coefficient. The need for a high thermal strain during cooling is dictated by the desire to glaze the surface. A glaze may be defined as a thin glassy coating fired on the surface of a ceramic article. Although always "glassy", many contain appreciable volume fraction crystalline phases. A glaze serves many purposes beyond decoration. Properly glazed ceramics are substantially stronger, present a smoother surface, are impervious to gases or liquids, have increased corrosion resistance, and (in the case of some electrical porcelains) may be semiconducting (Taylor and Bull, 1986). Glazes are typically designed to be in a state of residual compression during service. The stress state is determined during cooling after the glaze has congealed. If the effective thermal expansion coefficient of the substrate is higher than that of the glaze, residual compression is achieved. This is not always easy to achieve since glazes are usually more heavily fluxed than the body and most fluxes increase the thermal expansion coefficient. The thermal expansion mismatch is strongly affected by the silica content in both the glaze and the
71
substrate. Increasing the silica content of either tends to increase the level of residual compression in the glaze. This apparent paradox is understood when it is recognized that the silica in the glaze is a glass (and thus lowers the thermal expansion) whereas the silica in the substrate is crystalline. The contraction associated with the pto a-quartz transformation on cooling helps to increase the effective thermal expansion coefficient of the ceramic and achieve the desired state. When the glaze fuses at temperatures below 573 °C, cristobalite may be the desired polymorph since the displacive transformation occurs at 215°C. In this case, flint is the preferred form of quartz since the kinetics of conversion to cristobalite are relatively rapid (Worrell, 1986). The penalty to be paid for the use of displacive phase transformations as a mechanism for tailoring thermal expansion is poor mechanical properties. The abrupt contraction of quartz (or cristobalite) leads to the formation of microcracks (Warshaw and Seider, 1967). These authors observed that the extent and type of microcracks were dependent on particle size and that the efficacy of quartz in affecting the thermal expansion was diminished as the extent of cracking increased. Quartz particles on the order of 80-150 }im produced cracking which virtually eliminated any effect on expansion. The strength was observed to increase as quartz particle size was decreased to 25 jim. Further reductions did not increase strength. 2.2.4.2 Clay-Alumina-Feldspar, Clay-Zircon-Feldspar
The properties of triaxial formulations may be significantly modified by the choice of the filler. Although quartz is inexpensive
72
2 Oxide Ceramics
and provides some desirable properties, other fillers are sometimes used. The substitution of alumina for quartz increases the strength of the fired ceramic (Warshaw and Seider, 1967; Dinsdale, 1986). However, it increases density, decreases translucency, and reduces the effective thermal expansion coefficient. The density of alumina, 3.96 g/cm3, is roughly 50% larger than quartz, 2.65 g/cm3, therefore in formulations containing fifty weight percent filler the density difference is substantial. There is also a decrease in translucency due to the alumina's higher index of refraction, 1.76, which leads to a greater degree of internal light scattering. The reduction in thermal expansion coefficient is the result of a modestly lower thermal expansion coefficient and the absence of a phase transformation. This property leads to the need for specialty glazes. Electrical porcelains (ceramics used as electrical insulators) are one area in which the high strengths associated with alumina based formulations find application (Moulson and Herbert, 1991). Zircon has yet higher density (4.68 g/ cm3), higher index of refraction (1.95), and lower thermal expansion, roughly one-half of alumina. In fact, the most common application of zircon in the ceramic industry is as a crystalline phase dispersed in glazes. In this application, it serves to lower the thermal expansion, increase opacity and increase corrosion resistance of the glaze (Taylor and Bull, 1986). Zircon also tolerates substitutional solid solution of both transition metals and rare earths. This has lead to the development of a wide array of zircon pigments (Taylor and Bull, 1986). Zircon based ceramic bodies find application as low loss electrical insulators (Grimshaw, 1971) or as corrosion resistant refractories (Chesters, 1973; Adams, 1989). Zircon formulations exhibit good thermal
shock resistance; a product of low thermal expansion and high thermal conductivity. Ball clays and montmorillonite clays are typically employed in such formulations in order to increase the plasticity. 2.2.4.3 Pyrophyllite- and Talc-Based Formulations, Clay-Wollastonite-Nepheline Syenite
Pyrophyllite, talc, and wollastonite find wide application in the manufacture of both wall tile and electrical porcelain (both billion US dollar industries). Tile must be manufactured to precise dimensional tolerances. This is typically achieved by processing such that the piece experiences a minimum amount of firing shrinkage, usually through selection of raw materials and control of the firing schedule to minimize densification during firing. One result of this is that most wall tile is porous after firing. Although they have nominally similar formulations, electrical porcelains are densified in order to develop high strength and reproducible electrical properties. The thermal decomposition of pyrophyllite at 1000 °C produces a felted mass of cristobalite crystals and mullite that suffers negligible firing shrinkage (Grimshaw, 1971). The thermal strain associated with the cristobalite transformation aids in glazing. Whiteware grades of pyrophyllite contain appreciable amounts of sericite (very fine grained muscovite mica) and quartz with a small amount of kaolin (Reiger, 1992) and therefore are effectively a triaxial formulation as-mined. Two distinct types of talc based bodies are produced, cordierite and steatite (Worrall, 1986; Moulson and Herbert, 1991). (The names form a somewhat mismatched set, cordierite is the principal phase formed during firing of the former, whereas steatite is simply a mineralogical term referring to
2.2 Silicate Ceramics
a natural deposit of the mineral talc.) In both cases the major crystal phase is formed as a result of chemical reaction during firing. A typical steatite formulation contains 60-90% (by weight) talc, 5 - 8 % feldspar, 5-20% clay, with 7-20% alkaline earth carbonate. During firing to 1300°C the talc decomposes to form enstatite, MgSiO 3 , by the reaction Mg3(Si2O5)2(OH)2 -> 3MgSiO 3 Enstatite exhibits a very low dielectric constant and a high thermal expansion coefficient leading to its use in electrical applications (Lee and Heuer, 1987). Cordierite formulations are comprised of a mixture of clay (kaolinite) and talc with a low expansion filler. The trioctahedral and dioctahedral phyllosilicates react during firing to produce cordierite by the overall reaction 2Mg 3 (Si 2 O 5 ) 2 (OH) 2 -> 3Mg 2 Al 4 Si 5 O 18
6Al 2 Si 2 O 5 (OH) 4 10H 2 O.
In polycrystalline form, cordierite has a very low thermal expansion coefficient and finds applications requiring good thermal shock resistance, but glazing is difficult. Since the body is reactive there is the possibility of distortions during firing. This may be minimized by the addition of a nonreactive filler. In order to achieve a low thermal expansion coefficient, fillers such as mullite, calcined clay (fired clay products which are crushed and recycled are referred to as grog) (Worrall, 1990), or zircon are used (Grimshaw, 1971). Tremolitic talc is the preferred form of raw material (Johnson, 1992). This material contains in the range of 30-50% prismatic tremolite, Ca 2 Mg 5 Si 8 O 22 (OH) 2 , which aids in dry pressing.
73
Increasing cost of fuel(s) has provided motivation for firing schedules of shorter duration and lower maximum temperature. As a result, wollastonite is becoming an increasingly important filler (Reiger, 1992) particularly in wall tile formulations. A typical formulation is 65% (by weight) wollastonite, 30% china clay, and 5% nepheline syenite (Sainamthip and Reed, 1987). The wollastonite serves both as an auxiliary flux to the nepheline syenite and as a filler. Reaction between the clay and wollastonite produces some anorthite. The extent of the reaction depends on the firing cycle indicating the structure is not at equilibrium. As in the case of pyrophyllite, one of the desirable features of this system is the minimal firing shrinkage, on the order of one percent. 2.2.5 Summary and Analogies in Single Phase Ceramics
Silicate ceramics illustrate the close relationship between crystal structure, microstructure and properties. The crystal structure of the raw materials affects not only properties in the green state, such as plasticity, but also the microstructural development during firing. For example, the silicon in a densified clay-quartz-feldspar ceramic, although everywhere in tetrahedral coordination, is in at least three qualitatively different states: in mullite crystals; in the glass matrix; and a discrete crystalline phase. The system is designed to be far from equilibrium and the distribution of silicon is directly related to the crystal structure and particle size of the raw materials. Such a nonequilibrium partitioning is also characteristic of other elements. Although these materials are often classified as clay-based, many of the formulations have little or no clay. Also, many of the properties of a fired ceramic are con-
74
2 Oxide Ceramics
trolled by the nature and amount of the filler rather than the clay content. Finally many of the ceramics which are considered single oxides, e.g., commercial 96% alumina substrates and refractories as discussed in Sec. 2.4 or the liquid phase sintered tetragonal zirconia polycrystals discussed in Sec. 2.5.3.3 may be considered as limiting cases of triaxial formulations. One interesting area for research is to develop systems which behave in a manner analogous to a triaxial formulation in the green state, but which convert to single phase ceramics upon firing. An example is the production of a single phase alumina from a mixture of colloidal aluminum monohydroxide and alumina powder. There are two forms of aluminum monohydroxide, diaspore and boehmite. The latter is routinely synthesized and a commercial product. It has been recognized that the crystal structure of boehmite leads to the formation of high aspect ratio platey particles which exhibit rheological behavior similar to clays (Pierre and Uhlmann, 1986). Boehmite is a difficult material to process due to its small particle size and phase transformation behavior, see Sec. 2.4.1, but it has been shown that it significantly improves the rheological characteristics of alumina slips and pastes in the green state (Chen and Cawley, 1992; Chou and Senna, 1987; Kindl et al., 1991). During firing it is converted to a-alumina yielding a single phase ceramic.
2.3 MgO, Magnesia, Periclase Magnesia refractories are widely used particularly in the production of iron and steel because of their general availability, high thermal conductivity, refractoriness, and resistance to basic slags especially when combined with graphite. Section
2.3.2.3 will be concerned extensively with basic refractories including magnesia and doloma. There are presently few commercial applications of dense magnesia in engineering ceramics because it hydrates readily when exposed to air and has few property advantages over alumina. 2.3.1 Crystal Structure MgO is a highly ionic crystal with the M g - O bonds having about 80% ionic character. Its crystal structure is the simplest of any ceramic being cubic with the rock salt structure (discussed in Chapter 1). The cubic structure of MgO is maintained from room temperature to its melting point. Unlike many ceramics, it has no deleterious polymorphic transitions. 2.3.2 Mineral Sources and Production
MgO occurs rarely as the mineral periclase but is abundant as magnesite (MgCO3), and dolomite (Mg,Ca)CO 3 . High-purity magnesite ores can simply be beneficiated and calcined to MgO at 500-700 °C. Magnesia refractories are often called magnesites even though they contain MgO not MgCO 3 and may not even have been derived from magnesite ore. Doloma (CaO • MgO) refractories derived from dolomite are still widely used, particularly in Europe. Other commercial sources of magnesia are sea water, brines and deposits of Mg-rich salt. Sea water accounts for most MgO production in the USA, Japan and the UK. Worldwide mined natural magnesite accounts for about 67% of refractory MgO with synthetic sources for about 33% (Mikami, 1983). Sea water contains about 1 kg of MgO per 500 L as magnesium chloride and is reacted with an alkali source (usually lime or slaked doloma) to precipitate
75
2.3 MgO, Magnesia, Periclase
Mg(OH) 2 i.e
Table 2-5. Physical properties of raw materials used in refractory production (Brown and White, 1986).
(Ca,Mg)(CO)3 dolomite ore 1100
°C>
CaO 4- MgO burnt doloma
ZZ£>
Ca(OH)2 + Mg(OH)2
Composition (wt.%)
slaked doloma
2 Mg(OH)2 (s) + CaSO4(aq) + CaCl2 (aq) "spent" sea water
The hydroxide precipitate is washed, filter pressed, dried and calcined in large rotary kilns at 750-900 °C. The as-calcined crystal size from natural ores or hydroxide from sea water is well below 1 |im. Such powder has a large surface area and rapidly reacts with atmospheric CO 2 and H 2 O. Consequently, "mineralizers" such as NaCl or NaOH may be added to encourage grain growth and/or the ore is "dead burned" or calcined to high temperature (1500-1700 °C) to give 3-4 jim grains which are effectively resistant to water vapor and carbon dioxide. Adding silica or Fe 2 O 3 to the ore and partially melting while dead-burning gives sintered "clinker" grain which is used as the raw material for later brick or monolithic refractory production. Sea-water derived MgO contains enough excess lime and other impurities so that additions may not need to be made to produce adequate clinker. For the best quality refractories the MgO is fused above 2750 °C in an electric arc furnace which removes the undesirable, high-vapor pressure, impurities. Typical properties of the starting grains for refractory production are given in Table 2-5 (Brown and White, 1986). Very high purity MgO may be synthesized using chemical techniques. For example, Gardner and Messing (1984) used evaporative spray decomposition of solutions to prepare magnesia. Their results indicate that the efficiency of conversion and the state of agglomeration of the resultant powder are both dependent on the nature
MgO A12O3 Fe 2 O 3 CaO SiO2 B2O3
c/s
Bulk density (gem" 3 ) Grain porosity (vol.%)
Sintered MgO Clinker
Sintered Doloma Clinker
Fused MgO
96-99 39-40 97-98 0.05-0.25 0.3-0.8 0.1-0.2 0.05-0.2 0.6-1.0 0.1-0.5 0.6-2.4 57.5-58.5 0.9-2.5 0.1-0.5 0.6-1.1 0.3-0.9 0.005-0.6 0.004-0.01 2-4 1-5 3.5 3.4-3.45 3.15-3.25 2-3
5.5-7
0.5-2
of the precursor. Fine unagglomerated particles were obtained when an acetate precursor was employed, but either incomplete reaction or agglomeration was observed when chloride, sulfate, or nitrate precursors were employed. 2.3.3 Properties 2.3.3.1 Single-Crystal MgO MgO is often regarded as a model ionically bonded ceramic. Some useful physical property data are given in Table 2-6. It adopts the relatively simple rock salt crystal structure (see Chapter 1 of this Volume) which is a convenient structure for illustrating the effect of ionic bonding on crystal defect structure. As discussed more fully in Chap. 7, Sec. 7.4.2, the crystal structure of ionic materials increases the energy associated with both the generation and glide of dislocations. Both result from the localized charges associated with lattice sites. As illustrated in Fig. 2-16, a stable edge dislocation cannot be generated by the familiar hypothetical removal of a halfplane. Instead, pairs of half-planes must be
76
2 Oxide Ceramics
Figure 2-16. Illustration of the effect of electrostatic repulsion between next nearest neighbors on the hypothetical removal of a half-plane of atoms from a rock salt structure ionic ceramic.
Table 2-6. Physical property data for single-crystal MgO. Property 2800
Tm (°O Density (gem" 3 )
3.58
Thermal conductivity (W/mK)
100 °C 1000°C
7.1 37.6
Linear thermal expansion (xio-6/°Q
RT 200 °C 500 °C 1000°C
6.5 11 12.7 13.9
0-1000°C
13.5
Mean value Average refractive index Elastic modulus (GPa)
1.74 300
removed to achieve nearest neighbors with unlike charges in the relaxed structure. The formation of dislocations with such large Burger's vectors is energetically unfavorable. Permissible slip directions are also restricted by localized charges. Slip is restricted, at low temperature, to those com-
binations of planes and directions that do not require ions of like charges to be brought into contact in saddle point configurations. MgO is one of the few oxide ceramics to exhibit a high degree of plasticity. This is a result of the existence of slip planes with a minimum of electrostatic faulting, see Fig. 7-53. MgO has also been used as a model system to illustrate the consequence of ionic bonding on the formation of point defects. In discussing point defects, it is convenient to distinguish between the anion and cation sublattices. The thermal production of intrinsic defects may be described using the following pseudo-chemical reactions written in Kroger-Vink notation (Kroger, 1974), where the subscript refers to the site of species (V refers to a vacancy and i to an interstitial site), and the superscript refers to the charge relative to the lattice (' indicates negative, ' indicates positive, and x neutral relative charge), Anion Frenkel disorder
o o -> or + v o Cation Frenkel disorder Schottky disorder Null _> V "
4- V "
It is evident that the defect populations on the Mg and O sublattices are coupled through the Schottky defect reaction. Extrinsic defects produced by aliovalent impurities may also be written in pseudochemical form. For example, consider the dissolution of A12O3 in MgO, this may be written either as A12O3 or A12O3
MgOv
2.3 MgO, Magnesia, Periclase
The appropriate reaction depends on the energetics associated with the production of oxygen interstitials and magnesium vacancies. A qualitative argument based on ionic size is sometimes used to argue that the energy associated with the production of oxygen interstitials is prohibitively high and that trivalent impurities are more likely to be compensated by the production of vacant Mg sites. In principle, either direct spectroscopic measurements (Crawford, 1984) or indirect measurements of, for example, the effect of doping on mass transport can be used to determine the dominant defect species. However, it has become clear that the use of simple mass action laws based on the assumption of fully ionized point defects originally developed to describe the behavior of alkali halides does not give reliable predictions in the case of MgO (and other oxides). The first complication is the very high energies associated with the intrinsic defect reactions. As has been pointed out by Viera and Brook (1984), intrinsic diffusion will not be observed unless the total impurity level is below 10" 7 mole fraction (or 0.1 parts per million). This level of purity cannot be achieved in real materials; thus the observed behavior is determined by a competition between low level impurities, both intentional and incidental. Secondly, and more importantly, it has become clear the defect association, or clustering, is important in determining the defect structure of both undoped and doped MgO (Gourdin and Kingery, 1979; Yager and Kingery, 1984; Mackrodt, 1984). Defect clustering interferes with direct interpretation of experimental results in at least two ways. Firstly, it is difficult to estimate the energetics of defect clusters a priori, or to determine them from experiments of commercial purity. Secondly, when associa-
77
tion, or clustering, occurs during cooling the defect structure which is quantified through room temperature experiments may not correspond to either the equilibrium high temperature or room temperature structure, but a metastable mixture of point defects, associates, and clusters (Yager and Kingery, 1984). Due to these complications the details of the defect structure of even model oxide systems such as MgO are not completely determined. Single crystal MgO does not find wide commercial application. 2.3.3.2 Refractory Fabrication and Microstructure
The most important commercial use of magnesia is in the fabrication of basic refractories used in steelmaking. The historical development of basic bricks has been intimately linked with improvements in steelmaking techniques. Until the early 1970s most BOS (basic oxygen steelmaking) vessels had simple doloma linings. Doloma is an inexpensive material which is produced through the calcination of dolomite, (Mg,Ca)(CO 3 ) 2 , and has the nominal composition (Mg,Ca)O 2 . Blending doloma with magnesia or using all magnesia linings was observed to yield significantly increased vessel life. It was also noticed that vessels lined with bricks containing pitch or tar (added to prevent hydration) had longer lives. The less than 5% residual carbon left from the pitch after firing was beneficial since it inhibited wetting by slags and its high thermal conductivity improved thermal shock resistance. This led logically to systematic additions of much higher C levels (up to 20 wt.%) and the evolution of MgO-graphite bricks currently used to line BOS vessels. The simpler, but now less common, cases of magnesia and doloma bricks will be con-
78
2 Oxide Ceramics
Table 2-7. Chemical and physical properties of densified basic brick. Chemical analysis (wt.%) MgO Fe 2 O 3 A12O3 CaO SiO2 B2O3 Apparent porosity (%) Bulk density (gcm~ 3 ) Cold crushing strength (MPa) Thermal conductivity (W/mK) mean at 900 °C MOR (MPa) RT 1400°C 1600°C
91-97 0.4-5 0.1-2 1-3 0.8-2 <0.02 12-20 2.88-3.0 35-70 4
15-20 0.1-5 0-5
sidered before discussing the effects of carbon and graphite on these MgO-based materials. An understanding of the properties and microstructures of sintered MgO remains important since it is widely used as the grain phase in MgO-graphite refractories. Present day manufacture of a basic refractory brick from sized, dead-burned MgO powder typically involves adding a binder and liquid forming additions, pressing to a brick at around 100 MPa, drying in controlled low humidity at < 60 °C (due to its hydration tendency) and firing at 1500-1900°C for 3-5 days. The resulting bricks typically have the range of properties given in Table 2-7. Lower grade basic bricks are used in isolated applications such as in glass tank checkers and tin smelting hearths. Higher grades are used in: working sidewalls and hearths of modern electric arc furnaces, outlet zones of cement rotary kilns and the upper sections of glass tank regenerator packings and superstructures.
Critical microstructural factors affecting these properties and performance of bricks made by liquid phase sintering include: a) CaO/SiO2 molar ratio of the bonding phase, b) impurity content, in particular B 2 O 3 , and c) particle size of the MgO. Each of these will be discussed in the first of the next two subsections. Since most modern basic bricks contain added carbon, details of the production, microstructure and properties of such bricks will be given in the second of the next two subsections. Magnesia-Based Refractories Standard bricks contain, in addition to MgO, varying amounts of impurities. The source may be either the raw materials or deliberate additions. Materials such as SiO 2 , A1 2 O 3 , Fe 2 O 3 , Cr 2 O 3 , FeO and CaO are common and combine to form a silicate bonding phase. Predicting the thermochemical behavior of a system with
Fe
2°3
MF
MgO
CaO
Figure 2-17. Quaternary CaO-MgO-Fe 2 O 3 -SiO 2 phase diagram (from White, 1970).
2.3 MgO, Magnesia, Periclase
such a large number of components is difficult. Fortunately, because of the solid solubility of FeO in MgO, and Cr 2 O 3 and A12O3 in Fe 2 O 3 , these alloys can be approximated as components and the phase Table 2-8. Secondary phases commonly formed in MgO refractories. Mineral
Periclase Forsterite Monticellite Merwinite Dicalcium silicate Dicalcium ferrite Magnesium ferrite Magnesiochromite Spinel
Formula
Abbreviation
Tm(°C)
MgO 2MgOSiO2 CaO • MgO •SiO2 3 CaO MgO •2SiO 2 2CaOSiO2
M M2S CMS
2800 1890 1495
C 3 MS 2
1575
C2S
2130
2CaO-Fe 2 O 3
C2F
1435
MgO • Fe 2 O 3
MF a
1750
MgO • Cr 2 O 3
MK a
2400
MgO • A12O3
MA a
2135
a
All have the spinel crystal structure and are mutually soluble.
79
relationships can be determined by studying the quaternary system M g O - C a O SiO 2 -Fe 2 O 3 (White, 1970). As indicated in Fig. 2-17 and Table 2-8 many silicates and ferrites may occur as secondary phases. Provided the requisite impurities are present in sufficient amount, the major factor controlling which phases form in the microstructure of a basic brick is the CaO/SiO2 (or C/S) molar ratio. Table 2-9 shows the effect of C/S ratio on phase formation. Figure 2-18 shows the microstructure arising when C / S « l . A relatively large amount of liquid forms at relatively low temperature in the bond between the MgO clinker (which has its own liquid phase at grain boundaries) due to the low melting temperature of the CMS composition. Examining the bond phase (lower part of Fig. 2-18) shows rounded MgO grains surrounded by CMS composition crystals or glass formed from the liquid on cooling. The large amounts of liquid lead to poor refractoriness and causes excessive shrinkage during firing so that such bricks are rarely used commercially. The microstructure of a brick with C/S ratio about 2 con-
Table 2-9. Phases typically observed in the bond phase of basic refractories as a function of calcia to silica ratio. Phase formed
Typical firing temp. (°C)
Comments
CMS, M2S, (MA,MK,MF), MgO (ss)
1550
Towards C/S = 0 have M 2 S, towards CS = 1 form CMS liquid
1:1.5
CMS, C 3 MS 2 , (MA,MK,MF), MgO (ss)
1600
Less'CMS more C 3 MS 2
1.5:2
C2S, C 3 MS 2 , (MA,MK,MF), MgO (ss)
1700-1750
Increased refractoriness. Dusting from (3-y C2S
>2
C2S, (C2F, C4AF, i.e. Ca phases), (MA,MK,MF), MgO(ss)
Low Tm Ca-phases form
C3S, (Ca phases), MgO (ss)
Close to Portland cement
CaO, (Ca phases), C3S, MgO (ss)
Free lime present i.e. hydrating
C/S Ratio
<1
>2<3 >3
80
2 Oxide Ceramics
Figure 2-18. (a) Reflected light micrograph of magnesia brick with C/S-»l. Large MgO grains (M) are held together by a bond phase of small MgO grains in a CMS composition glass (G). (b) The large amount of liquid formed is indicated by the rounded morphology of the MgO in the bond phase (lower figure). The black features are pores.
tains more refractory crystal phases such as C2S at grain boundaries which form during cooling (Fig. 2-19). It is interesting to note that the large extent of solid solubility between many of the phases imparts some degree of tolerance on basic brick compositions. For example, a C/S ratio of about 3 is commonly used for commercial batches because the solubility of CaO in MgO means that the grain boundary C/S ratio is about 2 as desired. For higher refractoriness, C/S should be very low, ideally zero, yielding a fosterite bond or, alternately, C/S should be greater than two giving a C2S bond. Intermediate compositions lead to the formation of low melting phases such as CMS or C2F. The variation in hot modulus of rupture (MOR) with increasing C/S ratio is shown in Table 2-10 (Hancock, 1988). Boron is a critical impurity in basic refractories. B 2 O 3 fluxes the silicate bond, lowering its melting point so that the refractory grains literally float apart at temperatures as low as 1200 °C. The consequent disastrous effect on hot strength means that B 2 O 3 contents must be kept below 0.02%. To reduce B 2 O 3 levels in seawater magnesite, extra lime may be added during precipitation of Mg(OH) 2 from sea water so that the boron precipitates in alkaline salts which can be removed. MgO from natural ores has lower natural boron content. Alumina and iron
Table 2-10. Hot modulus of rupture (MOR) for basic brick containing a constant amount of bond as a function of calcia to silica ratio (Hancock, 1988) C/S Ratio Figure 2-19. Reflected light micrograph of magnesia brick with C/S -• 2. The bonding phase between the MgO grains (M) is made up of glass and crystals of phases such as C2S.
1.5 2.0 3.0
MOR at 1300°C (MPa) 3.6 15.0 6.4
2.3 MgO, Magnesia, Periclase
81
Table 2-11. Hot modulus of rupture of basic brick containing 1.5wt.% SiO2 and 3.0wt.% CaO as a function of B 2 O 3 level (Hancock, 1988) B2O3
MORat 1300°C(MPa)
0.05 0.1 0.15 0.2
14.3 7.1 3.6 1.4 100 JJ|£
Table 2-12. Hot modulus of rupture for basic brick containing 1.5 wt.% SiO2 and 3.0 wt.% CaO as a function of wt.% Fe 2 O 3 -Al 2 O 3 solid solution (Hancock, 1988) Fe 2 O 3 + A12O3
1.0 2.0 3.0 4.0
Figure 2-20. Various grades of MgO grain showing porosity and crystallite size, (a) Standard sintered MgO, (b) large crystal sintered MgO, (c) natural large crystallite MgO, (d) fused high-purity MgO (from Williams et al., 1990).
MOR (MPa) 1300°C
1500°C
14.6 12.8 12.1 11.8
7.8 4.3 2.7 1.8
oxide also have a detrimental effect on hot strength but less than that of B 2 O 3 . Tables 2-11 and 2-12 show, respectively, the effect of B 2 O 3 level, and Fe 2 O 3 + Al 2 O 3 levels (with constant 0.01% B 2 O 3 ), on the hot MOR of a refractory containing 1.5 wt.% SiO2 and 3 wt.% CaO (Hancock, 1988). The size of the MgO crystals within the magnesia grain is critically important in controlling the resistance to corrosive attack of basic bricks. As the size of the crystals increases there is a corresponding decrease in crystal surface area and open porosity which makes the grain less reactive to any infiltrating iron oxide rich slag. This is a particularly important variable for MgO-carbon refractories operating above 1650°C (Williams et al, 1990). Figure 2-20 shows reflected light optical mi-
crographs of four types of magnesia grain revealing the large crystal size available in some sintered grades Fig. 2-20 c and fused material Fig. 2-20 d. Figure 2-21 (Williams etal., 1990) shows the linear refractory wear rate due to corrosive slag attack as a function of the aggregate MgO grain size. Large crystal size (>100jim diameter) magnesias are now used extensively where corrosion resistance is required. Although basic refractories generally have adequate refractoriness, the large amounts of glass present in silicate-bonded materials may limit their high-temperature strength. Direct-bonded MgO refractories can be manufactured with higher load bearing capacity at elevated temperatures as a result of a solid crystalline bonding system. MgO bricks containing chrome ore additions can be manufactured in a manner similar to silicate bonded bricks. The chrome ore must be low in silica to prevent excess liquid formation and should also contain other sesquioxides such as A12O3 and Fe 2 O 3 . At Cr 2 O 3 levels in excess of 15%, second phase bridges or magnesium chrome spinel form between
82
2 Oxide Ceramics
Wear Rate (mm/hr)
100 150 Mean Periclase Crystallite Size (pm)
MgO grains i.e. Cr 2 O 3 + MgO -• MgCr 2 O 4 These bridges are the direct MgO-spinel and spinel-spinel bonds conferring high hot strength and high percentage of theoretical density, which increases the penetration resistance. While direct bonded bricks are still used in some argon-oxygen-decarburization and vacuum-oxygen-decarburization electric steelmaking furnaces, cement kilns and glass tank checkers, the toxic hazard of the Cr6 +-containing waste is leading to a decline in use. MgAl 2 O 4 spinel-bonded MgO refractories are currently being developed to replace MgCr 2 O 4 . MgO-Graphite Refractories In the 1960s and 1970s carbon additions to basic bricks led to much improved slag resistance. Carbon (as the bonding phase and as graphite flakes) was added to many other refractory oxides such as alumina, zirconia and silica. The reasons why high levels of carbon in MgO and doloma refractories improve their properties and resistance to slag attack are still the subject of discussion. Suggested mechanisms include:
200
Figure 2-21. Effect of mean crystallite size in MgO grain on the wear rate of magnesia bricks of identical composition based on rotary slag test studies (Williams et al, 1990).
1) Most molten metals and slags do not wet carbon and therefore liquid infiltration and slag attack is reduced. 2) Carbon reduces, for example, MgO to Mg vapor at high temperature which reoxidizes and deposits as a "dense layer" of secondary MgO at the slag-brick interface which prevents slag/metal ingress. 3) Carbon reduces iron oxide in the slag to Fe metal so that it does not attack the MgO-CaO and form low melting phases. 4) CO gas (formed on oxidation of carbon) and/or Mg vapor (from reduction of MgO) provides an overpressure which resists slag/metal ingress. Oxide-graphite refractories have now replaced the traditional aluminosilicate and basic bricks in many applications. These materials may contain from 4-30 wt.% natural graphite as well as carbon from the pitch bond or additional carbon black. A material with 20 wt.% graphite corresponds to a graphite content of about 50 vol. % due to its low relative density (2.26 g/cm3). MgO-graphites (graphite content 5-20 wt.%) are used in oxygen and electric primary steelmaking furnace linings and in secondary steelmaking units. MgOgraphites have replaced fired magnesia and unfired doloma bricks extensively as
83
2.3 MgO, Magnesia, Periclase
Table 2-13. Relative proportions of constituents in oxide-graphite refractories (Brant et al., 1989). •
Component Oxide Bond Graphite Additions
•
«
#
'
Composition (wt.%) e.g. MgO, ZrO 2 , A12O3 e.g. carbon (natural flake) e.g. metal (Al, Si) or ceramic (SiC)
50-90 3-7 5-30 0-10
the main lining material in basic oxygen furnaces. In electric arc furnaces they have evolved as the main slag line material and high graphite levels (20 wt.%) are used to maximize thermal conductivity and so enable the use of water cooling systems. MgO-graphite bricks are usually fired under reducing atmosphere in situ. Table 2-13 (Brant et al., 1989) gives the typical composition ranges for oxide-graphite refractories. Oxide-graphite refractories are true composite materials with each constituent contributing to the performance of the system. The oxide confers oxidation resistance while the graphite provides increased thermal conductivity, non-wetting behavior, and slag resistance. The oxide and graphite react at high temperature and cannot, therefore, be conventionally sintered. A third phase is required to bond the oxide and graphite particles. This may be a carbon bond derived from the pyrolysis of pitch or resin, but may also be a ceramic bond derived from clay or metallic additives which react during firing. Mixing the constituents can be difficult because the non-wetting behavior of the low energy graphite surfaces and high shear mixing techniques must be used (Cooper, 1980). For MgO-C brick low porosities and large sizes are required (up to 80 cm lengths) so that large capacity vacuum friction presses have been devel-
Figure 2-22. MgO-graphite brick with the pressing direction (a) parallel and (b) perpendicular to the plane of the paper. In (a) the pressing direction is indicated by the arrows. Bending of the graphite flakes (G) around sintered MgO grains is evident in (a).
oped. Due to its flaky morphology, graphite is prone to alignment during pressing resulting in an anisotropic microstructure (Fig. 2-22). This leads to anisotropic properties parallel and perpendicular to the pressing direction which must be taken into account during installation. The morphology of the graphite flakes creates an open microstructure with high porosity which is beneficial in that firing shrinkages are kept low. This is critical when bricks are fired in situ. Such microstructures are very resistant to crack propagation due to the absence of a continuous, brittle ceramic bond and because cracks must meander around the graphite flakes. Together with the high thermal conductivity of graphite this leads to excellent thermal shock resistance. The combination of thermal shock and slag attack resistance
84
2 Oxide Ceramics
Table 2-14. Typical properties of an MgO-graphite brick using large crystal magnesia primary aggregate with 4 - 5 wt.% added C. Bulk density (g cm 3) tempered coked at 1000 °C MOR (MPa) RT tempered coked at 1000 °C Apparent porosity (%) tempered coked at 1000 °C coked at 1700°C Cold crushing strength (MPa) tempered coked at 1000°C coked at 1700°C Thermal conductivity (W/mK) 400 °C 800 °C Thermal expansion at 1000 °C (xl0" 6 /°C)
3.12 3.06 12.0 6.3 2.6 9.2 16.5 80 35-50 25
0.1 0.2 Strain
Figure 2-23. Typical load-strain curve for a graphite refractory (from Cooper, 1987).
7.4([|) 9.8(l) a 8.2 8.5 10
Parallel and perpendicular to pressing direction.
is extremely desirable for refractories and has led to widespread use of these composite materials. Steelmaking refractory life has almost doubled since their introduction in the 1980s. Typical properties of an MgO-graphite brick using large crystal magnesia primary aggregate with 4-5 wt.% added C are given in Table 2-14. The bend strength of graphite-containing refractories is low by comparison to equivalent graphite-free oxides, due to microcracks introduced by the graphite which opens up along its cleavage planes (Cooper, 1987). The smaller the graphite flake size the higher the strength of the body. This is presumably due to the smaller defect size. Bend strength increases slightly with increasing graphite content in a carbon-bonded system. Unlike most brittle materials, bend test measurements of room temperature strength in oxidegraphites do not produce a linear curve (Fig. 2-23). After reaching a maximum stress the body maintains coherence even
Figure 2-24. Pull-out and crack branching through a graphite-containing refractory (from Cooper, 1985).
as the strength deteriorates showing "graceful failure". This behavior, and the increasing strength with increased graphite content, arises from the reinforcing effect of the graphite flakes which are essentially acting like the platelets in ceramic matrix composites (CMC). Figure 2-24 shows graphite pull out and crack branching in a clay-graphite refractory (Cooper et al., 1985) illustrating that the same mechanisms operate in these refractory composite systems as in the CMCs developed more recently. Additions are often made to oxidegraphite refractories to supply a propor-
2.4 AI 2 O 3 , Alumina, Sapphire, Corundum 180
85
Al-Mg addit on
160 140
„ Al-Si addit | Q p
Hot Modulus 120 of Rupture i nn (kg/cm 2)
y
-
j ^
Al
an
a( Idition
———
No addition 60 3
1
RT 600
800 1000 1200 Temperature °C
tion of ceramic bond which is known to improve hot strength and oxidation resistance. In the 1970's pure metal powders (such as Al and Si) were added during processing which reacted via the vapor phase on firing to form phases such as A14C3, A1N, A12O3 or SiC and SiO 2 . These phases provide ceramic bonding at high temperatures which improves hot strength, see Fig. 2-25, and reduces porosity levels since their volumes are 2-4 times greater than that of the metal additive. This reduction in porosity improves oxidation resistance (Yamaguchi, 1984; Brant et al., 1989). In the 1980s alloys of these metals were developed and it is now known that Al-Mg alloys produce the best high temperature properties. Current research in this area concerns the effect of ceramic additions such as SiC, ZrB 2 and B4C on the microstructure and properties of these materials.
2.4 A1 2 O 3 , Alumina, Sapphire, Corundum Alumina is the most widely utilized oxide ceramic. It is the only oxide ceramic widely used in single crystal form. Single crystal alumina, often incorrectly referred to as sapphire rather than corundum, is
1400
Figure 2-25. Effect of metal additions on the hot strength of MgO-C bricks. A1 2 O 3
used for both its structural and optical properties. The only other significant uses of bulk single crystal oxides are artificial gemstones and laser hosts (alumina also finds application in both of these fields). The overwhelming majority of alumina, however, is used in polycrystalline form. The major markets for alumina-based materials on a weight basis are refractories (50%), abrasives (20%), whitewares and spark plugs (15%), and engineering ceramics (10%). 2.4.1 Crystallography
There is only one thermodynamically stable phase of aluminum oxide, oc-alumina, which has the corundum structure (discussed in Chapter 1 of this Volume). The crystal structure is often described as having O 2 ~ anions in an approximately hexagonal close packed arrangement with Al3 + cations occupying two-thirds of the octahedral interstices. The properties of single-crystal a-alumina are given in Table 2-15. However, many processes such as the oxidation of aluminum metal and the thermal decomposition of gibbsite or vapor deposited amorphous alumina thin films involve the formation of intermediate metastable alumina phases. These transi-
86
2 Oxide Ceramics
Table 2-15. Typical properties of sapphire. General Chemical formula: A12O3 (aluminum oxide) Corundum, Sapphire, Names: a-Alumina Trigonal Crystal system: Hexagonal-scalenohedral class: Thermal Melting point: Maximum useful temperature Specific heat: Thermal conductivity: Thermal expansion coefficient
2053°C (3727°F)
0.181 cal/gm-K (25 °C) 0.300cal/gm-K (1000°C) 0.4W/cm-K(25°C) 0.1 W/cm-K(1000°C) (25-1000 °C) 8.8 x l O " 6 parallel to C-axis 7.9 x l O " 6 perpendicular to C-axis
PhysicalImechanical 3.96 gm/cm3 Density: (0.143 lb/in3) (25 °C) 6 Young's modulus: 435 GPa (63 x 10 psi) parallel to C-axis (25 °C) 386 GPa (56 x 106 psi) parallel to C-axis (1000 °C) Modulus of rigidity 175 GPa (26 xlO 6 psi) (shear modulus): Poisson's ratio: 0.27-0.30 orientation dependent Flexural strength: 1035 MPa (150 kpsi) parallel to C-axis (25 °C) 760 MPa (110 kpsi) perpendicular to C-axis (25 °C) Compressive strength: ^ 2 GPa (300000 psi) 25 °C Hardness: 9 Moh's scale 1900 Knoop parallel to C-axis 2200 Knoop perpendicular to C-axis
Optical Uniaxial negative Refractive index:
Ordinary ray (C-axis) 7VO= 1.768 Extraordinary ray JVe = 1.760 Birefringence: 0.008
Temperature coefficient of refractive 13 x 10" 6 °C" 1 (visible range) index: Spectral emittance: 0.1 (1600 °C) Spectral absorption 0.2-0.2 cm" 1 (Op. 66|im, 1600 °C) coefficient: Electrical Volume resistivity:
10 16 Q/cm(25°C) lO^Q/cm (500 °C) 106Q/cm (1000 °C) Dielectric strength: 480000 V/cm (1200 V/mil) Dielectric constant: 11.5(10 3 -10 9 Hz, 25 °C) parallel to C-axis 9.3(10 3 -10 9 Hz, 25°C) perpendicular to C-axis Loss tangent:
8.6xlO" 5 (at 10 10 Hz, 25°C) parallel to C-axis 3.0xl0" 5 (at 10 10 Hz, 25°C) perpendicular to C-axis
Magnetic susceptibility:
0.21 x l 0 ~ 6 parallel to C-axis -0.25 x l 0 ~ 6 perpendicular to C-axis
Chemical Acid resistance:
Weathering resistance: Sea water resistance: Biological resistance:
Insoluble in inorganic acids at room temperature. Attacked by boiling hydrofluoric acid. Slowly attacked or dissolved by molten salts and oxides at high temperatures (>1000°C). Unaffected by atmospheric exposure Unaffected by marine exposure Unaffected by in-vivo exposure Non-thrombogenic Non-reactive with body fluids
2.4 AI 2 O 3 , Alumina, Sapphire, Corundum
tion phases are denoted as y, %, r|, i, e, 8, 0 and K and are of particular importance because of their use as catalysts substrates and because the characteristics of oc-alumina can be affected by the crystal structure^) of the precursor(s). All of the metastable phases have partially disordered crystal structures based on a closepacked oxygen sublattice with varying interstitial aluminum configurations. As equilibrium is approached the structures become more ordered until stable oc-alumina is formed. The sequence of transition aluminas that form is strongly dependent on the starting material and how it is processed. For example, if the starting material is boehmite, AIO(OH), formed from solution or amorphous alumina then the most probable sequence is Y->8->9->OC. However, if the starting material is gibbsite, oc-Al(OH)3, then the sequence may include %-*Y-»X-> 0->a even though boehmite is formed prior to %. Diaspore, another polymorph of AIO(OH) transforms directly to a-Al 2 O 3 . Formation of the transition aluminas from hydrated compounds is often accompanied by development of a highly porous microstructure (Wilson, 1979). The crystal structures of the transition aluminas are characterized by the maintenance of an approximately f.c.c. anion sublattice (Wilson, 1979). While usually treated as cubic, y-alumina has a slightly tetragonally-distorted defect spinel structure (c/a about 0.99, the distortion varying with heat treatment). 5-alumina has a tetragonal superstructure with one unit cell parameter tripled with the cation vacancies thought to be ordered on the octahedral sites of the spinel structure. 0-alumina is monoclinic with space group A2/m but still similar to spinel and often observed to be twinned. r| is cubic spinel.
87
2.4.2 Mineral Sources and Chemical Synthesis Alumina occurs abundantly in nature, most often as impure hydroxides which are the essential constituents of bauxite ores. Bauxite is an impure mixture of boehmite and/or diaspore, which are a and P forms of AIO(OH), respectively, with gibbsite A1(OH)3. Most raw bauxite is refined by the Bayer process to remove impurities such as SiO 2 , Fe 2 O 3 and TiO 2 leaving a nominal 99.5% alumina product with Na 2 O as the dominant impurity. The high-purity grades of alumina manufactured from these ores of interest to the ceramics/refractories industries are: calcined, low-soda, reactive, tabular and fused. The production, composition and morphology of each of these powders will be discussed in the following sections. The refining of bauxite occurs in several stages. After physical beneficiation (crushing, grinding, and screening), the ore undergoes hydrothermal digestion to get the ions in solution using an NaOH solution under 0.5 MPa pressure at a temperature of 150-160°C. The aluminum hydroxides and much of the siliceous impurities go into solution, as sodium aluminate and sodium silicate respectively. Solid impurities such as TiO 2 and Fe 2 O 3 remain undissolved and are removed as red mud by filtration. After cooling the filtered solution is seeded with gibbsite and precipitation of gibbsite is induced by bubbling carbon dioxide through the solution. Since precipitation is heterogeneous, the temperature, alumina supersaturation and seed content all affect particle size. Drying of the precipitate invariably leads to agglomeration because the residual salts present in the solution precipitate as the water evaporates forming solid bridges between particles. A
88
2 Oxide Ceramics
Figure 2-26. SEM image of Bayer process gibbsite (from Southern, 1991).
typical Bayer gibbsite particle is shown in Fig. 2-26. Note the large number of angular crystallites about 20 jam diameter making up the agglomerate. Upon calcination, water loss begins at about 180 °C leading to high surface area, porous, transition alumina phases. Dehydroxylation of gibbsite begins by the opening of fissures parallel to (0001) as shown by the TEM image (Fig. 2-27). The surface area can reach over 350m 2 g~ 1 at about 400 °C although above this temperature the area decreases due to sintering. At 800 °C the surface area is reduced to about 100 m 2 g" 1 . As calcination proceeds a system of tubular pores parallel to [0001] of gibbsite and fissures parallel to the {0001} planes evolves. a-Al 2 O 3 finally forms at about 1150°C and the fissures are still clearly visible (Fig. 2-28). Consequently, the particle size and shape of the oc-alumina is determined by the crystal structure of the original hydroxide and the series of phase transformations which occur during calcination. Without the presence of mineralizers the structure is retained but the cell walls between the pores grow into small QC-A12O3
Figure 2-27. Bright-field TEM image showing fissures along (0001) forming in gibbsite upon dehydroxylation (courtesy of Alcan Chemicals Ltd., Banbury, UK).
Figure 2-28. SEM image showing fissures in a-Al 2 O 3 formed by dehydroxylation of gibbsite at 1150°C (courtesy of Alcan Chemicals Ltd., Banbury, UK).
2.4 AI 2 O 3 , Alumina, Sapphire, Corundum
89
Figure 2-29. Coral structure of unmincralizcd calcined Bayer alumina (from Southern, 1991).
crystallites while the aggregates retain a pseudomorphic relationship with the original gibbsite. This fine vermicular structure of the calcined alumina is often referred to as a coral structure (Fig. 2-29). As the calcination temperature increases the crystals grow eventually sintering together above 1600°C. Mineralizers such as fluorine, chlorine and boric acid are sometimes used to lower the transformation temperature to a although they also affect the crystal shape; for example, fluorine-mineralized alumina has very platey crystals (Fig. 2-30). Typical commercial aluminas are calcined at 1300-1400°C. High-temperature calcination produces almost 100% a-alumina while material calcined at lower temperatures, that has smaller crystallite size, may also retain some transition alumina phases, usually y. This may cause difficulties in subsequent processing of the powder. Although a-alumina is effectively insoluble in aqueous solutions, y-alumina readily dissolves in weak acid solutions. This leads to the formation of hard agglomerates upon drying of alumina suspensions since the dissolved y-alumina will precipitate at particle contacts as the water evaporates (Niesz and Bennett, 1978).
Figure 2-30. Platey calcined Bayer alumina crystals arising from addition of fluorine mineralizer (from Southern, 1991).
The Bayer process produces highly-aggregated powders which must be milled to release the crystallites and so enable high packing densities and reduced porosity in the green formed state. The degree of milling required depends both on the application and the alumina. The evolution of these commercial Bayer-process powder morphologies is controlled during precipitation and calcination to facilitate the formation of aggregates which are easiest to breakup during milling. Powder (aggregate and crystallite) size and shape control permits the production of aluminas having desired packing and/or sintering characteristics. Intense milling can produce very fine particle sizes but also may introduce intolerable amounts of contamination from the milling media. Careful control of the Bayer
90
2 Oxide Ceramics
process and calcination/milling conditions can give commercial aluminas of up to 99.99% purity. As shown in the Table 2-16 normal Bayer alumina grades contain about 0.5 wt.% Na 2 O which degrades many properties. The Na ion is mobile in an electric field causing deterioration of electrical properties and it can be leached during wet processing unfavorably influencing rheology, pH and slip stability. If sodium P alumina (Na 2 O • 11A12O3) forms on sintering the density, strength, thermal shock and corrosion resistance are all negatively impacted. Consequently, there is significant demand for low soda alumina. Table 2-17 indicates the Na 2 O contents required for common applications of calcined Bayer alumina powders (MacZura et al., 1992). Low soda alumina is produced by i) using low soda gibbsite prepared by adjusting the Bayer process precipitation conditions (US Patent 4014985); ii) washing alumina prepared at 900 °C that has a very high surface area followed by further hightemperature calcining to a alumina; or iii) adding chlorine, halides, sulfate or borates which react to form volatile or soluble sodium salts which can then be readily removed (e.g., French Patent 1389829, US Patent 3092452). Reactive alumina powders are defined (Southern, 1991) as those that give high fired densities at relatively low (i.e., about 1550-1600 °C) firing temperatures in a > 99.5% alumina body. For high reactivity the Bayer alumina is processed to be pure, fine, equiaxed and a phase. However, if the particle size is too small, handling and processing problems may give low green density and poor sintering. Reactive powders require low soda but high surface area. Table 2-18 (Southern, 1991) illustrates the effect of these variables on sintered density for several alumina powders, powder 3 be-
Table 2-16. Typical chemical analyses of Bayer process aluminas. Composition (wt.%) A12O3 SiO 2 Fe 2 O 3 Na 2 O
Normal Na 2 O >98.9-99.7 0.02-0.05 0.04-0.05 0.3-0.6
Low Na 2 O
Reactive
99.5-99.8 0.07-0.12 0.04-0.06 <0.13
>99.5 0.04-0.08 0.01-0.02 0.08
Table 2-17. Maximum Na 2 O content and particle sizes of aluminas for particular applications (MacZura et al., 1992). Application
]Median crystal Na 2 O content size (jam) range (%)
Electronic ceramics Sodium vapor lamps Structural ceramics Fused abrasives Ceramic fibers High tech. refractories Spark plugs
<0.5-5 <0.5 <0.5-5 <0.5-l <0.5-l 0.5-3 2.5->5
< 0.02-0.1 <0.02-0.1 0.02-> 0.4 0.2 - > 0 . 4 0.2-0.4 <0.1-0.25 0.02-0.2
Table 2-18. Effect of sodium content and surface area on reactivity of alumina (Southern, 1991). Alumina Na 2 O (wt.%) Surface area (m2 g"1) Milled surface area (m 2 g - 1 ) Sintered density (g cm ~3) 2h 1500°C 2h 1550°C 2h 1600°C 2h 1650°C
1
2
3
0.36 0.4 4.4
0.37 5.4 7.5
0.08 6.8 7.6
3.17 3.31 3.49 3.63
3.80 3.87 3.89 3.89
3.85 3.91 3.89 3.92
ing the most reactive. Reactive alumina powders are used in those applications requiring the best high-temperature mechanical behavior such as in zirconia toughened alumina, ZTA, and SiC-reinforced alumina ceramic matrix composites, CMCs.
91
2.4 AI 2 O 3 , Alumina, Sapphire, Corundum
Very high purity alumina powders are commercially prepared using alum, NH4A1(SO4)2 • 12H 2 O, as a starting material (Reed, 1988). Alum dissolves readily into aqueous solution at moderate temperatures. After filtering and purifying the solution, the alum is reprecipitated. The high purity alum is then calcined to yield high purity alumina. An alternate technique for producing high purity powders is the sol-gel process (Klein, 1987; Brinker and Scherer, 1990).
Table 2-19. Compositions of refractory grade alumina. Composition (wt.%) A12O3 SiO2 Fe 2 O 3 Na 2 O TiO 2 MgO Bulk density gem" 3 Porosity vol.%
Tabular
Fused White
Brown
>99.1 0.01-0.02 0-0.3 0.02-0.36
>99 0.02-0.05 0.03-0.15 0.02-0.5 0.02-0.02
3.56
3.86
95.5 1.2 0.18 0 2.6 0.45 3.92
3
3
1
2.4.2.1 Fused and Tabular Refractory Grades
Tabular grade refractory alumina powder is 99.9% pure with a low porosity and controlled particle size and shape (Fig. 2-31). Tabular aluminas are used extensively in alumina-graphite refractories, and
Figure 2-31. Milled tabular alumina powder.
in low-cement and ultra low cement castable refractory mixes. Tabular alumina crystals are produced by heating pellets of calcined alumina, 2 cm diameter, at temperatures > 1925 °C, just below the melting temperature, until near 100% conversion of the fine, oc-alumina crystallites into large (40 to > 200 pm), hexagonal, elongated tabletshaped crystals occurs. The recrystallized alumina is in the massive state and tabular alumina crystals are hard and dense with good thermal conductivity and high crushing strength. A wide range of particle sizes (25 jim to 6 mm) are made by crushing and grading the tabular alumina. Table 2-19 lists the composition and properties of tabular and fused alumina. In the process used to produce fused alumina the batch is mixed, charged and melted in a Higgins-type electric arc furnace using graphite electrodes with a removable, water-cooled, steel shell. The fused refractory grain is massive and requires crushing to obtain the desired particle size. Fused alumina is produced in two forms: white and brown. White fused alumina is made from calcined Bayer alumina
92
2 Oxide Ceramics
and different grades are available based on alkali content. It is used extensively in high-temperature refractory bricks as well as monolithic refractories. Brown fused alumina is made from bauxite ore under conditions which allow only partial removal of impurities as ferrosilicon. The residual impurities in the product lowers its melting temperature by about 50 °C, but it is much tougher than white fused alumina and has superior wear resistance. This less costly material is commonly used in refractories for blast furnace troughs and as induction furnace linings. X-ray diffraction of brown fused alumina reveals predominately a-Al 2 O 3 peaks whereas the higher Na 2 O content of white fused alumina (a residue from the Bayer process) produces detectable amounts of N a 2 O l l A l 2 O 3 ((3-alumina). 2.4.2.2 Abrasives
Alumina abrasives are commonly used in grinding wheels and coated abrasive paper (emery). The conventional route to synthesis of abrasive grain involves melting alumina powder, adding MgO dopant for grain size control, and allowing the melt to solidify. While used extensively, this route does have some drawbacks including: i) variations in cooling rate result in a variable product with a wide range of crystallite sizes and formation of unwanted MgAl 2 O 4 spinel; ii) the need to crush the solid abrasive which requires extensive, and energy intensive, grinding (unsuitablysized grains are discarded and recycled to the melt); iii) the high temperatures required are costly to achieve. An alternative sol-gel production route does not suffer from these disadvantages. Abrasive alumina can be made via a colloidal sol-gel production process in which aqueous pseudoboehmite particles are
peptized to a colloidal dispersion with acid addition. The sol is doped by adding an Mg salt, gelled and dried. The brittle, but soft, gel can be crushed and sieved prior to calcination to produce oc-alumina. This allows fine grit to be produced with far less energy consumption than is necessary when grinding dense oc-alumina. Calcination at 135O°C gives alumina with a 300 nm crystallite size which is much smaller than the melt-derived fused grain and imparts improved abrasive properties. Alumina-zirconia grain may also be manufactured using a similar route (Segal, 1989). 2.4.2.3 Fibers
Aluminosilicate ceramic fibers based on alumina have been commercially available for many years. The largest use for highalumina aluminosilicate refractory fibers (containing less than 28 wt.% silica) is as high-temperature low-thermal-mass furnace insulation. The non-continuous or wool-like fibers are used as loose wool, blankets, felts, paper and board. The loose wool is made by melt spinning or air jet blowing of kaolin-based materials. In the melt spinning process the molten material is fed onto a vertically oriented, rapidly rotating disc from which fibers are thrown by centrifugal force. In the blowing process the molten material is poured into the path of a high-velocity blast from a stream of compressed air which shreds the stream into droplets and elongates them into fibers (Cooke, 1991). Only melts containing substantial amounts of silica are suitable for these processing routes. The resultant fibers therefore are of limited refractoriness, which precludes their use in CMCs. However, fibers with 52% alumina can be used as insulation up to 1250°C and those containing 65% A12O3 can be used up to 1450°C.
2.4 AI 2 O 3 , Alumina, Sapphire, Corundum
Non-continuous alumina fibers were developed in the 1970s (Sowman, 1988) using a sol-gel processing route from a basic aluminum chloride salt starting solution. The sol is doped with a silica source which acts as a grain growth inhibitor. The fiber wool is made by dry centrifugal spinning of a controlled viscosity sol and the green fiber is then calcined to ceramic. The benefit of this route over using kaolin-based melts is that lower silica contents can be used since melt fluidity is not a factor in fabrication, yielding fibers that are more refractory. The room temperature fracture strengths of commercial alumina fibers are typically in excess of 1 GPa; note the fiber is still only 96% alumina. Continuous alumina fibers were developed in the late 1970s and are produced on a much smaller scale than the insulating fibers discussed above (Stacey, 1988). Commercial continuous alumina fibers are dry spun, drawn or extruded from an alumina precursor which may be a solution, sol or slurry dispersion to give green fibers which are calcined, often in several stages, to form the ceramic fiber. For example, one process uses a starting mixture of basic aluminum chloride in solution with 0.5 jim a-Al 2 O 3 and dissolved organic polymers such as polyvinyl alcohol. These processing routes are flexible in terms of the compositions that can be employed but require careful control of quite complex process conditions. The microstructure of the final product is strongly affected by purity, uniformity, molecular weight and size distribution of the starting material used as well as by processing conditions. During the development of the fiber microstructure from the amorphous precursor various intermediate transition aluminas form before the thermodynamically stable a-Al 2 O 3 . Grain growth and pore shrinkage accompany the formation of the
93
different transition aluminas as the temperature is increased. The main effect of silica or magnesia additions during processing is to increase the stability region of r| and 5 aluminas and to restrict grain growth, respectively. Most fibers are made from gel precursors fired at 1000-1300 °C so they may often consist of these intermediate polymorphs and not a-Al 2 O 3 . Grain growth and consequent strength degradation limits the temperature of fiber use as a reinforcing phase. Additionally, phase transformations may occur if the fiber is not in the thermodynamically stable state. A recent development is the growth of single-crystal pure alumina fibers from a melt using a modified Czochralski method termed edge-defined film-fed growth (EFG) developed by LaBelle (1980). In this technique the fiber is grown through a small diameter molybdenum crucible and wound continuously onto spools. Various crystal orientations can be grown and the properties of one commercial fiber are given in Table 2-15. Obvious benefits of single crystal fibers for high-temperature CMC reinforcements include the lack of weakening grain boundary phases and no propensity for grain growth. In addition to the EFG process, it is possible to grow continuous single crystal alumina fibers using the laser heated float zone (LHFZ) technique. In this method of fiber production a small molten zone is produced by local heating of a cylindrical rod using a CO 2 laser {X = 10.6 jim) as a focused heat source, see Fig. 2-32. The molten zone is held in place by surface tension. A tapered seed fiber is brought into contact with the molten tip of the feed rod and lowered until it is wet by the liquid. The pull rate of the seed fiber and feed rate of the feed rod are adjusted to allow growth of crystals with the required dimensions. The absence of containers eliminates
94
2 Oxide Ceramics
which failed at nearly the same applied stress are shown in Fig. 2-33 b. It was observed that the critical flaw in DS-eutectic fiber was considerably larger, implying a higher fracture toughness. 2.4.3 Ceramic Fabrication and Microstructural Evolution
Figure 2-32. Laser heated floated zone of a chromedoped single crystal alumina fiber. An extruded green rod is fed upwards through a brass mandrel into the region heated by the laser at which point fusion occurs. The dark band immediately above the fusion zone is carbon due to combustion of the organic binder. (Courtesy of A. Sayir, CWRU)
contamination from crucible corrosion, can allow for more efficient outgassing of the melt and permits the use of very large thermal gradients during growth (Haggerty etal., 1976). In addition to single-phase alumina fibers, it is possible to produce directionally solidified (DS) eutectics such as A12O3 -YAG (yttrium-aluminum-garnet). Data on the failure strength of experimental A12O3 and DS-eutectic A12O3-YAG fibers are compared in Fig. 2-33 a and the failure origins on two representative fibers
High density, high-alumina ceramics can be categorized as a) those densified with the aid of a liquid by viscous flow and b) those where there is essentially no liquid phase and sintering is via the solid state. Solid state sintered aluminas are highly pure (>99.7wt.% A12O3) requiring very pure starting powders and careful processing. They are used in the most demanding applications requiring good mechanical properties and/or extreme corrosion resistance at high temperature such as sodium vapor lamp envelopes. Liquid phase sintered, LPS, aluminas are less pure typically ranging from 80-99.7% A12O3. Although, it should be noted, there is some doubt as to whether 0.3% impurities is sufficient for LPS. Many high alumina LPS compositions with only small amounts of grain boundary glass are used for electrical and engineering applications. For example, 96% A12O3 compositions are used as substrates in microelectronic circuits. 2.4.3.1 Bulk Single Crystal Alumina
Bulk single crystal alumina is exploited in a number of commercial applications beyond the structural fibers discussed in Sec. 2.4.2.3. Historically, the first commercial uses of synthetic sapphires and rubies were as jewelry, abrasion resistant thread guides, components in the clockwork mechanism in watches and draw plates for wire drawing (Belyaev, 1980). Another more familiar applications is that of ruby, chromium doped single crystal alumina, as
2.4 AI 2 O 3 , Alumina, Sapphire, Corundum
ISiS (a) 4000 ,—
As-received ^sapphire fiber
3000
Tensile Strength MPa
200
As-grown YAG-AI fiber
°
1000
I (b)
0
I
I
1
1
1
1
200 400 600 800 1000 1200 1400
95
Figure 2-33. (a) A comparison of the fracture surfaces of directionally solidified A12O3/YAG eutectic fiber (left) and c-axis sapphire (right). The high tensile strength of the eutectic fiber, 911 MPa, in spite of the large flaw size (void) « 3.3 jim demonstrates the dramatic improvements against crack propagation (high toughness). The sapphire fibers have low toughness and are highly sensitive to small surface and internal flaws (voids). In this case, a fiber with a »1.4um flaw fractured with a tensile strength of 400 MPa. (b) The tensile strength of directionally solidified A12O3/Y3A15O12 (YAG) eutectic fibers as a function of temperature. This oxide-oxide aligned microcomposite fiber system has been engineered to have strength retention at elevated temperatures (800 MPa at 1400 °C). High temperature strength is retained in the eutectic system due to the presence of the non-twinable YAG phase. High temperature creep resistance is attributed to the large aspect ratio (thickness to length) of the eutectic structure along the fiber axis, resulting in a high dislocation climb barrier. (A. Sayir, CWRU and L. E. Matson, Wright Laboratories, Wright-Patterson Air Force Base, OH)
Temperature °C
the active optical element for an important class of solid state lasers. Variants of the EFG process have led to the exploitation of the unique combination of properties offered by single crystal alumina in diverse applications. These include: substrates for silicon-on-sapphire integrated circuits; arc tubes for lighting applications; hollow fibers as optical waveguides for medical applications of lasers; and (one of the most important
commercial applications) as abrasion resistant windows for supermarket laser scanners. One example of the flexibility of the EFG process is the hemispherical missile dome shown in Fig. 2-34. 2.4.3.2 Solid State Sintering
Solid state sintering of polycrystalline alumina developed from a commercial need (see, for example, Bennison and
96
2 Oxide Ceramics
Figure 2-34. An example of bulk single crystal aluminum oxide. A hemispherical missile dome fabricated using the EFG process. (Saphikon, Inc., Milford, NH)
Harmer, 1990 a). In the late 1950s researchers at the General Electric Company laboratories in the USA required a translucent material which was resistant to alkali attack at high temperatures for use in envelopes in sodium-vapor discharge lamps, the sort now used extensively for street lighting. The primary problem was the inherent opacity in sintered material due to the presence of pores which efficiently scatter visible light. Coble (1961) determined that the addition of 0.25 wt.% MgO enabled alumina to be sintered to a finegrained, low porosity, translucent state after firing at 1900°C in hydrogen atmosphere, see Fig. 2-35. This material was given the trade name Lucalox for transLUCent ALuminum OXide. Determining the mechanism(s) of grain growth inhibition in A12O3 by MgO has been a major research task ever since the pioneering work of Coble. However, early studies of solid state sintering were complicated by the presence of both liquid phases
at the grain boundaries (produced by unintentional impurities) and porosity due to agglomerates in the starting powder. Only recently have these difficulties been overcome. For example, Handwerker et al. (1989) have shown that the growth of large, anisotropic, and facetted grains in nomi-
Figure 2-35. SEM image of cquiaxcd grain structure in high-density MgO-doped alumina (from Handwerker et al., 1989).
2.4 AI 2 O 3 , Alumina, Sapphire, Corundum
nally undoped alumina was due to the presence of a liquid phase at sintering temperatures. In a set of experiments employing very high purity material, Bennison and Harmer (1990 b) have demonstrated that the MgO suppresses grain boundary migration rate by a factor of 50 times. Rodel and Glaeser (1990 a, b) have further shown that the effect of MgO is dependent on the crystallography of the individual grains. The effect of MgO doping in model experiments was to suppress the migration of the {1120} planes. The results of Baik and Moon (1991) suggest an indirect effect producd by MgO doping. Both Mg and Ca (always present, even in the most pure aluminas) segregate to grain boundaries. The segregation of Ca is highly sensitive to crystallographic orientation whereas Mg is insensitive. When both Ca and Mg are present, the anisotropy of Ca segregation is reduced. 2.4.3.3 Liquid Phase Sintering
Most commercial aluminas have intentional additions of CaO and SiO 2 . SiO 2 has low solubility in the alumina and segregates to the grain boundaries forming a liquid phase at high temperature. The effect of MgO-doping in liquid phase sintering is analogous to that observed for solid state sintering; the grains of LPS alumina without MgO are anisotropic and facetted whereas the presence of MgO in LPS A12O3 homogenizes the grain size distribution. The abnormal grain growth, see Fig. 2-36, in commercial-purity alumina comes from the presence of impurities, such as Ca and Si, in the glassy grain boundaries (Handwerker et al., 1989). Chemical inhomogeneities in the starting powders are, in fact, more likely to be responsible for ab-
97
Figure2-36. Microstructure after lOmin. at 1440 °C of an alumina containing substantial liquid-forming impurities (from Morrell, 1985).
normal grain growth than morphological inhomogeneities such as large grains or hard agglomerates. A qualitative correlation is observed between faceted discontinuously grown grains and a liquid phase at the facet-matrix interface during sintering. Song and Coble (1990) observed platelike abnormal grains in alumina doped with 0.25 mol.% of Na 2 O + SiO 2 , CaO + SiO 2 , SrO + SiO2 and BaO + SiO 2 . They determined that the driving force for platelike grain formation is the difference in solubility between growing and shrinking grains due to the curvature and anisotropic interfacial energies of A12O3 with respect to the liquid. Grain growth is controlled by pore drag until the compact reaches a critical density, beyond which the interfacial reaction step of the dissolution-precipitation process becomes controlling. The dopants both increase the interfacial reaction rate and make the basal plane the lowest energy plane. Hansen and Phillips (1983) observed facetting on the (0001), {1012} and {1120} planes in 99.8% LPS alumina. The addition of MgO in addition to other liquid forming impurities leads to an equiaxed microstructure with a narrow distribution of dihedral angles close to
98
2 Oxide Ceramics
120° suggesting that all grain boundary energies are about equal. MgO therefore has a homogenizing effect of the LPS microstructure and the MgO reduces the anisotropy of alumina similar to its effect in solid state sintered alumina. In LPS alumina, however, the grains may still be abnormally large compared to solid state sintered alumina. The mechanism of this homogenizing effect must be entirely different when liquid is present; it has been suggested that the MgO changes the wetting behavior of silicate liquids in alumina. It is known (Handwerker et al., 1989) that addition of MgO to the system increases the solubility of SiO 2 in alumina leading to a reduction in silica content at grain boundaries when MgO is present. Kaysser et al. (1987) determined that the growth rates of matrix grains decreased in the order: undoped A12O3, Al 2 O 3 + anorthite, Al 2 O 3 + anorthite + MgO, A12O3 + MgO. They attributed this behavior to differences in mobility between clean grain boundaries and those with intergranular glass. If the glass is inhomogeneously distributed throughout the microstructure this will lead to coarsening as grains grow at different rates. TEM studies have indicated that silicate liquid only wets the long <0001> facets on alumina grains and not the ends. Shaw and Duncombe (1991) also found that an anorthitic glass only wets some grain boundaries in alumina depending on the mismatch in crystallographic orientation across the boundary. In summary, MgO is a microstructural stabilizer in both solid state and LPS alumina. MgO reduces the grain boundary mobility through solid solution pinning leading to a reduced tendency for poregrain boundary separation, protection against abnormal grain growth arising from inhomogeneous green state components, and/or non-uniform liquid phase
distribution. It is interesting to note that the microstructures resulting from anisotropic grain growth and/or in the presence of liquid are more likely to display desirable R curve behavior since the elongated grains can serve as bridges to apply crack closure forces in the crack wake (see Chap. 7, Sec. 7.3.4.2). 2.4.3.4 Microstructures of Commercial Aluminas and Relation to Properties
The microstructures formed in commercial aluminas are closely related to the macroscopic properties. Morrell (1985) subdivides commercial aluminas into six categories in terms of the wt.% alumina content i.e. Solid state sintered: Liquid phase sintered:
>99.7 i) 99.0-99.7 ii) 96.5-99.0 iii) 94.5-96.5 iv) 86-94.5 v) 80-86
Pure a-Al 2 O 3 is denser, harder, stiffer and more refractory than most silicate ceramics so that increasing the proportion of second phase in an alumina ceramic tends in general to decrease the density, Young's modulus, strength, hardness and refractoriness (Morrell, 1987). However, fabricating products with the higher alumina contents is expensive requiring pure starting materials and high firing temperatures. Intentional additions are made to alumina for a number of reasons including: lowering the firing temperature, allowing cheaper, less pure starting materials to be used, improving rheology in shape forming and modifying the properties of the product (Morrell, 1987). A broad range of materials are commercially available with a concomitant broad range of properties. Trends in data given in the following sec-
99
2.4 A I 2 0 3 , Alumina, Sapphire, Corundum
tions are meant as a general guide, Other microstructural variables such as, porosity, grain size and second phase composition may also have important effects on properties such as strength and thermal conductivity. Solid state sintered alumina is produced from high purity powders which densify to give single-phase ceramics with uniform grain size. Products fired in air may contain some residual porosity but firing in reducing atmosphere (usually hydrogen) leads to complete elimination of porosity. Firing is usually in air at 1600-1700 °C. The reason for the persistence of ^ 5 % porosity is simply that in the last stages of sintering all of the pores are isolated within the oxide matrix. Therefore further shrinkage of the pore requires the gas within the pore to dissolve in the oxide and diffuse to the external surface. Nitrogen is not soluble in alumina at the sintering temperature and therefore the pores only shrink until the increased internal gas pressure balances the reduction in surface energy driving the process. Coarse-grained translucent alumina used for sodium vapor lamp envelopes is fired at 1700-1800 °C in hydrogen to improve the rate of elimination
of porosity. The material is fired in hydrogen since the hydrogen has a relatively large solubility and high diffusivity. It is fired at high temperatures to increase the average grain size. Since alumina has an index of refraction which is anisotropic (see Table 2-15), some light scattering occurs at each grain boundary. The large grain size reduces the linear density of grain boundaries and thereby increases the total transmission for visible light. When 99.8% A12O3 is used in very high temperature refractory applications, for example as crucibles, MgO cannot be used since it is prone to evaporation at high temperature. As a result, aluminas used in these applications typically have coarse-grained microstructures. These "recrystallized" alumina refractories are relatively weak, see Table 2-20, as a result of the large mean grain size. When even small amounts of MgO, as low as 0.1 % are added to control grain growth the resultant LPS alumina is much stronger and can be used in applications requiring high temperature insulating ability, i.e., in kiln furniture and thermocouple insulation and for small section and thin walled components, e.g., rods or tubes.
Table 2-20. Typical properties of high density alumina. A12O3 (wt.%) Density (g cm ~ 3) Hardness (GPa), HV 500 g RT Fracture toughness, XIC (MPa m1/2) Young's modulus (GPa) Bend strength (MPa) at RT Thermal expansion coefficient (10~6/K) 200-1200°C Thermal conductivity at RT (W/mK) Firing range (°C) a b
"recrystallized" without MgO with MgO
>99.9
>99.7 a
>99.7 b
99-99.7
3.97-3.99 19.3 2.8-4.5 366-410 550-600 6.5-8.9
3.6-3.85 16.3 — 300-380 160-300 5.4-8.4
3.65-3.85 15-16 — 300-380 245-412 5.4-8.4
3.89-3.96 15-16 5.6-6 330-400 550 6.4-8.2
38.9 1600-2000
28-30 1750-1900
30 1750-1900
30.4 1700-1750
100
2 Oxide Ceramics
Vehicle-
Film Substrate Grain boundary glass Wet Film
Dry Film
Underfired
Fired Film
Overtired
Figure 2-37. Schematic illustration of the firing of thick film circuitry on the surface of a debased (glass-containing) alumina substrate. During firing the glass forms a mechanical interlock between the substrate and the metallic layer. If the system is overfired the glass is rejected entirely from the metal, resulting in a weak bond.
Many engineering alumina ceramics contain 99-99.7% alumina and so have a significant glass content. Grain sizes in the range 2-25 jim are typical and the products can be particularly strong (Table 2-20). The fine grain sized 99% aluminas may be used in demanding applications such as hip prostheses whereas coarser grained materials are preferred for electrical insulation. Aluminas with 94.5-99% A12O3 have a large proportion of grain boundary glass which must be of carefully controlled composition to confer the required densification behavior and final state properties. The grain boundary glass is usually an aluminosilicate containing additional oxides such as CaO or MgO. Microstructures in aluminas where the glass is used simply as a densification aid show a uniform distribution of alumina crystals completely separated by glass. In other aluminas which are fired to higher temperatures some recrystallization of the alumina may occur to give an interconnected network. In these materials pores are usually located at the
interface between the alumina and the glass. Typical properties are given in Table 2-21. Although these aluminas cannot be used in applications requiring very high temperature stability they can be tailored for use in many electrical applications. The second phases present depend in general on the composition used, the firing temperature, and the cooling rate (more glass being present with faster cooling). Phases such as anorthite (CaAl2Si2O8), mullite (Al6Si2O13), cordierite (Mg 2 Al 4 Si 5 O 18 ) and celsian (BaAl2Si2O8) may form on cooling or be crystallized from the glass by prolonged heating above 900 °C. PowellDogan and Heuer (1990) characterized the microstructures of a series of 96% alumina ceramics containing 2 - 3 wt.% SiO 2 , 0.41.4wt.% MgO, 0.06-1.5 wt.% CaO and 0.05-0.25 wt.% Na 2 O. The ease of crystallization was observed to be strongly dependent on the MgO to CaO ratio in the intergranular glass phase. The mechanical properties of glass-containing alumina ceramics have been observed to depend on
101
2.5 Zirconia
Table 2-21. Typical properties of debased alumina. A12O3 (wt.%) Density (gcm~3) Hardness (GPa), HV 500 g Young's modulus (GPa) Bend strength (MPa) Thermal expansion coefficient (x 10"6/K) 200-800 °C Thermal conductivitiy at RT (W/mK) Firing range (°C)
99-96.5
94.5-96.5
86-94.5
80-86
3.73-3.8 12.8-15 300-380 230-350 8-8.1
3.7-3.9 12-15.6 300 310-330 7.6-8
3.4-3.7 9.7-12 250-300 250-330 7-7.6
3.3-3.4 — 200-240 200-300 —
24-26 —
20-24 1520-1600
15-20 1440-1600
— —
the thermal expansion coefficient of the glass and the extent of crystallization (Powell-Dogan etal., 1991; Knapp and Cawley, 1991). In particular, the volume change associated with the devitrification of the grain boundary glass appears to induce microcracking which degrades the fracture strength. The presence of a grain boundary glass is not, however, necessarily deleterious. For example, the metallization of a substrate is often necessary to allow brazing or soldering and to provide a conducting surface. Procedures such as the molymanganese process (Kohl, 1967), or thick-film circuitry (Harris and Lall, 1991) rely on interactions during firing between the powder particles, which are painted on, and pre-existing intergranular glass. Figure 2-37 provides a schematic of the microstructural development in a thick-film circuit. The thick-film paste, which is a mixture of desired metals or conductors and a low temperature melting glass frit, is painted on the desired region and the substrate. During firing the metal particles fuse together to provide the conduction path while the glass particles fuse and begin to dissolve the more refractory glass in the ceramic substrate. The result is a strong bond with graded properties.
Aluminas with 80-94.5% A12O3 are generally used as electrical insulators or low-temperature mechanical components or refractories. The glass-bonded insulators and mechanical components are fired < 1500 °C and may suffer viscous flow of the glass at comparatively low temperatures. If non-equiaxed alumina particles are used, the fluid nature of the glass during processing may allow their reorientation leading to anisotropic grain structures and properties.
2.5 Zirconia The traditional applications of ZrO 2 and ZrO 2-containing materials are foundry sands and flours, refractories, ceramic and paint pigments and abrasives. These applications still account for most of the tonnage used. However, the thermomechanical and electrical properties of zirconia-based ceramics have led to a wide range of advanced and engineering ceramic applications. Early reviews of the then state of knowledge of ZrO 2 are given by Ryshkewitch (1960) and Garvie (1970). The recent level of research interest in ZrO2 can be gauged by examining the series of conference proceedings on the Sci-
102
2 Oxide Ceramics
ence and Technology of Zirconia (published by the American Ceramic Society Volumes I-IV (1981, 1984, 1988, 1992). Tough, wear resistant and refractory, ZrO 2 is being developed for applications such as extrusion dies, machinery wear parts, and piston caps. Composites containing ZrO 2 as a toughening agent such as ZTA (zirconia toughened alumina) also show promise in applications such as cutting tools. Ionically-conducting ZrO 2 can be used as a solid electrolyte in oxygen sensors, fuel cells, and furnace elements (see Chap. 1, Sec. 7 and Chap. 11, Sec. 4 of this Volume). 2.5.1 Mineral Sources and Powder Production
The main source of zirconia is the mineral zircon (ZrSiO4) which typically contains significant A12O3, HfO2 and TiO 2 impurity. Commercial zircon is mined from beach sand sources with large deposits found in Australia, India, South Africa, Russia, China and the USA most of which are used directly in the manufacture of refractories for basic steelmaking and glass tank furnace linings, as investment and sand casting foundry sands and flours (for mold washes), and abrasives (Garnar, 1983). Another source of ZrO 2 is the mineral baddeleyite, which is 80-90% monoclinic ZrO 2 with TiO 2 , HfO 2 , SiO2 and Fe 2 O 3 as the major impurities. Commercial baddeleyite deposits are found in Brazil and South Africa. Production of zirconia can be considered in terms of four stages (Clough, 1985): a) zircon decomposition, b) dissolution of Zr species, c) precipitation of Zr species and d) calcination to ZrO 2 . There are two main processes used in zircon decomposition: thermal decomposition into SiO 2 and ZrO 2 ; and chemical decomposition into Zr and Si-containing compounds (Heathcote,
1991). The technique used depends on the purity, particle size, morphology and surface area required in the product. A common thermal decomposition method involves injection of zircon sand into a plasma arc above 6000 °C where it melts and dissociates into the constituent ZrO 2 and SiO 2 . The material is rapidly quenched as it leaves the plasma and therefore recombination does not occur. The spheroidised product is then either a) boiled with caustic soda to dissolve and remove the silica or b) treated with sulfuric acid to dissolve and remove the ZrO 2 as sulfate. Zircon is also thermally decomposed by reaction with carbon forming a cyanonitride which readily oxidizes to ZrO 2 . The chemical decomposition methods can be further subdivided into two groups, attack by chlorine and attack by alkalis. Zircon sand can be chlorinated by reacting it with coke and Cl 2 at 800-1200°C to produce gaseous ZrCl 4 and SiCl4 which are separated by condensers. The zirconium tetrachloride gas is bubbled through water to form a solution of ZrOCl 2 . Zircon can also be decomposed by reacting with oxides, hydroxides and carbonates from groups IA or IIA of the Periodic Table such as NaOH, Na 2 CO 3 and CaO. Reaction with NaOH or Na 2 CO 3 at high temperature forms sodium zirconate, sodium zirconate silicate and sodium silicate (Farnworth et al., 1980). The sodium silicate is removed by leaching with water, the zirconate ions hydrolize to form a complex hydrated hydroxide. In either process the Zr-containing decomposition product is dissolved in an acidic solution. Pure ZrO 2 is isolated from the acid-soluble impurities by precipitation and the product calcined. In some cases "stabilizing oxides," such as CaO, MgO or Y 2 O 3 (see Sees. 2.5.2 and 2.5.3) may be coprecipitated with the ZrO 2
2.5 Zirconia
or dispersed as a salt (e.g., yttrium nitrate) with the zirconia powder during spray drying. Many novel techniques for the production of ultrapure ZrO 2 powders are currently being examined. For example, powders have been prepared by fusion casting (Blackburn et al., 1988), vapor phase reaction (Hori et al, 1984), hydrothermal precipitation (Hishinuma et al., 1988) and solgel processing (Tokudome and Yamaguchi, 1988). In general, these techniques are characterized by high raw material and processing costs and therefore they are likely to be used only in specialized applications. 2.5.2 Crystal Structure, Polymorphism and Physical Properties of Single Crystal ZrO 2
Zirconia occurs in three well established polymorphs: monoclinic (m), cubic (c) and tetragonal (t), see Chap. 1, Sees. 1.3.1 and 1.7 of this Volume. In pure ZrO 2 the monoclinic phase is stable up to 1170°C above this temperature it transforms to tetragonal symmetry and then to cubic symmetry at 2370 °C before melting at 2680 °C. The transformation from monoclinic to tetragonal exhibits a hysteresis. The transformation from t to m on cooling occurs over a temperature range of about 100 °C below 1170°C. The transformation to monoclinic is martensitic and during cooling results in a volume increase on the order of 3-4%. This volume change is sufficient to exceed the elastic limit of the ZrO 2 grains and cause cracking. Thus the fabrication of large, pure zirconia bodies is impossible. However, Garvie et al. (1975) proposed using this transformation to improve both the strength and toughness of ZrO 2 ceramics. They suggested that metastable tetragonal particles constrained in a cubic matrix
103
could be caused to transform to monoclinic symmetry when a propagating crack relieves the constraint. The volume change and shear strain associated with the martensitic reaction oppose the opening of the crack so increasing the resistance of the ceramic to crack propagation i.e. increasing its toughness. Reviews of so-called "transformation-toughening" in zirconia alloys are given by Green et al. (1989), Evans (1984) and Claussen (1984). It should be recognised, however, that the toughness and strength increases arising from the presence of tetragonal ZrO 2 particles in a cubic matrix come from several sources including crack deflection (as found in all two phase ceramics), transformation toughening and microcracking (Faber and Evans, 1983). A more complete discussion of the toughening of ceramics in general and transformation toughening in particular is given in Chap. 8, Sec. 8.3, respectively. In powder mixtures, the polymorphs of pure ZrO 2 can be differentiated using Xray diffraction although distinguishing between cubic and tetragonal peaks is difficult. Garvie and Nicholson (1972) and Schmid (1987) describe XRD techniques for quantitative analysis of mixtures of the zirconia polymorphs. However, in a ternary system of cubic, tetragonal and monoclinic, there is no real possibility of quantitative analysis using XRD. Under such circumstances, the only accurate method is neutron diffraction (Howard and Hill, 1991). Distinguishing between polymorphs becomes more difficult in ZrO 2 alloy systems. The lattice constants are known to vary with the type and concentration of the anion and distortion of the unit cell affects the structure factor. Consequently, quantitative analysis in the alloy systems is difficult. Systematic experimental calibration is
104
2 Oxide Ceramics
Table 2-22. Physical properties of single crystal zirconia. Polymorph Melting point (°C) Density (g cm ~ 3) Hardness (GPa), HV 500 g Thermal expansion coefficient (xl0- 6 /K)0-1000°C Thermal conductivity (W/mK)
100 °C 1300°C
Refractive index
Cubic a
Tetragonal
Monoclinic
2500-2600 5.68-5.91 7-17 7.5-13
2677 6.10 12-13 8-10 || a-axis 10.5-13 || c-axis
— 5.56 6.6-7.3 6.8-8.4 || a-axis 1.1-3.0 || b-axis 12-14 || c-axis
1.675 2.094 2.15-2.18
Properties dependent on stabilizer type and content, typical ranges given.
needed and, while equations have been developed, they should only be applied to the specific system and thermal history for which they were determined (Evans et al., 1984). Table 2-22 lists some typical properties of single-crystal zirconia. 2.5.3 Ceramic Fabrication and Microstructural Control of Binary Zirconia Alloys
The high melting temperature and chemical inertness of pure ZrO 2 make it an attractive material for applications as a refractory. However, during thermal cycling the displacive tetragonal-to-monoclinic transition leads to gross cracking. Most applications of zirconia therefore require that the structure be fully- or partially-stabilized through alloying with alkaline earth or rare earth oxides. The term "stabilized" refers to a kinetic stabilization of a solid solution in the cubic polymorph to room temperature. By avoiding formation of a tetragonal phase at intermediate temperatures the displacive transformation of that polymorph to monoclinic is avoided at low temperature. Full stabilization refers to compositions which exhibit single phase behavior from absolute zero
to the solidus. Although such alloys avoid the deleterious volume change of the t - m transition, thermal shock resistance is still an important issue. This is due to a simultaneous increase in the thermal expansion coefficient and a reduction in the thermal conductivity. The low thermal conductivity tends to cause steep thermal gradients during heating or cooling and the high thermal expansion coefficient results in large thermal strains, or high stresses. The discovery that thermal shock resistance was improved by only adding enough of the alloying element to partially stabilize the cubic phase led to the use of the partially stabilized zirconia (PSZ) as a refractory and its later development as an engineering ceramic due to its high toughness arising from transformation toughening. In addition to the most commonly used stabilizers (the oxides of Ca, Mg, Ce, and Y) virtually all the rare earth elements form solid solutions with zirconia. In general, where the zirconium ion is in eight fold coordination (i.e. tetragonal or cubic) ions will stabilize the zirconia phase provided that the ionic radius is within approximately 40% of that of Zr 4 + . The exact mechanism of stabilization remains unclear. In some cases it appears that the pro-
2.5 Zirconia
portion of ionic bonding is increased which renders the cubic structure more stable. In addition, many alloy additions promote anion ordering (the cations remain disordered) rendering a more stable lattice. The behavior, processing and microstructure of partially stabilized zirconias are discussed in terms of the binary phase diagrams and the type of heat treatments used in processing the material to obtain the optimum microstructure in the following sections. 2.5.3.1 ZrO 2 -MgO The diagram reported by Grain (1967) is the most widely reported and is shown in Fig. 2-38. A typical composition for a magnesia-partially stabilized zirconia, MgPSZ, may be around 8 mol.% MgO. The first step in processing involves a solution heat treatment in the cubic single phase field (2-4 h at about 1800°C depending on composition) followed by a rapid cool. This quench is too rapid to allow the equi-
105
librium amount of tetragonal phase to precipitate out, but it does promote homogeneous nucleation of very fine tetragonal precipitates. The maximum cooling rate must, however, be limited to avoid thermal shock. Reheating to 1400 °C and holding isothermally (aging) leads to coarsening of the tetragonal particles by rejection of MgO into the cubic matrix. If overaging is avoided, the resultant microstructure is one of finely divided precipitates in a cubic matrix. Small tetragonal particles, 0.2 |im, may be metastably retained upon cooling due to the presence of the cubic matrix. Coarser particles spontaneously transform to monoclinic symmetry during cooling. The microstructure of an optimally processed Mg-PSZ containing metastable tetragonal or monoclinic precipitates in a cubic matrix is shown in Fig. 2-39. If the tetragonal precipitates are above a critical size they will transform to monoclinic symmetry either spontaneously or as a result of applied stress. It should be noted that this critical size depends on many
2200
p
1800 -
HI
cc Z>
LU £L
1400
-
1000
-
LU
5
10
MOLE % MgO
15
Figure 2-38. Zirconia-rich end of the ZrO 2 -MgO phase diagram (from Grain, 1967). The shaded region indicates the composition range of commercial MgPSZs.
106
2 Oxide Ceramics
Figure 2-39. Bright-field TEM image of the microstructure of an optimally-aged Mg-PSZ consisting of oblate tetragonal precipitates in a cubic matrix (courtesy of A. H. Heuer, CWRU).
factors including the degree of constraint (whether particles are in a bulk matrix or powder form), temperature and composition. The influence of the precipitates including the effect of particle shape and size on the fracture strength and toughness of dense ceramics is discussed in detail in Chap. 8, Sec. 8.3.1. Commercial Mg-PSZ undergoes a further sub-eutectoid ageing treatment at 1100°C to improve the room temperature properties. The microstructure of commercial PSZ is rarely optimized; more usually it is that produced by a furnace cool after sintering in the single cubic phase field, or possibly a rapid cool from the sintering temperature to an isothermal hold temperature. This heat treatment schedule allows more heterogeneous nucleation of tetragonal particles to take place. Consequently, a thicker grain boundary tetragonal film is produced which spontaneously transforms to monoclinic on cooling. In addition, heterogeneously nucleated precipitates form within the grains. Such precipitates grow rapidly during a subsequent isothermal hold at 1400 °C. The precipitates thus formed, are also large enough to transform to monoclinic on cooling, thereby reducing
the total residual metastable tetragonal available for transformation toughening. It is well known that grain boundary structure strongly influences the properties of ceramics, for example, impurity grain boundary phases can provide crack nucleation sites and reduce high temperature strength. With PSZ materials, the starting powders invariably contain 0.1-0.4% SiO 2 , some A12O3 together with other impurities (Leach, 1987). The SiO 2 arises from two main sources. In coprecipitated powders, SiO2 is derived from the precursor ZrSiO 4 . If the powder is further milled using silica milling media, the SiO2 level increases, arising from wear debris of the milling media (Ruhle et al., 1984). In MgO and Y 2 O 3 doped zirconia ceramics, a silicate grain boundary liquid forms which acts as a sintering aid. In MgO-PSZ, the grain boundary phase, its distribution and wettability, depend on the Mg silicate formed. Forsterite (Mg2SiO4) occurs as isolated pockets and appears to be nonwetting whereas enstatite (MgSiO3) exhibits wetting behaviour spreading along all grain boundaries. The isolated forsterite particles, strongly associated with monoclinic regions, are thought to reduce the extent of microcracking by making nucleation of the tetragonal to monoclinic transformation more difficult. The loss of MgO from the matrix to the grain boundary does, however, promote the formation of monoclinic to the detriment of mechanical properties. Recently, Drennan and Hannink (1986) have discovered that addition of 0.25% SrO enhances mechanical properties by altering the grain boundary phases. 2.5.3.2 ZrO 2 -CaO There are strong analogies between CaPSZ and Mg-PSZ. Although there have
2.5 Zirconia i
^^^
2500 -
v
2000 -
i
L + CaZrO 3
i
\
Css
LJJ QC
QC
107
C s s + CaZrO3
1500
LU
1 3 1 0 ± 40°C
1140 ± 4 < \ y - • - ^ C s + CaZr O S 4 9
LU
TS8-*- CaZr 4 Og
M
/ "
/
0 ZrO2
CaZr4O9 +
CaZrO 3
30
40
Mss+ CaZr4O9 10
20 CaZr 4 O 9
50 CaZrO 3
Figure 2-40. Part of the ZrO 2 -CaO phase diagram (from Hellman and Stubican, 1983).
MOLE % CaO
been numerous examinations of the C a O ZrO 2 phase diagram, the version proposed by Stubican and Ray (1977) and further refined by Hellman and Stubican (1983 a, b) has been generally adopted and is shown in Fig. 2-40. The stability of the CaZr 4 O 9 has not been definitively proven, and consequently it is omitted in some versions (e.g. Stubican et al, 1984) which include instead Ca 6 Zr 1 9 O 4 4 (at 27 mol.% CaO). Different temperatures and compositions have been reported for the eutectoid decomposition. Marder et al. (1983) reported a temperature of 1000 °C and 15 mol.% CaO when decomposing a cubic solid solution. Alternatively, Hellman and Stubican (1983 a, b) report a eutectoid temperature of 1140±40°C and a composition of 17 + 0.5 mol.% CaO, on prolonged heat treatment of reactive powders. The latter technique would be expected to achieve equilibrium more rapidly and therefore may be regarded as more reliable.
As with other zirconia systems, the eutectoid transformation is very sluggish, and is, therefore, not usually seen in conventionally heat treated samples, and metastable extensions of the phase fields dominate. A large cubic phase field exists which, in conjunction with the sluggish eutectoid transformation, allows a fully cubic structure to be retained by rapid cooling, and this is the basis of e.g. calcia stabilized zirconia solid electrolytes. In particular, as with the MgO system, the structure actually consists of cubic containing a fine distribution of homogeneously nucleated tetragonal particles. Suitable heat treatment allows the growth of these particles to a point where they become metastable and will transform with the application of stress from a propagating crack. The best mechanical properties are achieved at a particle size of about 0.1 jim. However, the temperature/composition window where such a treatment is practicable is small.
108
2 Oxide Ceramics 2500
2000
iilk
\ UJ
\ U. (
1500
cr
tss
< UJ
a.
PSZ
1
\
'
\
*ss +
V \
1000
Css
\
c
TZP
ssM 500
\
\ m
m
ss
ss + c ss \ \
1
2 Y2O3
t
1
1
4
6
8
10
Figure 2-41. Zirconia-rich end of the ZrO 2 -Y 2 O 3 phase diagram (Scott, 1975). The shaded regions indicate the compositions and processing temperatures for commercial partially stabilized zirconia (PSZ) and tetragonal zirconia polycrystals (TZP).
CONTENT (mole %)
OOiVmj
Figure 2-42. Bright-field TEM image of the microstructure of Y-TZP. Note the fine grain size and lack of porosity (courtesy A. H. Heuer, CWRU).
2.5.3.3 ZrO 2 -Y 2 O 3 The phase diagram proposed by Scott (1975), Fig. 2-41, is universally quoted since it agrees well with experimental findings, although there have been more recent studies. In particular, those of Riihle et al. (1984) and Lanteri et al. (1984) have at-
tempted a more accurate assessment of the position of the t / t + c and t + c / c phase boundaries. The most significant feature of this diagram is the extensive solubility for Y 2 O 3 in the terminal tetragonal solid solution. Up to approximately 2.5 mol.% Y 2 O 3 will be taken into solid solution which, in conjunction with the low eutectoid temperature, allows a fully tetragonal ceramic to be obtained (so-called tetragonal zirconia polycrystals or TZP) first reported by Rieth et al. (1976). Fine grain sizes are obtained by using ultra fine powders and sintering in the range 1400-1550 °C where the coarsening rate can be controlled (see Fig. 2-42). Similar to the critical precipitate size in PSZ materials, TZP ceramics exhibit a critical grain size (about 0.3 jim) above which spontaneous transformation occurs leading to low strength and toughness. The critical size depends on the composition (being about 0.2 jim for 2 mol.% Y 2 O 3 and 1.0 ^m for 3 mol.% Y2O3) and the degree of mechanical constraint.
2.5 Zirconia
TZPs have a significant advantage over Mg-PSZs because sintering can be carried out at comparatively low temperatures (1400-1550 °C compared to 1800°C) bringing the production of TZPs within the scope of existing furnaces in ceramic manufacturing plants. The bulk of commercial TZPs contain 2-3mol.% Y 2 O 3 and mainly consist of fine equiaxed tetragonal grains of a diameter typically in the range 0.2-2 jim. In addition, many materials contain a small amount of cubic phase, the grain size of which is usually larger than the tetragonal phase. Although cubic is more common in the highly stabilized materials, being ubiquitous in those with 3 mol.% Y 2 O 3 and above, it is also present with lower solute additions especially where inhomogeneous powders are used. The uncertainty of the ZrO 2 rich end of the phase diagram, in particular the position of the t /1 + c phase boundary makes an accurate prediction of the amount of cubic difficult. In a survey of 10 commercially available TZPs containing 2 - 3 mol.% Y 2 O 3 Riihle et al. (1984) found cubic phase ranging from 0 to 42%. The morphology of the cubic phase varied, but often contained fine (10 nm) tetragonal precipitates, believed to form during slow cooling from sintering. The grain morphology of the polycrystals varies; although well faceted grains are more typical, rounded grains are observed in materials containing an appreciable amount of silicate glass phase at the grain boundary. A grain boundary glass often plays an important role in sinterability. In one experimental study ultra-pure coprecipitated powders were difficult to sinter whereas the same powders sinter easily after milling. This effect was presumed to be the result of the presence of a silicate liquid produced by contamination from the milling media. However, the composition of the glass can
109
have a significant effect on properties. Lin et al. (1990) showed that an aluminosilicate glass leached out the Y stabilizer whereas a borosilicate glass did not. Leaching of the stabilizing component led to less desirable mechanical properties in the sintered TZP. In a systematic study Riihle et al. (1984) found a wide variation in the microstructures of commercial TZPs. Large solute variations were reported both within grains and throughout the ceramic. The variation within a grain is a result of the slow diffusion of the solute within ZrO 2 , although transport is rapid along the grain boundary glassy phases. However, the dramatic variations in solute concentration from grain to grain in many TZP's indicated that they had not reached equilibrium at the end of sintering. This was thought to be a result of the mixed oxide powder processing route employed. It was also suggested that A12O3 had been added deliberately by some manufacturers. Different starting powders gave a variation in toughness from 5.5 to 11 MPa m 1/2 for nominally identical solute levels. A large cubic plus tetragonal phase field exists in the ZrO 2 -Y 2 O 3 system which permits the formation of a PSZ structure. In this region, sintering has to be conducted at higher temperatures (up to 1700°C) to ensure sufficient yttria is taken into solution for the generation of fine, metastable tetragonal particles. Although in many ways analogous to Mg-PSZ and Ca-PSZ, the structures formed in Y-PSZ are more complex. Under conditions of slow cooling from sintering and subsequent aging, a diffusional reaction occurs giving tetragonal precipitates in a cubic matrix. The morphology of the tetragonal precipitates depends on the aging temperature and time. However, under more rapid cooling conditions a displacive transformation occurs which gives another tetrag-
2 Oxide Ceramics
110
onal phase, commonly called t' (t-primed), which has a lower c/a ratio than the normal tetragonal and contains the same quantity of yttria as the cubic. The microstructures generated in the zirconias with higher yttria contents than 3 mol.% >Y2O3 are generally referred to as partially stabilized since, as with the Mg-PSZs the structure is two phase. 2.5.3.4 ZrO 2 -CeO 2 This system shows a very wide tetragonal phase field as shown in Fig. 2-43 (Tani et al., 1983), with a solubility limit of 18 mol.% CeO 2 . The eutectoid temperature, 1050 °C is somewhat higher than in the Y 2 O 3 system but the size of the tetragonal phase field still makes it possible to retain a fully tetragonal structure as in the Y 2 O 3 system. Sintering temperatures are very similar, with 1550°C being common,
20
40
(wt7o) 60
80
100
2800 -
Liquid 2400-
V Cubic * 1600
Tet. j Tet.
D • Ol-tr o g. 1200 R D O D
^
Cubic (1050±50'C) A
t—
800
400
and again an ultra fine powder is required to generate a fine grain size in the ceramic. There are many similarities between the Ce and Y-TZPs although a fully tetragonal structure can be obtained in Ce-TZP for CeO 2 additions between 12 and 20 mol.%, representing a much wider range than with Y-TZPs (Tsukuma and Shimada, 1985). The minimum composition required for a fully tetragonal structure clearly depends on the sintering temperature and the grain size produced. Ce-TZPs densify via liquid phase sintering in a similar manner to YTZPs. Ultra-pure powders give low densities, with impurities such as Si and Ca essential for full densification. In addition, Ce-TZPs are more susceptable to reduction during sintering. Even with a plentiful oxygen supply during sintering, the center of a large sample will become discolored, turning orange to brown to black, attributed to a reduction in the oxygen content. For an equivalent fracture toughness, the grain size is larger in Ce-TZP compared to Y-TZPs. For example, a K1C of 12 MPa m 1/2 could be achieved in a YTZP with a grain size of 2 pxn compared to 8 jim in a Ce-TZP (Tsukuma and Shimada, 1985). Very high toughness values can be achieved in these materials, with nominal values of up to 30 MPa m 1/2 being reported, although the absolute value depends strongly on the test method used.
A Mono.
0 ZrO 2
o
\
2.5.4 Properties and Applications of Selected Zirconia Ceramics
o
\
o
2.5.4.1 Mg-PSZ Monoclinic Cubic
20
40 60 (mol°/o)
80
100 CeO2
Figure 2-43. ZrO 2 -CeO 2 phase diagram constructed by Tani et al. (1983).
Representative mechanical and thermal properties for commercial PSZs are given in Table 2-23. While a useful guide the data should be treated with caution since the particular values obtained depend on the test method especially for K1C. Further, these general values are, of course, affected
111
2.5 Zirconia Table 2-23. Physical properties reported for commercial partially stabilized zirconias (PSZ).
Wt.% stabilizer Hardness (GPa) RT fracture toughness, K1C (MPa m 1/2 ) Young's modulus (GPa) Bend strength (MPa) RT Thermal expansion coefficient (x 10~ 6 /K) at 1000°C Thermal conductivity at RT (W/mK) 2.8% MgO,
b
4% CaO,
c
Mg-PSZ
Ca-PSZ
Y-PSZ
Ca/Mg-PSZ
2.5-3.5 14.4a 7-15 200 a 430-720 9.2a
3-4.5 17.1 b 6-9 200-217 400-690 9.2 b
5-12.5 13.6C 6 210-238 650-1400 10.2c
3 15 4.6 — 350 —
1-2
1-2
1-2
1-2
5% Y 2 O 3
700 -
Modulus of Rupture (MPa)
2
3 4 Stabilizer (wt. % MgO)
by material variables in the ceramic microstructure (stabilizer content, grain size etc.) and external variables such as atmosphere and temperature. Figure 2-44 shows the effect of MgO content on the bend strength and fracture toughness of various MgPSZs while Fig. 2-45 shows the effect of temperature on the bend strength and fracture toughness of a commercial Mg-PSZ (Dwovak et al., 1984). 2.5.4.2 Y-TZP Typical mechanical and thermal properties for commercial TZPs are given in Table 2-24. The exact yttria content in Y-
Figure 2-44. Bend strength and fracture toughness behavior of various Mg-PSZ ceramics at room temperature (from Dworak et al., 1977).
TZP plays an important role in the transformability of the tetragonal phase and therefore the toughness (Fig. 2-46). Toughness is also a strong function of grain size (Fig. 2-47). A major obstacle to the full exploitation of TZP ceramics is that spontaneous surface transformation of tetragonal to monoclinic occurs if the ceramic is held at temperatures in the range of 150-250°C at times ranging from hours to days, which can lead to severe degradation in strength. In the worst case, complete material disintegration can occur. The extent of surface degradation is greatly enhanced by the presence of water vapor at temperatures
112
2 Oxide Ceramics
Test Conditions 4 point bending dG/d = 1.75MPa/sec
Fired Temp. • 1400°C A 1 500°C O 1600°C
12
Bend Strength 400(MPa) 300-
\
2001000 0
250 500 750 Temperature (°C) ->
1000
3
4
Mol % Y 2 O 3
Figure 2-46. Fracture toughness (Klc) of Y-TZP ceramics as a function of Y 2 O 3 content and sintering temperature (from Tsukuma et al, 1984). 10 Mg - PSZ (ZN40) Single Edge Notched Beam
- 2 m/o yttria - zirconia
A'
12 Fracture 5Toughness (MPaVm)
K,c MPax/m 4 _-
0
250 500 750 Temperature (°C) ->
1000
0
A i
i
1
2
Grain Size Gum)
Figure 2-45. Bend strength and fracture toughness, Klc, of a commercial Mg-PSZ as a function of temperature (Dworak et al., 1984).
Figure 2-47. Grain size dependence of the fracture toughness (XIC) for a 2mol.% Y-TZP (from Swain, 1986).
Table 2-24. Typical physical properties of tetragonal zirconia polycrystals (TZP).
below 200 °C and is accelerated as the water vapor pressure is increased (Sato et al., 1985; Sato and Shimada, 1985). The final amount of monoclinic produced at 200 °C is constant, indicating that water vapor effects the rate of degradation rather than the equilibrium. Matsumoto (1985) has demonstrated that full strength recovery is possible if the degraded sample is annealed at 1000 °C for 24 h. This is little comfort for engineers, however. Alternative strategies lie in the addition of ceria and alumina to the TZP (Sato etal., 1986; Nettleship and Stevens,
Y-TZP Mol.% stabilizer Hardness (GPa) RT fracture toughness, Klc (MPa m1/2) Young's modulus (GPa) Bend strength (MPa) Thermal expansion coefficient (x 10 " 6 /K) 20-1000 °C RT thermal conductivity (W/mK)
2-3
10-12 6-15
Ce-TZP 12-15 7-10 6-30
140-200 800-1300 9.6-10.4
140-200 500-800
2-3.3
—
—
2.5 Zirconia
1987) or reducing the grain size below that at which microcracking occurs. Additions of CeO 2 decrease the amount of degradation to the point that no monoclinic is observed with the addition of 10% CeO 2 to 3 Y and 4 Y, and 15% CeO 2 to 2 Y (Sato and Shimada, 1985; Sato et al., 1986). However, additions exceeding 6 - 8 % CeO 2 yield a material with compromised mechanical properties (Sato et al., 1984). Additions of A12O3 to TZP reduce transformability by increasing matrix constraint and reduce, but do not eliminate, the degradation (Sato and Shimada, 1986; Tsukama and Shimada, 1985). Zirconia ceramics have the highest toughness of any ceramic which, combined with high strength, hardness and chemical resistance, should allow their application in harsh environments under severe loading conditions. Wear resistant applications of Mg-PSZ as drawing dies, bearings, seals and bone replacement devices (mostly ball and socket joints) have been developed. The low thermal conductivity of ZrO 2 can be used to advantage in automotive engines in piston crowns, head face plates and piston liners so that heat loss from the combustion chamber can be reduced and flame temperature increased resulting in higher efficiency. Wear resistant applications in engines include those in the valve train as cams, cam followers, tappets and exhaust valves. The thermal expansion coefficient of zirconia closely matches that of cast iron so that these materials can be joined (typically by an active substrate process with a Ti-based bond) to give relatively inexpensive automotive components. PSZ refractory crucibles, shaped by slip casting or isostatic pressing are used in vacuum induction or air melting of refractory metals such as Co-base alloys or precious metals such at Pt, Pd or Rh. The relatively high cost of ZrO 2 compared to
113
other refractories limits its use to special applications where it has particularly desirable properties. PSZ is comparatively stable to both acid and basic slags and molten steel. This amphoteric behavior, combined with its superior erosion and thermal shock resistance, enables its use for submerged entry tundish nozzles in continuous casting of steel. PSZ inserts are also used in alumina-graphite sliding and rotary gate valves when high oxygen or calcium-bearing steels are used and increased corrosion/erosion resistance is required. Zirconias are also used in a number of cutting applications for difficult materials such as glass fibres, magnetic tape, plastic film and paper items such as cigarette filters (Stevens, 1986). 2.5.4.3 ZTA Composites
Zirconia has been added to a variety of other oxide matrices such as mullite, spinel, cordierite, zircon and MgO in order to improve their toughness. The first system developed was zirconia toughened alumina (ZTA) simultaneously with the PSZ systems (Claussen, 1976). This material demonstrated that the inclusion of unstabilized zirconia can lead to retention of t-ZrO 2 in the sintered product if the particle size is small enough. The toughening mechanism primarily involves transformation and microcrack formation although dispersion strengthening is also active in this system. Less than 20 vol. % zirconia unstabilized particles are typically used although subsequent work has attempted to increase the ZrO 2 content by partial stabilization of the zirconia with Y 2 O 3 , CeO 2 or TiO 2 (Lange, 1982). Unstabilized ZTA's can have strengths of 1200 MPa and toughnesses of 16MPam 1 / 2 with about 15vol.% ZrO 2 compared to values of 600 MPa and 4 MPa m 1/2 respectively for
114
2 Oxide Ceramics
Figure 2-48. Backscattered electron SEM image of ZTA containing 18 vol.% ZrO 2 . The light phase is the
typical dense alumina. The dual phase microstructure is clearly seen in the backscattered SEM image of Fig. 2-48 where the zirconia is the light phase. ZTA was first used as toughened abrasive for industrial grinding wheels where large improvements in grinding efficiency were detected over conventional materials. Other applications are found in metal cutting tools and engine components.
2.6 Summary The crystal structures, mineral sources and powder synthesis, processing methods, and microstructure-property relationships of the industrially important single oxides share many common features. However, the end uses of MgO, A12O3, and ZrO 2 vary greatly. MgO is rarely used as a polycrystalline ceramic due to its large thermal expansion and tendency to react at room temperature with atmospheric water and carbon dioxide. Instead, it is used in refractories (where its high melting point is an advantage) with a coarse grain and some form of prophylactic protection such as an organic resin. A12O3 suffers no such problem and is most commonly liquid phase sintered to give a polycrystalline
ceramic whose microstructure can be tailored to give a range of properties. Alumina is a "workhorse ceramic", which, while having no outstanding single property, offers an exceptional combination of very reasonable properties (mechanical, optical, and electronic). With ZrO 2 , proper chemistry and careful microstructural control allow phase transformations to be exploited to yield ceramics with outstanding strength and toughness. Zirconia is being applied to uses previously thought outside the realm of ceramics, notably in engine components. Furthermore, its unique electrical properties lead to a wide variety of applications in sensor applications. While the properties of these ceramics and the silicates may differ considerably, one of the intentions of this chapter was to illustrate that the principles behind the microstructure-processing-property relations are in essence the same for dinnerware, a refractory brick, or a hip prosthesis. Oxide ceramics were one of the first materials utilized by mankind and as a result of recent developments, some of which were discussed in this chapter, it is clear that exciting new applications will continue to be found for them in the future.
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2.7 References
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2 Oxide Ceramics
Kendall, K. (1978), Proc. Roy. Soc. A361, 245. Kindl, B., Carlsson, D. X, Deslandes, Y, Hoddenbagh, J. M. A. (1991), J. Can. Ceram. Soc. 60, 5 3 58. Kingery, W. D., Bowen, H. K., Uhlmann, D. R. (1976), Introduction to Ceramics, 2nd ed. New York: Wiley. Klein, L. C. (1987), Sol-Gel Technology for Thin Films, Fibers, Preforms, Electronics, and Specialty Shapes. Park Ridge, NJ: Noyes. Klein, C , Hurlbut, C. S. (1985), Manual of Mineralogy, 12th ed. New York: Wiley. Knapp, X X, Cawley, X D. (1991), Metal-Ceramic Joining: Kumar, P., Greenhut, V. A. (Eds.). Warrendale, PA: TMS, pp. 181-204. Kohl, W H. (1967), Handbook of Materials and Techniques for Vacuum Devices. New York: Reinhold. Kroger, F. A. (1974), in: The Chemistry of Imperfect Crystals, Vol. 2; 2nd ed. New York: North-Holland, p. 14. LaBelle, H. E. (1980), / Cryst. Growth 50, 8-17. Lange, R R (1982), /. Mater. Sci. 17, 255. Lanteri, V., Heuer, A. H., Mitchell, T. E. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia II. Columbus, OH: American Ceramic Society, pp. 118-130. Le Chatelier, H. L. (1887), Bull. Soc. Fr. Mineral 10, 204-211. Leach, C. A. (1987), Mater. Sci. Technol. 3, 321 -324. Lee, W. E., Heuer, A. H. (1987), /. Am. Ceram. Soc. 70, 349-360. Lehman, R. L., Weinstein, J. G., Phelps, G. W, Adams, K. M. (1984), Bull. Am. Ceram. Soc. 63, 1039-1050. Lin, Y-X, Angelini, P., Mecartney, M. L. (1990), /. Am. Ceram. Soc. 73, 2728-2735. MacKenzie, K. J. D., Brown, R W. M., Meinhold, R. H., Bowden, M. E. (1985), J. Am. Ceram. Soc. 68, 293-297. MacKenzie, K. J. D., Brown, I. W. M., Meinhold, R. H., Bowden, M. E. (1986), J. Am. Ceram. Soc. 68, 266-272. Mackrodt, W. C. (1984), in: Advances in Ceramics, Vol. 10: Structure and Properties of MgO and A12O3 Ceramics. Columbus, OH: American Ceramic Society, pp. 62-78. MacZura, G., Moody, K. X, Anderson, E. M. (1992), Bull. Am. Ceram. Soc. 71, 780-782. Marder, J. M., Mitchell, T. E., Heuer, A. H. (1983), Ada Metall. 31, 387. Matsumoto, R. (1985), J. Am. Ceram. Soc. 68, C213. McColm, I. J. (1983), Ceramic Science. Glasgow: Blackie and Sons. Mikami, H. M. (1983), Ceram. Eng. Sci. Proc. 4, 9 7 118. Millot, G. (1978), Sci. Am. 240 (4), 109-118. Morrell, R. (1985), Handbook of Properties of Technical and Engineering Ceramics, Part 1: An Introduction for the Engineer and Designer. London: HMSO.
Morrell, R. (1987), Handbook of Properties of Technical and Engineering Ceramics, Part 2: Data Reviews. London: HMSO, Sec. 1. Moulson, A. X, Herbert, J. M. (1991), Electroceramics: Materials, Properties and Applications. London: Chapman and Hall, pp. 206-221. Nettleship, I., Stevens, R. (1987), Int. J. High Tech. Ceram. 3, 1-32. Niesz, D. E., Bennett, R. B. (1978), in: Ceramic Processing Before Firing: Onada, G. Y, Hench, L. L. (Eds.). New York: Wiley. Norton, F. H. (1976), Fine Ceramics: Technology and Applications. New York: McGraw Hill. O'Bannon, L. S. (1984), Dictionary of Ceramic Science and Engineering. New York: Plenum Press. Phelps, G. W. (1976), Bull. Am. Ceram. Soc. 55, 528532. Pierre, A. C , Uhlmann, D. R. (1986), in: Materials Research Society Proceedings. Vol. 73: Better Ceramics through Chemistry. New York: Elsevier, pp. 481-487. Powell-Dogan, C. A., Heuer, A. H. (1990), /. Am. Ceram. Soc. 73, 3670-3676; 3677-3683; 36843691. Powell-Dogan, C. A., Heuer, A. H., Readey, M. X, Merriam, K. (1991), J. Am. Ceram. Soc. 74, 648649. Reed, J. S. (1988), Introduction to the Principles of Ceramic Processing. New York: John Wiley. Reiger, K. C. (1992), Bull. Am. Ceram. Soc. 71, 821. Rieth, P. H., Reed, J. S., Naumann, A. W. (1976), Bull. Am. Ceram. Soc. 55, 111. Robertson, I. D. M., Eggleton, R. A. (1991), Clays Clay Miner. 39, 113-126. Rodel, X, Glaeser, A. M. (1990a), / Am. Ceram. Soc. 73, 3292-3301. Rodel, X, Glaeser, A. M. (1990b), /. Am. Ceram. Soc. 73, 3302-3312. Riihle, M., Claussen, N., Heuer, A. H. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia II. Columbus, OH: American Ceramic Society, pp. 352-370. Ryshkewitch, E. (1960), Oxide Ceramics. New York: Academic Press. Sainamthip, P., Reed, J. S. (1987), Bull. Am. Ceram. Soc. 66, 1726-1730. Sato, T., Shimada, M. (1985), / Am. Ceram. Soc. 68, 356. Sato, T., Shimada, M. (1986), in: Ceramics for Engines, Proc. 2nd Int. Conf. Mat. Engines, LubeckTravemunde. pp. 291-298. Sato, T., Ohtaki, S., Endo, T., Shimada, M. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia II. Columbus, OH: American Ceramic Society, pp. 29-37. Sato, T., Ohtaki, S., Shimada, M. (1985), /. Mater. Sci. 20, 1466-1470. Schmid, H. K. (1987), J. Am. Ceram. Soc. 70 (5), 367-376. Scott, H. G. (1975), / Mater. Sci. 10, 1527-1537.
2.7 References
Segal, D. (1989), Chemical Synthesis of Advanced Ceramic Materials. London: Cambridge University Press. Seron, A., Beguin, R, Bergaya, R (1992), Mater. Set Forum, 91-93. Shaw, T. M., Duncombe, P. R. (1991), /. Am. Ceram. Soc. 74, 2495-2505. Shinohara, K. (1991), in: Powder Technology Handbook, Iinoya, K., Gotoh, K., Higashitani, K. (Eds.). New York: Marcel-Dekker, pp. 481-501. Singer, R, Singer, S. S. (1963), Industrial Ceramics. London: Chapman and Hall. Song, H., Coble, R. L. (1990), /. Am. Ceram. Soc. 73, 2077-2085. Southern, X C (1991), Brit. Ceram. Proc. 47, 1-12. Sowman, H. G. (1988), Am. Ceram. Soc. Bull. 67 (12), 1911-1916. Srikrishna, K., Thomas, G., Martinez, R., Corrall, M. P., De Aza, S., Moya, J. S. (1990), J. Mater. Sci. 25, 607-612. Stacey, M. H. (1988), Br. Ceram. Trans. J. 87, 168172. Stevens, R. (1986), An Introduction to Zirconia. Twickenham, UK: Magnesium Elektron. Stubican, V. S., Ray, S. P. (1977), /. Am. Ceram. Soc. 60, 534-537. Stubican, V. S., Corman, G. S., Hellman, J. R., Senft, G. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia II. Columbus, OH: American Ceramic Society, pp. 96-106. Sugahara, Y, Kuroda, K., Kato, C. (1984), J. Am. Ceram. Soc. 67, C-247-C-248. Sugahara, Y, Sugimoto, K., Kuroda, K., Kato, C. (1988), /. Am. Ceram. Soc. 71, C-325-C-327. Swain, M. V. (1986), /. Mater. Sci. Lett. 5, 11591162. Tani, E., Yoshimura, M., Somiya, S. (1983), /. Am. Ceram. Soc. 66, 506-510. Taylor, J. R., Bull, A. C. (1986), Ceramics Glaze Technology. Oxford: Pergamon Press, 21 -22; 132-134.
117
Tokudome, K., Yamaguchi, T. (1988), in: Advances in Ceramics, Vol. 24: Science and Technology of Zirconia III. Columbus, OH: American Ceramic Society. Tsukuma, K., Shimada, M. (1985), J. Mater. Sci. 20, 1178-1184. Tsukuma, K., Kubota, Y, Tsukidate, T. (1984), in: Advances in Ceramics, Vol. 12: Science and Technology of Zirconia. Columbus, OH: American Ceramic Society. Van Olphen, H. (1977), Colloidal Chemistry of Clays. New York: Wiley. Velde, B. (1985), Developments in Sedimentology, Vol. 40: Clay Minerals: A Physico-Chemical Explanation of Their Occurrence. Amsterdam: Elsevier. Viera, J. M., Brook, R. J. (1984), in: Advances in Ceramics, Vol. 10: Structure and Properties ofMgO and A12O3 Ceramics. Columbus, OH: American Ceramic Society, pp. 438-463. Warshaw, S. I., Seider, R. (1967), /. Am. Ceram. Soc. 50, 337-343. White, J. (1970), in: High-Temperature Oxides, Part 1: Magnesia, Lime and Chrome Refractories, Alper, A. M. (Ed.). New York: Academic Press, pp. 77141. Williams, P., Taylor, D., Soady, X S. (1990), in: Proc. Conf. Refractories for the Steel Industry Commission of European Community. Amsterdam: Elsevier. Wilson, S. X (1979), Br. Ceram. Soc. Proc. 28, 281294. Worrall, W. E. (1986), Clays and Ceramic Raw Materials. London: Elsevier. Yager, T. A., Kingery, W D. (1984), in: Advances in Ceramics, Vol. 10: Structure and Properties of MgO and A12O3 Ceramics. Columbus, OH: American Ceramic Society, pp. 139-151. Yamaguchi, A. (1984), Taikabutsu Overseas 4,14-18.
3 Nitride Ceramics Stuart Hampshire
Materials Research Centre, University of Limerick, Limerick, Ireland
List of 3.1 3.2 3.3 3.3.1 3.3.2 3.3.2.1 3.3.2.2 3.3.3 3.3.3.1 3.3.3.2 3.3.4 3.3.5 3.3.5.1 3.3.5.2 3.3.5.3 3.3.5.4 3.3.6 3.3.6.1 3.3.6.2 3.3.6.3 3.3.7 3.3.8 3.3.9 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.4.5.1 3.4.5.2 3.4.5.3 3.4.6
Symbols and Abbreviations Introduction Transition Metal Nitrides Silicon Nitride Historical Development Crystal Structure Structures of a and (3 Silicon Nitrides The ot-p Silicon Nitride Phase Transformation Reaction-Bonded Silicon Nitride (RBSN) Overview of the Reaction-Bonding Process Reaction Mechanisms and Microstructural Development Formation of Silicon Nitride Powders Formation Routes for Dense Silicon Nitride Hot-Pressed Silicon Nitride (HPSN) Sintered Silicon Nitride (SSN) Sintered Reaction-Bonded Silicon Nitride (SRBSN) Hot Isostatically Pressed Silicon Nitride (HIPSN) The Role of Additives in the Densification of Silicon Nitride Formation of Oxynitride Liquids in Silicon Nitride Ceramics Sintering Kinetics Phase Relationships, Microstructure and Effects on Properties Properties of Silicon Nitride Ceramics Oxidation of Silicon Nitride Ceramics Summary of Approaches to Optimisation of Properties Sialons p'-Sialons Phase Relationships in the S i - A l - O - N and Related Systems Sintered P-Sialons Properties of (3-Sialon Ceramics a'-Sialons Introduction The Structure of oc-Sialons Formation of oc-Sialon Ceramics oc/P-Sialon Ceramics
Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.
121 122 122 123 123 124 124 127 127 127 129 132 133 133 134 135 135 136 136 137 140 142 144 148 149 149 150 151 152 153 153 153 154 155
120
3.5 3.5.1 3.5.2 3.5.3 3.5.4 3.5.5 3.6 3.6.1 3.6.2 3.6.3 3.6.4 3.6.5 3.7 3.7.1 3.7.2 3.7.3 3.7.4 3.8 3.8.1 3.8.2 3.8.3 3.8.4 3.8.5 3.9 3.10 3.11 3.12
3 Nitride Ceramics
Silicon Oxynitride Introduction The Silicon Oxynitride Structure Sintering and Properties of Silicon Oxynitride Ceramics O'-Sialon Ceramics O'-P'-Sialons Oxynitride Glasses and Glass Ceramics Introduction Solubility of Nitrogen in Glasses Sialon Glasses Nitrogen Coordination in Oxynitride Glass Structures Nucleation and Crystallisation in Oxynitride Glasses Aluminium Nitride Introduction Structure of Aluminium Nitride Synthesis of Aluminium Nitride Fabrication and Properties of Aluminium Nitride Ceramics Aluminium Oxynitride (A1ON) Ceramics Introduction Structure of A1ON Phase Relationships in the A l - O - N System Formation of A1ON Ceramics Properties of A1ON Ceramics Boron Nitride Future Potential of Nitride Ceramics Acknowledgements References
155 155 155 156 157 157 158 158 158 159 161 161 163 163 163 163 163 165 165 165 166 166 166 167 167 168 168
List of Symbols and Abbreviations
List of Symbols and Abbreviations E AG° AH A//e k M P T Tg
Young's modulus change in Gibbs free energy activation enthalpy enthalpy change of reaction Boltzmann constant Ca, Li or Y ion partial pressure absolute temperature glass transition temperature
Q
density
A1ON AN CVD FTIS HIP HIPSN HPSN RBSN sialon SN SRBSN SSN XPS YAG YAM YN
aluminium oxynitride ceramic aluminium nitride chemical vapour deposition Fourier transform infrared spectroscopy hot isostatic pressing hot isostatically pressed silicon nitride hot-pressed silicon nitride reaction-bonded silicon nitride ceramic from the S i - A l - O - N or related system silicon nitride sintered reaction-bonded silicon nitride sintered silicon nitride X-ray photoelectron spectroscopy yttrium aluminium garnet yttrium aluminate, monoclinic yttrium nitride
121
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3 Nitride Ceramics
3.1 Introduction One of the major advantages of ceramics over metals is their high temperature behaviour, reflected in the fact that ceramics have higher strengths at temperatures above 1000 °C and better oxidation and corrosion resistance. In addition to these advantages, one class of ceramic materials, the nitrides, combine superior hardness with high thermal and mechanical stability, making them suitable for applications as cutting tools, wear-resistant parts and structural components at high temperatures. Transition metal nitrides, because of their extremely high hardness and stiffness, have been developed for wear-resistant applications. They have also generated considerable interest because of their high thermal and electrical conductivities. However, the greatest impetus to research and development on nitride ceramics has been the attempt to produce a ceramic gas turbine engine for which application silicon nitride has been a main contender. Silicon nitride is the primary material in a family of nitride or "nitrogen" ceramics developed for engineering applications and is a generic term used for a variety of types made by different processing methods or having different compositions or both. The attainment of their intrinsic properties requires that attention be given to control of processing and microstructural development. Sialon (Si-Al-O-N) ceramics retain the structure of silicon nitride with incorporation of aluminium and oxygen in solid solution. These ceramics have already been successfully commercially exploited as cutting tool inserts. The other nitride ceramics within the S i - A l - O - N system include silicon oxynitride and aluminium nitride. The latter has intrinsically a very high thermal conductivity, the achieve-
ment of which depends on careful optimisation of processing and microstructure. This chapter provides an overview of nitride ceramics and a more in-depth exploration of silicon nitride and aluminium nitride ceramics including their structure, microstructure, properties and processing.
3.2 Transition Metal Nitrides Nitrides of the transition metals including titanium, vanadium, zirconium, niobium, molybdenum, hafnium and tantalum are extremely hard refractory materials with thermo-mechanical stability and thus find applications as cutting tools, wear-resistant parts (Sproul and Rothstein, 1985) and high-temperature structural components. Previous methods of preparation are outlined by Toth (1971). Several methods involve contact of a metal oxide with solid carbon under nitrogen to achieve reduction and nitridation. Later refinements (Oyama et al., 1988) involve passing a gas over the precursor oxide to produce the nitrides in high surface area form (NbN: 3.6 m 2 g" 1 ; Mo 2 N: 22 m 2 g" 1 ). No report is given of the sinterability of these powders. TiN and ZrN powders are available commercially and they are being used as dispersed phases in other ceramic matrix composites, notably alumina and silicon nitride. In the former case, starting from Al 2 O 3 -TiN, the product consists of A1NTiO 2 . With TiN as a second phase in ceramic composites, electrical discharge machining is feasible in view of the very high electrical conductivity of TiN, which approaches the range for metals. In wear, bearing and cutting applications, transition metal nitrides are applied as coatings, and the chemical vapour deposition (CVD) method has been the most frequently used technique (Stinton et al.,
3.3 Silicon Nitride
1988). This involves depositing the nitride material from gaseous precursors onto a substrate, typically a hard metal such as tungsten carbide. Table 3-1 lists the gaseous mixtures used in CVD processes for transition metal nitrides and the deposition temperatures. Titanium nitride has received more attention than the other nitrides and has been successfully commercialised as a coating for a range of materials including Cobonded WC tool inserts. The coating provides increased hardness and wear-resistance but also prevents reaction of the cobalt binder with the metal workpiece at the high temperatures generated by machining. However, titanium nitride is susceptible to oxidation above 800 °C. Laugier (1988) showed that TiN coatings have a good scratch resistance at all temperatures up to 1050 °C confirming the excellent adhesion of these types of coating. This is due to interdiffusion of Ti and N into the underlying material at the relatively high processing temperature and this produces very high strength bonding at the interface. The use of transition metal nitrides as bulk ceramics rather than coatings has reTable 3-1. Transition metal nitrides produced by CVD (after Stinton et al., 1988).
Coating TiN HfN ZrN TaN VN NbN
Gas mixture
Deposition temperature
TiCl 4 -N 2 -H 2 HfCl x -N 2 -H 2 HfI 4 -NH 3 -H 2 ZrCl 4 -N 2 -H 2 ZrBr 4 -NH 3 -H 2 TaCl 5 -N 2 -H 2 VC14-N2-H2 NbCl 5 -N 2 -H 2
900-1000 900-1000 >800 1100-1200 >800 800-1500 900-1200 900-1300
123
ceived relatively little attention compared with the large research effort on ceramics based on silicon and aluminium nitrides.
3.3 Silicon Nitride 3.3.1 Historical Development Silicon nitride was first mentioned in 1857 by Deville and Wohler and later, in 1910, Weiss and Engelhardt observed the formation of a bluish-white coating on silicon after heating to 1320°C in nitrogen. The chemical formula was given as Si 3 N 4 but it remained a chemical curiosity to researchers, mainly in Germany, until over forty years later, when refractories utilising silicon nitride as a bond for silicon carbide and other materials were developed (Wroten, 1954). At the same time, silicon nitride with good thermal stability was developed for use as thermocouple tubes, crucibles for molten metals and also rocket nozzles (Collins and Gerby, 1955). This type of material was formed by nitriding silicon powder compacts and was later termed reaction-bonded silicon nitride (RBSN). Interest began to grow in this new ceramic material, particularly in Britain, for potential use in gas turbines. Physical, chemical and structural characteristics were investigated and it was clearly established that silicon nitride existed in two crystallographic modifications, a and (3. By 1960, Parr, Martin and May had published a comprehensive review of the properties and structure of silicon nitride (RBSN), outlining the technology which they had developed which would be the major processing route for silicon nitride ceramics for at least the next decade. One of the major obstacles to the use of RBSN in engine applications was its limited mechani-
124
3 Nitride Ceramics
cal strength as a result of the presence of 20-30% microporosity. In 1961, Deeley et al. succeeded in achieving increased densities by hot-pressing previously formed silicon nitride powder with various sintering additives. With magnesium oxide, full density material was produced by hot-pressing at 1850°C under 23 MPa and strength was substantially improved over that of RBSN. Magnesia was also used as the densification additive in the first commercial development of HPSN, although the precise role that the oxide played in densification remained unknown at that time. However, the initial predominantly a silicon nitride powder was observed to transform to the (3 modification during the hot-pressing process, and this was thought to be responsible for the development of high strengths (Lumby and Coe, 1970). In 1971, a full-scale effort to produce the ceramic gas turbine was initiated in the USA. It was realised early in the programme that the objectives would not be achieved, because a major problem was the difficulty of component fabrication, since hot-pressing is limited to simple shapes. It was therefore necessary to consider the possibility of sintering without pressure where shaping could be carried out by more conventional methods. One breakthrough was the discovery of the "sialons" in Japan and Britain (Oyama and Kamigaito, 1971; Jack and Wilson, 1972). These are silicon nitride ceramics in which oxygen can replace nitrogen in the P silicon nitride structure if at the same time silicon is replaced by aluminium to maintain charge neutrality. Pressureless sintering to theoretical density proved feasible provided that a sintering additive such as MgO or Y 2 O 3 is included. Since the 1970s, the search for improved materials has led to a better understanding
of the role of additives in the densification and microstructural development of silicon-nitride-based ceramics and the consequences for final properties. Improvements in powder manufacture and forming techniques and the development of alternative firing process has led to a wide range of materials including RBSN, HPSN, sintered sialons of different types, sintered silicon nitrides (SSN), sintered reaction-bonded silicon nitride (SRBSN) and hot isostatically pressed silicon nitride (HIPSN). 3.3.2 Crystal Structure 3.3.2.1 Structures of a and P Silicon Nitrides
Vassiliou and Wilde (1957) obtained the first evidence for the existence of two forms of silicon nitride by reporting a "hexagonal" type (II) with a different X-ray diffraction pattern from that of the "orthorhombic" (I) silicon nitride extracted from silicon steels by Leslie et al. (1952). Turkdogan et al. (1958) described how changes in the time and temperature of nitriding of silicon affected the X-ray diffraction pattern, some peaks completely disappearing after prolonged nitriding above 1600°C. The silicon nitride remaining was designated |3 and the apparently lower temperature form which disappeared was designated a, both with the same chemical composition (Si3N4) and the same measured densities (3.19 + 0.01 gcm~3). Popper and Ruddlesden (1957) had claimed that the two forms observed previously were (I) orthorhombic and (II) rhombohedral. Following these early misinterpretations of X-ray diffraction patterns, Hardie and Jack (1957), using samples from Turkdogan et al. showed that both forms are hexagonal, the essential difference being that the c dimension of a is approximately twice that of (3, as shown in Table 3-2.
3.3 Silicon Nitride
125
Table 3-2. Comparison of unit cell parameters for oc and p silicon nitrides (Hardie and Jack, 1957). Silicon nitride
Unit cell contents
a (A)
c(A)
c/a
F(A3)
Calculated density (gem" 3 )
a
Si 12 N 16 Si6N8
7.748 7.608
5.617 2.9107
0.7250 0.3826
292.0 145.9
3.184 3.187
P
A complete structure determination assigned P silicon nitride to space group P63/m. The structure is based on the phenacite type, Be 2 SiO 4 , in which the oxygen atoms are replaced by nitrogen and the beryllium atoms by silicon. A further structure refinement (Wild et al., 1972 a) was in broad agreement with the earlier work and the two sets of data for the atomic positions are compared in Table 3-3. The bonding leads to a framework of SiN4 tetrahedra (slightly distorted) joined by sharing nitrogen corners so that each ni-
Table 3-3. Final parameters for (3-Si3N4 (space group P6 3 /m-C 6 2 h , No. 176).
trogen is common to three tetrahedra. The (3 structure is composed of puckered rings of alternating Si and N atoms as shown in Fig. 3-1 (Hampshire etal., 1978). Because the fractional heights are z = 0.25 and 0.75, these joined rings can be considered as layers with a stacking sequence ABAB and forming long continuous channels in the c direction as shown in Fig. 3-2 (Redington, 1989). The oc silicon nitride structure has aroused more controversy. Hardie and Jack (1957) deduced a space group of P 31c.
Idealised Si - N layers
(a) From Hardie and Jack (1957). X
6 Si in 6 (h)at 6N1 in 6 (h)at 2N2 in 2 (c) at
0.172 0.333 0.333
y -0.231 0.033 0.667
z 0.250 0.250 0.250
(b) From Wild et al. (1972 a). X
y
z
6 Si in 6 (h) at
0.1773 ±0.0003
-0.2306 0.0003
0.2500 0.0000
6 Nl in 6 (h) at
0.3323 ±0.0008
0.0314 0.0007
0.2500 0.0000
2 N2 in 2 (c) at
0.3333 ±0.0000
0.6667 0.0000
0.2500 0.0000
Reliability index R = 0.021; number of planes in refinement 61; total number of planes 68.
^•ABAB
Figure 3-1. The AB layers in the crystal structure of (3 silicon nitride (after Hampshire et al., 1978).
126
3 Nitride Ceramics Idealised Si-N layers
OOABCD
Figure 3-2. The ABAB stacking of layers in the p silicon nitride structure giving rise to long continuous channels in the c direction (after Redington, 1989).
Where the layers of atoms in P are linked along the [001] direction in the sequence ABAB, the a structure has the sequence ABCDABCD. The CD layer, shown in Fig. 3-3, is similar to the AB layer except that it is rotated by 180° on the c-axis. The long continuous channels seen in the P (ABAB) form are thus closed off into two large interstices, centred at 1/3, 2/3, 3/8 and 2/3, 1/3, 7/8 (see Fig. 3-4). Wild et al. (1972a), from data on bond lengths and angles, abnormal site occupation numbers, density and oxygen content, concluded that oc silicon nitride was a defect structure with up to 1 in 30 nitrogen atoms replaced by oxygen with corresponding silicon vacancies as in: 1.5-^15
0.5
They proposed that a and p, respectively, are high- and low-oxygen-potential modifications. Roberts et al. (1972) nitrided F e Si alloys at low temperatures (500- 720 °C)
Figure 3-3. The CD layers in the crystal structure of a silicon nitride (after Hampshire et al., 1978).
Figure 3-4. The ABCD stacking of layers in the a silicon nitride structure giving rise to two closed interstices per unit cell (after Redington, 1989).
and found that pure p was only precipitated at very low oxygen potentials whereas oc was formed at higher oxygen potentials, again suggesting that a and P are not merely low and high temperature forms of the same compound. An extensive thermo-
3.3 Silicon Nitride
dynamic investigation of the S i - O - N system, also by Wild et al. (1972 b), supported these conclusions. Marchand et al. (1969) previously found no significant variation in bond lengths and no evidence for segregation of oxygen atoms in the nitrogen positions. Further work by Kohatsu and McCauley (1974) and Kato et al. (1975) concluded that a can exist without a small amount of "stabilising" oxygen. Priest et al. (1973) and Edwards et al. (1974) showed that a forms at much lower oxygen contents than those previously proposed by Wild et al. (1972 a). Jack (1983) later provided evidence showing that 26 different a silicon nitride samples from these different preparation routes had a relatively wide range of unitcell dimensions (a = 7.7491 -7.7572 A; c = 5.6164-5.62213 A), but similar c/a ratios, and concluded that this must be due to variations in their compositions, particularly oxygen content. Clearly, oxygen may indeed stabilise the oc structure, but it is not a necessary requirement. However, as discussed in Sec. 3.3.3, during nitriding of silicon, the formation of a silicon nitride is favoured by the presence of oxygen in the nitriding environment. 3.3.2.2 The a-p Silicon Nitride Phase Transformation The a->p transformation in silicon nitride requires a lattice reconstruction. This type of process occurs usually only when the transforming material is in contact with a solvent. The greater solubility of the more unstable form drives it into solution after which it precipitates as the less soluble, more stable form. A variant of this process may occur in the vapour phase. The transformation is observed during liquid phase sintering of silicon nitride (see Sec. 3.3.6) at temperatures in excess of
127
1400°C where the original a phase is in contact with a metal-silicon-oxynitride liquid. Further discussion of this topic is given in Sec. 3.3.6.2. The thermodynamic investigation of Wild et al. (1972 b) showed that a (containing oxygen) becomes unstable with respect to (3-Si3N4 + Si 2 N 2 O at 1400 °C with R ~10~ 2 0 atm. o2 If p and a silicon nitrides are true high and low temperature polymorphs with a specific transformation, then it should be possible to transform p to oc. However, this has never been observed experimentally, giving further credence to the idea that a is a defect structure. 3.3.3 Reaction-Bonded Silicon Nitride (RBSN) 3.3.3.1 Overview of the Reaction-Bonding Process Reaction-bonded silicon nitride was the first commercially available form of the ceramic and relies on a simple inorganic chemical reaction, the nitridation of silicon: 3Si + 2N 2
(3-1)
The required shape is first formed from silicon powder by techniques such as isostatic pressing or injection moulding. Because the reaction tends to be slow, for useful production rates, high surface area silicon powders must be used (mean particle size <10|im). The silicon compact is then nitrided under an atmosphere of molecular nitrogen starting at 1100°C and slowly increasing the temperature up to 1420 °C (melting point of silicon) over a period of a number of days. Reaction (3-1) is strongly exothermic with AH° ~ — 733kJmol~ 1 . The rate of temperature rise needs to be carefully controlled, to attain adequate reaction rates while holding the temperature below the melting point of
128
3 Nitride Ceramics
silicon or of silicon-metal eutectic temperatures, where other impurities are present. The resulting product usually consists of mixed a and (3 silicon nitrides with 1 5 30% porosity. Figure 3-5 shows micrographs of RBSN at different stages of the nitriding process. The true density of silicon is 2.33 g cm" 3 and that of silicon nitride is 3.187 g cm" 3 so that a volume expansion of 21.7% occurs during nitride formation. Classical sintering does not occur during this process and therefore shrinkage is not a fea-
ture. However, considerable internal rearrangement of the product material can occur within the pre-existing void space of the powder compact and, therefore, the original dimensions of the silicon compact remain virtually unchanged (linear shrinkage <0.1%) during nitriding. This allows complex shapes to be machined to approximately the final size either before nitriding or after partial nitriding. Often, a pre-reaction annealing step under argon at 1100° C is included, which results in slight neck formation between particles as a result of sur-
%-;
SIS?
•mm:
mam
(c)
(b) (d) Figure 3-5. Micrographs of RBSN at different stages of the nitriding process: (a) in the early stages of reaction; (b) when only the large particles are unreacted; (c) two particles, illustrating that reaction does not take place at the nitride-silicon interface; (d) pores migrating inwards in a silicon particle (white: silicon; grey: nitride; black: pores) (after Atkinson et al., 1974).
3.3 Silicon Nitride
face diffusion and strengthens the silicon compact for the machining process. On completion of the nitriding process, the close dimensional tolerances are maintained and the product requires no or very little subsequent machining. The reaction bonding process is thus suitable for economic mass production. 3.3.3.2 Reaction Mechanisms and Microstructural Development
Thermodynamic calculations show (Ziegler et al., 1987) that silicon can react in all physical states with nitrogen according to + 2N 2 (g)^Si 3 N 4 (s) AG°= - 7 2 3 + 0.315 TCkJmol" 1 )
(3-2)
3Si(l) + 2N 2 (g)^Si 3 N 4 (s) AG° = - 8 7 4 + 0.405 T ( k J m o r 1 )
(3-3)
2N 2 (g)-+Si 3 N 4 (s) AG° = -2080 + 0.757 T ( k J m o r 1 )
(3-4)
Reactions (3-2) and (3-3), which are catalysed by impurities such as iron in the silicon powder, usually result in the formation of the P modification whereas a silicon nitride is formed mainly by the gas-phase reaction (3-4) (Jennings and Richman, 1976; Moulson, 1979). Because of trace impurities of oxygen and water vapour in the nitriding gas, silicon monoxide may be formed according to Si(s) + ±O2(g) - SiO(g) Si(s) + H2O(g) • SiO + H 2
(3-5) (3-6)
The maximum silicon monoxide partial pressure possible within the compact is controlled by the dissociation equilibrium: 2SiO(g) -> Si(s) + SiO2(s)
(3-7)
giving a value for P Sio of approximately 0.5 kPa at 1370°C, which is much higher
129
than that for PSi, suggesting that an alternative route for formation of a silicon nitride may be through the reaction of silicon monoxide and nitrogen according to 3SiO(g) + 2N 2 (g) -+ Si3N4(s) + |O 2 (g) (3-8) However, AG° for this reaction is positive at nitriding temperatures but the reaction becomes feasible if oxygen can be removed easily as a gaseous species. During the early stages, sufficient silicon is available to react with oxygen to form more silicon monoxide [reaction (3-5)]. The partial pressure of oxygen is influenced by the presence of hydrogen in the nitriding atmosphere and reaction (3-8) can thus be very significant during nitridation (Lindley et al., 1979) depending on overall gas composition, pressure, temperature and heating rate. The above processes occur in both the production of silicon nitride powder by the nitriding route and also RBSN ceramics. In the ceramic bodies, the overall microstructural development depends on many parameters already outlined as well as on the silicon powder characteristics (mean particle size and particle size distribution, impurity concentrations, etc.) and the method of fabrication which determines the overall particle packing, green density and porosity. The silicon powders actually used commercially can vary somewhat in terms of impurity levels and particle size. A typical analysis of a commercial silicon powder used for RBSN is given in Table 3-4. The particle size of the silicon powder crucially affects the rate of the reaction which increases substantially at lower temperatures as specific surface area increases. Many impurities, such as iron, aluminium, calcium, carbon and oxygen, present in the silicon powder can affect the kinetics of the nitri-
130
3 Nitride Ceramics
Table 3-4. Typical analysis of a commercial silicon powder used for RBSN. Impurities
wt.%
Fe Al Ca Carbon Oxygen
0.80 0.25 0.05 0.05 0.40
Mean particle size 15 urn; particle size range 1—40 um; specific surface area 1 — 2 m2 g" 1 .
dation process and, hence, the microstructural development. The final microstructure of RBSN consists of needle-like grains of oc and more equi-axed grains of P silicon nitride, some unreacted silicon, impurity phases and re(a)
sidual porosity of 12 to 30 vol.%. The pore size distribution is very wide with very small interconnected micropores of 0.01 1.0 jim diameter and much larger isolated macropores up to 50 jum diameter generally associated with "melting-out" of impurity phases (e.g., Fe^Si) with eutectic temperatures below the peak for the nitriding process. A proposed model by Atkinson et al. (1976) is useful in understanding the overall nitridation process although later studies (Lindley et al., 1979) disagree in certain details. The overall process is shown schematically in Fig. 3-6. At the commencement of the reaction, silicon nitride nuclei are formed at the silicon surface through chemisorption. Atkinson et al. (1974) pro-
(b) h2N2-+Si3N4+1.5O2 Nitride
Nuclei
(c)
(d)
(e)
(f)
Figure 3-6. Schematic diagram of the growth of silicon nitride during the reaction-bonding process.
3.3 Silicon Nitride
posed that silicon is transported by evaporation-condensation or surface diffusion from the surrounding surface (semiconductor grade silicon). In commercial processes, oxygen present in the gas results in the formation of SiO vapour (Lindley et al., 1979) which reacts with nitrogen to form oc silicon nitride, which is deposited on existing nuclei, releasing oxygen for continuation of the cyclic reaction. As silicon is consumed from the surrounding areas, surface pits or larger pores are formed between the growing nuclei. Eventually a dense silicon nitride layer is formed and, as the surfaces impinge, the underlying silicon surface within the pores may be sealed off from the nitriding gas. Alternatively, new silicon nitride nuclei may be formed within the "new" pores. This proposed mechanism for reactionbonding is consistent with the fact that no change in overall dimensions occurs during the process even though the volume of solid material increases by —22%. Microstructural examination revealed that nitridation does not take place at solid-solid interfaces. The reaction involves the counter transport of silicon and nitrogen through the silicon nitride product layer. Jennings and Richman (1976) studied the kinetics of formation of the oc silicon nitride layer and found a parabolic correlation between reaction product and time, suggesting that diffusion of nitrogen through this nitride layer is the rate-limiting process. The kinetics approximately follow the relationship: where D is the diffusion coefficient, K a constant, t time, r the radius of the particles (spherical) and x the fraction reacted. Other processes are concurrent with the formation of this a matte within the compact, notably the formation of a silicon
131
nitride whiskers at the compact surface through a vapour-liquid-solid mechanism (aided by impurities present such as iron) and also the commencement of P phase formation. The influence of iron impurities has been studied in more detail. Iron is known to accelerate the nitriding of silicon and Fig. 3-7 shows the effect of Fe on the reaction yield (Boyer and Moulson, 1978). Oxygen contents for silicon powders can vary between 0.3 and 3 wt.% and, assuming this is present as silica, molar contents of SiO2 can vary between 1.2 and 12 mol.% (Lange, 1980). Boyer and Moulson (1978) suggest that iron disrupts the SiO2 surface layer on the silicon, resulting in crystallisation and cracking and exposing the underlying silicon to the nitriding atmosphere. The iron reacts with silicon to form a liquid phase (Fe^Si). Si vapour from the liquid reacts with the nitrogen to form a phase whereas nitrogen can dissolve in the liquid and (3 phase is precipitated. 1350°C
Percentage 50
r -—
Beta yield -B- Alpha yield - 0 - Total reaction
40
20
0
1000
2000
3000
4000
5000
Fe Concentration (ppm)
Figure 3-7. Effect of Fe impurity on silicon nitridation reaction kinetics (after Boyer & Moulson, 1978).
132
3 Nitride Ceramics
Lange (1980) suggests that the FexSi liquid reacts with available oxygen to form SiO, which combines with nitrogen by a vapour-phase reaction to form silicon nitride (as shown in Fig. 3-6). The liquid then dissolves more silicon from the surrounding regions, creating new pores for subsequent accommodation of nitride growth. The presence of a liquid is assumed to favour P silicon nitride formation (Mitomo, 1977 a; Longland and Moulson, 1978) and the P content of a completely nitrided compact is related to the amount of impurity in the original silicon, which controls the amount of liquid formed (Moulson, 1979). As nitrogen can diffuse easily through the large hexagonal channels within the p silicon nitride crystals, the reaction at the Si/Si3N4 interface is the rate-controlling process in this case and the reaction product-time relationship for P formation is linear, not parabolic (Jennings and Richman, 1976).
3.3.4 Formation of Silicon Nitride Powders In contrast to the porous reaction-bonded form of the ceramic, the dense material requires the use of a silicon nitride precursor. There are now a large number of commercial silicon nitride powders available worldwide made by four different routes: (a) The nitridation of silicon Si 3 N 4
(3-1)
This is the most developed process commercially. The nitridation reaction proceeds in a similar way to that described in Sec. 3.3.3. Reaction "bonding" occurs such that the product is in a solid form and requires pulverising and milling to form a powder. (b) Chemical vapour deposition 3SiCl4 + 4NH 3
Si 3 N 4
12HC1 (3-10)
This process results in formation of an "amorphous" powder with very high surface area. Heat treatment at ~1300°C results in the development of crystallinity. (c) Carbo-thermal reduction of silica 3SiO 2 + 6C + 2N 2
Si 3 N 4
6CO (3-11) This process requires excess carbon in order to ensure complete reaction of the SiO 2 . Any residual carbon is subsequently burned off at temperatures up to 600 °C. SiO and SiC can be formed during the process unless the composition and temperature are controlled. (d) Silicon diimide precipitation SiCl4 + 6NH 3 -> Si(NH)2 + 4NH 4 C1 (3-12a) 3Si(NH)2 -* Si 3 N 4 + 2NH 3 (3-12b) Each method yields powders suitable for sintering but with different morphologies, crystallinity, specific surface area, oxygen, carbon and impurity contents, all of which can significantly influence the rate of densification. The ideal powder should have the following characteristics: (i) equiaxed particle morphology for good green compaction; (ii) high surface area for good sinterability;
(iii) high a silicon nitride content to favour better microstructural development during sintering; (iv) low levels of impurities to avoid unwanted reactions and to allow development of better high-temperature mechanical properties. In all cases the oxygen is present usually as a surface layer of SiO 2 around each powder particle. Typical characteristics of silicon nitride powders produced by the four different routes are given in Table 3-5 (Wotting and
3.3 Silicon Nitride
133
Table 3-5. Characteristics of Si 3 N 4 powders, processed by different preparation methods Technique:
Nitridation of Si
Sample no.:
1
2
23 1.4 0.2 0.07
11 1.0 0.25 0.4
Chemical vapour deposition
Carbothermal
Diimide precipitation
tuuvuuii
Specific surface area (m2 g" 1 ) O (wt.%) C (wt.%) Fe,Al,Ca(wt.%) Other impurities (wt.%) Crystallinity (%)
a/(a + p) (%) Morphology
100 95 E
100 92 E
1
2
4 10 1.0 3.0 _ 0.005 0.005 f Cl: 0.04 [Mo + Ti:0.02 60 0 95 E+R E+R
10 2.0 0.9 0.22
1
2
11 1.4 0.1 0.01
13 1.5 0.1 0.015
Cl: 0.1 100 98 E+R
98 86 E
0.005 95 E
E: equiaxed; R: rod-like.
Ziegler, 1986). An understanding of the effect of powder characteristics on densification behaviour and microstructural development is essential to produce materials with better properties. 3.3.5 Formation Routes for Dense Silicon Nitride For an intrinsically high strength, high hardness material such as silicon nitride, the high energy covalent chemical bonds giving rise to these properties are a disadvantage in fabrication. Self-diffusivity in silicon nitride is quite low and species only become sufficiently mobile for sintering at temperatures where the decomposition of silicon nitride commences (>1850°C). Thus, alternative approaches have been developed by the use of densification additives to create the conditions for liquidphase sintering either with or without applied pressure to assist the process. These techniques include hot-pressing, pressureless sintering, of both silicon nitride powder compacts and reaction-bonded silicon nitride, and hot-isostatic-pressing of all of the previously formed types. Initially, ad-
ditives such as MgO or Y 2 O 3 were used to densify silicon nitride, and this resulted in the formation of secondary phases at the silicon nitride grain boundaries. Later, mixed oxide additives such as Y 2 O 3 + A12O3 and various rare earth oxides were explored to develop specific microstructures by modifying the nature of the grain boundary phase. The role of the additives in the liquid phase sintering process and microstructural development is discussed in Sec. 3.3.6. 3.3.5.1 Hot-Pressed Silicon Nitride (HPSN) Hot-pressing of silicon nitride, which involves the application of both heat and uniaxial pressure, is carried out in graphite dies heated by induction to temperatures in the range 1650-1850 °C for 1 to 4 hours under an applied stress of 15 to 30 MPa. Boron nitride is applied as a coating to the graphite die and plungers to prevent reaction of these with the silicon nitride. Boron nitride powder is also used as a solid high temperature lubricant to facilitate removal of the hot-pressed material from the die,
134
3 Nitride Ceramics
but surface contamination is usually a problem. This can be minimised by prepressing the powder mix in a metal die to form a compact prior to its introduction into the graphite die. Material produced by Coe et al. (1972) by hot-pressing high-oc phase silicon nitride powder with only 1 wt.% MgO had a mean bend strength of 900 MPa, which reduced to 800 MPa at 950 °C. However, HPSN is limited to simple shaped (cylindrical) billets and components must be machined from these using expensive grinding. A typical microstructure is shown in Fig. 3-8.
Figure 3-8. Scanning electron micrograph of a polished etched section of HPSN (after Ziegler et al., 1987).
3.3.5.2 Sintered Silicon Nitride (SSN) A more cost-effective method of production of complex-shaped components in dense silicon nitride, without the requirement for machining to any extent, is pressureless sintering, which involves firing of the shaped component at 1700-1800 °C under a nitrogen atmosphere at 0.1 MPa. As with hot-pressing, the additives provide conditions for liquid phase densification but, in the absence of applied pressure, the reduction in surface energy becomes the major driving force for sintering and so the use of high surface area powders is necessary. This increases the oxygen content of the powders, which can also affect the quantity of liquid phase formed and affect the overall composition of the secondary phase. A typical microstructure is shown in Fig. 3-9. Without pressure, dissociation of Si 3 N 4 becomes a problem at high temperatures. During pressureless sintering at temperatures much above 1700°C, Terwilliger and Lange (1975) showed that density starts to decrease at longer times as a result of increasing weight losses. The use of so-called "powder beds", where the component to
11 jim
Figure 3-9. Scanning electron micrograph of an etched fracture surface of SSN.
be sintered is surrounded by a mixture of powder of its own composition and inert boron nitride, has proved successful in reducing volatilisation (Wotting and Hausner, 1983). This creates a local gas equilibrium immediately adjacent to the silicon nitride compact, thus minimising volatilisation. An alternative is to increase the nitrogen pressure to higher levels (10 MPa), and development work, particularly in Japan, has demonstrated substantial improvements in properties by this method. Densities of 97-99% of the theoretical value are routinely achieved with bend strengths of >1000 MPa.
3.3 Silicon Nitride
3.3.5.3 Sintered Reaction-Bonded Silicon Nitride (SRBSN) Silicon nitride powder compacts have low green densities (~45-55% theoretical) and, thus, sintering to high densities requires volume shrinkages of 45-55%. Consequently, control of the firing process for complex shapes becomes more difficult. As RBSN has a density within the range 70-85% of the theoretical value, it was considered as a suitable starting material for sintering by Giachello and Popper (1979) and Mangels and Tennenhouse (1980). Additives such as MgO or Y 2 O 3 are mixed with the silicon prior to shaping and nitriding as for RBSN. A further heattreatment in the range 1800=2000 °C under a nitrogen atmosphere (0.1 to 8 MPa), and using a protective powder bed to reduce volatilisation, allows densification to 98% theoretical density with only 6% linear shrinkage. A typical microstructure is shown in Fig. 3-10. Bend strengths of 700 MPa have been reported (Mangels, 1983).
135
^ ,. \
Figure 3-10. Scanning electron micrograph of a polished and etched section of SRBSN (after Kleebe and Ziegler, 1989).
3.3.5.4 Hot Isostatically Pressed Silicon Nitride (HIPSN) Hot isostatic pressing (HIP) was originally developed for processing metals, special alloys and hard metals. Further development of the technique for ceramic parts required parallel developments in special HIP equipment to allow sintering by HIP at temperatures above 1700°C. The silicon nitride components are placed in an "autoclave" and subjected to high temperature and high pressure using argon or nitrogen as the pressure transmission medium to consolidate a shaped powder compact or to remove porosity from pre-fired, RBSN, SSN or SRBSN. In all cases, a small amount of sintering additive is required but because a lower quantity may be used,
Figure 3-11. Transmission electron micrograph of HIPSN (after Rouxel, 1990).
properties should be superior to those of other forms of Si 3 N 4 . A typical microstructure is shown in Fig. 3-11. For HIP of a powder compact or RBSN, where there is a large volume fraction of open porosity, an encapsulation technique is used to prevent penetration of the pressurised gas into the open pore network (Larker, 1979). The green or reaction-
136
3 Nitride Ceramics
bonded body is coated with a layer of glass powder and the pressure vessel is evacuated to "degas" the component. The temperature is then raised to melt the glass to form an impermeable barrier and the gas pressure increased to 200 MPa as the peak temperature reaches 1700-1900°C. During controlled cooling, the glass capsule cracks off and the component is given a surface treatment such as sandblasting. For pre-sintered materials such as SSN and SRBSN where there is no open porosity, encapsulation is unnecessary (Larker, 1983) and the major reason for applying the HIP treatment is to remove residual porosity. Ziegler and Wotting (1985) show that HIP of SSN results in a substantial improvement in reliability (higher Weibull modulus) because of flaw-healing and removal of porosity. 3.3.6 The Role of Additives in the Densification of Silicon Nitride 3.3.6.1 Formation of Oxynitride Liquids in Silicon Nitride Ceramics
In the early development of hot-pressed silicon nitride, it had not been realised that every powder particle of silicon nitride is surrounded by a surface layer of silica. Oxide additives react with this silica and some of the nitride to form an oxynitride liquid at high temperature which cools as an intergranular phase. Wild et al. (1972 c) showed, by detecting silicon oxynitride and enstatite (magnesium silicate) as devitrification products in silicon nitride hotpressed with magnesia, that this phase was a glass containing nitrogen. The glass was first observed directly by electron microscopy by Drew and Lewis (1974), who suggested that the mechanism of sintering involves solution and reprecipitation of silicon nitride crystals. Attempts were made to determine the glass composition (Powell
and Drew, 1974), and it was found that impurity ions such as calcium could be accommodated in the glass. The glass softening temperature is lowered as a result, and there is a clear correlation between this and the drastic reduction in strength observed at high temperatures. The characteristics of the oxynitride liquids formed with different densification additives differ widely, and the second phase formed on cooling may be crystalline or vitreous. The role of the additives is summarized by a-SLN, + SiO. + MYOV -> P-Si3N4 + M - S i - O - N phase
(3-13)
Hampshire and Jack (1981) observed that the temperature of initial liquid formation with additions of metal oxide to silicon nitride containing 4 wt.% surface silica is appreciably lower than the lowest solidus temperature in the corresponding metal oxide-silica system, confirming that nitrogen, as an additional component, lowers the eutectic temperature. For example, liquid formation occurs with MgO at 1390°C and with Y 2 O 3 as low as 1450°C. With A12O3 the lowest eutectic is at 1470 °C, and extra additives will lower this further. During sintering, shrinkage usually starts at the temperature of liquid formation and is subsequently accompanied by the a->p phase transformation. Weston and Carruthers (1973) showed that, during hotpressing with MgO, full densification could be achieved via liquid silicate formation before any a-»P transformation had taken place. Terwilliger and Lange (1974) suggested that the liquid would allow transport of Si and N, but they did not consider that oc->P transformation was required for densification. Figure 3-12 shows the shrinkage and transformation at different temperatures (constant time: 30 min) during pressureless
137
3.3 Silicon Nitride 40 -|
7wt. c /o Y 2 O 3
4U-
5 wt. % MgO p = 0.95
30-
30-
J 20-
20-
o _2~-
"O
p
O
= 0.75
10-
10-
y
0—i— 1300
'
1400
i
i
1500
i
1600
100-1
i
i
1
1700
-o—o-c
50-
1300
1400
1500
1600
1700
1600
1700
100-i
50U'
CO
CO.
™_«V oJ
01300
1400
1500
1600
1700
T (°C)
—r 1300
1400
1500
T CC)
Figure 3-12. Shrinkage and transformation as a function of temperature for pressureless sintering of silicon nitride with Y 2 O 3 and MgO (after Hampshire and Jack, 1981). Q is the relative density.
sintering of silicon nitride (Hampshire and Jack, 1981) and emphasises the differences between magnesia and yttria as additives. With MgO, nearly complete densification is achieved with only partial transformation to (3 during hot-pressing, as found by Weston and Carruthers (1973) and Bo wen et al. (1978 a), whereas with Y 2 O 3 complete transformation occurs with only limited densification. Clearly, the behaviour of different additives requires interpretation and studies of the densification and transformation kinetics are thus important. 3.3.6.2 Sintering Kinetics
Terwilliger and Lange (1974) were the first to study the kinetics of densification of
silicon nitride hot-pressed with 5wt.% MgO, and their results were interpreted using the liquid phase sintering model of Kingery (1959) without any firm conclusions regarding the model itself. Mitomo (1976) also used the Kingery model in analysing hot-pressing kinetics. The only systematic study of pressureless sintering kinetics is that by Hampshire and Jack (1981), again using the Kingery liquid-phase sintering model in which three stages are identified, as summarized by the log-shrinkage/log-time plot of Fig. 3-13. The stages are: (i) particle rearrangement within the initial liquid, where the rate and the extent of shrinkage depend on the volume and vis-
138
3 Nitride Ceramics
u-
-1/
2-
SolutionDiffusionReprecipitation
Elimination of closed porosity
Particle rearrangement
Log time
Figure 3-13. Three stages during the liquid phase sintering of silicon nitride (after Hampshire and Jack, 1981).
cosity of the liquid; this is the incubation period for the a ->(3 transformation; (ii) solution-diffusion-reprecipitation, where shrinkage can be expressed as (see Kingery, 1959) AF/F 0 oc tlln
(3-14)
where t is time, n = 3 if solution into or precipitation from the liquid is rate controlling and n = 5 if diffusion through the liquid is rate-controlling, assuming that the particles are non-spherical; the oc->(3 transformation begins in this stage; (iii) final elimination of closed porosity during which the liquid acts to form a more rounded grain morphology; final density is greater than 95% of the theoretical value. During pressureless sintering of silicon nitride with 5 wt.% MgO and 7wt.% Y 2 O 3 respectively, Hampshire and Jack (1981) observed that the rearrangement stage with MgO accounts for half of the total shrinkage required for full densification, whereas with Y 2 O 3 it is responsible for less than a quarter of the shrinkage required. The reason for the difference is the larger volume and lower viscosity of the magnesium silicon oxynitride liquid compared with the yttrium-containing
liquid. Different silicon nitride powders, containing different levels of impurity and surface silica, densify to different extents during this first stage, as these affect the volume of liquid formed. During the stage (ii) solution-precipitation, for MgO, n = 3, indicating a reactioncontrolled process; for Y 2 O 3 , n = 5 and this suggests that diffusion through the more viscous liquid is rate controlling. This is confirmed by the fact that for Y 2 O 3 transformation starts immediately after stage (i) rearrangement and is complete at a relative density of 0.75. Solution-precipitation is more rapid than diffusion and so the oc->p transformation occurs with little material transport and hence with very little densification. On the other hand, with MgO, a reasonable level of densification is attained by rearrangement, which corresponds to the incubation period for oc-> P transformation. During stage (ii), the relatively rapid transport of material through the low-viscosity liquid ensures that transformation is accompanied by shrinkage. Figure 3-14 illustrates schematically the liquid phase sintering process. For both additives, solution of oc into the oxynitride liquid occurs preferentially at the contact areas between the particles. With MgO, rapid transport of material allows precipitation of p on the free surfaces so that the distance between particle centres is reduced allowing shrinkage to occur. With Y 2 O 3 , diffusion is slow, and appreciable precipitation of P occurs in the contact areas without significant material transport. Thus, transformation takes place without much densification. In hot-pressing silicon nitride with MgO, Brook et al. (1977) also observed the rearrangement and solution-diffusionreprecitation stages, but interpretation of the kinetics is based on a grain boundary diffusion-controlled creep model of Coble
3.3 Silicon Nitride
Ideal
Complete densification
Solution control e.g. MgO
Partial transformation
Incomplete densification
Diffusion-Control e.g. Y 2 O 3
Full transformation
Kingery Model Figure 3-14. Schematic illustration of the stage (ii) solution-precipitation process during liquid phase sintering of silicon nitride (after Hampshire and Jack, 1981).
(1963,1970), in which surface energy effects are assumed to be negligible in comparison with applied pressure, and therefore this is not applicable in the case of pressureless sintering. Brook et al. suggested that, following a rapid rearrangement process, the major part of the densification occurs by dissolution of a silicon nitride at points of compressive stress, diffusion of material through a grain-boundary phase down the stress gradient, and then reprecitation of P silicon nitride at unstressed points, with diffusion being the rate-controlling step. The densification rate is given by At
47 QWDPA kTG3
(3-15)
where Q is the volume transported by each atom of the slow-diffusing species, W the boundary thickness, D the diffusion coeffi-
139
cient, PA the applied stress, and G the grain size. W is related to the quantity of second phase present, which is in turn proportional to the amount of additive used, and the linear dependence of W with densification rate was confirmed. Although transformation occurs together with densification, it was not seen by Brook et al. as a necessary factor in bringing about densification, even though the activation energies for both densification and transformation were found to be similar. Changes in the slopes of the Arrhenius plots were found at 1550°C, i.e., close to the solidus in the MgSiO 3 -SiO 2 system, and according to the authors indicated a change from diffusion through a "secondphase solid" boundary to diffusion through a liquid grain-boundary film. The activation enthalpies were found to be: Below 1550°C Densification AH = — 450 kJ mol ~* Transformation AH = — 500 kJ mol~ x Above 1550°C Densification AH= - 6 9 5 k J m o r 1 Transformation AH = - 6 9 0 k J m o l " 1 The concept of liquid silicate formation is oversimplified, since there is general agreement that a magnesium silicon oxynitride liquid is formed, and at a lower temperature (1515 °C: Lange, 1978; 1390°C: Hampshire and Jack, 1981). While Brook et al. (1977) and Bowen et al. (1978 a) found that the activation enthalpies for transformation and densification with MgO were the same, suggesting that mass transport mechanisms are the same for both processes, this was not found to be the case for Y 2 O 3 , Y 2 Si 2 O 7 and Li 2 SiO 3 additions (Bowen et al., 1978 b). In the pressureless sintering study by Hampshire and Jack (1981), the activation energies for the oc->p transformation were
140
3 Nitride Ceramics
found to be the same for both MgO and Y 2 O 3 additives and are similar to the dissociation energy of the Si-N bond, i.e., 435 ±38 kJ mol" 1 . The mechanism of transformation seems to be the same for both additives, each merely providing a solvent for a reconstructive transformation involving the breaking of Si-N bonds, which would usually occur only when there is contact between solid and a solvent. The less stable, more soluble form (a) goes into solution and is precipitated as the less soluble, more stable form (P). So the free energy change AG(a_p) may be expected to contribute to the driving force for solution-precipitation densification, especially as the temperature is increased. 33.6.3 Phase Relationships, Microstructure and Effects on Properties As well as limiting or aiding densification, the type and amount of additive determines the nature and quantity of the resulting grain boundary phase as indicated in Eq. (3-13), and this can affect hightemperature strength, creep resistance and oxidation resistance. Thus it is important to understand the phase equilibria in M - S i - O - N and related systems and then apply this knowledge to processing, the development of beneficial microstructures and the relationship between these and properties. The concept of "grain boundary engineering" sought to control the structure of, and reactions occurring at, the grain boundary in silicon nitride based materials. Significant advances in materials development were realized as a result of this new approach. The original work by Gazza (1973,1975) suggested that improvements in high-temperature properties could be achieved by finding a system in which the softening point of the intergranular glass phase is
increased, and this was the reason for investigating Y 2 O 3 as an alternative to MgO as the densifying additive. However, with Y 2 O 3 , one or more of four quaternary, crystalline yttrium-silicon oxynitrides can be formed in preference to glass, depending on the amount of surface silica on the silicon nitride powder. Figure 3-15 shows the Y - S i - O - N behaviour diagram (Jack, 1986). This representation is the same as that of a reciprocal salt system, and the concentrations are expressed in equivalents. The bottom right hand corner is Si 3 N 4 (3Si 4+ and 4N 3 ") and, maintaining 12 positive and 12 negative valency units throughout, the other corners are then Si 3 O 6 , Y 4 O 6 and Y 4 N 4 . For any composition, the equivalent concentrations of silicon (eq.% Si) and nitrogen (eq.% N) are given by eq.% Si =
4[Si] x 100 4[Si] + 3[Y]
(3-16)
3[N] x 100 2[O] + 3[N]
(3-17)
where [Si], [Y], [O] and [N] are, respectively, the atomic concentrations of silicon, yttrium, oxygen and nitrogen.
6/5(Y 2 Si0 5 )
2/5(Y 6 Si 3 N 10 )
6/7(Y 2 Si 2 0 7 ) 2/3(Y 2 Si 3 N 6 ) 4/5(YSi3N5)
Figure 3-15. The Y - S i - O - N behavior diagram: (1) N-apatite, (2) N-YAM, (3) N-oc-Wollastonite and (4) N-melilite (after Jack, 1986).
141
3.3 Silicon Nitride
Earlier work by Rae et al. (1978) shows slightly different compatibility, as YN was obviously not used as a starting component. Similar phase relationships are also reported in the earlier studies of Wills et al. (1976) and Lange et al. (1977), but in these cases the diagram is shown as the Y 2 O 3 SiO 2 -Si 3 N 4 ternary system in molar units. The four phases in the system are: (1) (2) (3) (4)
N-melilite, Y 2 Si 3 O 3 N 4 N-apatite, (Y, [ ])10(SiO4)6(O,N)2 N-YAM, Y 4 Si 2 O 7 N 2 N-oc-wollastonite, YSiO2N
where (Y, [ ])10 means ten lattice sites for Y but with some vacancies and YAM is yttrium aluminate, monoclinic. All are isostructural with the corresponding silicates or aluminates and may accommodate in solid solution the impurities such as calcium that would otherwise be incorporated into a glass. Thus the strengths, at temperatures in excess of 1200 °C, of silicon nitrides densified with yttria are much higher than materials in the M g - S i - O - N system because of the much larger volumes of residual glass of lower viscosities formed with MgO. Unfortunately, materials containing the quaternary crystalline oxynitrides undergo much worse strength degradation at lower temperatures (900-1200°C) because these phases, particularly N-melilite, oxidize to form a yttrium silicate and silica with a marked change in specific volume, which leads to induced stresses in the surface scale and catastrophic failure (Lange et al., 1977; Rae et al., 1978) (see Sec. 3.3.8). It is desirable to produce a final product within the compatibility region Si 3 N 4 Si 2 N 2 O-Y 2 Si 2 O 7 in order to have good oxidation resistance, but this must then contain glass and will have poor creep resistance.
Giachello et al. (1980) developed materials using a combination of Y 2 O 3 + MgO as the densifying additives. The grain boundary glass phase can be crystallized to form Mg 5 Y 6 Si 5 O 24 , and strength at 1000°C is improved as a result. Figure 3-16 shows the effect of MgO additions on the densification of silicon nitride with 7 wt.% Y 2 O 3 at 1650°C for 30min (Hampshire, 1986). There is a substantial increase in densification with MgO while the difference in oc->(3 transformation is negligible. In addition to the requirement of a crystalline second phase, it appears that the morphology of the |3-Si3N4 grains is im-
50-
0
2
4
6
8
wt. % MgO
Figure 3-16. Effect of MgO additions on densification and transformation of silicon nitride with 7 wt.% Y 2 O 3 at 1650°C for 30 minutes (after Hampshire, 1986). •: apparent solid density; o: bulk density; •: % P-Si3N4.
142
3 Nitride Ceramics
portant in determining high-temperature strength. Materials in which the p-phase particles have a very fibrous morphology have better strengths and improved fracture toughness. Lange (1973) suggested that the aspect ratio (length: diameter), R, of the grains is empirically related to the starting a: P ratio through the relationship K= l + |
(3-18)
However, Wotting and Ziegler (1984) showed for silicon nitrides sintered with different Y2O3-AI2O3 mixtures but with the same level of porosity and the same grain size that fracture toughness and aspect ratio vary in the same way with composition. Other studies, concerned with sintering of silicon nitride with MgO-Y 2 O 3 mixtures (Hampshire and Pomeroy, 1985), have also shown that the aspect ratio of grains is dependent on composition and firing time. Prismatic growth in the longitudinal direction occurs to give aspect ratios of 8 to 9 as shown in Fig. 3-17. As the grain boundary
composition changes, the aspect ratios of P grains vary and there is also evidence of grain coarsening as the firing time is increased. Aspect ratio may vary not only with the volume of liquid phase but also with viscosity and nitrogen solubility in the liquid. In particular, the use of rare earth oxides (Nd 2 O 3 , Sm 2 O 3 , Dy 2 O 3 , etc.) usually in combination with MgO (Hampshire etal., 1986, 1987) results in the formation of microstructures with high aspect ratio P silicon nitride grains. These microstructural features have a crucial effect on subsequent mechanical properties. 3.3.7 Properties of Silicon Nitride Ceramics
Mechanical properties of silicon nitride ceramics are shown in Table 3-6. Even within each material type, the properties, particularly fracture strength and fracture toughness, show large variations, again attributable to micro structural differences. Young's modulus of elasticity, £, for RBSN decreases with an increase in total porosity according to (Moulson, 1979) = E0 e x p ( - 3 P )
Figure 3-17. ture surface MgO/Y 2 O 3 grains (after
Scanning electron micrograph of fracof silicon nitride sintered with mixed additives showing high aspect ratio (3 Hampshire, 1984).
(3-19)
where P is the total volume fraction of porosity and Eo is the Young's modulus for silicon nitride with zero porosity, taken as 300 GPa. Materials with the same total porosity but different pore size distributions have very similar elastic moduli. For dense silicon nitrides, values of Young's modulus vary between 260 and 330 GPa, depending on the amount and orientation of other phases present in the material, including porosity. For RBSN, fracture strength is dependent on the volume fraction of porosity but, more particularly, on the size of the largest pores which are created by the melting out of iron impurities present in the original silicon powders. Thus, for a
143
3.3 Silicon Nitride
Table 3-6. Mechanical properties of silicon nitride ceramics. Material type:
RBSN
HPSN
SSN
Relative density 70-88 (% of theoretical) 99-100 95-99 Young's modulus E (GPa) 120-250 310-330 260-320 0.20 0.27 0.25 Poisson's ratio Flexural strength a{ (MPa) 150-350 450-1000 600-1200 at 25 °C 140-340 250-450 340-550 at 1350°C 19-40 15-30 10-25 Weibull modulus m Fracture toughness 5.0-8.5 4(MPam1/2) 1.5-2,8 4.2-7.0
given density, the strength of RBSN shows significant scatter. For the achievement of high strength, it is better to have a homogeneous microstructure with a narrow pore-size distribution at moderate densities than a high density material with large voids present (Ziegler et al., 1987). The grain size, which is finer than the macropore size, has much less effect on strength. Typical average fracture strength values at ambient temperature for HPSN are 600 MPa with MgO additive and 800 MPa with Y 2 O 3 additive, the major difference being the morphology of the (3 grains in the microstructure. With MgO, the liquid phase during hot-pressing allows easy densification but an equiaxed grain morphology, whereas the liquid formed with Y 2 O 3 has a higher viscosity resulting in c-axis growth of the (3 grains and hence a higher aspect ratio (Hampshire and Pomeroy, 1985) giving higher strength and fracture toughness. Improvements in the processing of sintered silicon nitride have resulted in values as high as or exceeding those of HPSN. Weibull modulus tends to be higher for the HPSN and, in particular, the HIP processes as these result in flaw-healing and pore size reduction.
SRBSN
HIP-SN HIP-RBSN HIP-SSN
93-99
99-100
280-300 0.23
310-330 0.23-
0.27
500-800 350-450 10-20
600-1050 350-550
500-800 250-450 20-30
600-1200 300-520
5.0-5.5
4.2-7.0
2.0-5.8
4.0-8.0
For any particular material type, the room temperature mechanical strength and fracture toughness are dependent on, firstly, the aspect ratio of the (3 silicon nitride grains and, secondly, the overall grain size. Figure 3-18 shows schematically how fracture strength and fracture toughness change during the sintering process for silicon nitride. As the ot-form transforms to |3-phase? the aspect ratio changes from equiaxed crystals to fine elongated crystals giving improved strength and toughness but, once the a-»(3 transformation is complete, grain growth results in an increase in grain diameter with a consequent decrease in these properties. The reason for the improvement with higher aspect ratios is that the interlocking, elongated (3 grains have better resistance to crack propagations because of crack branching and deviation as well as grain pull-out, resulting in higher energy requirements for crack growth. The high strength values now achieved for sintered silicon nitrides are a result of process optimisation including modifications to the type and composition of the grain boundary phase by varying the amount and type of sintering additive. The use of mixed oxide additives (e.g., Y 2 O 3 + A12O3, MgO + Nd 2 O 3 , etc.) allows control
144
3 Nitride Ceramics ASPECT RATIO: varies with powder properties, volume, viscosity of liquid phase, processi ng parameters (t,T)
800
100 .
600
90 CL
80
fc 400-^ I
§ 200
L
70 60
Figure 3-18. Schematic plot showing changes in aspect ratio and grain diameter (thickness) of Si 3 N 4 as a function of sintering (soaking) time and resulting strength and fracture toughness (KIc). 2 3 4 Soaking time (h)
of the properties of the sintering liquid such as volume and viscosity which determine the growth of the J3 grains along the preferred c-axis direction and also the grain diameter. The variation of strength with temperature for the different types of silicon nitride based ceramics is shown in Fig. 3-19. Because of the presence of porosity, RBSN has the lowest flexural strength (150350 MPa) at ambient temperature but since there is no glass phase the strength is retained up to very high temperatures (>1400°C). With SSN, much higher strengths are achieved (600-1200 MPa) at ambient temperature but, at temperatures exceeding 1000 °C, this may decrease rapidly due to the softening of the intergranular glass.
Strength is retained to much higher temperatures when the secondary phase is crystalline (Katz and Gazza, 1977; Lewis et al, 1987; Ziegler et al, 1987). HPSN and HIPSN, with zero porosity and much lower levels of additives and hence less glass, generally have higher strengths than SSN at higher temperatures. 3.3.8 Oxidation of Silicon Nitride Ceramics
Oxidation of silicon nitride in air begins as low as 800 °C and a thin protective layer of amorphous SiO2 is formed on the surface of the silicon nitride according to Si 3 N 4
3O 2 ^ 3 S i O 2 + 2N 2
(3-20)
This simple equation describes the situation for reaction-bonded silicon nitride
145
3.3 Silicon Nitride
FLEXURAL STRENGTH (MPa)
Figure 3-19. The ranges of flexural strength values for silicon nitride ceramics and the effect of temperature. 200
400
600
800
1000
1200
1400
1600
TEMPERATURE (°C)
with no additives and for hot-pressed silicon nitride at lower temperatures. However, Tripp and Graham (1976) found that oxidation of commercial silicon nitrides hot-pressed with magnesia was much more complex because the reaction products at 1400 °C include, as well as SiO 2 , magnesium silicate (enstatite). Some of the silica was crystalline and present as oc-cristobalite but conferred a protective layer on the nitride which remained coherent for several hundred hours. These workers and others report that the weight-gain versus time curves at all temperatures follow classical parabolic kinetics. Figure 3-20 shows parabolic plots of oxidation at 1400°C of silicon nitrides densified with different additives. The rate of oxidation varies according to the amount and type of additive used. The parabolic kinetics suggest that the rate of oxidation is a diffusion-controlled process, limited by inward diffusion of oxygen and outward diffusion of nitrogen as shown schematically in Fig. 3-21. Parabolic oxidation behaviour was observed by Cubicciotti et al. (1977), but they demonstrated that the rate of oxidation is
unaffected by removal of the oxide layer suggesting that diffusion through the layer is not rate-controlling. They concluded that the rate of oxidation was limited by outward diffusion of metallic impurity ions from the grain boundary glass phase within the material into the SiO2 scale. Clarke + 5MgO + 10Sc2O3 + 5Y0O3-5AI2Of10CeO ? 20CeCL
<
+ 5Y 2 O 3 -5SiO 2 z = 4(3'-sialon + 15Y,O,
^ZZ-^Z.^---~ ^r^~~
,
50 Hours
— "~
+5ZrO2' —-, +5ZrO, -5AI 2 O 3 100
Figure 3-20. Effect of different densification additives in silicon nitride ceramics on oxidation rates at 1400 °C. Am: change in mass; A: surface area.
146
3 Nitride Ceramics
Scale
Silicon Nitride surface
Mg 2 + -
Air
MgO<
2e
SiO 2 +2/3N 3-
2e~+N-
Si3N4
MgSiO 3 (Enstatite) «
2/3 N3-
2 0 ~<<
- • 2/3 N 3 " -
and Lange (1980) also agreed with these findings and suggested the sequence of reactions outlined in Fig. 3-21. Their proposed mechanism involves a number of simultaneous processes to account for the formation of silicon oxynitride under the subscale and magnesium silicate (enstatite) within the scale. After initial oxidation of the surface to produce SiO2 the diffusion of Mg 2 + to the surface occurs, driven by the potential for the Mg-containing phase in the grain boundaries to equilibrate with the SiO 2 to form MgSiO 3 . Internal oxidation then occurs without inward diffusion of oxygen to produce Si 2 N 2 O and to release 2/3 N 3 ~ which diffuses out of the material into the scale along with the Mg 2 + to maintain charge neutrality. Thus, oxidation kinetics will depend on inward-moving oxygen and outward-moving magnesium and other impurity cations. Clarke and Lange (1980) also confirm the results shown in Fig. 3-20 that the oxidation resistance of different Si 3 N 4 "alloys" is critically dependent on composition since this determines the volume fraction of glass phase present in the ceramic. This, in turn, determines the creep resistance.
2e
2e~ + N •
Figure 3-21. Schematic diagram showing mechanism of oxidation of dense silicon nitride with grain boundary M g - S i - O - N glass phase.
Good creep resistance is found in silicon nitride hot-pressed with high additive levels of yttria because of the formation of the refractory quaternary oxynitride phases (see Sec. 3.3.6.3) instead of glass at the grain boundaries. The material shows reasonable oxidation resistance at 1400 °C because of the formation of a coherent "protective" glaze. Unfortunately, failure occurs catastrophically at lower temperatures (900-1200 °C) in an oxidising environment. The extensive cracking that occurs is due to induced stresses in the surface scale as a result of the oxidation of the oxynitride phases to produce Y 2 Si 2 O 7 and cristobalite, which have quite different specific volumes. The reaction of the Y-Nmelilite phase occurs with a specific volume change of 30% according to: Y 2 Si 3 O 3 N 4
2 O 22 -* Y 2 Si 2 O 7 + 2N 2
AV/V0 = 30%
(3-21)
The cracks then expose fresh surfaces for attack and the process is progressive. The materials become porous and friable as oxidation continues. Figure 3-22 compares the oxidation behaviour at 1000 °C of two samples originally hot-pressed with different levels of yttria. Sample (a) contains
3.3 Silicon Nitride
none of the oxynitride phases whereas sample (b) contains a substantial amount of N-melilite. Lange et al. (1977) observe that materials within the compatibility triangle Si 3 N 4 -Si 2 N 2 O-Y 2 Si 2 O 7 have excellent oxidation resistance from 900-1400°C and these materials will not contain the oxynitride phases. Goursat et al. (1980) show that the rate of oxidation of materials within this compatibility triangle follows parabolic kinetics, whereas oxidation of the N-YAM and N-wollastonite phases follows linear kinetics with the formation of a porous silicate scale. Above 1200°C, the scales becomes more plastic and stresses are relieved (Goursat et al., 1980). A protective oxide coating is formed on the surface which prevents direct access of oxygen to the interior grain boundaries. Any carbon present in the original powder reduces the effective silica impurity content of the silicon nitride during firing and hence influences which of the oxynitrides is formed and the overall oxidation resistance of the material (Hampshire and Jack, 1984). It had been claimed (Knoch and Gazza, 1979) that degradation at about 1000 °C occurs only when carbon or carbon compounds are present in the silicon nitride during fabrication and processing. Hampshire and Jack (1984) show that when different silicon nitride powders, with and without additional carbon, are hotpressed with 15 wt.% Y 2 O 3 , the phase assemblages observed depend on the initial oxygen and carbon contents present. The carbon reacts with the surface SiO 2 on the Si 3 N 4 powders according to SiO2 + C -> SiO + CO
(3-22)
and therefore with silicon nitride containing lower levels of silica and large amounts of carbon, N-melilite is formed. Conversely with high SiO2 content Si 3 N 4 powder
147
Figure 3-22. Effects of oxidation at 1000 °C on silicon nitrides densified with Y 2 O 3 and containing (a) no crystalline grain boundary phase, (b) Y-melilite as second phase.
(nominally carbon-free), N-apatite is the secondary phase which is observed (see Fig. 3-15). On subsequent oxidation at 1000°C, materials made from high carbon content Si 3 N 4 powder and hence containing Nmelilite were badly cracked, whereas those containing N-apatite showed no cracking
148
3 Nitride Ceramics
although there were porous regions associated with the surface. It is clear that the presence of N-melilite is deleterious to oxidation resistance of Si 3 N 4 at 1000 °C and the formation of this phase should be avoided. The use of mixed oxide additives, particularly Y 2 O 3 , rare earth oxides + MgO, or mixed rare earth oxides, has been successful in producing sintered silicon nitrides with high strengths. Patel and Thompson (1988) studied the oxidation of a range of silicon nitride ceramics densified with these additives in which the grain-boundary phases were either vitreous or crystalline. They found that if the total specific volume change is > 1 %, cracking is likely to occur. This is in good agreement with a Hooke's law calculation which would suggest that, for a Young's modulus of 300 GPa and a strength of 800 MPa, the maximum strain tolerance is 0.8%. In all materials, the amount and type of sintering additive has a considerable effect on the oxidation kinetics of the ceramic. Parabolic rate constants are all different, reflecting the difference in volumes of intergranular glass phase in the materials. If this volume is large, the area over which diffusion can occur is large and the cation diffusion flux is directly proportional to this area. Pomeroy and Hampshire (1989) have shown that after longer oxidation times for a silicon nitride densified with MgO + Nd 2 O 3 , there is a deviation from the parabolic weight gain per unit area-time relationship and this is due to the devitrification of amorphous grain boundary phases. This will result in additive, and possibly impurity, cations becoming effectively "locked" into a crystalline phase and thus there is a reduction in the diffusion rate of cations to the reaction interface and hence a reduction in oxidation rate. Thus,
a devitrification heat treatment before use should prove beneficial.
3.3.9 Summary of Approaches to Optimisation of Properties
In the present phase of materials development, the need is to find a suitable combination of additives that will provide the necessary liquid phase densification while control can be exercised over the a ->p transformation and |3 grain growth to give the optimum properties at ambient temperatures. Improvements in high temperature properties require that the grain boundary phases are stable, that is, are compatible with silicon nitride in an oxidising atmosphere and do not easily deform at the service temperature. The different approaches being explored to optimise the properties of silicon nitride ceramics are summarised as follows (Ziegler et al., 1987): (a) Reduction of the impurity and additive concentration in the starting composition combined with the application of high pressure during sintering (HIP or gas-pressure sintering). (b) Use of densification aids with high solidus temperatures and high viscosities, which may form refractory phases on crystallisation. (c) Conversion of the amorphous phase to crystalline phases on cooling or during subsequent heat treatment. (d) Selection of a composition which allows the elimination of the liquid phase by vaporization during extended heat treatment. (e) Selection of a composition which allows the sintering additives to be subsequently dissolved in the silicon nitride crystal lattice to form a single-phase solid solution.
3.4 Sialons
This latter approach has been referred to as "ceramic alloying" and is demonstrated by the "sialons".
3.4 Sialons "Sialon" is the acronym for phases in the S i - A l - O - N and related systems discovered independently by Oyama and Kamigaito (1971) in Japan and Jack and Wilson (1972) in England. 3.4.1 P'-Sialons
p silicon nitride has exactly the same atomic arrangement as phenacite, Be2SiO4 (Hardie and Jack, 1957), and a silicon nitride had been reported as a defect structure (Wild etal., 1972 b) with metal and non-metal atom vacancies and in which about 1 in 30 nitrogen atoms is replaced by oxygen. Accepting that a few nitrogen atoms were replaced by oxygen, it was predicted (Wild et al., 1968) that more nitrogen could be similarly replaced if silicon was simultaneously replaced by aluminium. By analogy with the mineral silicates, the same structure can be maintained provided that the appropriate charge or valency compensation is made elsewhere in the structure. In all silicates, the fundamental structural unit is the SiO 4 tetrahedron carrying four negative charges. These are joined by sharing oxygen corners to form rings, chains, two-dimensional sheets or three-dimensional networks. An A1O4 tetrahedron with five negative charges is about the same size as the SiO 4 tetrahedron and so it can replace SiO 4 without structural change provided that electrical neutrality is maintained by introducing additional cations.
149
Thus, it seemed possible to replace N 3 by O 2 " in silicon nitride if at the same time Si 4+ was replaced by Al 3+ . Charge compensation might also be possible by introducing other metal atoms and it was suggested that a variety of new materials, vitreous as well as crystalline, could be built up of (Si, A1)(O,N)4 tetrahedra in the same way that the wide range of mineral silicates is built up of (Si,Al)O4 tetrahedra. Replacement of Si and N by Al and O in the p-Si 3 N 4 structure was obtained by Jack and Wilson (1972) by hot-pressing silicon nitride with alumina. At 1700°C, up to 65 wt.% A12O3 could be accommodated in the (3-Si3N4? with lattice parameters increasing with increasing A12O3 concentration. This expanded p-Si 3 N 4 structure was designated P'-sialon and two alternative compositions, both of which satisfy valency requirements, were considered: P-Si! 4+ N§ 4 " (
(3-23)
6-3JC/4
(3-24)
Because X-ray analysis showed only one single-phase crystalline product, it was concluded, on the basis of limited chemical analyses, that the P' composition was that given by Eq. (3-23). Jack (1976) explains how further work, involving reaction of silicon nitride with equimolar mixtures of A12O3 and A1N, indicated that the p'-phase field in the Si 3 N 4 -AlN-Al 2 O 3 system appeared to extend not only along the Si 3 N 4 -Al 2 O 3 join [the "x" composition of (3-23)] but also along the Si 3 N 4 -Al 3 O 3 N join [the "z" composition of (3-24)] and the region between these limits. Deductions made by Oyama (1972) were identical, but both are now known to be incorrect. Lumby et al. (1975) raised doubts about this range of
150
3 Nitride Ceramics
homogeneity for P' from their measurements of high-temperature creep and by confirming the presence of glass by microstructural observations. Compositions along the Si3N 4 -Al 3 O 3 N join, i.e., the V composition (3-24), with a metal:nonmetal atom ratio of 3M:4X, showed minimum creep. Further work by Gauckler et al. (1975), Jack (1976) and Lewis et al. (1977) showed that in the Si 3 N 4 -AlNAl 2 O 3 -SiO 2 system, (3' extends only along the join Si 3 N 4 -Al 3 O 3 N from z = 0 to about z = 4.2 at 1750°C. 3.4.2 Phase Relationships in the S i - A l - O - N and Related Systems Figure 3-23 shows the most recent version of the S i - A l - O - N behaviour diagram (Jack, 1986), which shows the phase relationships and extent of liquid formation at 1800°C, again using the reciprocal salt representation with concentrations expressed in equivalents. In addition to the P'-sialon phase, a number of other phases have also been observed in this system in-
cluding X-phase (Jack and Wilson, 1972), so-called because its structure was unknown; O', i.e., silicon oxynitride with partial replacement of Si and N by Al and O (Jack, 1973); and six phases with ranges of homogeneity extending along lines of constant M:X ratio between (3' and A1N (Gauckler et al., 1975; Jack, 1976). The phases based on a wurtzite-type structure have been fully characterised as a new kind of polytypoid related to A1N (Roebuck and Thompson, 1977). The structures are directly related to their compositions M m X m + 1 and are described by the Ramsdell symbols 8H, 15R, 12H, 21R, 27R and 2H5, where H stands for hexagonal, R rhombohedral and 8 disordered. Pressureless sintering of p'-sialons can be achieved to near theoretical density but this still requires the use of an additive such as MgO, Y 2 O 3 or Nd 2 O 3 . Because of the complexity of these systems, it is easier to represent these five component M - S i - A l O - N systems by the Janecke (1907) triangular prism. The N d - S i - A l - O - N prism is shown in Fig. 3-24. The basal plane of
4/7(3AI 2 O 3 -AIN)
4/3(AI 2 O 3 -AIN)
3/2(Si 2 N 2 O)
Figure 3-23. The Si-AlO - N behavior diagram at 1800°C (after Jack, 1986). SUN
3.4 Sialons
Nd,N,
(a)
151
and [N] are, respectively, the atomic concentrations of oxygen and nitrogen within any composition. The edge of the prism is scaled such that x + y = 12. The vertical plane is scaled such that each division is two valency units. The point P thus has a composition Nd 6 + Si 4+ Al 2 + O 6 - 6 ~N 5 - 4 in valency units and hence Nd 2 . 0 Si 1 . 0 * Al0#67O3#3N1>8 in atomic units.
3.4.3 Sintered p-Sialons
Figure 3-24. (a) Janecke prism representation of the N d - S i - A l - O - N system, (b) Vertical plane in prism at equivalent concentration of N of y/(x + y),
the prism is the S i - A l - O - N square which, in this case, represents the Si 3 N 4 -Al 4 N 4 Al 4 O 6 -Si 3 O 6 system (see Sec. 3.3.6.3 and Fig. 3-23). Addition of a fifth component such as Nd, produces a prism with the back triangular face being a ternary oxide system and the front face the nitrides. The concentrations of all components are expressed in equivalent units so that any point in the prism represents a combination of 12 positive and 12 negative valencies. As shown by Fig. 3-24, the distance, x, of any point P from the front face represents the concentration (in equivalent units) of oxygen, and the distance y represents the equivalent concentration of nitrogen, i.e., the equivalent concentration ratio of nitrogen = y/(x + y) = 3 [N]/(2 [O] + 3 [N]) where [O]
In the commercial production of P'sialons, mixtures of silicon nitride powder (+surface silica) and the AIN-polytypoids are used along with a sintering additive such as yttria, and following reaction-sintering a P' of z ~ 1 is formed. Mixed oxide and nitride powders corresponding to p'sialon compositions produce larger volumes of lower viscosity liquids with yttria than are formed by silicon nitride and its surface silica under similar conditions. Although the sintering mechanism remains that of solution-precipitation (Lewis et al., 1977) and the kinetics can be interpreted on the basis of the Kingery model (Hampshire and Jack, 1981), some of the liquid is transient and can be incorporated into the structure after densification is complete. Thus the amount of residual glass is substantially reduced, and improvements in properties result. Post-preparative heat treatment at 1350°C of these sialon ceramics allows the matrix and the grain-boundary glass to react to give a slightly modified P' composition and a crystalline yttrium aluminium garnet, Y3A15O12. This material has excellent creep resistance and is the strongest sialon ceramic developed to date. Heat treatment at 1050°C results in the crystallization of a different product, Y2SiAlO5N, and shows that phase relationships vary
152
3 Nitride Ceramics
with temperature and some phases are metastable over certain temperature ranges (Jack, 1986). Thus, it is important to study phase relationships over the complete range 1000-1800 °C. By changing the powder composition and heat treatment, the amount of crystalline or vitreous intergranular phase can be controlled and hence the mechanical properties modified to match particular applications. These ceramics are being exploited commercially as cutting tool inserts and are being assessed for use as engine components.
3.4.4 Properties of P-Sialon Ceramics
Sintered sialons are of two types with different microstructural features (see Fig. 3-25): (1) p'-sialon grains plus glass, (2) P'sialon grains plus crystalline YAG (Jack, 1986; Lewis et al., 1987). The strength of type (1) is similar to HPSN at ambient temperatures but it decreases as the intergranular glass softens above 1000 °C. Type (2) sialon has a lower ambient strength but this is retained to higher temperatures (500MPaat 1400 °C). (a)
(b)
Figure 3-25. Transmission electron micrographs of two types of P'-sialons with EDS analysis of grain boundary phase: (a) type (1): P' + glass; (b) type (2): P' + YAG (after Lewis et al., 1986 a).
3.4 Sialons
A characteristic property of silicon nitride ceramics containing intergranular glass phases is a transient rise in fracture toughness near to the glass softening point. This is associated with the onset of subcritical crack growth (SCG) within a creep cavitation zone at the primary crack tip. The rise in Klc is due to energy absorption by plastic deformation as a result of viscous flow of residual glass bridging crack surfaces. In type (2) sialons containing the crystalline YAG phase there is no evidence for a zone of SCG preceding rapid fracture even at temperatures over 1450°C in an inert environment (Lewis etal., 1986 a), whereas this phenomenon results in degradation at much lower temperatures of type (1) sialons. This is also the case for sintered silicon nitrides containing glass. Creep behaviour is mainly controlled by grain-boundary sliding along the amorphous phase. In addition to the volume of glass, its viscosity is an important consideration. The Y - S i - A l - O - N system offers a combination of moderately low liquidus temperature with a comparatively high residual glass viscosity and glass transition temperature, particularly compared with glasses present in sintered silicon nitrides, e.g., those in the M g - S i - O - N system. Thus, the Y - S i - A l - O - N system exhibits far superior high temperature properties. Ceramics have been developed which have survived very long times to failure at temperatures well in excess of 1300°C and stresses above 400 MPa (Lewis et al., 1986 a). This has been achieved by careful optimisation of sintering and subsequent crystallisation of the grain-boundary glass. This treatment supresses creep cavitation and minimises the creep rate at high applied stress levels.
153
3.4.5 a'-Sialons 3.4.5.1 Introduction
Jack and Wilson (1972) reported that a silicon nitride structures had been obtained by reaction of lithium silicon nitride, LiSi 2 N 3 , with alumina. The unit-cell dimensions of one example (a: 7.822 A; c: 5.677 A) gave a cell volume about 3% greater than that of a silicon nitride. Subsequent work (Jama et al., 1975) showed a variation in dimensions for the Li-ar-sialon when lithium aluminate, LiAlO 2 , was reacted in different proportions with Si 3 N 4 . However, other phases, e.g., p'-sialon and nitrogen eucryptite, were always present and the product never contained more than about 30% of the a phase. a-Sialons have also been observed by Masaki et al. (1975) during nitriding of silicon with A1N and A12O3 additions and have been reported as second phases to P'-sialons in the M g - S i - A l - O - N system (Jack, 1976) and the Y - S i - A l - O - N system (Mitomo, 1977 a). Pure a'-sialons based on the Si 12 N 16 unit cell of oc silicon nitride were first prepared by Hampshire et al. (1978), from Si 3 N 4 -AlN-M JC O y mixtures where M is Li, Ca or Y. 3.4.5.2 The Structure of a-Sialons
The structure of oc'-sialon is based on the a-Si 12 N 16 unit cell and so is hexagonal (see Sec. 3.3.2.1). As shown in Fig. 3-4 the stacking of Si-N layers in the a silicon nitride structure follows a sequence ABCDABCD, thus closing off two interstices at 1/3, 2/3, 3/8 and 2/3, 1/3, 7/8. In the oc'-sialon, partial replacement of Si 4+ by Al 3+ occurs if, at the same time, charge compensation is effected by the accommodation of other ions, such as Li + , Ca 2 + , Y 3 + or other rare earth ions, in the two interstitial sites in the unit cell (Hampshire et al., 1978). The
154
3 Nitride Ceramics
structural principle is similar to that in the formation of the "stuffed" quartz derivatives in which Al 3+ replaces Si 4+ and valency charge balance is maintained by "stuffing" Li + or Mg 2 + into the interstitial sites. |3-Eucryptite forms a series of solid solutions with (3-quartz from [Si2O4] to Li[SiAlO4]. Hampshire et al. (1978) noted small but distinct differences between the intensities of certain reflections of the X-ray diffraction patterns of a and a' as a result of the presence of the cations in the interstitial sites in oc'-sialon. A complete structure determination on a composition close to CaSi 9 Al 3 ON 15 identified that each of the two sites contains on average 0.5 Ca atoms. Izumi et al. (1982) in a detailed Reitveld structure refinement of a'-sialon formed with Y 2 O 3 confirmed the previous hypothesis and showed that Y in the interstitial sites had seven nearest neighbours of nitrogen or oxygen atoms, with bond lengths for Y - N (or O) in the range 2.35-2.68 A. Later structure refinements on a'-sialon with Ca by Jack (1983) and by Izumi et al. (1984) confirmed that the Ca was in a similar 7-coordinated environment with an average C a - N bond length of 2.53 A. Overall, Hampshire et al. (1978) gave the general formula per unit cell as M JC Si 12 _ (m+n) Al m+n O n N 16 _ n
(3-25)
with x < 2, as there are only two interstitial sites per cell. The two factors, m and n, indicate the level of substitution in the structural network. m(Si-N) bonds are replaced by m(Al-N) bonds and n(Si-N) bonds are replaced by n(Al-O) bonds with valency compensation by cation insertion into the two interstices. Hampshire et al. (1978) related the observed changes in the cell dimensions a and c to the compositional
factors m and n. However, a survey of the published literature by Redington et al. (1991) suggests that the degree of correlation between cell dimensions of oc'-sialon and these compositional factors is low. They propose a much better correlation between cell dimensions and both the factor m and the radius of the modifying cation M, though no explanation is given as to how the ion size can have a dominant influence on cell dimensions as the composition changes. 3.4.5.3 Formation of a-Sialon Ceramics a-Sialon is derived from the reaction of silicon nitride, aluminium nitride and oxide of the appropriate modifying cation M(Y 2 O 3 , CaO etc.). The mixed powders can be shaped into a green ceramic body using appropriate fabrication techniques. As with silicon nitride and (3-sialons, densification occurs by liquid phase sintering. Slasor and Thompson (1986) discuss the difficulties of densifying single phase Y-a'sialons. The overall composition is nitrogen-rich and the amount of oxynitride liquid available for densification is small and of high viscosity. As a-sialon is formed during the reaction, the amount of liquid gradually reduces until, theoretically, complete formation of the a' solid solution occurs. In practice, some unreacted material or residual glass will be present after sintering. Cao (1991) suggests that a-sialon formation from the reaction between Si 3 N 4 , A1N and Y 2 O 3 proceeds independently of the quantity and composition of the liquid phase and is a reaction-controlled process. By using larger amounts of oxide additives than necessary for the reaction more liquid is formed, facilitating densification but resulting in residual grain boundary phases with their consequent deleterious effect on high temperature mechanical behaviour.
3.5 Silicon Oxynitride
Gas pressure sintering was also employed to achieve full densifieation. Oxidation resistance is crucially dependent on the amount of intergranular glass phase. 3.4.6 a/p-Sialon Ceramics
155
2000-
1500-
1000-
Phase relationships between a-sialon and P-sialon are shown in Fig. 3-26. The (3-sialon phases are represented by the line Si 6 _ z Al z O z N 8 _ z where 0 < z < 4.2. The Y-oc-sialon has a two-dimensional extension in the plane Si 3 N 4 -YN • 3A1N|(A1N • A12O3). The phases are compatible and can be prepared from the appropriate nitrides and oxides by pressureless sintering up to 1825°C in a single-stage firing. The rates of a' and p' formation are different and so, by varying composition, heating rate and peak sintering temperature, the microstructure can be varied to produce the characteristics required. In applications such as metal-cutting, it is important to retain strength and hardness to high temperatures. Hardness can be as high as 1800 in sintered sialons containing both (3' and a! phases compared with 1600-1800 for HPSN materials and 13501600 for sintered silicon nitrides. The hardness differential due to the presence of a' in sialon composites is retained up to high temperatures as shown in Fig. 3-27. At 1000°C these materials are much harder than alumina ceramics. 4YN 4/3(AIN-AI2O3) YN-3AIN
-•Z*
4AIN
500-
Alumina
0
500
1000
Temperature (°C)
Figure 3-27. Effect of a' content on the hot hardness (Vickers hardness) of a'/p'-sialon composites (after Ekstrom and Ingelstrom, 1986).
3.5 Silicon Oxynitride 3.5.1 Introduction
Silicon oxynitride, Si 2 N 2 O, is the only compound in the SiO 2 -Si 3 N 4 system. It was first reported by Schumb and Lefevre (1954) who identified its composition reasonably accurately. Forgeng and Decker (1958) suggested a formula of Si 2 NO for their product of nitridation of silicon in an atmosphere with a high oxygen partial pressure. Idrestedt and Brosset (1964) obtained silicon oxynitride from a silicon/ quartz mixture by heating at 1450 °C in nitrogen, and confirmed the true composition of Si 2 N 2 O. Silicon oxynitride has received less attention as an engineering ceramic than silicon nitride, but has good potential because of its excellent resistance to thermal shock (Boch and Glandus, 1979) and oxidation (Billy et a!., 1981). Its mechanical strength appears to be lower than that of silicon nitride.
3SiO
3.5.2 The Silicon Oxynitride Structure Figure 3-26. Janecke prism representation of the Y - S i - A l - O - N system showing the positions of a and p-sialon phases (after Ekstrom, 1989).
Silicon oxynitride has an orthorhombic crystal structure and unit cell dimensions
3 Nitride Ceramics
156
with silicon nitride according to:
as follows:
a (A)
b(k)
c(A)
5.498
8.877
4.853
8.843
5.473
4.835
Reference Forgeng and Decker (1958) Idrested and Brosset (1964)
The unit cell contains four formula units, Si 8 N 8 O 4 , and the structure is made up of a series of interconnected SiN 3 O tetrahedra and can be viewed as a series of parallel sheets of Si-N atoms joined by Si-O-Si bonds. Structural similarity exists between silicon oxynitride and lithium silicon nitride, LiSi 2 N 3 , and the two are mutually soluble, with the range of solid solubility as follows: LiSi2N3 <- Li1_xSi2N3_JCOJC -• [ ]Si 2 N 2 O (3-26) Jack (1986) suggests that, as the Li + ions are located between the parallel silicon-nitrogen sheets, these ceramics might provide fast cation transport and so could be developed as solid electrolytes. 3.5.3 Sintering and Properties of Silicon Oxynitride Ceramics Silicon oxynitride (see micrograph in Fig. 3-28) is formed by the reaction of silica
SiO2 + Si 3 N 4 -> 2Si 2 N 2 O
(3-27)
The reaction is facilitated by the presence of a liquid phase, thus it is necessary to include a metal oxide densification additive. The reactants dissolve through the liquid phase, diffusion occurs enabling reductions in porosity and silicon oxynitride is precipitated in a similar way to reactionsintering of sialons (see Sec. 3.4.3). Billy et al. (1981) hot-pressed silicon oxynitride with 5 wt.% MgO and the intergranular phase was a M g - S i - O - N glass. Despite this, the oxidation resistance was superior to that of silicon nitride. More recently, Ohashi et al. (1988) hotpressed silica/silicon nitride mixtures with various rare-earth oxides at 1750°C and they studied the high temperature flexural strength of the silicon oxynitride produced. By optimising the type and level of additive and the hot-pressing conditions, strengths of 600 MPa are achieved which can be retained up to 1400 °C. In a later study Ohashi et al. (1991) outlined the special case of cerium oxide as an additive. In the early stages of hot pressing, formation of a C e - S i - O - N liquid phase occurs allowing reaction and precipitation of silicon oxynitride. As Si 2 N 2 O for-
Figure 3-28. Scanning electron micrograph of silicon oxynitride (hot pressed) (after Siddiqi et al., 1986).
3.5 Silicon Oxynitride
mation proceeds, the Ce 2 O 3 :SiO 2 molar ratio of the intergranular phase increases. Initially this is amorphous but at larger hot-pressing times, as full conversion to silicon oxynitride takes place, the intergranular phase is crystalline Ce-N-apatite, Ce 5 (SiO 4 ) 3 N-Ce 467 (SiO 4 ) 3 O. High temperature strength increases from 600 MPa at 1000°C to 650 MPa at 1400°C in the silicon oxynitride with the amorphous grain boundary phase whereas there was a decrease from 600 MPa at 1000 °C to 200 MPa at 1200°C in the material containing apatite. The temperature dependence of flexural strength is strongly influenced by the difference in thermal and mechanical properties of the intergranular phase, and by environmental effects. For the amorphous grain-boundary phase, at temperatures > 1000 °C, healing of flaw-tips occurs (assisted by oxidation) as a result of softening of the vitreous phase enabling stress relaxation and crack-blunting. However, the Napatite phase is unstable and decomposes to an amorphous phase. This degradation, together with softening of residual glassy films containing large concentrations of impurity cations that remained at the grain boundaries following crystallisation, is responsible for the marked decrease in strength at high temperature. 3.5.4 O'-Sialon Ceramics
Trigg and Jack (1984) showed that approximately 0.8 mol% alumina could be incorporated into the structure of silicon oxynitride to form an O'-sialon solid solution. Its range of composition is shown in Fig. 3-23. A suitable additive such as Y 2 O 3 is used as a sintering aid to mixtures of silicon nitride/silica/alumina which react at 16001800°C to form a much larger volume of
157
liquid than in the case of pure silicon oxynitride. Thus, pressureless sintering of O sialon to near theoretical density can be achieved and the constituents of the liquid phase are subsequently incorporated into the O' solid solution, leaving only a small volume of intergranular glass phase. This can be devitrified by suitable post-preparative heat-treatment to give Y 2 Si 2 O 7 . These ceramics have flexural strengths of over 400 MPa, low coefficients of thermal expansion (a = 2.9 x 10~6 K" 1 ) and good thermal shock resistance. 3.5.5 O'-P'-Sialons
Figure 3-23 shows that there exists a two-phase O'-p' region in the S i - A l - O - N system extending up to a p'-sialon of z = 0.8. Sun et al. (1986) prepared these two-phase composites by sintering in the range 16001800°C using Y 2 O 3 as the densification aid. Reaction proceeds rapidly above 1600°C to form O' in a Y - S i - A l - O - N liquid matrix with undissolved a silicon nitride. As the temperature is raised, a dissolves and P'-sialon is precipitated from a liquid with a constantly changing composition. At lower temperatures the liquid is more oxygen-rich, precipitating the moreoxygen rich product (O'), whilst at the higher temperature the liquid becomes more nitrogen-rich, precipitating the more nitrogen-rich product (p'). The selective precipitation of the two phases allows the possibility of tailoring the microstructure by carrying out heat treatments at intermediate temperatures. Devitrification of the intergranular glass gives Y 2 Si 2 O 7 and YAG. The production of high aspect ratio crystals of O' in a P' matrix should lead to a material with good mechanical properties, but the potential of these newer sialon ceramics is still being assessed.
158
3 Nitride Ceramics
3.6 Oxynitride Glasses and Glass Ceramics
produce a more rigid glass network as follows: - S i - O - S i - -> - S i - N - S i -
(3-28)
I
3.6.1 Introduction
The ease of shaping glasses, the possibility of producing glass ceramics containing refractory oxynitride crystalline phases, and the occurrence of oxynitride glasses as grain-boundary phases in silicon nitride based ceramics has provided the impetus for a number of investigations on oxynitride glass formation and properties. Originally, small concentrations of nitrogen in oxide glasses were reported to increase their softening temperature, viscosity and resistance to devitrification. Crystallization of selected glasses has been investigated principally to complement more extensive studies of phase equilibria in M - S i - A l - O - N systems and the effects of vitreous phases on high-temperature mechanical properties of silicon nitride based ceramics including sialons and silicon oxynitride. 3.6.2 Solubility of Nitrogen in Glasses
Mulfinger (1966) was one of the first investigators to study the solubility of nitrogen in glasses and found, by bubbling nitrogen gas through the glass melt, that the physical solubility of nitrogen in glasses was very low. However, by bubbling ammonia gas through the glass melt for five hours at a temperature of 1400 °C, the chemical solubility of nitrogen in the melt reached a value 105 times higher. Using this method, 0.33 wt.% nitrogen was introduced into soda-lime-silica glass. Mulfinger suggested that the substitution of nitrogen for oxygen must lead to a higher than average coordination of non-metal atoms and that increased cross-linking should
-SiElmer and Nordberg (1967) observed that devitrification of certain glasses could be induced electrolytically. Incorporation of nitrogen into these glasses inhibited the electrolytically-induced devitrification and this they attributed to increased viscosity, due to the presence of (=NH) and (=N-) groups in the glass structure. This was one of the first observations of an improvement in some physical property resulting from the incorporation of nitrogen into the glass structure. In this case, ammonia was again used as the nitriding agent and nitrogen contents of the order of 3 wt.%, or ten times that reported by Mulfinger, were obtained. Davies and Meherali (1971) suggested that the solubility of nitrogen in glass melts was chemical rather than physical, and they found that severe reducing conditions had to be imposed in order to dissolve significant amounts of nitrogen in the glass melts. They discovered that the solubility of nitrogen increased with increasing basicity, indicating that bridging rather than non-bridging oxygen atoms were involved in the dissolution reaction. Dancy and Janssen (1976) investigated the solubility of nitrogen in CaO-SiO 2 A12O3 slags. They compared physical and chemical methods of dissolving nitrogen in these melts and found that under one atmosphere of nitrogen an equilibrium solubility of 0.25-2.5 wt.% nitrogen was achieved after 24 h. By contrast, when Si 3 N 4 was added to the melt, again under an atmosphere of nitrogen, nitrogen incorporation was very rapid and reached significantly higher levels (4 wt.%).
3.6 Oxynitride Glasses and Glass Ceramics
3.6.3 Sialon Glasses Jack (1976) observed the close similarity between the building units for the structure of silicate glasses (SiO4 tetrahedra) and those in silicon nitride (SiN4 tetrahedra) and also the similarity between the lengths of Si-N, Si-O and Al-O bonds, and proposed that nitrogen could be incorporated into the network of silicate and aluminosilicate glasses. Jack (1977) prepared oxynitride glasses in the following systems: Si 3 N 4 -Al 2 O 3 SiO 2 , Si 3 N 4 -MgO-SiO 2 , and A1NY 2 O 3 -SiO 2 , with nitrogen levels up to 10at%. Changes in physical properties due to incorporation of nitrogen were not reported at this point. Subsequently, considerable investigation by Drew et al. (1981, 1983, 1984) has been carried out on glass formation and glass properties in a wide range of M - S i - O - N and M-Si-AlO - N systems where M=Y, Mg, Ca, Al or Nd and the effects of increasing nitrogen content on properties of these glasses have also been reported. Both Shillito et al. (1978) and Loehman (1979,1980) were among the first to report correlations between amounts of nitrogen incorporated into oxynitride glasses and changes in their physical properties. Shillito et al. reported a linear increase in the Knoop hardness of a Y - S i - A l - O - N glass as the nitrogen content increased. Loehman produced more detailed results of changes in physical properties due to incorporation of nitrogen when he prepared glasses in the same system with up to 7 at.% nitrogen. Glass transition temperature (Tg), microhardness and relative fracture toughness all increased with increasing nitrogen content, whilst the thermal expansion coefficient decreased. IR spectroscopic analysis carried out by Loehman indicated that the incorporated nitrogen
159
became chemically bonded to silicon in the glass network, and by substitution for oxygen, produces a more tightly and highly linked structure. However, whilst these results did indicate improvements in properties of glasses related to incorporation of nitrogen, these property changes could not be attributed solely to the incorporation of nitrogen, since it is well known that viscosities of glasses may increase or decrease depending on field strength, polarisability and size and coordination requirements of the modifying cation. Thus for glasses with a constant nitrogen: oxygen ratio, changes in Al or M concentration may cause changes in viscosity, Tg and hardness and these variances remained unaccounted for. Drew et al. (1981, 1983) carried out extensive systematic studies on nitrogencontaining glasses in M - S i - O - N and M - S i - A l - O - N systems. Glasses with a fixed cation composition with varying nitrogen: oxygen ratios were prepared, to allow direct comparison between different M - S i - A l - O - N systems and determination of the effect on properties of replacing oxygen by nitrogen within each system. The Janecke prism representation was adopted by Drew et al. (1981, 1983) and Hampshire et al. (1985) to describe the limits of glass formation in different metal sialon systems. The limits of the metal alumino-silicate glass regions were plotted on the oxide face of the prism and it was possible to observe how the glass region extended into the M - S i - A l - O - N prism on replacing oxygen by nitrogen. The three dimensional representation of the complete glass forming regions in both the M g - and Y^Si-Al-O-N systems is shown in Figs. 3-29 and 3-30 respectively. Prior to this, investigation of these systems had been carried out by Jack (1977) and Loehman (1979) but adequate exploration
160
3 Nitride Ceramics Mg6N4
Mg 6 O (
3/2MgAI 2 O 4
Figure 3-29. Glass formation region in the Mg-sialon Janecke prism.
Y.O,
Figure 3-30. Glass formation region in the Y-sialon Janecke prism. Si 3 O 6
of the full extent of glass formation in these systems was not completed. From Fig. 3-29 it can be seen that the extent of the glass forming region in the M g - S i - A l - O - N system expands away from the oxide face with increasing replacement of oxygen by nitrogen. This increase continues until 10eq.% nitrogen is incorporated, after which the glass forming region contracts with a simultaneous shift towards slightly more Mg-rich compositions. This also shows that whilst MgO is a network modifier in oxide systems, in oxynitride glasses
it appears to act as a network former. In the Y - S i - A l - O - N system (Fig. 3-30) the expansion away from the oxide face is less at 10 eq.% N but the maximum nitrogen solubility is much greater. Depending on the particular system it was found that a limit of 17-25 eq.% of the oxygen could be replaced by nitrogen. Drew et al. (1981) found that, for glasses with a constant cation ratio, incorporation of nitrogen resulted in increasing viscosity, Tg, resistance to devitrification, refractive index, dielectric constant and ac conductivity, in all the
3.6 Oxynitride Glasses and Glass Ceramics
Mg-, Ca-, Y- and Nd-sialon glasses. The corresponding M - S i - O - N systems displayed a much smaller glass-forming region, thus showing the ability of A12O3 to extend the range of glass formation. 3.6.4 Nitrogen Coordination in Oxynitride Glass Structures
The resulting improvements in glass properties by substitution of nitrogen for oxygen was usually attributed to the replacement of a 2-coordinated bridging oxygen atom, by a nitrogen atom coordinated by three silicon ions. Thus, it was assumed that properties were improved due to an increase in the cross-linking of the silicate network due to the 3-coordinated nitrogen. Published IR data by Loehman (1979) and Schrimp and Frischat (1983) only suggested the presence of Si-N bonds in the structure. Brow and Pantano (1984) carried out more extensive studies on the coordination of nitrogen in oxynitride glasses by analysis using Fourier Transform Infrared Spectroscopy (FTIR) and X-ray Photoelectron Spectroscopy (XPS). At this point direct evidence of the formation of Si-N bonds and of the presence of 3-coordinated (nitride-like) nitrogen groups was obtained. It was concluded that nitrogen was present in the structural network, because introduction of the nitrogen caused shifting of the position of the Si-O-Si stretching peak towards that of Si-N. If nitrogen existed as precipitated Si 3 N 4 the position of the Si-O-Si peak would not be expected to change. Rand and Roberts (1973) also observed a similar shift of the Si-O-Si stretching vibration to lower wavelengths in nitrided silicon thin films. XPS studies by Brow and Pantano also revealed that nitrogen is usually present in more than one form, and they proposed
161
that non-bridging nitrogen ions may also be present, similar to the following: -Si-N--Si=Si-N 2 ~
(3-29) (3-30)
The interpretation of the XPS analysis was based on an analogous situation involving bridging and non-bridging ions in silicate glasses. The local charge on the non-bridging nitrogen ions is balanced by the presence of interstitial metal ions in their vicinity. Thus, while it has not been proven beyond doubt that nitrogen is present in oxynitride glasses in a 3-coordinated state, all evidence indicates that this is the symmetry that it accepts. No theory to indicate that it is present in some other form has been put forward to date. 3.6.5 Nucleation and Crystallisation in Oxynitride Glasses
Reports of formation of various Msialon glasses have been described with resultant changes in physical properties due to incorporation of nitrogen. After formation of these glasses, suitable heat-treatment results in the formation of tiny nuclei, upon which crystals then grow. This process results in the formation of glass ceramics which have superior properties to the parent glass. Using suitable heat treatments, properties of glass ceramics can be tailored to particular requirements. Many glasses require the addition of a nucleating agent to promote the crystallisation process, but in general oxynitride glasses are self-nucleating. Abromovici and Ish-Shalom (1985) investigated the effect of nitrogen on nucleation and crystallisation in SiO 2 -Al 2 O 3 MgO and related glass forming systems. In the SiO 2 -Al 2 O 3 -Li 2 O system they found the presence of nitrogen to influence the phase composition of crystallised samples
162
3 Nitride Ceramics
to only a limited extent. In the SiO 2 Al 2 O 3 -MgO system they reported that in samples with TiO 2 as a nucleating agent the addition of nitrogen leads to a more advanced and finer crystallisation. They concluded from this that nitrogen promotes nucleation and in some cases advances crystallisation, but they failed to give any explanation. Nitrogen is known to be an inhibitor of crystallisation because it increases viscosity, and a more probable explanation of their observation is that nitrogen does in fact inhibit growth of large crystals, but in some cases this may be compensated for by a more extensive growth of smaller crystals, where less matter transport would be required for their propagation. The crystalline phases formed in glasses on heat-treatment and the extent of their formation will determine the properties of the particular material. The phases formed will depend on both the composition of the parent glass and the heat-treatment process. Ahn and Thomas (1982) carried out preliminary studies on crystallised Y-sialon glasses. Appreciable crystallisation was only effected after glasses were doped with up to 5 wt.% ZrO 2 which acted as a nucleating agent. The main crystalline phase was Y 2 Si 2 O 7 . Winder and Lewis (1985) carried out further work in this system and reported that low nitrogen: oxygen ratios again favour formation of yttrium disilicate (Y2Si2O7), whilst the increased glass viscosity associated with an increase in the nitrogen: oxygen ratio favoured suppression of Y 2 Si 2 O 7 crystallisation and preferential formation at higher temperatures of yttrogarnet (Y3A15O12). More extensive studies of crystallisation in Y-sialon glasses were carried out by Lewis and Leng-Ward (1985). On heattreatment at 1250 °C the oxide glasses fully
crystallised to yttrium disilicate, mullite and A12O3. Again, with increasing nitrogen content the disilicate phase was progressively replaced by yttrium aluminium garnet and nitrogen was mainly incorporated into Si 2 N 2 O. Heat-treatment of the nitrogen glasses at 1100°C produced partial crystallisation involving intermediate phases related to nitrogen wollastonite. In further investigations, Lewis et al. (1986 b) investigated crystallisation in the Mg-sialon system and found that fosterite was the main crystallising phase. They also identified secondary phases and these included a magnesium substituted p'-sialon, designated as p" which was first reported by Drew et al. (1981). At higher temperatures, this is replaced by a Mg-Si-AlO - N petalite phase. More recent work by Morrissey et al. (1990) and Lonergan et al. (1991) reports on a two-stage heat treatment process for formation of glass ceramics in the N d - S i A l - O - N and M g - N d - S i - O - N systems. Figure 3-31 shows a typical microstructure of apatite crystals crystallised from the parent glass. The area of oxynitride glasses and glass ceramics offers encouraging possibilities for developing improved materials, but more detailed property evaluation must be
Figure 3-31. Micrograph of apatite crystals crystallised from a Mg-Nd-Si O - N glass.
3.7 Aluminium Nitride
carried out before these materials can be exploited fully. Whilst several investigators have demonstrated the benefits of nitrogen inclusion in oxide glasses, few have produced any detailed property measurements on the corresponding glass ceramics. The possibility of developing quality oxynitride glass ceramics by suitable heat-treatments makes the future of this field very attractive.
3.7 Aluminium Nitride 3.7.1 Introduction
Aluminium nitride was developed as an insulating substrate and packaging material for high power, high-speed microelectronic applications where its high thermal conductivity allows good heat dissipation. In this regard, it is a cheaper, non-toxic alternative to beryllium oxide. The intrinsic thermal conductivity of aluminium nitride is 3 2 0 W m ^ K ' 1 (Slack, 1973), but until recently values for the polycrystalline ceramics were in the range 50-80 Wm" 1 • K 1 . Because of the growing interest in A1N for electronic purposes, there have been further developments of improved powders and processing, which have led to better materials and renewed consideration of the ceramic for thermo-mechanical applications. 3.7.2 Structure of Aluminium Nitride
As with other covalent nitrides with equal numbers of metal and non-metal atoms, aluminium nitride adopts the wurtzite structure (2H) with nitrogen atoms in a close-packed hexagonal arrangement (ideally) and with aluminium atoms occupying half of the tetrahedral interstitial sites in the structure. The cell dimensions are a = 3.114 A, c = 4.986 A.
163
3.7.3 Synthesis of Aluminium Nitride
Aluminium nitride was reported as early as 1907 (Fichter) by reacting molten aluminium with nitrogen. This is the simplest method of synthesis of the powder according to: 2A1 + N ,
2A1N
(3-31)
but the reaction is highly exothermic and careful control is required to avoid the formation of large molten globules of aluminium. Long nitriding times result in crystal growth, and the product requires extensive milling which introduces impurities. The powder can also be produced by carbothermal reduction of alumina in nitrogen according to: A12O3 + 3C + N 2 -> 2A1N + 3 CO (3-32) Any excess carbon is removed by a low temperature oxidation step (Kuramoto and Taniguchi, 1986). Aluminium compounds may be reacted with ammonia according to: A1CL + N H , -+ A1N + 3HC1
(3-33)
but this has only limited commercial interest because of the HC1 by-product. The purity, particle size and particle size distribution, oxygen content and specific surface area all affect the sinterability and properties of A1N ceramics. 3.7.4 Fabrication and Properties of Aluminium Nitride Ceramics
The ceramic is fabricated from aluminium nitride powder mixed with densification additives such as CaO, Y 2 O 3 or a rare earth oxide by a process of die pressing or tape casting into thin sheets followed by blanking out. The green shapes are then sintered at 1650-1900 °C in a nitrogen atmosphere. Hot pressing has been
164
3 Nitride Ceramics
employed to fabricate material for assessment of mechanical properties. Aluminium nitride powder always contains oxygen within the surface layers, and reaction occurs with the additives to form a liquid phase which allows sintering to near theoretical density (3.26gem"3). With yttrium oxide as a sintering aid, the yttrium aluminium garnet (YAG) is formed at the grain boundaries. In addition to aiding densification, the oxide additive forms a secondary phase (usually an aluminate) which removes the oxygen from the aluminium nitride grains. In order to improve the thermal conductivity, secondary phases should be localised at triple points or removed completely. Russel etal. (1991) show that the thermal conductivity increases dramatically with Y 2 O 3 content. This is because at low yttrium levels (<0.8wt.%), YAG forms as an almost continuous grain-boundary phase inhibiting the conduction between A1N grains (thermal conductivity 50g O W m ^ K " 1 ) . With increasing yttrium levels, YAG forms as larger grains (up to 15|im) leaving "clean" contacts between individual A1N grains. At 4.2 wt.% yttrium, thermal conductivity is 160Wm" 1 K" 1 . Microstructural development which isolates the secondary phase obviously leads to thermal conductivity improvements. An alternative approach has been modification of the additive or processing conditions in order to eliminate the secondary phase completely. Kuramoto et al. (1989) describe the development of a translucent aluminium nitride ceramic produced from a very pure starting powder. The sintering aid was tricalcium aluminate, 3 CaO • A12O3 (C3A). Firing was carried out up to 1800°C allowing the formation of a liquid phase which promoted particle rearrangement, solution-precipitation and grain growth. After initial heating to the sintering tem-
perature, a fully dense material with thermal conductivity of 9 0 W m ~ 1 K " 1 is formed with Ca concentrated at triple points within the grain boundaries. During an isothermal soak at 1800°C, thermal conductivity increases to 1 7 5 W m ^ K " 1 and the material becomes translucent, as the Ca content decreases because the liquid phase is eliminated from the ceramic. The additive (C3A) is necessary for this process in order to remove oxygen from the A1N. A1N without additives has much lower thermal conductivity because oxygen is still retained within the grains. A further approach reported by Ueno and Horiguchi (1989) is to eliminate the oxide phase by a carbothermal nitridation process. The A1N was sintered with 5 wt.% Y 2 O 3 at 1900 °C in a carbon sagger under nitrogen. YAG (A15Y3O12) or YAM (A12Y4O9) are formed as grain boundary phases. These react with carbon and nitrogen according to: (3-34)
The microstructural changes are shown schematically in Fig. 3-32. Because of the surface reaction (3-34), an oxygen concentration gradient is developed and grainboundary diffusion of the oxide phase to the surface occurs with further conversion to YN. The whole process is controlled by the surface reaction. The surface YN is removed by treatment with water following sintering. Thermal conductivity for these ceramics is reported as high as 266Wmr 1 K~ 1 . These translucent A1N ceramics have been used commercially as heat sinks for various thyristor modules and substrates for discrete packages of laser and light emitting diodes. The mechanical properties at ambient temperatures would suggest that aluminium nitride has less poten-
3.8 Aluminium Oxynitride (AION) Ceramics
165
N2 -•
>1800°C
CO
H90
Y(OH)3+NH3T
Figure 3-32. Schematic diagram of the surface reaction on AIN in contact with carbon which converts the grain boundary yttrium aluminate to YN (after Ueno and Horiguchi, 1989).
tial as a material for high stress applications, though some limited studies have been carried out at temperatures up to 1200 °C (Billy and Mexmain, 1985). Oxidation at > 800 °C limits its usefulness. In summary, aluminium nitride offers two major advantages: it can be produced as a ceramic with a high thermal conductivity, and in a translucent form.
3.8 Aluminium Oxynitride (AION) Ceramics 3.8.1 Introduction
Aluminium oxynitride spinel (AION) is a new ceramic which can be processed into a fully dense transparent material that could replace translucent alumina in applications where optical transparency in the infra red and visible regions is required. Yamaguchi and Yanagida (1959) reported that a spinel cubic form of A12O3 could be stabilized above 1000 °C and concluded that this was due to incorporation of nitrogen. Further work on formation of this spinel oxynitride was carried out by Michel etal. (1966) and Collongues et al. (1967). The major impetus for further work of these materials was the developments in
sialon ceramics (see Sec. 3.4) which generated an interest in understanding phase equilibria in the Si-Al-O-N system and sub-systems including A12O3-A1N. 3.8.2 Structure of AION
Goursat etal. (1981) have determined the crystal structure of AION by neutron diffraction and have confirmed that it is a cubic spinel assigned to space group Fd3m. A number of authors give solid solubility limits which are shown in Table 3-7 along with the oxynitride spinel structure models applicable. The lattice parameter of the aluminium oxynitride spinel varies from a = 7.938 A — 7.951 A as nitrogen concentration increases (Lejus, 1964; McCauley
Table 3-7. Solubility limits and spinel models for aluminium oxynitride (AION). Range of solubility (mol.% AIN) 33-50 27-40 27-40
Oxynitride spinel structure model
Reference
Al (2+x)/3 [] ( 3_ 4x)/12 O (3 _ x) N x Adams etal. 0<x<3/4 (1962) . Lejus (1964) Al(8 + x)/3 [ ](1 - x)/3 O(4 - x) ^ A1
n
O
/ 1
1M x
^ (64 + x)/3L J(8-i)/3 u (32-x) ! > l
0<x<8
McCauley (1978)
166
3 Nitride Ceramics
and Corbin, 1979) compared with a = 7.914 A for y-Al 2 O 3 . 3.8.3 Phase Relationships in the A l - O - N System Corbin (1989) lists thirteen different aluminium oxynitride phases. y-AlON (A123O27N5) and <£'-AlON (Al 22 O 30 N 2 ) are the spinel types reported by McCauley (1978). A (S-A1ON spinel has been observed by many researchers (Long and Foster, 1961; Adams et al., 1962; Lejus, 1964; Gauckler and Petzow, 1977; Goursat et al., 1981). Goursat et al. found /-A1ON spinel to be an oxidation product of A1ON. In addition, (/>-AlON was determined to be monoclinic (Michel, 1972). The polytypoids of aluminium nitride, which are based on the Wurtzite structure, all extend from the Si-Al-O-N system to the A1 2 O 3 A1N binary. These are 12H (A16O3N4), 21R (A17O3N5), 16H (A18O3N6), 27R (A19O3N7). In addition there exists 20 H (Al 10 O 3 N 8 ) and 32H (A116O3N14) in the A12O3-A1N system only. McCauley and Carbin (1979) constructed the phase diagram for the A12O3-A1N system and undertook an extensive microstructural analysis as part of that study. 3.8.4 Formation of A1ON Ceramics
Optically transparent A1ON has been prepared by both hot pressing and pressureless sintering. In order to achieve transparency it must not contain pores or secondary phases. McCauley and Carbin (1979) used a reaction sintering process to convert mixtures of A1N and A12O3 to A1ON at 2025 °C under nitrogen. Hartnett and Gentilman (1984) used a two stage process involving firstly the formation of A1ON powder by reaction of A12O3 with carbon under nitrogen or reaction of A12O3 with A1N. The A1ON powder was
blended with rare earth oxides (Y 2 O 3 , La 2 O 3 , etc.) as densification additives and sintered at 1930 °C for 24 to 48 hours (Gentilman et al., 1985). Ado et al. (1985) suggest that sintering occurs by a volume diffusion mechanism. Kim and Richards (1985) report that ionic conductivity occurs in A1ON in the range 1300-1500 °C, which is evidence that bulk ionic diffusion occurs. Maguire et al. (1987) describe a mechanism of liquid phase sintering involving formation of a transient liquid phase which is subsequently incorporated into the A1ON structure giving a fully dense material with no secondary phases, and hence "clean" grain boundaries. 3.8.5 Properties of A1ON Ceramics
Selected properties of A1ON ceramics are listed in Table 3-8. The optical and dielectric properties make it suitable for potential use as an electromagnetic window material. The thermal conductivity is much lower than for A1N and therefore the material is not suitable for the same types of microelectronic applications. The thermal expansion coefficient is comparable with that of A12O3, and thermal shock resistance is actually lower (Quinn et al., 1984). At 306 MPa the flexural strength is similar to that found for A1N, and reduces to 267 MPa at 1000 °C. This was obtained on coarse-grained (25-100 jim) material (Quinn et al., 1984) and the critical flaw was a large grain or residual pore. Fracture toughness is quite low at 2.02.9MPam 1/2 . Oxidation resistance is better than for A1N (Goursat et al., 1981) and little degradation occurs below 1200°C. Further development of processing will result in significant property improvements. The ma-
3.10 Future Potential of Nitride Ceramics
167
Table 3-8. Selected properties of A1ON ceramics. Property Refractive index at X — 0.55 um IR cut-off UV cut-off Dielectric constant at20°C, 100 Hz at500°C, 100 Hz Loss tangent at20°C, 100 Hz at500°C, 100 Hz Thermal conductivity at 20 °C Thermal expansion coefficient at 25-1000 °C Flexural strength at20°C at 1000°C Fracture toughness
terial is poised to replace a-Al 2 O 3 in many applications where optical transparency combined with high strength and high temperature stability are important.
3.9 Boron Nitride Boron nitride is isoelectronic with carbon and exists as two structural modifications similar to graphite (hexagonal or HBN) and diamond (cubic or CBN). HBN is soft and platelike and is manufactured as a ceramic by hot-pressing, producing a material which exhibits anisotropy because platelets are oriented in directions perpendicular to that of the applied pressure (Morrell, 1985). Thin-walled shapes, for applications such as crucibles for special glasses, may be produced by a chemical vapor deposition (CVD) or pyrolytic method, the boron nitride being deposited on a suitably shaped graphite substrate which is subsequently removed. Thermal (and electrical) conductivity parallel to and perpendicular to the plane of the substrate are substantially different.
Value
Reference
1.77-1.88 5.12 urn 0.27 um
McCauley and Corbin (1979) Hartnett and Gentilman (1984) Hartnett and Gentilman (1984)
8.5 14.0
Corbin and McCauley (1982)
0.002 1.0 10.89 W m ^ K - 1 7.6xlO 6 K~ 1
Corbin and McCauley (1982)
306 MPa 267 MPa 2.0-2.9 MPa m 1/2
Quinn et al. (1984) Quinn et al. (1984) Quinn et al. (1984)
Quinn et al. (1984) Quinn et al. (1984)
The cubic form of BN, with a much higher density, is very hard and produced from the hexagonal form at high temperature and pressure, similar to the synthesis of diamond. CBN is used as grinding material in grit form or as a solid ceramic for the manufacture of metal-cutting tools.
3.10 Future Potential of Nitride Ceramics Nitride ceramics have been commercialised for applications in cutting, as wear parts, bearings and seals. As a result of the developments outlined in this chapter there has been an increasing interest in and much wider use of ceramics in engineering applications over the last twenty years. The goal that still eludes the ceramic technologists is the production of the allceramic advanced gas turbine, and no commercial process is yet available for manufacturing nitride ceramics with the combination of properties, reliability and reproducability for this exacting application. The development of these ceramics as
168
3 Nitride Ceramics
automotive components, particularly in diesel engines, will be a much easier task and they are already in production as turbocharger rotors and other components. Further developments in nitride ceramics will follow from a more fundamental understanding of the relationships between processing, microstructure and properties. In the long term, the requirement will be for high performance ceramics that can be produced consistently, reliably and cheaply if they are to compete with existing developed materials.
3.11 Acknowledgements The author wishes to thank Ms D. O'Reilly, Mr R. Flynn and Mr D. O'Sullivan for their help in the preparation of this article. Research on nitride ceramics at the University of Limerick has been sponsored by the European Community and EOLAS, the Irish Science and Technology Agency.
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3 Nitride Ceramics
Lewis, M. H., Mason, S., Szweda, A. (1986a), in: Non-oxide Technical and Engineering Ceramics: Hampshire, S. (Ed.). Barking: Elsevier Applied Science, pp. 175-190. Lewis, M. H., Leng-Ward, G., Wild, S. (1986b), /. Mater. Sci. 21, 1647-1653. Lewis, M. H., Leng-Ward, G., Mason, S. (1987), in: Engineering with Ceramics 2: Freer, R., Newsham, S., Syers, G. (Eds.). Br. Ceram. Proc. 39, 1-12. Lindley, M. W, Elias, D. P., Jones, B. R, Pitman, K. C. (1979), J. Mater. Sci. 14, 70-85. Loehman, R. E. (1979), J. Am. Ceram. Soc. 62, 4 9 1 494. Loehman, R. E. (1980), J. Non-Cryst. Solids 42, 433446. Lonergan, X, Morrissey, V., Hampshire, S. (1991), in: Special Ceramics 9: Freer, R., Stevens, R. (Eds.). Br. Ceram. Proc. 49, 57-66. Long, G., Foster, L. M. (1961), /. Am. Ceram. Soc. 42, 255. Longland, P., Moulson, A. J. (1978), J. Mater. Sci. 13, 2279-2280. Lumby, R. X, Coe, R. F. (1970), Proc. Br. Ceram. Soc. 15, 91-101. Lumby, R. X, North, B., Taylor, A. X (1975), in: Special Ceramics 6: Popper, P. (Ed.). Stoke-onTrent: Br. Ceram. Res. Assoc, pp. 283-298. Maguire, E. A., Hartnett, T. M., Gentilman, R. L. (1987), U.S. patent 4686070. Mangels, X A. (1983), in: Progress in Nitrogen Ceramics: Riley, F. L. (Ed.). The Hague: Martinus Nijhoff, pp. 231-236. Mangels, X A., Tennenhouse, G. X (1980), Am. Ceram. Soc. Bull. 59, 1216-1218. Marchand, R., Laurent, Y, Lang, X, Le Bihan, M. Th. (1969), Ada Crystallogr. Sect. B 52, 21572160. Masaki, H., Oyama, Y, Kamigaito, O. (1975), Jpn. J Appl. Phys. 14, 301. McCauley, X W (1978), / Am. Ceram. Soc. 61, 372. McCauley, X W, Corbin, N. D. (1979), J. Am. Ceram. Soc. 62, 476. Michel, D. (1972), Rev. Int. Hautes Temp. Refract. 9, 225. Michel, D., Perez y Jorba, M., Collongues, R. (1966), C. R. Acad. Sci., Ser. C 263, 837. Mitomo, M. (1976), J. Mater. Sci. 11, 1103-1107. Mitomo, M. (1977a), /. Mater. Sci. 12, 273-276. Mitomo, M. (1977b), Yogyo Kyokaishi 85, 50. Morrell, R. (1985), Handbook of Properties of Technical and Engineering Ceramics, Part 1, An Introduction for the Engineer and Designer. London: HMSO. Morrissey, V., Lonergan, X, Hampshire, S. (1990), in: Fabrication Technology: Davidge, R. W, Thompson, D. P. (Eds.). Br. Ceram. Proc. 45, 23-32. Moulson, A. X (1979), J. Mater. Sci. 14, 1017-1051. Mulfmger, H. O. (1966), /. Am. Ceram. Soc. 49, 462467.
Ohashi, M., Tabata, H., Kanzaki, S. (1988), /. Mater. Sci. Lett. 7, 339-340. Ohashi, M., Kanzaki, S., Tabata, H. (1991), J. Am. Ceram. Soc. 74, 109-114. Oyama, Y (1972), Jpn. J. Appl. Phys. 11, 160-111. Oyama, Y, Kamigaito, O. (1971), Jpn. J. Appl. Phys. 10, 1637. Oyama, S. T, Schlatter, X C , Metcalfe, III, X E., Lambert, Jr., X M. (1988), Ind. Eng. Chem. Res. 27, 1639-1648. Parr, N. L., Martin, G. R, May, E. R. W (1960), in: Special Ceramics 1: Popper, P. (Ed.). London: Heywood, pp. 102-135. Patel, X K., Thompson, D. P. (1988), Br. Ceram. Trans. J. 87, 70-73. Pomeroy, M. X, Hampshire, S. (1989), Mater. Sci. Eng. A109, 389-394. Popper, P., Ruddlesden, S. N. (1957), Nature 179, 1129. Powell, B. D., Drew, P. (1974), /. Mater. Sci. 9,18671970. Priest, H. R, Burns, R C , Priest, G. L., Skaar, E. C. (1973), /. Am. Ceram. Soc. 56, 395. Quinn, G. D., Corbin, N. D., McCauley, X W (1984), Am. Ceram. Soc. Bull. 63, 723-730. Rae, A. W X M., Thompson, D. P., Jack, K. H. (1978), in: Ceramics for High Performance Applications II: Burke, X X, Lenoe, E. N., Katz, R. N. (Eds.). Proc. 5th Army Mater. Tech. Conf. Chestnut Hill, Mass: Brook Hill, pp. 1039-1067. Rand, M. X, Roberts, X P. (1973), J. Electrochem. Soc. 120, 446. Redington, M. (1989), Ph.D. Thesis, University of Limerick. Redington, M., O'Reilly, K., Hampshire, S. (1991), /. Mater. Sci. Lett. 10, 1228. Roberts, W, Grieveson, P., Jack, K. H. (1972), /. Iron Steel Inst. London 210, 931-937. Roebuck, P., Thompson, D. P. (1977), in: High Temperature Chemistry of Inorganic and Ceramic Materials: Glasser, R P., Potter, P. E. (Eds.). London: The Chemical Society, pp. 222-228. Rouxel, T. (1990), These pour Docteur de l'Universite de Limoges, France, p. 129. Russel, C , Hofmann, T, Limoner, G. (1991), CFI, Ceram. Forum Int. 68, 22-26. Schrimp, C , Frischat, G. H. (1983), /. Non-Cryst. Solids 56, (1-3) 153-160. Schumb, W C , Lefevre, R. A. (1954), /. Am. Chem. Soc. 76, 5882. Shaw, T. M., Thomas, G. R. (1983), in: Progress in Nitrogen Ceramics: Riley, R L. (Ed.). The Hague: Martinus Nijhoff, pp. 331-336. Shillito, K. R., Wills, R. R., Bennett, R. E. (1978), /. Am. Ceram. Soc. 61, 537. Siddiqi, S. A., Higgins, I., Hendry, A. (1986), in: Non-oxide Technical and Engineering Ceramics: Hampshire, S. (Ed.). Barking, UK: Elsevier Applied-Science, pp. 119-132.
3.12 References
Slack, G. A. (1973), J. Phys. Chem. Solids 34, 321. Slasor, S., Thompson, D. P. (1986), in: Non-oxide Technical and Engineering Ceramics: Hampshire, S. (Ed.). Amsterdam: Elsevier, pp. 223-230. Sproul, W. D., Rothstein, R. (1985), Thin Solid Films 126, 257. Stinton, D. P., Besmann, T. M., Lowden, R. A. (1988), Am. Ceram. Soc. Bull 67, 350-355. Sun, W. Y, Walls, P. A., Thompson, D. P. (1986), in: Tailoring Multiphase and Composite Ceramics: Tressler, R. E., Messing, G. L., Pantano, C. G., Newnham, R. E. (Eds.). Mater. Sci. Res. 20, 93. Terwilliger, G. R., Lange, F. F. (1974), /. Am. Ceram.
Soc. 57,25-29. Terwilliger, G. R., Lange, F. F. (1975), J. Mater. Sci. 10, 1169-1174. Toth, L. E. (1971), Transition Metal Carbides and Nitrides. New York: Academic. Trigg, M. B., Jack, K. H. (1984), in: Ceramic Components for Engines: Somiya, S., Kamai, E., Ando, K. (Eds.). Tokyo: KTK Scientific, pp. 199-207. Tripp, W. C , Graham, H. C. (1976), J. Am. Ceram. Soc. 59, 399. Turkdogan, E. T, Bills, P. M., Tippett, V. A. (1958), J. Appl. Chem. 8, 296-302. Ueno, F, Horiguchi, A. (1989), in: Euroceramics 1: De With, G., Terpstra, R. A., Metselaar, R. (Eds.). Amsterdam: Elsevier, pp. 383-387. Vassiliou, B., Wilde, F. G. (1957), Nature 179, 435436. Weiss, L., Engelhardt, T (1910), Z. Anorg. Chem. 65, 38. Weston, R. X, Carmthers, T. G. (1973), Proc. Brit. Ceram. Soc. 22, 197. Wild, S., Grieveson, P., Jack, K. H. (1968), The Crystal Chemistry of Ceramic Phases in the Si-N-0 and Related Systems, Prog. Rep. No. 1, Ministry of Defence Contract N/C/CP.61/9411/67/4B/MP.387. Wild, S., Grieveson, P., Jack, K. H. (1972a), in: Special Ceramics 5: Popper, P. (Ed.). Stoke-on-Trent: Br. Ceram. Res. Assoc, pp. 385-395. Wild, S., Grieveson, P., Jack, K. H. (1972b), in: Special Ceramics 5: Popper, P. (Ed.). Stoke-on-Trent: Br. Ceram. Res. Assoc, pp. 271-287.
171
Wild, S., Grieveson, P., Jack, K. H., Latimer, M. J. (1972c), in: Special Ceramics 5: Popper, P. (Ed.). Stoke-on-Trent: Br. Ceram. Res. Assoc, pp. 377382. Wills, T. T., Holmquist, S., Wimmer, J. M., Cunningham, J. A. (1976), J. Mater. Sci. 11, 1305-1309. Winder, S. M., Lewis, M. H. (1985), J. Mater. Sci. Lett. 4, 241-243. Wotting, G., Hausner, H. (1983), in: Progress in Nitrogen Ceramics: Riley, F. L. (Ed). The Hague: Martinus Nijhoff, pp. 211-218. Wotting, G., Ziegler, G. (1984), Ceram. Int. 10, 18. Wotting, G., Ziegler, G. (1986), Inter ceram 35, 3235. Wroten, W. L. (1954), Mater. Methods 40, 83-85. Yamaguchi, G., Yanagida, H. (1959), Chem. Soc. Jpn. Bull. 32, 1264. Ziegler, G., Wotting, G. (1985), Int. J. High Technol Ceram. 1, 31-58. Ziegler, G., Heinrich, J., Wotting, G. (1987), J. Mater. Sci. 22, 3041-3086.
General Reading Ceramics and Glasses (1991), Vol. 4 of Engineered Materials Handbook. Materials Park, OH: ASM Int. Chen, I.-W, Becher, P. K, Mitomo, M., Petzow, G., Yen, T.-S. (1993), Silicon Nitride Ceramics - Scientific and Technological Advances. Mater. Res. Soc. Symp. Proc. 287. Hampshire, S. (Ed.) (1986), Non-oxide Technical and Engineering Ceramics. London: Elsevier. Morrell, R. (1985), Handbook of Properties of Technical and Engineering Ceramics, Part I: An Introduction for the Engineer and Designer. London: Her Majesty's Stationery Office. Riley, F. L. (Ed.) (1977), Nitrogen Ceramics. Leyden: Noordhoff. Riley, F. L. (Ed.) (1983), Progress in Nitrogen Ceramics. The Hague: Martinus Nijhoff.
4 Boride and Carbide Ceramics Rainer Telle
Rheinisch-Westfalische Technische Hochschule Aachen, Institut fur Gesteinshiittenkunde, Aachen, Federal Republic of Germany
List of 4.1 4.2 4.2.1 4.2.1.1 4.2.1.2 4.2.1.3 4.2.2 4.2.2.1 4.2.2.2 4.3 4.3.1 4.3.1.1 4.3.1.2 4.3.1.3 4.3.1.4 4.3.1.5 4.3.2 4.3.2.1 4.3.2.2 4.3.2.3 4.3.3 4.3.3.1 4.3.3.2 4.3.3.3 4.4 4.4.1 4.4.1.1 4.4.1.2 4.4.1.3 4.4.1 A 4.4.2 4.4.2.1 4.4.2.2 4.4.3
Symbols and Abbreviations 175 Introduction 176 Chemical Bonding and Crystal Chemistry 176 Chemical Bonding of Carbides 176 Structure of Boron Carbide and Isotypic Compounds 177 Structure and Polytypes of Silicon Carbide 180 Structure of Transition Metal Carbides 182 Chemical Bonding of Borides 185 The Crystal Structure of Borides 185 A1B2-Type Structures 186 Phase Systems 188 Binary Phase Diagrams Containing Carbides 189 The B - C System 189 The Si-C System 189 The T i - C System 190 The W - C System 191 Other Transition Metal-Carbon Systems 191 Binary Phase Diagrams Containing Borides 192 The T i - B System 193 The Z r - B System 193 Other Transition Metal-Boron Systems 194 Ternary and Higher Systems 194 Boron-Carbon-Metal Systems (Ceramic Systems) 195 Systems with Transition Metal Carbides or Borides and Metallic Binders . 197 Systems with Two Transition Metals and Carbon or Boron 198 Material Preparation 201 Preparation of Silicon Carbide 201 Technical Scale Production 201 High-Purity Material 203 Organometallic Precursors 203 Poly type Formation During SiC Synthesis 206 Preparation of Boron Carbide 207 Technical Scale Production 207 High-Purity Material 208 Preparation of Transition Metal Carbides 209
Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.
174
4.4.4 4.5 4.5.1 4.5.1.1 4.5.1.2 4.5.1.3 4.5.2 4.5.2.1 4.5.2.2 4.5.2.3 4.5.2.4 4.5.2.5 4.5.3 4.5.3.1 4.5.3.2 4.5.3.3 4.6 4.6.1 4.6.2 4.6.3 4.6.4 4.6.5 4.6.6 4.6.7 4.7 4.8
4 Boride and Carbide Ceramics
Preparation of Transition Metal Borides Sintering Behavior of Carbide and Boride Ceramics Densification of Boron Carbide Pressureless Sintering without Additives Pressureless Sintering with Additives Hot-Pressing and Hot Isostatic Pressing Densification of Silicon Carbide Pressureless Sintering with Additives Hot-Pressing, Hot Isostatic Pressing and Shock Wave Consolidation High Pressure Self-Propagating Combustion Synthesis Microstructural Development and the |3-to-a Transformation in Sintered Silicon Carbide Recrystallized and Si-Infiltrated Silicon Carbide Densification of Transition Metal Borides Pressureless Sintering Hot-Pressing and Activated Sintering Cemented Borides Microstructural Reinforcement of Boride and Carbide Ceramics Metal Matrix Reinforcement Grain Size Refinement Silicon Carbide and Boron Carbide Particulate-Reinforced Materials . . . . Transition Metal Carbide Particulate-Reinforced Materials Transition Metal Boride Particulate-Reinforced Materials Multiphase Hard Materials Based on Carbide-Boride and Carbide-Nitride-Boride-Silicide Composites Transformation Toughening of Borides and Carbides Fields of Application and Outlook References
210 211 212 212 213 216 219 219 223 224 224 226 229 229 230 231 235 236 239 239 241 242 248 250 253 258
List of Symbols and Abbreviations
List of Symbols and Abbreviations a,b,c A, H, HA (B 4 C)
3C,4H,6R Cp Et (g)
h°
H
KIc,Klco (1) liquid Liquid m M Me Ph r (s) T Te Tm Vc,si X
[100] (100) D
a,fty (p, CO, T
CVD FTIR HIP HK HR HV SEM TEM TZP
lattice constants stacking positions solid solutions polytype notations of SiC (C: cubic, H: hexagonal, R: rhombohedral) cyclopentadienyl ethyl vapor phase neutral hole in a crystal lattice hardness fracture toughness in MPa m 1/2 liquid phase binary liquid ternary liquid Weibull modulus metal methyl phenyl radius solid phase ternary phases eutectic temperature absolute melting temperature vacancy in carbon or silicon sublattice carbon-to-metal ratio lattice directions Miller indices symbol for vacancy in a chemical formula polytypes or phases ternary phases fracture strength in bending, modulus of rupture chemical vapor deposition Fourier transform infrared (spectroscopy) hot isostatic pressing Knoop hardness Rockwell hardness Vickers hardness scanning electron microscope transmission electron microscope tetragonal zirconia polycrystals
175
176
4 Boride and Carbide Ceramics
4.1 Introduction Materials with exceptional mechanical, chemical, electrical and thermal properties are permanently sought in industrial research and development. For successful economic application, these materials should be available without any limitations; prepared by relatively simple methods, they should exhibit a low specific gravity, high reliability, long lifetime and of course - they should be available at low cost. Unfortunately, most materials do not satisfy all of these requirements and, hence, disadvantages and disappointments have to be tolerated in development and application. A new class of materials with extreme hardness, wear resistance and corrosion reistance in comparison to metals is advanced ceramics. They are about to penetrate the market in areas where high-temperature application combined with wear resistance, thermal shock resistance and corrosion resistance is required. The most important materials besides oxide ceramics such as alumina, zirconia, silicon nitride, and sialons, are carbides such as silicon carbide, titanium and other transition metal carbides, the latter also being constituents of hard metals and cermets. These materials have been developed to such high performance that they are ready for use not only as wear-resistant, structural components in automotive engines and other machinery, but also as cutting tools or as high-temperature materials for conventional and nuclear power plants, aerospace and military applications. Amongst these advanced ceramics, boride-based materials are not yet in as widespread use as the other materials, although they have some interesting properties such as extreme hardness, which make them superior to oxides and nitrides. The
unique interaction of metallic, covalent and ionic types of bonding also results in a high melting point combined with metallic, electric and thermal conductivity and excellent wetting by metallic melts. The combination of all of these properties makes it worthwhile to consider the borides, including boron carbide, as an interesting class of wear-resistant materials if their major disadvantages, namely brittleness and poor sinterability can be overcome.
4.2 Chemical Bonding and Crystal Chemistry The nature of the chemical bonding is the key to the physical and chemical behavior of matter. Carbides and borides possess exceptional properties due to a high amount of covalent bonding in combination with small band gaps or even metal-like transport properties. The formation of polytypes in the case of silicon carbide, or many unique crystal structures found only in borides, reflects the outstanding nature of these materials. 4.2.1 Chemical Bonding of Carbides
Carbon forms a variety of binary compounds which are very different in structure and properties. Elements of the first, second and third column of the periodic table form salt-like compounds which can be described as derivatives of methane (C4~ anion, e.g. A14C3) or acetylene (C\~ anion, e.g. CaC 2 ). The carbides of the first and second groups are comparatively soft, translucent if of high purity, and electrically non-conducting. The Ilia group carbides are opaque with a partially semimetallic luster. Metallic carbides of technical relevance exist for the IVa, Va, and Via groups, as well as for the Vila
4.2 Chemical Bonding and Crystal Chemistry
and Villa groups. These materials have high hardness and electrical conductivity. Carbides possessing properties close to diamond and thus having exceptionally high hardness and semiconductivity are SiC and B 4 C. BeC2 can probably also be included in this group. Finally, compounds with hydrogen, oxygen, nitrogen, sulfur or halides exist which are volatile or gaseous species and are thus not of interest in this context. It is obvious, however, that carbon initiates all three types of bonding. The unique properties of the transition metal carbides result from a mixture of ionic, covalent, and metallic bonds being simultaneously active in one crystal structure, as pointed out in the discussions on the particular compounds. A summary of the carbide forming elements in the periodic table is given in Fig. 4-1 (Benesovsky, 1966). 4.2.1.1 Structure of Boron Carbide and Isotypic Compounds
Boron carbide, referred to as (B4C) in brackets indicating the solid solution in contrast to B 1 3 C 2 , for example, meaning the stoichiometry, crystallizes in the trigonal-rhombohedral space group Kim. The unit cell is shown in Fig. 4-2. The structure may be described as a cubic primitive lattice elongated in the direction of the space diagonal with almost regular icosahedra at the corners. Parallel to the space diagonal, which becomes the oaxis in hexagonal notation, a linear chain consisting of three boron atoms interconnects the adjacent icosahedra. Thus the unit cell contains twelve icosahedral sites and three sites on the linear chain. If B atoms are attributed to the icosahedral positions and C atoms are considered to be situated in the linear chain, a stoichiometry of B 1 2 C 3 , i.e. B4C, results. The icosahedra exhibit two topologically different positions, first the Bl
177
position (also known as 6/?^ which consists of a planar array of three atoms perpendicular to the linear chain around the outer atoms. Thus, this position occurs six times in the unit cell. The second distinguishable icosahedral site is the B2 (or 6h2) position which is situated in the middle of the edges of the rhombohedral unit cell and accounts for a further six atoms. A special position is the centrosymmetric B 3 (or lb) site in the linear chain, which is considered to be preferentially occupied by larger atoms such as Al and Si that form solid solutions (La Placa and Post, 1961; Lipp, 1966 b; Lipp and Roder, 1966 a, b; Matkovich and Economy, 1977 b). For the binary solid solution series the question is whether the linear chain is formed by a C - C - C , a C - B - C or a C - C - B array throughout the homogeneity range and how to explain the variations in the stoichiometry (Clark and Hoard, 1943; Allen, 1953; Neidhard et al., 1970; Ploog, 1974; Will and Kossobutski, 1976; Kirfel et al., 1979; Werheit and de Groot, 1980; Conard et al., 1986; Tallant et al., 1989; Aselage et al., 1989, 1990; Aselage and Emin, 1991; Morosin et al., 1991). The majority of the authors agree that the linear chain is of the C - B - C type and does not change with the C content, which fits the stoichiometry of the most stable compound in the system, B 1 3 C 2 . The linear chain thus contains a closed shell of ten valence electrons which is achieved by a charge transfer to the B 1 2 icosahedra to which 38 valence electrons are formally assigned. The charge difference between B and C within the chain results in even stronger electrostatic binding forces (Kirfel et al., 1979), but the energetic differences estimated by density-ofstate calculations are very small (Kleinman, 1991). Since there is a deficiency of one electron in the icQsahedron, additional C as an electron donor preferentially re-
IA
IIA
IMA
IVA
VA
VIA
VIIA
VIM
IB
ne
IIIB
IVB
VB
VIB
salt-like carbides, acetylides, metal-graphite compounds
0
VIIB
!
metaiiic carbides of IVA to VIA subgroup metals
j |
metaiSic carbides of ferrous metals, including Cr and Mn
i
j H4C HxCy
| j
/ He
i/
I metallic carbides of the VB main group
LiA
il
diamond-like carbides
Be 2 C
B4C
|| (NC)2
oc o?c
F4C
ii
S2C
CI4C
volatile nonmetallic carbon compounds
1 NaC 8 1 NaC16
MgA Na 2 C 2
[?]
carbides possible but unknown
0
no carbides but solubility in the melt
MgC 2
V 2 C*> ,KC8 |KC 1 6 KC60
CaC 2 Sc 15 C 19 VC
RbC 8 RbC16 RbC60
CsC 8 CsC 16
Cr2A
Sc 4 C 3 K2C2
Rb 2 C 2
Cs 2 C 2
Fr?
SrC 2
BaC 2
Ra?
AI 4 C 3
* several modifications
YC1X Y 15 C 19
Nb2C*» Nb3C2
YC2
NbA NbC
La 2 C 3 LaC 2 **>
i
Ta2C*> Ta 3 C 2 Ta 4 C 3 TaC
CrA J Cr3C2
Mn 23 C 6 Mn 15 C 4 Mn 3 C
MnA MnA
Ar
Tc?
Ru
Co,C
Ni3C
!' Cu2C2
ZnC 2
Ga
Ge
! As 2 C 6
Se2C
Br 4 C
Te?C
J4C
/ i
•
Kr
I
/
I
Xe
Mo 2 C*'
Pd
Rh /
W2C*> WC,.,
WC
Os
PrC PrA PrC 2
Nd 2 C 3 NdC 2
PmC 2
ThC
PaC
UC
NpC
u2c3
Np 2 C 3 NpC 2
PaC 2
i Ag2C2
Sn
CdC 9
Sb
i
i
Pt
,
Au 2 C 2
Po?
Pb
HgC 2
ReC
Ce 2 C 3 CeC 2
ThC 2
|
h
Fe3C FeA Fe?C
Sm 3 C
Figure 4-1. Carbide forming elements in the periodic table (Benesovsky, 1966). ***Actinides
PA
Ne
/
j /
Ac? ***)
* Lanthanides
SiC
!
I
UC2
SrriA SmC2 PuC PuA PuC 2
EuC 2
Am?
Gd 3 C Gd 2 C
Tb 3 C
Dy 3 c Dy2C
Ho3C Ho 2 C
Er3C Er2C
Tm 3 C
Yb 3 C
Lu3C
Gd 2 C 3 GdC 2
Tb 2 C 3 TbC 2
Dy 2 c 3 DyC 2
Ho 2 C 3 HoC 2
Er 2 C 3 ErC 2
Tm 2 C 3 TmC 2
Yb 2 C 3 YbC 2
Lu2C3 LuC 2
Cm?
Bk?
Cf?
Es?
Mv?
No?
Lw?
Fm?
4.2 Chemical Bonding and Crystal Chemistry Atom
Symbol
Site
179
! trigonal | axis (c)
C.Si?: ( ) interstitial position
Figure 4-2. Crystal structure of boron carbide arranged according to the threefold axis of the rhombohedral lattice.
places B in one of the icosahedral sites (Armstrong et al., 1983, Emin, 1986; Morosin et al., 1991). The B2 site was established as the most favorable position for such a replacement (Silver and Bray, 1959; Hynes and Alexander, 1974; Becher and Thevenot, 1974; Bouchacourt and Thevenot, 1981; Aselage and Emin, 1991; Kleinman, 1991). Thus the total structure can be written as (B 11 C)"(CBC) + . Carbon-rich boron carbide being in eutectic equilibrium with graphite was prepared by fusion or diffusion couples and subsequently analyzed with a microprobe (Schwetz and Karduck, 1991) yielding a composition of B 4 3 C (i.e. a maximum carbon concentration of 18.87 at.%). Optical absorption spectroscopy of this material
indicated that 81.4% of the linear chains had a C - B - C structure and 18.6% consisted of a C - B - B array; the chains were statistically distributed (Kuhlmann et al., 1992). Concluding from Fourier transform infrared (FTIR) spectroscopic data, Kuhlmann et al. (1992) argue that in contrast to the generally accepted continuous substitution of B 1 2 for BX1C icosahedra and C - B - B for C - B - C chains with decreasing carbon content, the structure consists of statistical mixtures of these units. With decreasing C content, a growing portion of unit cells without any central linear chain is formed. As already mentioned, the linear chain can accommodate other main group elements such as Al, Si, P, As, and O without
180
4 Boride and Carbide Ceramics
a change in the structure type. Solid solutions formed with (B4C), however, are only known for Al and Si, which can partially occupy one of the positions within the C - B - C chain, e.g. Al is placed in the centrosymmetric B3 site which causes a slight kinking of this linear array, whereas Si replaces up to one third of the carbon sites at the ends of the chain. The total solid solubility of both species is comparatively small (max. 2.5 at.%) (Lipp and Roder, 1966 b; Telle, 1990), although a complete solid solution series between B 12 (C, B, Si)3 and the silicon boride "SiB 4 " was considered (Meerson et al., 1966). Due to the large size of the Si atom, however, the formation of a two-atom chain is favored, as in the cases of P, As, and O. The isotypic binary borides of these elements thus fit into the general stoichiometry B 12 (XQX). This arrangement favors a charge transfer to the B 12 icosahedron. The ideal structure of B 12 O 2 may be written as (B 12 ) 2 ~(OO) 2+ which exactly yields a filled-band configuration. In reality, for all these compounds a considerable disordering has to be taken into account, which results in the compositions B12P1 8 , B 12 As 2 0 , and B 1 2 O 1 82 (corresponding to B 6 6O) (La Placa and Post, 1961). In the case of "SiB 4 ", the real stoichiometry is (B 10 4Si1>6) (SiSi) = SiB2 89 which is attributed to an Si-Si chain and two sites in the icosahedron being partially occupied by Si (Matkovich and Economy, 1977 a; Hoard and Hughes, 1967; Magnusson and Brosset, 1962). 4.2.1.2 Structure and Polytypes of Silicon Carbide The fundamental structural units of the silicon carbide lattice are the covalently bonded coordination tetrahedra SiC4 and CSi 4 . These tetrahedra are assembled in
plane layers having common edges and one apex out of the layer plane which forms the connection to the next stack of tetrahedra. Thus four tetrahedra are linked through each corner to satisfy the four-fold coordination at any point of the resulting framework. This structure can equally be described as a close-packing of spheres with a constant radius and smaller spheres occupying a quarter of the tetrahedral positions yielding two formula units per unit cell. If the stacking sequence of the tetrahedra is ABC, a cubic zinc blende structure results, but if it is ABAB, a hexagonal wurtzite structure is the result. In contrast to these regular structures of the ZnS-type, however, the tetrahedra in SiC are not regular but possess acentric apices. In the layers of reverse stacking sequences ACAC, the A and C layers are rotated relative to each other. While both cubic and simple hexagonal stacking sequences can be found in SiC, known as /? and a structures, respectively, these sequences may alternate in a more complex, intermixed order resulting in large periods of stacking. Disordering and short-range twinning are common. The phenomenon of different one-dimensional ordering of structures is called polytypism, and the resulting structures are called polytypes. The most common hexagonal, hightemperature polytype consists of a zigzag stacking of three layers in the odirection (i.e. perpendicular to the layers) which may be derived from the cubic polytype by insertion of <111> rotation twin boundaries every three layers (Fig. 4-3). The stacking sequence may then be described as ABCB'A'C'-with A', B', C indicating a plane rotation of that particular layer. According to the notation of Ramsdell (1947), this polytype is named 6/7, indicating that after six stacking sequences the initial layer position is obtained again.
4.2 Chemical Bonding and Crystal Chemistry
3C (cubic)
SH (hexagonal)
2H (hexagonal)
&H (hexagonal)
181
UH (hexagonal)
15/? (rhombohedral)
Figure 4-3. Atomic arrangement in the most common SiC polytypes (Ryan et al, 1968).
In that nomenclature the capital is related to the Bravais lattice type, i.e. C means cubic, H hexagonal, and R rhombohedral. In Fig. 4-3 the most common polytypes are visualised (Ryan et al., 1968). Long-range ordering with sequences of 90 layers have been observed. Although the various polytypes can be readily distinguished by structural analysis their differences in physical properties can
almost be neglected. Since all structures are close-packed and the density is constant at 3.17 g/cm3 because of the same next-neighbor relation, all polytypes have nearly the same energy of formation. Calculations of stability between room temperature and 2300 °C, taking wide-range neighborhoods into account, show only slight differences between 3C and 6H polytypes (Bind, 1979). This means that
182
4 Boride and Carbide Ceramics
neither pressure nor temperature can satisfactorily explain the preferential formation and relative stability of certain poly types. Attempts to do so therefore involve the influence of impurities or different dislocation energies (e.g., Verma and Krishna, 1966). Heine et al. (1991) showed by ab initio quantum calculations of the relative polytypes in bulk that the cubic /? phase should not be stable at any temperature. Taking impurities acting as electron donors into account and allowing for the formation of differently oriented double layers, Heine et al. (1991) demonstrated that jS-SiC is the favored structure. Nevertheless, more or less exact conditions for polytype transitions during sintering or heat-treatment of ceramics have been established empirically (see Sees. 4.4.1.4 and 4.5.2.4). 4.2.1.3 Structure of Transition Metal Carbides
The structure of metallic carbides is generally governed by the ratio of the atomic radii of the metal and the carbon atom (Hagg's rule). Starting with the closepacked lattice of the metallic elements, the successive incorporation of the smaller C atoms into the octahedral sites results in the development of structures with various sequences of occupied carbon layers. A simple, systematic model for the formula type of transition metal carbides can be derived from geometrical considerations of the degree of interstitial site occupation. Complete occupation of the octahedral sites in a space-centered cubic host-lattice yields the face-centered cubic sodium chloride structure of the IVa and Va group monocarbides. The characteristic structural element is thus the M 6 C octahedron (where M stands for metal) with the possibility of defect structures resulting in a
huge homogeneity range. In the primitive hexagonal lattices of the monocarbides MC, half of the six-fold coordinated carbon positions are unoccupied. The structural unit of the hexagonal phases is thus the M 6 C triangular prism with carbon in the center, or the C 6 M with a six-fold coordinated metal atom. Hence this so-called WC structure type shows similarities to the nickel arsenide structure in which the metal atom is located in an octahedral coordination sphere (Fig. 4-4). In the hemicarbides M 2 C of the IVa, Va and Via group elements, the hexagonal Cdl 2 structure (P3 m 1) and the Z/3 structure (P63/mmc) are predominant, which can be derived from half occupied, octahedral sites of a close-packed hexagonal host-lattice. Due to the presence of such a high amount of vacancies, ordering can occur in the metalloid sublattice, which has a comparatively narrow homogeneity range M 2 C 1 _ ;c . Problems of carbon sublattice ordering have been intensively discussed by Epicier (1990 a, b). In carbides with a carbon-to-metal ratio exceeding unity, the carbon atoms form couples resulting in tetragonally distorted NaCl lattices (CaC2-type). The dicarbides of the lanthanide and actinide elements crystallize in this structure and have a less metallic character. The C2-coordination is
Figure 4-4. Crystal structure of hexagonal tungsten monocarbide; black: carbon, white: tungsten.
4.2 Chemical Bonding and Crystal Chemistry
183
Crystal lattice
^ - Bonding
t 2g Orbitals T
- Bonding
ddCT- Bonding
also present in space-centered cubic M 2 C 3 carbides of the actinides. As the ratio of carbon and metal radii for carbon accommodation in closepacked host-lattices approaches the critical value of 0.59 (optimum packing at rc/rM = 0.414) elements of the iron and chromium group react with small atom fractions of carbon to form interstitial structures of the M 23 C 6 -type. With both an increasing ratio of the radii and an increasing content, complex structures of low symmetry become stable (e.g. hexagonal M 7 C 3 , orthorhombic M 3 C 2 and M 3 C) and can also be found in carbides of iron and chromium group elements. In the following sections, the carbides used in ceramic composites as reinforcing particulates are treated in more detail since their metallic behavior brings about interesting prospects for the mechanical behavior and transport properties of these usual-
Figure 4-5. Crystal structure of TiC with orbital overlapping; black circles titanium, white circles: carbon (Neckel, 1990).
ly more ionically or covalently bonded matrix materials. Cubic Monocarbides The technically important monocarbides of the six group IV and V transition metals TiC, ZrC, HfC, VC, NbC, and TaC are isotypic and crystallize in the face-centered cubic NaCl structure (space group Fm3m). Every metal and carbon atom is surrounded by eight next-neighbors of the respective other species in an octahedral configuration (Fig. 4-5). Hence the unit cell consists ideally of two atoms of each species, i.e. of two formula units. The real composition of the transition metal carbides exhibits, however, a huge non-stoichiometry represented by the formula MCX where x is the carbon-to-metal ratio. Within the range of x = 0.5-0.97 the crystal structure does not change. The carbon
184
4 Boride and Carbide Ceramics
deficiency is accounted for by carbon atom vacancies in the carbon sublattice. This high vacancy concentration of at least 2 - 3 % exceeds that obtained in metals or semiconductors by mechanical or radiation damage. Ordering is observed in VC and NbC at certain carbon-to-metal ratios (e.g., at x - 0 . 8 3 3 - 5 / 6 or at x = 0.875 = 7/8). Since a decreasing stoichiometry is related to the reduction of C-M bonds relative to x=l, the concentration of vacancies influences systematically the bonding strength-related properties such as the cohesive energy, the melting point, elastic constants, the hardness, and the plastic deformation behavior at high temperatures, as well as defect-related transport properties such as heat, electrical conductivity and diffusion behavior (Williams, 1988). Analysis of the binding character in this NaCl-type structure by self-consistent Augment Plane Wave calculations reveals that there are contributions from all three main types of chemical bonding (Neckel, 1990). The metallic fraction is due to nonvanishing densities of states at the Fermi energy and a relatively high electron density in the region between the atomic spheres. Ionic bonding is caused by charge
transfer from the metal atom to the carbon yielding electrostatic forces. According to calculations for TiC, approximately 0.36 electrons are transferred from a titanium atomic sphere relative to the charge of a hypothetical crystal of non-interacting neutral atoms. The covalent bonding fraction was calculated for TiC by linear combination of molecular orbitals (Neckel, 1990), taking degeneration of energy levels by octahedral ligand field of the carbon atoms into account. The five 3 d orbitals of a Ti atom are thus split into three orbitals of t2g symmetry and two of eg symmetry. The lobes of the Ti eg orbital thus extend towards the neighboring carbon 2p x orbitals and form pd a bonds (Fig. 4-6), whereas the Ti t2g orbitals overlap forming pd n bonds with the adjacent C 2p y orbitals as well as forming dd a bonds with the corresponding t2g orbitals of the neighboring Ti atom. It is established that the latter intermetallic bonds are strengthened by an increased substoichiometry. More detailed studies on the nature of chemical bonding in transition metal carbides and their nonstoichiometry have been published by, e.g., Neckel (1983), Schwarz and Blaha (1983), De Novion and Landesmann (1985), and Redinger et al. (1985, 1986).
Figure 4-6. Electron density in the (100) plane of three occupied band states of TiC for wave vector k = n/a (1, 0, 0) (Schwarz and Blaha, 1983). Ay U22mRyd
A2. 62QmRyd
As 636mRyd
4.2 Chemical Bonding and Crystal Chemistry
Hexagonal Monocarbides Tungsten monocarbide, WC, crystallizes in a primitive hexagonal structure (space group P6m2, resembling the NiAs structure type) consisting of alternating W and C layers with ordered C vacancies (Fig. 4-4), where the W atoms occupy the 0, 0, 0 positions (i.e. the simple hexagonal hostlattice) and the C atoms are in the Va, 2/a, Vi positions and thus occupy only half of the triangular prismatically coordinated holes. The c/a-ratio of the unit cell is 0.98. The cell thus contains a single formula unit (Ishizawa and Tanaka, 1986). Due to the close structural relationship to the closepacked cubic transition metal monocarbides, solid solutions of WC in other IVa and Va group metal carbides exhibit an NaCl structure with huge homogeneity ranges and probable complete mutual solubility at very high temperatures (see Sec. 4.3). Examples are (M, W)x _x with M = Ti, Zr, Hf, Nb, V, Ta. Because of the various MoC x _x structures, (MOi .yWyC^ -x solid solutions of the hexagonal P6m2 and P63/mmc, as well as the cubic Fm3m, space group exist (Rudy et al., 1978). 4.2.2 Chemical Bonding of Borides
The nature of the chemical bonding in boron compounds is governed by the wellknown two-electron-three-center bond, i.e., three boron atoms share two common electrons. These electrons are thus more or less delocalized. The resulting sp2 hybridization leads to the plane B 3 X 3 hexagon as the main structural element in BN, B 2 O 3 , H 3 BO 3 and related compounds, and to the B 3 triangle as a fraction of the typical five-fold symmetric icosahedron of elemental boron, the group of boranes and their derivatives. Depending on the saturation of the electron deficiency, soft and non-conducting, salt-like com-
185
pounds or semimetallic to metallic materials of exceptionally high melting point and hardness and excellent electrical conductivity can exist. As pointed out in the following section, the latter boron compounds, like the corresponding carbides, may contain ionic, metallic and covalent fractions of bonding forming very stable compounds due to the well-balanced electron transfer between metal and boron sublattice. 4.2.2.1 The Crystal Structure of Borides
Similar to silicates, the crystal structures of borides can easily be classified according to the arrangement of the boron atoms. Boron may occur as an isolated atom or form B-B bonds with an increasing degree of interconnection in the chains, double chains, layers and frameworks and combinations thereof (Fig. 4-7). Due to the strong covalent bonding between the boron atoms and the electron deficiency of the three-center bond a number of complex and unique structures result which have been the subjects of investigation for many years (Kiessling, 1950; Lundstrom, 1969 a). In general, compounds with a boron-to-metal ratio of less than 1.0 are built up of isolated boron atoms or pairs with a low B-B interaction (e.g., Ni 3 B, Ru 7 B 3 , Fe 2 B, Cr 5 B 3 ), in zigzag chains with additional, isolated B (e.g., #-Ni4B3). At a ratio of 1.0 to 1.3, infinite chains are formed which may be parallel to one or even two crystallographic axes (e.g., mNi 4 B 3 , FeB, CrB, MoB), whereas in M 3 B 4 borides double chains are predominant (e.g., Cr 3 B 4 ). With increasing boron content, two-dimensional nets are stable, yielding preferential stoichiometries between M 2 B 3 and MB 4 . The most important structure type group thereof is the A1B2 type, which is covered in more detail
186
4 Boride and Carbide Ceramics
[No [connections
[Chainsl
Partial
Single
Multiple
O
o o
o-o
o
I
o
o-o
| 2-D netsj
|Units helping to form 3-D frameworks]
B12-Type
sp 2 -Type
later on. Three-dimensional frameworks exist in so-called higher borides with typical stoichiometries of MB 4 , MB 6 , MB 1 2 , and MB 6 6 . Channels with rectangular cross-sections were found in e.g. CrB 4 and MnB 4 which is unique for the three-center bond of boron (Andersson and Lundstrom, 1968). A rigid boron skeleton consisting of B 6 octahedra is a characteristic of the CaB 6 structure group (important member: LaB6), whereas the UB 1 2 structure contains B 1 2 cubo-octahedra. Other borides of MB 6 and MB 1 2 stoichiometry or a higher boron-to-metal ratio, especially the main group element borides, can be derived from the trigonal rhombohedral a-boron or /?-boron structure with the B 1 2 icosahedron as the most important structural unit. Some general systematics on chemical bonding and crystal chemistry have been published by Matkovich and Economy (1977 a), and Aronsson et al. (1965, 1968), who also refer to the struc-
B 6 -Type
Figure 4-7. Structural classification units of the borides (Spear, 1977).
tural similarities in silicides and phosphides. 4.2.2.2 A1B2-Type Structures
The transition metal borides of the A1B2 structure type group are of great technical interest for ceramics, as are the ternary co, cp and x type borides as compounds for cermets and coatings. The A1B2 structure is conveniently described as a sequence of alternating metal and boron layers of hexagonal symmetry. The metal layers are close-packed and stacked in an A-A-A sequence, resulting in a basal-centered unit cell. The boron atoms are six-fold coordinated and situated in the center of trigonal prisms of metal atoms (//position). Hence they generate a planar primitive hexagonal, two-dimensional, graphite-like network (Fig. 4-8). The total stacking sequence is then AHAHAH. . . and belongs to the space group
4.2 Chemical Bonding and Crystal Chemistry
o
Metal
187
Boron
Figure 4-8. The A1B2 structure type (redrawn after Spear, 1976 a; Higashi and Takahashi, 1986). a2
P6/mmm. The unit cell contains one formula unit MB 2 . Since this structure is very versatile at accommodating metal atoms of various sizes and electron configurations, M could be Mg, Al, group IVa, Va, Via, actinide or lanthanide elements. Additionally, other transition metal borides of various stoichiometries can be derived from the A1B2 structure type by introducing the metal layer positions B and C in analogy to close-packings and the boron layer types A^and K', which may be slightly puckered. By allowing stacking sequences
such
as
AHAK-BHBK-CHCK. . .
(MoB 2 . 3 = "Mo 2 B 5 "), AHAK'-BHBK. . . (WB2.o-2.7 = "W 2 B 5 "), or AH'AK'BH'BK'. . . (Ru 2 B 3 ) and AK'BK'. . . (ReB2), and vacancies in the boron K layers, other structures and symmetries can be generated (Fig. 4-9) (Lundstrom, 1969 b; Aronsson et al., 1968). Calculation of the band structures of AlB2-type compounds shows that no band gaps are present, and all the compounds are predicted to be conductors, which is in agreement with experimental results. For the main-group element diborides the boron 2 p a and 2p7i orbitals are the main
constituents of the states at the Fermi edge, while for the transition metal diborides it is the localized metal 3 d orbitals which are the predominant component of the valence and conduction bands. All diborides exhibit a strong electron transfer from the metal atom to the boron which gives rise to a strong ionic contribution to the bonding. In the transition metal diborides, the charge transfer decreases from 2.28 electrons in ScB2 to 1.09 electrons in MnB 2 (Armstrong, 1987); lower values have been presented by Samsonov and Kovenskaya (1977 a, b). The additional electrons occupy the 2p7i orbitals of the boron where the electrons are involved in both the B-B bonding as well as the metal-boron interactions. Cluster calculations of main group element diborides show that the metal-metal bonds are weak, the metal-boron interaction is significant and the boron-boron interactions are very strong. In the transition metal diborides the metal-metal bonds within the layers are considerably stronger than in main-group diborides and reaches a maximum for VB 2 . This internal bonding within the layers is clearly of a metallic type and is thus re-
188
3 ^
4 Boride and Carbide Ceramics
2.983 A
A.B: metal H,K': boron
Figure 4-9. The Mo 2 B 5 structure type (Higashi and Takahashi, 1986).
sponsible for the metallic transport properties. The metal-metal interlayer bonding, as well as the metal-boron interactions, also increase from ScB2 to MnB 2 , whereas the contribution of the boron-boron bonding decreases in this order. Due to the existence of vacancies in the boron layer and the possible occupation of interstitial sites by additional boron atoms, the boron sheets may also exhibit metallic or semimetallic conductivity. The considered metallic fraction does not, however, account very much for the transport properties. In contrast, the interaction between metal and boron layers contains a more efficient metallic portion which explains the electric conductivity along the oaxis (Aravamudhan, 1967). In ideal boron layers, the donor capability of the metal governs the extent of electron localization in the sp states of the boron atoms. Thus the covalent character of the B-B bonds decreases from group IV to group VI metal diborides (Samsonov et al., 1972). As it has been established that the boron network is rather rigid and governs the lattice expansion in the a direction whereas
the lattice dilatation perpendicular to the metallic layers strongly depends on the metal species, it seems likely that the metal atoms are distorted in some cases (Hoard and Hughes, 1967; Spear, 1976 a). The c/a ratio is thus a function of the rmetal/rboron ratio and depends furthermore on the valency electron concentration (Aravamudhan, 1967).
4.3 Phase Systems Knowledge of the phase diagrams for compounds of technical interest and of the environmental phases in contact with these compounds is the key for materials development and for the understanding of materials behavior in application. Not only can the thermal stability of particular phases be calculated by means of thermodynamic data, but suitable sintering procedures can also easily be considered and decomposition in aggressive media can be predicted. Generally recommended data books on binary and ternary systems are, e.g., Hansen (1958), Elliott (1965), Shunk
4.3 Phase Systems
(1969), Mofatt (1976, 1979), Massalski (1990), and Petzow and Effenberg (1988ff.). Phase diagrams of the most important carbide and boride phases will be presented and discussed, starting with the binary systems, then selected ternary systems that are of technical interest. In the subsequent sections particular phase systems will be treated in respect to sintering of B4C, SiC, and TiB2 (Sec. 4.5) or in the context of microstructural design and mechanical strengthening (Sec. 4.6). 4.3.1 Binary Phase Diagrams Containing Carbides
Problems in the presentation of binary systems containing carbon usually arise from uncertainties in the stoichiometry range of the particular carbides due to the formation of vacancies or from uncertainties concerning the very high melting or decomposition points which are not readily accessible by experiments. Generally, this work concentrates on data accepted by the Office of Standard Reference Data of the U.S. National Institute of Standard and Technology, as published by e.g., Massalski (1990). A special review treatise on binary and ternary transition metal carbide phase diagrams is published by Holleck (1984). Most of these data are based upon the important experimental work by Rudy et al. (1965) and Rudy (1973) or thermodynamic calculations. 4.3.1.1 The B-C System In contrast to early publications by Samsonov and Schuravlev (1956) and Schuravlev and Makarenko (1961) considering several boron carbide phases it is generally accepted today that only one binary phase B 13 C 2±JC exists with a wide homogeneity range of 8.8 to 20.0 at.% C.
189
This phase melts congruently at 2450 °C (Elliott, 1965) at the composition B 13 C 2 (18.5 at.% C, 20.2 wt.% C). For the B-rich corner of the phase diagram, Bouchacourt and Thevenot (1979) proposed a degenerated peritectic with elemental boron at 2075 °C, according to measured element distribution coefficients. In this diagram the melting point of boron is placed at 2020 °C. Since the melting point of B accepted today is 2092 °C the resulting reaction with boron carbide should be a eutectic one, assuming that the nonvariant equilibrium at 2075 °C is correct. The maximum carbon content is usually given as 20.0 at.% corresponding to the stoichiometry of B4C. Beauvy (1984) suggested a carbon content steadily increasing with temperature from 21A at.% (20°C) to 23.1 at.% (2375°C). Recent microprobe analyses by Schwetz and Karduck (1991) indicated, however, that the maximum carbon content of fused boron carbide being in equilibrium with graphite, is only 19.2 at.%, corresponding to the formula B 4 3 C. The eutectic with carbon is given at 2375± 5°C and 29 at.% C, which is in agreement with thermodynamic calculations (Lukas, 1990) stating 2357 °C as the eutectic temperature. The phase diagram is presented in Fig. 4-10. 4.3.1.2 The Si-C System Silicon carbide (SiC) is the only intermediate solid compound in the Si-C system that crystallizes either in the cubic /?-form or in the hexagonal a-form with many poly types (stacking variations). SiC has no nominal solid solubility for C or Si, but non-stoichiometries due to carbon vacancies have been reported leading to 2 at.% Si in excess (Prochazka, 1989). The £-to-a transition is discussed extensively in Sees. 4.2.1.2, 4.4.1.4, and 4.5.2.4 in respect to
190
4 Boride and Carbide Ceramics
2600
(Kleykamp, 1992) report the peritectic reaction at 2830 °C, yielding Si liquid of 13 at.% C which is actually partially vaporized at normal pressure. SiC and Si react eutectically at 1404 + 5 °C and 0.75 + 0.5 at.% (Dolloff, 1960), whereas Kleykamp (1992) gives 1412 °C and 0.02 at.% C as the correct eutectic point. A comprehensive summary of the conflicting data up to 1984 is given by Olesinski and Abbaschian (1984 a). 1
1"
10
20 C (atom-%)
M
1 30
4.3.1.3 The Ti-C System
Figure 4-10. The B-C phase diagram; uncertainties arise from the localization of carbon in the crystal structure indicating that the C-rich limit may be B 4 3C rather than B4C. The degenerated reaction at the B-rich corner is most probably a eutectic.
crystal structure, materials preparation and sintering. SiC decomposes peritectically forming liquid silicon and solid carbon. The assessed phase diagram (Fig. 411) presents this reaction at 2545 +40 °C involving Si liquid with 27 at.% (13.7 mass %) C (Dolloff, 1960). Uncertainties arise from the high vapor pressure of Si at this temperature. More recent investigations
10
£500
20
Transition metal-carbon systems contain a monocarbide phase with an extraordinarily wide homogeneity range due to more than 2-3 % of vacancies in the f.c.c. carbon sublattice of NaCl type structures. In the case of T i C ^ ^ , the maximum homogeneity range is 32 to 48.8 at.% at 1870°C, while the phase melts congruently at 3067°C with a composition of 44 at.% C (Fig. 4-12; Rudy et al., 1965). Other melting points reported range between 1940 and 3250 °C. At approximately 1900°C, another carbide Ti 2 C (33 at.% C) apparently forms congruently having ordered vacancies. This ordered phase is in
wt.% C 30 £0 50 60 7080 100 3000 G a s
4000^ 3500- 3200 ° C
0 Si
10
20 30
G+C
G+L
"y""-""-"-"-•
£0
50 60
at.% C
70
80
90 100 C
Figure 4-11. The Si-C phase diagram (Massalski, 1990); the decomposition of SiC results in an Si vapor phase.
0 Ti
10
20
30 £0 at.% C
50
60
70 C
Figure 4-12. The Ti-C phase diagram (Rudy et al., 1965).
4.3 Phase Systems
eutectic equilibrium with jS-Ti solid solution at 1648 °C and 1.8 at.% C. The phase relations at lower temperatures are unknown, but TiC 1 _ x undergoes a peritectoidal reaction with /?-Ti to form a-Ti solid solution. There is probably another ordered phase of Ti 8 C 5 stoichiometry present at low temperatures, Towards the carbon-rich corner, TiC 0 97 forms a eutectic with C at 2776 °C and approximately 63 at.% C (Rudy et al, 1965). A summary of the data available on the Ti-C system up until 1987 is presented by Murray (1990). 4.3.1.4 The W-C System Figure 4-13 shows the tungsten-rich part of the binary W - C equilibrium diagram basically taken from Sara (1965), and Rudy and Hoffman (1967), as assessed by Massalski (1990). Three stoichiometries of condensed phases have been proven, hexagonal W 2 C crystallizing in three modifications, the PbO 2 , Fe 2 N, and Cdl 2 types, denoted /?, /?', and /?", respectively, the cubic subcarbide W C ^ , crystallizing in the NaCl type structure denoted y, and the hexagonal WC denoted 3. W 2 C exhibits a mass-% C 2 3 U 3000
5
191
comparatively wide homogeneity range of 25.5 to 34 at.% C at 2715°C. This phase originates from a eutectoidal reaction between elemental W and <S-WC at 1250 °C and melts congruently at 2785 +10 °C. /?W 2 C reacts eutectically with the W solid solution at 2715 + 5 °C and with y - W C ^ at approximately 2758 °C. Phases of W 2 C stoichiometry are obtained as intermediate products during WC production. The yphase results from a eutectoidal reaction between /? and 5 at 2535 °C and melts at approximately 2785 °C. It can be obtained at room temperature by extremely rapid cooling, e.g., in plasma sprayed layers. The technically important <5-WC is the only binary phase being stable at room temperature and has almost no solid solubility at temperature up to 2384 °C but may become carbon deficient between this temperature and its incongruent melting point (peritectic reaction with liquid and graphite) at 2785 ± 5 °C. 4.3.1.5 Other Transition Metal-Carbon
Systems From the IVb group of the periodic chart, the phase diagrams of Zr-C and
6
7 8 9
Figure 4-13. The W-C phase diagram (Sara, 1965; Rudy and Hoffman, 1967); for explanation see text.
1000
20
30 at.% C
40
50
60
192
4 Boride and Carbide Ceramics
Hf-C are governed by the particular monocarbides MC that have a wide solid solubility range like the Ti-C system which has already been presented. Ordered structures have been observed at the stoichiometry of ZrC 0 7 5 . The systems of the Vb group elements, V-C, Nb-C, and TaC are characterized by the subcarbides M 2 C and the monocarbides M C ^ ^ again having large homogeneity ranges. At high temperatures the M 2 C phases are disordered but at low temperatures they rearrange to form ordered structures with distorted metal host-lattices. Depending upon the type of ordering, £-Fe2N, fFe 2 N, and Cdl 2 type structures may occur. The monocarbides also tend to order in the C-sublattice at low temperatures. Hexagonal far-distance ordering was observed in the case of M 6 C 5 stoichiometry with transition temperatures decreasing from 1250 °C (M = V) to less than 900 °C (M = Ta). In the V-C system, ordering of the stoichiometry V 8 C 7 at 1100°C was also recognized. In respect to stoichiometries and crystal structures in the VIb group the Cr-C system is of particular interest. Stable compounds such as Cr 2 3 C 6 , Cr 7 C 3 , and Cr 3 C 2 are formed which do not consist of close-packed metal sublattices as the atomic radius of Cr is too small compared to the C atom. Instead of interstitial sites being accupied by carbon forming octahedral polyhedra of coordination, the trigonal prism now dominates as the construction unit of the crystal lattice. In the Mo-C system again the subcarbide Mo 2 C and the monocarbide MoC with several modifications M o C ^ ^ at high temperatures are stable. The W - C system has already been presented in the preceding section. With increasing occupation of the dshells by electrons, the carbides of the Vllth and VHIth group transition metals
become less stable or even metastable. Manganese forms the carbides Mn 2 3 C 6 , Mn 1 1 C 3 , Mn 3 C, Mn 5 C 2 , and Mn 7 C 3 , whereas rhenium probably does not form a stable carbide under normal conditions, only under high pressure. Similarly, the equilibrium conditions in the Co-C and Ni-C systems are also still uncertain. Several metastable phases of Co 2 C, Co 3 C, and Ni 3 C compositions have been identified (Hansen, 1958; Elliott, 1965; Shunk, 1969) although the equilibrium diagrams only show a simple eutectic reaction between the elements. Carbides of the more noble metals and the group II and group I elements most probably do not exist. 4.3.2 Binary Phase Diagrams Containing Borides
Many attempts have been made to correlate the binary metal boride phase equilibria, the boride crystal chemistry, and the ranking of the elements in the periodic table. As stated by Spear (1977), larger metals and those with unfilled d-shells favor the formation of boron-rich phases with two- or three-dimensional boron frameworks. The smaller metals having a high number of d-electrons prefer the formation of metal-rich phases with only a few boron-rich bonds, whereas more noble metals such as Ru, Rh, and Pd tend to generate defect structures. Systematic work on crystal structures and stabilities has been performed by Aronsson et al. (1965) and Lundstrom (1969 a, 1977). Spear (1976 b, 1977) presented a systematic compilation of binary phase diagrams resulting in predictions of phase relations. Guillermet and Grimvall (1989, 1990) systematized thermodynamic data of transition metal diborides with emphasis on the enthalpy of formation, the vibrational entropy, and the melting temperature, in
4.3 Phase Systems
order to account for the transition from stable to metastable phases with increasing atomic number. As a result, an entropy-related free energy term was introduced which correlates linearly with cohesive energies and melting points. By this means, stabilities of boride, carbide, and some nitride phases have been successfully predicted. In the following sections some binary systems of technical interest are presented.
solution at 1540 °C and 7 at.% B. The existence of the Ti 3 B 4 phase was proven by Fenish (1966), and its peritectic reaction with TiB 2 and liquid was placed at 2020 °C. Rudy and Windisch (1966 a), however, omitted this phase from their binary diagram, probably because it could not be observed in melt-derived samples close to the decomposition point of TiB. In 1981, Ti 3 B 4 was reinvestigated by Neronov et al. (1981) in reaction layers between Ti and B; later, in 1986, it was confirmed by Spear et al. by arc melting and annealing studies. TiB2 reacts eutectically with elemental boron at 2080 +20 °C and approximately 98 at.% B.
4.3.2.1 The Ti-B System The most recent compilation on the Ti-B system was by Murray et al. (1986). The assessed phase diagram (Fig. 4-14), being in good agreement with thermodynamic calculations, consists of three intermediate phases, orthorhombic TiB (FeB type structure), orthorhombic Ti 3 B 4 (Ta 3 B 4 structure), and hexagonal TiB 2 (A1B2 structure). While TiB and Ti 3 B 4 decompose peritectically at 2180 and 2200 °C, respectively, TiB2 melts congruently at 3225 ± 25 °C (Rudy and Windisch, 1966 a). TiB has a narrow homogeneity range of about 49-50 at.% B (Fenish, 1966) and reacts eutectically with Ti solid wt. % 5
c
10
193
4.3.2.2 The Zr-B System Similar to the Ti-B system, ZrB 2 is an important phase having an AlB2-type structure and a melting point of 3250 °C (Fig. 4-15; Massalski, 1990). It reacts eutectically with elemental Zr at approximately 1680°C and 86 at.% Zr. In contrast to the Ti-B system, no ZrB or Zr 3 B 4 phases exist, but there is a ZrB 12 phase with a UB 1 2 structure which melts incon-
B
20
it i
40 50 60
10
3225
L
3000-
/ 2500-
\
/
\
/
2200
2080
\
20001670
1500-
^
1540
-pr\
B— T i B
1000-
884
~
— TiB 2
-crTi 5000
Ti
Murray et al.,'87
10
20
30
40 50 60 Qt % B
-
70
80
90
100
B
Figure 4-14. The Ti-B phase diagram (Murray et al., 1986).
194
4 Boride and Carbide Ceramics
03050
80
mass% Zr 90
1 00
3500
500 0 B
10 20 30
iO 50 60 70 at.% Zr
80 90 100 Zr
Figure 4-15. The Zr-B phase diagram (Massalski, 1990); note the absence of a ZrB and a Zr 3 B 4 phase and the presence of a ZrB 12 phase in comparison to the Ti-B system.
gruently at 2030 °C forming ZrB 2 and liquid. 4.3.2.3 Other Transition Metal-Boron Systems In the other transition metal boron phase systems of groups III, IV, and V, the MB 2 phase is also the dominating compound with respect to the melting point. Exceptions are the Y - B , lanthanide metalB and actinide metal-B systems which possess very stable MB 4 - and MB6-type compounds. In group V the number of known phases increases, and the tendency for the MB phase to be more stable than MB 2 is obvious on advancing from V to Ta. Destabilization of the A1B2 structure to the benefit of the MB structure is evident in the group VI where the MB 2 phase forms an individual structure type that can be derived from the A1B2 structure by the introduction of variations in the stacking sequences. The phases MoB 2 0 and WB 2 0 have formerly often been denoted Mo 2 B 5 and W 2 B 5 , respectively, but there is evidence that the homogeneity range is nar-
row and close to the 1:2 stoichiometry (Aronsson et al., 1968; Lundstrom, 1969b; Higashi and Takahashi, 1986). As an exception, AlB2-type WB 2 has been produced under nonequilibrium conditions by chemical vapor deposition (CVD) (Woods et al., 1966). In the Vllth and Vlllth group metal-boron systems the melting points of the borides decrease becoming significantly lower than the melting points of the elements. 4.3.3 Ternary and Higher Systems Many ternary, quaternary and higher systems containing carbides and borides have been intensively investigated basically for three reasons: firstly, to elaborate suitable sintering systems for these highmelting and thus difficult to densify compounds; secondly, to avoid probable chemical complications such as phase changes and decomposition during application; and thirdly, to investigate ways of optimizing materials properties by the fabrication of tailored composites or solid solutions. Most of these investigations have been concerned with military-, nuclear- or aerospace-related research for new hightemperature materials, fabrication of cutting tools (e.g., transition metal carbides for hard metals and cermets), or wear resistant parts (high strength and high toughness structural ceramics based on composites). For the last decade, more systematic studies related to the edition of alphabetic volumes on ternary systems, or to the investigation of peculiarities of chemical bonding in multicomponent phases, have also been started. Hence the data available can be divided into three groups: boron-carbon-metal/semimetal systems (basically ceramics: sintering systems, composites), transition metal car-
4.3 Phase Systems
bide or boride systems with low melting metals (for densification of hard metals, cermets and other cutting tools), and systems with two transition metals and carbon or boron (development of solid solutions of exceptional properties or with emphasis on the substitution of tungsten and other strategic metals). In the following sections some ternary systems are selected as technically important examples of these three categories. 4.3.3.1 Boron-Carbon-Metal Systems (Ceramic Systems) Aluminum is an effective sintering aid for B4C and SiC ceramics if combined with boron and carbon. Phase relations in the B-C-Al-Si system may hence indicate suitable procedures to initiate transient liquid phase or enhanced solid state sintering. Furthermore, Al melt may be used to infiltrate porous B4C bodies acting as a reinforcing phase, and SiC is advantageous in reinforcing Al-based piston alloys. Although the binary boundary phase diagrams of the Al-B-C system are rather well established there is only limited experimental information on the ternary equilibria. Six ternary phases have been discovered, B4OA1C4, B48A12C8 which have a B4C-structure and thus are probably B 12 (B, C, Al)3 solid solutions, orthorhombic B 51 A1 2 C 8 , hexagonal and orthorhombic B 48 A1 3 C 8 , and hexagonal B4A18C, denoted T. The temperature stabilities of these phases are not known. The ternary solid solubility of B 12 (B, C, Al) 3 was discovered by Lipp and Roder (1966 a) and described in more detail by Neidhard et al. (1970). An isothermal section calculated by Lukas (1990) neglecting all boron-rich ternary phases except T is presented in Sec. 4.5.1.2 (Fig. 4-32). A literature survey on previous investigations of the A l - B - C
195
system is summarized by Lukas in Petzow and Effenberg(1988ff). The B-C-Si system was first treated by Kieffer et al. (1972), calculated by Dorner (1982), reinvestigated by Telle and Petzow (1987 b) and Telle (1990) and recalculated by Lukas (1992). Uncertainties arise from the binary B-Si system comprising three silicon borides, S i B 2 8 9 _ 3 6 5 , SiB 6 , and SiB 1 2 _ 1 4 . Both the homogeneity range and the decomposition temperatures have not yet been completely established (e.g. Elliott, 1965; Ettmayer et al., 1970; Dorner, 1982; Olesinski and Abbashian, 1984 a). Experimental problems in both binary and ternary phase studies are related to the comparatively high vapor pressure of Si at temperatures exceeding 1400 °C. The characteristics of the B-C-Si system as assessed today, comprise the stability of a B 12 (B, C, Si)3 solid solution with a maximum of 2.5at.% Si (Lipp and Roder, 1966 b; Telle, 1990), being in equilibrium with a boron-saturated silicon melt. No ternary phase exists. The unlimited solid solubility between B4C and SiB 2 8 9 , as postulated by Meerson et al. (1966), could not be verified. According to Secrist (1964) and Shaffer (1969), the B 4 C-SiC section is of a quasi-binary type with a eutectic equilibrium between 2250 and 2420 °C and 30-35 mol% SiC. This section is, however, of a real ternary type since the eutectic melt postulated by Secrist and Shaffer is in fact a binary equilibrium between solid carbon and Si-B-C liquid. Implications of the resulting phase equilibria in particular comprising B4C, SiC and Si liquid on the sintering processes of both SiC and B4C will be addressed in Sec. 4.5.1.2. An isothermal section is presented in Fig. 4-65, an isopleth along the B-C boundary in Fig. 4-33. The ternary B-C-Ti system was intensively studied by Rudy et al. (1965) and has
4 Boride and Carbide Ceramics
196
been considered for the fabrication of ceramic cutting tools (Nowotny et al., 1961; Ordan'yan e t al., 1975; Holleck, 1982; Holleck et al., 1987). No ternary phases have been discovered. TiB 2 coexists with i-^ (quasi-binary eutectic equilibrium at 2620 +15 °C and 57±2mol% T i C ^ (Fig. 4-16, Rudy et al., 1965). Furthermore, TiC1_x is stable together with TiB up to approximately 2100 °C. TiB 2 also forms a quasi-binary eutectic with B4C at 2310°C and 88±3mol% B 4 C, as well as with C at 2507 °C and 33 ± 3 at.% C. This means, that TiC is not stable in the presence of B4C but reacts to form TiB 2 + C. On the other hand, TiB 2 -B 4 C composites can be fabricated from TiC and B by reaction sintering. Composites of TiC t _ x and TiB 2 have been investigated for coherent grain boundaries (Holleck, 1987). The ternary system has four eutectics, at 2400°C (TiB2 + TiC 1 _ x 4- C-* liquid), 2240°C (TiB2 + B4C + C->liquid), 2016°C (TiB2 + B 4 C ss + B^liquid), and 1510°C (TiB + TiC! _ x + Ti -> liquid), and one peritectic at 2160 °C (TiB2 + TiC1_JC -•TiB + liquid). Figures 4-17 and 4-18 show isothermal sections of the T i - B - C system at 1700 °C and 2300 °C, respectively (Rudy et al., 1965). The corresponding sec-
3225±20
_) 0) 3J
o CD Q_ CD f—
Liquid
\ 3000 A I
\ TiB 2+ L
28002600-
X,
^
\ 2620 + 15
20
30 TiC,., 50 60 at.% C
70
80
90
C
10 20
10
20
A
A
A
A~
30 TiC^ 50 60 at.% C
70
80
90
C
Figure 4-18. Isothermal section of the ternary T i - B C system at 2300°C in at.% (Rudy et al., 1965). Three liquid phases appear but TiB 2 , TiC 1 _ x and C form solid phase equilibria.
57±2
<2
2400-
TiB 2+
1
2200 -j 0 TiB 9
1
10
Figure 4-17. Isothermal section of the ternary T i - B C system at 1700°C in at.% (Rudy et al., 1965).
Ti
3200 -j 0
Ti
20
60
80
100 TiC n q 9
Figure 4-16. Isopleth of the quasi-binary TiB 2 -TiC phase diagram (Rudy et al., 1965).
tion at 2000 °C is presented in Sec. 4.6.4 (Fig. 4-65). The diagrams based upon the work of Rudy et al. do, however, not take the Ti 3 B 4 phase into account. Hence the equilibria close to the Ti-B border may be incorrect at temperature below 2100 °C.
4.3 Phase Systems
Ti
Ti5Si3
i5Si^ TiSi TiSi2 at.% Si
Si
Figure 4-19. The calculated ternary Ti-Si-C system (Spencer and Holleck, 1989); isothermal section at 1200°C in at.%.
The Ti-Si-C system has been studied by Brukl (1965), Borisova et al. (1986), Holleck (1989), calculated by Touanen et al. (1989) and experimentally re-examined by Wakelkamp et al. (1991). Besides stability studies of TiC-SiC equilibria for ceramic cutting tools, wear parts and coatings, the system is of interest because of the interaction between SiC and metallic Ti for active brazing or SiC fibre reinforcement of Ti-based alloys. More recently, the ternary phase Ti 3 SiC 2 was considered for heat storage in satellites. Unfortunately, the system is not fully characterized yet; only really between 1100°C and 1250 °C. The hexagonal Ti 3 SiC 2 phase, denoted T, has a negligible solid solubility (less than 1 at.%) for the elements; its decomposition temperature is unknown. The homogeneity range of Ti 3 Si 3 extends into the ternary system up to 10 at.% C. This carbon rich solid solution is sometimes called T2 or Ti 5 Si 3 C x , but is in fact structurally identical to Ti 5 Si 3 and hence is not a separate phase. The presence of Ti 3 SiC 2 and
197
Ti 5 Si 3 C x means that Ti reacts with SiC to form these ternary compounds together with silicides or TiC1_x, depending upon the local composition. C-rich T i C ^ ^ and SiC react eutectically at approximately 2700 °C and 47 mol% SiC (Fig. 4-19; calculated by Spencer and Holleck, 1989). SiC also forms a quasi-binary equilibrium withTiSi 2 . The quaternary B-C-Si-Ti system has not yet been established completely, Evidently TiB2 and SiC form a eutectic and can be cast after arc-melting (Telle et al., 1991). TiB 2 -B 12 (B, C, Si) 3 -SiC composites may be prepared by reactive infiltration of porous B4C bodies with an SiTiSi2 eutectic melt (Taffner et al., 1988).
4.3.3.2 Systems with Transition Metal Carbides or Borides and Metallic Binders
The ternary and quaternary systems with metallic binders studied most thoroughly belong to the WC- and TiC-based hard metals and cermets. Well-known examples are the traditional composites WC-Co and TiC-Ni with numerous variations due to the substitution of W and Ti by other transition metals, with the emphasis on increasing the hardness and chemical inertness of the carbides. Furthermore, many successful attempts have been made to increase the toughness, strength, and wear behavior, but also to improve the sintering behavior by alloying the Co- or Ni-based binder phase. These systems will, however, not be addressed here since they are subjects of other Chapters in this Series. Here some emphasis is put on binary and ternary borides which are in equilibrium with metals and as such are similar to hard metals but are also of interest in ceramic systems or coatings.
198
4 Boride and Carbide Ceramics
The Ti-Fe-B, Ti-Ni-B, and related systems are addressed in Sec. 4.5.3 (sintering) and in Sec. 4.6.1 (toughening by metal matrices). No ternary phases have been reported in the Ti-Fe-B system, which makes it possible to fabricate TiB2-based composites using an Fe binder. Although there are some discrepancies in opinion on the quasi-binary TiB 2 -Fe phase diagram (Figs. 4-57 and 4-58), it is now obvious that the formerly observed reaction resulting in the decomposition of TiB 2 and yielding Fe 2 B is due to the presence of carbon impurities (Sigl and Jungling, 1992). In contrast to this very convenient sinter system, the Ti-Ni-B phase diagram contains a congruently melting ternary phase, denoted T, with a composition of Ni 21 Ti 2 B 6 and a Cr 2 3 C 6 structure (Figs. 4-54 and 4-55; Schobel and Stadelmaier, 1965; Lugscheider et al., 1980, 1982). This phase forms in coatings or particulate reinforced metals as a consequence of the reaction between TiB 2 and Ni-based alloys, and is also found with other transition metals replacing Ti (e.g. Zr, Hf, Nb, Ta) or binders (e.g. Co, Cr). Other types of ternary phase also exist, e.g. MIMIIB((p), M 2 M n B 2 (co) and M I M II B 2 . The refractory and extraordinarily hard M I B 2 phases are hence in equilibrium with a comparatively soft and brittle MjjB^ phase and the corresponding ternary compounds (Figs. 4-60 and 4-61). Figure 4-20 presents an isothermal section of the Ni-Ta-B system at 950°C (Lugscheider et al., 1980). 4.3.3.3 Systems with Two Transition Metals and Carbon or Boron
The phase diagrams of two transition metals and carbon are of particular interest in the case of W and Ti as well as for the substitutions of these strategic metals in tool materials. Moreover, the formation of
at.% Ta
Figure 4-20. Isothermal section of the Ni-Ta-B system at 950°C in at.% (Lugscheider et al., 1980).
a solid solution may bring about better oxidation and corrosion resistance, improved wetting by liquid metals and optimized high-temperature and wear properties. An excellent survey on transition metal-carbon systems is presented by Holleck (1984). Some basic experimental work on the Ti-W-C system was carried out by Nowotny et al. (1954), and Rudy (1973). No ternary phases exist. The phase diagram is governed by the wide homogeneity field of the cubic face-centered TiC 1 _ x phase extending the direction of hexagonal WC (Fig. 4-21). At temperatures above 2535 °C there is complete miscibility between TiC^-x and the corresponding subcarbide WC1_X (Fig. 4-22). According to Rudy et al. (1965), this solid solution possesses a congruent melting point of 3130°C at an approximate composition of (Ti o . 56 W O44 ) C 0 . 75 . Below 2535 °C the homogeneity range is strongly temperaturedependent and decreases to about 50mol% WC at 1400 °C (Figs. 4-23 and 4-24). Similar behavior to the cubic face-
199
4.3 Phase Systems
1600Ti
10
20
30 40 50 60 70 fMWJi) solid solution
80
90
W
~i—•—r-1—•—r 20 40 60 Mol% WC
0 TiC
at.% W Figure 4-21. Isothermal section of the ternary Ti= W-C system at 1750°C in at.% (Rudy, 1973).
100 WC
Figure 4-23. Isopleth of the pseudobinary TiC-WC section in mol.% (Rudy, 1973).
3200-
Liquid
3000-
\
\
L
+
C
/
,
2800jre 1
u 0
2600-
E(Ti.W)C
"5 2400CL
/ b+£ /
// /7 //
2200-
CD
2000-
/ \ / /E(Ti,W)C+ ^{Ti,W)C+f3(W.Ti)\ / // W2C+6WC
18001600-
-JL-,
j
20 [3W W
TiC n
,_—j
,\ /
/
40 60 Mol% WC n 7 .
80
100 WC n 7
Figure 4-22. Isothermal section of the ternary T i W-C system at 2500 °C in at.% (Rudy, 1973).
Figure 4-24. Isopleth of the pseudobinary TiC0 7 7 WC0 77 section in mol.% (Rudy, 1973). Note the extension of the e-(Ti, W)C solid solution at high temperatures.
centered monocarbides with complete solid solubility at high temperatures was observed for the following systems with the maximum temperature of the immiscibility gap given in brackets: Ti-Zr-C (2050 °C), Ti-Hf-C (1850 °C), Ti-Mo-C (1860 °C),
Zr-Mo-C (1860°C), Hf-W-C (2530 °C), V-Nb-C (1480°C), V-Ta-C (1330°C), V-W-C (2530°C), Nb-Mo-C (1860°C), Nb-W-C (>2530°C), Ta-Mo-C (>1860°C)? and Ta-W-C (>2530°C). A special case is the Mo-W-C system in
200
4 Boride and Carbide Ceramics
which the hexagonal monocarbides MoC and WC are completely soluble below 1180°C (Fig. 4-25, Rudy et al., 1978). Complete solid solubility of the monocarbides throughout the temperature range was reported for the systems T i - V - C , T i Ta-C, Zr-Hf-C, Z r - N b - C , Zr-Ta-C, Hf-Nb-C, Hf-Ta-C, and Nb-Ta-C. The formation of solid solutions of the sub-carbides (M1, M n ) 2 C can be described in the same way. They are completely miscible in the systems V - N b - C , V-Ta-C, V-Mo-C, V-W-C, Nb-Ta-C, Ta-Mo-C (>2230°C), T a - W - C (>2530°C), and M o - W - C . In binary systems without a quasi-binary equilibrium between the particular M 2 C phases, one of the monocarbides is in equilibrium with the other transition metal having a more or less extended homogeneity range in that direction (e.g. in the T a - W - C and N b - M o - C systems). Decreasing mutual solubility and immiscibility gaps at lower temperatures are generally of interest for the improvement of mechanical properties of alloys. Hardening and in situ reinforcement of supersatu3000
Figure 4-25. Isopleth of the pseudobinary MoC-WC section in mol.% with decreasing solid solubility of (W,Mo)C at high temperatures (Rudy et al., 1978).
rated mixed crystals by precipitation of the particular phases which are stable at low temperatures has been investigated in many of the above-mentioned systems. Ternary systems involving Cr have no comparable solid solubilities since the chromium carbides Cr 3 C 2 , Cr 7 C 3 , and Cr 23 C 6 do not have an isotypic structure being very soluble in the cubic face-centered host-lattice. They form comparatively low melting quasi-binary eutectic systems (Fig. 4-26, Rassaerts et al., 1966). Concentrating solely on the mutual solid solubility of the monocarbides, quasiternary systems have been investigated to elaborate the probable limits of homogeneity and the opportunity for phase precipitation in the immiscibility gaps. Data are available for the systems TiC-HfCMoC (Rogl et al., 1977 a), TiC-HfC-WC (Rogl et al., 1977b), VC-ZrC with TiC, TaC, and NbC (Norton and Mowry, 1951), TiC-HfC-WC (Kieffer et al., 1969), Z r C - N b C - M o C ^ (Fuake et al., 1977), and HfC-VC with MoC and WC (Rogl et al., 1977rc, d). As a pseudoquaternary system the interaction of the monocarbides WC-TaC-TiC-VC has been studied by Mader et al. (1977). Boron-based ternary phase diagrams for transition metals have been investigated for similar reasons to the carbide systems. The outstanding position of the monocarbides is resembled by the diborides with an A1B2 structure, which have high hardness and a high melting point. Due to the identical crystal structure, most of the transition metal diborides are considered to be completely soluble (Post et al., 1954; Kuz'ma et al., 1969; Pastor, 1977; Zdaniewski, 1987; Telle et al., 1992). Precise experimental data are, however, rare or are not readily available. Complete solid solubility with an immiscibility gap was proven for the TiB 2 -CrB 2 system (Fig. 4-71), limited
4.4 Material Preparation
201
10
i
Ti
Figure 4-26. Isothermal section of the ternary Ti-Cr-C system at 155O°C in at.% (Rassaerts et al., 1966).
Y
50 60 at.% Cr
TiCr2
80
90
Cr
solubility and large homogeneity ranges have been observed for the TiB 2 -WB 2 and CrB 2 -WB 2 systems (Fig. 4-72).
breccias and Siberian kimberlites. The cubic /?-phase was found in the Green-River district, U.S.A.
4.4 Material Preparation
4.4.1.1 Technical Scale Production
4.4.1 Preparation of Silicon Carbide
Silicon carbide was first synthesized in the early 19th century, probably by Berzelius who reported on it in 1810, but its technical importance was recognized by Cowless and Cowless (1885), Moisson (1891, reported 1899), Acheson (1892, 1893 a, b) and Schiitzenberger (1893) who prepared it from the elements, by reduction of silica with carbon ("caborundum"), and by crystallization from molten Si-bearing gray cast iron. In nature, oc-SiC is occasionally found in association with diamond in iron meteorites of the Canyon Diablo type and is called Moissanite. Other occurrences are in Boehemian volcanic
The technical production of silicon carbide is carried out by a carbothermic reduction process, the so-called Acheson process (Acheson, 1893 a, b; Mehrwald, 1992). More than 700 000 t/a are currently produced by fusion of quartz sand or crushed quartzite (58-65%), graphite, petroleum coke or ash-free anthracite (35-42%), sodium chloride (1-2%) and wood chips (0.5-1 %) as additives at 2200-2400°C in electric resistance furnaces: SiO2 + 3C -> SiC + 2CO-119kcal (4-1) (corresponding to 2970 kcal/kg SiC, 528 kJ/mol SiC). The starting material may also consist of rice hulls which contain 20 wt.% SiO2 (Lee
202
4 Boride and Carbide Ceramics
and Cutler, 1975; Krishnarao et al., 1991). The process requires 7-12 MWh/t electric energy of which only 37% is consumed in the formation of SiC and 63 % in thermal losses. The furnace consists of a removable refractory brick-wall construction of 1020 m in length and up to 3-4 m in width and height, containing up to 400 t material. The graphite electrodes are placed at the ends (Fig. 4-27). The ingot consists of an intimately mixed blend of the chunky raw materials. The electrodes are interconnected by a linear packing of blocky, dense petroleum coke or recrystallized graphite, the so-called core. For the release of CO and other volatile by-products, degassing channels are provided in the packed ingot. Upon heating of the core, the reaction starts from the inner zone and moves subsequently to the external parts of the furnace. Starting from the core with the purest (green) material, several zones can be distinguished with increasing contamination by carbon, aluminum and other impurities (black SiC). Although the reduction of silica occurs between 1550 and 1750 °C the temperature is raised to 2200-2400 °C to obtain coarse SiC crystals grown from the vapor phase reaction. At these very high temperatures, Boudouard equilibria involving Si, SiO, CO and CO 2 are active which contribute to local self-purification
processes (Miiller et al., 1972; Miller et al., 1979; Schei and Larsen, 1981; Filsinger and Bourrie, 1990) SiO2 + 3C
1550-1750°C
SiO2 + CO CO 2 + CO <SiO(g) + 2C
SiC+ 2 CO (4-2)
SiO(g) + CO 2
(4-3)
2 CO
(4-4)
1527°C
SiC + CO
(4-5)
2SiO 2 + SiC 1625-1900°C ,
SiO2(l) + Si SiO(g) + SiC
3SiO(g) + CO 2SiO(g)
(4-6) (4-7)
2Si(g) + C 0 (4-8)
Almost complete recovery of the CO gas is achieved by a process developed by the Elektroschmelzwerk Kempten that uses plain electrodes at the ground on which the blend of starting materials is piled up (Fig. 4-28). The entire setup is finally covered with a plastic sheet, which is blown up by the generated CO gas. The reaction gases are collected and used for energy conversion (Schwetz, 1987). After 40 h reaction time the yield is generally 50 t of blocky a-SiC of large crystal size (several mm to cm) with carbon impurities (Wecht, 1977). Incompletely reacted mantle material in the cooler parts of the furnace (so-called siloxicon) is removed and added to the next cycle. The reacted material close to the core is classified into
Figure 4-27. Schematic sketch of a conventional Acheson-furnace (Oel et al., 1990). a, b: bottom and wall construction with refractory bricks or concrete, c: wall support, d: coal/graphite electrode (core material), e: SiC rim for electric coupling, f: inner reaction zone with volatile byproducts, g: outer shell of the reaction zone, h: unreacted raw material mixture.
4.4 Material Preparation Reaction mixture Resistance core
SiC
Canopy
CO collection
203
reactions involving Si(g), silane or silicon tetrachloride, for example: (a) from the elements by solid phase reaction or sublimation in an inert atmosphere
Porous bed •3 m-
Si(s) + C
>13OQ C
Si(g) + C
>2500 c
° >
(4-9)
° >
(4-10)
(b) from vapor phase reaction with methane
-30mCore
Si(g) + CH 4 ^ lectric arc > SiC + 2H 2
(4-11)
(c) or silane in hydrogen SiH4 + carbon-containing compounds -• SiC (4-12) Ground electrode
Power supply
Figure 4-28. Acheson furnace constructed by the Elektroschmelzwerk Kempten with CO retainment and stationary electrodes on the ground (Schwetz, 1987).
three to five different qualities, crushed and milled to the desired grit size. For use as a ceramic material, subsequent washing and leaching is required to remove the metallic impurities. The graphite residue is oxidized at approximately 400 °C. Oxidation layers can be removed by hydrofluoric acid leaching. Cubic /?-SiC is preferentially prepared by the General Electric process (Prener, 1960), which starts with an aqueous solution of sugar and silica gel. Upon dehydratization, carbon and silica are intimately mixed. The temperatures required for electrothermic reduction are thus as low as 1800°C.
(d) vapor phase reaction of silicon tetrachloride SiCl4 with toluene or other hydrocarbons in hydrogen such as methane, hexane, or chloroform SiCl4 + C 6 H 5 - C H 3 1200 1 800 c "H 2 ° > SiC + 4HC1 (+ C)
(4-13)
4.4.1.3 Organometallic Precursors Laboratory-scale procedures can be used to produce extremely well-defined materials comprising monomeric, organometallic compounds which are pyrolyzed at relatively low temperatures in a vacuum, hydrogen or an inert gas atmosphere. For the synthesis of SiC without a free carbon residue it is important to start with precursors which exhibit an Si/C ratio close to unity. Suitable processes are: (a) Pyrolysis of dichloromethylsilane or trichloromethylsilane
4.4.1.2 High-Purity Material
CH 3 SiHCl 2 iooo-i5oo°c)
High-purity SiC single crystals, whiskers or powders are synthesized from the elements, silicon melts, and by vapor phase
CH 3 SiCl 3 >noo-i9oo°c )
S i C + 2 HCl
+ H2
S i C + 3 HCl
+ H2
(4-14) (4-15)
204
4 Boride and Carbide Ceramics
Below 1400 °C, polycrystalline material and coatings are obtained whereas above this temperature stoichiometric single crystals and whiskers can be grown (Brenner, 1960; Bonnke and Fitzer, 1966). Various techniques for the fabrication of fibres and laminates including kinetic data have been extensively described by Fitzer et al. (1987). (b) Pyrolysis of methylsilane, CH 3 SiH 3 , tetramethylsilane (CH3)4Si or other organopolysilanes, (c) 1,1,1,2,3,3,3-heptamethyl-2-vinyltrisilane II
I
H 3 C-Si—Si—Si-CH 3 I I I CH3CH CH3 CH2 (d) Tetraphenylsilane Ph4Si (Ph = phenyl)
SiC+C+CH 4 (4-16) (6-50% yield)
(e) Diphenyldipropenylsilane PhSi(CH2CH = CH 2 ) 2 (3-15% yield) (f) Triphenylvinylsilane Ph 3 Si-CH = CH 2
CH3
-hSi-CH2-h H
(2-69% yield)
(g) Phenyltrimethylsilane Ph-Si(CH 3 ) 3 (1-27% yield) (h) Triphenylsilane Ph3SiH
purity if a carbon residue can be avoided, the process can be carried out at relatively low temperatures and yields near-netshape parts of high surface quality. Furthermore, the resulting material is usually amorphous and may be crystallized at temperatures above 1800°C. Thus a tailored microstructure of desired grain size can be grown by annealing treatments. Disadvantageous effects are the relatively small yield and the vaporization of pyrolysis byproducts such as methane, hydrogen, hydrochloric acid, ammonia and others which create high porosity or rupture of the ceramic body. Another difficulty is the control of the resulting stoichiometry of Si and C which can easily lead to a strong excess of free carbon. The starting materials for the SiC synthesis are polycarbosilanes, polysilanes and polycarbosiloxanes (e.g., Yajima et al., 1981; Schilling et al., 1983),
(1-15% yield)
Since approximately 1974, the molding and pyrolysis of polymerized organometallic compounds have been investigated in detail and a promising method was developed for the preparation of continuous fibres, coatings, and monolithic or composite SiC material by a "non-ceramic process" in which the powder route is avoided. In the case of coatings and bulk material, the advantages of using pyrolysis are that the material obtained is of high
Polycarbosilane
Ph CH3 I I -Si—Si— I I CH 3 CH 3
R I -r-Si-O-f I R
Polysilane
Polycarbosiloxane (4-17) SiC —Si3N4 composite materials have been synthesized from (a) Polysilazanes (Verbeek, 1974) R R I I 4-Si-N-f I R (b) Alkalenetrisilazane
(10-20% yield)
-CH2 I —N-Si-N-Si-N-Si-N(CH3)2 (CH3)2_ 3) H2C-
4.4 Material Preparation
(c) 7V,Af-Diphenyltetraphenylcyclodisilazane (5-15% yield) ph I N / \ Ph2Si SiPh2 \ / N I Ph (d) iV-6,9-Bis (trimethylsilyl) adenine (1-33% yield) [-Si(CH 3 ) 2 ] n I C N I
CN II
c c c N
N Si(CH3)3
(e) Bis (diethylamino) dimethylsilane
The preparation of crack-free ceramic bodies derived from polycarbosilane was achieved by the conversion of dichlorodimethylsilane and dichloromethylvinylsilane in an N a - K alloy at 68 °C with 94% yield. The product consists of an insoluble and infusible polycarbosilane with reacted vinyl groups that can be processed as premolds and subsequently pyrolyzed at 1100°C. The final products are monolithic amorphous SiC parts with a hardness of HV 18.5 GPa (Riedel et al., 1990). The considerably lower value compared to crystalline SiC is attributed to the presence of residual carbon. In a similar process (Riedel et al., 1992), infusible black polysilazane was synthesized by heat-treating commercial polysilazane at 350 °C for 3 h. Formation of the infusible black polysilazane was attributed to a cross-linking reaction (4-18)
(CH 3 ) 2 Si[N(CH 2 CH 3 ) 2 ] 2 (f)
205
1,1,33-Tetramethyldisilizane
(CH3)2Si-N-Si(CH3)2 I I H H Precursors for SiC — B4C composites are (a) Carboran-siloxane
(60-65% yield)
CH 3 -Si-CH 3 (BB8C2B)
C6H5
H3C-Si-O-Si-OI
I
CH3
C6H5
(b) Poly(borodiphenyl)siloxane (43% yield)
(CH 3 ) 3 -Si-f-O—Si—O-j-Si-(CH 3 ) 3 phBH2
Subsequently, the product was milled to powder and molded by cold isostatic pressing. Pyrolysis of that organometallic green body yields an amorphous silicon carbonitride material of the composition Sii.5N1#35C1>0, if carried out in an argon atmosphere at 1000 °C. In an ammonia atmosphere, a pure, colorless Si 3 N 4 is obtained that starts to crystallize at 1200 °C. The resulting ceramic material is almost dense and crack-free since the volatile pyrolysis products can degass easily due to the open porosity of the green compact. Another method starting with polysilsesquioxanes of the general formula (RSiO 15 ) n with R = H, CH 3 , C 6 H 5 and CH = CH 2 , mixed with reactive fillers of metallic titanium limits the strong release of gaseous pyrolysis by-products to hydrogen, which can easily diffuse due to its
4 Boride and Carbide Ceramics
small ion size (Greil and Seibold, 1993). In this process called "active filler controlled pyrolysis" the polymer compound and the filler metal are molded at 200 °C and annealed for 60 min to allow a cross-linking reaction to occur in the green compact due to an addition mechanism e.g. in the vinylsubstituted polysiloxane
H CH I I -Si- + -Si-
200°C ,
H H I I I I -Si-C-C-SiI I I I H H (4-19)
A pore-free, green part is obtained which can easily be machined. Upon pyrolysis at 900-1400 °C for 1 h the precursor is converted to SiC, C and CH 4 . Since C and CH 4 react with metallic fillers such as, e.g., titanium to form TiC, only hydrogen is released. No porosity or cracking was thus found. As an additional benefit, dispersed TiC works as a reinforcing phase. Almost dense parts of complicated near-net-shape morphology have been produced up to 40 mm in size. It is possible also to use other reactive fillers such as silicides, as well as inert materials such as transition metal carbides or borides in fiber or platelet shape which reduce shrinkage to almost zero. 4 A.I A Poly type Formation During SiC Synthesis a-SiC is generally obtained by vaporliquid-solid mechanisms or the Lely process and related methods (Knippenberg, 1963), preferentially in the temperature range 2300-2700 °C, whereas the formation of /?-SiC is favored by growth from silicon melts or by hydrogen reduction of organo-silanes at temperatures below
2000 °C. Upon heat-treatment between 2100 and 2300 °C j8-SiC transforms irreversibly to the a-polytype. In contrast to this general picture which indicates that a-SiC may be the high-temperature form, some a-polytypes also form at temperatures as low as 1300-1600 °C, e.g. 2Hwhiskers produced by the decomposition of methyltrichlorosilane CH3SiCl3 (Merz and Adamsky, 1959; Merz, 1960), or by traveling solvent processes. On the other hand, yS-SiC has been obtained above 2600 °C (Scace and Slack, 1959). Ryan et al. (1968) stated that a small excess of atmospheric pressure may favor the formation of a jS-polytype at any temperature (Fig. 4-29). Furthermore, impurities such as aluminum, nitrogen or boron may influence the generation of screw dislocations or stacking faults, which also determine the polytype. Kistler-De Coppi and Richarz (1986) have shown that particle size and shape must also be taken into account. Figure 4-30 gives some general temperature/process-dependent stability fields of both polytypes (Ryan et al., 1968). Other comprehensive treatments of polytype stability may be found in Verma and Krishna (1966). Polytype transformation and other reaction processes related to sintering phenomena and important microstructural features will be dealt with in Sec. 4.5.2.4. uu -
a _Q
CD
c o
p-SiC
10 -
ieco mpoj
206
i"n
1 -
/ ^
tx-SiC
/vapor! 0.1 -
i
i
i
i
i
i
i
1800 2200 2400 Temperature °C) Figure 4-29. Influence of atmospheric pressure on the formation of a- and /?-SiC polytypes (Ryan et al., 1968).
uoo
4.4 Material Preparation
[3-Polytype
207
a-Polytype
3000Decomposition 28002600 o
2Z.00-
g
2200-
Vapor phase processes at 35 bar Ar or 1-35 bar N2
P to a trcinsformation
a. — 2 2000 1800-
Lely-process vapor phase processes
Growth from silicon melts
Films and coatings Travelling solvent method
nt <1 hnr 1 600 -
atmospheric pressure
1 / nH
1 4UU -
Pyrolytic processes \
Figure 4-30. Temperatureprocess-dependent stability regimes of a- and jS-SiC (Ryan et al., 1968).
\ Melting point of Si
12001000 -
4.4.2 Preparation of Boron Carbide
Boron carbide was first prepared by Joly (1883) and labeled as B6C by Moisson (1899). In 1934, Ridgeway suggested the composition B4C which is still under controversial discussion (see Sec. 4.2.1.1). 4.4.2.1 Technical Scale Production
B 2 O 3 + 3CO -> 2B + 3CO 2
Boron carbide powder is produced on a technical scale by the carbothermic reduction of boron oxide with graphite or petroleum coke 2B 2 O 3 + 7C
4C +
6COt
formed, the reaction of Eq. (4-20) is accelerated to the benefit of B 4 C. Both volatilized boron oxides and carbon monoxide generate an internal Boudouard equilibrium within the raw material mixture and thus contribute to a self-propagating purification process, which can be expressed by
(4-20)
The process is carried out in huge electric arc or resistance furnaces and is comparable to the Acheson process. The reaction takes place between 1500 and 2500 °C, is strongly endothermic and requires 1812kJ/mol, i.e. 9.1 kWh/kg (Lipp, 1965, 1966 a). Since large quantities of carbon monoxide (approximately 2.3 m3/kg) are
2 CO
<-•
CO 2 + C
(4-21) (4-22)
4B + C -• B4C (4-23) The furnace is usually cooled externally to limit the loss of volatiles and hence the outer mantle stays unreacted. The core contains blocky boron carbide of relatively high purity (total metallic impurities <0.5 wt.%), reproducible stoichiometry (B/C ratio = 4.3, Schwetz and Karduck, 1991), and several percent of residual graphite. The chunks are crushed and milled to the final grain size.
208
4 Boride and Carbide Ceramics
A similar process with lower productivity is used for the synthesis of high-purity B4C of controlled stoichiometry. At temperatures of 1600-1800 °C, hydroboric acid reacts with acetylene black, high purity sugar, or ethylene glycol in a vented tube furnace 4H 3 BO 3 + 7C -> B4C + 6H 2
(4-24)
Powders of 0.5-5 jim particle size are obtained (Dufek et al, 1976). Boron oxide can also be converted to boron carbide by exothermic magnesiothermic reduction in the presence of carbon black at 1000-1800 °C (Gray, 1980) 2B 2 O 3 + 6Mg + C -> B4C + 6MgO (4-25) The process is performed by single point ignition (thermite process) or in a carbon tube furnace in a hydrogen atmosphere. The problem is the removal of magnesia, magnesium borides, and unreacted magnesium metal which are usually extracted by hydrochloric or sulfuric acid. Since MgO acts as a grain growth inhibitor, submicron powders with Mg compounds as the only impurities are produced (Schwetz and Lipp, 1985; Thevenot, 1990b). Further chemical refinement by high-temperature vacuum treatment, however, induces an undesirable coarsening of the particles. The 1990 total annual production of boron carbide in the western world is estimated at approximately 500-600 t. 4.4.2.2 High-Purity Material In laboratory-scale production, boron carbide can also be synthesized in the form of high-purity powders or coatings: (a) from the elements by arc melting at 2500 °C, or self-propagating synthesis above 1100°C 4B + C -> B4C
(4-26)
(b) by chemical vapor deposition reducing boron trichloride in the presence of carbon in a hydrogen atmosphere 4BC13 + 6H
B4C + 12HC1 (4-27)
(c) by pyrolysis of boron trihalides with methane or carbon tetraiodide as carbon carriers, in high-frequency furnaces 4B(Cl,Br) 3 + CH 4 + 4H 2 900-1800°C * B4C + 12HCl(HBr)
(4-28)
4BI 3 -hCI 4 900-1100°C
(4-29)
The latter methods yield boron-enriched solid solutions with a maximum of 20.4 wt.% carbon. Very fine boron carbide powders of spherical shape and 20-30 nm in size have been prepared by chemical vapor deposition according to (c). In an A r - H 2 - C H 2 BC13 atmosphere a radio frequency plasma produces stoichiometries between B 1 5 8 C and B 3 9 C (McKinnon and Reuben, 1975; Ploog, 1974). Also laser-induced pyrolysis of similar gas mixtures with or without acetylene has been employed for the preparation of nano-sized particles (Knudsen 1987). With similar success, composites of B4C and SiC have been produced by the pyrolysis of boroncontaining polysilanes (Walker et al., 1983). The general problem associated with the production of submicron powders by pyrolysis is the comparatively low yield of these highly expensive procedures and the excess of free carbon which cannot usually be avoided. The advantages of high purity and well-defined composition are limited due to the pick-up of oxygen by the large and hence extremely reactive surface area of the particles when exposed to air.
4.4 Material Preparation
4.4.3 Preparation of Transition Metal Carbides The production of transition metal carbides on an industrial scale occurs by sinter-carbonization of the oxides or hydroxides with carbon black in huge induction furnaces between 1500 and 2000 °C (ZrC, HfC, VC? NbC, TaC) or 2000-2200 °C (TiC) in a vacuum or hydrogen atmosphere TiO2 + 3C -> TiC + 2COt
(4-30)
Other reduction processes for oxides are aluminothermic and, less common, silicothermic reactions. The reaction then occurs above the melting point by arc melting or by induction melting. Only mixed carbides with relatively low melting temperatures [e.g., (Cr, Mo)C, (V, Ta, Nb)C] or eutectic mixtures (e.g., WC/W2C) are usually produced by this method. Purer melt-derived carbides are prepared by the auxiliary bath technique {menstruum process) by dissolution and re-crystallization of contaminated carbides in a liquid metal of no or little solubility. The melt temperature ranges between 1700 and 2000 °C; after cooling the refined carbide crystals of 100-1000 jim in size are extracted by an acid treatment of the metallic matrix. High-purity tungsten carbide (WC), molybdenum carbide (Mo 2 C), and Cr 3 C 2 are produced by the strongly exothermic reaction of the metals with carbon black under hydrogen or in a vacuum between 1400 and 1600 °C. Powder blends of Ti, Zr, Hf and carbon black are flammable. Solid solutions of the transition metal carbides are obtained by homogenization annealing between 1600 and 1800°C. Recent developments include direct tungsten and tungsten carbide production from the raw material scheelite (CaWO4) with several tungsten oxides as intermediate products.
209
In combined methods, a mixture of oxides and metals is carburized. Recycled chunks of metals are hydrogenized for embrittlement, crushed and milled. The metal hydrides are then added for carburization. Thus, ungraded commercial metal carbides are usually prepared from a large amount of recycled material, and they therefore contain other transition metal carbides and solid solutions thereof as significant impurities. The total WC production is estimated to be approximately 12000 tons/year. Vapor phase deposition methods yielding chemically well-defined powders or coatings make use of reactions of volatilized transition metal chlorides: (a) Conversion of titanium tetrachloride and methane by a heated wire H2 1600-2000°C
TiCL+CH 4
TiC + 4HCl (4-31)
(b) Decomposition of titanium tetrachloride with acetylene in hydrogen plasma + §H 2 ^ TiC + 4HCl (4-32) (c) Reaction of titanium trichloride with metallic aluminum powder and carbon black 2
TiCl3 + Al + C
700 1100 c
~
° > TiC + AlCl 3 (4-33)
All these reactions are strongly endothermic. The formation of MC in (a) and (b) occurs via CH radicals as a product of the methane and acetylene pyrolysis and yields particles of 10-100 nm diameter. More recently, the preparation route via organometalic precursors has become of increasing interest. Tfre aim is the synthesis of extremely pure, fine-grained powders or
210
4 Boride and Carbide Ceramics
pre-alloyed composite powders, fibers, coatings, or even monolithic materials. Possible precursors for titanium carbide are: - Ti2 + : titanocene and its derivatives: Cp 2 Ti(CO) 2 ,Cp 2 Ti(PMe 3 ) 2 , CpTiPh • 2OEt 2 and Ph 2 Ti. - Ti 3 + : (Cp 2 TiPh) 2 , Cp 2 TiMe. - Ti 4 + : Cl x TiR 4 _ x . Cp = cyclopentadienyl and Me = methyl.
4.4.4 Preparation of Transition Metal Borides Large-scale production of metal borides occurs preferentially in electric furnaces by the following high-temperature reactions: (a) Carbothermic reduction of the metal oxide, graphite or carbon black + B2O3
MB 2 + 5CO (4-34)
The carbothermic method yields carbon contaminated powders and is suitable for materials in which a C content of <3wt.% can be tolerated. For instance, TiB 2 , ZrB 2 , and the technically important hexaboride CaB 6 are synthesized by this method. (b) Reduction of metal oxides with carbon and/or boron carbide, known as the boron carbide process 2MO 2 + B4C + 3C -> 2MB 2 + 4CO (4-35) M 2 O 3 + 3B 4 C -> MB 6 + 3CO (4-36) where M = rare earth elements. The boron carbide process can also start from blends of metal carbides, metal hydrides, boron oxide, boron carbide and carbon black 3MB 2 + 9COt
(4-37)
MC + MO 2 + B4C (4-38)
-> 2MB 2 + 2COT
This material usually contains only small amounts of residual carbon or boron carbide but no metals, and is thus the favored process for the technical synthesis of less contaminated borides. The process is carried out in tunnel furnaces under hydrogen or in a vacuum at 1600-2000°C, i.e., below the melting point of the boride. It is thus a reaction sintering procedure yielding a high-porosity product which can easily be crushed and milled. Additional refinement is obtained by multiple vacuum treatments with metallic or B4C additives to compensate non-stoichiometries. The final product is then called "vacuum quality". (c) Aluminothermic, silicothermic, magnesiothermic reduction of mixtures of metal oxides and hydroboric acid + B 2 O 3 + Al(Si,Mg) + Al 2 O 3 (SiO 2 ,MgO)
(4-39)
The yield is usually contaminated by residual metals or oxides and thus has to be purified by subsequent leaching, or a hightemperature vacuum treatment. High-quality borides of the transition metals with defined stoichiometry and crystal structure are synthesized by the following laboratory-scale methods: (a) From the elements or metal hydrides by fusion in an arc or resistance furnace, or by diffusion during sintering or hot pressing M + 2B -> MB 2
(4-40)
MH 2 + 2B -> MB 2 + H 2
(4-41)
(b) Borothermic reduction of metal oxides MO 2 + 4B
+ B2O2t
(4-42)
4.5 Sintering Behavior of Carbide and Boride Ceramics
(c) Conversion of metal carbides with boron and/or boron carbide yielding powder mixtures or - carried out during powder metallurgical densification, i.e., sintering or hot pressing - composites MC + 2B
MB 2 + C
(4-43)
MC + 6B
MB 2 + B4C
(4-44)
2MC + B X -> 2MB 2 + 3C
(4-45)
(d) Electrolysis of fused salts containing metal oxides, boron oxide or hydroboric acid plus alkaline borates and fluorides. (e) Molten metal/boron dissolved in Al, Cu, Sn, or Pb melts (auxiliary-metal bath method). (f) Chemical vapor reaction of metal halides and boron halides in a hydrogen atmosphere under plasma conditions. This method yields, however, material of varying stoichiometry and crystallinity. Limiting factors for commercial fabrication are the relatively high costs of elemental boron and the low production rate in the reactors.
4.5 Sintering Behavior of Carbide and Boride Ceramics Sintering of covalently-bonded materials is generally much more difficult than densification of oxide ceramics or metals. This is not only due to the low self-diffusion (poor tendency for grain boundary and volume diffusion), high ratio of grainboundary-to-surface energies and high vapor pressure of particular constituents (strong tendency for surface diffusion and evaporation-recondensation), but also due to their extreme sensitivity to environmental factors such as sintering atmosphere, traces of contaminants, particle size and shape distribution, temperature
211
gradients, etc. The phenomenon of a "terminal" density, i.e., the density obtained after sintering which is far below the theoretical density for pore closure, above which neither an increase in the temperature nor a prolonged sintering time would assist further densification, was frequently observed for B4C, SiC and Si 3 N 4 . The reason for this, as proposed by DeHoff et al. (1966), Greskovich and Rosolowski (1976) and Prochazka (1989), is that upon sintering the decrease in the specific surface area (driving force for densification) is consumed to a much greater extent for pore and particle coarsening (Ostwald ripening) than for grain boundary movement and pore removal. Figure 4-31 shows a socalled DeHoff diagram correlating the specific surface area and the fractional density on which the path of an ideally densifying material is illustrated by the diagonal line. The lines plotted for A12O3, SiC and B4C powders make it obvious that in the first step of sintering, the surface energy is dissipated very fast due to coarsening (Prochazka, 1989). Since a doubling in particle size corresponds to a decrease in the densification rate by a factor of ten, it is no wonder that densification comes to an end before pore closure is achieved. As pores are favorably removed by grain boundary movement, it is essential to generate a pore size distribution below a critical size above which pores are stable or even tend to grow (i.e., the driving force for pore shrinkage is <0) and to induce grain growth at moderate rates so that vacancies may be suitably removed from the surface of the pores. In conclusion, sintering of covalentlybonded materials requires highly sophisticated procedures for optimization of the many technical parameters dependent on powder quality, sintering additives and furnace capability, and thus in most cases
212
4 Boride and Carbide Ceramics
a
o - B ^ C , cycle A
are
i.u 0.9 0.8 •
a -SiC, powder A
0.7 -
A - Al 2 O 3 + MgO
cu a
sur
i—
—
0.4 •
mini
03 •
t!
• - SiC, powder B
0.5 •
8.
—
• - B 4 C , cycle B
0.6 -
\
\
\
\
\ \ : ^
. \ Figure 4-31. De-Hoff diagram showing the sintering behavior of doped and undoped A12O3, B4C and SiC ceramics (Prochazka, 1989).
\ 0.2 •
\
0.1 •
\
n40
50
60
70
90
100
Density [%]
is only achievable by an "Edisonian approach". According to Prochazka (1989) "Sintering of these materials is no more difficult than of any other ceramic, if it works. However, the problem is that sometimes it does not". 4.5.1 Densification of Boron Carbide 4.5.1.1 Pressureless Sintering Without Additives
Densification of pure stoichiometric boron carbide is extremely difficult. Due to the high fraction of covalent bonding (>90%), pore eliminating mass transport mechanisms such as grain boundary and volume diffusion become effective at temperatures above 2000°C, i.e., at temperatures close to the melting point. At lower temperatures, surface diffusion and evaporation-recondensation reactions are the favored mechanisms, resulting in neck formation (increase of contact area), pore coalescence and particle rounding (decrease of specific surface area), or euhedral growth of particles by vapor phase reactions, respectively. Grabchuk and Kislyi (1976) proved that the regime of predominant surface diffusion extends from
1500°C to 1800°C, whereas sublimation occurs above 1800 °C with boron being the more volatile species. Only the latter sintering mechanism causes an enhanced shrinkage of the ceramic body. However, a poor tendency for plastic deformation, a high resistance to grain boundary sliding, and low surface energies hinder a considerable particle rearrangement or shape accommodation before grain boundary or volume diffusion is effective. Even submicron powders cannot thus readily be densified completely by pressureless sintering if they are not mechanically or chemically activated. The general preconditions for the densification of pure stoichiometric boron carbide are to start with very fine powders (preferably <^ 3 jam) of low oxygen content and to use temperatures in the range of 2250-2350 °C. Above 2000 °C, a rapid coarsening occurs which usually results in unremovable, entrapped residual porosity. Sintering parameters and obtained densities have been presented for many compositions in the homogeneity range of boron carbide by e.g. Adlassnig (1958) (2250-2300 °C; 80-87% density; 2450 °C: > 90 %) and Grabchuk and Kislyi (1974) (2300°C: 99-99.5% density) who
4.5 Sintering Behavior of Carbide and Boride Ceramics
used finer powders. A considerable reduction in temperatures can be achieved by microwave sintering using 2.45 GHz radiation. After a 12 min treatment at 2000 °C, 95% of the theoretical density was obtained (Katz et al., 1988). The energy conservation compared to hot-pressing is, however, rather low. Starting from powders with a smaller particle size, e.g. < 1 pxn, would possibly result in lower sintering temperatures and higher final densities. Boron carbide, however, becomes pyrophoric with increasing specific surface area and is hence strongly oxygen-loaded or even dangerous in handling. 4.5.1.2 Pressureless Sintering with Additives
Activation of grain boundary and volume diffusion and thus densification at lower temperatures is possible by increasing the density of point defects or dislocations: (i) mechanically by high-energy milling (attrition milling), (ii) by doping with trivalent ions which substitute for carbon and thus introduce electron deficiencies and vacancies, e.g., by adding boron or aluminum, (iii) by introducing sintering additives which remove oxide layers on the surface of the boron carbide particles and thus increase the surface energy, e.g., by adding carbon, aluminum carbide, silicon carbide or related compounds which also inhibit exaggerated grain growth (Dole and Prochazka, 1985). Other methods make use of additives which possess a comparatively low melting point and have a suitable wetting behavior on boron carbide to provide a rapid path for mass transport via the melt and thus to initiate liquid phase sintering. Dense bodies of boron carbide have also been obtained by liquid phase infiltration of highly porous
213
powder compacts or presintered ceramic bodies. Kislyi and Grabchuk (1975) reported that volume diffusion is enhanced in the boron-rich area of the homogeneity range of boron carbide due to the generation of point defects. In fact, pressureless sintering with boron additives results in an onset of shrinkage at temperatures which are 300 K lower than those required for stoichiometric B4C. Since aluminum also substitutes for carbon, a similar mechanism may be activated. Accordingly, 95-99.2% of the theoretical density is obtained at 21002200°C with 3-15%, preferentially < 1 % Al additive (e.g., Kriegesmann, 1989). Other Al-providing sintering additives are A14C3, A12O3 and A1F3 (Lange et al., 1980; Kanno et al., 1987; Kriegesmann, 1989) which also use carbon or fluorine as deoxidizing agents. The use of metallic additives is limited due to the low thermodynamic stability of boron carbide reacting with metals to form metal borides and free carbon, except in the case of Cu, Zn, Sn, Ag, and Pb. Nevertheless, Mg, Cr, Co, and Ni have been used (Glasson and Jones, 1969; Janes and Nixdorf, 1966, Lange et al., 1980), with minor success. Stibbs et al. (1973) have proposed additions of 5 10 wt.% Al, Mg or TiB2 to obtain > 9 9 % density between 2150 and 2250 °C. TiB 2 , CrB 2 , and W 2 B 5 additives inhibit grain growth by grain boundary pinning or, as in the case of W 2 B 5 at >2220°C, initiate liquid phase sintering if a eutectic reaction occurs (Zakhariev and Radev, 1988). Sintering of submicron powder with an addition of 1 wt.% Be2C resulted in 94% density when sintered between 2200 and 2280 °C (Prochazka, 1977). The only technically important sintering additive for boron carbide is carbon, as discovered almost simultaneously by Schwetz and Vogt (1977), Henney and
214
4 Boride and Carbide Ceramics
Jones (1978), and Suzuki et al. (1979). An amount ranging from 1 to 6 wt.% is sufficient to obtain almost theoretical density. Schwetz and Grellner (1981) added phenolic resin (corresponding to 1-3 wt.% C) to a submicron B4C powder and obtained > 9 8 % density at 2150°C. The sinter activation was attributed to an increase in surface energy due to the removal of oxide layers. Moreover, residual graphite particles which have been observed at the grain boundaries may inhibit surface diffusion and evaporation and may also control the grain boundary movement (Dole and Prochazka, 1985; Dole et al., 1989). Firing of B4C with 6 wt.% C additive at 2220°C results in a 97% dense microstructure of 1-5 jLim equiaxed particles, i.e. almost no coarsening has occurred. Abnormal growth of individual grains to 10-30 jim starts above 2235 °C; at 2250 °C, extensive Ostwald ripening and twinning is observed. The local growth of faceted grains exceeding 500 jim in size was attributed to liquid phase sintering processes due to the presence of low melting impurities (Dole and Prochazka, 1985). The method of in situ pyrolysis of organic additives such as Novolaque-type resins to amorphous carbon was also studied by Bougoin et al. (1985). The advantage of the precursor method is the improved homogeneity of the carbon distribution and the extraordinarily fine, resulting average grain size of 2 |im and less. Furthermore, the resin may act as a molding aid upon cold isostatic pressing, or may even be the plasticizer for injection molding. Thus complicated parts can be fabricated easily and subsequently pyrolyzed and pressureless sintered. Combined additives consisting of carbon and a metal carbide or boride make use of both the deoxidizing effect of carbon and the diffusion-enhancement by the
metal, or the grain growth inhibiting and reinforcing effect of nonreacting phases, e.g., B + C, SiC + C, SiC + Al, or TiB2 + C (e.g., Bougoin et al., 1985; Grabchuk and Kislyi, 1975; Oh et al., 1985). Weaver (1982 a, b) sintered relatively coarse (average size 9 jim) boron carbide powders with 2-40 wt.% SiC and 0-10 wt.% Al additives to > 85 % density. In similarity to the decomposition of an A14C3 addition, metallic Al is dispersed very homogeneously by evaporation and condensation in the still porous ceramic body (Borchert and Kerler, 1975; Kriegesmann, 1989). Starting from submicron powders, Schwetz et al. (1983) prepared composite materials consisting preferentially of 9-10 wt.% SiC and 1-3 wt.% C with 97-99.7% density at 2000-2100 °C. Residual porosity was removed completely by a post-HIP (hot isostatic pressing) treatment at 19502050 °C. Both C and SiC may also be introduced in the form of organometallic precursors, e.g., by infiltration of a porous B4C body with polycarbosilane and phenolic resin, and subsequent pyrolysis. Bougoin and Thevenot (1987) reported on the fabrication of composite bodies containing 5 wt.% SiC residue but no free graphite. Sintering for 15 min at 2175 °C results in a density of > 9 2 % . The microstructure of 7.5 wt.% polycarbosilane material exhibits relatively large, faceted B4C particles (20-50 jim) with entrapped pores and local enrichments of SiC implying that liquid phase sintering may be active. Increasing the amount of polycarbosilane to 17.5 wt.% results in a more uniform microstructure that is characterized by /?-to-a transformed SiC platelets of 50 Jim size. Pressureless sintering with liquid phases was studied in the B 4 C-A1 and B 4 C-Si systems. Since Al melts below 600 °C and exhibits a significant vapor pressure at only slightly higher temperatures, the equilib-
4.5 Sintering Behavior of Carbide and Boride Ceramics
rium between 1000 and 1880 °C, at which liquid Al is stable with an Al-saturated B 12 (B, C, Al) 3 solid solution (Fig. 4-32, Lukas, 1990), cannot readily be utilized for liquid phase sintering. Moreover, problems in wetting due to oxide layers on the surface of both Al and B4C powder particles have to be overcome. As shown by Halverson et al. (1989), it is more effective to infiltrate compacted or presintered porous B4C bodies with liquid Al. Since the resulting material is a metal-reinforced B4C cermet rather than a liquid-phase sintered B4C ceramic, it will be treated in detail in one of the following sections. According to the B-C-Si phase diagram, liquid phase sintering of B4C should generally be possible above 1560°C with a B-rich Si liquid (Telle, 1990; Telle and Petzow, 1987 b). Starting from powder mixtures of B4C, B, and Si, the first unit is generated at 1380°C, which is in equilibrium with SiB6 and SiC and thus may cause the partial decomposition of B 4 C. Above
215
1560°C, however, a B 12 (B, C, Si)3 solid solution is in equilibrium with the liquid (Fig. 4-33). Besides the complications due to iterative changes of the wetting behavior due to dissolution and precipitation reactions upon heating, a strong limitation on the final densification arises from the continuous evaporation of Si, which may cause degassing channels and thus even open porosity (Fig. 4-34).
2600 2400220020001 800 — E 1600-
U0012001000
Figure 4-33. Isopleth through the ternary B-C-Si system parallel to the B-C edge at 5 at.% Si. The B 12 (B,C,Si) 3 solid solution forms a ternary eutectic with Si (B) liquid.
90
80 (B 4 C)
B AIB12 20
30
£0 50 60 at.% Al
70
80
90
Al
Figure 4-32. Isothermal section of the ternary A l - B C system at 1600 °C after Lukas (1990); liquid Al is stable with an Al-saturated B12(B,C,A1)3 solid solution.
Figure 4-34. Degassing channels in a B 12 (B,C,Si) 3 ceramic; pressureless liquid phase sintered at 2050 °C (SEM micrograph).
216
4 Boride and Carbide Ceramics
4.5.1.3 Hot-Pressing and Hot Isostatic Pressing Since pressureless sintering allows the fabrication of complex shapes but results in coarse microstructures and approximately 3-7 vol.% of residual porosity, this process is only applicable for wear parts or shieldings which are not subjected to high stresses because these materials exhibit a low strength (ah < 300 MPa) and a low fracture toughness (Xlc < 3 MPa m 1/2 ). Hence, for high densification at reasonable temperatures a hot-pressing treatment that causes particle rearrangement and plastic flow is required. Grain boundary sliding, strain-induced twinning, creep and, at a later stage, bulk diffusion combined with recrystallization were identified as the mechanisms of mass transport (Kuzenkova et al., 1979; Ostapenko et a l , 1979; Brodhag et al., 1983). Densification maps and diffusion diagrams of B-rich boron carbide and C have been established by Beauvy and Angers (1980), and Bouchacourt et al. (1981). Figure 4-35 shows the predominant mechanisms of densification related to the fraction of re-
Phase D: volume diffusion
Phase C: plastic flow
20 feO
10 ft
Phase B: rearrangement of particles
o
1700
1800
1900
2000
2100
2200
Temperature (°C) Figure 4-35. Densification map of boron carbide (Beauvy and Angers, 1980).
sidual porosity. Suitable preconditions are (i) the use of submicron powders, (ii) temperatures in the range 2100-2200 °C, (iii) pressures of 25-40 MPa, (iv) 15-20 min hold, and (v) a vacuum or an argon atmosphere. To resist the high pressures at these temperatures and to provide carbon as a sintering aid, the use of boron nitridecoated, graphite crucibles is favored. In Fig. 4-36, literature data on the obtained fractional densities of pure B4C are related to the particular hot-pressing conditions. It is obvious that both high temperatures and high pressures are required to achieve a density of > 9 5 % . Only formation of sinter necks is obtained at 20 MPa pressure and 2000 °C (Fig. 4-37). However, a strong coarsening has to be taken into account at higher temperatures and average particle sizes of > 100 jam in commercial ceramics are not rare. Similar to pressureless sintering, additives may be used for hot-pressing of boron carbide to reduce temperatures required for grain boundary and bulk diffusion and to retard grain growth. Figure 4-38 shows a typical microstructure of a hot-pressed stoichiometric and B-doped material with strain-induced polysynthetic twinning. Suitable dopants are B (Ekbom and Amundin, 1980; Champagne and Angers, 1979), C (Schwetz and Grellner, 1981), Mg, Al, Si, Ti, V, Cr, Fe, Ni, and Cu (Glasson and Jones, 1969; Janes and Nixdorf, 1966; Stibbs et al., 1973; Ekbom and Amundin, 1980; Telle and Petzow, 1987b). As demonstrated by Telle and Petzow (1988), combined B-Si or B-Si-Ti additions lubricate the grain boundary sliding and prevent coarsening by forming a thin SiC or TiB 2 grain boundary phase (Fig. 4-39) which pins the grain boundary movement and controls the surface diffusion. Compounds used as additives are various glasses, A12O3, sodium silicate with
4.5 Sintering Behavior of Carbide and Boride Ceramics
217
70 601 :E CD \
5040 -
I 30-
CD
• * • o A v o X
99-100 97-98 95-96 90-94 80-89 70-79 60-69 < 59 th. D. O
O
7
V
A
•
«
•
•
•
•
2010 1800
2000
2200
Temperature ( ° C ) Figure 4-36. Density-hot-pressing condition map of pure B4C (literature survey); the continuous line separates the conditions which lead to closed porosity (% th.D. = fraction of theoretical density).
Figure 4-37. Fracture surface of stoichiometric B4C, hot-pressed at 2000 °C; only the formation of sinter necks was initiated.
Mg(NO 3 ) 2 , and Fe 2 O 3 which may reduce the hot-pressing temperature down to 1750 °C (Vasilos and Dutta, 1974). A comparison between isothermal densification of pure B4C and a multiple additive material is shown in Fig. 4-40. MgF 2 , A1F3 (Lange et al., 1980) and ethyl silicate (Furukawa and Kitahira, 1979) are other additives which are active at particle surfaces and grain boundaries. Hot-pressing with
Figure 4-38. Microstructure of hot-pressed, coarsegrained B4C; note the presence of polysynthetic twinning in large grains due to pressing stresses.
218
4 Boride and Carbide Ceramics
Figure 4-39. Thin SiC grain boundary phase between B12(B, C, Si) 3 particles pinning the grain boundary movement and thus controlling the grain growth; transient liquid phase-assisted, hot-pressing of B 4 C~ Si-B powder blends; SEM micrograph.
10
40
100
400
1000
Time [min]
Figure 4-40. Comparison between isothermal densification of pure (•) and multiply-doped (o) B4C (Vasilos and Dutta, 1974).
l-5wt.% of the above-mentioned additives usually requires a temperature of 1750-1900 °C to obtain > 9 5 % density. In most cases, grain size refinement and distributed second phases result in improved mechanical properties such as strength and fracture toughness.
Hot isostatic pressing (HIP) of boron containing ceramic powders creates special difficulties due to the choice of the canning material. In general, containers made from metals or usual glasses cannot be used because of reactions with the sample material. In the presence of metals, boron carbide decomposes forming metal borides plus graphite which embrittles the capsule. In the case of silica glass, boron diffusion from the outer layers of the specimen into the glass strongly changes the viscosity and the glass transformation temperature. Hence the softening of the container and the pressure transfer to the specimen cannot be controlled reliably. Moreover, boron oxide gas may be released from both the capsule and the sample and hence result in blowing of the container. Promising techniques have been developed by Asea Cerama AB, Sweden, and Elektroschmelzwerk Kempten, Germany, using diffusion barriers and a special type of boron oxide glasses (Larker et al., 1988). These methods are also applicable to silicon nitride and silicon carbide ceramics and make the fabrication of complex parts, e.g., injection-molded sand blasting nozzles, in large-scale production feasible. In the case of boron carbide, this treatment was applied to additive-free submicron powder obtained by sedimentation of commercial powder in an aqueous suspension by changing the pH value from 10 for dispersion to 3 for flocculation. The sedimented powder exhibited a particle diameter <^ 3 pm and yielded a final density of 100% after HIP above 1700 °C for 60 min at a hydrostatic pressure of 200 MPa. In Fig. 4-41, a fracture surface is shown which illustrates that no grain growth has occurred during the heat treatment. A three-point bending strength of 714 MPa was reported with a Weibull modulus m of 8.3 (Larker et al., 1988). The increase in
4.5 Sintering Behavior of Carbide and Boride Ceramics
Figure 4-41. Fracture surface of hot isostatically pressed, pure B4C; note that almost no grain growth occurred and that a high density was obtained at 1700°C (sample courtesy of J. Adlerborn, ABB Robertsfors).
strength compared to normal hot-pressed material is almost three-fold. The fracture toughness was, however, not influenced at all since values of Klc = 2.5-3.2 MPa m 1/2 have been measured in all cases by the indentation method. Generally, all presintered or hot-pressed materials with closed porosity (i.e. > 9 5 % density) can be fully densified by a postsintering HIP-treatment (Schwetz et al, 1986). Best results for C-SiC-doped B4C are obtained at 2000 °C and 200 MPa isostatic pressure. 4.5.2 Densification of Silicon Carbide
Densiflcation of silicon carbide is carried out by various techniques leading to different microstructures, mechanical properties, and capabilities of manufacturing large parts which are of particular importance for specific applications. Material which has been densified by pressureless sintering is known as SSiC (sintered silicon carbide), /zot-/?ressed material as HPSiC, hot zsostatically pressed material as HIPSiC or, if the HIP-treatment was one on pre-sintered parts to remove the residual porosity, the material is called HIPSSiC.
219
These materials are usually of high-quality with a homogeneous microstructure, a small amount of residual porosity, and a well-defined phase composition. Parts prepared in this manner have optimum strength and toughness for use as structural ceramics (wear parts, components in engines, heat exchangers, electronic devices, etc.). Low-cost materials used for large parts, e.g., kiln furniture or other refractory applications, are fabricated by recrystallization, known as RSiC, or by infiltration of a porous SiC-C body with liquid Si9 called SiSiC or RBSiC (reaction-bonded SiC). The advantage of the latter processes is that almost no shrinkage occurs on sintering, thus these methods are preferred for the manufacture of large parts that are not subjected to high loads, since their microstructure exhibits a considerable amount of residual porosity, carbon or metallic silicon and an exaggerated grain size. In the following sections, the state of the art in SiC sintering will be treated according to the various techniques. 4.5.2.1 Pressureless Sintering with Additives
Like other covalently bonded compounds, SiC does not sinter without specific additives. The reason for this behavior was attributed to the relatively poor volume diffusion due to the strong unidirectional bonding, as well as to vapor transport mechanisms (evaporation-recondensation) which generate neck-formation between adjacent particles but do not contribute to shrinkage (Popper and Davies, 1961). One precondition for densification by grain boundary or volume diffusion is the use of submicron powder either of the hexagonal a- or the cubic /J-polytype. The
220
4 Boride and Carbide Ceramics
amount of sintering additives is relatively small compared to that required for boron carbide and ranges between 0.2 and 3.0wt.%. Prochazka (1973a, b, 1974a) demonstrated that the simultaneous additon of 0.3 wt.% B and 0.2 wt.% C to fine £-SiC powder yields 95-99% of the theoretical density upon sintering at 2040 °C in a flowing He atmosphere. No shrinkage was only observed with a carbon addition. The absence of any detectable second phase except carbon led to the conclusion that densification had occurred by solid state diffusion. Normally, B substitutes for C, but it may also enter an Si site. A possible defect reaction as proposed by Prochazka (1981) is B
(4-46)
i.e., B enters the sublattice trivalently, acquires an electron to complete its bonding pairs and creates a neutral hole h° and a vacancy V in the other C or Si sublattice, respectively. Another reaction which does not require the formation of a vacancy is B + C -> BSi
(4-47)
Here B occupies an Si site and creates a hole, whereas C enters a C site. According to Shaffer (1969), and Vodakohov and Mokhov (1973), the solid solubility of B in a-6H SiC is limited to 0.2 mol%, which is considered to be the reason for the lower limit of the B additive. Investigations of the self-diffusion of Si and C in doped SiC reveal, however, that the formation of electronic defects is not sufficient to obtain complete densification by volume diffusion. Data on diffusion coefficients in both a- and /?-SiC are presented by Hong et al. (1979), Hon et al. (1980), and Birnie (1986). According to Prochazka (1974 b), another crucial precondition for pore closure is that the grain boundary energy to sur-
face energy ratio should be small. The advantageous effect of combined B and C doping is attributed to an increase in the surface energy of SiC, since oxide layers are removed by C to form SiO gas, CO gas, and secondary SiC, as well as to a decrease in grain boundary energy due to the segregation of B at the grain boundaries. Prochazka's hypothesis is strongly supported by the observation that silica and silicon inhibit sintering of B-doped SiC (Prochazka, 1973 b). More recent studies on the role of B and C in sintering SiC have revealed contradictory results. Microstructural studies with high-resolution techniques have shown that no B is enriched at the grain boundaries (Hamminger et al., 1983 a, b; More et al., 1986; Carter et al., 1988); the contrary was observed by Riihle and Petzow (1981) and Browning et al. (1987) who found B, C, BN, or B4C inclusions at the interfaces. Graphite inclusions of < l - 5 |im within the SiC grains have been reported by Hamminger et al. (1987), intra-SiC inclusions of B12(B, C, Si)3 were identified by More et al. (1986). Since these particular observations on the studied materials have not usually been easily related to the processing techniques nor to the sintering steps, these results may not be used as excluding arguments against the proposed sintering mechanisms. Investigations of the various sintering stages of aSiC by Wroblewska et al. (1990) have revealed that a thin (> 100 nm), uniform layer forms on the SiC particles at 1500°C, which also contains B and O impurities. A rapid migration of B was observed at 1350 °C by Suzuki and Hase (1979). At approximately 1900 °C, SiO2 reacts with C forming secondary SiC particles while the C layer becomes significantly thinner ( « 1 jim) and is almost depleted of B and O. The final, dense material was found to consist of B-enriched SiC and polycrys-
4.5 Sintering Behavior of Carbide and Boride Ceramics
talline C inclusions. Thus the study by Wroblewska et al. (1990) implies a combined deoxidizing and volume-diffusionenhancing sintering mechanism to be active. In addition to the solid state sintering processes in the previous discussion, liquid phase sintering was proposed, in which a B-containing liquid was considered to generate dissolution-reprecipitation mechanisms which would explain the rapid growth of faceted grains (Lange and Gupta, 1976; Bocker and Hausner, 1978; Prochazka, 1981). A recent re-investigation of the B-C-Si system by Telle and Petzow (1987 a) and Telle (1990) proves the existence of ternary B 12 (B, C, Si) 3 -SiCliquid and B 12 (B, C, Si)3-SiB5-liquid equilibria above 1560°C which have to exist if B or, specifically, B4C is present in an amount exceeding the solid solubility in SiC. This generally happens locally at phase boundaries between additive particles and SiC grains. Another explanation for the presence of a liquid phase considers the segregation of Si at the grain boundaries which is due to the recrystallization of stacking faults and point defects, yielding an excess of 2at.% Si (Prochazka, 1989). B can be introduced as B 4 C, BN, BP, A1B4, or SiB 6 . LiBH 4 and C mixtures (decomposing into the elements above 270 °C) or H3BO3 + C blends have been proven not to contribute to the densification to a similar extent since boron is lost by evaporation (BH 3 , B 2 O 3 ). Carbon may suitably be added in the form of carbon black or as an organic compound, preferentially a phenolic resin or a novolak to obtain an optimum distribution, whereas graphite seems to be ineffective due to its poor dispersability. Besides B, aluminum is also an effective sintering aid if combined with C or B, as
221
demonstrated by Billington et al. (1965), Bocker and Hausner (1978), Bocker et al. (1978, 1979), and Schwetz and Lipp (1980). Starting with submicron a-SiC powder and Al additives of <2.0wt.%, densities of > 97 % have been obtained at temperatures between 2050 and 2250 °C. The doping was successfully carried out with metallic Al, A1N, A14C3, A1B2, A1P, and Al 4 SiC 4 . A12O3 and LiAlH 4 were not found to be very efficient due to evaporation of volatile reduction or decomposition products. There is evidence that a-SiC exhibits a solid solubility for Al compounds such as A14C3 and A1N (Cutler et al., 1978; Schwetz and Lipp, 1980) which stabilize the AH polytype. Thus, similar to B, the beneficial effect of Al is the enhancement of volume diffusion. In comparison to the SiC-B-C sinter system, Al additives result in a lower temperature of onset of sintering or of the maximum densification rate (Bocker and Hausner, 1979; Inomata et al., 1980). This was also observed for materials sintered with combined B, Al, and C additions and is mainly attributed to the formation of a liquid phase which significantly triggers a rapid grain growth by active dissolution-reprecipitation mechanisms (Fig. 4-42). This strong coarsening can be suppressed by minimizing the amount of additives to <0.5 wt.% B and <0.3wt.% Al, i.e. beyond the solid solubility in SiC (Stutz et al., 1985, starting with /?-SiC; Tajima and Kingery, 1982 a, b). A more general problem arises from the inhomogeneity of the Al distribution which may result in a local enrichment of the liquid phase. Annealing steps between 1650°C and 1850°C produce a convenient dispersion via the vapor phase; subsequent sintering between 1940 and 2000 °C yields a fine microstructure ( < 2 | i m average grain size) and 98% density (Greil and Stutz, 1987) (Fig. 4-43).
222
4 Boride and Carbide Ceramics
Figure 4-42. SiC ceramic sintered with combined B, Al, and C additions; note that a rapid grain growth was initiated by dissolution-reprecipitation mechanisms (Greil and Stutz, 1987).
Figure 4-43. Annealing of material from Fig. 4-42 between 1940 and 2000 °C yields a fine microstructure (<2um average grain size) and 98% density (Greil and Stutz, 1987).
Extensive studies on the even more complex atmospheric effects have been published by Prochazka et al. (1978). As an example, silicon vapor pressure exceeding the equilibrium pressure over SiC may result in coarsening of pores and thus act as a "poison" for densification (Prochazka, 1981). Due to their high vapor pressures at the sintering temperature, additives such as B and Al may be lost by evaporation. In particular, this is an important effect if small quantities of oxygen in the form of carbon monoxide are present which may
generate Boudouard-type equilibria with BO, SiO, or A12O, resulting in accelerated evaporation. Besides adding Al, B, C, and compounds of these elements to enhance diffusion processes, there have also been many attempts to transfer the fundamental mechanisms of liquid phase sintering of silicon nitride to silicon carbide. Alliegro et al. (1956) have already used A12O3 for hotpressing of SiC. Pressureless liquid phase sintering of SiC with combined A1 2 O 3 Y 2 O 3 additions was first described by Cutler and Jackson (1988) making use of eutectic compositions involving an yttriumaluminum/garnet. Compared to Si 3 N 4 , SiC can be sintered at much higher temperatures with smaller amounts of liquid phase which can be concentrated in triple points and subsequently crystallized as garnet upon annealing (Fig. 4-44). The resulting homogeneous microstructures are more than 99.8 % dense and can be varied over a wide range. Small equiaxed particles of only 1 |im in size are preferred (Fig. 4-45) since they contribute to a high strength of 900 MPa.
Figure 4-44. Liquid phase sintered SiC ceramic, plasma etched; the particles are partially removed whereas the glassy phase at the grain boundaries resists (courtesy of Bocker and Hamminger, Hoechst AG).
4.5 Sintering Behavior of Carbide and Boride Ceramics
9 3 . 4 - + SiC-(B,C) Weibull modulus=5.7 Average strengthr386 63.2 -
/
MPa
3 0 . 8 - *SiC-(AI,Y,0) Weibull modulus=16.0 12.7Average strength=601 MPa/ 4.91.8100.0
+
/
/
|
A
§
/
/ +
' '1 300.0 Fracture stress (MPa)
4.5.2.2 Hot-Pressing, Hot Isostatic Pressing and Shock Wave Consolidation As demonstrated at the GTE Laboratories by Nadeau (1973), pure SiC can only be densified by hot-pressing in a belt press as used for the synthesis of diamonds, if extremely high pressures in the range of 2 GPa and temperatures exceeding 2100 °C are applied (Fig. 4-46). In 1956, Alliegro et al. found that a small amount of sintering additives results in reasonable densification conditions. Starting with 1 \xm average size /?-SiC powder with 0.4 wt.% B additive, a density of >99.4% is obtained at 1950 °C using a pressure of 69 MPa for 30 min (Prochazka, 1973 a). However, this reduction in temperature compared to pressureless sintering does not significantly suppress the grain growth. It is obvious that the influence of grain growth and polytype transformation controlling additives are of much more importance than the hot-pressing conditions. Thus, the preferentially utilized dopants are basically the same as those used for pressureless sintering. Contrary to pressureless sintered materials, silica glasses may be found at grain boundaries since a complete deoxidation of SiO2 contaminants by carbon is not likely to occur because of the rapid
223
i
Figure 4-45. Weibull plot of liquidphase sintered SiC. The homogeneous and fine grained microstructures result in high strength and high reliability (courtesy of Bocker and Hamminger, Hoechst AG).
*/ x/
1 500.0
700.0
closure of degassing channels (Prochazka, 1981). On an industrial scale, hot-pressing is today the most important densification technique for small parts of simple geometry for high-strength materials. Hot isostatic pressing of nonoxide materials requires a special canning method (see B4C) to avoid diffusion between the glass container and the sample, and to provide the optimum glass viscosity at the high temperatures. Larker et al. (1988) have densified as-received SiC powder (1-3 jim average grain size) to 95.6% to 1900 °C using a pressure of 160 MPa for 60 min, whereas
103
100
Figure 4-46. Conditions for the densification of highpurity SiC (Nadeau, 1973; Prochazka, 1981); (a) Bdoped SiC at 2100 °C, (b) pure SiC at 2100 °C, (c) pure SiC at 2300 °C.
224
4 Boride and Carbide Ceramics
they achieved 99.4% for submicron powders. An addition of 1.0 wt.% B resulted in a decrease in the temperature required to 1750 °C (200 MPa for 60 min; 99.0% density). In all cases, the obtained grain sizes are very fine (1-3 jim). Post-HIP of parts sintered to closed porosity is a common procedure for the removal of residual porosity. The treatment is usually carried out at slightly higher temperatures than the sintering, typically between 2050 °C and 2200 °C at 100-200 MPa for 30120 min. The presintered density of 95 % is then improved to >98 %, and results in a considerable increase in the fracture strength (e.g., Watson et al., 1986). The fabrication of 98.6% dense SiC compacts from almost pure, coarse 10 \im powder by explosive-driven flying plates was reported by Akashi et al. (1985). The microstructure exhibits small amounts of molten materials due to the high temperatures generated upon shock wave consolidation. During pressure release, however, extensive cracking occurred. 4.5.2.3 High Pressure Self-Propagating Combustion Synthesis
Parts of simple shape can be prepared by combined reaction and densification under very high pressures by combustion synthesis. Starting with an intimately mixed Si-C powder compact, an igniter, usually a heat source, initiates the exothermic reaction to form SiC. The high, externally applied pressure of up to 3 GPa prevents the composite from exploding. The resulting material reported by Yamada et al. (1985) was basically /?-SiC of 5 \im average grain size and had 96.6% of theoretical density. Starting from the ignition area, the reaction runs across the powder compact. Depending upon the initial grain size of the powders the reaction may be incomplete.
Since the heat released upon formation of SiC is not as high as for Ti compounds, the reacted fraction is always less than 100%. Thus this method of SiC densification will probably not become of technical importance. 4.5.2.4 Microstructural Development and the /?-to-a Transformation in Sintered Silicon Carbide
The microstructure observed in sintered SiC reflects the specific factors which control its development, such as high grain boundary energy, grain boundary anisotropy, planar faulting and abnormal grain growth, which is usually linked to poly type transformations. A typical microstructure of B-doped /?SiC exhibits elongated grains of several micrometers in size that are faulted and possess irregular grain boundaries. Pronounced curvatures are characteristic of /?SiC particles. Above 2000 °C, jS-SiC partially transforms into a-polytypes, most frequently into 6H, 4H, and 15 R structures. Upon this transformation, an exaggerated grain growth occurs yielding tabular particles of several hundreds of micrometers in diameter. This transformation can be triggered by the addition of small amounts of aphase to the initial /?-powder. According to Shinozaki and Kinsman (1978) and Heuer et al. (1978), the a-plates grow coherently inside the /?-SiC particles which extend ahead of the growing a-crystal. Due to the grain boundary anisotropy, a lateral growth in the <10T0> direction is favored, and only in the later stages of sintering do the a-plates grow axially in the [0001] direction consuming the /Mayer from the inside (Mitchell et al., 1978). The jS-to-a transformation starts at about 2000 °C. Both growth rate and nucleation rate ac-
4.5 Sintering Behavior of Carbide and Boride Ceramics
celerate significantly above 2100 °C (Fig. 4-47). The growth is finished at 2150°C, then another grain morphology governs the microstructure which is typically Bdoped j8-SiC sintered at above 2200 °C, large feather-shaped particles appear due to the enhanced /?-to-a transformation (Fig. 4-48). The feathers consist of stackings of several a-polytypes in the (1120) plane, most commonly of 6H and AH, and 15 R. Particular branches of the feathers form penetration twins with (11015) being the plane and [151502] being the twinning direction for 6 if, (1106) and [3301] for AH, and (Tl 038) and [191901] for 15 R (Lancin, 1984; Lancin et al., 1987). Cahn (1954) emphasized that the twinning is due to the release of mechanical stresses upon polytype transformation. These feather-like aggregates grow to up to millimeter size in the direction of their apices. Johnson and Prochazka (1977), Suzuki and Hase (1979), and Greil and Stutz (1987) established that small amounts of Al additives promote this particular grain morphology. In contrast, combined Al and C additions result in a homogeneous microstructure of fine (~5 Jim), elongated particles of preferred 3C and AH polytypes at 2100°C (Stutz, 1983). Systematic polytype studies of undoped, B-C doped and A l - B - C doped /?-SiC have been carried out by Williams et al. (1985) and Shinozaki et al. (1985). They proved that Al mostly influences the /?->a transformation. 15 R and 4 H are the initial phases formed above 1850°C, with 6H appearing above 1950 °C. Both 15 R and 6H are transitory, whereas 4 H is the dominant phase above 2100 °C (Fig. 4-49). In sintered a-SiC, the particle morphology is governed by the B/C ratio (Bocker and Hausner, 1979). At 2060 °C, a B/C ratio of 0.125 yields a fine, uniform microstructure of equiaxed particles, whereas B/C = 0.33 results in faceted platelets of
225
Figure 4-47. Large, elongated, lath-like a-SiC particles in pressureless sintered material grown at 2100 °C at the expense of /?-SiC.
Figure 4-48. Typical microstructure of B-doped /?SiC sintered at above 2200 °C; note the large, feathershaped particles due to the enhanced /?-to-a transformation (courtesy of D. Peuckert).
rather uniform size. An increased ratio of B/C = 0.8 promotes the rapid growth of very large plates of several hundred microns in size. Sintering of B-doped a-SiC above 2100 °C induces abnormal grain growth of the 6H polytype stabilized by B. A growth rate of 3 mm/h was reported by Prochazka (1974 b) causing entrapped porosity inclusions of silicides and unreacted boron carbide (Fig. 4-50). Above 2200 °C, a conversion of 6H to 4H was
226
4 Boride and Carbide Ceramics
100
o
1000
A
-
Figure 4-49. /?-to-a transformation rate of Al-B-C-doped SiC after Williams et al. (1985) and Shinozaki et al. (1985). Both 15 R and 6H are transitory, whereas 4H is the dominant phase above 2100 °C.
o
1200 U00 1600 1800 2000 Sintering temperature (°C)
reported by Williams et al. (1984). In case of Al addition to a-SiC the rapid grain growth is suppressed even at temperatures as high as 2300 °C. The uniform growth of
2200
faceted crystals of several micrometers is attributed to the preferred formation of the 4H poly type, which is stabilized by Al (Knippenberg and Verspui, 1965). 4.5.2.5 Recrystallized and Si-Infiltrated Silicon Carbide
Figure 4-50. Transmission optical micrograph showing entrapped pore (center) and opaque inclusions of unreacted boron carbide in sintered SiC; note the enrichment of inclusions at the surface of the pore and the depletion in the concentric layer.
The necessity for the fabrication of very large parts (up to meter size) for high-temperature application as refractory materials requires procedures which consolidate powders almost without any shrinkage and with very little residual stresses after cooling from the fabrication temperature. Materials used for kiln furniture, heating elements, recuperators or combustion nozzles must exhibit excellent thermal shock resistance and high temperature conductivity rather than high strength, high toughness and high hardness. Industrially
4.5 Sintering Behavior of Carbide and Boride Ceramics
applied manufacturing processes for these usually not completely dense parts use vapor phase assisted sintering of powder mixtures, wrongly called "recrystallization". On the other hand, Si infiltration of porous SiC-C compacts may yield high density products with improved oxidation resistance. Thus this method is used to fabricate bearings, valve guides or parts for combustion technology. Recrystallized SiC (RSiC) is prepared by pressureless sintering of powder mixtures which exhibit a distinct bimodal particle size distribution (Fitzgerald, 1899; Kriegesmann, 1990). Since surface diffusion and evaporation-recondensation reactions are the favored mechanisms of mass transport at high temperatures rather than grain boundary or volume diffusion, the smaller-sized particle population evaporates and is deposited again preferentially at the neck-near surfaces of the larger SiC particles. This reaction is thought to be triggered by the oxygen present in the SiO2 which may generate a local Boudouard equilibrium 2SiO2
2SiOg
SiC + SiO gas
2Sigas + CO
(4-48) (4-49)
These reactions resemble the processes involved in the preparation of SiC by the Acheson method (see Sec. 4.4.1.1). Moreover, the increasing partial pressure of Si over SiC at high temperatures may also contribute to the vapor phase reaction. The driving force for the neck growth of the large particles upon the dissolution of the smaller ones is, (i) the decrease in the total specific surface area, and (ii) the difference in vapor pressure between concave (negative) and convex (positive) curvatures. Since grain boundary or volume diffusion are not active, particle reorientation or a decrease in the next-neighbor dis-
227
tances are not initiated. This means that consolidation is achieved without shrinkage. Since only neck growth but no nucleation of new crystallites occurs the term "recrystallization" is not applicable in the scientific sense but it is still generally used. An important technical precondition for the fabrication of parts by "reerystallization" is a high density for the starting powder compact. As the density does not increase upon sintering, the initial green body microstructure determines the final properties of the product. Thus, the particles of the larger grain size distribution should touch each of their next-neighbors, whereas the smaller particles should just fill the interspacings; similar to a closepacking structure with filled octahedral and tetrahedral sites. Since compacting-assisting waxes must not be used because of the residual graphite content after dewaxing, slip-casting is the preferred molding method, rather than isostatic compaction or extrusion. After sintering typically at 2100-2300 °C, the materials possess very clean grain boundaries since any oxides or metallic impurities have evaporated. This results in an increased thermal conductivity, whereas the residual porosity of 2030% guarantees a suitable resistance against thermal shock. The product is, however, sensitive to oxidation because of its comparatively large surface area. Silicon-infiltrated silicon carbide (SiSiC), also known as reaction-bonded SiC (RBSiC) or REFEL-SiC, is prepared from precompacted a-SiC and C powder blends where graphite, lamp black, polyphenylacetylene, polysaccharides, epoxy or phenolic resins or cracking products of other waxes may be used as carbon sources (e.g., Kennedy and Shannon, 1973). Since organic binders provide homogeneously distributed carbon, molding of SiSiC parts is preferentially performed by extrusion, in-
228
4 Boride and Carbide Ceramics
Figure 4-51. Microstructure of Si-infiltrated SiC; light areas: elemental silicon in pores and particle interspacings (courtesy of V. Carle, MPI, Stuttgart).
jection molding or wax-assisted cold pressing. Slip-casting is applied to primary powders which have been coated by resins. The infiltration occurs either by Si liquid provided from an outside source which is sucked into the porous body due to capillary forces at above 1450 °C, or by a vapor phase consisting of elemental Si, SiH4 or another volatile Si species. Silicon reacts exothermically with C according to Si + C -* jS-SiC
ly reduces the strength of the component and may also cause chemical damage to the furnace walls. Thus optimized graphite of a favored porosity ranging between 0.5 and 2.0 jim in size has been developed which may be infiltrated and converted to SiC completely with an amount of residual Si of less than 1 vol.% (Fitzer and Gadow, 1986). Some difficulties in process control arise from the exothermic reaction. Since the wetting angle of liquid Si on a pyrolytic C surface is close to zero but depends upon the environmental Si and SiO vapor pressure, the temperature range of the infiltration is limited to between 1412 and 1700 °C and has to be carefully controlled (Whalen and Anderson, 1975; Kriegesmann, 1991). Growth of an SiC film on the carbon particles prior to impregnation has to be avoided since the wetting angle of Si on SiC is only 30-40°. The Si viscosity at 1500°C was calculated as 0.45 Pa s which implies a rapid infiltration (Turovskii and Ivanova, 1974). Contact between the porous body and the liquid reservoir is obtained by a graphite fiber wick to allow a
(4-50)
Since the formation of secondary /?-SiC is accompanied by a 1.8 to 2.5 fold increase in volume, the initial pore volume of the powder compact must exceed the volume of the reaction product in order to prevent early closure of the infiltration channels. This is even more important if vapor phase reactions are employed. After the reaction has come to an end residual Si liquid fills the pores, and in an ideal case a fully dense body with 8-15 vol.% of unreacted Si is obtained (Fig. 4-51). Residual elemental Si, however, limits the application temperature to 1410 °C (i.e. to the melting point of Si) since liquid or vaporized Si drastical-
Figure 4-52. Precursor-infiltrated carbon fiber woven, pyrolyzed and subsequently infiltrated by liquid silicon; fracture surface (courtesy of Kochendorfer, DLR Stuttgart); note the brick-like packing of fiber bundles interconnected by in situ reacted SiC layers.
4.5 Sintering Behavior of Carbide and Boride Ceramics
slow continuous flux of Si. Other methods use Si powder that is put on top of the preform and penetrates the pores after melting. As well as powder compacts, C or SiC filaments, wovens, SiC-fiber-reinforced polycrystalline SiC or C or other composites thereof can also be successfully bonded by either liquid phase or vapor phase inpregnation (Hillig and Mehan, 1974,1975). Fitzer and Gadov (1986) have studied the conversion of an SiC/C fiberreinforced, porous carbon matrix into SiC and present an excellent overview of the physics and the thermodynamics of infiltration, as well as of the mechanical properties of various containing composites (Fitzer et al., 1987). Depending upon the geometry, crystallinity, surface quality and chemical composition of both SiC or D fibers, the infiltration and reaction kinetics may change drastically. Si-containing organo-metallic precursors may also be used as the reactive or deposited liquid or vapor phase (e.g., Naslain et al., 1980). Thus large parts for lightweight, highstrength application even under extreme temperatures can be fabricated, e.g., for aerospace or combustion technology (Fig. 4-52).
229
initiate grain boundary and volume diffusion, and thus to obtain more than 95 % of the theoretical density. One disadvantage is that the borides undergo a similar abnormal grain growth at high temperatures to B4C or SiC. Furthermore, at lower temperatures evaporation-recondensation reactions are generated which induce a growth of faceted crystals. Thus it is nearly impossible to achieve completely dense bodies by pressureless sintering, as no shape accommodation occurs without external pressure and the large pores tend to coarsen. 4.5.3.1 Pressureless Sintering According to Samsonov and Koval'chenko (1961), three stages have been distinguished in the sintering TiB 2 ; slight densification by neck-formation at temperatures up to 1900 °C (Fig. 4-53), no
4.5.3 Densification of Transition Metal Borides The densification of single phase and pure ceramics of transition metal diborides is complicated by two characteristics of these compounds, the high melting point and the comparatively high vapor pressure of the constituents. As a rule, sintering temperatures exceeding 70 % of the absolute melting temperature have to be applied. For instance, titanium diboride, TiB2 (r m = 3250°C), requires firing temperatures of the order of 1800-2300 °C to
Figure 4-53. SEM micrographs showing neck formation in pressureless sintered TiB2 at 1900 °C. a) fracture surface, b) polished section.
230
4 Boride and Carbide Ceramics
shrinkage between 1900 °C and 2100 °C, and further densification by volume diffusion and plastic flow, accompanied by exaggerated grain growth. This behavior was attributed by Coble and Hobbs (1973) and Kislyi and Zaverukha (1970) to the competing mechanisms of evaporation-recondensation and volume diffusion exhibiting the same rate of mass transport, whereas gas-transport reactions are favored due to the lower activation energy. The powder size-dependent sintering behavior of TiB 2 was studied by Kislyi et al. (1972). Starting with high-purity submicron size powder, synthesized from TiCl4 and BC13 in hydrogen in a plasma-arc heater, Baumgartner and Steiger (1984) achieved densities of 98.4-99.4% at 2000-2100°C combined with a comparatively fine microstructure (average grain size 1-18 jim) due to TiC and TiO inclusions. Further heating, or a prolonged holding time generate exaggerated grain growth to 80 |im, whereas the density does not improve. This is attributed to entrapped porosity which can only be removed by volume diffusion. In contradiction to reports of the other authors, no significant weight loss was observed even after several hours hold at 2250 °C, which could be related to active evaporation reactions. Since the small grain size of 1 |im could be retained up to 2000 °C, the porosity was preferentially removed by grain boundary diffusion. Thus, contrary to carbothermically-produced TiB2 powder, high densities have been obtained below the critical temperature promoting rapid grain growth. This implies that both the initial particle size and the presence of impurities significantly influence the densification kinetics. Baik and Becher (1987) have studied the effect of oxygen contamination of submicron TiB2 powders and concluded that in the case of hot-pressing between 1400 and 1700°C, oxygen pro-
motes grain coarsening by enhanced evaporation-recondensation of B 2 O 3 . Upon pressureless sintering between 1700 and 2050 °C oxygen remains primarily as titanium oxides and suboxides which increase the surface diffusivity and thus the pore and particle coarsening rather than the densification. A maximum total amount of oxygen of less than 0.5 wt.% in the powder or reducing additives such as carbon is recommended. Sintering is usually carried out under vacuum in a resistance furnace with a graphite, tantalum or tungsten resistor or in a high-frequency furnace with a graphite susceptor. Ar or H 2 gas atmospheres can also be used. If carbon crucibles are used, boron nitride diffusion barriers have to be inserted to prevent eutectic melting of the borides and carbon in the temperature range of 2200-2500 °C. The considerable losses of volatile boron or boride species may be reduced by powder-bed sintering (Pastor, 1977). 4.5.3.2 Hot Pressing and Activated Sintering Densities above 95 % have been achieved by axial hot-pressing at pressures exceeding 20 MPa and temperatures above 1800°C. The microstructures consist typically of particles of >20 jim in size. Another problem is related to the hexagonal layered structure of the AlB2-type borides. Because of the strong anisotropic behavior of the physical properties, especially of the coefficients of thermal expansion, the coarsening can be very detrimental to the mechanical properties, by producing spontaneous microcracking and residual strains. Pressureless sintering and hot-pressing of transition metal borides can be activated either physically by starting from submicron powders or by extensive milling, or chemically by doping with small additions
4.5 Sintering Behavior of Carbide and Boride Ceramics
(0.3-3 wt.%) of transition metals such as Fe, Ni, Co, Cr, Pt, or their halides. The mechanisms of sinter activation by doping are not yet readily understood but an increase of volume diffusion and a retardation of evaporation seems to be likely. Crystallographic studies on Co-, Nb-, Cr-, and Re-doped ZrB 2 by Cech et al. (1965) indicate that the metals substitute for Zr in the metal sublattice, which is also confirmed for Mo and W (Rasskazov, 1970). Other borides such as VB 2 , NbB 2 , TaB2 or W 2 B 5 and Mo 2 B 5 could not be satisfactorily densified by pressureless sintering. For an extensive survey on powder molding, compaction and sintering of various transition metal borides, containing detailed descriptions of additives, the reader is referred to Pastor (1977). Reaction sintering starting from chemically incompatible compounds may also lead to high densities, especially if combined with hot-pressing, since that synthesis is strongly exothermic and provides high internal temperatures (Rise et al., 1986). The so-called self-propagating, hightemperature combustion synthesis was used for TiB 2 , ZrB 2 , NbB 2? and TaB2 starting from the elements, B4C mixtures with metallic Ti, Zr, Cr, or Nb (Krylov et al., 1976), and Ti-B-TiB 2 blends (Munir, 1988; McCauley et al., 1986). In the case of other reactants, e.g., blends of metal oxides and boron carbide or Al-TiO 2 -B 2 O 3 mixtures (Richardson et al., 1986), the formation of gaseous by-products often prevents complete densification but may result in bodies of well-defined porosity. The kinetics of the combustion synthesis of TiB2 from the elements have been studied by Holt et al. (1985). Ouabdesselam and Munir (1987) investigated the sinterability of directly synthesized TiB2 powder but could not find any significant difference to carbothermically produced powders.
231
4.5.3.3 Cemented Borides In order to achieve lower sintering temperatures, many metallic additives such as Ni, Co, and Cr, or borides of these elements have been used at higher concentrations to allow liquid phase sintering. These transition metals react with e.g. TiB 2 forming various metal borides with a low melting point (approx. 900-1100 °C) and a suitable wetting behavior. In the case of Ni-bonded TiB 2 , a ternary r-phase with the composition Ni 21 Ti 2 B 6 forms by the dissolution of TiB 2 . At 800 °C, the i-phase is in equilibrium with Ni, Ni 3 B, Ni 3 Ti, and TiB 2 , as shown in the isothermal section in Fig. 4-54 (Schobel and Stadelmaier, 1965). A pseudobinary eutectic with Ni exists at 1077 + 5 °C, whereas the relationships in the TiB2-rich corner are more complicated. An isopleth (Fig. 4-55) across the line Ni-TiB 2 reveals a solid state equilibrium below 980 °C involving TiB 2 , T, and Ni3B (Lugscheider et al., 1982). A liquid phase forms above that temperature because of the decomposition of T. Above 1100°C, Ni 3 B also decomposes completely in the presence of TiB 2 , which accelerates the liquid phase sintering. During sintering or hot-pressing, the i-phase is generally not obtained. The formation of T may be suppressed either by the presence of TiO or TiO 2 (Angelini et al., 1986), or for kinetic reasons. Hence the residual matrix phase consists mainly of Ti-containing Ni 3 B solid solution (Sklad and Yust, 1981; Telle and Petzow, 1988; Angelini et al., 1986). Since other Ni-borides such as Ni 2 B and Ni 3 B 4 and even metallic Ni are found after hot-pressing at 1600°C (Telle and Petzow, 1987 b), equilibrium conditions are obviously not easy to obtain. Typical metal contents required for a successful liquid phase hot-pressing of TiB2 are 5-25 wt.% (i.e. 2-12 at.%) Ni or
232
4 Boride and Carbide Ceramics B 10
90
20 T= Ni21Ti2B6 TiB
Figure 4-54. Isothermal section of the Ti-B-Ni system at 800°C in at.% (Schobel and Stadelmaier, 1965). Ni
90 at.% Ni
2800 —
Isopleth TiB 2 -r-Ni
----^ \
o 2400-
x
ure
o
o
2000 — -
CD Q_
1 600 —
L + TiB 2 \
F CD I—
r=Ni 21 Ti 2 B 6
L + TiB2+Ni3B
1 200 —
..... 800-
^
TiB2+Ni3B .
TiB 9
\
,
.
I . 20
'
i
•
|
60
r I
Figure 4-55. Isopleth across the Ni-TiB 2 line in at.% (Lugscheider et al, 1982).
r+Ni
i
80
i
|
i
Ni
at.% Ni
Co. In order to avoid reactions consuming TiB 2 , the borides of Ni or Co have also been used. By this method, the sintering temperatures have been decreased from 2100 °C to 1400 °C (Murata et al., 1967; Takatsu and Ishimatsu, 1981; Pastor, 1977; Watanabe 1977, 1980). The liquid phase intensifies the mass transport but causes an accelerated grain growth. The
microstructures of composites prepared by liquid phase sintering are similar to those of hard metals. The TiB 2 particles form a rigid skeleton of faceted crystals whereas the binder, e.g., Ni 3 B, Ni 2 B, Ni 3 B 4 , or comparable compounds of Fe, Cr, or Co, is the matrix phase. The TiB2 grain size usually exceeds 20 jim (Fig. 4-56). Depending upon the wetting behavior, which
233
4.5 Sintering Behavior of Carbide and Boride Ceramics
is influenced by the surface oxidation of the hard material phase, round pores may accumulate at particle/matrix interfaces or close to triple junctions which have not been completely infiltrated by the liquid phase. Moreover, the evaporation of Fe-, Co-, or Ni-borides may cause entrapped gas pores. Hence, hot-pressing is still required for a homogeneous distribution of the liquid phase, particle rearrangement, and complete removal of the residual porosity. In contrast to hard metals, the matrix phase is very brittle, e.g., the Klc of Ni 3 B equals 1.4-1.9 MPa m 1/2 (Finch et al., 1984), and hence does not improve the mechanical properties. The fabrication of TiB2-based cermets resembling the well-known WC-Co hard metal by combining the high toughness and ductility of a metallic binder with the hardness of the boride phase was recently achieved by using Fe instead of Ni and Co (Yuriditsky, 1990; Sigl and Schwetz, 1991a; Ghetta et al. 1992; Jiingling et al., 1991 a; Sigl and Jiingling, 1992). Although there are still some controversies concerning the phase diagram (Shurin and Panarin, 1974; Smid and Kny, 1988; Ottavi et al., 1992 a, b), TiB2 is in an eutectic equilibrium with liquid Fe at 1340 °C (eutectic concentration 6.3 mol% TiB2) which enables liquid phase sintering. Discrepancies exist for the phase equilibria at lower temperatures because of the problem of whether the observed, undesired Fe 2 B is an equilibrium phase or results from impurities in the starting materials used (Figs. 4-57 and 4-58). It is, however, obvious that oxygen and carbon contaminants introduced by the manufacturing processes of the starting powders significantly affect the wetting behavior of the liquid Fe (Fig. 4-59). Both constituents do indeed cause dramatic changes in the phase equilibria and sintering kinetics, and thus have to be compen-
\
/
Figure 4-56. Coarse TiB2 ceramic, hot-pressed without additives at 2000 °C.
Fe
10 20 Fe2Ti
FeTi at.% Ti
70
80 90
Ti
Figure 4-57. Isothermal section of the ternary F e Ti-B system at 1000 °C (Federov and Kuzma, 1967); shaded area: quasi-binary TiB 2 -Fe equilibrium; any losses in titanium result in the formation of brittle Fe2B and FeB phases.
Figure 4-58. Isopleth of the TiB 2 -Fe phase diagram (Shurin and Panarin, 1974).
234
4 Boride and Carbide Ceramics
8070 -\
_CD60 4
en c o 1
Figure 4-59. Oxygen contamination significantly affects the wetting behavior of the Fe liquid on sintered TiB2 at 1300°C(Ghetta et al., 1992); oxygen content in mass.%: curve 1: 0.68, curve 2: 0.33, curve 3: 0.26, curve 4: CVD substrate.
* *
O
**
30 :
^ *
20 500
1000 Time (s)
1500
sated for by the addition of metallic Ti, Mo or Nd to form TiC, or Ti 2 O 3 and Nd 2 O 3 , respectively, to act as a carbon or oxygen trap. Since the eutectic concentration in the quasi-binary TiB 2 -Fe system with 14 vol.% TiB 2 is considerably closer to the metal corner than in the similar WC-Co system (32 vol.% WC), a much smaller amount of liquid phase is generated upon sintering which makes densification more difficult. A simple increase in temperature cannot satisfactorily balance the lack of liquid because it is accompanied by accelerated coarsening of TiB 2 due to Ostwald ripening (Sigl and Schwetz, 1991a). The volume fraction of binder phase thus ranges between 10 and 30%. A typical microstructure is very similar to that of WC-Co hard metals. Euhedral TiB 2 particles are embedded in a continuous Fe matrix. The densification mechanisms are typically dissolution and reprecipitation as well as coalescence, i.e., rearrangement and intergrowth of particles with common faces of the same orientation. The latter mechanism is active if the volume fraction of liquid exceeds 30 % but may result in the
2000
growth of elongated platelets. The residual porosity after pressureless sintering between 1500°C and 1800 °C depends upon the initial liquid phase composition. At 1500 °C, 88 % of the theoretical density has been obtained for the TiB 2 -Fe system (99% at 1800°C), whereas at 1450 °C a Ti addition results in 98 % and combined Ti-Nb additives result in 96.7%. Hotpressing and hot isostatic pressing yield densities > 98 % at a lower binder content. Cemented borides with a metallic matrix have also been fabricated from the ternary transition metal borides of T-, cp- and cotypes since these composites can easily be liquid phase sintered with metallic melts. The T-phase with a general composition of M 2 1 M 2 B 6 has been observed in ternary systems where MJ = Fe, Ni, or Co and M n = Zr, Hf, Nb, Ta, or W, with M1 as the liquid phase (Schobel and Stadelmaier, 1965; Lugscheider et al., 1980, 1982). T-phase-containing cermets are successfully used for the production of wear and corrosion resistant coatings by plasma spraying, flame spraying and reactive welding (Lugscheider and Eschnauer,
235
4.6 Microstructural Reinforcement of Boride and Carbide Ceramics
1987). The stoichiometries of the cp- and co-phases are IV^M11!* and M I 2 M II B 2 , respectively, where M1 represents Cr, Mo, Ta, or W and M n holds for Fe, Ni, or Co and solid solutions thereof. As an example, an isothermal section of the B-Co-Mo system is shown in Fig. 4-60 in which both the T- and the (^-phases are linked with Co as the binder (Haschke et al., 1966). However, in systems with Fe replacing Co, a cp-phase does not exist. Hence co is in equilibrium with liquid metal and is thus likely to form a cermet material with Fe (Fig. 461). Phase compositions situated in the pseudo-binary equilibria with a metal can easily be pressureless liquid phase sintered at temperatures between 1500°C and 1700 °C. Wear-resistant parts have been developed from Mo 2 FeB 2 -Fe cermets with Ni or Cr additives (Takagi et al., 1984, 1987 a, b).
10 20
Co
10
20 M o C o 3
Z,0Mo6Co7 60 at.% Mo
70
80
90
Mo
Figure 4-60. Isothermal section of the B-Co Mo system at 1000°C in at.%; formation of liquid phase in the vicinity of T indicated by "liq." (Haschke et al., 1966).
4,6 Microstructural Reinforcement of Boride and Carbide Ceramics Most of the strengthening and toughening concepts which have been derived from considerations of fracture mechanics and successfully applied to oxide and nitride ceramics have also been shown to be effective for boride- and carbide-based materials. The first steps for the improvement of the mechanical propertiers of a ceramic should always be
Fe
10
20
30
40 M ° 6 i = e 7 60 at.% Mo
70
80
90
Mo
Figure 4-61. Isothermal section of the B-Fe-Mo system at 1000°C in at.% (Haschke et al., 1966).
- sintering to densities > 9 8 % , - avoiding flaws and microstructural inhomogeneities such as large pores, inclusions, agglomerates, abnormally grown particles etc., - reducing grain growth, and - devitrification of glassy grain boundary phases.
In addition, strengthening and toughening strategies such as - metal matrix reinforcement, - grain size refinement using sintering additives, - transformation toughening,
236
4 Boride and Carbide Ceramics
- crack impediment, crack deflection or crack branching, and - crack bridging and flank friction have been studied intensively. In contrast to oxide ceramics, the applicability of these mechanisms for boride and carbide materials is much more limited because of chemical complications. In the following sections particular materials combinations are discussed in detail with respect to the preparation techniques and the improvement obtained in the mechanical properties. Special attention is given to the micro structural features which make the desired toughening and strengthening mechanisms operational. 4.6.1 Metal Matrix Reinforcement The fabrication of metal matrix cermets with boron carbide as a dispersed phase is very limited under equilibrium conditions since B4C reacts with all metals, except Ag, Cu, Sn, and Zn, forming metal borides and graphite or metal carbides (e.g., Hamjian and Lidman, 1952). In systems with sluggish reaction kinetics, however, complex low-temperature materials with interesting mechanical properties have been investigated. A development from the Ukraine makes use of a Ti-containing bronze as a binder phase in which the reaction of Ti with B4C to give TiB 2 is employed for active brazing and improvement of the wetting behavior. The use of pure Cu, Sn, or Zn, or alloys thereof for the infiltration of B4C power compacts usually fails since the wetting behavior is rather poor (wetting angle > 90°), but this can be improved by adding Cr or other metals which may react with the B4C when approaching equilibrium conditions. Other metal matrix composites with B4C-particulates have been obtained using
aluminum because of slow reaction kinetics. The process is based on an infiltration of liquid Al into a porous body of B4C at temperatures between 700 °C and 1200 °C. Since Al melts at 600 °C and exhibits a significant vapor pressure at only slightly higher temperatures, the equilibrium between 1000 and 1880°C at which liquid Al is stable with an Al-saturated, B12(B, C, Al)3 solid solution cannot readily be utilized for liquid phase sintering with small volume fractions of liquid. A shown by Halverson et al. (1989), it is more effective to infiltrate compacted or presintered, porous B4C bodies with liquid Al. The resulting material is a metal-reinforced, B4C cermet rather than a liquid-phase sintered B4C ceramic. The wetting behavior is strongly influenced by oxidation layers formed on the surface of the B4C particles (Halverson et al., 1985), but can be improved by superheating the melt. Between the melting point of Al and approximately 1000°C, wetting angles of 100-150° are observed which decrease to reasonable values with prolonged soaking for thousands of hours (Halverson et al., 1989). Hence, in that temperature range, only hot-pressing or hot isostatic pressing result in high-density cermets. Above 1000-1200 °C, a suitable wetting behavior is obtained within minutes of annealing. Due to capillary forces and phase reactions both densification and adhesion of the metal-ceramic interface are excellent. During infiltration, reactions of Al with B4C occur. Below 1200 °C, A14BC, A1B2, A1B12, and A1B12C2 are formed within tens of hours whereas above 1200 °C the generation of A14C3, A1B12, and A1B24C4 is more favored (Halverson et al., 1989). If the composite is prepared by fast heating, infiltration and rapid cooling, most of the aluminum matrix is retained unreacted. The matrix can then be hardened by a subse-
4.6 Microstructural Reinforcement of Boride and Carbide Ceramics
quent heat treatment at 800 °C for 20 hours due to the precipitation of aluminum carbides and borides. Since the mechanical properties are determined by the Al matrix, a Klc of 5-16 MPa m 1/2 and a flexural strength of 200-680 MPa can be obtained depending on the quality and volume fraction of the metallic binder. The Vickers microhardness of 15.70 GPa for a 31 vol.% Al composite is improved by annealing to 19.40 GPa. Similar metal matrix composites with B4C, SiC, and TiB2 as fillers have been fabricated by the so-called Lanxide- or Dimox-process (direct metal oxidation) where an Al- or Ti-based liquid mixed with ceramic particles - preferably of whisker or platelet shape - is slowly converted in air, oxygen or nitrogen to alumina or titanum nitride, respectively (Newkirk et al., 1986; Antolin and Nagelberg, 1992; Nagelberg et al., 1992). This self-propagating reaction yields columnar crystals of the oxide or nitride phase, with B4C, SiC, or TiB2 inclusions and residual metal-filled channels which contribute significantly to the strength and toughness. SiC-Al 2 O 3 composites have an excellent fracture toughness of 8-15 MPa m 1/2 and a flexural strength of 500-800 MPa. They have also been demonstrated to be highly resistant against erosive wear (Weinstein, 1989). Another approach to fabricate metalmatrix-based boride and carbide composites according to the Lanxide process starts with reactive blends of B4C and Ti or Zr metal. Upon conversion to TiB 2 or ZrB 2 , respectively, a strong heat release is observed which can easily lead to partial melting of the composites. Depending upon the starting composition, residual metallic Ti or Zr, or B4C may be found after reaction. Interesting microstructures can also be obtained if TiC or ZrC are added as fillers (Johnson et al., 1991).
237
An excellent literature survey on SiCparticulate reinforced, metal matrix composites is given by Ibrahim et al. (1991) with special emphasis on the processing and mechanical behavior of Al-based alloys with SiC contents of less than 40 vol.%. According to the thermodynamics of the SiC-Al system (Lee et al., 1988), SiC reacts with Al below 1820°C 4Al + 3SiC ->Al 4 C 3
(4-51)
4Al + 4SiC -> Al 4 SiC 4 + 3Si
(4-52)
These reactions are kinetically enhanced above the ternary eutectic at 580 °C where Al is in the liquid state. Above 1820°C an Si and C rich Al-melt is in equilibrium with SiC but this high temperature is certainly not suitable for the fabrication of composites because of the high evaporation rate of Al. The formation of interfacial A14C3 reaction layers has to be taken into account during low-temperature wetting and infiltration; these give good adhesion but may also increase the risk of interfacial cracks and voids. Accordingly, a variety of manufacturing processes have been developed such as liquid metal-ceramic particulate mixing, e.g., SiC powder injection into the melt or several stirring procedures, liquid metal infiltration of powder or fibre preforms, rheocasting of particles dispersed in metallic melts, formation of blended pellets by atomization of a metal melt together with injected SiC particles (Osprey process) or solid state sintering (Ibrahim et al., 1991). Transition metals such as Co and Ni are useful for liquid phase sintering of TiB2type borides causing Ostwald ripening, but they react chemically to form M^B^-type or more complex ternary phases which are very brittle. No metal-reinforced composites can thus be produced except where reactions can be at least partially avoided
238
4 Boride and Carbide Ceramics
by fast heating during hot-pressing. In contrast, Co- and Ni-based alloys can be successfully improved for wear resistance by the incorporation of TiB 2 and CrB 2 particles if reaction layers of lower hardness can be tolerated. Cemented borides with a metallic matrix have recently been developed using the TiB 2 -Fe system (Yuriditsky, 1990; Sigl and Schwetz, 1991a, b; Ottavi et al., 1992a,b; Ghetta et al., 1992; Jungling et al., 1991 b). Although there are still some uncertainties on the phase diagram which the synthesis of pure two-phase cermets is based upon (Fig. 4-58), the authors agree that the presence of oxygen and carbon impurities introduced by carbothermic synthesis of the TiB 2 starting powder is detrimental to the wetting behavior and responsible for the presence of the embrittling but hardening Fe2B phase which controls the sintering behavior and thus the properties, see also Sec. 4.5.3.2. The characteristic mechanical property compared to that of WC-based hard metals is the significantly higher hardness with HV10 ranging from 1500 to
1800 GPa at 16-20 vol. % binder and 2000-2300 GPa at 6vol.% binder, while the bending strength of 550-900 MPa and the fracture toughness of 6-10 MPa m 1/2 are lower than for commercial hard metals with an intermediate Co content (Yuriditsky, 1990; Sigl and Schwetz, 1991). Fig. 4-62 shows a comparison between the hardness/toughness relationship of TiB 2 -Fe cermets and various WC-Co hard metals. Additions of metals such as Mo, Cr, Ni, and Co to the Fe matrix may be used to fabricate composites with improved mechanical and corrosion properties. Figure 4-63 shows significant variations in the bending strength with increasing amounts of Mo in the binder phases of different volume fractions (Yuriditsky, 1990). As discussed in Sec. 4.5.3, hard metallike composites can be prepared by pressureless sintering of ternary borides with Fe, Ni, or Co melts. Materials with T-phase ( M ^ M ^ B ^ where MJ = Fe, Ni, or Co, and M11 = Zr, Hf, Nb, Ta, or W with M1 as the matrix phase) have not been developed for technical use but Ni-based alloys with
\ •
3000
single phase TiB 2
o
2500 -
CO
single phase WC C/) C/)
CD
2000 -
c
"P
TiB2-20 vol.% Fe
05
1500 -
Figure 4-62. Hardness-toughness relationship between hard metals and TiB 2 -Fe composites (courtesy of L. Sigl, ESK).
* WC/Co numbers are vol.% Co
20
1000 5
10
15
Fracture toughness, MPa Vm
20
4.6 Microstructural Reinforcement of Boride and Carbide Ceramics 900 o QL
800 en c CD
_b 700
c600 CD
500
0
10 20 30 40 Mo in binder phase, wt.%
Figure 4-63. Variation of strength with Mo content in the binder phase of TiB2-Fe-based cermets (Yuriditsky, 1990). A, 12.5 vol.% of binder; •, 15vol.%; • 17.5 vol.%.
T are in use as wear- and corrosion-resistant coatings on steels (Lugscheider and Eschnauer, 1987). (p- and co-phases have M ! M n B and ! M 2 M11 B 2 stoichiometry, respectively, where M1 = Cr, Mo, Ta, or W and M n = Fe, Ni, or Co and solid solutions thereof. Although the ternary phases are rather brittle, the cermets exhibit excellent toughness and strength (
Sintering additives that inhibit grain growth have been studied for B4C and SiC. Generally, the selected species form phases such as A12O3, A13C3, or SiC in the case of a B4C matrix, and B4C in the case of an
239
SiC matrix, upon sintering. They pin the grain boundary movement mechanically or segregate at the grain boundaries and thus change the chemical properties of the particle interfaces and hence the diffusion kinetics. If the grain growth of the major phase proceeds too rapidly, e.g., typically during the sintering of SiC, the new phases formed by deoxidation of the initial powders or by chemical reactions between the additives and the compounds may, however, be incorporated into the growing crystals. Currently, inclusions of graphite, B4C, Al, or A14C3 are a common feature of coarse-grained technical SiC ceramics. Compared to these materials, liquid phase sintered SiC with A12O3 and Y 2 O 3 additions exhibits an up to 50% higher fracture strength (Fig. 4-45). Presintered and hot-isostatically pressed materials can have a bending strength of up to 900 MPa (Storm, 1991). Due to a homogeneous and fine microstructure, the Weibull exponent is also increased from a typical 5-6 for SiC sintered with combined B-C additives, to 16 for liquid phase sintered materials. Moreover, the crack path changes from transgranular to intergranular. Together with effective micro-cracking, the fracture toughness is optimized at 6-7 MPa m 1/2 (Kleebe and Evans, 1990). In contrast to the monolithic ceramics, one benefit of all the particulate reinforcement discussed in the following sections is the grain growth retardation of the matrix phase, which directly affects the strength of the composite. 4.6.3 Silicon Carbide and Boron Carbide Particulate-Reinforced Materials
Silicon carbide in the form of whiskers, fibers or platelets is a well-known material for reinforcing advanced ceramics with alumina, mullite, cordierite, silicon nitride
240
4 Boride and Carbide Ceramics
and related matrices. Since these materials will be treated extensively in Vols. 11 and 13 this section is dedicated to nonoxide composites only. An excellent overview on fibre-reinforced SiC is given by Fitzer et al. (1987). In boron carbide-based composites, silicon carbide can be dispersed as isolated particles, e.g., by simple powder mixing (Schwetz et al., 1983), mechanical alloying, or as a grain boundary phase which is formed in situ by liquid phase reactions (Telle and Petzow, 1987 a). Another method of coating B4C with SiC which was mentioned in Sec. 4.4.1.3, is the deposition of a polysilane precursor on powder particles prior to sintering which can be converted to SiC by a pyrolytic heat treatment (Lorcher et al., 1990). In all the examples, the presence of SiC retards the strong coarsening of the matrix at temperatures above 1900 °C (Fig. 4-64). In general, B4Cand SiC-matrix ceramics can be toughened by the incorporation of SiC whiskers, but polytype changes are encountered because of the high temperatures required for complete densification, and the decomposition temperature of 2160 °C may easily be reacted in the B 4 C-SiC system. Pressureless sintering is difficult because of back-stress-
Figure 4-64. Micro structure of B 4 C-SiC composites derived from hot-pressed polysilane-coated B4C particles (light area: SiC).
es which cause porosity in the vicinity of the fibers. Moreover, the toughening and strengthening effect is not very large since the thermal expansion coefficients of matrix and inclusions are about the same. Thus, misfit stresses are small and only load transfer mechanisms due to differences in the Young's modulus may be operational rather than crack deflection. Reinforcement of TiB2 by dispersed SiC particles is generally possible since both materials are chemically compatible. As a result, crack impediment is obtained but the increase in strength and toughness is small (Ly Ngoc, 1989). This composite material has, however, not yet been studied extensively. Kang and Kim (1990) have investigated the improvement of TiB2 with a dispersion of B4C particles. Using 1 wt.% Fe as a reactive additive, hot-pressing at 1700°C for 60min at 35 MPa resulted in 99% dense composites with a clear maximum in strength of 700 MPa at 10 vol.% B4C and in Klc of 7.6 MPa m 1/2 at 20 vol.% B 4 C. This optimizing effect was attributed to both grain growth inhibition and change in fracture mode from transgranular to intergranular by the B4C addition. Since studies on the B4C-rich side of this system also indicate optimum properties at approximately 60-70 vol.% B4C (see Sec. 4.6.5) a change in strenthening and toughening mechanisms most occur at a composition between 40 and 50 vol.% B 4 C. The total system was investigated by Nishiyama and Umekawa (1985) by pressureless sintering of ultrafine B4C and TiB 2 powders. Besides other properties such as oxidation and wear resistance, they report a maximum in strength of 650 MPa at 35 vol.% TiB2 and an optimum hardness of HR A = 94 at 20 vol.% TiB 2 .
4.6 Microstructural Reinforcement of Boride and Carbide Ceramics
4.6.4 Transition Metal Carbide Particulate-Reinforced Materials
An interesting composite material would be a combination of boron carbide and transition metal carbides. Unfortunately, such a material is thermodynamically impossible since both phases react above 900 °C yielding transition metal borides plus graphite, as shown in the isothermal section of the quaternary B-C-Si-Ti phase diagram at 2000 °C (Fig. 4-65). The reaction can be used, however, to fabricate metal borides or metal boride/boron carbide composites in a controlled way during densification if boron carbide or free boron is used in excess, or if carbon is bonded by another additive. Although the incompatibility of B4C and metal carbides is well known, many attempts have been undertaken to produce composites or coatings thereof but failed as soon as equilibrium conditions are approached. Physical or chemical vapor deposition of B4C on hard metal substrates, or WC coatings on boron carbides are typical problems (e.g. Rey and Male, 1987). In both cases, interlayers of
241
graphite form and hence result in an unsatisfactory adhesion of the deposited coating to the substrate. Very promising carbide/carbide composites have been developed in the SiC-TiC system with SiC as the matrix phase (Wei and Becher, 1984; Janney, 1986, 1987; Jiang et al., 1989; and others). Dispersed TiC-particles significantly improve both the strength and the toughness. Although an addition of TiC does not reduce the densification temperature significantly below 2100 °C, the coarsening of SiC is completely retarded which raises the strength to 700-800 MPa (Wei and Becher, 1984; Janney, 1986; Jiang et al., 1989; Ly Ngoc, 1989). The increase in fracture toughness to 6.5-7.5 MPa m 1/2 is attributed to the misfit of the thermal expansion coefficients of TiC and SiC introducing considerable radial tensile stresses at the phase boundaries and hoop compressive stresses in the matrix. These stresses enable crack deflection, crack branching and microcracking above a critical particle size. Figure 4-66 shows an example of crack deflection and crack bridging resulting in stress-shielding
Figure 4-65. Isothermal sections of the ternary B-C-Si and B-C-Ti systems at 2000°C in at.%.
242
4 Boride and Carbide Ceramics
4.6.5 Transition Metal Boride ParticulateReinforced Materials
Figure 4-66. SEM micrograph showing crack deflection and crack bridging in SiC-TiC composites; light areas: TiC; dark matrix: SiC (courtesy of D. Ly Ngoc).
of the crack tip by interlocking of the crack flanks. Frictional forces have to be overcome for further crack opening. The optimum volume content of TiC ranges between 20 and 30vol.%, as indicated in Fig. 4-67.
As shown in the phase diagram in Fig. 4-68, the combination of TiC and TiB 2 is thermodynamically stable up to 2500 °C undergoing a quasi-binary eutectic reaction (Ordan'yan et al., 1975). In that system, excellent wear-resistant materials have been produced by hot-pressing or even by pressureless sintering of eutectic compositions at 1600-1700 °C (Holleck et al., 1987). A Vickers hardness of HV2 = 23 GPa was measured at room temperature which is lower than that of the pure materials with values of 27.5 GPa for TiC and 28.5 GPa for TiB 2 . At 600 °C, however, the hardness of the composite, 8.3 GPa, far exceeds the hardness of monolithic TiC and TiB 2 , which decrease to 6.8 GPa and 7.8 GPa, respectively. The fracture toughness is notably improved to 7.1 MPa m 1/2 . The significant decrease in wear during turning or milling of steel compared to the monolithic materials was mainly attributed to "phase boundary toughening" due to the favored occurrence of common coher-
900
^3225±20°C 800
3200o Q_
700 ==•
3000-
600
2800-
TiB2+Liquid
D
"a
2600-
\s V \2450°C
CD
Q. C 500
Liquid
\
o
CD
c
^
o
c
E 1— CD
2400-
2310+15 °C 88±3%;
2200- ^<2 %
CD
200010
20
30
Volume of a second phase (%) (TiB2 or TiC) Figure 4-67. Volume-dependent mechanical properties of SiC-TiC and TiB 2 -B 4 C composites.
1
1
20
r
1
60
80
100
Mol%
Figure 4-68. Isopleth of the quasi-binary TiB 2 -B 4 C system (Rudy et al., 1965).
4.6 Microstructural Reinforcement of Boride and Carbide Ceramics
ent (lll) TiC /(0001) TiB2 particle interfaces (Holleck, 1987). Besides this very sophisticated toughening effect, mechanisms which influence the crack propagation such as crack deflection or crack impediment due to thermal misfit effects between the boride and carbide phases certainly contribute to the increase in toughness, whereas grain growth retardation due to the pinning of grain boundaries by incorporated particles affects the strength positively. As another example, WC is used for grain size refinement of TiB 2 , and TiB2 is used as an additive for WC-based materials (Murata et al., 1967; Binder, 1975). High-temperature reinforcement by in situ precipitation of TiC and TiB2 from supersaturated solid solutions has already been used with interesting results. In the TiC-TiB 2 system, either TiC or TiB 2 can be the host crystal for the corresponding minority phase or the precipitate (Venables, 1967; Williams, 1966; Ramberg and Williams, 1987). The addition of a small fraction of boron to TiC can increase the critical resolved shear stress at 1600 °C by a factor of six if TiB 2 precipitates are formed at the (111) slip plane of TiC. Boron carbide-based composites with transition metal diborides - in particular with TiB2 - have been extensively studied for cutting tools and wear parts (Nowotny et al., 1961; Ordan'yan et al., 1975; Lange and Holleck, 1985; Holleck et al., 1987; Hofmann and Petzow, 1986; Telle and Petzow 1986, 1988; Telle et al., 1988). Since both phases are thermodynamically stable up to 2300 °C (Rudy, 1969) composites can be prepared either by pressureless sintering with an Fe additive at 2175 °C (Kim and Kim, 1988), or by hot-pressing and HIP without additives. Another method of densification makes use of reaction hot-pressing or self-propagating combustion sintering of MC-B powder mixtures under pres-
sure MC + 6B
243
(4-53)
Since sintering of MB 2 -B 4 C powder mixtures yields similar complications to the sintering of the pure compounds due to favored surface diffusion and evaporation-recondensation reactions, the combustion route is more likely because heat is generated inside the sample due to the exothermic conversion, the bulk diffusion is significantly enhanced and a grain size refinement occurs as the carbide phase decomposes. A certain risk is the evaporation of volatiles such as CO, CO 2 , B 2 O 3 as deoxidation products, or even of Bgas which may be formed because of the high heat release. Temperatures exceeding 2300 °C have been reported during fabrication of TiC and TiB2 from the elements (Rice et al., 1986; Richardson et al., 1986; McCauley et al., 1986; Holt et al., 1985; McCauley, 1988). The reaction velocity can be retarded by the addition of the final conversion product to the starting powder which then behaves inert. Thus in the case of TiC/B mixtures, TiB2 is added or B4C which also takes part in the reaction 2MC + B4C ^ 2MB 2 + 3C
(4-54)
3C + 12B -+ 3B 4 C
(4-55)
In this case, B4C also undergoes a grain size refinement which is very beneficial for the mechanical properties. In Fig. 4-69, a micrograph of a reacted TiC-B powder mixture is presented which still exhibits TiB 2 -B 2 C agglomerates of the size of the initial TiC particles. Note that the average particle size of both reaction products is approximately 1 Jim. Generally, this reaction can be employed for most of the transition metal boride-boron carbide composites since the borides are usually more stable than the particular carbides.
244
4 Boride and Carbide Ceramics
Figure 4-69. SEM micrograph of a reaction hotpressed TiC-B powder blend; visible phases: light: TiB 2 , dark: B4C.
Dense composites of MB 2 and B 4 C, in particular of TiB 2 and B 4 C, regardless of their fabrication technique exhibit improved mechanical properties compared to the particular single phase materials. The increase in strength of hot-pressed or HIPed materials to oh = 600-800 MPa is mostly attributed to a retardation of the grain growth, whereas the improved toughness is due to crack deflection around TiB 2 particles. Klc values of 5 7.3 MPa m 1/2 have been reported for B4Cbased composites with LaB 6 , TiB 2 , ZrB 2 , NbB 2 and W 2 B 5 (Lange and Holleck, 1985). At 2150°C, pressureless sintered B 4 C/TiB 2 composites with 1 wt.% Fe additive exhibit a maximum bending strength of a b = 420 MPa at an optimum volume fraction of 20% TiB 2 . The lower strength compared to the hot-pressed material is mainly attributed to the embrittling FeB intergranular phase. With increasing sintering temperature and amount of additive, the strength even drops to 100250 MPa due to the exaggerated coarsening of the B4C matrix by one order of magnitude. Another example of successful materials development is B 4 C-TiB 2 -W 2 B 5 composite ceramics prepared by reaction hot-
pressing (Hofmann and Petzow, 1986; Telle and Petzow, 1988). Due to a grain size refinement of the B4C matrix to approximately 0.8-1.2 {im and of the transition metal borides to 1-2 |im, the flexural strength of HIPed material was improved to (Tb = 900-1100 MPa. A fracture toughness of Klc = 4.5-5.2 MPa m 1/2 was measured by an indentation technique and attributed to active crack deflection and, possibly, also to crack/microcrack interactions (Telle and Petzow, 1988). Silicon carbide-based composites with transition metal boride particulates have been developed for electroconductive applications such as heating elements and igniters (Jimbou et al., 1986; McMurtry et al., 1986) but also as wear resistant structural parts for high temperatures such as valve-train components and rocker arm pads in super-hot running engines (Janney, 1986, 1987). These composites combine the high thermal and electric conductivity of e.g. TiB 2 and ZrB 2 with the oxidation resistance of SiC. Additionally, due to thermal mismatch stresses of the order of 2 GPa toughening mechanisms such as crack deflection and stress-induced microcracking with a pronounced process zone, as well as crack flank friction have been proven to occur. Cai et al. (1990) and Faber et al. (1991), have presented a detailed analysis of the contributions of the particular mechanisms to the total fracture toughness, stating that stress-induced microcracking is operational in a process zone of approximately 150 (im width. Typical conditions for densification by axial hot-pressing are 2000-2100 °C, at a pressure of 20-60 MPa for 30-60 min which results in 96-99.8% density. The particle sizes of the matrix and dispersed phases range between 1-5 and 4-8 jjm, respectively. An optimum volume fraction of reinforcing particulates of 25-30 vol.%
245
4.6 Microstructural Reinforcement of Boride and Carbide Ceramics
has been reported, yielding a flexural strength of 710 MPa and a fracture toughness of 5.0-5.7 MPa m 1/2 , as shown in Fig. 4-70 (Ly Ngoc, 1989). Composites with a lower TiB 2 content of 15 vol.% exhibit a mean strength of 485 MPa combined with a Klc of 4.5 MPa m 1/2 (Janney et al., 1987). The strength of SiC-based materials with 50 vol.% ZrB 2 , HfB 2 , NbB 2 or TaB2 particles also ranges between 400 and 500 MPa (Jimbou et al., 1986). Similar strength values (480 MPa) combined with an exceptionally higher fracture toughness of 7-9 MPa m 1/2 have been reported for large-scale lots of pressureless sintered 16 vol.% TiB 2 composites (McMurtry et al., 1986). Since the sintering was carried out with temperatures exceeding 2000 °C (no details given) yielding 98-99% of the theoretical density and an average TiB 2 particle size of 2.0 |im, it is obvious that the reinforcing phase also acts as a grain growth inhibitor for SiC. The high temperature strength of SiC/TiB2 and SiC/ZrB2 composites was found to remain nearly constant at 480 MPa up to 1200 °C, and is hence superior to that of many sialons (Jimbou et al., 1986; McMurtry et al., 1986). Combinations of diborides of different transition metal borides have been studied, especially in the TiB 2 /CrB 2 and TiB 2 / W 2 B 5 systems, for wear applications and to a minor extent - for electrodes in HallHerould cells (Koval'chenko et al., 1979; Klimenko and Shunkowski, 1981; Watanabe and Kouno, 1982; Watanabe, 1977, 1980; Zdaniewski, 1987). Since the transition metal diborides crystallize in the same structure type, namely the A1B2 layered structure, the formation of solid solutions has been extensively investigated and used for hardening effects. As an example, the quasi-binary system CrB 2 -TiB 2 exhibits a continuous mutual solid solubility be-
• TiC 1.5 (im o TiC 8.0 \irr\ n TiB 4.0 (im
[ 70-
K1CQ=
3.1* MPa Vm
: 60-
fscH £302 20o .c 100
10 20 30 40 50 TiB2 and TiC content in SiC (vol.%)
Figure 4-70. Volume-dependent mechanical properties for TiB2-particulate reinforced SiC with various TiB2 particle sizes (Ly Ngoc, 1989).
tween 2000 °C and 2100 +50 °C, approximately (Post et al., 1954; Telle et al., 1992, Fig. 4-71), but there is evidence of a solubility gap below 2000 °C where the solubility of TiB 2 in CrB 2 is about 40 mol% at 1500°C and the solubility of CrB 2 in TiB 2 is less than 1 mol% below approximately 1800 °C. The presence of CrB 2 aids the densification of TiB 2 due to its higher diffusion coefficient. Above 2100 °C, CrB 2 containing materials melt partially which is due to an almost horizontal solidus line 35003225Liquid
3000 •
2500
°r
2000"
(Cr,Ti)B2
1500-
V ' \
TiB 2 + (Cr,Ti)B2 1000 0
TiB 2
10
20
30
40
50
60
Mol% CrB2
70
90
100
CrB 2
Figure 4-71. Isopleth of the quasi-binary TiB 2 -CrB 2 system.
246
4 Boride and Carbide Ceramics
between approximately 40 mol% CrB 2 and pure CrB 2 . This fact enables liquid phase sintering of TiB 2 but with the risk of exaggerated grain growth and evaporation of chromium and chromium borides, since the vapor pressure of Cr is four orders of magnitude higher than that of Ti. Prereacted and hot-pressed materials of that system exhibit a flexural strength of 350500 MPa (Koval'chenko et al., 1979; Klimenko and Shunkowski, 1981). In the TiB 2 -W 2 B 5 system, the borders of the (Ti, W)B 2 homogeneity range have been intensively studied between 1500°C and 1700°C, at 2000 °C and around the quasi-binary eutectic temperature. TiB 2 and WB 2 react eutectically at Te = 2230 ± 40 °C and 90 ± 3 mol% WB 2 (Fig. 4-72). The solid solubility of WB 2 in TiB 2 at this temperature is approximately 63 mol%, whereas the solid solution of the (W, Ti)2B5-type contains only 3 mol% TiB 2 at the eutectic equilibrium. The homogeneity range of the (Ti, W)B2 solid solution narrows significantly with decreasing temperature and is 46-49 mol% at 2000°C and 8-10 mol% WB 2 at 1500°C.
A high-temperature treatment of TiB 2 W 2 B 5 powder mixtures inside the solid solubility range of (Ti, W)B 2 at above, e.g., 2000 °C, for 30-720 min results theoretically in a uniform, single phase microstructure. Subsequent annealing at, e.g., 1500°C, causes the epitaxial precipitation of very fine platelets of (W, Ti)2B5-type crystals with (0001)W2B5 being parallel to (0001)TiB2 in the host-crystal (Fig. 4-73). After 30-240 min annealing, these precipitates measure 0.5-5 jam in length and 0.05-0.2 jam in thickness and can be aged by prolonged heating or by the choice of a higher temperature to a convenient size (Fig. 4-74). The growth of platelets can also be initiated from very thin precipitates close to a grain boundary of the host crys-
Figure 4-73. SEM micrograph of WB2 precipitates (light) in a (Ti, W)B2 matrix.
3500 3225 Liquid
3000o 2 2500 D
(T,W)B 7
"a | 2000
2365 2230±/,0
CD I—
1500
(Ti,W)B 9 AIB2-type
(W,Ti)B 7 W2B5-type
1000 0 10 20 30 -CO 50 60 70 80 90 100 TiB 2 Mol% WB 2 WB 2
Figure 4-72. Isopleth of the quasi-binary TiB 2 -WB 2 system.
Figure 4-74. Aged in situ reacted (Ti,W)B 2 -WB 2 composite with grown WB2 particles (light).
247
4.6 Microstructural Reinforcement of Boride and Carbide Ceramics
tal. The precipitate is then able to grow across the grain boundary into a neighboring W-rich (Ti, W) B 2 grain and thus create an interlocking microstructure, as shown in Fig. 4-75. Crack propagation studies confirm that crack deflection is operational around the W2B5-type phases. This process is assisted by differences between the Young's moduli of the particular phases, and differences in the thermal expansion coefficients and their anisotropic behavior generating residual misfit stresses. Of similar importance for crack-interactions are the grain boundaries of the W-depleted host crystals and neighboring Wrich solid solutions. Here, an active crack deflection was observed which indicates that both the elastic constants and thermal misfit stresses of TiB2-type solid solutions vary significantly with composition. Hightemperature XRD (X-ray diffraction) measurements of the lattice constants of (Ti, W) B 2 solid solutions confirm this observation (Fig. 4-76, Telle et al., 1992). Hot-pressed composite materials developed from the more complex systems of the type TiB 2 -M I B 2 -M n with M1 being Hf, V, Nb, Ta, Mo, or Mn and M n being sintering additives such as Co and Ni, exhibit bending strengths between 850 and 1000 MPa which are due to the grain growth inhibiting influence of the 1 5wt.% of M n B 2 particulates (Watanabe and Kouno, 1982; Watanabe, 1977, 1980; Petzow and Telle, 1987, Fig. 4-77). During liquid phase sintering in a Co- or Niboride melt, both TiB2 and M1 are partially dissolved and reprecipitated as a solid solution. The effect of grain growth retardation as well as of strength and hardness increments is attributed to stresses at the TiB2/(Ti, M J )B 2 phase boundaries generated by the mismatch of the lattice parameters between the unreacted TiB 2 acting as a nucleus and the epitaxially precip-
Figure 4-75. Interlocking grain boundaries by intergrowth of WB2 precipitates.
100 WB ?
Mol% WB 9
Figure 4-76. Thermal expansion (Ti,W)B2 solid solutions.
coefficients
of
1200 Q TiB2+1m%CoB • TiB2+5m%TaB2+1m%CoB TiB2+5rn%W2B5+1m%CoB
5 10 15 Average grain size (|im)
20
Figure 4-77. Strength and grain size of various TiB 2 MB 2 -M composites (data from Watanabe and Kouno, 1982). (m%=mass%.)
248
4 Boride and Carbide Ceramics
itated (Ti, M I )B 2 solid solution. In the case of a TiB 2 -5 wt.% W 2 B 5 /TaB 2 material with 1 wt.% CoB binder the lattice strain ranges between 9 x l O ~ 4 and 14 x 10 ~ 4 depending on the hot-pressing temperature (Watanabe and Kouno, 1982). The addition of 1.7% TiC to the abovementioned base composition reduced the porosity from 0.3-0.7 to 0.1-0.2 vol.% after hot-pressing at 1500°C and a pressure of 20 MPa for 1 h. The improved sintering behavior was achieved by intensive ball milling resulting in an average particle size of 1 jim, but increased oxygen contamination. Watanabe and Shoubu (1988) reported the formation of a (Ti, Ta) (C, O) solid solution which is considered to initiate the improved densification resulting in a flexural strength of 1000 MPa. In a similar multiphase system, transition metal carbides were used as additives for pressureless sintering of TiB 2 yielding composites of binary and ternary borides (Petzow and Telle, 1987; Telle and Petzow, 1988). Attrition milled powder mixtures of TiB 2 with 3-10 wt.% Co or Ni and 20-35 wt.% WC have been sintered in a vacuum at temperatures between 1500 and 1700°C for 60 to 120 min yielding 98-99%. Densification starts above 980 °C due to the formation of a liquid phase in the Ti-B-Co/Ni system (Fig. 4-54). At this early stage, a rigid skeleton of TiB2 and WC develops. Due to dissolution and re-precipitation, a (Ti, W)B 2 solid solution grows on the residual TiB2 particles. Subsequently, crystals of cophase form with compositions of WCoB or W 2 NiB 2 , respectively. Upon cooling, the residual liquid phase crystallizes as Cand Ti-enriched Co 3 B or Ni 3 B solid solution. A typical microstructure is shown in Fig. 4-78. Sintering at 1700°C for 2 h yields an average particle size of 0.8 jim resulting in a flexural strength ah = 600680 MPa. The K,c of 6.5-7.5 MPa m 1/2 is
Figure 4-78. SEM micrograph showing the microstructure of a (Ti,W)B 2 -W 2 NiB 2 (co)-Ni 3 B composite; light areas: W 2 NiB 2 ; intermediate: Ni3B; dark: TiB 2 .
mainly attributed to crack deflection because of the weak Co- or Ni-boride intergranular phases. 4.6.6 Multiphase Hard Materials Based on Carbide-Boride and Carbide-NitrideBoride-Silicide Composites A systematic study on the rule of mixtures for the mechanical and electrical properties of TiB 2 -TiC-SiC composites was carried out by de Mestral and Thevenot (1990). They modeled "iso-response" curves in the quasi-ternary phase diagram for each property by fitting 20 independent coefficients of a third-order polynomial developed by Phan-Tan-Luu et al. (1989) to the results of experimental test points. Calculated iso-bend strength curves as well as tests on hot-pressed materials indicate a maximum of 1100 MPa close to the TiB 2 TiC binary edge of the system (Fig. 4-79). The best fracture toughness value of 6.4 MPa m 1/2 was obtained on the binary SiC-TiC edge (measured and calculated), on the binary TiB 2 -SiC edge and in the ternary region close to the TiB 2 phase (67mol% TiB 2 , and 16.5 mol% SiC and TiC, respectively) (Fig. 4-80). The calculated rule of mixtures could also be con-
4.6 Microstructural Reinforcement of Boride and Carbide Ceramics
249
TiB,
890±25
970+75
1030+UO
630+^0
950+100
625+15
500 + SiC
1080 + 160
830+130
910±70
1040±75
550+55 TiC
Figure 4-79. Iso-bend strength curves of composites in the SiC-TiC-TiB 2 system (de Mestral and Thevenot, 1990).
Figure 4-80. Iso-toughness curves of composites in the SiC-TiC-TiB 2 system (de Mestral and Thevenot, 1990), 5.5+0.3
6.3+0.9
6.4 + 0.2
250
4 Boride and Carbide Ceramics
firmed in the case of hardness measurements. Ternary composites of Ti(C, N ) - T i B 2 MoSi2 were studied by Shobu and Watanabe (1987) in order to improve the oxidation resistance of Ti(C, N)-TiB 2 materials. Full density was obtained after sintering composites with less than 80wt.% TiB 2 and less than 60wt.% MoSi2 at 1750 °C. The oxidation resistance above 1000 °C was good for small Ti(C, N) concentrations, i.e. when all the carbonitride particles were surrounded by a phase of either TiB2 or MoSi 2 . The formation of rutile (TiO2) and silicate glass was observed and considered to prevent further oxygen diffusion. TiB 2 -20wt.% MoSi2 composites sintered at 1800 °C in a vacuum exhibited a flexural strength of 600 MPa and a hardness of HV 2100, whereas the fracture toughness was only 3.7 MPa m 1/2 . Composites of 70wt.% Ti(C,N)-30wt.% TiB 2 showed a three-point bending strength of 800 MPa and a Klc of 5 MPa m 1/2 . With a hardness of HV > 2500, the material was tested as a cutting tool and exhibited a longer lifetime upon machining plain carbon steel at 300 m/min than conventional hard metals or cermets (Shobu and Watanabe, 1987). 4.6.7 Transformation Toughening of Borides and Carbides
One of the most important toughening strategies for oxide ceramics, namely transformation toughening by dispersed tetragonal zirconia particles, is not applicable to borides and carbides to a similar extent. Chemical interactions between ZrO 2 , with its pronounced tendency for oxygen losses, and the thermodynamically less stable borides and carbides lead to the formation of boron oxides or carboxides, respectively, which in some cases result in
the total degradation of the composite. This is particularly the case under reducing conditions and at high temperatures which are both required for successful densification of hard materials. For example, boron carbide decomposes in the presence of zirconia
B 4 C + 2ZrO2 -» 2ZrB2 + CO B 2 O 3 (Lange and Holleck, 1985), whereas silicon carbide reacts with zirconia forming silicides, e.g. (45?) _ -* Zr 5 Si 3 In both cases, a pronounced bloating of the samples is observed due to the release of gaseous compounds. Another limiting factor is the chemical, geometrical and mechanical destabilization of tetragonal zirconia if combined with transition metal diborides. Stabilizing additives such as MgO or Y 2 O 3 tend to migrate to grain boundaries since the bivalent or trivalent cations in the zirconia lattice are substituted by the more favored such as Ti4 + . A geometrical destabilization results from the strong coalescence of ZrO 2 causing a particle coarsening due to the high sintering temperatures. Large crystallites exceeding a critical size cannot be retained in the tetragonal modification upon cooling to room temperature and hence transform spontaneously to the monoclinic modification. Moreover, if associated in clusters, a transforming zirconia particle may trigger the transformation of all the other crystals by an autocatalytic reaction. This mechanical destabilization results from the anisotropy of the thermal expansion of the diborides which introduces radial tensile stresses in the vicinity of the zirconia inclusions. This initiates the spontaneous tetragonal-to-monoclinic transformation or at least reduces the contribution of the ZrO 2 volume expansion
4.6 Microstructural Reinforcement of Boride and Carbide Ceramics
during stress-induced transformation to toughening (Telle et al., 1988 b). Zirconia titanium diboride has been studied intensively as a possible candidate for active transformation toughening (Watanabe and Shobu, 1985; Shobu et al., 1987; Telle et al., 1988; Swain, 1991; Franz et al., 1992; Turnback et al., 1992). Composites with ZrO 2 additives show an improved densification behavior and a grain growth inhibiting effect for the TiB2 (Fig. 4-81). Hot-pressing of composites with 22-60 wt.% ZrO 2 between 1700°C and 1900°C at 20 MPa yields densities exceeding 99.8% (Watanabe and Shobu, 1985), whereas 98 % of the theoretical density is obtained by pressureless sintering at 2100°C (Telle et al., 1988). Volume fractions of unstabilized ZrO 2 between 15 and 30 % result in a significant increase in both the strength and the toughness. Depending upon the microstructure and the density, a maximum ah of 800 MPa is measured at 22 or 35vol.%, respectively, and the maximum Klc varies between 8.5 and 9.5 MPa m 1/2 (Figs. 4-82 and 4-83). The hardness decreases linearly with the amount of ZrO 2
251
200 0
1 0
20 30 ZrO2 (vol.%)
Figure 4-82. Strength of TiB 2 -ZrO 2 composites with various ZrO 2 contents (data from Watanabe and Shobu, 1985; Telle and Petzow, 1988).
12.0
20 30 Vol.% ZrO2
Figure 4-83. Fracture toughness of TiB 2 -ZrO 2 composites with various ZrO 2 contents (dots: data from Watanabe and Shobu, 1985; notch-beam technique, error bars within character size; squares: data from Telle and Petzow, 1988, indentation technique).
Figure 4-81. SEM micrograph showing the microstructure of a (Ti,Zr)B 2 -(Zr,Ti)O 2 composite; dark areas: unreacted TiB2 core; intermediate areas: (Ti,Zr)B2 reaction layer; light areas: ZrO 2 and (Zr,Ti)O2
additive and is thus of the order of 1618GPa at the optimum ZrO 2 content (Fig. 4-84). This improvement in the mechanical properties is attributed to enhanced sintering and grain size refinement of TiB 2 , active transformation toughening (Watanabe and Shobu, 1985) crack deflection and microcracking (Shobu et al., 1987; Telle et al., 1988).
252
4 Boride and Carbide Ceramics
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If yttria is added to the system, the contribution of stress-induced transformation to the toughening is more likely. An average bending strength of 1250 MPa (maximum ah = 1500 MPa) is obtained at 40 wt.% of 1.94mol% Y 2 O 3 -dopedZrO 2 , whereas the fracture toughness is, however, only 4-6 MPa m 1/2 but increases with higher Y-ZrO 2 contents (Shobu et al., 1986; Fig. 4-85). The reason for this comparatively small increase in toughness is the high stiffness of the matrix phase which reduces the dilatational strain associated with the tetragonal-to-monoclinic transformation of ZrO 2 (McMeeking, 1986; Swain, 1991). A similar behavior of the mechanical properties has been observed for composites of Ti(C, N) containing Y-doped tetragonal zirconia composites where a significant increase in the strength and hardness with Y-ZrO 2 content is accompanied by a modest increment in the toughness. The presence of untransformed tetragonal ZrO 2 particles in TiB2-based composites without an yttria addition can be explained by a pronounced mutual Ti- and Zr-inter-diffusion resulting in (Ti, Zr)B 2 and (Zr, Ti)O 2 solid solutions. The (Zr, Ti)O 2 may contain 14-16 mol.% TiO 2 at
a a.
i
0 20 40 60 80 100 Tetragonal ZrO2 content (mass%) Figure 4-85. Mechanical properties of TiB 2 -Y-TZP composites sintered at 1500°C (Shobu et al, 1987).
1700°C in outer layers of the ZrO 2 particles and hence result in a stabilization of the tetragonal modification. The maximum ZrB 2 content in TiB 2 at 1700 °C was found to be 3.2 mol.%. Moreover, after sintering between 2000 °C and 2100 °C there is evidence of an intergranular phase between adjacent TiB2 and ZrO 2 particles consisting of zirconium titanate (Zr, Ti) 2 O 4 which forms peritectically from a TiO 2 -ZrO 2 melt (McHale and Scott, 1986; Telle et al., 1988). This embrittling phase can be avoided by the substitution of TiB 2 with ZrB 2 since zirconium zirconates do not exist. These composites are, however, very sensitive to a spontaneous tetragonal-to-monoclinic transformation resulting in extensive microcracking (Fig. 4-86). Above 2100 °C, the boride-ZrO 2 ceramics
4.7 Fields of Application and Outlook
decompose due to an accelerated boronoxygen inter-diffusion. Starting at the grain boundaries, transition metal suboxides, borates and boron oxides form which evaporate and cause a swelling of the composite. As well as TiB 2 , WC, ZrC, TiC and mixtures thereof have also been transformation toughened with Y-stabilized ZrO 2 (Ogata, 1989). Hot-pressing of WC-TZP blends with up to 50 vol. % ZrO 2 at 1600°C yields almost dense composites with a flexural strength of 2300 MPa and a hardness of HV 1800 (HRA = 93.4). A reaction between zirconia and tungsten carbide has not been observed but the appearance of a liquid phase is reported. Like TiB 2 -ZrO 2 and Ti(C, N)-ZrO 2 , the ZrO2-reinforced carbides possess a metallic character and can readily be shaped by discharge machining. An obvious conclusion from the results of strengthening and toughening efforts is that the maximum strength obtained by crack-propagation influencing mechanisms operational in composites is about 1-1.2 GPa and the fracture toughness usually obtained in optimized microstructures is about 6-7 MPa m 1/2 . It is also clear that simple two-phase composites are generally superior to materials of more complex
Figure 4-86. TEM micrograph showing spontaneous microcracking in ZrB 2 -ZrO 2 composites.
253
composition. Metal-matrix composites may exhibit a much higher toughness than ceramics but are limited in high-temperature use due to creep and corrosion. With the possible exception of the very promising TiB 2 -Fe cermets, these materials are thus of more interest for strengthening metals similar to oxide-dispersed alloys. A certain challenge is still the transformation toughening of borides by Y-stabilized ZrO 2 , increasing the toughness by a factor of two compared to simple particulate reinforcement. In competition with oxide and nitride ceramics the carbides and borides have thus been developed with similar excellent mechanical properties but still suffer from their considerably high price and poor oxidation resistance at high temperatures.
4.7 Fields of Application and Outlook Besides the well-known application of carbide grits (e.g. improving the wear resistance of concrete on sidewalks, or steps in areas frequently used by pedestrians such as subways or railway stations, or acting as grinding, lapping, and polishing particles), ceramic bulk materials are widely used in mechanical, chemical, thermal and electrical areas. Mechanical applications are currently by far the most important aims for the development of materials and parts based on carbides and borides. This may easily change to thermal and electrical applications if there is an improvement in the understanding and control of the semiconductivity of SiC or B4C and a breakthrough in the manufacture of suitable parts. Moreover, thermal applications may increase considerably in importance as more efficient energy conversion or re-
254
4 Boride and Carbide Ceramics
covery becomes a significant requirement in the construction of conventional, nuclear and solar power plants, waste incineration plants and other high-temperature technologies. At the time this article was written, optimism concerning the application of advanced ceramics was, however, declining considerably, especially in respect to structural parts for automotive engines or to substitutes for other highstrength, high-toughness materials. This tendency is not just in Europe or the U.S.A., but is also the case in Japan and can easily be attributed to the following problems, (i) difficulties related to reliable large-scale production at reasonable costs and qualities (problems of "zero-flaw" processing and part testing), (ii) difficulties in a material-appropriate design of parts (problems of substitution and new construction taking the relative brittleness of ceramics into account), (iii) the comparatively high price of high-quality starting materials and manufacturing processes (problems of purity and fine grain size), and (iv) the current world-wide economic recession stopping any activities in materials development. Considering these facts, the following paragraphs will give some basic ideas on the actual and most probable applications which have already been demonstrated up to now to be feasible. Most of the applications of carbides and borides related to mechanical aspects make use of their extraordinarily high hardness and wear resistance. Also, their high Young's modulus (stiffness) and the excellent high-temperature behavior - in the case of SiC, combined with an extreme oxidation and corrosion resistance - are attractive properties. The high-temperature hardness of the most important ceramics and hard materials is shown in Fig. 4-87. It is obvious that carbides and borides are superior to most oxide ceram-
ics. At high temperatures, however, the metallic transition metal borides and carbides suffer from a strong decrease in hardness due to enhanced plastic deformability (thermal initiation of slip systems). Additionally, oxidation has to be taken into account at temperatures above 600 °C. On the other hand, at room temperature B4C is only inferior to diamond and cubic boron nitride which tend to weaken above 500-600 °C due to the beginning of the transformation from the diamond structure into the graphite structure. Above 1100°C - and in a nonoxidizing atmosphere - B4C is the hardest compound known up to now. B4C is thus used for wear resistant parts and inserts for mortars and ball mills, wear plates, sand blasting nozzles, dressing tools for grinding wheels, lightweight armour plates for helicopters, and in composites of glass fiber-reinforced plastics as bullet-proof protection for personnel. Depending upon the microstructure SiC has a higher hardness than /?-Si3N4 but it decreases slightly more rapidly. Similar to Si 3 N 4 , SiC ceramics also possess a high thermal conductivity and thus an excellent thermal shock resistance (Fig. 4-88). They are widely used for wear parts in machinery such as sliding rings, valves, valve seats and other components of simple geometry, but in automotive engines the comparatively much stronger and tougher Si 3 N 4 is the favored material. Sintered and hot isostatically pressed SiC is, however, considered for turbochargers and turbine wheels, also for valve train components, roller and ball bearings, plungers and rocker arm pads. Here, TiC- or TiB2-particulate reinforced SiC composites have been elucidated and developed for large-scale production. Although SiC-based materials exhibit interesting advantages over metallic parts in relation to weight, stiffness and high-
4.7 Fields of Application and Outlook
255
8000
Diamond
-C,IYA-Me-B YA-Me-ICNJ 400
800 Temperature (°C)
Figure 4-87. High-temperature hardness of ceramic materials in comparison to diamond and cubic boron nitride.
1200
200 180 -
Figure 4-88. Temperature-dependence of the thermal conductivity of ceramic materials.
20
0
200
400
600 800 1000 1200 Temperature (°C)
4 Boride and Carbide Ceramics
256
Sintered, reaction-bonded or Si-infiltrated SiC materials, whose mechanical properties are not so exceptional, are widely used for kiln furniture, rollers for fastfiring furnaces, and other refractory components in the production of iron, steel, non-ferrous metals and glasses. Limiting factors for such applications are the comparatively high Si vapor pressure at very high-temperatures (> 1700°C) and the transition from passive to active oxidation in reducing atmospheres, where SiO and Si gas emerge from the layers beneath the oxidized surface of the component rather than new SiO2 being deposited. Since transition metal carbides and borides also exhibit high melting points, extreme high-temperature stability, and in most cases a lower metal vapor pressure than the silicon compounds, they have often been considered as potential aerospace materials but realization has been hindered by economic factors, fabrication difficulties, inherent brittleness and low thermal stress resistance. Moreover, in oxidizing atmospheres, the application of metal carbides and borides is limited to moderate temperatures due to the onset of oxidation. Additionally, the tendency for plastic deformation above 800-1000 °C is another
temperature stability, a simple substitution for existing, well-established metallic materials is difficult to achieve. Figure 4-89 shows some examples of parts in piston engines which may be fabricated from SiCbased ceramics. Carbon- or SiC-fiber based composites with an SiC matrix fabricated either by liquid silicon infiltration or vapor phase impregnation have been developed as light-weight, high-temperature resistant parts in aerospace applications such as nozzles, combustion chambers, and heat protection components for re-entry missiles and shuttles. Similar composites are also considered for use as high-friction brakes in high-speed trains. Thermal shock resistance, high-temperature stability, high thermal conductivity, and oxidation resistance are also important reasons for the favored application of SiC in heat exchangers in, e.g., waste incineration plants, power plants, and solar energy conversion, but also as burner nozzles for heavy oil and natural gas combustion in conventional power plants and furnaces. Moreover, heat recuperators in blast furnaces and other branches of the steel- or glass-fabricating industries are made from SiC.
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Figure 4-89. Possible fields of application of SiC parts in piston engines (Schwetz et al, 1983).
4.7 Fields of Application and Outlook
257
Valve spring retainer Cam shaft head Exhaust gas outlet Valve
Ignition chamber
Valve seat
Glow plug
Liner
Piston cap
Cam shaft liners Cams
problematic factor. The development of composite materials was thus favored and depended strongly on military- or areospace-based research. Besides the wellknown carbide-containing cutting tools such as cemented carbides and cermets, boride-containing cermets have also been investigated with TiB 2 and Mo 2 (Fe, Ni) B 2 as the hard phase and an Fe binder. TiB2-Fe cermets have been proven to be suitable for machining aluminum alloys whereas ternary boride cermets are suitable for injection molding nozzles, bearings, wire drawing cones and other wear resistant parts which are not exposed to high temperatures. Composites of TiB 2 / TiC, TiB2/TiN, TiB2/ZrB2/TaN, and also comprising B4C as a component as in B 4 C/ TiB 2 , B4C/SiC, and B4C/SiC/TiB2 have been exploited for cutting tools (brass, bronze, Al-alloys) and drilling tools (rocks and concrete) due to their comparatively high toughness. Figure 4-90 shows a comparison between several particulate-reinforced materials during abrasive model
Figure 4-90. Erosion tests of boride and carbide composites (redrawn, after Lange and Holleck, 1985).
tests in which a pin of the candidate material is tested against an SiC grit dispersed on a gray cast iron-wheel (Lange and Holleck, 1985). The applications of transition metal borides such as TiB2 are thus more concerned with the high electric conductivity and its resistance against metallic melts combined with an excellent wetting behavior. Well-known examples are TiB 2 -AlNBN evaporator dies (e.g. for the evaporation of Al, Cd, Ge, Pb, Bi, Cr, Cu, Ag, Au, Mg, Fe, Zn, and Sn for the coating of plastics, paper and parts) and electrodes for the aluminum electrolysis in Hall-Herould cells. In the latter case, there is a very high demand for such a material having a high electric conductivity and extraordinary corrosion resistance against cryolite melts, but some undesired grain boundary reactions (infiltration of the melt along impurity-loaded grain boundaries) and the poor thermal shock resistance (strongly anisotropic thermal expansion) are the limiting factors for a successful replacement of
258
4 Boride and Carbide Ceramics
graphite electrodes. Other diborides such as ZrB 2 have been studied for use as structural parts such as bearings, nozzles and molds for injection molding, valves and sealings, but further development is still necessary for an industrial breakthrough. For example, ZrB 2 -MoSi 2 composites exhibit remarkable corrosion resistance up to 2000 °C. Functional applications of borides are also related to the high cross-section of boron for the absorption or retardation of thermal neutrons. B4C sintered products have been used as moderating elements and radiation-protecting components in nuclear reactors of several designs. Moreover, a combination of B4C and graphite exhibits a considerable thermal power suitable for the construction of thermal couples working up to 2300 °C. Doped SiC may become an important material for high-temperature semiconductor devices and diodes emitting blue light. In conclusion, carbide and boride ceramics are materials of high potential for use in mechanical and electric fields as well. Most research on carbides is concerned with thermal and mechanical properties. In the case of borides, however, much research is focused on the basic questions of atomic bonding and physical transport properties rather than on application-related problems. So there is a chance that - depending upon the economic situation and the demand for future key technologies - these materials may extend their importance.
4.8 References Acheson, E. G. (1892), Br. Patent 17911. Acheson, E. G. (1893 a), U.S. Patent 402 767. Acheson, E. G. (1893 b), J. Franklin (9). Adlassnig, K. (1958), Planseeberichte fur Pulvermetallurgie 6, 92.
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Wakelkamp, W. J. X, van Loo, F. J. X, Metselaar, R. (1991), /. Europ. Ceram. Soc. 8, 135. Walker, B. E., Rice, R. W, Becher, P. R, Bender, B. A., Coblenz, W. S. (1983), Ceram. Bull. 62(8), 916. Watanabe, T. (1977), J. Am. Ceram. Soc. 60(4% 176. Watanabe, T. (1980), Am. Ceram. Soc. Bull. 59(4), 465. Watanabe, T., Kouno, S. (1982), Ceram. Bull. 61(9), 970. Watanabe, T, Shobu, K. (1985), J. Am. Ceram. Soc. 68(2), C34. Watanabe, T., Shobu, K. (1988), Yogo-Kyokai-Shi 96(7), 778. Weaver, G. Q. (1982a), U.S. Patent 4320 204. Weaver, G. Q. (1982b), U.K. Patent GB 2093 481 A Wecht, P. (1977), in: Techn. Mineralogie 11: Vienna: Springer. Wei, G. C , Becher, P. F. (1984), J. Am. Ceram. Soc. 67(8), 571. Weinstein, X (1989), in: Proc. Int. Symp. Advances in Processing and Characterization of Ceramic Metal Matrix Composites, CIM/ICM; Vol. 17: Mostaghaci, H. (Ed.). Oxford: Pergamon, 132. Werheit, H., de Groot, K. (1980), Phys. Status Solidi 97, 229. Whalen, T. X, Anderson, A. T. (1975), J. Am. Ceram. Soc. 58, 396. Will, G., Kossobutski, K. H. (1976), 7. Less-Common Met. 47, 43. Williams, W. S. (1966), Trans AIME 236, 211. Williams, W S. (1988), J. Mater. Sci. Eng. A105/106, 1. Williams, R. M., Juterbock, B. N., Peters, C. R. (1984), J. Am. Ceram. Soc. 64, C-62. Williams, R. M., Juterbock, B. N., Shinozaki, S. S. (1985), Bull Am. Ceram. Soc. 64(10), 1385. Woods, H. P., Wawner, F. E., Fox, B. G. (1966), Science 151, 75. Wroblewska, G. H., Nold, E., Thummler, F. (1990), Ceram. Int. 16, 201. Yajima, S., Okamura, K., Hayashi, X, Omori, M. (1976), / Am. Ceram. Soc. 59, 324. Yajima, S., Okamura, K., Hasegawa, Y., Iwai, T., Yamamura, T. (1981), /. Mater. Sci. 16, 1349.
Yamada, O., Miyamoto, Y, Koizumi, M. (1985), Am. Ceram. Soc. Bull. 64(2), 319. Yuriditsky, B. Y. (1990), Refractory Mater. Hard Mater. 3, 32. Zakhariev, Z., Radev, D. (1988), J. Mater. Sci. Lett. 7, 695. Zdaniewski, W. A. (1987), J. Am. Ceram. Soc. 70(11), 793.
General Reading Binder, F. (1975), Radex-Rundschau 4, 531. Clougherty, E. V., Pober, R. L. (1964), Nucl. Metall 10, All. Emin, D., Aselage, T., Beckel, C. T., Howard, I. A., Wood, C. (Eds.) (1986), Boron-Rich Solids. New York: Am. Inst. Phys. Fluck, E. (Ed.) (1986), Gmelin Handbook of Inorganic Chemistry, Si, Suppl. Vol. B3: Silicon Carbide, Part 2. Berlin: Springer. Freer, R. (Ed.) (1990), The Physics and Chemistry of Carbides, Nitrides and Borides. Dordrecht: Kluwer. Matkovich, V. I. (Ed.) (1977), Boron and Refractory Borides. Berlin: Springer. Post, B., Glaser, F. W, Moskowitz, D. (1954), Acta Metall. 2, 20. Thevenot, F. (1990), /. Eur. Ceram. Soc. 6, 205.
Recommended Periodicals Planseeberichte fur Puhermetallurgie, Ortner, H. M. (Ed.), Reutte: Plansee-Tizit. Journal of Less-Common Metals, since 1992: Journal of Alloys and Components, Lausanne: Elsevier Sequoia. Raub, C. (Ed.). Journal of Hard Materials, Brookes, C.A., Field, X E., Warren, R. (Eds.). Abingdon: Carfax.
5 Glass-Ceramics Bruce Aitken and George Beall Corning Glass Works, Research and Development Division, Corning, NY, U.S.A.
List of 5.1 5.2 5.2.1 5.2.2 5.2.3 5.3 5.3.1 5.3.1.1 5.3.1.2 5.3.1.3 5.3.2 5.3.2.1 5.3.2.2 5.3.2.3 5.3.2.4 5.3.2.5 5.3.3 5.3.3.1 5.3.3.2 5.3.4 5.3.4.1 5.3.4.2 5.3.4.3 5.3.4.4 5.3.5 5.3.5.1 5.3.5.2 5.4 5.4.1 5.4.2 5.4.3 5.4.4 5.4.5
Symbols and Abbreviations Introduction Nucleation and Crystallization of Glass-Ceramics Theoretical Considerations Practical Considerations Examples Classification by Chemical Composition Silicate Glass-Ceramics Lithium Silicates Calcium Silicates Magnesium Silicates Aluminosilicate Glass-Ceramics p-Quartz Solid Solution (3-Spodumene (Keatite) Solid Solution Indialite (Hexagonal Cordierite) Nepheline Other Aluminosilicates Fluorosilicate Glass-Ceramics Mica (Sheet Silicates) Chain Silicates Phosphate Glass-Ceramics Apatite BPO 4 NZP SiP 2 O 7 Oxide Glass-Ceramics Spinel Perovskite Microstructure Dendritic Ultrafine Grained Cellular Membrane Relict House-of-Cards
Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.
269 270 270 271 272 274 276 276 276 277 277 278 278 279 280 280 280 280 281 283 285 285 286 286 286 287 287 287 288 288 289 290 290 290
268
5.4.6 5.4.7 5.4.8 5.5
5 Glass-Ceramics
Acicular Interlocking Coast-and-Island Lamellar-Twinned References
291 292 293 294
List of Symbols and Abbreviations
List of Symbols and Abbreviations a, c AG h H / k n ns nv t T 7^
crystal axes molar free energy change upon crystallization Planck constant enthalpy of fusion steady state nucleation rate in a one-component system Boltzmann constant composition variable steady state nucleation rate per unit volume of the epitaxial phase number of formula units per unit volume of liquid temperature in °C absolute temperature melting temperature
Vm x
molar volume of the crystal stoichiometric variable
£ rj A v a i
crystal growth rate viscosity diffusion j u m p distance vibrational frequency surface tension between crystal a n d liquid time
AVC Crb. FKR NZP r.e.m. TTT
automatic viscosity control cristobalite fluorrichterite NaZr 2 (PO 4 ) 3 replica electron micrograph transformation-temperature-time
269
270
5 Glass-Ceramics
5.1 Introduction The development of glass-ceramics is a recent advance in the science of materials. The dramatic growth in applications for these novel materials since the serendipitous discovery, some thirty years ago, of internal nucleation and crystal growth in lithium silicate glass (Stookey, 1985), is a testament to their usefulness and great versatility in a wide range of applications. Glass-ceramics are polycrystalline solids prepared by the controlled crystallization of glass. They are generally well over 50% crystalline by volume and are fine-grained with crystal sizes below 10 jam. A key feature of glass-ceramics is the maintenance of shape of a previously-formed glass article. This is most effectively achieved through internal nucleation and growth of crystals. There are several important requirements for choice of a glass-ceramic system. The composition must form a glass with adequate viscosity at the liquidus to allow shaping of the required glass article. Internal nucleation must be efficient, in order to produce a fine-grained body, and to avoid the adverse effects of directional crystallization from the glass surface. Crystal growth upon the nuclei must also be controlled to avoid large crystals whose grain boundaries frequently act as planes for ease of fracture propagation. In order to maintain the shape of the original glass article, deformation through gravitational sag or warpage due to volume changes during crystallization in a thermal gradient must be controlled. Glass-ceramics have significant advantages over traditional powder-processed ceramics. One is in the flexibility and ease of forming afforded by high speed processes such as rolling, pressing, blowing, and drawing. A total lack of internal
porosity is an important characteristic of glass-ceramics. The uniformity of microstructure and reproducibility of properties which depend on structural consistency is another major advantage resulting from the homogeneous nature of the melting process. The ability to produce unique properties inherent in extremely finegrained crystalline materials is also important. For example, transparency can be achieved in glass-ceramics from a combination of efficient nucleation and sluggish crystallization at high viscosities resulting in crystallites smaller than the wavelength of visible light. Also, homogeneous, low thermal expansion characteristics can be achieved because the stresses accompanying crystal anisotropy are minimized by the fine-grained nature of the crystallites. There are manufacturing advantages in the process economy associated with high volume glass making. Also, any defects present in the glass can be observed prior to crystallization allowing simple reject inspection. Although the published literature on glass-ceramics is not as extensive as that for glasses, for additional information the interested reader is directed to the books by Strnad (1986) and McMillan (1979).
5.2 Nucleation and Crystallization of Glass-Ceramics The properties of glass-ceramics are controlled by the physical properties of the crystalline phases developed in the glass upon heat treatment and by their microstructure - the textural relationship between the crystalline phases and the residual glass. The uniformity and reliability of these properties in glass-ceramics is a consequence of the uniform grain size of the crystalline phases. An important prerequi-
5.2 Nucleation and Crystallization of Glass-Ceramics
site, therefore, to the formation of glass-ceramics is efficient nucleation of the crystalline phases. Accordingly, the heat treatment (ceramming) of glasses to produce a glass-ceramic typically involves two or more steps: a lower temperature step to induce nucleation, and one or more higher temperature treatments to promote growth of the crystalline assemblage and to develop the desired microstructure. 5.2.1 Theoretical Considerations
Various workers have attempted to derive a mathematical model for the processes of nucleation and crystal growth. For example, James (1982) has derived the following expression for the steady state nucleation rate, /, in a one-component system:
nvkT I = -—^r-expl
-
3AG2kT
(5-1)
where nv is the number of formula units of crystal per unit volume of liquid, T is the absolute temperature, I is the diffusion jump distance, rj is the viscosity, a is the surface tension between crystal and liquid, vm is the crystal's molar volume, AG is the molar free energy change upon crystallization, and k is Boltzmann's constant. This relationship is strictly applicable to the case of homogeneous nucleation, i.e. where crystallization occurs within a homogeneous liquid without addition of foreign particles. Homogeneous nucleation, however, is a relatively rare phenomenon, occurring in only a few glasses, such as Li 2 Si 2 O 5 , BaSi 2 O 5 , and Si 2 P 2 O 7 , whose composition is the same as that of the crystallizing phase. No glass-ceramic systems of industrial importance are known to nucleate homogeneously. In most glass-ceramic systems, internal nucleation is heterogeneous and occurs by
271
the epitaxial growth of the dominant crystalline phase upon nuclei of an earlierformed phase. The latter is most commonly a relatively refractory and/or insoluble phase, such as rutile, anatase, ZrO 2 , ZrTiO 4 , Cr 2 O 3 , or one of the noble metals, but can also be the exsolved globules of an inmiscible glass. As a result, "nucleating agents" or "nucleants" such as TiO 2 , ZrO 2 , P 2 O 5 , Au, or Ag are specifically included as essential components in the bulk composition of most commercial glass-ceramics. Nevertheless, the process of heterogeneous nucleation is governed by essentially the same parameters that affect homogeneous nucleation, and, as a result, the equations describing heterogeneous nucleation have the same form as the above, but with ny replaced by ns, the number of formula units per unit volume of the epitaxial phase in contact with the nucleant, and with a replaced by the surface tension between the epitaxial phase and the nucleant. The latter is a measure of the degree of lattice mismatch between the nucleant and crystallizing phase, and, therefore, the effectiveness of heterogeneous nucleation depends in part on the structural relationship between nucleant and epitaxial phase. Although exact evaluation of the nucleation rate equation is not possible due to the lack of relevant data, this equation can be used as a crude guide for adjusting the composition and/or heat treatment of a glass-ceramic to achieve efficient internal nucleation. For example, the nucleation rate is expected to increase as AG becomes large. Although AG is largely beyond experimental control, introduction of components which preferentially enter into solid solution with the crystalline phase may lower its free energy relative to the liquid, thus increasing AG and, hence, the nucleation rate. The rate equation further
272
5 Glass-Ceramics
suggests that increasing viscosity will lower the nucleation efficiency, presumably due to impeded transport of nutrients to the nucleus. Thus reducing the viscosity at the optimum nucleation temperature is desirable, although in practice this is limited by sagging of the material during the nucleation hold. Finally, the presence of the factor a 3 in the above equation indicates that lowering the interfacial energy should have the largest effect on increasing nucleation efficiency. This might be accomplished by variations in glass composition, for example through the addition of small amounts of WO 3 or MoO 3 , which components are known to be effective in reducing surface tension. The rate of crystal growth is also governed by parameters similar to those used in the description of nucleation. This can be illustrated using an equation derived by Jackson (1967) for continuous growth by random attachment of atoms to surface sites:
hv
HAT
£ = 6nX2rjkT T exp m
H
-
(5-2)
The rate of crystal growth £ is, in this description, dependent on the enthalpy of fusion H, the diffusion jump distance X, the viscosity r\, the vibrational frequency v, and AT, the temperature difference between the melting temperature Tm and the growth temperature T Although the parameters governing nucleation and crystallization are similar, the dependence of the nucleation rate and the crystal growth rate on these parameters is not. Consequently, nucleation and crystal growth rates generally peak at distinct temperatures, with the maximum for crystal growth occurring at a higher temperature than that corresponding to nucleation (for an illustration of this effect, as well as a more complete treatment of the theoretical
basis of nucleation and growth, the interested reader is referred to Chap. 3 by Scherer in Vol. 9 of this Series). The heat treatment of a glass to form a glass-ceramic therefore typically includes at least two steps. The first of these is the nucleation hold: a soak or gradual heating ramp at relatively low temperature, usually about 50 to 100 °C above the annealing point of the glass. Following the nucleation hold, the temperature is raised rapidly to that of the crystallization step, at which point the nucleated glass is heated isothermally or at a slow rate until crystal growth is complete and the desired microstructure attained. 5.2.2 Practical Considerations In actual practice, the existing mathematical models have proven to be of little utility in determining the optimum conditions for the efficient internal nucleation of glass. Thus compositional adjustments, including the selection of appropriate nucleants, as well as changes in the temperature and time of heat treatment steps have relied mainly upon empirical observations. Nevertheless, it is possible to infer an experimental time-temperature profile for ceramming by controlling the apparent viscosity of a heated glass within a specified range, typically 109 to 10 11 N s m " 2 . An experimental automatic viscosity control (AVC) curve for a phosphate glass-ceramic is shown in Fig. 5-1. The viscosity of crystallizing glass should be held below l O ^ N s m ^ t o allow viscous flow to release stresses caused by differential crystallization and thereby prevent fracturing. The lower limit of 109 N s m " 2 is due to the need to avoid gravitational sag, which can lead to unacceptable distortion if the viscosity of the residual glass becomes too low.
5.2 Nucleation and Crystallization of Glass-Ceramics
273
CONTROL VISCOSITY = 1 x 1010 N • s • m"2
500
During the crystallization hold, distortion can arise not only from gravitational sag of the glass, but also from thermal gradients across the article, which can cause one portion to crystallize before the rest. As most crystalline phases are denser than the precursor glasses, shrinkage of several percent is typical and must be accommodated uniformly throughout the article. This is particularly true of massive glass bodies, which are slow to heat in the central portions because of their low thermal conductivity. Furthermore, exothermic effects can be severe in large articles for the same reason: thermal waves due to the crystallization of massive articles can cause the central portion to become up to 50 °C hotter than the other areas of the ceramming furnace. In view of the typical temperature regime, the heat treatment of glass to produce glass-ceramics can be described as subsolidus crystallization. The expected crystalline phases in glass-ceramics, therefore, are those of the equilibrium subsolidus assemblage appropriate for the bulk composition of the precursor glass and the temperature of the crystal growth step. However, in many glass-ceramic systems, the crystalline phases observed are metastable so that, with glass rather than a
Figure 5-1. Experimental automatic viscosity control curve for a phosphate glass-ceramic.
melt as the initial state, it is possible to form solid phases which never develop under conditions of "equilibrium crystallization". Perhaps the best example of this phenomenon is the precipitation of p-quartz solid-solutions from lithium aluminosilicate glasses when these are cerammed at about 900 °C for a relatively short time. (3-Quartz is not only metastable at this temperature, it also has no thermodynamic stability, i.e. this phase is not a member of any equilibrium assemblage at any temperature for these bulk compositions. Prolonged heating at 900 °C, or raising the ceram temperature, causes the P-quartz glass-ceramic to invert to a stable assemblage containing P-spodumene solidsolution, as illustrated by Fig. 5-2 a. Nevertheless, the early formed p-quartz glassceramics persist indefinitely when cooled to room temperature and such glass-ceramics can withstand indefinite thermal cycling between room temperature and 900 °C without inverting to a p-spodumene glass-ceramic. A convenient technique for displaying the relationship between metastable and stable phases for a given glass-ceramic composition is the use of a "TTT" diagram, which plots phase transformation boundaries as a function of temperature
274
5 Glass-Ceramics
you
V
900
9
(3 SPODUMENE SS /3 QUARTZ SS + /3 SPODUMENE SS
^^c^rr——
*n8A4 0
o
S.
CL
/3 QUARTZ SS
780 GLASS
•
,
f3 QUARTZ SS
720
1600
1 ' 1 ' 1 ' I
GLASS
-
^S^
1 15
J>^ T V ~ ""
M
1
1200
1 10 TIME (h)
t,
1400-
o
(a)
^
T
-
r^—^-^ K ^ ^ X .
(
— "
-
1000-
800-^L
^
-
^
^
^
^
^
*2£ff-s;
^
"
P
(b) 1 O.I
1
1.0 —^
1
10
1 100
•
^
^
*
Figure 5-2. (a) Time-temperature metastable phase diagram for the glass-ceramic composition SiO2 65 wt.%, A12O3 23 wt.%, Li2O 3.8 wt.%, MgO 1.8 wt.%, with excess TiO 2 2 wt.%, ZrO 2 2 wt.%, and As 2 O 5 1 wt.% (after Beall and Duke, 1969). (b) Crystallization in MgO • A12O3 • 3SiO 2 glass with addition of ZrO 2 , depicted as TTT diagram. QP (s.s.): solid solution of |3-quartz, K: cordierite, P: Mg-petalite, S: spinel, C: cristobalite, M: mullite, ZT: tetragonal ZrO 2 , ZM: monoclinic ZrO 2 , ZS: zircon, Q: phase similar to a-quartz, tx and tg: liquidus and glass-transformation temperatures (after Conrad, 1972).
r(h)
and time. Figure 5-2 a is a rather simple example for a multicomponent lithium aluminosilicate glass-ceramic nucleated with zirconium titanate, where the oxide nuclei separation temperatures and times were difficult to measure. A more complete TTT-curve was developed by Conrad (1972) for a simpler composition MgO • A12O3 • 3SiO2 with the addition of 6% ZrO 2 (Fig. 5-2 b). The typical C-shaped curves of metastable and stable phases are shown. This simple fourcomponent glass shows no fewer than
eight metastable phases (glass, P-quartz solid solution, a-quartz solid solution, Mgpetalite, spinel, mullite, tetragonal and monoclinic zirconia), as well as the stable assemblage cordierite, silica (cristobalite over the main thermal range), and zircon. 5.2.3 Examples As noted above, a good example of a glass that displays homogeneous nucleation is BaSi 2 O 5 . Heat treatment of barium disilicate glass by nucleating at 700 °C
5.2 Nucleation and Crystallization of Glass-Ceramics
for one hour and crystallizing at 850 °C for one hour suffices to convert this material to a fine-grained glass-ceramic consisting of a mixture of dendritic a-BaSi2O5 crystals and residual glass (MacDowell, 1965). During the nucleation hold, submicrometer, spherulitic nuclei of 0c-BaSi2O5 develop randomly throughout the glass, which has remained homogeneous up to the nucleation temperature with no evidence of liquid-liquid phase separation. The commercial lithium aluminosilicate glass-ceramics based on phases with either the P-quartz or P-spodumene structure are good examples of heterogeneous nucleation by a well-dispersed insoluble phase (Beall, 1986). In this case, the nucleating agent TiO 2 or the combination of TiO2 + ZrO 2 is deliberately added to the base glass. Ceramming is accomplished by subjecting the glass to a nucleation hold at about 800 °C, followed by a crystallization hold at about 900 °C (P-quartz glass-ceramic) or 1100°C (P-spodumene glass-ceramic). During the nucleation hold, the spherical droplets of an exsolved Ti-rich liquid phase crystallize to form a uniform dispersion of exceedingly fine-grained (<100 A) titanate crystallites. The latter, in turn, serve as the substrate for the heterogeneous nucleation of the silicate phases; thus both the nucleating agent and the major crystalline phase are heterogeneously nucleated. With a crystal growth hold at 900 °C, the result is a highly crystalline, yet transparent, glass-ceramic consisting of very fine-grained (~500 A) equant grains of a hexagonal lithium aluminosilicate phase with the P-quartz structure. If, however, crystallization takes place at 1100°C, a strong, opaque glass ceramic containing relatively coarse ( 1 2 jxm), interlocking grains of lithium aluminosilicate crystals with the P-spodumene structure is produced. Thus, in these mate-
275
rials, adjustment of the heat treatment gives one control of not only the microstructure, but also the nature of the dominant crystalline phase. Whereas lithium aluminosilicate glasses are internally nucleated by titanate crystallites, lithium silicate glasses are readily nucleated by a dispersed noble metal such as Ag or Au. Thus, the effectiveness of a given nucleant is strongly dependent upon glass composition and, in particular, the structure of the epitaxial phase. In the case of photo-sensitive lithium silicate glass-ceramics (Stookey, 1954), the nucleation event can be catalyzed by exposure to ultraviolet radiation. Cerous (Ce 3+ ) ions present in the glass are photo-oxidized, leading to the precipitation of metallic silver in the exposed portion of the glass: Ce 3 + + Ag + + /zv->Ce4 + + Ag° By subjecting the exposed glass to a nucleation hold, the silver particles coalesce to the point where they can serve as the substrate for the subsequent crystallization of dendritic lithium metasilicate (Li2SiO3). By using a mask during the exposure step, nucleation and, hence, later crystallization can be confined to selected areas of the glass. Heterogeneous nucleation in glass-ceramics can take place on substrates other than insoluble crystalline phases. In the case of mullite glass-ceramics, aluminarich droplets separate from the siliceous matrix as the precursor aluminosilicate glass is quenched from the melt (MacDowell and Beall, 1969). Heat treatment of this phase-separated glass at 950 °C or above causes the aluminous droplets to crystallize to mullite. Thus, the physical surface between the two immiscible glasses acts as the nucleation site.
276
5 Glass-Ceramics
5.3 Classification by Chemical Composition Class-ceramics are most conveniently classified by their bulk chemical composition and more particularly by the composition of the major crystalline phase. The broadest classification includes silicates, phosphates, and oxides. Silicates can be further subdivided into simple silicates, aluminosilicates, and fluorosilicates. 5.3.1 Silicate Glass-Ceramics Simple silicate glass-ceramics are composed primarily of alkali and alkaline earth silicate crystals whose properties dominate that of the glass-ceramic. The most important are the lithium silicates, both lithium metasilicate (Li2SiO3) and lithium disilicate (Li2Si2O5), enstatite (MgSiO3), diopside (CaMgSi2O6), and wollastonite (CaSiO3). 5.3.1.1 Lithium Silicates Lithium silicate glass-ceramics consist of two composition groups, both of commercial importance. The first, nucleated with P 2 O 5 , develop high expansion glassceramics which match the thermal expansion of several nickel-based superalloys, and are used in a variety of high-strength hermetic seals, connectors, and feedthroughs (Headley and Loehman, 1984). The second group, photosensitively nucleated by colloidal silver, produce a variety of chemically machined materials which are useful as fluidic devices, display screens, lens arrays, and other patterned devices. Lithium disilicate glass-ceramics nucleated with P 2 O 5 are characterized by high body strength, 140-210 MPa, good fracture toughness, ~ 3 MPa • m 1/2 , and moderate to high thermal expansion coef-
ficient, 80-130 x 10" ^C"" 1 . The compositions typically comprise 70-85 weight percent SiO 2 , 10-15 Li 2 O, 3-10 A13O3, 1-5 P 2 O 5 as well as a minor amount of other modifiers including K 2 O, Na 2 O, CaO and ZnO. The glasses phase separate on heat treatment and lithium orthophosphate (Li3PO4) precipitates as the first crystal phase. Lithium metasilicate and/or lithium disilicate then form, the latter predominating with further heat treatment. Cristobalite and P-spodumene are often auxiliary phases, and residual glass is usually present in excess of 15 volume percent. The microstructure consists of tabular interlocking lithium disilicate crystals typically from 1 to 10 |im in diameter encased in residual glass and other crystalline phases. The randomly oriented tabular crystals appear to deflect or blunt cracks in such a way as to impede crack growth, thus accounting for the high strength and toughness. Dielectric properties are surprisingly good, with dielectric constants below 6 and loss tangents below 0.01 over a wide range of temperature and frequency. Photosensitive lithium silicate glass-ceramics contain metals, namely 0.1% Ag and 0.001% Au, which can be precipitated thermally after ultraviolet sensitization. The metallic colloids so produced nucleate a dendritic form of lithium metasilicate which is far more easily etched in hydrofluoric acid than is the parent glass, allowing an irradiated pattern to be selectively removed. The resulting photo-etched glass can then be flood exposed to ultraviolet rays and heat-treated beyond the temperature region of metastable lithium metasilicate. The stable lithium disilicate phase is then produced and the resulting glass-ceramic is strong (~140 MPa), tough, and faithfully replicates the original photoetched pattern.
277
5.3 Classification by Chemical Composition
Table 5-1. Silicate glass-ceramic compositions. wt.%
Fotoform/ Fotoceram Corning 8603
SiO 2 Li 2 O MgO CaO A12O3 Na 2 O K2O Ag Au CeO 2 SnO 2 Sb 2 O 3 B2O3
79.6 9.3 — — 4.0 1.6 4.1 0.11 0.001 0.014 0.003 0.4 — —
P2O5
Major crystal phases
Li 2 O-SiO 2 G.E./Sandia
71.8 12.6 — — 5.1 _ 4.8 — — — — — 3.2 2.5
MgO-SiO 2 Corning
58.0 0.9 25.0 — 5.4 —
ZnO MnO Fe 2 O 3 S ZrO.
lithium lithium disilicate, metasilicate, lithium metasilicate, lithium disilicate cristobalite
Specific applications include magnetic recording head pads, fluidic devices, cellular faceplates for gas-discharge displays, and charged plates for ink-jet printing. 5.3.1.2 Calcium Silicates For over two decades, inexpensive glassceramics based on blast furnace slags have been produced in Eastern Europe. Referred to as "slag-sitall" in the Soviet Union, these glass-ceramics presently constitute the largest volume application for crystallized glass. The most popular slag-sitall is a white product manufactured in the U.S.S.R. from low-iron (<0.5% Fe 2 O 3 ) slag (Berezhnoi, 1970). Wollastonite (CaSiO3) is the major phase present in ~ 1 |im equiaxial grains. The glass is formed into sheets with embossed rollers to create patterned wall cladding. It is heat treated near
Minelbite Hungary
54.0 — 33.0 — — —
60.9 — 5.7 9.7 14.2 3.2 1.9
Slag-Sitall U.S.S.R.
55.5 — 2.2 24.8 8.3 5.4 0.6
-
-
-
— _
— —
2.0 2.5 0.6
1.4 0.9 0.3 0.4
1.07
13.0 diopside
wollastonite
enstatite, enstatite, P-spodumene, zircon tet. zirconia
1000 °C. Zinc-manganese sulfide acts as a thermal nucleated agent for internal crystallization of calcium silicate. Recently attractive translucent architectural panels of related wollastonite glassceramics have been manufactured by Nippon Electric Glass and sold in Japan and the U.S.A. under the trade name Neoparium. 5.3.1.3 Magnesium Silicates Although no commercial applications have yet been found, glass-ceramics based on enstatite (MgSiO3) (Lee and Heuer, 1987; Beall, 1989) are interesting because this phase undergoes a martensitic transformation on cooling, producing toughening from fracture energy absorption by fine lamellar twinning. Unfortunately, enstatite does not form a stable glass, so compositions must be diluted with other
278
5 Glass-Ceramics
glass-forming components. Nevertheless, refractory, tough and fine-grained enstatite glass-ceramics have been produced in the SiO2-MgO-ZrO2 and SiO2-MgOAl 2 O 3 -Li 2 O-ZrO 2 systems. These materials contain from 50-85 weight percent enstatite, with auxiliary phases zircon, p-spodumene, minor tetragonal zirconia and small amounts of glass. 5.3.2 Aluminosilicate Glass-Ceramics Aluminosilicate glass-ceramics are important commercial materials because of the combination of their exceptional thermal shock resistance, thermal stability, and outstanding chemical durability. In particular, glass-ceramics based on the p-quartz or P-spodumene solid solutions in the Li aluminosilicate system have exceptionally low thermal expansion coefficients. As these phases can be melted and quenched to a stable glass, this permits the manufacture of virtually monophase P-quartz or P-spodumene glass-ceramics which contain only minor amounts of nucleant phases and residual glass. 5.3.2.1 p-Quartz Solid Solution In the Li aluminosilicate system, a hexagonal phase with the P-quartz structure is known for compositions ranging from near SiO2 to LiAlSiO4. In other words, the p-quartz solid solution can be described as Li2O • A12O3 • nSiO 2 , where n ranges from 2 to 10. Over most of this range, p-quartz is actually a metastable phase. The Li-rich endmember, LiAlSiO4 (P-eucryptite), has an ordered arrangement of Al and Si, resulting in a doubling of its c axis, but is otherwise structurally identical to the intermediate members of this series; compositions with n>4 have disordered Si/Al distributions and are truly isostructural with P-SiO2. Li-rich compositions from
the latter range have been referred to as "virgilite". P-Quartz glass-ceramics are made by crystallizing TiO2- or TiO 2 + ZrO2-nucleated Li aluminosilicate glasses at 850-900 °C (Beall and Duke, 1969). Despite the metastability of P-quartz, these glass-ceramics persist indefinitely and can survive repeated thermal cycling provided that a maximum temperature of about 900 °C is not exceeded. If heated above 900 °C, P-quartz will transform to P-spodumene. A more general compositional representation of the P-quartz solid solution is (Li 2 ,R)O- Al 2 O 3 -«SiO 2 , where R is a small divalent cation, typically Mg or Zn. Replacement of Li by Zn and, in particular, Mg results in an increase in the thermal expansion coefficient of P-quartz. Thus, whereas the expansion coefficient of a pure Li P-quartz is about -15 x 10 " 7 °C ~ * from 25 to 300 °C, Mg- and/or Zn-substituted varieties can have zero or very small positive expansion coefficients. In commercial glass-ceramics, advantage is taken of the compositional flexibility of p-quartz. In the first place, Mg and Zn are included to produce materials with near zero thermal expansion and, consequently, excellent thermal shock resistance. Furthermore, n in the above formula is selected to range between 6 and 8, because the high silica content of these compositions furnishes a melt that is sufficiently viscous to be rolled, pressed, blown, and vacuum formed. The combination TiO 2 + ZrO 2 has proven to be the most effective nucleating agent in precipitating p-quartz from lithium aluminosilicate glasses. Heat treatment of glasses so nucleated yields ZrTiO 4 , a phase with the fluorite structure, which serves as the substrate for the subsequent nucleation and epitaxial growth of P-quartz crystallites. P-Quartz crystals with grain sizes on the order of 60 nm can be
5.3 Classification by Chemical Composition
produced if the nucleant concentration is on the order of 4 weight percent, resulting in a transparent glass-ceramic. The combination of transparency, low thermal expansion, optical polishability, and strength greater than glass has generated a multitude of applications for P-quartz glass-ceramics, including see-through cookware, telescope mirror blanks, woodstove and fire windows, infrared-transmitting range tops, and optically stable platforms, including ring-laser gyroscopes.
279
from heat treatments at temperatures in excess of 1000°C (Stookey, 1959). Glass-ceramics containing p-spodumene are coarser-grained than their P-quartz analogues. Grain sizes are typically in the range of 1-2 |im and, as a result, these glass-ceramics are opaque. If TiO 2 is used as a nucleating agent instead of the combination TiO 2 + ZrO 2 , the phase transition from P-quartz to P-spodumene, which occurs between 900 and 1000 °C during the ceramming process, is accompanied by crystallization of rutile, yielding a glass-ceramic with a high degree of opacity. As with p-quartz glass-ceramics, the thermal expansion of these materials is very low and can be tailored to the desired value by adjusting the Li/Mg ratio or the total silica content (cf. Fig. 5-3). Corningware is a good example of a P-spodumene glass-ceramic, and is formed by crystallizing a TiO2-nucleated aluminosilicate glass at a maximum temperature of 1125°C. This material is highly crystalline (>93vol.%) containing P-spodumene as the dominant phase and minor amounts of spinel, rutile, and residual siliceous glass. The coarse-grained, interlocking microstructure of p-spodumene crystals gives this material its relatively
5.3.2.2 p-Spodumene (Keatite) Solid Solution p-Spodumene is a tetragonal phase that is isostructural with keatite which, like P-quartz, is a polymorph of SiO 2 . p-Spodumene is therefore characterized by the same stoichiometry as P-quartz, although the compositional range of the solid solution is more restricted, with n ranging from 4 to 10. P-Spodumene glassceramics can be made from the same glasses that yield p-quartz glass-ceramics simply by altering the heat treatment: pquartz glass-ceramics are formed by crystallizing at or below 900 °C, whereas Pspodumene glass-ceramics are obtained
n= 4
0.28 Co 0
101
en <
a. X IxJ
-j
LLJ
UNI1
O i
0.24 — 0.20 — n =5
0.16 — 0.12 0.08 _ 0.04 0.00
—
/
^»*
•
n=6
my^
n = 7 %^"\
****
#
•
# #
^.
•*"
#
n = 8 n = 9
"U.UH-
-0.08 0
t i l l
200
400
1
.
1
1
1
600 800 1000 TEMPERATURE (°C)
.
1
1200
Figure 5-3. Volume thermal expansion in Li2O • A12O3 • «SiO2 (after Ostertag et al., 1968).
280
5 Glass-Ceramics
high abraded flexural strength of about 100 MPa. 5.3.2.3 Indialite (Hexagonal Cordierite) Mg aluminosilicate glass-ceramics based upon indialite, the hexagonal, high temperature polymorph of cordierite (Mg 2 Al 4 Si 5 O 18 ) are characterized by excellent dielectric properties, high strength, good thermal stability and shock resistance. Indialite is isostructural with the well known beryllium silicate, beryl. As with the latter, the thermal expansion of indialite is low and anisotropic; the c axis expands and the a axis contracts with rising temperature, resulting in virtually zero volume expansion. Similar to Li aluminosilicates, indialite is efficiently precipitated from Mg aluminosilicate glasses by using TiO 2 as a nucleating agent (Stookey, 1960). In order to optimize the liquidus viscosity of the precursor glass, the commercial glass-ceramic, which is used for missile radomes, is formulated to be silica-rich with respect to stoichiometric Mg 2 Al 4 Si 5 O 18 , resulting in crystallization of cristobalite as well as indialite. Consequently, the glass-ceramic has an intermediate expansion coefficient of 45 x 1 0 - 7 o C - i (Q-700°C); its loss tangent and dielectric constant at 8.6 GHz are, respectively, 0.0003 and 5.5. 5.3.2.4 Nepheline Fine-grained nepheline (NaAlSiO4) glass-ceramics can be formed from TiO 2 nucleated Na aluminosilicate glasses (Duke et al., 1967). Nepheline is a stuffed derivative of tridymite, a high temperature polymorph of silica. TiO 2 is again used as an internal nucleating agent, and crystallizes as anatase upon heat treatment, thereby increasing the opacity of the glassceramic. Barium is added to the commer-
cial formulation in order to promote the formation of celsian (BaAl2Si2O8), which has a lower thermal expansion coefficient (SOxlO'^CT 1 ) than nepheline, thereby improving the thermal shock resistance of the glass-ceramic. These materials have thermal expansion coefficients around 5 0 x l O " 7 o C " S near that of nepheline, and reflecting the expansion behavior of the tridymite framework. A typical composition of this material, which is used for a wide range of products including large electric insulators and heat-resistant kitchenware, is given in Table 5-2. 5.3.2.5 Other Aluminosilicates Mullite glass-ceramics can be produced from modified binary Al 2 O 3 -SiO 2 glasses (MacDowell and Beall, 1969). In these materials, internal nucleation of mullite is catalyzed by phase separation of the bulk material into alumina-rich droplets within a connected siliceous glass. Upon heat treatment, the droplets are converted into mullite spherulites. Transparent mullite glassceramics, when doped with ions such as Cr 3 + , have unique luminescent characteristics. Glass-ceramics in the cesium aluminosilicate system are highly refractory. Pollucite (CsAlSi2O6) glass-ceramics, containing mullite as a secondary phase, can be made by heat treating Cs aluminosilicate glasses at 1600°C. These materials have a thermal stability that is 350 °C higher than that of fused silica; due to their refractory nature, they must be melted at 1900 °C and formed near 1800°C. 5.3.3 Fluorosilicate Glass-Ceramics Fluorosilicate glass-ceramics are characterized by unique mechanical properties dependent upon highly anisotropic crystals which assume a one- or two-dimen-
281
5.3 Classification by Chemical Composition
Table 5-2. Aluminosilicate glass-ceramics. P-quartz
Li 2 O Na 2 O K2O MgO ZnO BaO Fe 2 O 3 TiO 2 ZrO 2 A12O3 SiO2 P2O5
As 2 O 3 Phases
Na 2 O K2O Cs 2 O MgO CaO BaO Fe 2 O 3 TiO 2 ZrO 2 A12O3 SiO 2 As 2 O 3 Phases
P-spodumene
Visions Corning
Zerodur Schott
Neoceram Narumi
Corningware Corning
2.7 0.2 0.1 1.8 1.0 0.8 0.1 2.7 1.8 19.2 68.8 — 0.8
3.7 0.5 — 1.0 1.4 — — 2.3 1.9 25.3 55.5 7.9 0.5
4.2 0.6 0.3 0.5 — — — 2.0 2.3 22.6 65.1 1.2 1.1
2.8 0.4 0.2 2.6 1.0 _ 0.1 4.7 0.1 17.8 69.7 — 0.6
P-quartz, ZrTiO 4
P-quartz, ZrTiO 4
P-quartz, ZrTiO 4
P-spodumene, rutile
Code 9606 Corning
Code 9609 Corning
Corning experimental glass
Corning experimental glass
— 14.7 0.1 — 0.1 8.9 — 19.8 56.1 0.8
13.5 — _ — — 5.5 — 6.6 _ 29.8 43.5 1.1
__ — — — 10.0 — _ — 40.1 50.0 —
— 25.0 — _ — — — — 40.0 35.0 —
indialite, rutile, MgTi 2 O 5 , cristobalite
nepheline, celsian, anatase
mullite
pollucite, mullite
sional form. Thus, mica glass-ceramics display mechanical machinability, whereas glass-ceramics based on amphiboles and other chain silicates have shown extreme strength and toughness. The fluorine anion is required in both cases to stabilize the mica (sheet) and amphibole (chain) structures.
5.3.3.1 Mica (Sheet Silicates) Machinable glass-ceramics are based on internally nucleated fluormica crystals in glass. One commercial material, Macor, has found wide application in such diverse and specialty areas as precision electrical insulators, vacuum feed throughs, win-
282
5 Glass-Ceramics
dows for microwave tube parts, sample holders for field ion microscopes, seismograph bobbins, gamma ray telescope frames, and boundary retainers on the space shuttle. The precision machinability of Macor with conventional metal-working tools, combined with high dielectric strength (~ 40 kV/mm) and a very low helium permeation rate, is particularly important in high-vacuum applications. Although the Macor glass-ceramic is based on the mica fluorphlogopite (KMg 3 AlSi 3 O 10 F 2 ), this stoichiometry does not form a glass. The bulk composition has to be altered largely through additions of B 2 O 3 and SiO2 to form a stable glass (see Table 5-3). The boric oxide component is particularly important in reducing the viscosity of the residual glass, thereby allowing preferential lateral growth of mica. The Macor composition is thus melted to an opal glass which is subsequently crystallized by heating to a maxi-
mum temperature of 950 °C (Chyung et al., 1974). It goes through a metastable crystallization sequence starting with the phase chondrodite (2Mg 2 Si0 4 • MgF 2 ), which crystallizes in the magnesium-rich matrix at the interface of the aluminosilicate droplets that constitute the parent opal glass. The chondrodite subsequently transforms to norbergite (MgSiO4 • MgF 2 ), which finally reacts with the components in the residual glass to produce fluorphlogopite mica and minor mullite. Recently, another commercial material, Dicor, has been developed for use as dental restorations. This glass-ceramic, with improved chemical durability and translucency over Macor, is based on the tetrasilicic mica, KMg 2 5 Si 4 0 1 0 F 2 (Grossman, 1972). Good strength (~ 150 MPa) is associated with the development of anisotropic flakes at relatively high temperatures (>1000°C). Translucency is achieved by roughly matching the refractive index of
Table 5-3. Fluorosilicate glass-ceramic compositions. Pyroceram Tableware Corning
wt.%
Macor Corning
Dicor Dentsply
SiO 2 B2O3 A12O3 MgO K2O Na 2 O CaO Li 2 O BaO
47.2 8.5 16.7 14.5 9.5 — — — — — — — — 6.3
56-64 0-2 15-20 12-18 — — — — — — 0-5 0.05 4-9
67.1 1.8 14.3 4.8 3.0 4.7 0.75 0.3 1.0 0.2 — — 3.5
57.3 2.0 — 8.8 8.0 20.2 — — — — — — 6.2
fluorphlogopite
tetrasilic fluormica
F-K-richterite, cristobalite
canasite
P2O5
Sb 2 O 3 ZrO 2 CeO 2 F Major crystalline phases
Code 9634 Corning
5.3 Classification by Chemical Composition
both crystal and glass while maintaining a fine-grained (~1 jim) crystal size. Ceria is added to simulate the fluorescent character of natural teeth. The unique features of Dicor for dental restorations include the close match to natural teeth in both hardness and appearance. The glass-ceramic may be accurately cast using a lost-wax technique and conventional dental laboratory investment molds. The high strength and low thermal conductivity of the material provide advantages over conventional metal-ceramic systems. 5.3.3.2 Chain Silicates In order to improve the basic body strength of glass-ceramics, polymeric crystals, in which chains of silica tetrahedra form a rigid backbone, have been grown in acicular form in glass. The texture of these glass-ceramics resembles that of natural nephrite jade, whose interlocking and acicular microstructure is responsible for its toughness. Two chain silicates have been identified as capable of producing tough glass-ceramics: potassium fluorrichterite and fluorcanasite. Potassium Fluorrichterite Glass-ceramics with the amphibole potassium fluorrichterite (KNaCaMg5Si8O22F2) as the principal crystalline phase possess great strength and toughness due to their random acicular microstructure in which fractures follow a tortuous path around rod-like crystals. Complex fluorosilicate glasses in the system SiO2-MgO-CaONa 2 O-K 2 O-F, with minor additions of A12O3, P 2 O 5 , Li 2 O, and BaO, have been found to form such glass-ceramics. Table 5-4 lists an optimized composition with its derivative glass-ceramic phases. It was found important to formulate a bulk composition substantially richer in silica than
283
that of stoichiometric richterite. This yielded a stable glass with sufficient viscosity at the liquidus to meet high-speed forming requirements. The excess silica, crystallizing in the form of cristobalite, also increased the final thermal expansion coefficient of the glass-ceramic, enabling a compressive glaze to be applied. The early stages of nucleation in this glass-ceramic are controlled by an amorphous emulsion in which one of the two phases is evidently close to tetrasilicic fluormica, KMg 2 + 0 5 x Li 1 _ : x Si 4 O 1 0 F 2 , in composition. Crystallization of this component is rapid near 600 °C. Because fluormica incorporates the major fluxes in the system, the crystallization occurs at very high viscosity. Precipitation of diopside (CaMgSi2O6) follows above 700 °C, and metastable mica and diopside then react above 850 °C with the residual glass to produce the stable assemblage richterite + cristobalite, the latter growing above 900 °C. The composition of the residual glass was calculated to be siliceous and enriched in A12O3 and P 2 O 5 , indicating strong chemical resistance. Combined with the chemical stability of the constituent crystals, richterite and cristobalite, this allows a glass-ceramic of exceptional chemical durability. The high thermal expansion coefficient ( l l S x K r ^ C T 1 from 0-300°C) of this material allows the development of compressive strengths through conventional glazing. Thus, the flexural strength of the body (150 + 15 MPa) can be increased to 200 ± 15 MPa. The final glazed material is high-gloss white and displays a translucency similar to that of bone china. This glass-ceramic is currently being manufactured as high-performance institutional tableware and mugs for the retail Corelle line.
Table 5-4. K-F-richterite glass-ceramic: estimated phase assemblage and composition. wt.%
Amphibole F-K-richterite
-50% F-K-Ra
Mica taeniolite
KNaCaMg 5 Si 8 O 22 F 2
a
57.3 — 24.1 6.7 3.7 5.7 — _ — — 4.5
KMg 2 LiSi 4 O 10 F 2 28.7 — 12.1 3.4 1.9 2.9 — — — — 2.3
59.3 — 19.9 — — 11.6 3.7 — — — 9.4
Cristobalite
-20% Crb c
95SiO2 • 5LiAlO2 5.9 — 2.0 — _ 1.2 0.4 — — — 1.0
95.0 4.0 — — — — 1.0 — — — -
19.0 0.8 — — — — 0.2 — — — -
Total crystals
bulk
80%
(anal.)
Residual glass -20% (calc.)
53.6 0.8 14.1 3.4 1.9 4.1 0.6 — — — 3.3
67.1 1.8 14.3 4.7 3.0 4.8 0.75 0.3 1.0 0.2 3.5
68.6 5.1 1.5 6.6 5.6 3.6 0.8 1.5 5.1 1.0 1.0
102.0 0-F2.0
103.9 0~F3.9
101.5 O^Fl.5
100.4 0~F0.4
100.0
100.0
100.0
100.0
F-K-R: fluorrichterite;
b
F-T: fluortaeniolite;
c
Crb: cristobalite.
en
3-Cerc
SiO2 A12O3 MgO CaO Na 2 O K2O Li 2 O BaO P2O5 Sb 2 O 3 F
-10% F-T b
3
8"
5.3 Classification by Chemical Composition
Fluorcanasite Fluorcanasite (Ca5K2 _ 3 Na 3 _4Si12O30F4) has been synthesized from glasses close to its stoichiometry. Internal nucleation is achieved through precipitation of CaF 2 crystallites and spherulitic growth of canasite upon these nuclei. Addition of excess calcium fluoride to the composition results in improved nucleation and a finer-grained material. Thus, canasite glass-ceramics can be highly crystalline and essentially monophase. Canasite glass-ceramics show typical flexural strengths near 300 MPa, a Young's modulus near 80 GPa, and a thermal expansion coefficient of about 125 x l O " 7 0 ^ 1 . The strain at rupture is approximately 0.35, high for a silicate material. The measured fracture toughness of 5.0 MPa • m 1/2 infers a fracture surface energy of approximately 150 J/m2, higher than that reported for natural nephrite jade. Fluorcanasite glass is easy to melt, having a viscosity curve some 150°C lower than that of soda-lime silicate glass. Although it has a relatively low liquidus viscosity (about 250Nsm~ 2 at 950°C), it can still be rolled, pressed, or cast. It can be crystallized below 900 °C in less than one hour. Because of its lower silica content, it is inferior in chemical durability to sodalime glass, but nevertheless is far superior to many other building materials such as marble. Potential applications for fluorcanasite glass-ceramics include architectural cladding, interior partitioning, thin housewares, and magnetic memory disk substrates. 5.3.4 Phosphate Glass-Ceramics Phosphate glass-ceramics do not have nearly the commercial importance of their silicate analogues, possibly due to their higher material costs and generally poorer chemical durability. Nevertheless, many
285
phosphates possess a number of unique material advantages, such as biocompatibility, which render them superior to silicates for certain applications. Furthermore, pyrophosphates and, particularly, orthophosphates have excellent durability, allowing them to be competitive with traditional silicate materials. 5.3.4.1 Apatite Apatite, Ca 5 (PO 4 ) 3 (OH,F), is a hexagonal, volatile-containing calcium orthophosphate. As hydroxyapatite [Ca5(PO4)3OH] is the major constituent of bone, synthetic materials consisting of or containing apatite are expected to exhibit biocompatibility or even bioactivity, the ability to bond with bone. Fluorapatite glass-ceramics have been prepared from fluorine-bearing CaAl phosphate glasses as well as alkali-MgCa aluminosilicate glasses containing from 2 to 10% P 2 O 5 (Vogel and Holand, 1989). CaAl phosphate glasses exhibit poor internal nucleation, with apatite developing as dispersed spherulites upon heat treatment near 500 °C. Crystallization is completed by subsequent precipitation of (Al, Fe)PO 4 . The silicophosphate glasses are characterized by microscopic phase separation involving three distinct glassy phases. Heat treatment from 600 to 1050 °C results in the initial nucleation of apatite on the surface of a CaO-P2O5-F-rich glassy phase. At higher temperature, reaction between the other two inmiscible liquids, one siliceous and the other R 2 O-Al 2 O 3 -F-rich, leads to the crystallization of mica. Both of these synthetic glass-ceramics are characterized by bioactivity and have been successfully used as implants in Germany. Moreover, the presence of mica as an additional phase in the silicophosphate material imparts machinability to this glass-ceramic.
286
5 Glass-Ceramics
5.3.4.2 BPO 4
5.3.4.3 NZP
Very fine-grained glass-ceramics containing tetragonal BPO 4 as the sole crystalline phase disseminated in an amorphous silica-rich matrix can be made from ternary glasses in the system B 2 O 3 -P 2 O 5 SiO2 (MacDowell, 1989). BPO 4 is isostructural with (3-cristobalite, a high temperature polymorph of SiO 2 . This phase can be nucleated homogeneously from a featureless glass upon heat treatment at temperatures as low as 900 °C, yielding a transparent glass-ceramic. Ceramming at 1000 to 1100°C produces coarser 0.2 to 0.5 jim grain sizes and, hence, opacity. Crystallization of these materials results in a remarkable improvement in chemical durability, particularly in neutral and acidic solutions, where weight losses of BP0 4 glass-ceramics are seen to be more than three orders of magnitude less than those of the precursor glasses. The thermal expansion coefficient of BP0 4 glass-ceramics ranges from 45 to 65xlO~ 7 o C~ 1 , with silica-rich compositions having the lowest coefficients. The materials have exceptional dielectric properties, with DC resistivities of 1016 at 250 °C, loss tangents less than 10 ~ 3 below 200 °C, and dielectric constants of 4.5. Heat treatment between 900 and 1100°C of similar glasses made under reducing conditions yields a hydrogen microfoam or "gas-ceramic". These are unique lightweight materials consisting of 1-10 jam hydrogen-filled bubbles which are uniformly dispersed in a BPO 4 glassceramic matrix. The hydrogen is evolved upon ceramming, possibly due to a redox reaction involving structural OH" groups and reduced phosphorus species, such as phosphate (PO3"3) radicals. These materials can have densities as low as 0.5 g/cm3 and dielectric constants as low as 2.
NZP [NaZr2(PO4)3] is a hexagonal orthophosphate which exhibits extensive solid solution. For example, Na can be replaced by most mono- and divalent cations, including the other alkalis, alkaline earths, Zn, Cd, and Pb; most tri- and higher valent transition metals, such as Nb, Ti, Fe 3 + , as well as Al, Ga, and Sn can substitute for Zr. Fine-grained NZP glassceramics can be prepared from a wide range of Zn and/or alkaline earth modified transition metal phosphate glasses by ceramming at temperatures between 800 and 1000 °C (Aitken, 1989). The presence of > 8 wt.% TiO 2 is sufficient to ensure good internal nucleation. The outstanding property of these materials is their extraordinary range in thermal expansion. Measured values of the expansion coefficient from room temperature to 300 °C run from
-30 to esxio^c- 1 . 5.3.4.4 SiP 2 O 7 Silicon phosphate (SiP2O7) glass-ceramics can be made from simple binary glasses in the system SiO 2 -P 2 O 5 through heat treatment at 1000 to 1100°C (Weeding et al., 1985). These glasses do not contain an added nucleating agent and, thus, SiP 2 O 7 apparently nucleates homogeneously from the precursor glass. Another binary compound, Si 5 O(PO 4 ) 6 can also be crystallized from these glasses by heat treating at lower temperature. These materials are of scientific interest as SiP 2 O 7 and Si 5 O(PO 4 ) 6 are among the very few crystalline solids, stable at atmospheric pressure, in which silicon is octahedrally coordinated by oxygen. The unusually high coordination number for silicon is reflected by the relatively large expansion coefficient of 60 x 10" ^ C " 1 of these materials. Due to
5.3 Classification by Chemical Composition
volatilization of phosphorus during heat treatment, the surface of these glass-ceramics becomes sufficiently enriched in silica that it remains amorphous; thus, these materials are self-glazing. 5.3.5 Oxide Glass-Ceramics As network formers such as SiO2 and P 2 O 5 represent the dominant component of most glasses, heat treatment typically results in the crystallization of silicates or phosphates. Nevertheless, true oxide phases, such as spinels or perovskites, can constitute the major crystalline phase in glass-ceramics made from certain aluminarich silicate glasses or highly modified silicate and phosphate glasses. Although none of these are, as yet, commercial materials, they are nonetheless of great interest for their unusual optical and, especially, electrical properties. 5.3.5.1 Spinel Spinels are cubic oxide phases with the general formula AB 2 O 4 , where A is commonly a tetrahedrally-coordinated divalent metal such as Zn, Fe, or Mg, and B an octahedrally-coordinated metal such as Al, Cr, or Fe. Spinels ranging in composition from gahnite (ZnAl 2 O 4 ) towards true spinel (MgAl2O4) can be crystallized from alumina-rich Zn or ZnMg aluminosilicate glasses (Beall and Duke, 1969). ZrO 2 is the most efficient nucleating agent for these materials. Upon ceramming at 1000 °C, following a nucleation hold at about 800 °C, an extremely fine-grained (< 500 A diameter) and, hence, transparent glass-ceramic is produced. These materials can retain their transparency up to about 1200 °C and, thus, are more refractory than the commercial p-quartz glass-ceramics, suggesting possible applications as lamp envelopes.
287
5.3.5.2 Perovskite Perovskites are oxide phases with the ABO 3 stoichiometry, where A is a relatively large 8- to 12-coordinated metal such as an alkali or alkaline earth, and B is a smaller, octahedrally-coordinated higher valent metal such as Ti, Zr, or Nb. Strictly speaking, peroskites are cubic, but the term is used here to refer to both true perovskites as well as related phases which show slight structural deviations from cubic symmetry. Perovskite glass-ceramics can be made from highly modified silicate and phosphate glasses, and are characterized by unusual electrical properties such as ferroelectricity or high conductivity. BaTiO 3 , a ferroelectric phase used in the fabrication of ceramic capacitors, is a familiar example of a perovskite. This phase can be crystallized from highly modified BaTi aluminosilicate or borosilicate glasses by heat treatment between 700 and 800 °C (Herczog, 1964). Although the nucleation mechanism in these glasses is not understood, it is likely that the precursor glasses are phase separated into immiscible siliceous and TiO2-rich droplets, and that BaTiO3 nucleates on the surface of the latter. Subsequent heat treatment at 900 to 1000 °C results in the crystallization of hexacelsian (BaAl2Si2O8) from the residual glass. In this way, highly crystalline ferroelectric glass-ceramics containing up to 60 vol. % BaTiO3 with dielectric constants as high as 1200 at 25 °C, 1 kHz can be formed. As with ceramic BaTiO 3 , various oxide dopants can be added to these materials to vary the temperature at which the dielectric constant attains a maximum value, as well as the height and width of that maximum. If PbO is used as a modifier, a phase with the pyrochlore (A 2 B 2 O 7 ) structure commonly forms instead of perovskite, resulting in a dramatic decrease in dielectric constant.
288
5 Glass-Ceramics
Transparent glass-ceramics containing another perovskite, LiTaO 3 , can be made by heat treating LiTa silicate glasses at 950 to 1000 °C, following a nucleation hold at about 750°C (Beall, 1971; Ito et al., 1978). Alumina is added to these glasses to prevent spontaneous devitrification during the glass-forming step. In view of their transparency, these materials may find application in the fabrication of electrooptic devices. Glass-ceramics containing WO 3 _ X , a tungsten suboxide with a distorted perovskite structure, can be formed from certain glasses in the system WO3-TiO2P 2 O 5 . Ceramming at temperatures in the range of 800 to 1000 °C results in the initial formation of ultra fine-grained (50-100 A) WO 3 _ X crystallites, followed by precipitation of coarser titanium pyrophosphate (TiP2O7) which partitions the former into a connected grain-boundary phase. These materials are metallic conductors, having exceptionally low electrical resistivity for a glass-ceramic: at room temperature, the resistivity can be as low as 10 ~2 Q • cm. Furthermore, the resistivity is virtually constant with temperature over the range of 25 to300°C.
5.4 Microstructure Microstructure is as important as bulk composition in determining the physical properties of glass-ceramics. Mechanical properties such as strength and fracture toughness are particularly sensitive to microstructure. A fine-grained interlocking texture of crystals in the 1-5 |im range generally gives optimum strength. The presence of anisotropic rod-shaped crystals that can act as reinforcing whiskers may further increase strength. On the other hand, shrinkage voids or pores in-
herited from glass-forming defects may greatly weaken the material. Large crystal clusters, such as spherulites, may also serve to reduce strength. Microstructure can be the major influence on optical scattering. A wide range of appearances from totally transparent to highly opaque can be achieved simply by varying microstructure. Thermal shock characteristics can also be influenced by microstructural features. Thus, microcracks developing along grain boundaries between crystals with very different thermal expansion coefficients can improve thermal shock resistance, as can cleavage planes within crystals which can cause deflection, blunting, or branching of fractures. Machinability, whether achieved by chemical or physical mechanisms, is also effected by microstructure. There are many microstructural types observed in glass-ceramic materials. Many show no great property benefits; indeed, some like coarse spherulites are deleterious. Some which promote useful material characteristics are as follows: dendritic, ultrafine, cellular membrane, relict, house-of-cards, acicular interlocking, coast-and-island, and lamellar twinned. Each of these merits elaboration. 5.4,1 Dendritic
Dendritic or skeletal crystallization is caused by accelerated growth in certain lattice directions. The general outline of the dendrite may mimic normal crystal morphology, but the internal structure is typically skeletal with a high percentage of residual glass remaining within the dendrite. Dendritic growth may be enhanced by depletion of a species required for the crystal development in the immediate surrounding of the nucleus. It is also enhanced by high enthalpy of crystallization
5.4 Micrestructure
which increases the temperature along the main growth planes of the crystal, allowing edges and particularly corners to grow quickly into cooler areas. The dendritic microstructure of lithium metasilicate crystals in the chemically-etchable glassceramic Fotoform is illustrated in Fig. 5-4. The hexagonal nature of the intersecting crystals can be observed. The dendrites form a continuous path in three dimensions, allowing the glass-ceramic to be selectively etched with hydrofluoric acid, which attacks the low-silica Li 2 Si0 3 crystallites at a far greater rate than the more durable aluminosilicate residual glass. Since the lithium metasilicate dendrites can be photosensitively nucleated by silver, a complex etchable pattern can be transferred into the glass.
289
Figure 5-4. Microstructure of Fotoform glass-ceramic as revealed by REM (bar = 1 urn).
5.4.2 Ultrafine Grained
Highly crystalline glass-ceramics can be achieved with crystal sizes in the range of a few hundred angstroms. A typical example involves the crystallization of stuffed P-quartz solid solution crystals upon nuclei of zirconium titanate. In this case, rapid impingement of the growing P-quartz crystallites produces a uniform texture with an average crystal size of 600 A. Only 2 mol% each of ZrO 2 and TiO2 are required in a typical lithium aluminosilicate glass of commercial interest in order to guarantee effective zirconium titanate nucleation at about 50 °C above the glass transition. The original nuclei are less than 50 A in width, but are easily observed in transmission electron microscopy at the center of the highly-crystalline P-quartz glass-ceramic (Maier and Miiller, 1989, cf. Fig. 5-5). The low birefringence of the constituent p-quartz solid solution crystal also serves to minimize any scattering. Thus, a material as transparent as glass can be de-
Figure 5-5. Transmission electron microphoto of impinging p-quartz solid solution crystals showing tetragonal ZrTiO 4 nuclei at the center. Note continuous residual glass and precipitation of excess ZrTiO 4 along crystal boundaries (white bar = 200 nm) (after Maier and Miiller, 1989).
veloped and used for such applications as transparent cookware and precision optical instruments, such as the ring-laser gyroscope.
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5 Glass-Ceramics
5.4.3 Cellular Membrane
5.4.4 Relict
The residual glass in many glass-ceramics can develop in a cellular membrane form; that is, the developing crystal phases allow a stable film of siliceous glass to envelope the impinging grains during ceramming. A good example is provided by solid solutions of metastable (3-quartz and stable p-spodumene in TiO2-nucleated Li aluminosilicate glasses. Here the titanate nuclei catalyze the growth of crystals which contain less silica than the bulk composition. Impingement of the (3-quartz or P-spodumene crystals is prevented by the increasing reluctance of the siliceous and, hence, viscous residual glass to crystallize. This viscous, glassy phase adheres to the grains, forming a membrane-like network throughout the body which can provide some benefits in glass-ceramic properties (Chyung, 1969). The siliceous glass acts as a barrier to the diffusion of aluminum ions which control secondary grain growth in P-spodumene glass-ceramics. Thus, these materials show very good grain stability at high temperature and can be used for long periods at temperatures as high as 1200°C without the crystals approaching a size where thermal expansion stress anisotropy could initiate microcracking on repeated thermal cycling. The cellular residual glass can also aid in reforming the highly crystalline glass-ceramic. High creep rates at subsolidus temperatures have been attributed to solution precipitation phenomena involving the glassy film wetting the grains (Raj and Chyung, 1981). According to this creep model, based upon species transport through the glass phase, grain shape elongates in the direction of tensile stress. In this way, a glass-ceramic sheet can be vacuum formed into sinks or other complex shapes at temperatures well below the initiation of melting, even with crystallinity as high as 95%.
Certain glass-ceramic textures faithfully preserve a pre-existing microstructure. Typically, the first stage of nucleation in glass-ceramics involves amorphous phase separation whereby droplets of one glassy component are dispersed in the other. In the case of binary alumina-silica glasses, high alumina droplets approaching mullite in composition are dispersed in a siliceous matrix (MacDowell and Beall, 1969). Upon heat treatment, the unstable aluminous glass crystallizes to mullite which inherits the spherical morphology of the parent droplets. Because transport of aluminum ions through the siliceous matrix is slow, this morphology persists to temperatures well in excess of 1000 °C. Since the droplets were originally only a few hundred angstroms in diameter, the mullite crystals do not scatter light despite the large refractive index mismatch between mullite and silica glass. Figure 5-6 shows the relict structure of such a transparent mullite glass-ceramic. 5.4.5 House-of-Cards The random internal crystallization of two-dimensional silicates like mica can produce an interlocking house-of-cards structure where the crystal phase is continuous and encloses polyhedra of residual glass (Fig. 5-7). Such a microstructure is typical of the machinable glass-ceramics which include the commercial materials Macor and Dicor (Beall, 1986). The machinability of this material is due not only to the soft mica crystals, but also to the ability of these crystals to blunt, deflect, and cause branching of fractures initiated by the machine tool tip. Thus, fracture propagation proceeds as a series of self pulverizing fragmental ablation as opposed to the normal catastrophic mode
5.4 Microstructure
291
Figure 5-7. House-of-cards structure in machinable fluormica glass-ceramic. Note phase separated residual borosilicate glass and affinity of siliceous droplets for mica flakes (white bar = 1 urn).
Figure 5-6. Relict structure in transparent mullite glass-ceramic reflecting original amorphous phase separation (white bar = 1 urn).
that is typical of ceramics. The continuity of the mica phase, even when comprising as little as 40 volume percent, can result in outstanding electrical resistivity and dielectric strength values. The former can be as high as 1011 Q • cm at 500 °C and the dielectric strength at room temperature is typically near 80 kV/mm (Chyung et al., 1974). Such insulating qualities arise from the continuous interlocking form of the mica sheets. Moreover, as the basal plane of mica closely approximates a hexagonal close-packed arrangement of oxygen anions, permeability of gases such as hydrogen and helium is also very low. This is important in high-vacuum applications. Some fracture toughness increase is also caused by the house-of-cards microstructure. Values as high as 2.2 MPa m 1/2 have been measured. In order to achieve the house-of-cards microstructure, individual
fluormica crystallites must grow in a high aspect ratio form. This can be achieved by decreasing the viscosity of the residual glass medium, for example, by adding B 2 O 3 or by formulating a K2O-deficient composition, thus impeding grain growth in the c direction where potassium ions loosely crosslink the tetrahedral-octahedral-tetrahedral layers characteristic of the mica structure. 5.4.6 Acicular Interlocking
A glass-ceramic microstructure composed of interlocking rod- or blade-like chain silicate crystals has shown the strongest and toughest mechanical behavior (Beall, 1989). Figure 5-8 shows the microstructure of an amphibole glass-ceramic based on the phase potassium fluorrichterite. The microstructure is characterized by randomly oriented rods which simulate whisker reinforcement in ceramics. Abraded flexural strengths as high as 150 MPa have been measured in this material; the fracture toughness is 3.2 + 0.2 MPa m 1/2 as measured by the
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5 Glass-Ceramics
oped along grain boundaries during cooling of canasite glass-ceramics. 5.4.7 Coast-and-Island
Figure 5-8. Fracture surface (r.e.m.) of K-F-richterite glass-ceramic showing the effects of rod reinforcement toughening.
short bar technique (Beall, 1991). The fluorrichterite grows at relatively high temperatures from a metastable mixture of diopside, mica, and glass. Even more impressive mechanical properties are observed with highly crystalline, monophase glass-ceramics based upon another chain silicate fluorcanasite, shown here in Fig. 59. Cleavage splintering is observed, causing energy absorption through crack branching and deflection. The toughness of canasite glass-ceramics has been measured at 5.0MPam 1 / 2 with abraded flexural strengths near 300 MPa. The fracture toughness decreases from 5 MPa at room temperature to below 2 at 600 °C (Beall et al., 1986). This is attributed to the effects of anisotropic thermal expansion stress microcracking which is believed to be a source of toughening. The thermal expansion coefficient in the chain direction for canasite is 82 x 10" 7 o CT x from 0-700°C. Perpendicular to the chain direction, the a and c expansions are 159 and 2 4 8 x l O " 7 o C " 1 over the same thermal range. Considerable stress is thereby devel-
A coast-and-island microstructure typically develops when an equilibrium crystal phase forms along the grain boundaries of a metastable assemblage of phases. One example is the precipitation of pollucite from previously existing mullite and glass in partially crystalline Cs aluminosilicate glass-ceramics (Beall and Rittler, 1982). The remains of the mullite-glass mixture become enveloped by the pollucite matrix as observed in Fig. 5-10. Since pollucite is one of the most refractory crystalline phases, with a melting point in excess of 1900°C, the matrix severely limits hightemperature viscous deformation and has a viscosity of l O ^ N s m " 2 at 1430°C,
Figure 5-9. Fracture surface (r.e.m.) of fluorcanasite glass-ceramic showing interlocking blades and effects of cleavage splintering.
5.4 Microstructure
293
some 350 °C higher than that of fused silica. Cordierite glass-ceramics provide another example of this microstructure. Above 1100°C, cordierite forms at the expense of oc-quartz, sapphirine (Mg 4 Al 10 Si 2 O 23 ), and magnesium dititanate. In bulk compositions containing excess silica, cristobalite and rutile form islands surrounded by cordierite. The residual glass is isolated at grain boundary nodes, leading to an interlocking structure with good mechanical strengths and toughness. 5.4.8 Lamellar-Twinned
Several important glass-ceramic crystalline phases undergo structural transformations on cooling. This can result in fine polysynthetic twinning, yielding a lamellar microstructure that can serve to increase Figure 5-11. Fracture surface (r.e.m.) of enstatitezircon glass-ceramic showing interlocking twinned enstatite grains and nodular zircon. Note the step splintering effect of the intersection of cleavage and twinning.
Figure 5-10. Pollucite-mullite glass-ceramic. "Coast and island" microstructure shows regions of pollucite (heavily etched) interlocking with regions of mullite and glass (white bar = 1 urn). (Cerammed: 1600 °C, lh.)
the fracture toughness of such materials. Examples include enstatite, anorthite, and leucite. Enstatite glass-ceramics have shown the highest fracture toughness values, averaging 4-5 MPa m 1/2 (Beall, 1991). Figure 5-11 depicts the microstructure of a typical enstatite-zircon glass-ceramic. The enstatite grains are seen to be highly twinned and are composed of a mixture of clino- and protoenstatite. The enstatite forms initially as protoenstatite, but undergoes a martensitic transformation to the clino form on cooling below 1000 °C. Some protoenstatite is quenched in, leading to hysteresis in both thermal expansion and stress/strain behavior. The unusual
294
5 Glass-Ceramics
toughness is due to a combination of the lamellar microstructure, which deflects fractures and absorbs energy, and the high elastic modulus of enstatite itself. Intersecting cleavage planes at right angles to the twinning may also play a part in fracture energy absorption.
5.5 References Aitken, B. G. (1989), 15th Int. Cong. Glass 3 a, 96101. Beall, G. H. (1971), U.S. Pat. No. 3 573939. Beall, G. H. (1986), Advances in Ceramics 18, 157173. Beall, G. H. (1989), Rev. Solid State Sci. 3, 333-354. Beall, G. H. (1991), J. Non-Crystalline Solids 129, 163-173. Beall, G. H., Duke, D. A. (1969), J. Mat. Sci. 4, 340-352. Beall, G. H., Rittler, H. L. (1982), Advances in Ceramics 4, 301-312. Beall, G. H., Chyung, K., Stewart, R. L., Donaldson, K. Y, Lee, H. L., Baskaran, S., Hasselman, D. P. H. (1986), /. Mat. Sci. 21, 2365-2372. Berezhnoi, A. I. (1970), Glass-Ceramics and PhotoSitalls. New York: Plenum. Chyung, C. K. (1969), J Am. Ceram. Soc. 52, 242245. Chyung, C. K., Beall, G. H., Grossman, D. G. (1974), 10th Int. Cong. Glass 14, 33-40. Conrad, M. A. (1972), J. Mat. Sci. 7, 527. Duke, D. A., MacDowell, J. R, Karstetter, B. R. (1967), /. Am. Ceram. Soc. 50, 67-74. Grossman, D. G. (1972), /. Am. Ceram. Soc. 55, 446449. Headley, T. I, Loehman, R. E. (1984), J. Am. Ceram. Soc. 67, 620-625. Herczog, A. (1964), J. Am. Ceram. Soc. 47, 107-115. Ito, S., Kokubo, T., Tashiro, M. (1978), / Mat. Sci. 13, 930-938.
Jackson, K. A. (1967), Prog. Solid State Chem. 4, 53-80. James, P. F. (1982), Adv. Ceram. 4, 1-29. Lee, W. E., Heuer, A. H. (1987), /. Am. Ceram. Soc. 70, 349-360. MacDowell, J. F. (1965), Proc. Brit. Ceram. Soc. 3, 229-240. MacDowell, J. F. (1989), 15th Int. Cong. Glass 3 a, 90-95. MacDowell, J. R, Beall, G. H. (1969), /. Am. Ceram. Soc. 52, 17-25. Maier, V., Miiller, G. (1989), J. Am. Ceram. Soc, 70, C-176-178. McMillan, P. W. (1979), Glass-Ceramics, 2nd. ed. London: Academic Press. Ostertag, W, Fisher, G. R., Williams, J. P. (1968), /. Ceram. Soc. 51 (11), 651. Raj, R., Chyung, K. (1981), Ada Met. 29, 159. Stookey, S. D. (1954), Ind. Eng. Chem. 46, \1A-\16. Stookey, S. D. (1959), Ind. Eng. Chem. 51, 805-808. Stookey, S. D. (1960), U.S. Patent No. 2920971. Stookey, S. D. (1985), Journey to the Center of the Crystal Ball. Westerville, Columbus, OH: Am. Ceram. Soc. Strnad, Z. (1986), Glass-Ceramic Materials. Amsterdam: Elsevier. Vogel, W, Holand, W. (1989), 15th Int. Cong. Glass 3a, 102-107. Weeding, T. L., de Jong, B. H. W S., Veeman, W. S., Aitken, B. G. (1985), Nature 318, 352-353.
General Reading Berezhnoi, A. I. (1970), Glass-Ceramics and PhotoSitalls. New York: Plenum. Lewis, M. H. (1989), Glasses and Glass-Ceramics. London: Chapman and Hall. McMillan, P. W. (1979), Glass-Ceramics. London: Academic Press. Stookey, S. D. (1985), Journey to the Center of the Crystal Ball. Westerville, Columbus, OH: Am. Ceram. Soc. Strnad, Z. (1986), Glass-Ceramic Materials. Amsterdam: Elsevier.
6 Diffusion in Ceramics Alan Atkinson Materials Chemistry Department, AEA Technology, Oxfordshire, U.K.
List of 6.1 6.2 6.2.1 6.2.2 6.3 6.3.1 6.3.2 6.3.3 6.3.4 6.3.5 6.3.5.1 6.3.5.2 6.3.5.3 6.3.5.4 6.4 6.4.1 6.4.2 6.4.3 6.4.4 6.5 6.5.1 6.5.2 6.6 6.6.1 6.6.2 6.6.3 6.6.4 6.6.5 6.6.6 6.7 6.7.1 6.7.2 6.7.3 6.8
Symbols and Abbreviations Introduction Point Defects in Ceramics Classification of Ceramics Point Defects Theory of Diffusion Phenomenology of Diffusion Thermodynamic Forces Diffusion as a Random Walk Atomistic Description of Diffusion in Ceramics Types of Diffusion Tracer Self-Diffusion Tracer Solute Diffusion Interdiffusion Chemical Diffusion Diffusion Experiments Tracer Self-Diffusion Solute Diffusion, Interdiffusion and Chemical Diffusion Identifying the Diffusion Mechanism Experimental Precautions and Problems Computer Simulations Energy Minimization Molecular Dynamics Examples of Diffusion in Ceramics Refractory Oxides A12O3 and MgO Transition Metal Oxides Fluorite Structure Oxides Complex Oxides Carbides and Nitrides Glasses Short-Circuit Diffusion Phenomenology and Measurement of Short-Circuit Diffusion Dislocation and Grain Boundary Diffusion Surface Diffusion Processes Involving Diffusion
Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.
297 299 299 299 300 302 302 303 304 304 305 305 306 307 308 309 309 310 310 311 313 314 314 315 315 316 319 320 322 324 325 325 327 328 329
296
6.8.1 6.8.1.1 6.8.1.2 6.8.2 6.8.3 6.8.4 6.9 6.10 6.11
6 Diffusion in Ceramics
Solid State Reactions De-Mixing in a Chemical Gradient Complex Oxide Formation Creep of Ceramics High Temperature Oxidation Optical Waveguide Fabrication by Ion Exchange Conclusions Acknowledgement References
329 329 330 331 333 334 335 336 336
List of Symbols and Abbreviations
297
List of Symbols and Abbreviations a, b, c A a0 ax [A] b b Bt Ct d Dc Dd Dt Dj D%h D def v Deff D creep D D* e E / /M>/O g gf,gm AG° hA hf, hm JkB fcp K AK £ Lq,Xq Lik n P P Q r
lattice parameters constant lattice parameter chemical activity of component X mole fraction of component A oxygen to metal ratio in an oxide magnitude of the Burgers vector of a dislocation mobility of particles of type i number of particles of type i per unit volume diameter of a dislocation diffusion coefficient of vacancy-solute complex diffusion coefficient in the high diffusivity region of a dislocation partial diffusion coefficient of particles of type i diffusion coefficient due to the mass transport through the bulk of the lattice diffusion coefficient in the grain boundary region diffusion coefficient of defects, vacancies effective diffusion coefficient diffusion coefficient due to the creep rate chemical or interdiffusion coefficient tracer diffusion coefficient electronic charge electric field correlation factor correlation factor for metal, oxygen tracer grain size Gibbs energy for formation or motion of a defect standard Gibbs energy enthalpy of association between defects enthalpy of formation or motion of a defect flux density of particles of type i Boltzmann constant parabolic rate constant equilibrium constant kinetic energy partitioning in isotope effect spacing between short-circuit pathways L,X specifically associated with the transport of heat transport coefficient describing the flux of particles of type i due to a force on particles of type k order of the power dependence of defect concentration on component activity fraction of defects in complexes stress activation energy jump distance
298
6 Diffusion in Ceramics
R R s s s f ,s m t T Tm u Vm V M ,o [V] w x x X Xk Y zt
ionic radius gas constant segregation coefficient of a component to a grain boundary, dislocation or surface entropy entropy of formation, or motion, of a defect time absolute temperature melting temperature internal energy molecular volume vacancy o n a metal, oxide site mole fraction of sites vacant exchange rate between defects a n d a t o m s spatial co-ordinate stoichiometric variable reaction layer thickness thermodynamic force on particles of type k modulus of elasticity number (and sign) of units of electronic charge e carried by particles of type i
aM y F 8 3 8 s0 e rji 9 lit v (j)
Madelung constant activity coefficient j u m p frequency deviation from stoichiometry grain boundary width relative permittivity permittivity of free space steady state creep rate electrochemical potential of species i boundary misorientation angle chemical potential of species i vibrational frequency electrical potential a n d fraction of short-circuit sites
b.c.c. EPMA f.c.c. MO SIMS
body-centred cubic electron probe microanalysis face-centred cubic metal oxide secondary ion mass spectroscopy
6.2 Point Defects in Ceramics
6,1 Introduction Mass transport in ceramics is important for their fabrication, functional properties and long term stability. In fabrication, mass transport controls the rates of sintering, solid state reactions and grain growth. The performance of ceramics as fast ion conductors, diffusion barriers and creepresistant engineering components is crucially dependent on their mass transport characteristics. Finally, the length of time for which ceramic components can resist degradation through chemical reactions or radiation damage is also determined by diffusion. In this chapter we survey diffusion in ceramics and its role in some of their properties. At the scientific level the historical goal of most diffusion studies has been to understand how the diffusion process takes place atomistically and thereby gain the ability to predict the mass transport characteristics of new materials. At the technological level mass transport studies aim to provide quantitative input to the phenomenological description of the properties of materials. Both aspects are dealt with in this chapter, which is structured in the following way. First we survey the different classes of ceramics and the characteristics of point defects in their lattice structures. Both the phenomenological and atomistic theoretical frameworks of diffusion are then described. After surveying the experimental and computational techniques used to study diffusion, some illustrative examples of data from various classes of ceramic materials are presented, followed by consideration of the effect of extended microstructural defects (dislocations, grain boundaries and surface) on mass transport. Finally, the role of diffusion in some technological applications is illustrated.
299
The reader is referred to texts by Adda and Philibert (1966), Kofstad (1972), Schmalzried (1981) and Philibert (1985) for extended discussion of the background material underlying the topics covered in this chapter.
6.2 Point Defects in Ceramics 6.2.1 Classification of Ceramics Ceramic materials cover the complete spectrum of bonding types in both crystalline and amorphous forms. Ionic bonding similar to that of the alkali halides is to be found in alkaline earth halides (e.g., SrF2), alkali metal oxides (e.g., Li2O) and alkaline earth oxides (e.g., MgO). These materials have negligible electronic conductivity (wide band gap) and negligible deviations from stoichiometric composition. Covalent bonding similar to that found in elemental semiconductors is dominant in compounds of light elements (e.g., SiC, Si 3 N 4 , B 4 C 3 , A1N, BN). These ceramics are either semiconductors or insulators. Most oxide ceramics fall between these two extremes and have some characteristics of both. They may be semiconducting (e.g., TiO2), ionically conducting (e.g., Ca-stabilized ZrO 2 ) or mixed conductors (e.g., LiCoO2). Oxides of elements tending to show fixed valency (e.g., A12O3) have negligible deviation from stoichiometry whereas those of variable valency elements (e.g., transition metal oxides) can display large departures from stoichiometry. Metallic conductivity and large deviations from stoichiometry are to be found in the nitrides and carbides of the heavier elements. These distinctions, together with the crystal structure, are important when discussing transport in individual ceramic compounds.
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6.2.2 Point Defects The atomistic description of diffusion (Sec. 6.3.4) involves the concentrations and mobilities of point defects, such as vacancies and interstitials. In the previous section we saw that the broad classification of ceramic materials covers wide variations in bonding, stoichiometry and electronic properties; all of which are intimately linked with point defect characteristics. In order to understand these relationships in ceramics it has been found useful in practice to extend the ionic description across the whole range by introducing electronic carriers (electrons, e, and holes, h) into the point defect system. The approach as developed for ionic crystals has been summarized by Lidiard (1957) and Kroger (1964) and its application to oxide ceramics by Kofstad (1972). The idea is to express reactions between point defects, electronic defects, two crystals and a crystal and its environment as though they were chemical reactions. "Mass action laws" can then be used to derive relationships between the concentrations of these defects at equilibrium and the free energy changes of the defect reactions. For example, the creation of a pair of vacancies (Schottky disorder) in a metal oxide MO would be written: null = V^ + VQ
(6-1)
where "null" is the perfect lattice. The reaction is written here using the Kroger-Vink notation for the defects. In this case V denotes vacant sites and the subscript (M or O) indicates whether the vacancy is on a metal or an oxygen site. The superscript symbols indicate the effective (with respect to the perfect lattice) number of electronic charges on the defect with the dash denoting a negative charge (missing positive ion) and the dot a positive charge (missing neg-
ative ion). Defects having no effective charge are denoted by the superscript x. In such reactions point defects are formed and thus the free energy change of the reaction is the free energy of formation of the defect(s), gf. Since these reactions must preserve the electrical neutrality of the crystal and conserve the stoichiometric ratio of lattice sites, defects are never created singly. They may be combinations of lattice point defects, as in this example, or mixtures of point defects and electronic carriers. The equilibrium constant, K, for the defect-forming reaction is then related to the free energy of formation of the defects), g{9 by = hf-
Ts{=
-kBT\nK
(6-2)
As for chemical equilibria, K is expressed in terms of the activities of the defects participating in the reaction. In the limit of low defect concentrations the activity is equal to the molecular fraction. The upper limit of molecular fraction at which such an approximation is valid is probably about 10~4. Nevertheless, it is common practice to use this approximation at much higher concentrations (e.g., up to about 10 ~ 2 ). The apparent success of the dilute approximation, well outside its expected range of application, has been achieved by approximating some of the interactions between point defects in terms of the formation of associated, or complex, defects. A common example is the trapping of an electronic defect at an oppositely charged lattice defect such as: f
M
(6-3)
This approximation is good when the complex is strongly bound and behaves as a single entity for most of the time. A complementary approach to dealing with interactions between defects is to use activity coefficients, y, in a similar way to
6.2 Point Defects in Ceramics
the approach taken in aqueous electrolytes. For charged defects, again at low concentrations, this can be done using the Debye-Hiickel theory of electrical screening. Using this method Wagner (1975) showed that for V'Cu and h' defects in C u 2 _ p at 1000 °C the activity coefficient is about 0.5 when 3 = 10" 3 . Since the Debye-Hiickel theory assumes a continuum, it is inappropriate when a significant fraction of defects is to be found on nearestneighbour sites. Theoretical treatments have been developed to analyse this regime (Allnatt and Loftus, 1973; Murch, 1980), but they are not convenient for routine interpretation of experimental data. In ceramics approaching full ionic character the dominant reactions are those which preserve stoichiometry through Schottky disorder [Eq. (6-1)] or Frenkel disorder (again for the binary oxide MO): (6-4 a) and = Vo +
(6-4 b)
Schottky and Frenkel point defects can be created or destroyed at external surfaces or internal sources and sinks, such as dislocations and grain boundaries. In insulating and semiconducting materials electronic carriers can be excited across the band gap (null = h" + e'). In ceramics involving elements of variable valency (e.g., the transition metal oxides) oxidation/reduction reactions with the external environment tend to dominate. For the oxide MO the reaction would be with oxygen: I O 2 = V^ + Oxo + 2 h' (oxidation) (6-5 a) MO = M;' + 2 e' + | O 2 (reduction) (6-5 b) The oxidation reaction promotes p-type semiconduction and the reduction reaction
301
promotes n-type. Since these reactions involve the gas phase they can only occur at external surfaces. Application of the ideal mass action laws to the defect reactions, when combined with the condition for overall electrical neutrality, predicts that mole fractions of defects are simple power functions of oxygen activity, aOl (equal to the oxygen partial pressure in bar) when redox reactions are involved: [defect] oc anO2
(6-6)
Care has to be taken to maintain a selfconsistent use of "mole fractions" when dealing with solid compounds. For example aluminium vacancies in alumina could be expressed as a fraction of ideal aluminium lattice sites in the crystal structure, or as a fraction of A12O3 "molecules". This is not a problem provided that the free energy of the defect-forming reaction is taken to refer to the corresponding number of defects. The exponent, n, is characteristic of the defect type and therefore measuring a property, such as diffusion, as a function of oxygen activity enables the defect which is responsible to be identified, or at least the range of possibilities is narrowed. For example, if Eq. (6-5 a) is dominant then (6-7) Since electrical neutrality requires = [h], it follows that [VM]<*<6
and
[hlojf
Hence deviation from stoichiometry, metal diffusion (by a vacancy mechanism) and electronic conductivity in this oxide are all expected to have n = 1/6. In practice it is often found that these different properties have slightly different values of n. This is an experimental manifestation of the
302
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nonideal nature of the defects already referred to. To fit the experimental data, point defect models have become rather complicated in some cases and, furthermore, the fit is often not unique. Therefore, when thermodynamic parameters describing these models are presented in the literature the nature of this force-fitting (i.e., assuming ideal solid solution under conditions where it is not really valid) must be borne in mind. When ceramics are doped by solutes (impurities) the doping reaction can be written in the same formalism. A common situation arises when the solute has a different valency from the host (e.g., a trivalent solute B in a divalent host oxide AO) B2O3
(AO)
(6-8)
In summary, the concentrations of defects are determined by their entropies and enthalpies of formation, s{ and hf. Reactions to create defects, or between defects,
are expressed as chemical reactions having equilibrium constants. The chemical activities of defects are usually sufficiently wellapproximated by their molar fractions, provided that interactions between defects are taken into account as explicit defect associates. More sophisticated methods are available to handle large concentrations of defects. Typical concentrations of defects to be found in various types of ionic crystal are illustrated in Fig. 6-1.
6.3 Theory of Diffusion 6.3.1 Phenomenology of Diffusion The exact description of diffusion in the solid state is not straightforward and the reader is referred to Chapter 2 of Volume 5 of this encyclopaedia (Murch) and books by Schmalzried (1981), Adda and Philibert (1966) and Philibert (1985) for extensive discussion of the underlying subleties. The
New phases
-2 Anion Frenkel defects in fluorites
NonstojchfomeHc solids
L_
I Cation Frenkel defects in silver halides >
Figure 6-1. Typical values of the concentrations of point defects at thermal equilibrium in ionic crystals as a function of temperature relative to the melting temperature. (After Stoneham, 1985.)
Extrinsic (impurity controlled)
2.5
1.5 Tm/T
6.3 Theory of Diffusion
salient features are summarised in this, and subsequent, sections. The basic phenomenological mass transport equation is that of Fick for particles of type i: J, = -
*dx
(6-9)
in which J. is the flux density of particles, Ct their number per unit volume and x a spatial co-ordinate. Dt is known as the partial, or intrinsic, diffusion coefficient for particles of type i. In general, the particles in solids interact chemically and particles do not move independently (e.g., when a vacancy moves an atom moves in the opposite direction). Thus Dt is one of a variety of so-called "chemical diffusion coefficients". Since a solid state diffusion process may involve a shift of the whole crystal lattice (e.g., the Kirkendall effect) it is also necessary to specify the frame of reference in which the fluxes, and hence D/s, are defined (Schmalzried, 1981). The frame of reference most often used is one fixed to local lattice planes. This is usually convenient in ceramics since one component often has negligible mobility (e.g., the interdiffusion of mobile cations in a close-packed oxide in which the anions have much lower mobility than cations). Since it is possible, at least in principle, to measure particle concentrations and fluxes, the partial diffusion coefficients are experimentally measurable quantities. Their extraction from experiments having a wide variety of boundary conditions and initial conditions can be found in books by Crank (1975) and Carslaw and Jaeger (1959).
303
case of mass transport in response to a wide range of driving forces. These forces can arise from electric fields, magnetic fields, chemical reactions, temperature gradients and so on. In general, a gradient in any thermodynamic quantity will give rise to a driving force for transport that will lower the gradient and lower the free energy of the system. However, the description now becomes more complicated because there is not only transport of matter, but also of electrical charge and heat. This more general phenomenological approach is required to deal with ionic conductivity, interdiffusion, solid state reaction and the redistribution of atoms in a temperature gradient. The generalised expression for transport of the ith species in a system with k components can be written Lt X
(6-10)
where the L's are transport coefficients and X's are driving forces. Xq and Liq are specifically associated with the transport of heat. A full description of this approach was given by Howard and Lidiard (1964) and is summarized in Chap. 2 of Volume 5 by Murch. For mass transport in ceramics it is often sufficient to ignore cross coefficients (i.e., Lik = 0 for i # k) and to consider only the electrochemical driving force Xt= - gmd [it + zteE
(6-11)
In this expression E is the local macroscopic electric field, e the modulus of the electronic charge and*zf the number of electronic charges that moves when species / moves. The chemical potential, fi, for an ideal system is given by
6.3.2 Thermodynamic Forces
Fick's law only describes mass transport driven by a spatial variation in the concentration of a mobile species. This is a special
rt =
fcBTln[q
(6-12)
Since E = — grad (f> the electrical and chemical forces may be combined in the
304
6 Diffusion in Ceramics
6.3.3 Diffusion as a Random Walk
electrochemical potential
The transport coefficients, Lik, can be related to experimentally measurable quantities. Their value is to enable a complete description of mass transport to be made under a general set of driving forces and with no interactions between different particle fluxes being omitted (Howard and Lidiard, 1964). In simple cases the coefficients can be expressed in terms of measurable diffusion coefficients or electrical conductivities (Wagner, 1975). Often it is convenient to ignore the cross term (i.e., put Lik = 0 for i =# /c), in which case
In solids the atoms take up reasonably well-defined positions. Mass transport occurs by atoms making transitions between these positions in such a way that the time of transit is much less than the residence time at any particular position. Thus, diffusion can be thought of as occurring by particles hopping in a random way on a lattice of sites distributed in space. If an individual atom is labelled its motion can be followed and related to the phenomenological tracer diffusion coefficient. For a cubic lattice (i.e., diffusion is isotropic) the tracer diffusion coefficient is given by (Lidiard, 1957)
Jt~ -BtC^
D*=\fTr2
rjt = fit -\- zte
(6-13)
(6-14)
where Bt is the mobility (drift velocity per unit force). This is equivalent to neglecting correlation effects (see Sec. 6.3.5.1) and permits transport to be analysed under the combined action of chemical gradients and electric fields in a relatively simple way. However, it should be noted that in general the most reliable way of ensuring that all the subleties of coupled electrical and mass transport are included correctly is to formulate the problem in terms of transport coefficients and thermodynamic forces. If the cross coefficients are neglected the mobility is related to the partial (intrinsic) diffusion coefficient by dlnJ/ dlnC,
(6-15)
where y is the activity coefficient and Vm the molecular volume. The term in curly brackets is often referred to as the "thermodynamic factor". A similar analysis of tracer diffusion, again neglecting the cross coefficients, reveals that Df ~ kB TBt.
(6-16)
where F is the jump frequency to a nearest neighbour site and r is the jump distance. The factor / is called the correlation factor and is included to account for situations in which the walk might not be truly random and there is some correlation between successive jumps, i.e., there is a bias depending on preceding events. This correlation depends on the details of the diffusion mechanism (LeClaire, 1976) and will be discussed later. The hopping event between sites involves the particle crossing an energy barrier, the necessary energy coming from thermal fluctuations with a probability described by the Boltzmann distribution. Hence, the diffusion process is thermally activated and the diffusion coefficient has the Arrhenius form D = Do exp I —
KT
(6-17)
6.3.4 Atomistic Description of Diffusion in Ceramics Thus far we have neglected the details of how the diffusing particle (atom or ion)
6.3 Theory of Diffusion
makes the transition from one lattice site to another. In order to progress further it is necessary to consider the atomistic mechanism involved in the jump. Examples of such mechanisms are given in Fig. 6-2 and are discussed in detail in Chap. 2 of Volume 5. No experimental evidence has yet been forthcoming to support the direct interchange mechanism of diffusion in solids and therefore it can be asserted that solidstate diffusion occurs only by mechanisms involving lattice point defects. In ceramics, most diffusion processes are believed to occur either by the vacancy or interstitialcy mechanisms. In either case the jump prob-
O
ability, f, will depend on the jumping particle being adjacent to a defect as well as the number of times that it makes an attempt to jump (the vibrational frequency, v) and the probability that it has sufficient thermal energy to surmount the activation barrier. For a vacancy mechanism on a f.c.c. or b.c.c. lattice Eq. (6-16) then leads to the result = a20w0f[V]
(6-18)
where [V] is the fraction of sites vacant and a0 is the lattice constant. The rate of exchange between vacancies and particles is w0 and is given by (6-19)
o oo O
305
Vacancy
where sm and hm are the entropy and enthalpy of motion of the defect. The concentration of defects depends on their type and varies strongly from one material to another. In general, the defect concentration is also thermally activated so that for vacancies [V] = A exp (^-
Interstitial
o oo Collinear interstitialcy
(6-20)
where sf and hf are the entropy and enthalpy for defect formation. The constant A depends on the type of defect and the reaction by which it is formed. 6.3.5 Types of Diffusion 6.3.5.1 Tracer Self-Diffusion
Non-collinear interstitialcy
Figure 6-2. Schematic illustration of diffusion mechanisms in a two-dimensional "simple cubic" lattice.
Diffusion of tracer host atoms of the ceramic should be studied in systems at chemical equilibrium so that the only driving force for change is the mixing of tracers (isotopes) under the influence of their concentration gradients. The jumps of the tracer are not truly random and this is accounted for by the correlation factor, / in Eqs. (6-16) and (6-18). The correlation fac-
306
6 Diffusion in Ceramics
tor is less than unity and depends on the diffusion mechanism and the crystal structure (e.g., in the f.c.c. lattice / = 0.78146 for the vacancy mechanism). Some values of / are summarized in Chap. 2 of Volume 5. It is often useful to express the tracer diffusion coefficient in terms of the diffusion coefficient of the defect responsible for diffusion, D def , D* = DdeJ [defect]
(6-21)
Since the concentration of defects is usually low, it follows that Ddef ^> D*. Comparing Eqs. (6-18) and (6-21) shows that, for the vacancy mechanism, DY = a% w 0
(6-22)
The tracer self-diffusion coefficient is related to the partial diffusion coefficient by Df = f Dt for pure compounds having only small deviations from stoichiometry (the thermodynamic factor in Eq. (6-15) being unity in such a case). 6.3.5.2 Tracer Solute Diffusion
There are two experimental regimes which must be considered for diffusion of a solute (or impurity) tracer. When the solute is present only as a very small concentration of diffusing tracer the
point defect populations will be the same as in the pure host ceramic. However, jump rates of atoms in the neighbourhood of the solute atom will be different. The case of both solute and host diffusing by a vacancy mechanism in an f.c.c. lattice has been treated using a five-frequency model (Fig. 6-3). The jumps of frequency w3 lead to dissociation of the solute and vacancy whereas those of frequency w4 lead to association. Their combination can be accounted for by the enthalpy of association, /zA, between the vacancy and solute (with hA being negative for an attractive interaction between them). The tracer diffusion coefficient in the dilute limit then becomes - n *2 = a w 2 / 2 [V]exp
-
(6-23)
where the subscript 2 denotes the solute atom. The correlation factor, / 2 , is now a complicated function of the jump frequencies in Fig. 6-3. The maximum value of f2 is unity and is approached when w2<^w0, i.e., the vacancy exchanges with host atom much more rapidly than with solute atoms. In the opposite extreme when w2^>w0, f2 tends to wo/w2 and can be very small. This corresponds to a situation in which
Solute Figure 6-3. The "five frequency model" for solute diffusion in an f.c.c. lattice. The other exchange frequencies are w0 (no solute present) and w4 (the reverse of w3). (After Howard and Lidiard, 1964.)
6.3 Theory of Diffusion
the solute and vacancy spend most of their time repeatedly exchanging places. (In this discussion we have assumed that w1 « w3 «w 0 .) Equation (6-23) indicates that the activation energy for tracer solute diffusion, Q2, in the dilute limit, has extra contributions from hA and the temperature dependence of / 2 , in addition to the contributions from defect concentration and defect-solute exchange. When the solute is present as a significant dopant (of uniform concentration) as well as a tracer (of non-uniform concentration) the influence of the solute on the point defect population must be taken into account.
307
same valency [e.g., a solid solution (A, B) O], the interdiffusion coefficient is given by (Manning, 1968) n AB
where yB is the activity coefficient of B in the solid solution. Expressions such as Eq. (6-25), in which the component with lower mobility tends to dominate the result, are said to be of Nernst type. When the interdiffusing ions in an ionic conductor have different valency the more general form of Eq. (6-25) is (Cooper and Heasley, 1966) , 91nyB
6.3.5.3 Interdiffusion
Interdiffusion occurs when two components of a solid solution migrate in opposite directions down their coupled chemical potential gradients. A typical example would be the homogenising of two substitutional metal ions in a metal oxide solid solution. The simplest case occurs when the interdiffusing species have the same valency and the other component (oxygen in this example) is effectively immobile. Since electrical neutrality must be maintained, an internal electric field (Nernst field) will be generated to couple the transport of electrically charged particles. This is known as ambipolar diffusion and the resulting electrical potential is known as the diffusion potential. The interdiffusion is defined in the laboratory frame of reference by the equations JA (laboratory) = — DAB dx =
^AB —~ = ~ JB (laboratory)
(6-24)
If the ceramic is an ionic conductor and the interdiffusing atoms A and B have the
In metallic and semiconducting systems (or for uncharged particles) the electronic carriers redistribute themselves so as to prevent the generation of a diffusion potential. Provided that there are sufficient internal sources and sinks through which the point defect populations can maintain local equilibrium, the interdiffusion coefficient is given by (6-27)
This equation, in which the more mobile component dominates, is called a Darken type of interdiffusion equation. Even in metallic and semiconducting ceramics strong coupling between the interdiffusing fluxes will occur if there are no internal sources and sinks for point defects. The resulting requirement to preserve all the lattice sites couples the fluxes in a similar way to the electric field in ambipolar diffusion and the final expression for interdiffusion will be of the Nernst type. However, for interdiffusion in dilute solid solutions ([B] -> 0) of all systems the interdiffusion
308
6 Diffusion in Ceramics
coefficient tends to the same limit (6-28) which is equivalent to Eq. (6-23). More complicated situations arise if diffusion of the third component cannot be neglected (Allnatt and Lidiard, 1987). A typical example of such a case is when Ca and Zr interdiffuse in zirconia where the tracer diffusivities of the two cations are both much slower than that of oxygen. Interdiffusion can be approached alternatively in an atomistic formalism rather than the phenomenological one. A common example of interdiffusion in ceramics arises for a trivalent solute in a divalent host. If diffusion is by a vacancy mechanism the pair association model of Lidiard (1957) can be used to provide an atomistic description. In this model the solute (B2O3) in AO) can only diffuse if it is associated with a vacancy on a neighbouring site, leading to Dg = Dcp, where p is the fraction of solute atoms associated into vacancy-solute complexes and Dc the diffusion coefficient of the complex. Dc may be formulated in terms of the jump frequencies in Fig. 6-3. Thus the thermodynamic factor in Eq. (6-28) is equivalent to the variation of p with concentration of solute. 6.3.5.4 Chemical Diffusion
Most ceramics are compounds and therefore even a pure ceramic can support a gradient in the chemical potentials of its two components. In an oxide ceramic this is often established experimentally as a gradient in molecular oxygen activity. A gradient in oxygen activity will generate a gradient in composition through the point defect-forming reactions. Thus chemical self-diffusion may be regarded as interdiffusion between crystal components and
lattice defects (e.g., by placing two crystals of the same compound, but having different degrees of non-stoichiometry, in contact). The fluxes in the laboratory frame define the chemical diffusion coefficient, D, in the same way as for DAB in interdiffusion. Wagner (1975) has shown how, in a non-stoichiometric semiconducting oxide Mi + <5Ob, the chemical diffusion coefficient is related to the tracer diffusion coefficients of the mobile species. If metal ion diffusion is more rapid than oxygen diffusion the result is D**uu 6 In | <51 9 In a,o2
-l
(6-29)
The process of chemical diffusion involves the migration of both ions and electrons in response to the chemical gradient and is thus ambipolar. It is controlled by the majority ionic or electronic defect having the lowest diffusion coefficient and, in semiconducting oxides, will be the dominant ionic defect. If this is a metal ion vacancy then Eq. (6-29) becomes D=
2\n\[VM]f
Dyb 2\n\
(6-30)
where n is characteristic of the point defect structure (see Sec. 6.2.2). This illustrates a general conclusion that the chemical diffusion coefficient is of the same order as the diffusion coefficient of the slowest majority defect; in this example a metal ion vacancy. (Conversely, in an ionically conducting ceramic chemical diffusion will be controlled by the mobility of the electronic carriers.) Since the defect diffusion coefficient is usually orders of magnitude greater than the tracer diffusion coefficient, D is also usually much greater than D*.
6.4 Diffusion Experiments
6.4 Diffusion Experiments Experimental methods for studying diffusion are described in Chap. 2 of Volume 5 and, in more detail, in reviews in the literature (Rothman, 1990). In this section we concentrate on aspects of experimental techniques which are important for studies of ceramic materials. There are many phenomena depending on mass transport that could be analysed to obtain a diffusion coefficient (see Sec. 6.8). However, these "indirect" methods have proven to be unreliable because assumptions concerning the transport mechanisms have to be made that are often invalid and cannot be verified by independent means. The most reliable data have to be those derived from experiments in which the concentration of diffusant is determined as a function of position following one-dimensional diffusion from a planar source. This is known as depth-profiling. 6.4.1 Tracer Self-Diffusion
For self-diffusion measurements an isotopic tracer of the host element is used. If, as is often the case, this is a radioactive isotope then the depth profile is usually determined by sectioning and counting. When diffusion distances are large the most convenient technique for sectioning is by grinding the ceramic sequentially parallel to the diffusion source plane. By using careful polishing techniques it is possible to obtain a depth resolution of about 0.5 Jim, but for shallow depths of diffusion microsectioning techniques have been developed. These were first applied to diffusion in metals and have since been adapted for use with oxides. They are based on ion erosion with the source of ions being either a radiofrequency plasma (Atkinson and Taylor, 1977), or an ion beam source
309
(Mundy and Rothman, 1983). A constant fraction of the sputtered material is collected on a substrate which can then be counted subsequently. Both configurations have been automated and are capable of an ultimate depth resolution of about 5 nm. The dynamic range of concentration which can be explored by a radiotracer technique can be as large as 5 or 6 decades and, even if the diffusant is a solute, the tracer still does not dope the oxide significantly in many cases. Unfortunately, for studies of many ceramics, there is no convenient radioisotope. This is true for O, N, Al and Si. However, there are sometimes stable isotopes, e.g., 17 O and 18 O. In early experiments with these particular isotopes total exchange with 16 O was measured as a function of time on a powdered sample. Subsequently, depth profiling techniques were developed for 18 O, based either on nuclear reaction analysis (Amsel et al., 1971), or secondary ion mass spectrometry, SIMS (Kilner et al., 1984). It is now recognised that the depth profiling methods are more reliable than the total exchange methods. The dynamic range of useful stable isotope concentration is limited by the naturally-occurring background levels of these isotopes and is inferior to that of radioactive isotopes. The solutions to the diffusion equations for one-dimensional diffusion from a finite thin source, finite thick source, or source of constant surface concentration may be found in standard texts (Crank, 1975; Adda and Philibert, 1966). In many practical cases, however, significant deviations from ideal behaviour may be observed resulting from the assumed theoretical boundary conditions not being met. These are often evident in studies of oxygen diffusion by exchange with the gas phase and the basic solutions have been modified to account for such perturbing factors as loss of mate-
310
6 Diffusion in Ceramics
rial by evaporation, or gain by condensation, and a relatively slow exchange of isotopes at the source plane (Routbort and Rothman, 1985). 6.4.2 Solute Diffusion, Interdiffusion and Chemical Diffusion
For solute (impurity) diffusion it is possible to use either a radiotracer, if it is desired to keep the total concentration negligible, or the actual chemical species. For the former, all the comments made in the discussion of tracer self-diffusion apply. When the solute is not labelled it is convenient to use electron probe microanalysis (EPMA) for large penetration depths and SIMS for shallow depths. If the solute concentration range is so large that the diffusion coefficient is concentration dependent [e.g., as would be predicted from Eq. (6-25)] then the Boltzmann-Matano method can be used to extract the interdiffusion coefficient from the concentration profile (Chap. 2, Volume 5). The chemical diffusion coefficient, 5, may be measured by monitoring the relaxation of a bulk parameter following a sudden change in the external thermodynamic activity of one of the components (e.g., oxygen activity for an oxide). Electrical conductivity or mass (i.e., deviation from stoichiometry) are the parameters usually chosen (e.g., Fahri and Petot-Ervas, 1978). In recent years the measurement of mass changes coulometrically has become popular for oxides. In this technique a solid electrolyte oxygen ion conductor is used both to control the thermodynamic activity and monitor the uptake of oxygen by a sample (Millot and de Mierry, 1985). 6.4.3 Identifying the Diffusion Mechanism
From the nature of the defect-forming reactions (Sec. 6.2.2) it follows that, when
redox reactions are involved, the point defect concentrations, and hence the diffusion coefficients, are predicted to have a simple power law dependence on the thermodynamic activity of the components of the ceramic compound. This has been exploited particularly successfully in oxides to identify the nature of the defect responsible for diffusion. It is usually possible, using this approach, to distinguish between the diffusing defect being a vacancy or interstitial and, in favourable cases and with good experimental technique, the effective charge on the defect can be determined. This usually demands supplementary data for the variation of electrical conductivity and non-stoichiometry with component activity; especially when considering diffusion by a minority defect. From the discussion of correlation effects it is clear that the correlation factor, /, is potentially able to characterize the diffusion mechanism. Although, / cannot be measured directly an estimate of / has proved useful for narrowing down the range of possible diffusion mechanisms in many cases. One way of estimating / experimentally is by combining measurements of D*, D and non-stoichiometry in Eq. (6-30). Unfortunately the combined measurement errors are usually too large for a useful determination of / by this method. A second is by comparing the diffusion coefficients of two isotopes (a and P) of the same element. For a single atom jump mechanism this gives the so-called "isotope effect" (Chap. 2, Volume 5) ; where M a and M p are the atomic masses of the isotopes. AK is related to the distribution of kinetic energy between the jumping atom and its neighbours when it reaches
6.4 Diffusion Experiments
the saddle point. AK is less than, and close to, unity and depends on the diffusion mechanism. Values of / AK for different mechanisms have been summarised by LeClaire (1976) and examples of its use are to be found in studies of diffusion in transition metal oxides by Peterson et al. (1980). 6.4.4 Experimental Precautions and Problems
The main source of experimental difficulty in studies of diffusion in ceramic materials has proved to be the fabrication of suitable specimens. This applies to single cystals, high density polycrystalline specimens and the joining of couples for interdiffusion experiments. As a consequence, diffusion data for ceramics tend to be less precise and more variable (from worker to worker or from sample to sample) than those for metals. It is therefore essential that the samples should by comprehensively characterized (composition and microstructure) in any study of diffusion in a ceramic material. These specimen fabrication problems are often compounded by the need to carry out diffusion anneals at high temperatures which emphasize effects of evaporation, condensation of impurities and instabilities in surface topography. If attempts are made to avoid these problems by working at lower temperatures, others are often encountered as a result. For example, surface exchange reactions may become dominant, or penetration depths may be too shallow for accurate determination. Despite such problems, it is possible to take precautions which will minimize their effects. Perhaps the most important of these is to establish the thermodynamic state of the ceramic before the diffusion anneal. This is done by equilibrating the sample, in a pre-anneal under the same con-
311
ditions of temperature, pressure and thermodynamic activity (e.g., aOl for oxides) as the intended diffusion anneal. The time required for complete equilibration can be calculated if the chemical diffusion coefficient is known. However, since D ^> D* in most ceramics it is usually sufficient to carry out the pre-anneal for the same duration as the diffusion anneal. In the case of interdiffusion experiments an external surface is often necessary for the local defect structure to relax as composition changes with time. This can result in interdiffusion profiles which depend on position with respect to an external surface and departures from local equilibrium becoming evident. Diffusion by short-circuits (gas-phase, surfaces, grain boundaries, dislocations, porosity, second phases, etc.) can be studied in its own right, or can be a source of error in bulk diffusion studies. Their influence can be assessed by a variety of techniques such as: removing material from the back and sides of the sample; using spatial imaging techniques to observe the distribution of diffusant (EPMA, imaging SIMS and autoradiography); and, carrying out diffusion anneals as a function of time to verify the expected time dependence of the assumed diffusion process. Impurities are often a problem in diffusion studies in ceramics because the defect populations are sensitive to their presence; especially heterovalent impurities in ionic ceramics. However, water is an impurity that is seldom controlled experimentally and is now known to have a large influence in some oxides. For example, water has an enormous influence on the diffusivity of oxygen in amorphous silica. Norby (1987) has surveyed the literature for oxides and concluded that for most oxides the effect of water is manifest as an interstitial proton, Hi. Figure 6-4 illustrates how the interstitial proton could dominate the point defect
312
6 Diffusion in Ceramics
[Hil = [H']
n ION
2 [ V Q 1 = /?
ro c_
s
t—
cV o
s
y^
s
'**•
s
[ Hj]
©
s / s
oi o
[VQ]
y
log 1 0 a
H20
\ \ \
Region I " Intrinsic
\
\
\
ent
I \
M_ QJ O LJ
(Diff iJSIO
c
en o
\V Cation \
\ \ \ \ \
Anion\
\
V \\ v \ \\ \\ \\ "I 1 1 I I t
\
<£ \ ^ Association
\
Figure 6-4. Illustrative defect concentrations as a function of water vapour activity in an oxygen deficient oxide in which the dominant defects are normally oxygen vacancies and electrons. The electrical neutrality conditions and characteristic slopes are given on the curves. (After Norby, 1987.)
\ \
\
\
Precipitation
\ \\
I » 1
Figure 6-5. Schematic Arrhenius plot illustrating different regions (roman numerals) of diffusion behaviour in a ceramic in which cation diffusion is faster than anion diffusion.
population in an oxide as the water vapour pressure increases. In this example water vapour is expected to suppress oxygen diffusion. The complicated nature of point defect populations in most ceramics means that there is, in general, no simple relationship between the Arrhenius parameters, Do and Q, and the point defect thermodynamic quantities, gi and gm. The general form of an Arrhenius plot of D* for cations and anions in a ceramic in which cation defects predominate is illustrated in Fig. 6-5. In region I (highest temperatures and purest materials) diffusivity is said to be intrinsic (i.e., a property of the pure compound) and the activation energy contains contributions from hf and hm. If the ceramic is nonstoichiometric, and the experiments are carried out at constant composition, the activation energy for cation diffusion will be equal to hm for the dominant cationic defect. However, it is rare that sufficient knowledge of non-stoichiometry, as a func-
6.5 Computer Simulations
tion of temperature and component activity, exists for this approach to be viable. It is more usual to carry out diffusion experiments as a function of temperature at a constant value of component activity (and conversely as a function of activity at constant temperature). Therefore, in most cases the contribution of hf to Q depends on the details of the dominant defect-forming reactions. In the extrinsic regions (II, III and IV) the point defect populations are controlled by solute impurities or dopants. In region II the defects are assumed to be noninteracting and therefore <2, in this region, is equal to hm. This region is seldom evident in practice because the defects associate strongly leading to region III straight from region I. Finally, the interactions become so strong that they lead to the formation of large defect aggregates and, ultimately in region IV, the precipitation of a second phase. Doping is often regarded as a method for probing the host defect populations, but the effects of doping are seen to be rather complicated. Useful qualitative information is obtained by observing whether a particular dopant results in an increase or a decrease in diffusivity. However, quantitative interpretation of the activation energy in the extrinsic region is usually not straightforward.
6,5 Computer Simulations In principle, diffusion coefficients can be predicted if the free energies of formation and migration of point defects are known. In ionic crystals these energies were first estimated theoretically by including only electrostatic energy in a continuum approximation. In this way the energy to form a Schottky defect pair in alkali
313
halides becomes (Lidiard, 1957) uf = 1 , i R R a Snsne
(6-32)
In this expression jRa and Rc are the radii of the anion and cation, s is the dielectric constant and aM the Madelung constant for the crystal structure. The first term therefore represents the increase in potential energy required to remove the ions from their lattice sites and place them on the crystal surface. For NaCl this is about 9 eV. The second term represents the lowering of electrostatic energy by the polarisation of the dielectric medium under the field of the effective charge on each vacancy. For NaCl this is 4.8 eV and hence uf = 4.2 eV, which illustrates the large contribution made by the polarisation energy. (The experimental value of h{ is about 2.5 eV.) Furthermore, both electrostatic terms increase as the square of the ionic charge and therefore highly charged ions are associated with large defect formation energies. This simple calculation neglects many other important contributions to the energy of formation of a defect, such as: interatomic repulsion, relaxation of ionic positions in the vicinity of the defect, ionic polarisation (dipolar), ionic distortion (quadrupolar), temperature and defect-defect interactions. (When these are included the experimental data and simulations for alkali halides are in good accord.) The rapid expansion in computational power has enabled these effects to be dealt with in sophisticated computer simulations of defect energetics and dynamics as described in a recent detailed review by Harding (1990). Two different approaches have been taken; one in which energy is minimized as a function of atomic position (sometimes
314
6 Diffusion in Ceramics
referred to as "static lattice" calculations) and the other in which the atoms are in motion (molecular dynamics). 6.5.1 Energy Minimization In this method the total energy is calculated as a function of the positions of the atoms and their positions are varied in order to determine the minimum energy configuration. This corresponds to calculating internal energies at constant volume and absolute zero of temperature, but, by a fortunate coincidence, these are almost equal to enthalpy changes at constant pressure. The energy of motion of a defect in this method is calculated by postulating the general direction of the atomic jump and calculating the energies en route to determine the energy of the saddle point configuration. These methods have been applied extensively to bulk oxides by Catlow (1984) and Mackrodt (1984) and, more recently, to ceramic surfaces, grain boundaries and dislocations. The entropies of defect formation and motion can be calculated from the relationship (for temperatures above the Debye temperature) s=
-
vn (defective) vn (perfect)
(6-33)
where vn are the vibrational frequencies of the perfect crystal and the crystal containing the defect. This expression gives the entropy change at constant volume, whereas most experiments are carried out at constant pressure, and therefore Eq. (6-33) has to be modified to make comparison with experiments. It has only recently been possible to calculate entropies from the atomic configurations resulting from the energy minimization techniques. It is clear, however, from Eq. (6-33) that sf and sm are of the order kB.
6.5.2 Molecular Dynamics In molecuar dynamics simulations a fixed number of atoms in a "box" with periodic boundary conditions is set in motion with a distribution of velocities corresponding to that of thermal equilibrium at temperature T. The particles follow the equations of motion whilst interacting through an assumed interatomic potential. Because of the complexity of the equations of motion for a large number of interacting particles, the interatomic potential is constrained to be much simpler than that used in energy minimization and would not normally include polarisation, distortion and directionality. A detailed description of the method may be found in Sangster and Dixon (1976). Since the time step of the simulation is necessarily small in comparison with the vibrational frequency it follows that diffusion and defect generation are rare events unless the temperature of the simulation is high, the solids highly defective, or motion abnormally rapid. Thus molecular dynamics simulations have made most impact on studies of highly disordered systems and fast ion conductors (e.g., Gillan, 1989). Both computer simulation methods are at their most powerful when used in close association with experiments. The interaction between theory and experiment serves to enhance both and the simulations have proved to be particularly useful in guiding the identification of point defect types and their migration pathways. The absolute defect energies from even the best simulations are unlikely to be more accurate than ± 0.2 eV. Nevertheless, relative energies are expected to be more precise and trends (e.g., with ionic size) revealed in simulations should be reliable.
315
6.6 Examples of Diffusion in Ceramics
6.6 Examples of Diffusion in Ceramics
-10
1600
1400
1
1
(c) N
In this section examples of diffusion in some different types of ceramic are described in order to illustrate the principles discussed in previous sections and demonstrate the breadth of diffusion behaviour. The review is not meant to be a compilation of data, for which the reader is referred to the general literature and bibliographies (e.g., Freer, 1980).
1100
1000
Jb) \
-12-(f)
\(e)
\
\
\
\ \(g)
\ -16-
\ \ \ (i)
6.6.1 Refractory Oxides A1 2 O 3 and MgO
Both these oxides have been studied extensively; alumina because of its commercial importance and magnesia because it is highly ionic and has many similarities with the alkali halides. The experimental problem with these oxides is that because the energy to form defects in the pure material is very large, it is not possible to access the intrinsic region. Consequently measured diffusion coefficients vary from sample to sample. In alumina the oxygen tracer diffusion coefficient is extremely low (Fig. 6-6) with an activation energy as high as 7.6 eV. Cation diffusion in alumina is faster than oxygen diffusion (by about 4 orders of magnitude at 1500°C). Direct experimental evidence for the diffusing defects is sparse and controversial. Ando (1987) found that the diffusion of Mg in A12O3 was proportional to [Mg] and therefore deduced that both Mg and Al diffuse in alumina by an interstitialcy mechanism. Studies of oxygen diffusion in alumina doped with MgO or TiO 2 (Reddy and Cooper, 1982) revealed that Mg had no effect whereas Ti lowered Dg. These observations are difficult to reconcile with the behaviour of D^ g in A12O3 and illustrate the
T in°C 1200
\
1
-18
7 T in K-1
Figure 6-6. Tracer diffusion coefficients for oxygen in oxides having a close-packed oxygen lattice. Discrepancies between different workers for CoO, MgO and A12O3 illustrate experimental difficulties, (a) FeO at PColpco2 = !> (b) M n O a t 0o2 = 1 ( r l l > (c) C o ° a t aO2 = 02, (d) CoO at aO2 = 0.2, (e) NiO, (f) MgO, (g) MgO, (h) A12O3 and (i) A12O3. (After Atkinson, 1989.)
unsatisfactory state of understanding for this technically important ceramic. In MgO magnesium diffusion is also faster than oxygen diffusion, but there is much greater consensus on the nature of the point defect populations than for alumina. Oishi et al. (1987) found that Li-doping increased oxygen diffusion, from which they concluded that oxygen diffusion was occurring by oxygen vacancies induced by the reaction MgO Mg
(6-34)
The studies of D^g in MgO do not give any indication of the diffusion mechanism. However, studies of the interdiffusion and tracer diffusion of Cr in MgO (Osenbach et al., 1981) have been interpreted using
316
6 Diffusion in Ceramics
the Lidiard pair association model and demonstrate convincingly that, since 5 CrMg = 2 D$r (see Fig. 6-7), Cr diffusion is by a ( C r ^ V y , complex. The experimental evidence therefore indicates that Schottky defects would be formed in MgO if the intrinsic region could be accessed. This is consistent with computer simulations (Jacobs and Vernon, 1990) which indicate that the Schottky pair has a formation energy of about 8 eV compared with over 12 eV for either cation or anion Frenkel pairs. The simulations also indicate that both the cation and anion vacancies have approximately equal migration energies of about 2 eV which would lead to intrinsic Arrhenius energies of about 6 eV for both magnesium and oxygen. Since the experimental values are about 3 eV for Mg and 4 eV for oxygen (Matzke, 1986), impurity-vacancy binding seems to be important. Wuensch (1983) has summarized data for the diffusion of divalent solute ions in MgO (Fig. 6-8) which show that the smaller ions tend to diffuse faster. Trivalent cations are observed to diffuse more slowly
3.0-
o •
1768 K 1717 K
A 1656 K
i—^— 2.0 -
•AOA*OA#A
o
o
AmA
o<
A
1.0i
1
I
1
1
0.5 10 Ionic radius in A
Figure 6-8. Solute diffusion coefficients for divalent cations in MgO as a function of ionic radius. The temperatures are: • 1000 °C, o 1500 °C (After Wuensch, 1983.)
than divalent ones in MgO. For Cr in MgO, Eq. (6-23) becomes D%T = 0.5 a2 w2 [Cr] exp
-
(6-35)
and Weber et al. (1980) deduced that the activation energy for w2 is 1.73 eV and that hA = — 0.9 eV. This attractive association between the Cr solute and the magnesium vacancies would be expected to make Cr diffuse faster than magnesium. However, the opposite is found in reality and this implies that w2 ^ w0 for solutes of greater charge than the host, reflecting the dominance of coulomb interactions in ionic systems. Unfortunately this is not supported by the relative values of the activation energies for w2 (1.73 eV from experiment) and w0 (2 eV from computer simulation).
I
3 [Cr]
Figure 6-7. The ratio of the interdiffusion coefficient of Cr and Mg in MgO to the tracer diffusion coefficient of Cr in MgO as a function of chromium concentration. The temperatures are: o 1768 K, • 1717 K, A 1656 K. (After Osenbach et al., 1981.)
6.6.2 Transition Metal Oxides The transition metal oxides exhibit a rich variety of behaviour and their point defect and mass transport properties have been widely studied. The general ability of
6.6 Examples of Diffusion in Ceramics
these elements to exhibit more than one valence state means that oxidation and reduction reactions of the type exemplified in Eqs. (6-5 a) and (6-5 b) tend to dominate. Diffusion in some of these oxides (TiO 2 , Cr 2 O 3 , MnO, FeO, Fe 3 O 4 , Fe 2 O 3 , CoO, NiO and Cu 2 O) has recently been reviewed by Atkinson (1987) and the best values for thermodynamic parameters for the point defects have been summarized. TiO 2 (rutile) has generally been regarded as oxygen deficient (TiO 2 _J, but the weight of available evidence now seems to favour metal excess (Ti 1+x O 2 ). Titanium diffusion takes place by an interstitialcy mechanism involving a mixture of Tif" and Tif * defects (the relative proportion depending on temperature and oxygen activity). The activation energy for migration of the Ti interstitial is 0.68 eV and the activation energy for titanium diffusion (at constant oxygen activity) is 2.8 eV (Hoshino et al., 1985). Oxygen diffusion is much slower than titanium diffusion and probably occurs by a vacancy which has a high activation energy for migration; about 2.9 eV (Derry et al., 1981). The rocksalt structure oxides (NiO, CoO, MnO and FeO) are all cation deficient (M^^O) with S generally increasing on going from NiO to FeO. It is well established that cation diffusion in these oxides is by a vacancy mechanism, but there is still argument about the extent of interaction between defects, particularly at large values of S. Activation energies for cation vacancy migration in these oxides are about 1.5 eV and more complex defects (where these are definitely known to exist, as in FeO) are relatively immobile. Atomistic calculations of point defect properties are in fair accord with experimental observations in these oxides. A recent notable success has been a calculation of gf and gm for cation diffusion in CoO which has allowed
317
direct calculation of the diffusion coefficient (Fig. 6-9) and is within an order of magnitude of the measured value (Harding and Tarento, 1987). Oxygen diffusion is extremely slow in these oxides (Fig. 6-6) and activation energies at constant oxygen activity are large (about 5 eV). Although the oxygen lattice is a close-packed structure, both experimental and theoretical studies seem to favour oxygen diffusion by an interstitialcy mechanism, or a mixture of interstitialcy and vacancy diffusion (Dubois etal., 1984). Fe 3 O 4 (magnetite) has been particularly well-studied by Dieckmann etal., (1977). Iron diffusion is much faster than oxygen diffusion and takes place by iron vacancies at high oxygen activity and iron interstitials at low oxygen activity. The two defect types give rise to a characteristic "v" shape of the plot of diffusion coefficient as a function of oxygen activity (Fig. 6-10). The isotope effect studies of Peterson et al. (1980) in this oxide are a particularly good example of their use in helping to clarify a diffusion mechanism.
-6
1
i
T -7 (/)
E Simulation
5 _8 r-Pi
u
Experiment -9 -
-4
i
I
-3
-2
i
-1
l°9io Figure 6-9. The tracer self-diffusion coefficient for Co in CoO as a function of oxygen activity comparing the results of experiment with those of computer simulation. (After Harding and Tarento, 1987.)
318
6 Diffusion in Ceramics
-6F
Figure 6-10. The tracer diffusion coefficient of Fe in Fe 3 O 4 as a function of oxygen activity. The positive slope at high aOl is indicative of iron vacancies and the negative slope at low aOl indicates iron interstitials.
Fe 2 O 3 (hematite), on the other hand, is oxygen deficient and, on present evidence, it appears that oxygen vacancies are the dominant defects. Nevertheless, iron diffuses more rapidly than oxygen in hematite; probably by an interstitialcy mechanism. The activation energy for iron diffusion at constant oxygen activity is high (6.0 eV) even though iron is the faster diffusing species. The situation in Cr 2 O 3 is controversial because of the very low defect concentrations in this oxide and the resulting experimental difficulties. On the balance of present evidence it appears that the dominant defects are chromium interstitials at low oxygen activity and chromium vacancies at high oxygen activity. In this respect it is similar to Fe 3 O 4 . The activation energy at constant oxygen activity for chromium diffusion in the vacancy region is high (about 6eV). A typical example of the influence of heterovalent doping on host diffusion is that of Al in NiO (Atkinson etal., 1981). The substitution of trivalent aluminium for divalent nickel creates more nickel vacancies
(the intrinsic majority defect) by the reaction A12O3
NiO
(6-36)
The observed diffusion of Ni in Al-doped NiO (Fig. 6-11) is deduced to be in regions III and IV of the generalized behaviour illustrated in Fig. 6-5. In all regions diffusion of Ni occurs by isolated vacancies, but in region III they are in equilibrium with relatively immobile associates, (Al^V^i)', and in region IV with both associates and precipitates of the spinel NiAl 2 O 4 . The association enthalpy of the dimeric defect was deduced to be hA= — 1.0 eV, which is approximately equal to that deduced for the similar dimer (CrMgVMg)' in MgO discussed in the previous section. Tracer diffusion coefficients for a range of cation impurities in CoO and NiO have been reported by Hoshino and Peterson (1984) and Monty (1983). In general, the results (Fig. 6-12) show a trend in which small ions diffuse more slowly than large ones and have larger activation energies for Df. (There are exceptions, however,
6.6 Examples of Diffusion in Ceramics
such as Ca 2 + which is large and diffuses slowly with high activation energy.) Theoretical estimates (Harding et al., 1990) of the activation energy of w2 tend to support this trend, but the measured values of Qi~ Qo a r e n o t i n good agreement with calculated ones in most cases. For example, the measured activation energies of Df for Fe and Mn in NiO are about 0.7 eV lower than that of D^i? whereas theory suggests they should all be the same to within 0.1 eV. Indeed, it is difficult to envisage how such low activation energies could arise for any divalent ions. This is because even if the impurity jump w2 is very fast, the limiting value of f2 is approximately wo/w2 and hence D2/D0 has the limiting T in °C
-6
2000
1600 1400 1200
Association
1000 900
800
700
Association and precipitation
0.9
Ionic radius in
Figure 6-12. The difference between the activation energy for solute diffusion, Q2, and that for self-diffusion, Qo, for cationic solutes in CoO (•) and NiO (•) as a function of the ionic radius of the solute ion. (Data from Harding et al., 1990.)
value exp[— hA/(kBT)]. Physically, this corresponds to the impurity repeatedly exchanging with the same vacancy. A low activation energy can thus only occur if hA is appreciable and negative (in this case about — 0.7 eV). This could be explained if Fe and Mn are present as trivalent (rather than divalent) ions in NiO at low concentrations.
-10
3 -12
6.6.3 Fluorite Structure Oxides
-14
-16
0.8
319
5
6
7
8
1 0 * / T i n K-1
Figure 6-11. The tracer self-diffusion coefficient for Ni in undoped NiO (solid lines) and NiO doped with aluminium to [Al] = 4.7 x 10" 3 (experimental points). The change in activation energy at about 1150°C is due to the precipitation of NiAl 2 O 4 spinel at lower temperatures. (After Atkinson et al., 1981.)
The class covers such oxides as UO 2 , ThO 2 , PuO 2 ? ZrO 2 and related oxides, e.g., Y 2 O 3 . In these oxides oxygen diffuses far more rapidly than the metal cations. They can be ionic or electronic conductors depending on the individual oxide, doping, oxygen activity and temperature. UO 2 has been studied particularly thoroughly because of its importance in nuclear power systems.
320
6 Diffusion in Ceramics
Diffusion and defects in UO 2 have been summarized by Breitung (1978) and Matzke (1983,1986). The dominant defects in oxygen-rich non-stoichiometric UO 2+(5 are oxygen interstitials and compensating electron holes (similar to U 5 + ions), but as the , oxygen activity is reduced, and stoichiometry is approached, oxygen Frenkel disorder (O" and Vo') dominates. This results in oxygen diffusion exhibiting two activation energies (at constant 5) with the temperature of transition between the two regions being dependent on 3 (Fig. 6-13). The activation energy for migration of the O" defect is 0.52 eV from the activation energy for oxygen tracer diffusion in the oxygenrich region. Close to stoichiometry and in the oxygen deficient region the more mobile (but more difficult to form) oxygen vacancy is responsible for diffusion. Matzke (1986) has correlated lattice diffusion of cations in ThO 2 , UO 2 and CaF 2 and shown that they approximate to a common behaviour as a function of reduced temperature, T/Tm.
6.6.4 Complex Oxides So far we have discussed binary compounds or binary compounds containing small concentrations of solutes. In many practical applications ceramics are in the form of concentrated solid solutions or multicomponent complex oxides (e.g., the perovskite-structure ferroelectrics and superconductors). The rocksalt-structured oxides NiO, CoO, FeO and MgO provide typical examples of a solid solution series in which the cations are sufficiently similar in size that these oxides form complete ranges of solid solution. It is found (Schwier et al., 1973) that the influence of the homovalent solute on self-diffusion of the host cation is small, unless the concentration of the dopant is large. The main effect is on the energy of formation, /if, of the cation vacancy responsible for diffusion which varies linearly between the two end members of the solid solution (A, B) O, i.e., (6-37)
T in °C 2000
400
Figure 6-13. Tracer self-diffusion of oxygen in the fluorite-structure oxide UO2+<5 as a function of temperature, for different values of 3. The limiting behaviour at stoichiometric composition is dominated by oxygen Frenkel disorder. (After Breitung, 1978.)
6.6 Examples of Diffusion in Ceramics
321
This leads to an activation energy which varies linearly with composition. A typical example is Mg doping of CoO (Fig. 6-14) where the Mg reduces the diffusion coefficient of Co because it is more difficult to form cation vacancies in MgO than in CoO. The diffusion coefficients have the form b [MgO])
(6-38)
Extensive solid solution is only possible when the ions are similar in size. If the ionic sizes are very different then the solid solution is correspondingly limited and stronger interactions are generated between the dopant and defects on the host lattice. For example, if the dopant is larger than the host it will tend to attract host vacancies to minimise the strain associated with the size mismatch. This attractive interaction can be described by a binding energy between the dopant and the host vacancy. If the dopant is also relatively immobile then the dopant acts as a trap for host vacancies and would thereby be expected to reduce diffusion of the host cation. Typical values for the binding energy between defects due to size mismatch are up to 0.5 eV. Many ternary oxides have a well-defined stoichiometric ideal composition such as MgAl 2 O 4 , NiCr 2 O 4 , BaTiO 3 , etc. There have been few recent diffusion studies, but early experimental data for some ternary oxides were summarized by Birchenall (1968). Although early data should be viewed with some caution (in some oxides later studies have revealed that earlier work was unreliable because of poor sample quality) Birchenall's review does allow certain trends to be identified. When the ternary oxide (e.g., MgAl2O4) and the two binary components (MgO and A12O3) all have a close packed oxygen sublattice, diffusion rates in the ternary oxide tend to be intermediate between those of the two bi-
Figure 6-14. Tracer diffusion of Mg and Co in the solid solution C o ^ M g ^ ^ as a function of composition. The symbols are: A DJ O , O D£g. (After Dieckmann, 1984.)
nary oxides. This can be useful in estimating unknown diffusion coefficients in multicomponent compounds when data are available for the simpler component compounds. The high temperature superconductors are complex oxides which are currently of great interest. In these materials oxygen diffusion is much more rapid than cation diffusion (Fig. 6-15) because of the relatively large concentration of vacancies on the oxygen sublattice (Routbort et al, 1991). The compound YBa2Cu3O7_<5 is typical of the high temperature superconductors. It has a layered structure in which some of the layers contain only copper and oxygen
322
6 Diffusion in Ceramics
Figure 6-15. Tracer diffusion for oxygen and cations in the superconductor YBa 2 Cu 3 O 7 _ 5 . The symbols are: • Ag, • Zn, o Co, + Ni. The chemical diffusion coefficient D (A) is also shown. (After Routbort et al., 1991.) 1.3
ions and it is known that oxygen vacancies are formed easily in these layers. Thus oxygen diffusion is highly anisotropic; with oxygen diffusion in the plane of the layers (the ab plane) being about 103 times faster than diffusion perpendicular to the layers (the odirection). Rothman and Routbort (1990) have reviewed measurements of oxygen diffusion in La2_xSrJCCuO4 and YBa 2 Cu 3 O 7 _^ and drawn attention to the differences between D* and D. There is general agreement that in YBa 2 Cu 3 O 7 _j oxygen moves by a vacancy mechanism in the ab plane, but the details of the diffusion mechanism and the exact relationship of D* to D in this oxide are not yet clear. The experimental results show that D* and D are of the same order of magnitude (Fig. 6-15) and this appears to be true even when 3 approaches zero. This is difficult to understand if, as explained in Sec. 6.2.5.3, D is approximately equal to the diffusion coefficient of the vacancies and D* to the product of the vacancy diffusion coefficient and the vacancy concentration. The near-equality of D* and D implies either strong correlation ef-
fects and/or large departures from ideality in the thermodynamic behaviour of the vacancies. The current experimental data also exhibit some inconsistencies in that Rothman and Routbort (1990) found that D* is relatively insensitive to 5 whereas Tu et al. (1989) deduced that the activation energy of D varies from 1.3 eV at (5 = 0 to 0.5 eV at (5 = 0.38. Routbort et al. (1991) report that D* for copper diffusion is also highly anisotropic and increases as 3 increases in YBa 2 Cu 3 O 7 _ (5 . They interpret this as indicating that copper ions are also mainly mobile in the ab planes, which contain chains of copper and oxygen, and that oxygen vacancies in these planes lower the enthalpy for copper vacancy migration. It is clear that much further work will be required to clarify the mass transport characteristics of this important class of complex ceramics. 6.6.5 Carbides and Nitrides
Carbides and nitrides form an important class of ceramics for high temperature engineering and hard surface applications.
6.6 Examples of Diffusion in Ceramics
Diffusion in carbides and nitrides has been reviewed by Matzke (1990). In the carbides and nitrides of elements from the first transition series upwards in the periodic table there is a large discrepancy in size between the metal atom and the carbon or nitrogen atom. Consequently these compounds tend to form close-packed metal structures with the small atoms in interstitial positions, e.g., in mono-carbides and nitrides with the NaCl structure. Sometimes the interstitial space is large enough to accommodate two interstitial atoms, resulting in dicarbides. In most cases non-stoichiometry can be large and phase diagrams are complicated (e.g., in T i N ^ ^ , S can be as large as 0.4 in the phase with NaCl structure). Consequently in the mono-carbides and mono-nitrides with NaCl structure the
3000 I -6 —
2600
rin°C 2200 2000
1800
323
majority defects are C and N vacancies or interstitials depending on the sign of S. This is reflected in the diffusivities of the metal atoms being much lower than the diffusivities of C and N (Fig. 6-16). In SiC the atoms are closer in size and the bonding is strongly covalent Nevertheless, carbon diffusion in a-SiC is about 103 times faster than silicon diffusion, although both have approximately the same activation energy of about 8 eV (Hon et al., 1981). It has also been found that nitrogen doping of SiC increases silicon diffusion and decreases carbon diffusion. The band gap of SiC is relatively low (semiconductor) and therefore N^ or N^ will be chargecompensated by electrons. The extra electrons would tend to suppress existing donors and enhance existing acceptors.
1600
1400
Carbon
TiCo.97 NbC(0.77-0.87)
-12
TiCo.89
I
I
4
5 10* / T in K-1
-
Figure 6-16. Tracer self-diffusion of carbon and metal atoms in carbides of Ti and Nb. (After Matzke, 1990.)
324
6 Diffusion in Ceramics
( = Si —O —O —Si = ) are equivalent to a silicon vacancy and conversely = Si — Si = bonds are equivalent to an oxygen vacancy. Those species having unsatisfied V* = V c + e' (donor, n-type) (6-39 a) bonding requirements (dangling bonds) V*. = ySi + h" (acceptor, p-type) (6-39b) are the equivalent of electronic defects. On this basis, it is possible to describe diffusion However, the nature of point defects in in amorphous materials in analogous SiC is still largely a matter of speculation. terms to those used for crystalline materials. 6.6.6 Glasses In amorphous silica, self-diffusion of silicon is extremely slow and probably takes Diffusion in amorphous oxides has been place by the analogue of a vacancy mechasummarized by Frischat (1975). In the simnism. The activation energy is high (Fig. plest binary oxide glass, SiO 2 , the network 6-17) reflecting the large number of direcstructure may be regarded as being formed tional bonds that have to be broken and from SiO 4 tetrahedral units which genreformed for migration to take place. erate a three-dimensional network by Oxygen diffusion appears to occur by corner-sharing the oxygen atoms. The two mechanisms. The silica structure is sufnetwork defects are thus departures from ficiently open that an interstitial oxygen this network-forming rule. In this way, molecule can be accommodated in some two oxygens bonded to each other Thus it may be that diffusion is by carbon vacancy donors and silicon vacancy acceptors:
10
15 10V T in K-1
20
Figure 6-17. Diffusion coefficients for species in amorphous SiO 2 . (After Atkinson, 1989).
6.7 Short-Circuit Diffusion
parts of the structure. This molecule is known to diffuse as a direct interstitial species with a high diffusion coefficient. In dry conditions the interstitial oxygen does not exchange readily with oxygen in the network. Consequently the two oxygen diffusion pathways (interstitial and network) are independent and the tracer diffusivity of network oxygen is almost as low as that of silicon (Fig. 6-17). In relatively small amounts of water vapour (e.g., l - 1 0 p p m in the gas) the exchange between interstitial oxygen and network oxygen is catalyzed by - O H groups. Under these conditions the tracer diffusion coefficient is increased by several orders of magnitude. When the water vapour concentration is high (e.g., in steam at one atmosphere) interstitial water molecules themselves become the principal carriers of oxygen, rather than interstitial O 2 molecules. As a consequence the "diffusivity of oxygen" in amorphous silica covers an extremely wide range and care has to be taken in defining the exact parameters and the conditions (particularly of water vapour) under which it has been measured. Network-modifying ions, such as alkali metals and alkaline earths, diffuse much more rapidly than the network-forming species (Fig. 6-17). Diffusion in glasses tends to be faster than in their crystalline equivalents. For example diffusion of Na along the c-axis in crystalline oc-Na2Si205 (the crystal is anisotropic and diffusion is most rapid in the c-direction) is about an order of magnitude slower than in a glass of the same composition (Heinemann and Frischat, 1990).
6.7 Short-Circuit Diffusion The term "short-circuit diffusion" refers to mass transport pathways along which
325
diffusion is much more rapid than in the bulk solid. Potential short-circuit pathways are dislocations, grain boundaries, solid interphase boundaries and free surfaces. In all ceramic materials these pathways will provide short-circuit transport for at least one component of the ceramic and, in most cases, for all components. (Short-circuit diffusion is not significant for components exhibiting unusually rapid bulk diffusivity; e.g., in fast ion conductors. In such cases diffusivity in grain boundaries is often lower than in the bulk and, for practical applications, slow diffusion across a grain boundary is of more concern than rapid diffusion along it.) Short-circuit diffusion in ceramics has been reviewed by Atkinson (1984 and 1988). 6.7.1 Phenomenology and Measurement of Short-Circuit Diffusion
In order to solve the mass transport equations short-circuits are treated as discrete regions of a high diffusivity material embedded in the host of lower diffusivity. In the case of a dislocation the dislocation line and its high diffusivity region are approximated to be a cylindrical pipe of diameter d in which the diffusion coefficient, Z)d, is greater than that of the surrounding lattice, D. In a similar way, a grain boundary is approximated as a slab of width S in which the diffusivity is D gb . The slab model is also used for free surfaces and interphase boundaries. The solutions of the diffusion equations for these model structures are now established for a variety of boundary conditions and geometries and these are used to analyse diffusion experiments in which contributions from short circuits are present. The measurement techniques for shortcircuit diffusion are the same as for bulk diffusion; with tracer depth profiling (in a
326
6 Diffusion in Ceramics
specimen containing short-circuits parallel to the diffusion direction) being the most reliable. A key parameter in such experiments is the extent of lattice diffusion, y/~Dt, compared with the distance between short-circuit pathways, /, and the width of the short-circuit, d or 3. In most experiments 3 < y/Dt < t (known as type B conditions; Harrison, 1961) and, under such conditions, diffusion along the short-circuits (and sideways into the surrounding lattice) is evident as a low concentration "tail" extending tracer penetration to greater depth than the normal bulk diffusion profile (see Sec. 6.2.2.4 of Chap. 2, Volume 5). For isolated disclocations the diffusion equations were solved by LeClaire and Rabinovitch (1982). Analysis of the penetration profile gives the product Dd d2, provided that the disclocation density is known approximately. However, it is more usual to find dislocations existing as arrays or networks forming low angle boundaries. Such cases can be treated phenomenologically in the same way as high angle boundaries. For grain boundaries (and surfaces, which are formally half the grain boundary problem) the appropriate solutions to the diffusion equations have been provided by Whipple (1954), for a constant surface concentration, and by Suzuoka (1961) for a thin film source of diffusant. The "tail" region of the logarithmic concentration profiles in these cases has a slope proportional to y6/5 (where y is the penetration depth) and analysis of the full profile gives the product Dgb 3. When the conditions of the diffusion anneal are such that diffusion in the lattice is negligible, the diffusant is confined to the short-circuit path. This will occur when y/D~t is much less than d or 3 (type C diffusion; Harrison, 1961) and enables Dgb or Dd to be measured directly. A suitable combi-
nation of experiments of type B and type C then permits an estimate to be made of the width of the short-circuit path. The transition between types B and C and the analysis of experimental data in this region have been discussed by Atkinson and Taylor (1986). In some geometries (e.g., fine-grained polycrystalline samples) the extent of lattice diffusion may be sufficiently large that the individual short-circuit paths cannot be considered to be independent. When y/Dt > € the overall diffusion process is characterized by an effective diffusion coefficient (type A; Harrison, 1961) which is a weighted average of individual jumps: Deff = (1 - 4>) D + 0 DSc
(6-40)
where
327
6.7 Short-Circuit Diffusion
raphy for radioactive tracers and imaging analysis techniques (SIMS, Auger, EPMA) for non-radioactive isotopes or solutes.
1600
1200 1000
T in °C 800 700 600 500 1 i
\
Q
\
-0
\
\
\
6.7.2 Dislocation and Grain Boundary Diffusion
s
\ -10
Diffusion of Ag along isolated dislocations in A12O3 has been studied by Badrour et al. (1986). Diffusion along dislocations as low angle boundaries has been reported for Ni in NiO (Atkinson and Taylor, 1979) and Cr in MgO (Osenbach and Stubican, 1983). Dislocation diffusivities were deduced using the relationship
; \.+
r O.high + \ \ angle ; \ -12 -* boundaries \ - \
\
\Ni,high angle \boundaries \ \ \
\
Ni\
\
dislocation \
\
.
\Ni,lattice
o 0,dislocations\
\
\
-16
-18
\
0
0
•
\
yO.lattice \ \ \ \ \
(6-41)
where 6 is the misorientation of a low angle tilt boundary and b is the magnitude of the Burgers vector of the dislocations. Diffusion in tilt boundaries of this type is faster parallel to the tilt axis (i.e., along the dislocations) than perpendicular to the tilt axis (Osenbach and Stubican, 1983). Diffusion along high angle boundaries has been studied more extensively. The relative magnitudes of various diffusion coefficients in NiO are illustrated in Fig. 6-18. These data illustrate that both Ni and O diffusivity are enhanced at dislocations and grain boundaries and that the faster diffusion pathways have the lower activation energies. A similar data compilation for A12O3 (Moya and Moya, 1988) shows that the situation in this important oxide is less clear; with some short-circuit diffusion coefficients having activation energies equal to, or even higher than, their lattice counterparts. At first it was anticipated that the effective width of a grain boundary as a fast diffusion pathway in an ionic ceramic might be much more extensive than the geometric core region, which was expected
\
\
2
nd Dd9 4b
1
'
\
_
i
i
i\
i 8
\ \ 1
1
9
10
1
i
12
13
10V T in K-1
Figure 6-18. Short-circuit diffusion of Ni and O along dislocations and grain boundaries in NiO compared with the tracer coefficients for bulk lattice diffusion. The width of grain boundaries and dislocations has been assumed to be 1 nm. (After Atkinson, 1987.)
to be of the order of only a few lattice parameters. This anticipation was based on the fact that dislocations, grain boundaries and surfaces in ionic materials are electrically charged and have compensating space-charge regions extending into the surrounding crystal regions in which point defect concentrations are enhanced. However, direct determinations of d and d from diffusion studies in NiO indicates that the high diffusivity region is only about 1 nm in width (Atkinson and Taylor, 1979, 1981). Computer simulations have been very successful in clarifying the structure and mechanisms of short-circuit diffusion in ceramics. These have been carried out for
328
6 Diffusion in Ceramics
Table 6-1. Activation energies, Q (eV), for lattice and grain boundary diffusion in NiO (Duffy and Tasker, 1986). Calculation
Experiment
Ni diffusion (vacancy) O diffusion (interstitialcy)
1.78 2.5
2.56 5.6
dislocations in MgO (Rabier and Puls, 1985) and for a variety of grain boundaries in NiO (reviewed by Duffy, 1986). The simulations confirm the narrow width of the fast diffusivity region and show that fast diffusion is caused by the segregation of point defects to the core region where they have higher concentration and higher mobility than in the lattice. The quality of agreement between experimental activation energies and those derived from computer simulation is illustrated in Table 6-1.
QJQs
e gb
2/
e gb /e.
0.70 0.45
1.6-2.2 2.5
2.9 5.3
0.5-0.8 0.47
The point defect mechanism for dislocation and grain boundary diffusion is supported by measurements of diffusion coefficients as a function of oxygen activity in NiO and Cu 2 O. The experiments are consistent with a vacancy mechanism for Ni in NiO and an interstitial mechanism for oxygen in Cu 2 O (Fig. 6-19). Most impurities and dopants segregate strongly to grain boundaries in ceramics where they are often to be found at high concentration, or as second phases (ranging from sub-monolayer coverage to true three-dimensional solid phases). Segregation is particularly important in commercial ceramics which often contain significant dopants to assist in processing or properties. The effect of these segregants and second phases can be both complicated and dramatic leading either to further enhancement of short-circuit diffusion, or effectively blocking the fast diffusivity pathways (Atkinson, 1988). 6.7.3 Surface Diffusion
Figure 6-19. The product of grain boundary diffusion coefficient and boundary width for oxygen diffusion in Cu 2 O at 712 °C as a function of oxygen activity. The slope of 0.5 is consistent with diffusion by an uncharged oxygen interstitial. (After Perinet, 1987.)
Surface diffusion tends to be even faster than diffusion along high angle grain boundaries and often displays two activation energies as illustrated in Fig. 6-20. The lower activation energy is believed to correspond to a local motion involving jumps to nearest-neighbour sites as in solid state diffusion. Measurements of surface diffusivity in this region for Fe and Ni on Fe 3 O 4 and NiO as a function of oxygen activity suggest that, as with dislocations
6.8 Processes Involving Diffusion
2000
1500
1200
r in°C 1000
800
700
329
fusion) and the diffusing atom is almost freed into the vapour phase.
Pu on UO2
6,8 Processes Involving Diffusion 6.8.1 Solid State Reactions
rv -15
Cr on Mg 0(001)
Non-local
-16 -17
7
8
9
10VTin K-1
Figure 6-20. The product of surface diffusion coefficient segregation coefficient and surface layer "thickness" for Pu on UO 2 (Furuya and Koizumi, 1976) and Cr on MgO (Stubican et al., 1985).
and grain boundaries, a point defect segregation mechanism is responsible (Lin and Stubican, 1990). At high temperatures a non-local mechanism is believed to be dominant in which the "jump" distance is much larger. This extended "jump" requires more energy (hence the larger activation energy for dif-
Reactions between two ceramic materials often occur as crucial steps in the fabrication or the deterioration of practical engineering components. The variety of such reactions is remarkable and the reader is referred to the book by Schmalzried (1981) for a thorough description. Here we briefly consider two examples of solid state reactions; one in a single phase and the other involving formation of a new phase. 6.8.1.1 De-Mixing in a Chemical Gradient When a slab of an initially homogeneous solid solution single-phase oxide, of the type (A, B) O say, is subjected to different oxygen activities at its two external interfaces, the point defect populations at the two interfaces will be different. As a result, defects and atoms will begin to migrate until a steady state is reached as illustrated in Fig. 6-21. In this example (Schmalzried,
0.40
x/l
Figure 6-21. The redistribution of components in an initially uniform solid solution (Co0 5 1 ,Mg 0 49 )O placed in an oxygen activity gradient (a'oJa'O2 = 3) for 126 h at 1439 °C The circles are experimental points and the solid curve was derived theoretically. The distance x is measured with respect to the length of the specimen, L (After Schmalzried, 1981.)
330
6 Diffusion in Ceramics
1981) the oxide is the solid solution (Co0 51 , Mg 0 4 9 )O. The oxide is a p-type semiconductor with cation vacancies as the majority point defects and the tracer diffusion coefficients are shown in Fig. 614. Cation vacancies will be transported on the cation sublattice from the high oxygen potential side to the low oxygen potential side while the oxygen sublattice is effectively immobile. Thus new oxide lattice units are being formed at the high oxygen activity side and oxide is being destroyed at the low oxygen activity side with the nett result that the slab is moving as a whole towards the high oxygen activity side with a steady velocity. Since the vacancy-cobalt exchange rate is greater than the vacancy-magnesium exchange rate (Fig. 6-14) more cobalt than magnesium moves in the opposite direction to the vacancies and hence the high oxygen activity side is enriched in cobalt and the low oxygen activity side is enriched in magnesium. Thus the originally homogeneous solid solution has become inhomogeneous (demixing). The steady state may be analyzed by solving the coupled transport equations of cobalt ions, magnesium ions, vacancies and electron holes. These are subject to the constraints that local chemical equilibrium and electrical neutrality are maintained and the oxygen potential difference is fixed. If other simplifying assumptions are made (the solid solution is ideal, the extent of non-stoichiometry is small and correlation effects are neglected) then the steady state composition profile, the oxygen activity distribution and the displacement velocity can be calculated from the tracer self-diffusion coefficients. A comparison between the calculated composition profile and the experimental one is shown in Fig. 6-21. The quality of agreement between theory and experiment is seen to be good. Dis-
crepancies may arise for a variety of reasons, such as: local equilibrium not being achieved; slow reactions at the surfaces; fast diffusion at grain boundaries; and geometric instability of the low oxygen activity interface. 6.8.1.2 Complex Oxide Formation A typical example of a reaction involving several phases is that occurring between a monoxide (AO) and sesquioxide (B2O3) to form a spinel product (AB2O4). The oxides may be predominantly ionic and of fixed compositions (e.g., MgO + Al 2 O 3 = MgAl2O4) or semiconducting and non-stoichiometric (e.g., CoO + Cr 2 O 3 -> CoCr 2 O 4 ). In such reactions a layer of the reaction product will grow by consumption of the reactants as illustrated in Fig. 622. The thickness of the reaction product, X, increases as the square-root of time (X2 = kp t) where kp is the parabolic reaction rate constant. The general case is very
1500 I
7"in°C 1400
1300
1200
I
1
I
AO
AB 2 0 4
B2O3
\ O
f-10
2B+ '
3A + "
\ \
\
\o -12
I 5.5
I 6.0 1 0 V T i n K-1
1
6.5
Figure 6-22. Comparison of experimental (circles) and calculated (solid line) rate constants for the formation of NiGa 2 O 4 spinel by the reaction of NiO with Ga 2 O 3 in air. (After Schmalzried, 1981.)
6.8 Processes Involving Diffusion
difficult to analyze since it involves coupled chemical diffusion in three phases and moving phase boundaries. If, however, the solids have only small ranges of solid solution and non-stoichiometry then the analysis is greatly simplified (see Schmalzried, 1981). An example of this kind is the reaction between NiO and A12O3 to give NiAl 2 O 4 for which the solubility of Ni in A12O3 and of Al in NiO are both small and therefore diffusion in the reactants can be ignored. If the oxides are also dense, then no oxygen can be transported across the spinel product layer as either gas or oxygen ions, since oxygen ion diffusion is very much slower than cation diffusion in spinels. The stoichiometry of the interfacial reactions (electrical neutrality) demands that the particle currents are constrained by 3 JA + 2 JB = 0. This is achieved by the action of an internal electric field in the same way as for ambipolar interdiffusion. Hence the less mobile of the two cations will be rate-controlling and, since trivalent ions diffuse more slowly than divalent ions in spinels, this will be the B cation. The result is D B d(lna AO )
(6-42)
where aAO is the activity of oxide AO in the spinel and superscripts I and II indicate the two faces of the reaction product. Through the mass action laws of the point defects in the spinel we expect DB to be a power law function of the activity of AO l
D =D a
n
(6-43)
Integration of Eq. (6-42) then gives the result
K=
(6-44)
where AGAB2O4 *S the standard Gibbs energy of formation of the spinel. This predic-
331
tion has been verified experimentally for the formation of NiGa 2 O 4 as illustrated in Fig. 6-22. 6.8.2 Creep of Ceramics
Creep at high temperatures is controlled by diffusion. The driving force for the mass transport is the influence of local stress on the chemical potential of defects through the change in volume that accompanies defect-creating reactions. Thus an increase in vacancy concentrations is favoured at sites under tensile stress. In compounds, such as ceramics, it is the slowest-moving species that controls creep since the preservation of crystal sites requires stoichiometric proportions of components to be transported. The different creep mechanisms are discussed in the chapter on mechanical properties of ceramics by Cook and Pharr in this Volume. In large single crystals the steady state creep rate, e, is governed by dislocations untangling by climb. This occurs by vacancies diffusing through the lattice to be annihilated at the dislocation line (or interstitials being emitted from the dislocation). Direct quantitative expressions for s are not available, but it is possible to obtain a general proportionality between s and mass transport in the form p\my
m
creep
(6-45)
where P is the stress, Y the modulus of elasticity and Vm the molecular volume. The stress exponent, m, is usually about 4 and A is an unknown constant. For many oxide ceramics having a close-packed oxygen structure the oxygen ions have the lowest diffusivity and so Dcreep~D$. Therefore the activation energy of 8 and the dependence of e on aOz should be the same as for oxygen diffusion. These predictions
332
6 Diffusion in Ceramics
have been investigated for a variety of oxides and reviewed by Philibert (1984). Where reliable data exist for comparisons to be made, the level of agreement is generally good. In polycrystalline ceramics other creep mechanisms that involve changes in grain shape can dominate the overall creep rate depending on the ceramic grain size, g. The result is (Raj and Ashby, 1971): 8 ~
(6-46)
kBTg2
The first term in this equation represents mass transport through the bulk of the grains and is known as Nabarro-Herring creep. The second term represents diffusion along the grain boundaries and is known as Coble creep. This multiplicity of mechanisms is usually summarized graphically on a deformation map (Frost and Ashby, 1982). An example of such a map deduced for Fe 3 O 4 is shown in Fig. 6-23 and the rate-controlling diffusion process was deduced to be bulk diffusion of oxygen (ex-
rin°C 800
400
1200
cept at the lowest strain rates, stresses and temperatures). Creep in polycrystalline NiO has been measured in the Coble-creep region and compared with that expected from the measured grain boundary tracer diffusivity of oxygen in NiO (Jimenez-Melendo et al., 1987). The absolute creep rates were found to be about two orders of magnitude lower than predicted from diffusion measurements, but the activation energy for creep was in acceptable agreement with that for oxygen grain boundary diffusion in Ni. (However, this is also approximately equal to the activation energy for nickel lattice diffusion and therefore is not, of itself, sufficient to identify the rate-determining process.) Langdon (1991) has reviewed the role of diffusion in the creep of engineering ceramics including A12O3, SiC and Si 3 N 4 . Detailed analysis is hampered by the lack of good diffusion data for these materials. However, it is thought that in some cases (such as A12O3) the diffusing ions favour transport by different pathways during
1400
-3
-4
Figure 6-23. Creep deformation map estimated for Fe 3 O 4 as a function of the ratio of applied stress, P, to shear modulus, G, and reduced temperature. The grain size of the oxide has been assumed to be 10 um and the gas atmosphere is 1.5% CO in CO 2 . The curves correspond to different bulk strain rates. (After Crouch and Robertson, 1990.)
-2 -5 DIFFUSION
BOUNDARY
-7
0
1 0.2
0.4
T/Tm
6.8 Processes Involving Diffusion
creep at a given temperature (e.g., O 2 along grain boundaries and Al 3+ through the lattice). 6.8.3 High Temperature Oxidation
Exposure of a metal, or non-oxide ceramic, material to an oxidizing gas at elevated temperature nearly alway results in the formation of a solid ceramic oxide oxidation product layer. This layer is usually the only barrier to very rapid degradation and therefore the rate of growth of this layer by diffusion of reactants through it is of crucial importance to the useful lifetime of a component. The underlying principles of oxide layer growth are the same for metals and ceramics. However, the ceramics tend to be more complicated because oxidation often creates another gaseous species as a reaction product, e.g., Si 3 N 4 + 3O 2 = 3SiO 2 + 2N 2
(6-47)
In this short summary only oxidation of metals to an oxide product layer will be considered. For a detailed discussion see Atkinson (1985) and Kofstad (1988). As with other diffusion-controlled processes, the oxide layer thickness, X, in a pseudo steady state, grows according to parabolic kinetics, X2 = kp t. If the layer is uniform in thickness and compact then kp can be expressed in terms of the solid state diffusion properties of the oxide product layer. The situation differs from that of spinel formation considered earlier in that during oxidation an oxygen potential difference is established across the layer; ranging from a low value of alO2 at the metal/layer interface, to the external ambient of a"2 at the layer/gas interface. As a result, gradients of all defects are established in the oxide layer, including electronic defects, and they all try and move across the layer down their respective
333
chemical potential gradients. The different rates of motion generate an internal electric field (if the species are charged) which couples the fluxes such that electrical neutrality is maintained in the pseudo steady state. The process is analogous to the nonsteady state chemical diffusion in an oxide as a response to a sudden change in external oxygen potential. In both cases, the kinetics are controlled by the fastest-diffusing ionic component (for an electronically conducting oxide) or the electronic species (for an ionically conducting oxide). The solution of the coupled transport equations for an electronically conducting oxide leads to h
(6-48)
_
JO
where fM and fo are correlation factors for metal and oxygen tracer diffusion. This expression bears a marked similarity with that for spinel growth by solid state reaction [Eq. (6-46)]. To evaluate kp it is necessary to know how D* depends on aOl and this may be found either by direct measurement or by application of mass action to the reactions that control the formation of the point defects responsible for diffusion. For example, in the case of NiO (oxidation of nickel) D* ^> D* and D* = Dfr°(aO2)1/6The result for this particular example is kp = 6.4D^|n, where the superscript II indicates the diffusion coefficient appropriate to the externally applied oxygen activity, and the superscript o indicates unit activity of oxygen. Similar analyses have been applied to a range of oxides growing by high temperature oxidation of metals and for many it has been established that the expected relationship between kp and D is obeyed, provided that the temperature is high enough (typically when kp is greater than about
334
6 Diffusion in Ceramics
10 8 cm2 s *). These rates correspond to oxide layer growth that is much too fast to be acceptable in practical situations. At lower rates of growth (lower temperatures or more refractory oxides) it is found that the measured value of kp is higher than predicted from diffusion coefficients and, as the temperature is lowered, this discrepancy can reach many orders of magnitude. The reason for this is that at the lower temperatures short-circuit diffusion pathways become dominant and fcp is not only greater than expected from lattice diffusion, but is also dependent on the microstructure. This can be taken into account in the transport equations by considering all the diffusion pathways acting in parallel. For grain boundary and lattice diffusion this gives an effective diffusion coefficient 2(D%S) 9
(6-49)
where g is the grain size. In the case of NiO layer growth it has been shown that this effective diffusion coefficient can explain fcp quantitatively even at relatively low temperature (Fig. 6-24). It is thought that grain boundary diffusion controls the growth of most oxide layers under conditions of practical usefulness, but this remains to be definitively established for such important protective oxides as Cr 2 O 3 and A12O3. 6.8.4 Optical Waveguide Fabrication by Ion Exchange
The fabrication of optical waveguides by ion exchange is an important example of how diffusion is used as an integral processing step in the manufacture of devices in advanced technology. Buried planar channel optical waveguides must have higher refractive index than the surround-
1400 1200 1000
rin°C 800
700
600
500
-10
E -12
Predicted from lattice diffusion —^ -14
-16
-18
9 10 10V7" in K-1
Figure 6-24. The parabolic rate constant for the growth of NiO by the oxidation of Ni at an oxygen activity of unity. The solid line is the predicted kp based on lattice diffusion in NiO. The solid symbols are the measured values of /cp and the open symbols are calculated including the contribution from diffusion of Ni along NiO grain boundaries. (After Atkinson, 1985.)
ing material and their width and depth must be accurately controlled to give predictable waveguiding properties. The high refractive index region is created by replacing an ionic species present in the bulk optical medium with one of higher electron/atom ratio. This is achieved by diffusing the heavier ion from the external surface into the medium where it exchanges with the lighter ion which then diffuses out. Passive waveguides are thus made in glass by the diffusion of silver from a molten salt source and its exchange with sodium in the glass. Active, electro-optic, waveguides are produced by exchanging Li + in LiNbO 3 for Ti 4 + . In this case, which we will con-
6.9 Conclusions
335
Figure 6-25. The interdiffusion coefficient for Ti and Li in NiNbO 3 at 1050 °C as a function of the initial concentration of Li2O. The symbols are: • x cut, • y cut, A Z cut. (After Holmes and Smyth, 1984) 0.480
0.500
sider in more detail, the Ti source is a strip of Ti metal deposited on the LiNbO 3 crystal surface at the desired location of the waveguide. The example of Ti diffusion in LiNbO 3 is particularly interesting because it illustrates the complexities of defects in multicomponent crystals (Chang et al., 1987). In the case of LiNbO 3 , single crystals of optical quality are grown from the melt at the congruent composition (that is, when the liquid and the solid both have the same composition). This composition is deficient in Li in comparison with stoichiometric LiNbO 3 and contains 48.6 mol% Li 2 O (i.e., Li/Nb = 0.945). Originally this deficiency was believed to be accommodated by VLI, but the crystals were observed to have greater density than that expected from a full stoichiometric crystal. It is now believed from X-ray diffraction studies that the loss of lithium, with respect to the stoichiometric composition, is accompanied by the transfer of niobium to lithium sites corresponding to the structural formula (Li o . 941 , Nb 0 0 5 9 ) N b 0 5 3 O 3 , which has Li/Nb = 0.930. Thus the non-stoichiometric loss of lithium can be written = 3Li 2 O (6-50)
in which one set of LiNbO 3 sites has been lost from the crystal. This reaction predicts that the congruent composition is (Li0 9 5 4 , Nb 0 . 0 4 6 )Nb 0 . 9 6 3 O 3 when Li/Nb = 0.945. The interdiffusion of Ti and Li in LiNbO 3 has been measured by Holmes and Smyth (1984) for Ti concentrations below 6% by weight. The results (Fig. 6-25) show that the interdiffusion coefficient increases as the lithium content decreases. This suggests that during ion exchange both the Li + and Ti 4 + ions interdiffuse via the same set of defects and, from the known point defect structure, these are vacancies on the niobium sublattice.
6.9 Conclusions Diffusion in solids is a mature subject in which the basic phenomena are well-established and understood. In the case of ceramic materials, good quality experimental data are difficult to obtain and therefore tend to be lacking. This is particularly so for highly refractory materials and for diffusion at grain boundaries, dislocations and surfaces. Nevertheless, a strong foundation has already been built for diffusion in ceramic materials by integrating experimental studies, theory and computer simu-
336
6 Diffusion in Ceramics
lation and using these in applications of technological significance.
6.10 Acknowledgement The author is grateful to Dr. A. B. Lidiard for his constructive comments on the manuscript.
6.11 References Adda, Y, Philibert, I (1966), La Diffusion dans les Solides. Paris: Presses Universitaires de France. Allnatt, A. R., Lidiard, A. B. (1987), Rep. Prog. Phys. 50, 373. Allnatt, A. R, Loftus, E. (1973), /. Chem. Phys. 59, 2541. Amsel, G., Nadai, I P., D'Artemare, E., David, D., Girard, E., Moulin, I (1971), Nucl. Instr. and Methods 92, 481. Ando, K. (1987), in: Advances in Ceramics, Vol. 23: Non-Stoichiometric Compounds: Catlow, C. R. A., Mackrodt, W. C , (Eds.). Columbus (OH): American Ceramic Society, p. 149. Atkinson, A. (1984), Solid State Ionics 12, 309. Atkinson, A. (1985), Rev. Mod. Phys. 57, 437. Atkinson, A. (1987), in: Advances in Ceramics, Vol. 23: Non-Stoichiometric Compounds: Catlow, C. R. A., Mackrodt, W. C. (Eds.). Columbus (OH): American Ceramic Society, p. 3. Atkinson, A. (1988), Solid State Ionics 28-30, 1377. Atkinson, A. (1989), in: Selected Topics in High Temperature Chemistry: Defect Chemistry of Solids: Johannesen, O., Andersen, A. G. (Eds.). Amsterdam: Elsevier, p. 29. Atkinson, A., Taylor, R. I. (1977), Thin Solid Films 46, 291. Atkinson, A., Taylor, R. I. (1979), Philos. Mag. A 39, 581. Atkinson, A., Taylor, R. I. (1981), Philos. Mag. A 43, 979. Atkinson, A., Taylor, R. I. (1986), J. Phys. Chem. Solids 47, 315. Atkinson, A., Hughes, A. E., Hammou, A. (1981), Philos. Mag. A 43, 1071. Badrour, L., Moya, E. G., Bernardini, X, Moya, F. (1986), Scr. Metall. 20, 1217. Birchenall, C. E. (1968), Mass Transport in Oxides, NBS Special Publication 296: Wachtman, J. B., Franklin, A. D. (Eds.). Washington: NBS, p. 119. Bonzel, H. P. (1983), Surface Mobilities on Solid Materials: Fundamental Concepts and Applications, NATO ASI Series B, Vol. 86: Binh, V. T. (Ed.). New York: Plenum Press, p. 195.
Breitung, W. (1978), /. Nucl. Mater. 74, 10. Carslaw, H. S., Jaeger, J. C. (1959), Conduction of Heat in Solids. Oxford: Oxford University Press. Catlow, C. R. A. (1984), Solid State Ionics 12, 67. Chang, E. K., Mehta, A., Smyth, D. M. (1987), in: Advances in Ceramics, Vol. 23: Nonstoichiometric Compounds: Catlow, C. R. A., Mackrodt, W. C. (Eds.). Columbus (OH): American Ceramic Society, p. 351. Cooper, A. R., Heasley, J. H. (1966), Ada Metall. 49, 280. Crank, J. (1975), The Mathematics of Diffusion. Oxford: Clarendon Press. Crouch, A. G., Robertson, J. (1990), Acta Metall. Mater. 38, 2567. Derry, D. J., Lees, D. G., Calvert, J. M. (1981), J. Phys. Chem. Solids 42, 57. Dieckmann, R. (1984), Solid State Ionics 12, 1. Dieckmann, R., Schmalzried, H. (1977), Ber. BunsenGes. Phys. Chem. 81, 344. Dubois, C , Monty, C , Philibert, J. (1984), Solid State Ionics 12, 75. Duffy, D. M. (1986), /. Phys. C19, 4393. Duffy, D. M., Tasker, P. W. (1986), Philos. Mag. A 54, 759. Fahri, R., Petot-Ervas, G. (1978), /. Phys. Chem. Solids 39, 1169. Freer, R. (1980), /. Mater. Sci. 15, 803. Frischat, G. H. (1975), Ionic Diffusion in Oxide Glasses. Aedermannsdorf, Switzerland: Trans. Tech. SA. Frost, H. J., Ashby, M. F. (1982), Deformation Mechanism Maps. Oxford: Pergamon Press. Furuya, H., Koizumi, M. (1976), Nuclear Technology 28, 226. Gillan, M. J. (1989), in: Ionic Studies at High Temperature: Stoneham, A. M. (Ed.). Singapore: World Scientific, p. 170. Harding, J. H. (1990), Rep. Prog. Phys. 53, 1403. Harding, J. H., Tarento, R. J. (1987), in: Advances in Ceramics, Vol. 23: Non-Stoichiometric Compounds: Catlow, C. R. A, Mackrodt, W. C. (Eds.). Columbus (OH): American Ceramic Society, p. 239. Harding, J. H., Sangster, M. J. L., Stoneham, A. M., Tarento, R. J. (1990), Philos. Mag. A 62, 473. Harrison, L. G. (1961), Trans. Faraday Soc. 57, 1191. Heinemann, I., Frischat, G. H. (1990), /. Am. Ceram. Soc. 73, 3712. Holmes, R. I, Smyth, D. M. (1984), J. Appl. Phys. 55, 3531. Hon, J. D., Davis, R. R, Newbury, D. E. (1981), J. Mater. Sci. 16, 2485. Hoshino, K., Peterson, N. L. (1984), /. Phys. Chem. Solids 45, 963. Hoshino, K., Peterson, N. L., Wiley, C. L. (1985), J. Phys. Chem. Solids 46, 1397. Howard, R. E., Lidiard, A. B. (1964), Rep. Prog. Phys. 27, 161. Jacobs, P. W M., Vernon, M. L. (1990), J. Chem. Soc. Faraday Trans. 86, 1233.
6.11 References
Jimenez-Melendo, M., Dominguez-Rodriguez, A., Marquez, R., Castaing, J. (1987), Philos. Mag. A 56, 767. Kilner, I A., Steele, B. C. H., Ilkov, L. (1984), Solid State Ionics 12, 89-97. Kofstad, P. (1972), Non-Stoichiometry, Diffusion and Electrical Conductivity of Binary Metal Oxides. New York: John Wiley. Kofstad, P. (1988), High Temperature Corrosion. Amsterdam: Elsevier. Kroger, F. A. (1964), The Chemistry of Imperfect Crystals. Amsterdam: North Holland. Langdon, T. G. (1991), Defect and Diffusion Forum 75, 89. LeClaire, A. D. (1976), in: Treatise on Solid State Chemistry, Vol. 4: Hannay, N. B. (Ed.). New York: Plenum Press, p. 1. LeClaire, A. D., Rabinovitch, A. (1982), / Phys. C 15, 3455, 5727. Lidiard, A. B. (1957), Handbuch der Physik 20, 246. Lin, C. M., Stubican, V. S. (1990), J. Am. Ceram. Soc. 73, 587. Mackrodt, W. C. (1984), Solid State Ionics 12, 175. Manning, J. R. (1986), Diffusion Kinetics for Atoms in Crystals. Princeton (NJ): van Nostrand. Matzke, H.-J. (1983), J. Nucl. Mater. 114, 121. Matzke, H.-J. (1986), in: Advances in Ceramics, Vol. 17: Fission Product Behaviour in Ceramic Oxide Fuel. Columbus (OH): American Ceramic Society, p.l. Matzke, H.-J. (1990), in: Diffusion in Materials: Laskar, A. L., Bocquet, J. L., Brebec, G., Monty, C. (Eds.). Dordrecht: Kluwer Academic Publishers, p. 429. Millot, F., De Mierry, P. (1985), J. Phys. Chem. Solids 46, 191. Monty, C. (1983), Radiation Effects 74, 29. Moya, E. G., Moya, F. (1988), Mater. Sci. Forum 29, 237. Mundy, I N . , Rothmann, S. J. (1983), / Vac. ScL Technol. A 1,14. Murch, G. E. (1980), Atomic Diffusion Theory in Highly Defective Solids. Aedermannsdorf (Switzerland): Trans Tech SA. Norby, T. (1987), in: Advances in Ceramics, Vol. 23: Non-Stoichiometric Compounds: Catlow, C. R. A., Mackrodt, W. C. (Eds.). Columbus (OH): American Ceramic Society, p. 107. Oishi, Y, Ando, K., Yasumura, K. (1987), /. Am. Ceram. Soc. 70, C-327. Osenbach, J. W, Stubican, V. S. (1983), J. Am. Ceram. Soc. 66, 191. Osenbach, J. W, Bitler, W. R., Stubican, V. S. (1981), J. Phys. Chem. Solids 42, 599. Perinet, F. (1987), Thesis, Universite de Paris-Sud, Orsay.
337
Peterson, N. L., Chen, W. K., Wolf, D. (1980), J. Phys. Chem. Solids 41, 709. Philibert, J. (1984), Solid State Ionics 12, 321. Philibert, J. (1985), Diffusion et Transport de Matiere dans les Solides, Les Editions de Physique, Paris. Rabier, I, Puls, M. P. (1985), Philos. Mag. A 52,461. Raj, R., Ashby, M. F. (1971), Metall Trans. 2, 1113. Reddy, K. P. R., Cooper, A. R. (1982), / Am. Ceram. Soc. 65, 634. Rothman, S. J. (1990), in: Diffusion in Materials: Laskar, A. L., Bocquet, J. L., Brebec, G., Monty, C. (Eds.). Dordrecht: Kluwer Academic Publishers, p. 269. Rothman, S. I , Routbort, J. L. (1990), in: Diffusion in Materials: Laskar, A. L., Bocquet, I L., Brebec, G., Monty, C. (Eds.). Dordrecht: Kluwer Academic Publishers, p. 393. Routbort, J. L., Rothman, S. J. (1985) Diffusion and Defect Data 40, 1. Routbort, I L., Rothman, S. I , Chen, N., Mundy, J. N. (1991), Phys. Rev. B43, 5489. Sangster, M. J. L., Dixon, P. (1976), Adv. Phys. 25, 247. Schmalzried, H. (1981), Solid State Reactions, 2nd ed. Weinheim: VCH. Schwier, V. G., Dieckmann, R., Schmalzried, H. (1973), Ber. Bunsen-Ges. Phys. Chem. 77, 402. Stoneham, A. M. (1985), Chemistry in Britain 21, 5. Stubican, V. S., Huzinec, G., Damjanovic, D. (1985), /. Am. Ceram. Soc. 68, 181. Suzuoka, T. (1961), Japan Inst. Metals 2, 25. Tu, K. N., Yeh, N. C , Park, S. L, Tsui, C. C. (1989), Phys. Rev. B 39, 304. Wagner, C. (1975), Prog. Solid State Chem. 10, 3. Weber, G. W, Bitler, W. R., Stubican, V. S. (1980), J. Phys. Chem. Solids 41, 1350. Whipple, R. T. P. (1954), Philos. Mag. A 45, 1225. Wuensch, B. J. (1983) in: Mass Transport in Solids: Beniere, F , Catlow, C. R.A. (Eds.). New York: Plenum Press, p. 353.
General Reading Frischat, G. H. (1975), Ionic Diffusion in Oxide Glasses. Aedermannsdorf (Switzerland): Trans Tech SA. Howard, R. E., Lidiard, A. B. (1964), Rep. Prog. Phys. 27,161. Kofstad, P. (1972), Nonstoichiometry, Diffusion and Electrical Conductivity of Binary Metal Oxides. New York: John Wiley. Schmalzried, H. (1981), Solid State Reactions, 2nd ed. Weinheim: VCH. Philibert, J. (1985), Diffusion et Transport de Matiere dans les Solides. Paris: Les Editions de Physique.
7 Mechanical Properties of Ceramics Robert E Cook IBM Research Division, T. J. Watson Research Center, Yorktown Heights, NY, U.S.A. George M. Pharr Department of Materials Science, Rice University, Houston, TX, U.S.A.
List of 7.1 7.2 7.2.1 7.2.2 7.2.3 7.2.4 7.2.5 7.3 7.3.1 7.3.2 7.3.2.1 7.3.2.2 7.3.3 7.3.3.1 7.3.3.2 7.3.3.3 7.3.4 7.3.4.1 7.3.4.2 7.3.4.3 7.3.5 7.3.5.1 7.3.5.2 7.3.5.3 7.4 7.4.1 7.4.2 7.4.2.1 7.4.2.2 7.4.2.3
Symbols and Abbreviations Introduction Elasticity Interatomic Potentials and Forces Elastic Moduli of Single Crystal and Amorphous Ceramics Elastic Moduli of Polycrystalline Ceramics Elastic Moduli of Two-Phase Ceramics Elastic Moduli of Porous Ceramics Fracture Fracture at the Atomic Level Energy Balances in Fracture Unstable Equilibrium: The Griffith Equation Stable Equilibrium: Roesler's Law Stress Balances in Fracture Toughness and Stress Intensity Factors Crack Initiation in a Decreasing Stress Field Crack Propagation in an Applied Stress Field Microstructural Influences in Fracture Frames of Reference Toughening by Ligamentary Bridging Toughening by Phase Transformations Non-Equilibrium Fracture Crack Velocities in Destabilizing and Stabilizing Fields Kinetic Models for Crack Velocity Time-Dependent Failure Plasticity Slip at the Atomic Level Dislocation Glide in Ceramics Inherent Resistance to Glide Observations of Glide Plasticity Limitations on Slip and Loss of Ductility in Polycrystals
Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.
341 345 346 346 347 349 350 351 353 353 354 354 357 359 359 360 364 366 366 367 372 374 374 376 379 380 380 381 381 383 384
340
7.4.2.4 7.4.2.5 7.4.3 7.4.3.1 7.4.3.2 7.4.4 7.4.4.1 7.4.4.2 7.4.4.3 7.4.4.4 7.4.4.5 7.5 7.6
7 Mechanical Properties of Ceramics
Effects of Solutes and Impurities on Dislocation Glide Charged Dislocations in Ionic Ceramics High Temperature Plasticity Creep Testing Mechanisms of Creep Experimental Observations of Creep in Ceramics Stress Dependence Temperature Dependence Grain Size Dependence Effect of Porosity Effect of Soft Intergranular Phases Conclusions References
386 390 391 391 395 397 397 399 400 401 402 404 404
List of Symbols and Abbreviations
List of Symbols and Abbreviations A A A Ao B b b b c c c o ,Ci cm c A ,c B cijkl DA,DB Dh Dx D eff ^complex ^A>^B D\,DB d ds, dz E Eo E1 E2 EY £R e F Fc Fappl fij(6) G ^ ^a G* J Jo Ja J^ JA,JB
constant of interatomic attraction empirical constant crack area initial crack area constant of interatomic repulsion interatomic separation magnitude of Burgers vector Burgers vector crack dimension concentration of defects initial crack dimensions crack length at instability concentration of species A, B stiffness constants (element of stiffness tensor) diffusion coefficient of species A, B grain boundary diffusivity lattice diffusivity effective diffusion coefficient complex diffusion coefficient grain boundary diffusivity of species A, B lattice diffusivity of species A, B grain size path element Young's modulus Young's modulus in the absence of porosity Young's modulus of phase 1 in a two-phase material Young's modulus of phase 2 in a two-phase material Voigt bound on Young's modulus Reuss bound on Young's modulus elementary charge interatomic force critical force applied force function describing the angular depenency of a{j shear modulus mechanical energy release rate contribution of applied loading to mechanical energy release rate bound on shear modulus creep compliance contribution of interatomic bond rupture processes to the ./-integral contribution of applied loading to the J-integral contribution of microstructural tractions to the J-integral diffusional flux of species A, B
341
342
7 Mechanical Properties of Ceramics
K K Jf K* Jfa jfTp k lt M m N n Oj P P P* POl p <2 C QD M Mo x
r r r0 rc S sijkl T T To ST ^ 2T^ ST^ t tr U °U °tt* UE UM Us
bulk modulus of elasticity equilibrium constant stress intensity factor bound on bulk modulus applied loading contribution to stress intensity factor microstructural contribution to stress intensity factor Boltzmann's constant direction cosine of the axis of loading in direction i access of environmental species to reaction site grain size exponent number of bonds per unit area stress exponent for creep oxygen interstitials load volume fraction of porosity quantity characterizing effect of microstructural restraining force partial pressure of oxygen hydrostatic pressure activation energy energy for diffusion fracture resistance fracture resistance due to interatomic bonds microstructural contribution to fracture resistance maximum increment in the work of fracture distance between two atoms radial coordinate equilibrium interatomic separation critical interatomic separation source compliance constants (element of compliance tensor) traction exerted on the crack faces absolute temperatue material constant of stress-assisted thermal activation toughness intrinsic toughness microstructural contribution to toughness toughness in the limit of large cracks time time to rupture potential strain energy density strain energy density change strain energy mechanical potential surface potential
List of Symbols and Abbreviations
343
UT Uo u w* V V1, V2 Vf Fg W w
total potential of a system potential at r = r 0 crack opening displacement half crack opening necessary to cause ligament rupture volume volume fractions volume fraction of transformed particles volume fraction of a glassy intergranular phase work width of wake region
a a Fl y = 8tj 5 8 <5 e s0 8tj 8T 8* ess Afi
Madelung constant half crack opening at the end of the bridged zone half work per unit area necessary to rupture a ligament where i #=j variation in stoichiometric number characteristic bridging distance grain boundary thickness strain permittivity of free space strain constants (element of strain tensor) transformation strain maximum particle strain steady state creep rate difference between the longitudinal and transverse strain produced by tetragonal distortion angular coordinate dimensionless transformation constant grain size dimensionless geometric constant load point displacement Poisson's ratio crack velocity velocity related to the attempt frequency for kink migration reaction controlled reaction velocity transport controlled reaction velocity applied stress critical stress level above which a specimen breaks critical stress level necessary t o initiate a crack value of applied stress at instability stress at the tip of an elliptical hole in a uniformly stressed solid stress constants (element of stress tensor) line force large flaw limit of am small flaw limit of om
6 rj X fi fih v v v0 Vj vn (j a <7 f G{
344
7 Mechanical Properties of Ceramics
t T0 x
contribution to shear yield stress due to dislocation defect interaction material strength at 0 K order of reaction
X, i// Q
geometry parameters atomic or molecular volume
BS CT DT M-DCB NAS P-DCB PMMA SENB SLS Y-TZP
borosilicate compact tension double torsion constant-moment double cantilever beam sodium aluminosilicate load-controlled double cantilever beam poly(methyl methacrylate) single etched-notched beam soda-lime yttria tetragonal zirconia polycrystal
7.1 Introduction
7.1 Introduction Ceramics exhibit a wide variety of mechanical behaviors. The types of mechanical responses which are important for structural uses are elastic, fracture, and plastic, and these will be the focus of this chapter. The underlying processes which control the response under given loading and environmental conditions are governed by the material microstructure and interatomic bonding. The aim of this chapter will be to put microstructural mechanisms determining mechanical behavior behind the macroscopic continuum responses. Specific studies of experimental behavior are used throughout the chapter, and the theme has been to limit the introduction of theoretical work to that needed to explain, or place in context, experimental observations. Section 7.2 considers the elastic responses of ceramics, beginning with the connection between the stiffness constants of interatomic bonds and macroscopic elastic constants of single crystals. The combinations of elastic constants appropriate to polycrystalline ceramics, twophase ceramics, and porous ceramics are then considered and compared with experimental observations. In general, the elastic responses of ceramics are well described by considerations of the physics of the interatomic bonding and the mechanics of the microstructural interactions, although simple specification of the moduli of porous materials is not possible. Fracture properties are covered in Sec. 7.3, highlighting the influences of microstructure on crack initiation and fracture resistance, and the need for proper characterization of defects (cracks) to explain observed fracture strengths. Scaling relations for stable and unstable cracks in an energy balance framework are devel-
345
oped, followed by analogous relations developed in a stress framework. This latter is used to consider crack initiation in various ceramic microstructures. Variations in fracture resistance are compared with models of microstructural interaction during crack propagation. The influence of environment on non-equilibrium crack propagation is discussed and the consequences for time-dependent failure considered. The overall framework for fracture describes all observed ceramic fracture properties very well. However, the framework is mechanics based and makes a much smaller connection with the quantitative details of the bond rupture processes responsible for fracture, than with the microstructural details. Ceramics are, of course, the classic brittle materials, and for this reason any discussion of their mechanical properties must pay a great deal of attention to brittle behavior. Nevertheless, ceramics can also deform plastically, and in Sec. 7.4 the conditions under which plasticity is observed as well as the mechanisms which produce it are discussed. Plasticity resulting from simple dislocation glide is considered first. Glide is the dominant mechanism of deformation in ceramics like the alkali halide salts, many of which can be plastically deformed to large strains, even at room temperature. This is followed by deformation at high temperatures, where in addition to glide, plastic strain can be produced by diffusion, grain boundary sliding and dislocation climb. Specific microstructural and environmental effects on high temperature creep of ceramics are then studied. Specific atomic and microstructural mechanisms responsible for creep behavior are shown to be implied by suitable creep studies, and the models developed to describe creep are couched in much greater atomic detail than those for fracture.
346
7 Mechanical Properties of Ceramics
7.2 Elasticity Repulsive
7.2.1 Interatomic Potentials and Forces The fundamental entity underlying all mechanical responses of solids is the interatomic potential. For a pair of atoms at separation r the potential U may be written as
fe -1
7 1
1
where A, JB, n, and m are constants depending on the material composition and structure. The first term in Eq. (7-1) characterizes the attractive part of the potential and the second the repulsive part, with n <m. The interatomic force F is given by F(r)=-
dU(r) dr
nA
mB rm
+1
Attractive
-2
C " )
U(r)= - 4 + 4
V
-
a.
o en o
1
-1
(7-2) SEPARATION, r / r 0
An equilibrium atomic separation r0 is obtained by solving Eqs. (7-1) or (7-2) for F = - dU/dr = 0, to give (7-3)
Further differentiation of Eqs. (7-1) and (7-2) shows the equilibrium to be stable, and hence r 0 is the stable equilibrium separation of the atoms in the solid. Equation (7-3) shows that increasing the magnitude of the interatomic attraction, A, relative to the repulsion, B, decreases the equilibrium separation. Figure 7-1 plots U(r) and F (r), showing the attractive and repulsive contributions, and the stable equilibrium (dF/dr < 0) at r 0 . For small perturbations of the bond from equilibrium the force dF required is proportional to the extension dr, with the constant of proportionality (the bond stiffness) given by the curvature of the inter-
Figure 7-1. Plots of U (r) and F (r) for an interatomic force from Eq. (7-1), using n = 1 and m = 9 appropriate to an ionic solid, and Uo = — U (r0). The attractive and repulsive components of the potential are shown as the dotted lines.
atomic potential: dF =
d2U(r)
dr
(7-4)
Real materials, consisting of many bonds, thus show similar linear elastic relations between the macroscopic variables of stress and strain, and the constant or proportionality - the modulus of elasticity - is related to the bond stiffness. Consider a solid subjected to a hydrostatic pressure, p, such that a relative volume change dV/V is produced elastically. The bulk modulus of elasticity, K, is defined by
p=-K-
dV
(7-5)
347
7.2 Elasticity
We can relate K to the curvature of the interatomic potential: the average force on each bond arising from the imposed pressure is proportional to the cross-sectional area of each bond, dF = prl; the volume strain of the solid as a whole is about three times the linear strain of an individual bond, dV/V = 3dr/r0. Hence, Eqs. (7-4) and (7-5) may be combined to give r
. 1 (d2U(r)
3{
d2
(7-6)
and we have the general result that a macroscopic elastic modulus is related to an interatomic force constant via the equilibrium atomic separation. Equation (7-6) may be directly compared with experimental observations in cases where the potential function is known. In ionic solids the repulsive term may be neglected in the evaluation of the curvature at r 0 , and the potential written as U=
1 ote2 47l£ n r
(7-7)
where s0 is the permittivity of free space, e is the electronic charge, and n from Eq. (7-1) takes the value 1 here appropriate to an electrostatic Coulomb interaction. The dimensionless parameter a is the Madelung constant, evaluated from the crystal structure, and takes the values 1.75, 1.76, 1.64 for sodium-chloride, cesium-chloride, and zincblende structures, respectively (Ashcroft and Mermin, 1976). Using Eq. (7-7) in Eq. (7-6) leads to Koc^
(7-8)
which is observed experimentally for the alkali halides, as shown in Fig. 7-2. Simple predictions such as this may not be made for carbide, nitride, or oxide ceramics, as the interatomic potentials reflect much
0.2 0.3 0.4 0.5 INTERATOMIC SEPARATION, r0 (nm)
Figure 7-2. Bulk modulus K vs. interatomic separation r 0 for alkali halides (data taken from Ashcroft and Mermin, 1976). The line of slope — 4 on the logarithmic plot is the predicted dependence for an ionic solid.
lower degrees of ionic bonding, and the assumption leading to Eq. (7-7) may not be made for these materials (Anderson, 1965). 7.2.2 Elastic Moduli of Single Crystal and Amorphous Ceramics
The directional nature of interatomic bonding in crystalline solids leads to anisotropy in the elastic properties. Stresses and strains in a linear elastic body are related by a
ij
—
C
ijkl8kl
(7-9 a)
or, equivalently, (7-9 b) where a{] is the (tensorial) stress in the body and skl is the strain. cijkl are stiffness constants and sijkl are compliances (with ij, k, I = 1,2,3). The cijkl and siJkl are linearly related, and in general c # s" 1 . The 81 components of the fourth-order stiffness and compliance tensors are reduced to 36 by the symmetry of the stress and strain tensors, and to 21 independent terms by strain-energy considerations (Nye, 1957).
7 Mechanical Properties of Ceramics
348
only three independent stiffness constants:
To reflect these reductions in the number of terms the Voigt or matrix notation is used, such that Eq. (7-9) becomes
C
(7-10 a)
C
12 ~
(7-12)
23 ~~ C 31
C44 — ^55 =
and
C66
with all other components zero. The compliances are related to these by
(7-10b) where
-11 T" C 12
a
'22
a 31 -ii
J
i>
33
+2c12)
'12
-c
(7-11)
(7-13)
X2
^22
5
and the c0- and stj are referred to as components of the stiffness and compliance matrices. Crystal symmetry can further reduce the number of independent components in the stiffness or compliance matrices. In cubic crystals, which constitute many ceramic materials (e.g., MgO and NaCl), there are
44 — -44
Table 7-1 gives the stiffness constants for some cubic crystals. In an isotropic material, such as a silicate glass or a polycrystalline aggregate, symmetry reduces the number of indepenent stiffness constants to two, with the ad-
Table 7-1. Independent elastic constants of ceramic single crystals and glasses. Symmetry
Ref.
Material (GPa)
(GPa)
79 70 83
15 20 22
(GPa)
(GPa)
(GPa)
Isotropic (glasses)
silica borosilicate soda-lime
Cubic
MgO MgAl 2 O 4 ZrO 2 CaF 2 NaCl ZnS ZnSe TiC
286 279 410 164 49 108 81 500
87 153 110 47 12 72 49 113
148 153 60 34 13 41 44 175
Hexagonal
A12O3 ZnO
465 210
124 121
233 43
563 211
117 105
Tetragonal
BaTiO 3
158
64
44
153
63
Trigonal
SiO 2
87
8
57
108
15
a e
(GPa)
17
Holloway (1973); b Ingel and Lewis (1988); c Landolt-Bornstein Tables (1984); d Gilman and Roberts (1961); Huntington (1958); f Bateman (1962); g Pisarenko et al. (1985).
349
7.2 Elasticity
ditional constraint imposed on Eqs. (7-12) and (7-13) of
In this case the isotropic Young's modulus, £, relating longitudinal stress and strain,
In general, the elastic response of a crystal depends on the loading direction, leading to orientation-dependent Young's moduli and shear moduli (Nye, 1957). In particular, the Young's modulus of a cubic crystal in a specific direction is given by
(7-15 a)
(7-19 a)
C4.4. — (en
—
(7-14)
c12)/2
a = Es is given by
B-±-
(7-15 b)
an
d °f a hexagonal crystal by 2
The isotropic Poisson's ratio, v, relating lateral to longitudinal strain under longitudinal stress, S2 —
(7-16 a)
—V81
is given by S
12
(7-16b)
V=
The isotropic shear modulus, G, relating shear stress and strain. T
= Gy
(7-17 a)
(writing atj and stj, i =f=j, as t and y, respectively) is given by G=
1 2(Sll-s12)
2(1+v)
(7-17 b)
and the bulk modulus, defined in Eq. (7-5) is given by K=
3(Sll
1 + 2s 12 )
3(1-2v)
(7-18)
which also pertains for cubic crystals. The stiffness constants of some amorphous, isotropic materials are given in Table 7-1. For hexagonal crystals (e.g., A12O3), trigonal crystals (e.g., SiO2) and tetragonal crystals (e.g., BaTiO3), more elastic constants are independent. Table 7-1 gives the independent stiffness constants for some crystals of these symmetries as well.
Sll(l-li)
+
(7-19 b)
+ 533/S + (2^3+544) ( 1 - / 1 ) / I where l{ are the direction cosines of the axis of loading relative to the <100> directions for the cubic crystal, and l3 is relative to the [0001] direction for the hexagonal crystal. Figure 7-3 shows the variation of Young's modulus of some cubic crystals and some hexagonal crystals, using Eq. (7-19) and Table 7-1. Note that the variation for hexagonal crystals is symmetric for rotations about [0001], but that the variation for the cubic crystals is not symmetric for rotations about <001>.
7.2.3 Elastic Moduli of Polycrystalline Ceramics A polycrystalline aggregate displays isotropic elastic responses representative of the weighted average of the anisotropic elastic constants of the constituent crystals. The weighting of the constants may be performed in different ways, producing bounds on the predicted polycrystalline moduli dependent on the assumptions used to model the distribution of stresses and strains in the polycrystal (Hashin and Shtrikman, 1962; Ingel and Lewis, 1988). For cubic crystals it is convenient to express the bounds on the Young's modulus in terms
350
7 Mechanical Properties of Ceramics
The uniform strain, or Voigt, bound for the polycrystalline shear modulus, is given by
[001]
(7-22 a)
G* =
and the uniform stress, or Reuss, bound, by 450
[100]
G* =
5GtG2
(7-22 b)
Bounds based on minimizing the potential energy or complementary energy of the solid are more restrictive than the uniform stress and strain bounds, and have been calculated by Hashin and Shtrikman (1962):
[0001]
(7-23a) 5
Gi-G [1120]
Figure 7-3. Variation of Young's modulus in the (010) plane for the cubic crystals MgO and ZrO 2 , and perpendicular to the [0001] direction for the hexagonal crystals A12O3 and ZnO.
of the bulk modulus (using Eqs. (7-13) and (7-18)): +2c12
(7-20)
and the two single-crystal shear moduli (using Eqs. (7-13) and (7-17)): '12
G2 = c 44
where
The polycrystalline Young's modulus is then given by (combining Eqs. (7-17) and (7-18))
AI 2 O 3
c12
- 6 j » 2 V (7-23 b)
(7-21)
E=
9XG* 3K + G*
(7-24)
where the shear modulus for the appropriate bound, G*, is chosen. Figure 7-4 plots measured polycrystalline Young's moduli for some cubic materials against the predicted bounds given above, using the data in Table 7-1 and Table 7-2. Agreement is evident in most cases. Table 7-2 also gives the measured polycrystalline Young's moduli for other non-cubic ceramics and glasses. 7.2.4 Elastic Moduli of Two-Phase Ceramics
Many ceramics are multiphase, and the elastic properties of such materials are rep-
351
7.2 Elasticity
resentative of the weighted average of the elastic constants of the constituent phases. As with single-phase polycrystalline materials the weighting of the constants may be performed in different ways to produce bounds on the moduli (Christenson, 1982, gives a good review). The simplest bounds are those assuming uniform strain or uniform stress in the solid. Hence, for a two phase material, the uniform strain, Voigt bound on the Young's modulus of the composite is given by EY ==
V
2
E2 + V1 Ei
(7-25 a)
and the uniform stress, Reuss bound by R
~
E±E2 V2 + E2
v,
(7-25 b)
where Ei,E2 are the Young's moduli of the constituent phases, and V±, V2 are the respective volume fractions. We note that these bounds represent materials in parallel and in series, respectively. Bounds calculated by Hashin and Shtrikman (1963) are once again more restrictive than the Voigt and Reuss bounds and are expressed in terms of the bounds on the effective bulk and shear moduli of the composite:
0 100 200 300 400 500 PREDICTED YOUNG'S MODULUS, E (GPa)
Figure 7-4. Plot of measured polycrystalline Young's moduli for cubic crystals vs. predictions based on Voigt, Reuss, and Hashin-Shtrikman bounds. The Hashin-Shtrikman bounds are shown as the shaded boxes, the Voigt-Reuss bounds as the open boxes. Nominal 10% uncertainty is assumed in the observed moduli.
lower bound suggesting some porosity in the composite in those cases. 7.2.5 Elastic Moduli of Porous Ceramics Many ceramic materials are frequently less than fully dense, in which case the second phase in the material is porosity which
Kf =
(7-26 a)
[6(Kt + 2 Gt) Vt]/[5 Gt (3Kt + 4 Gt)] where ij = 1,2. The bounds on the Young's modulus are then given by Eq. (7-24), using both G* and K* as appropriate. Figure 7-5 plots the measured Young's moduli of some composite ceramics as a function of the relative volume fraction of the phases, and compares the behavior with the bounds calculated above. The observations lie within the Hashin-Shtrikman bounds, although in some materials nearer to the
(7-26 b)
has zero modulus. A brief inspection of any of the bounds in Eqs. (7-25) and (7-26) shows that a porous material will have a lower modulus than a fully dense material. Figure 7-6 plots the Young's modulus of some ceramic materials as a function of the volume fraction porosity - the general decrease is evident. Only the Voigt and Hashin-Shtrikman upper bounds on the
352
7 Mechanical Properties of Ceramics
Table 7-2. Young's modulus of polycrystalline and amorphous ceramics. Material
E (GPa)
Silica glass Borosilicate glass Soda-lime glass MgO MgAl 2 O 4 ZrO 2 CaF 2 ZnSe ZnS TiC SiC
Ref.
74 61 74 305 258 220 160 69 98 430 435 393 300
BaTiO.
123
a
Holloway (1973);b Chung (1963);c Stewart and Bradt (1980); d Ingel and Lewis (1988); e Rice etal. (1980); f Freiman etal. (1975); g Marshall etal. (1982); h Ceramic Source (1990); * Cook (1985); j Material Data Sheet of Coors Porcelain Co. (1985).
J
Q O
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 VOLUME FRACTION SECOND PHASE, V2
Figure 7-5. Young's moduli of composite ceramics vs. volume fraction of the more rigid phase. The dashed lines show the Voigt and Reuss bounds and the solid lines the Hashin-Shtrikman bounds. Data from the collation of Shaw and Uhlmann (1971) (Co-WC), Binns (1962) (glass-Al2O3), Stock etal. (1979) (Cement-sand), and Lange (1975) (ZrO 2 -Al 2 O 3 ).
0.0 0.1 0.2 0.3 0.4 0.5 POROSITY, P
Figure 7-6. Young's modulus as a function of porosity for some ceramics. Data from Marlowe and Wilder (1965) (Y2O3), and the collations of Datta et al. (1989) (Si3N4), and Wang (1984) (A12O3). The solid lines are linear best-fits to the data.
Young's modulus can be calculated in this case (the Reuss and Hashin-Shtrikman lower bounds are zero). However, the infinite ratio of the moduli of the constituent phases means that the stress and strain distribution in the solid depends critically on the pore morphology chosen. Hence, there is no single model which appears capable of describing all the observations such as those shown in Fig. 7-6 as a function of the single parameter characterizing the volume fraction of the porosity. Dean and Lopez (1983) have carefully examined data on a wide range of materials, and the large number of semi-empirical expressions suggested for the Young's modulus, and conclude that the best-fitting equation is of the form E = E0(l-bP) (7-27)
7.3 Fracture
where Eo is the Young's modulus in the absence of any porosity, P is the volume fraction of porosity, and b is an empirical constant which characterizes, amongst other things, the pore morphology. Such linear fits are shown in Fig. 7-6. Dean and Lopez also make the point that the apparent concave-upward trends in the E — P data of A12O3 and Si 3 N 4 observed in some collations (see Fig. 7-6) may be an artifact caused by the wide range of materials (and hence pore morphologies) examined in such cases.
7.3 Fracture
353
Figure 7-7. Plot of Fappl (r) from Eq. (7-28), using n = 1 and m = 9 appropriate to an ionic solid, and Fc = F(rc). The separation rc is a critical extension beyond which the bond can no longer stably support an applied force, and rupture occurs.
7.3.1 Fracture at the Atomic Level
To consider brittle fracture at the atomic level we invoke the applied force-separation function Fappl(r% for a single atomic bond. Taking the negative of Eq. (7-2) we gain
nA *.«+!
mB
(7-28)
This function is shown in Fig. 7-7. It can be seen that there is a critical applied force, Fc, beyond which the interatomic bond can no longer sustain stably an increased extension. To evaluate the critical separation, r c , at which instability occurs (the extension at maximum force in Fig. 7-7), the condition dFaappl /dr = 0 is imposed on Eq. (7-28) to yield =1.22 for n = l,m = where Eq. (7-3) has been used. A material consisting of many bonds as described by Eq. (7-28) will thus require a strain of about 22% for homogeneous rupture of a plane of bonds.
Table 7-3 gives typically observed strength values for some common ceramics: a typical fracture strength of a ceramic material is about 400 MPa, whilst a typical Young's modulus is about 200 GPa (Tables 7-1 and 7-2). Observed strains at fracture for ceramics are thus of order 0.2%, clearly much less than that required to cause homogeneous separation of the interatomic bonds across the fracture plane. Hence, some strain (and stress) concentration mechanism must be acting in order to generate the requisite conditions for bond rupture, and hence macroscopic fracture, in real materials. Inglis (1913) showed that the stress, c tip , at the tip of an elliptical hole in a uniformly stressed solid (see Fig. 7-8) was given by
2c b
(7-30)
where aa is the applied stress, which is uniform at large distances from the hole, 2 c is the length of the major axis of the ellipse, and 2 b is the length of the minor axis. If we imagine the ellipse to be extremelyslender,
354
7 Mechanical Properties of Ceramics
Table 7-3. Strength, fracture resistance, and toughness values of ceramics. Material
Strength Fracture Toughness Ref. (MPa) resistance (MPam 1/2 ) (Jm~ 2 )
Glasses Soda-lime Fused silica Bulk Fiber
140
8
0.75
a
90 1000
8 8
0.75 0.75
b
7.3.2 Energy Balances in Fracture b
Polycrystals A12O3 1 = 3 um A = l l jim
1 = 25 urn MgO Y2O3 SiC Si 3 N 4 ZrO 2 Ca-PSZ Y-TZP BaTiO 3
7.3.2.1 Unstable Equilibrium: The Griffith Equation Scaling Relations
488 400 302 275 300 600 520
39 36 54 10 13 39 65
3.9 3.3 4.6 1.8 1.5 4.1 4.4
800 2200 124
500 125 10
10 5 1.1
300 170
60 51
2.5 1.8
c d d
c d e f 8
,h i,j
k k c
Glass-Ceramics Pyroceram Macor
neous fracture. Fracture is then seen as the sequential rupture of interatomic bonds, with only the stresses and strains near a crack tip approaching those required for instability as shown in Fig. 7-8 and Eq. (7-30).
1d
Although the Inglis analysis provides a mechanism for fracture, by the concentration of stress at crack tip bonds, the analysis allows no mechanics to be derived, as the stress developed is scale invariant: large and small cracks of the same aspect ratio (c/b) have the same crack-tip stress, and therefore would be expected to fail at the same applied stress. The connection between crack size and specimen strength, and the beginnings of the mechanics of
1, d
The strengths are those observed for polished bars or discs, the toughness and fracture resistance values are those for complete saturation of any microstructural toughening effects. 1 is the grain size. a Dabbs et al. (1982);b Dabbs and Lawn (1985);c Cook etal. (1985); d Cook et al. (1987); e Davidge (1979); f Cook and Pascucci, unpublished work; 8 Cook and Roach (1986);h McHenry et al. (1976); ! Marshall et al. (1983 b); j Trantina (1979); k Swain and Rose (1986); Fairbanks etal. (1986).
approximating a crack, such that c > b, the stress concentration at the tip can be appreciable. In ceramic materials cracks typically have dimensions of c ~ 10 |im, with openings of b ~ 25 nm, such that stress concentrations of approximately 1000 are obtained. Hence, the conditions for bond rupture are achieved for applied stresses well below those required for homoge-
i
i 4(2c/b)o- a
Figure 7-8. Schematic diagram of the stress field around an elliptical slit in a solid under uniaxial tension.
7.3 Fracture
fracture were made made by Griffith (1920). Griffith realized that the critical condition for the fracture of a specimen containing a crack is really a manifestation of a critical energy balance. The first half of the energy balance was the surface energy introduced into the system by the ruptured bonds on the crack surface. For a specimen containing a crack of dimension c under uniform applied stress
Usoc2yc2 = 2yA
(7-31)
Us
y
y
y
355
y
y y y y y y y
5 ~ ~ \
Ao s.
\
N N \
\
UM\ CRACK AREA, A
Figure 7-10. Plot of the mechanical potential l/M, surface potential USi and total potential UT for a cracked, stressed solid, as shown in Fig. 7-9. The maximum in UT represents a point of unstable equilibrium for a solid containing a crack of area Ao.
where y is the excess energy per unit area associated with creating an equilibrium surface of the solid in the given environwhere \// is a dimensionless geometry term, ment (Rice, 1978), and A is the area of the and E is the Young's modulus. The negacrack. The second half of the energy baltive sign indicates that the mechanical poance involves the change in the mechanical tential of the system is reduced from its potential energy of the system due to the crack free state (due to the increased compresence of the crack. The mechanical popliance of the specimen). Physically, tential energy of the system is given by UM = UB — W, where UE is the strain energyEqs. (7-31) and (7-32) represent a scaling of the surface energy in the system with the in the solid, and W is the work done by the crack area, and a scaling of the strain enapplied loading (Lawn and Wilshaw, 1975). ergy in the system with the volume of mateUsing the Inglis analysis, Griffith was able rial affected by the crack, respectively. to show that for a solid under uniform apFigure 7-10 plots Eqs. (7-31) and (7-32) plied stress, cra, the mechanical potential as a function of crack area. The value of aa energy contribution, C/M, could be written is chosen as
356
7 Mechanical Properties of Ceramics
Fracture Resistance and Mechanical Energy Release Rate
We note from Eqs. (7-31) and (7-33) that the fracture resistance reduces to
In order to calculate the variation of strength with the initial crack size, the variation in the unstable equilibrium point with Ao and of must be found, and this is most conveniently done via the configurational forces associated with the surface and mechanical potential energies. The configurational force associated with Us is the fracture resistance, 01, defined by
M = 2 y (Homogeneous solid)
ATT
(7-33)
dA
and which quantifies the resistance to crack motion. The configurational force associated with UM is the mechanical energy release rate, ^, first introduced by Irwin (1958), which quantifies the crack driving force, and is defined by
(7-37)
for solids where M is invariant with crack length (hence homogeneous), such as single crystals or glasses, and from Eqs. (7-32) and (7-34), the mechanical energy release rate for uniform tension is (Uniform stress)
(7-38)
where \// = n1/2 for linear cracks, and \\t = 2/K1/2 for circular cracks (Tada et al., 1973). The instability condition, Eq. (7-36), is fulfilled at the maximum in Fig. 7-10, and imposition of the equilibrium condition, Eqs. (7-35), (7-37), and (7-38) yields
(2yE) 1/2 1/2
(7-39)
ATT
dA
(7-34)
The definitions of Eqs. (7-33) and (7-34) allow the equilibrium condition to be given by =M
(Equilibrium)
(7-35)
and the condition for instability to be written as
dA>dA
(7-36)
which is known as the Griffith equation. Griffith tested this prediction using linearly pre-cracked glass specimens, and an estimate of 2 y extrapolated from high temperatures. The results are shown in Fig. 7-11 a, and confirm the energy balance idea. Energy balances have been extended to many other fracture geometries which permit 01 to be measured under conditions more closely approaching strength tests. Some of the geometries used for ceramic materials are shown in Fig. 7-12. All of
2000
1000 -
0.02 0.05 0.1 0.2 0.5 1 Crack Length, c (in.)
10 20 50 100 200 500 Crack Length, c
Figure 7-11. Strength vs. crack length for glass specimens, showing agreement with the Griffith equation (Eq. (7-39)). Solid lines are predicted behavior using estimates of 2 y. (a) Data of Griffith (1920), annealed scratches, (b) Data of Glaesemann et al. (1987), annealed indentation flaws.
7.3 Fracture
/ \
TENSION oa
7.3.2.2 Stable Equilibrium: Roesler's Law P
DCB
t i
— 2c-
2d
——c — P
CT
P SENB
P/21
IP/2
357
TP
Figure 7-12. Unstable fracture geometries: simple tension; load-controlled double cantilever beam (PDCB); single edge-notched beam (SENB); compact tension (CT).
Not all fracture geometries are unstable, some are stable (d^/dc < 0), some are neutral (d^/dc = 0), and some alter their stability as a function of crack length. Perhaps the simplest example of a stable geometry is the cone crack, caused by the local loading of a blunt contact onto a brittle surface, shown in cross-section in Fig. 7-13 along with some other stable geometries. Roesler (1956) first demonstrated that fracture systems could be stable, by examining these cracks, sometimes called Hertzian cone cracks after their discoverer (Hertz, 1882). Roesler recognized that the mechanical potential energy of a fracture system could be expressed as the product of a strain energy density (the term in parentheses in
Table 7-4. Mechanical energy release rates for common geometries. Geometry
these geometries are known as "unstable" as in each case d^/dc > 0 (Table 7-4). Determination of M or 2 y is made in each case by measurement of a critical value of load or stress needed to propagate the crack, and the crack length and specimen geometry. Glaesemann et al. (1987) used measurements of 2 y from the double cantilever beam geometry for soda-lime glass, and predicted the strength of glass bend-specimens containing carefully characterized elliptical surface flaws (and hence known xj/). The agreement with the experimentally observed strengths was excellent, as shown in Fig. 7-1 l b , reinforcing in quantitative detail the Griffith condition of Eq. (7-39). Table 7-3 gives the 2y values of some ceramic materials with homogeneous fracture resistance, measured using the geometries of Fig. 7-12.
Mechanical energy release rate, #
Unstable I//2(T2C/E Tension Double cantilever beam \l/2P2c2/(Ed3w2) Single edge-notched ij/2P2s2c/{Ed4w2) beam \l/2P2(2s + c)2/[E(s-cfw2] Compact tension Stable ij/2A2E/c Displacement Double cantilever beam i//2A2Eh3/c4 \j/2P2l(Ec3) Indentation \l/2P2/{Ecw2) Wedge Neutral Double cantilever beam i//2 M2/(E d3 w2) V P2 s2/(E d w4) Double torsion ij/2A2E/d Infinite slab The width of the specimen is w, the geometry parameter \j/ is given in Tada et al. (1973), Atkins and Mai (1985), or Fuller (1979). Specimen dimensions and loading configurations are given in Figs. 7-12, 7-13 and 7-15.
358
7 Mechanical Properties of Ceramics
librium position. The stability condition
DISPLACEMENT A
DCB
— <--
dA
dA
(Stability)
(7-41)
is met here for homogeneous materials, and Eqs. (7-34), (7-35) and (7-37) lead to an expression for the stable equilibrium crack length as a function of contact load: WEDGE
Figure 7-13. Stable fracture geometries: indentation; displacement-controlled double cantilever beam (ADCB); simple displacement; wedge loading.
Eq. (7-32)) and a volume. In the case of uniform tension the strain energy density does not depend on the extent of the crack. Roesler used simple scaling laws, similar to those used above for uniform tension, to show for a cone crack under load P, that the strain energy density does depend on the crack length: P2
r* h
V2
(7-42)
Roesler showed that the earlier experimental observations of Tillet (1956) on sodalime glass were consistent with this prediction. Table 7-4 gives the mechanical energy release rates for some other common stable geometries. Some examples of neutral fracture geometries are shown in Fig. 7-15, and their mechanical energy release rates are given in Table 7-4. Examination of Figs. 7-12, 7-13 and 7-15 shows that unstable geometries are characterized by uniform stress or fixed load conditions, stable geometries are characterized by localized loads or fixed displacement conditions, and neutral geometries are characterized by crack lengths
P2
A '
(7-40)
where once again the term in parentheses is a strain energy density (P/c2 is a characteristic stress), and / is a dimensionless geometry parameter. Figure 7-14 plots Eqs. (7-31) and (7-40) as a function of A, with the value of P chosen such that a minimum in UT occurs at Ao. The minimum is a point of stable equilibrium: perturbations in A from Ao lead to increases in potential energy and the system returns to A =A0; changes in P result in the imposition of a new equi-
CRACK AREA, A
Figure 7-14. Plot of the mechanical potential l/M, surface potential Us, and total potential UT for a cracked, stressed solid, for the indentation example of Fig. 7-13. The minimum in UT represents a point of stable equilibrium for a solid containing a crack of area Ao.
7.3 Fracture
Fig. 7-16. The stress intensity factor is defined as the amplitude term of this dependence:
DCB
(2nr SLAB
P/2
P/21
359
I P/2
Figure 7-15. Neutral fracture geometries: double torsion (DT); constant-moment double cantilever beam (M-DCB); infinite slab.
(7-43)
112
where the radial and angular dependence of the stress field are totally separable (the choice of function fij(9) depends on the component of stress examined), and the amplitude and geometry of loading determine the numerical value of Jf (Tada et al., 1973; Atkins and Mai, 1985). The major convenience of stress intensity factors lies in their additivity: as the stresses defined by Eq. (7-43) are additive within the elastic limit, stress intensity factors are also additive. Hence the net driving force on a crack in the stress intensity factor framework may be determined by summing the stress intensity factors deriving from separate sources of loading. Consideration of the changes in the stress and strain fields around the crack tip for an incremental crack extension allows
large in comparison to all other system dimensions or fixed moment conditions. 7.3.3 Stress Balances in Fracture Applied Loading
7.3.3.1 Toughness and Stress Intensity Factors
It is frequently more convenient to study fracture properties of ceramics using a stress balance, rather than the energy balance discussed above. The parameter used in the stress balance is the stress intensity factor JT, characterizing the amplitude of the stress field around a crack tip and which plays an analogous role to ^ as a crack driving force in the stress picture. The dominant stress field around a crack tip is characterized by an r " 1 / 2 dependence (Tada et al., 1973; Atkins and Mai, 1985) where r is a radial coordinate shown in
r
Figure 7-16. Coordinate system at a crack tip, used in the definition of the stress intensity factor.
360
7 Mechanical Properties of Ceramics
Eqs. (7-50 a) and (7-50 b) reduce to
JT and ^ to be related by JT = (^E)
(7-44)
1/2
for plane stress conditions [under plane strain conditions, E is replaced by £/(l - v2)] (Atkins and Mai, 1985). A parameter analogous to M, characterizing the material resistance to fracture in the stress framework, is the toughness 2T, defined by
such that the equilibrium condition may be written as (analogous to Eq. (7-35)) Jf =
(Equilibrium)
(7-46)
and the stability conditions as (analogous to Eqs. (7-36) and (7-41)) dJf
(Instability)
>
(7-47)
dc
dc dST < —— (Stability) dc dc
(7-48)
For a homogeneous solid, the toughness is given by an invariant quantity ^ : 3T0 = (2yE)1/2 (Homogeneous solid) (7-49) and Table 7-3 gives the toughness values of some common ceramics. Stress intensity factors are determined by an integral of the stress field over the crack surface. For axially symmetric cracks this integral is
2 - a(r)rdr (nc)ll2l(c2-r2)112
(7-50 a)
and for lineally symmetric cracks
*-i(cY\ \n)
a(r)dr 2
2
(7-50 b)
I(c -r )^
2
where in each case a (r) is the stress over the crack, and r is a crack-plane coordinate (Tada et al, 1973). If the applied stress is uniform over the crack, such that a (r) = cra,
jf = xl/aa c 1/2
(Uniform stress)
(7-51)
implied by Eqs. (7-38) and (7-44). 7.3.3.2 Crack Initiation in a Decreasing Stress Field Stress Intensity Factor Calculation Many cases of ceramic fracture are determined by non-uniform stress fields, in particular, flaws are initiated and thence stabilized in decreasing stress fields. Specific examples include stress fields around expanding inclusions which decay as r " 3 (Swain, 1981), stress fields about point contacts on surfaces (r~2) (Lawn and Swain, 1975), stress fields in ion-exchanged or ion-implanted surfaces (r" 1 ) (Tandon and Green, 1990), and stress fields in thermally shocked surfaces (1 — r2) (Lawn and Marshall, 1977). Determination of the behavior of cracks under such circumstances is important in ceramics, as the resultant crack length thence determines specimen strength via Eq. (7-39). The simplest example of a decaying stress field is one represented by
= ah(l-[)r
r>b
(7-52)
where oh is the peak stress at r = 0, and b is the length scale at which the stress reaches zero. Combining Eqs. (7-50 a) and (7-52) leads to (Swain, 1981; Lawn and Evans, 1977)
361
7.3 Fracture
which is plotted in Fig. 7-17. We note that in the limit of c
(7-54 a)
appropriate for a uniform stress field, Eq. (7-51) (i.e., the decay of the field is not noticed by the crack), and in the limit c^> b to In1'2
b
c3/2
(Local loading)
(7-54 b)
appropriate for a point loaded circular crack, (i.e., the stress field acts as a point load of magnitude %P = ahnb2/2, implied by Eq. (7-40)). The asymptotes of Eq. (7-54) are also plotted in Fig. 7-17. The full stress intensity factor represents a transition from the destabilizing field of Eq. (7-54 a) to the stabilizing field of Eq. (7-54 b). Initiation Behavior Consider now the behavior of a cracklike defect of dimension c{ as the magnitude of oh is increased. For values of oh less than that required to produce an equilibrium instability at c = c{ the crack is unchanged, i.e. for I,
^/2
(7-55)
where 9~ is the toughness of the material. At the critical stress level ax the initial defect becomes unstable and increases in length - a crack initiates. However, as the stress intensity factor passes through a maximum the driving force for crack extension begins to decrease for large crack extensions, until a stable equilibrium condition is reached at a crack length c = c0 such that Jf (c0) = ST in Eq. (7-53). We see that decreasing c{ for a given toughness
1 2 3 CRACK LENGTH, c / b
4
Figure 7-17. Jf (c) function for an axially symmetric crack propagating in a decreasing stress field (Eq. (7-53)). Asymptotic solutions are shown as the dashed lines (Eq.(7-54)). Jfh = (2/n)1'2
increases the stress level o{ needed to initiate a crack, but that the final, stable crack length c0 is greater. Decreasing the toughness for a given c{ decreases ai and increases c0. The basic physics described above is seen in many ceramic fracture examples in which microstructural effects play a significant role in crack initiation, and which are shown schematically in Fig. 7-18. Increases in
362
7 Mechanical Properties of Ceramics (D)
r~°—'—i
(E) i
'
i
i
i
—hill
(F)
— Figure 7-18. Schematic diagrams of microstructural mechanisms capable of initiating stable cracks in ceramics, (a) Expanding inclusion arising from a dilational phase change or a lower thermal expansion coefficient (material cooling), (b) Tetragonal -unonoclinic phase transformation in a ZrO 2 material (on cooling or under stress), (c) Anisotropic thermal expansion coefficient or modulus (material under stress or temperature change). The arrows indicate directions of greater thermal expansion coefficient or smaller modulus, (d) Sintering of a porous matrix around a denser inclusion, (e) Thermal shock, (f) Mismatch in strain, modulus, or thermal expansion coefficient at an interface between a thin film and a substrate, (g) Contact or indentation by a sharp particle.
talline ceramics due to anisotropic thermal expansion effects (Fig. 7-18 c). For example, in A12O3 the grain size must be greater than about 100 |im for microcracking to occur, but only greater than about 1 }im
100 200 300 INCLUSION DIAMETER
400
Figure 7-19. Radial crack lengths vs. inclusion size, for NiS inclusions expanding in a glass matrix. The hatched region indicates inclusion sizes below which no cracks were observed (data from Swain) (1981).
in the more anisotropic YBa 2 Cu 3 O 7 _^ (Shaw et al, 1989). Figure 7-20 shows microcracks generated in YBa 2 Cu 3 O 7 _ 5 . Anisotropic Young's modulus effects will similarly generate cracks in polycrystalline materials under applied stress. Differential sintering rates may also generate stress fields which lead to the initiation of stable cracks - these cracks will radiate out from the less rapidly densifying region (Fig. 7-18 d). An example is shown in the MgO material in Fig. 7-21 (Ostertag, 1987). Rapid decreases in temperature of a ceramic lead to decaying tensile fields on the specimen surface as the surface cools and contracts more rapidly than the center (Fig. 7-18 e). Such thermal shocks can lead to the initiation of stable cracks if the tern-
7.3 Fracture
363
Figure 7-20. Optical micrograph of sintered YBa 2 Cu 3 O 7 _ a , showing microcracks arising from anisotropic thermal expansion coefficient effects on cooling. (Micrograph courtesy L. C. Stearns.)
Figure 7-21. Radial cracks in a model system of porous MgO sintering around a solid MgO disc (from Ostertag, 1987).
perature decrease is sufficiently large (e.g., in quenched A12O3 or glass) (Hasselman, 1970; Fairbanks et al., 1984). Temperature decreases smaller than a critical value will not lead to the initiation of cracks, as the peak stress generated will not reach the o{ value. Hence, the strenghts of thermally shocked specimens are expected to remain invariant for temperature drops below a certain value (as the strength is controlled by c{), beyond which the strength will be dramatically reduced and decrease with in-
creasing temperature drop (as the strength is now controlled by c0). Figure 7-22 shows the strength of some alumina specimens, confirming this prediction. Inhomogeneous thermal expansion or "intrinsic stress" effects may also lead to the spalling of tensile-stressed thin layers from substrates (Fig. 7-18 f). As the overlying film is stressed, cracks may be initiated from delaminations or other interface defects and stabilized in the substrate. If the film stress is sufficiently large the crack tra-
364
7 Mechanical Properties of Ceramics
400 300 200 -
-
100 -
-
n
200 400 600 800 TEMPERATURE DROP (°C)
1000
Figure 7-22. Strength of thermally shocked A12O3 specimens, showing a precipitous decrease in strength at a critical temperature drop. The hatched region indicates the strengths of unshocked specimens (data from Hasselman, 1970).
(a)
jectory becomes parallel to the interface and the mechanical energy release rate becomes neutral (Hu et al., 1988). As a final example of stable crack initiation, Fig. 7-23 shows a crack generated during the loading of a sharp indenter on a soda-lime glass surface. On unloading the strain mismatch of the remnant deformation zone imbedded in the surrounding elastically deformed matrix leads to a residual stress field (Fig. 7-18 g) (Lawn et al., 1980). Both the point loading field, and the residual mismatch field, decrease with distance from the contact and give rise to the initiation-stabilization phenomena discussed above. Figure 7-24 plots the lengths of the surface traces of such cracks as a function of indentation load, showing the P 2 / 3 dependence appropriate to a pointloaded circular crack. Many other crack types and development sequences occur at sharp contacts, and are reviewed by Cook and Pharr (1990). 7.3.3.3 Crack Propagation in an Applied Stress Field
100 pro
Once a stable crack has initiated, by one of the processes outlined above, it may reduce the strength of a specimen under subsequent applied stresses. In such cases however, the net stress intensity factor is now given by the sum of the stabilizing component controlling the initiation and the destabilizing component associated with the applied stress (Eqs. (7-51) and (7-45 b)): .3/2
Figure 7-23. Optical micrographs of a Vickers indentation flaw in soda-lime silicate glass, (a) Reflected light, showing radial and (sub-surface) lateral cracks, (b) Transmitted, cross-polarized light, showing birefringence associated with the residual strain field.
(7-56)
In contrast to the stress intensity factor of Eq. (7-53), the combination of fields in Eq. (7-56) shows a minimum in Jf as a function of c, Fig. 7-25. For fixed P, the position of the minimum depends on the
7.3 Fracture
365
Under equilibrium conditions then, the crack begins at c0 and moves stably to cm as the applied stress increases, until at the maximum stress cra = am the system becomes unstable and failure ensues. Equation (5-57) may be rewritten as 3^4/3
3
10'
1
2
10 10 INDENTATION LOAD, P (N)
10
3
Figure 7-24. Radial crack length vs. indentation load for Vickers indentation flaws on soda-lime silicate glass. The solid line is of slope 2/3 in accord with Eq.(7-42).
10
(7-58)
which predicts that the strength of components containing stabilized flaws should decrease with a — 1/3 power law dependence on P. Figure 7-26 shows the strength of some ceramics containing Vickers indentation flaws - the strength decreases with the dependence shown in Eq. (7-58). The separation of the data for the different materials in Fig. 7-26 is a reflection of different x and ST values. (In fact, once % is calibrated as a function of elastic/plastic material variables, 2T may be estimated from plots such as Fig. 7-26 or Fig. 7-24 (Chantikul et al,31981; Anstis et al., 1981).) The previous paragraph describes the general failure of most ceramic materials.
10" 1 10° 101 CRACK LENGTH, c / c m
1
\^^#^#
Figure 7-25. Jf (c) function for an initially stabilized crack propagating in a uniform stress field (Eq. (7-56)). Asymptotic solutions are shown as the dashed lines (Eqs. (7-51) and (7-54 b)). X h-
\ ^ 100 -
* ^
SLOPE = -1/3
GLASS CERAMIC
magnitude of the applied stress, cra. The value of the applied stress at which the minimum occurs at Jf = 3~ is given by (7-57 a)
rREt>
CD
if)
IOU
I
1
IO1
IO Z
10°
INDENTATION LOAD,P(N)
where the crack length is (7-57 b)
Figure 7-26. Strength vs. indentation load for specimens containing Vickers indentation flaws. The solid lines are of slope —1/3 in accord with Eq. (7-58).
366
7 Mechanical Properties of Ceramics
The strength-controlling defect is determined by the magnitude of the stabilizing field associated with its creation: phase transformation, contact, thermal expansion mismatch, etc. The strength is then determined by the magnitude of the destabilizing field required to produce a change in the stability of the system at the equilibrium condition. The specific details of various cases are then simply input to the system via the x, xj/, P and ST parameters. It is immediately obvious that strength is not a material property, as it depends on both a material-intrinsic variable {ST\ and environmental, or history-dependent extrinsic variables (x,P\ as well as the details of the loading geometry (x//) (Eqs. (7-39) and (7-58)). 7.3.4 Microstructural Influences in Fracture
lease rate. Hence, frames of reference become very important for correctly characterizing toughening processes (Mai and Lawn, 1986; Cook, 1990). From a crack tip frame of reference the net stress intensity factor is given by the sum of that arising from the applied loading Jfa, and any microstructural influence, JfM, where we note that JfM is a signed quantity and that JfM < 0 corresponds to sources of loading acting to close the crack. The equilibrium condition is then given by (7-59) = Jfa + X^ =
From the frame of reference of the applied loading the net toughness is the sum of the intrinsic toughness 2T^ and the microstructural influences, and hence the equilibrium condition here is Jl a = J
7.3.4.1 Frames of Reference
The dominant effect of microstructural interaction during crack propagation in ceramics is one of toughening - the fracture resistance or toughness of the material is increased above the level set by the interatomic bonds on the crack plane. Microstructural interactions cause this effect by redistributing the flux of energy from the applied loading to sinks other than the crack tip, or, alternatively, by redistributing the stress in the system away from the crack tip. In most cases these redistributions of energy or stress are a function of crack length, leading to "^-curve" or "ZTcurve" effects, in which the fracture resistance or toughness increase with crack length, before reaching a steady-state saturation value. Of course, from the point of view of the crack-tip bonds any toughening effects are indiscernible: toughening is simply perceived as a decrease in the applied stress intensity factor or mechanical energy re-
(Crack-tip frame)
= JQ — JL ^ = JQ + J^
(Applied-load frame)
(7-60)
This is a more useful frame of reference for the experimentalist, as usually only the parameters characterizing Jfa are directly amenable to experimental verification. In most cases the microstructural influences manifest themselves as stress distributions over the crack plane so that ^ = — Jf^, thereby allowing the evaluation of a microstructural contribution to toughening by a stress intensity factor calculation. Similar identifications of driving and resistance forces may be made in the energy balance framework. For crack propagation involving the "simple" rupture of interatomic bonds the work of fracture is given in Eq. (7-37), 2y = ^? 0 , and the equilibrium condition is <S = ^0
(Crack-tip frame)
(7-61)
In the presence of microstructural toughening mechanisms the equilibrium condition is (7-62) ^ a = ^ = g%Q + AM (Applied-load frame)
7.3 Fracture
where A^? characterizes microstructure related energy absorbing mechanisms arising during crack propagation. We note that the quadratic relationship between X and ^, and between 2T and 01, prevents a simple relation between the microstructural contributions to the fracture resistance. In particular, in the applied-load frame The two principal microstructural interactions which lead to toughening in ceramics are ligamentary bridging and phase transformations, and are considered in the next sections. Other microstructural interactions which may occur during fracture in some materials include crack deflection (perturbations in the crack path from planarity), crack bowing (perturbations in the crack front on the crack plane), and microcracking (cracks initiated ahead of the main crack front). The potential of these interactions as toughening mechanisms is reviewed by Green et al. (1989) and Evans (1990).
367
in residual stress arising from processing) (Swanson et al., 1987; Swain, 1986). Polycrystalline ceramics such as alumina are particularly susceptible to the grain-localized bridging processes during crack propagation. In a series of careful experiments Knehans and Steinbrech (1982) propagated cracks in alumina SENB specimens (Fig. 7-12) and observed an increase in 0i (Fig. 7-27). By renotching the crack behind the tip, and re-measuring the 01curve characteristics they were able to show that the fracture resistance reverted to the value obtained at shorter crack lengths, thus demonstrating that the toughening effects were due to processes behind the crack tip. Hiibner and Jillek (1977), Swain (1986), and Steinbrech et al. (1983), observed much interlocking of grains behind the crack tip, and subsequent studies examined the formation and rupture of ligamentary bridges behind crack tips in alumina and other materials in some detail (Swanson et al., 1987; Swanson, 1988; Cook, 1990).
7.3.4.2 Toughening by Ligamentary Bridging
Grain-Localized Bridges in Poly crystalline Ceramics Many polycrystalline ceramics are toughened by ligamentary bridging processes behind the crack tip. Such bridges restrain the crack opening displacement, thereby lowering the stress at the crack tip, or (in the energy balance framework) absorb energy during their own deformation. The bridges may be deliberately incorporated into the microstructure as in the case of fiber composites (Marshall etal., 1985) or ductile-particle reinforced ceramics (Sigl et al., 1986), or arise during the propagation of the crack as a consequence of local inhomogeneity (e.g., weak or more compliant grain boundary regions, or variations
250
~ or
200
-
UJ
•i
I
150 100
-
LJ Q:
LJ (Z.
0.2 CRACK LENGTH, c/d
Figure 7-27. Fracture resistance M as a function of crack extension c for A12O3 SENB specimens, showing the ability of re-notching to decrease ffl, confirming that the increases in $ are due to processes behind the crack tip (data from Knehans and Steinbrech, 1982).
368
7 Mechanical Properties of Ceramics
The two major types of bridges are shown in Fig. 7-28. The bridges either consist of locally unruptured groups of grains, Fig. 7-28 a, or frictionally interlocked crack faces arising from crack propagation parallel to the applied stress field, Fig. 7-28 b. Figure 7-29 a is a schematic of the crack paths observed in alumina and other ceramics. Close to the crack tip grains bridge the crack, further back from the tip, as the crack profile widens, these grains become separated from the interface, until at some distance behind the tip the grains either rupture or separate completely from the matrix. The restraining stress distribution
(a)
acting over the crack, averaged over many bridging sites, is shown in Fig. 7-29 b. The stress is high close to the crack tip as the full strength of the unruptured grains and frictional interlocking is felt, and diminishes behind the tip. We may represent this stress distribution by a line force o* centered a characteristic distance 3 behind the tip as shown in Fig. 7-28 c. The stress intensity factor for such a configuration is well approximated by (Cook, 1987) S1/2 [1 -
(5/'cf12}
(7-63)
where JX is a dimensionless geometry constant. We see that in the limit of small
(b)
VOU urn
50 ym
Figure 7-28. Micrographs of ligamentary bridges behind crack tips in A12O3 (from Cook, 1990). (a) Transmitted light micrograph of a discontinuous surface trace. The ends of the surface traces are labelled S. The sub-surface continuity of the crack leaves the surface as a region of restraint as shown in the schematic. The continuous crack in the bulk of the material is the dashed line labelled B and the closure tractions exerted by the bridged material on the crack walls are indicated by arrows, (b) Reflected light micrograph of frictionally interlocked grains. The schematic indicates the closure tractions exerted by the frictional contact on the separating crack walls.
369
7.3 Fracture
characterizing the effect of the microstructural restraining force. Hence in the large flaw limit (P ^> P*) we have the usual P~1/3 dependence (Eq. (7-58)):
(a)
^
(7-66 a)
(b)
and in the small flaw limit (P <^ P*) the tendency to a load independent plateau
CD
(7-66 b) and generally (7-67)
(0
Figure 7-29. Crack propagation in a ligamentary bridging material, (a) Schematic of crack propagation, showing grains bridging the crack close to the tip. (b) The restraining stress exerted by the bridges. (c) Model representing the effect of the restraining stress.
cracks (c/d -> 1) the toughness tends to &~0, and that in the large crack limit (c/S -» oo) to another invariant quantity (using Eq. (7-60))
Figure 7-30 plots the measured strengths of a series of alumina materials as a function of indentation load, normalized by the parameters in Eqs. (7-65) and (7-66 b). The definite ^?-curve tendencies of these materials are reflected in the ability of the model to describe the strengths - at low indentation loads the strengths become quite insensitive to the scale of the flaw used to initiate failure (compare the strength degradation with that of the untoughened ma-
(7-64) characterizing the saturation of the bridging process. Effect of Bridging on Specimen Strength For a stabilized (e.g., indentation) crack subjected to an applied stress in a material described by Eqs. (7-63) and (7-64), the strength as a function of indentation load may be derived by imposing the equilibrium instability condition as before. To do this it is useful to define the quantity P* =
(7-65)
'1O~3
10" 2 10" 1 10° 101 INDENTATION LOAD, P/P*
10 2
Figure 7-30. Strength vs. indentation load for A12O3 specimens containing Viekers indentation flaws. The solid line is a best fit to the data in accord with Eq. (7-67), the dashed lines are the asymptotes of Eq. (7-66) (data from Cook, 1987).
370
7 Mechanical Properties of Ceramics
terials of Fig. 7-26). The data of Fig. 7-30 may be used to predict successfully the maximum strength of such materials, as shown in Fig. 7-31. Ductile Particle and Fiber Reinforcement The behavior discussed above is simply one example of the way ligamentary bridging elements may toughen ceramics. The underlying general principle is that of energy dissipation caused by the deformation of the ligament imposed by increasing crack opening displacement at the ligament site. Explicit treatment of the energy balances during fractue is best handled by the path-independent J-integral (Rice, 1968), especially for steady-state crack propagation. Here we calculate the energy balances for a propagating crack with a ligamentary bridged zone, showing how such a zone manifests itself as toughening in an energy framework, and showing how various deliberately-added bridging elements in ceramics toughen on the basis of their constitutive equations for deformation.
The J-integral involves the integration of the strain energy density and tractions along paths beginning and ending on opposing crack faces. Making a circuit beginning at the crack mouth, around the exterior of the specimen, followed by return to the starting point traversing the crack surface, as shown in Fig. 7-32, leads to J. - J,, - Jo = 0
(7-68)
where J a is the contribution to the path from the applied loadings, JM the contribution from the superposed microstructural tractions, and J o the contribution from the interatomic bond rupture processes. Now, J a is simply ^ a = Jf^/E and j 0 = 2 y = ^Q2/E, and we are left with the evaluation of the contribution from the ligamented zone. For paths along the crack face there is no contribution from the strain energy and the J-integral is simply expressed in terms of the tractions exerted (Rice, 1968): J^= j
-T-(du/dr)ds-
c-b c-b
-
J -T'(du/dr)ds
(7-69)
c
where J i s the traction exerted on the crack faces in the bridged zone, u is the crack opening displacement, r is a radial coordinate, and ds is a path element. Making the assumption that the tractions are normal to the crack face such that T = a(u) and that ds = dr, Eq. (7-69) may be written as
200 300 PREDICTED STRENGTH (MPa)
Figure 7-31. Observed maximum strengths for the A12O3 materials in Fig. 7-30 vs. the values predicted from the bridging model.
c) = - 2 J a (u) du (7-70) o where 2 a is the crack opening at the end of the bridged zone (i.e., at r = c — b). The toughening effect of the bridging zone as a function of crack length may thus be calculated by explicitly inserting a constitutive equation for the bridging, o(u\ and a crack length dependence for the
371
7.3 Fracture
Figure 7-32. ./-integral path used to calculate contributions to fracture resistance from bridging ligaments.
crack opening, u(r,c\ and integrating Eq. (7-70). As the opening depends on the degree of toughening, an implicit equation for I±3t(c) results (Marshall et al, 1985), which is generally not analytic. However, the increase in fracture resistance resulting from a bridging process is easily seen from Eq. (7-70) to be proportional to the integrated area of the constitutive equation for ligament deformation. Figure 7-33 shows the form of the constitutive equations for several bridging processes in ceramics: ductile particles (e.g., WC-Co) (Sigl et al., 1986); debonding fibers (e.g., SiC-glass-ceramic) (Marshall et al., 1985); sliding fibers; debonding grains (e.g., A12O3 polycrystals). Obviously the greater area under the constitutive equation the greater the degree of toughening. In steady-state crack propagation the crack opening at the end of the bridging zone is equal to that necessary to cause ligament rupture. This crack opening is 2a = 2M*, and hence the integral in Eq. (7-70) may then be evaluated explicitly: Afmax = - 2) a(u)du = irx 0
(7-71)
(T*
ur
u
Figure 7-33. Schematic of bridging processes in ceramics and their constitutive relations: debonding fibers, ductile particles, sliding fibers or whiskers.
372
7 Mechanical Properties of Ceramics
The maximum increment in the work of fracture is equal to the work per unit area necessary to rupture a ligament. 7.3.4.3 Toughening by Phase Transformations Toughening
Mechanics
Zirconia ceramics may be toughened by phase transformation processes ahead of the crack tip, and considerable effort has been expended in this area since the original suggestion of Garvie et al. (1975), which is covered in some detail in the monograph of Green et al. (1989). If particles of the tetragonal phase of ZrO 2 are metastably retained by appropriate processing of the material, the enhanced crack tip stresses may trigger the transformation to the stable monoclinic phase. Associated with this phase transformation are dilational and shear strains which act to toughen the material. The toughening may be viewed as either a shielding of the crack by compressive stresses associated with the strained particles (in a stress intensity factor view) (McMeeking and Evans, 1982), or, by the work done in moving the particles through their constitutive relation for deformation (in a mechanical energy release rate view) (Mashall et al., 1983 a). Figure 7-34 shows particles in various states of deformation around a crack tip: Particles remote from the tip (extreme right) are simply elastically deformed. At a critical distance from the crack tip (shown as the cardioid-shaped process zone boundary) the stress field reaches a critical level which triggers the transformation, and a stress-free transformation strain develops. For particles closer to the crack tip (i.e., in the process zone) additional elastic strain may ensue. Particles in the crack tip wake region are elastically destraining, and at points remote from the tip (extreme left)
J/x=/ W 2Udz
Figure 7-34. Schematic of the crack-tip process zone and wake region for a transforming material, showing the movement through the constitutive equation for a transforming element.
such that no stress enhancement is felt, the particles are unstressed at the transformation strain sT. The strain energy density change °U * associated with the right-to-left cycle in Fig. 7-34 is simply the integrated area under the o (&) response of the transforming particles. For the same /-integral path as shown in Fig. 7-32 the only contribution in this case comes from the remote wake region (Fig. 7-34) (Rice, 1968): (7-72)
where °ll is the strain energy density along the path dz, and w is the width of the wake region. Once again the maximum increase in fracture resistance may be estimated without exact knowledge of the deformational constitutive equation. If all particles have been moved through the full transfer-
373
7.3 Fracture
mation cycle along the J-integral path in the wake then % in Eq. (7-72) may be written as
TC8T
(7-73)
where Vf is the volume fraction of transformed particles, e* is the maximum particle strain reached during the cycle, ac is a mean critical stress for particle transformation, and ah (e), and ov (s) are the loading and unloading parts of the constitutive relation, respectively. In this steady-state case, the integral of Eq. (7-72) reverts to = 2VfeTacw
(7-74)
Most analyses assume the critical mean stress at the process zone boundary to be unaltered from its form in the absence of transformation, such that the above equation is written generally as lx
= ?|F f £ T £w
(7-75)
where E is the Young's modulus of the matrix material, and rj is a dimensionless constant (~ 0.2) which accounts for the exact details of the constrained transformation process (Green et al., 1989). The linear dependence of A^ m a x on w predicted from Eq. (7-75) is reasonably well obeyed experimentally, as shown in Fig. 7-35. Figure 7-36 shows an indentation in a ZrO 2 material with transformation zones surrounding the contact impression and the initiated cracks.
5
10 15 20 ZONE WIDTH, w Qm)
25
Figure 7-35. Fracture resistance vs. zone width for Mg-ZrO 2 materials, showing the linear relation (Eq. (7-75)) (data of Swain, 1985).
tary bridging to increase fracture resistance. Such increases in fracture resistance are of course only obtained with correct processing. In particular, long heat treatments of ZrO 2 materials reduce the toughening as the tetragonal particles are coarsened. If the particles become too large, the metastability of the tetragonal phase is lost (i.e., the tetragonal phase particles become stable) and transformation and toughening disappear.
•*.•* ,J-J
>.
Transformation Toughening Effects in Zirconia Materials Figure 7-37 shows the ^-curves of a ZrO 2 material and a polycrystalline A12O3 demonstrating the power of the transformation process compared with ligamen-
Figure 7-36. Micrograph of an indentation flaw in a Y-TZP material, showing surface uplift indicative of the tetragonal to monoclinic transformation adjacent to the contact impression and the cracks. (Micrograph courtesy L. M. Braun.)
374
7 Mechanical Properties of Ceramics 0.12
key to this improved performance: the data shown in Fig. 7-39 are for a material optimized for thermal shock resistance at 11.5 vol.% ZrO 2 , greater or lesser amounts ZrO 2 added to the base A12O3 lead to weaker enhancement in properties or even degradation.
0.06 -
0.00
7.3.5 Non-Equilibrium Fracture 7.3.5.1 Crack Velocities in Destabilizing and Stabilizing Fields Zirconia
Crack motion is a non-equilibrium process reflecting the underlying kinetics of
0 1 2 CRACK EXTENSION, Ac (mm)
Figure 7-37. Fracture resistance vs. crack extension for polycrystalline A12O3 and a partially stabilized ZrO 2 showing the ability of the transformation process to considerably enhance fracture resistance. The data for A12O3 are from Swain (1986), and the data for ZrO 2 are from Readey et al. (1987).
1000 Toughened
Q_
• to
A
200 -
A
The ^-curves of ZrO 2 materials give rise to significant flaw tolerance in the strength characteristics. Figure 7-38 shows the strength of two ZrO 2 materials vs. indentation load. The material aged for peak toughening shows almost no decrease below the maximum strength with increased indentation load, whereas the over-aged material, although still showing some flaw tolerance, is less strong and shows a greater dependence of strength on indentation load. Ceramics containing ZrO 2 can also show increased resistance to thermal shock. Figure 7-39 shows the strength after thermal shock for a ZrO2-containing A12O3 material, in comparison with the base A12O3. The enhanced strength, and retained strength with increasing temperature drop, in comparison to the base, are obvious. Again it should be noted that processing is
50 10°
A
A
Overaged
100 i
•
A
A A
i
101 102 10 3 INDENTATION LOAD, P (N)
104
Figure 7-38. Strength vs. indentation load for ZrO 2 specimens containing indentation flaws, showing the significant flaw tolerance of specimens processed for optimum transformation toughening (data from Marshall, 1986).
1500 500 1000 TEMPERATURE DROP (°C) Figure 7-39. Strength of thermally shocked A1 2 O 3 ZrO 2 specimens vs. temperature drop showing the increase in strength and increased resistance to thermal shock (data from Becher, 1981).
7.3 Fracture
5
10 15 TIME (min.)
20
Figure 7-40. Crack length vs. time for a DCB glass specimen loaded beyond the unstable equilibrium point (data from Wiederhorn, 1967).
the atomic bond-rupture processes. If the kinetics of bond rupture are rapid then small perturbations of the system from equilibrium can lead to catastrophic results: crack lengths perturbed beyond unstable equilibrium points (Fig. 7-10) lead to rapid failure under such conditions - the specimen breaks. However, not all fracture kinetics in ceramics are rapid on human time-scales, as observed experimentally by Wiederhorn (1967). In fact, the common process of moisture-enhanced crack propagation in oxides, particularly glasses, is
375
quite slow. Figure 7-40 shows crack propagation vs. time in a soda-lime silicate glass for a load-controlled DCB specimen perturbed beyond unstable equilibrium. The crack velocity and crack length increase with time, as the system moves further from equilibrium (Table 7-4). Figure 7-41 shows crack propagation in a similar glass for rapidly initiated indentation cracks. The velocity decreases with time in this case as the system moves closer to equilibrium. The separation of the data for the different environments is an indication of the different environment-dependent kinetics operating, whilst the tendency to an environment-independent crack length value at long times is indicative of approach to a similar equilibrium point (c 0 , Eq. (7-42)). Figures 7-40 and 7-41 are characteristic of cracks propagating in destabilizing and stabilizing fields, respectively. Perturbations of the unstable geometries in Fig. 7-12 lead to similar increasing crack velocities (the most common of which is simple tension, which is regarded as a strength test when the kinetics are rapid). Perturbations of the stable geometries of Fig. 7-13 lead to decreasing velocities, and perturbations of the neutral geometries of Fig. 7-15 lead to constant velocities. Just as knowledge of
Figure 7-41. Crack length vs. time for rapidly initiated indentation radial cracks in soda-lime glass. Time, t(s)
376
7 Mechanical Properties of Ceramics
the geometry parameters (Table 7-4) allows 0i to be determined using these specimens, crack velocity as a function of mechanical energy release rate, v (^), can also be determined. The v (^) curve plays an analogous role in non-equilibrium fracture to that of 01 in equilibrium fracture, as both are specimen independent and only reflect material-environment interactions. Data such as Figs. 7-40 and 7-41 suggest that v (^) should be a monotonic increasing function of <§ with a zero at the equilibrium point of ^ = 2 y (in the crack-tip frame of Eq. (7-61), as this is where the bond rupture kinetics are determined).
in a pressure (or, chemical potential) gradient to the reaction site (Lawn, 1974) give the transport controlled velocity as vn = M #
(7-77)
where the parameter M represents the access of the environmental species to the reaction sites (i.e., large values of M imply little constraint in reaching the sites). The net velocity is given by (v/v,)2/* + (v/vn) = 1
(7-78)
7.3.5.2 Kinetic Models for Crack Velocity
where x is the number of environmental molecules consumed in the bond rupture process (i.e., the order of the reaction). In the limit of 2 y Eq. (7-76) takes the forward reaction (i.e., bond rupture) limit form:
Reaction and Transport Processes
v?
Two kinetic processes are considered to control crack velocities in ceramics: (i) the reaction kinetics between the environmental species and the rupturing bonds, and (ii) the transport kinetics of the environmental species to the reaction sites. For no reaction with the environment the crack velocity is thus expected to be rapid, as is observed for ceramics tested in "inert" conditions, e.g., dry N 2 gas, silicone oil (Dabbs et al, 1982; Wiederhorn et al., 1982). Models based on the motion of active kink sites along the crack front (Lawn, 1975; Pollet and Burns, 1977) give the reaction controlled velocity as
=(vo/2)exp(-2y/(2NkT)) (7-79)
(which is often approximated over a limited range as v oc A &n, or v oc A Jf n for empirical description of crack velocity behavior). Equation (7-78) is shown in Fig. 7-42 as the solid line and the asymptotic responses of Eqs. (7-77), (7-79) and the threshold, as the dashed lines. 10u 10,-2
Reaction
^Transport ~
V! = v0 sinh [(# - 2 y)/(2 N k T)]
(7-76)
where v0 is a scaling velocity related to the attempt frequency for kink migration, and N is the number of bonds per unit area in the crack plane. Equation (7-76) contains a zero at the equilibrium point, representing the ^-value at which equal numbers of bond-healing and bond-rupturing kinks are present on the crack front. Models based on flow of the environmental species
&
10,-6 10" 10-10 Threshold
10-12 0 2 4 6 8 10 (J m~2) Mechanical Energy Release Rate,
Figure 7-42. Crack velocity as a function of mechanical energy release rate using the reaction and transport models of Eq. (7-78).
377
7.3 Fracture
changing the threshold. Wiederhorn et al. (1982) have considered this last problem in some detail. Figure 7-44 shows some v (^) data for a polycrystalline alumina in comparison to some other structural materials - similar behavior is apparent, but the curvature of the data prevent use of the simple linear transport model of Eq. (7-77). Constraints on Reactive Species
o
10"12
10°
The basic process occurring at a crack tip in oxide (e.g., silicate) ceramics reacting with atmospheric moisture is represented by the reaction H 2 O + SiO2 -> Si-OH • • • HO-Si
(7-80)
10" 10" 10- 1 2 0 2 4 6 8 Mechanical Energy Release Rate, # (J m~2)
Figure 7-43. Crack velocity data for glass specimens, showing the fit of the reaction and transport model. Data for soda-lime (SLS) and borosilicate (BS) glasses from Wiederhorn and Bolz (1970), and for sodiumaluminosilicate (NAS) glasses from Gehrke and Ullner (1988).
20000
Figure 7-43 shows some crack velocity data in glass, demonstrating the ability of 500 the model of Eq. (7-78) to describe experi10 mental data. Three aspects of behavior are 10~ displayed: (a) different materials have separate v {*&) responses reflecting differences in 7 10~ surface and reaction chemistry; (b) increas10ing temperature increases crack velocity in Alumina the reaction-controlled region, but has lit10'-10 tle effect in the transport-controlled region; 30 34 38 42 46 (c) increasing the viscosity of the surroundMechanical Energy Release Rate, $ (J m~ ) ing medium decreases the velocity in the Figure 7-44. Crack velocity data for a polycrystalline transport-controlled region, truncating the alumina (Pletka and Wiederhorn, 1982), PMMA, and steel (Williams and Evans, 1973). reaction-controlled region but without
378
7 Mechanical Properties of Ceramics
where a strong, primary, ionic/covalent bond is replaced by a weak, easily ruptured, hydrogen bond. Similar processes may be imagined for Al, Mg, Zr, etc., cations. Michalske and Freiman (1982) have considered the reaction of Eq. (7-80) and have provided generalized constraints on the environmental species which may make the primary -> secondary bond switch in ceramics, thereby allowing slow nonequilibrium fracture. Michalske and Freiman consider a three step reaction, shown in Fig. 7-45: (1) A lone pair from the reacting molecule is attracted to the Si site; (2) A proton from the reacting molecule is transferred to the bridging oxygen at the same time as electrons are transferred to the Si; (3) The hydrogen bond between the transferred proton and the remaining portion of the reacting molecule is broken. As a consequence of this scenario Michalske and Freiman propose three constraints on the allowed reactive species:
(3) The acid and base site separation on the reacting molecule must conform to the Si-O bond length.
(1) The reacting species must possess a non-bonding electron pair, i.e., be able to act as a Lewis base. (2) The reacting species must have a labile proton, i.e., be able to act as a Bronsted acid.
Figure 7-46. Failure time vs. applied stress for abraded glass bend specimens tested in water. The stress is normalized by the strength in liquid N 2 , and the lifetime by the lifetime at half this stress level. Data from Mould and Southwick (1959).
Si
Predictions based on these constraints suggest that species other than H 2 O will be able to enhance crack propagation in ceramics. Experiments on NH 4 , N 2 H 4 , and CH 3 NO confirm these predictions, whilst the absence of effect in N 2 , nitrobenzene,
0.0
0.2 0.4 0.6 0.8 APPLIED STRESS, Ofjo^
1.0 N
Si 0
\
H
H-0 H;
H
I
Si
0
si
Si
| \
I 2 3 Figure 7-45. Schematic of the three stage reaction process envisaged for the rupture of silicate bonds in the presence of water.
200 250 300 350 400 450 APPLIED STRESS, aA (MPa)
Figure 7-47. Failure time vs. stress at failure for alumina specimens containing sawing flaws tested in water. The shaded band represents the strength in an inert environment.
7.3 Fracture
(a) Static Fatigue Applied Stress
Time (b) Dynamic Fatigue Applied Stress
Time
Figure 7-48. Applied stress vs. time behavior for the delayed failure data of Figs. 7-46, 7-47, and 7-49, representing two extremes of loading.
acetonitrile, diethyl ether, and pyridine is explained (Freiman et al., 1985). 7.3.5.3 Time-Dependent Failure
A consequence of the finite reaction rates for bond rupture is that specimens perturbed in destabilizing fields will have finite times-to-failure. Figure 7-46 shows
379
the failure time for abraded glass bend specimens as a function of the applied stress; the decrease in lifetime with increasing stress is apparent. Figure 7-47 shows a similar plot for some alumina bend specimens containing flaws associated with sawing damage. In Fig. 7-46 the data reflect a stress history of the sort shown in Fig. 7-48 a: the applied stress is constant until failure. In Fig. 7-47 the data reflect that of a constant stressing rate to failure, Fig. 7-48 b. Figure 7-49 shows some data for the same polycrystalline alumina specimens containing indentation flaws for this latter condition, using the more common strength vs. stressing rate plot. The connection between the results of Figs. 7-46 to 7-49 and v (^) curves may be made by integration procedures, and this has been considered in some detail by Fuller et al. (1983). Cyclic loading effects per se have been observed in transformation-toughened ZrO 2 materials (Dauskardt et al., 1987), suggesting that lifetimes for these materials will be reduced under cyclic loading conditions compared with monotonic or static loading (i.e., as in Fig. 7-48). Such effects were not present. However, in a polycrys-
500
Figure 7-49. Stress at failure (strength) vs. stressing rate for alumina specimens containing indentation flaws. 10-2 Stress Rate,a~/MPa s -1
380
7 Mechanical Properties of Ceramics
talline A12O3 toughened by ligamentary bridges, as observed lifetimes under cyclic loading merely reflect the integrated response of the v (^) curve over the stressing cycle (Lathabai et al., 1989). Clearly, the ^-curve behavior in a material depends on the exact stress-state of a specimen, and different mechanisms of toughening will depend in different ways on cyclic loading. The implication from the work on ZrO 2 and A12O3 is that the toughening induced by phase transformation is more susceptible to reduction by cyclic effects than that induced by bridging, at least for tensiontension fatigue.
7.4 Plasticity 7.4.1 Slip at the Atomic Level Just as fracture, plasticity is mediated by localized defects. To see this we consider the yield strain for homogeneous shear of two atomic planes in a perfect crystal (Fig. 7-50). Under the action of an applied
shear stress, one entire plane of atoms slips over the adjacent plane. At low shear stresses the atoms resist motion and undergo elastic deformation. As the stress is increased, the atoms ride up on those in the adjacent rows until, at a yield point, they attain an unstable position where forward or backward motion can occur. If the stress is increased beyond the yield stress, the atoms will slip over those in the adjacent rows. Easy slip, or glide, results as one row "bumps" over another. If the stress is removed, permanent deformation results. Quantitatively, the homogeneous slip model overestimates the yield stress and strain. If the three close-packed atoms represented on the left in Fig. 7-51 are subjected to a shear stress, their positions at the yield point are those shown on the right of the Figure. If the interatomic separation is b, the shear displacement at yield is b/2 and the original length perpendicular to this displacement is b cos (TC/6). Thus the shear strain at yield is y = (fe/2)/[fecos(7c/6)] -0.6
Figure 7-50. Schematic diagram of homogeneous shear of atomic planes.
That is, the homogeneous slip model predicts a shear strain of ~ 60% at yield. In practice yield strains are considerably less than 1%. Clearly the model is inadequate, and we must turn to a defect-based model to describe the observed behavior. Although the homogeneous slip model fails in the macroscopic sense portrayed in Fig. 7-50, the process of deformation shown in Fig. 7-51 must occur. Hence, some strain localization mechanism must be acting in order to generate macroscopic yield in real materials (just as a crack causes localized bond rupture strains during macroscopic fracture). Figure 7-52 shows how such a localization - a dislocation - may be produced. The dislocation
7.4 Plasticity
381
7.4.2 Dislocation Glide in Ceramics 7.4.2.1 Inherent Resistance to Glide b cos 30
Figure 7-51. Schematic diagram of local atomic configurations for calculation of yield strain in homogeneous shear. extra , half-plane !
i
Figure 7-52. Schematic diagram of rows of atomic planes showing the localization of strain at a disclocation.
may be thought of as an extra half-plane of atoms inserted into the structure, and the shear stresses necessary to drive dislocations are quite small. At the ends of the atomic planes in Fig. 7-52, far from the dislocation core, the atoms are almost in their correct lattice sites, and strains of order 60% are needed to cause slip. At the dislocation core, however, the bonds are highly strained and the atoms are close to the unstable position of the homogeneous slip model. Very small additional strains are required to move the extra half-plane to the left. Thus, a small macroscopic stress may be applied to a specimen as a whole, causing plastic deformation via the motion of dislocations at which the conditions for bond shear are met locally. The local shear distortions, characterized by the Burgers vector A, may be perpendicular or parallel to the line of dislocated atomic planes, and the dislocations are referred to as "edge" or "screw", respectively, in each case.
The predominant mechanism of plasticity in metals is dislocation glide because the inherent resistance of the crystal lattice to dislocation motion, the Peierls-Nabarro force, is small. This is largely due to the fact that metallic bonding is non-directional, so that distortions in the atomic arrangement near the core of a moving dislocation do not produce large increases in strain energy as the dislocation moves from one equilibrium position in the lattice to the next. The same, however, is not true of most ceramics. Dislocation glide is difficult, and as a consequence, most ceramics fracture before they plastically deform, at least at room temperature. The reasons for the resistance to glide can be understood largely in terms of bonding and complexities in ceramic crystal structures. Atomic bonding in most ceramics is covalent, ionic, or a mixture thereof. As shown in Fig. 7-53 a, dislocation glide in covalent materials is inherently difficult because it requires the breaking and bending of strongly directional bonds. As a consequence, glide plasticity in ceramics like diamond, SiC, and Si 3 N 4 is observed only at the extremes of temperature and stress. In ionic materials, it is the formation of electrostatic faults which produces the resistance to glide. Slip along the horizontal plane of the simple ionic structure in Fig. 7-53 b, for example, brings like signed ions into registry, so that the atomic arrangement near the dislocation core in the half-slipped configuration is a high energy one. Slip is thus possible only on those slip systems for which electrostatic faulting is minimized, like the 45° plane in Fig. 7-53 b.
382
7 Mechanical Properties of Ceramics
covalent bonds
(a)
(b)
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0
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©•'<§>
©
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©
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©
®
e
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e
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•
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Figure 7-53. Schematic illustrations of slip in (a) covalent and (b) ionic materials (after Ashby and Jones, 1986).
As in most close packed structures, slip occurs most easily on the close packed plane - in this case, the basal or (0001) plane - and the slip direction is that of the smallest unit repeat in the structure. On casual examination, one might thus expect [lOTO] slip, i.e., slip in the direction of closest packing in the anion plane (see Fig. 754 (a)). However, because the cation planes are not as closely packed as the anion planes, the smallest unit repeat in the structure is actually much larger, and the observed slip direction is rotated by 30° from [1010]. The Burgers vector b is 1/3 [1120], as shown by the large arrow in Figs. 7-54 a and b. The nature of this slip geometry led Kronberg to suggest that an edge dislocation in the a-Al 2 O 3 structure should dissociate into 4 quarter partial dislocations. The dissociation reactions are 1/3 [1120] -> 1/3 [1010] + 1/3 [0110]
Dislocation glide in ceramics can also be difficult due to complexities in crystal structure. One material in which crystal structure is thought to play a very important role is a-Al 2 O 3 (sapphire), in which significant slip occurs only at temperatures in excess of 900 °C. Details of the slip process in a-Al 2 O 3 , as first considered by Kronberg (1957), are now discussed. Figure 7-54 a shows the a-Al 2 O 3 structure. It consists of planes of oxygen anions in hexagonal arrays stacked in the A - B - A - B • • • stacking sequence, with aluminum cations occupying two thirds of the octahedral interstices. In a given cation plane, the aluminum ions form an ordered array, but the relative position of the array is shifted in consecutive aluminum layers to form three distinct cation planes. The hexagonal unit cell used to describe the structure is thus quite tall, consisting of three anion and three cation planes.
and 1/3 [1010] -> 1/9 [2110] + 1/9 [1120] and the slip steps corresponding to the formation of the partial dislocations are shown in Fig. 7-54 b. Kronberg further suggested that the motion of the partials is made difficult by the crystalline arrangement. The physical origin of the difficulty can be appreciated by considering the relative motion of the anions and cations during the advance of the first quarter partial, shown for selected atoms by the arrows in Fig. 7-54 c. Note that since the anion at point 1 displaces to a position which is occupied by a cation, the cation must simultaneously displace to an adjacent unoccupied octahedral site in the anion array, such as that made available by the movement of anion 2. The direction of motion of the anions and cations is thus different, and an inherently cooperative movement of the
7.4 Plasticity
383
[1120]
O
upper oxygen layer
#
lower oxygen layer
©
aluminum layer
two ionic species is required for the partial to advance. Referred to as "synchroshear", this process acts as a fundamental impediment to glide in A12O3 and other ceramics with complex structures, such as MgAl 2 O 4 (Poirier, 1985). 7.4.2.2 Observations of Glide Plasticity While dislocation glide is difficult in most ceramics, it is, nevertheless, observed. At elevated temperatures, for instance, many of the aforementioned constraints are eased, and at least a limited amount of dislocation glide occurs in almost all ceramics. In addition, in some ceramics, glide is possible even at room temperature and below. In general, these are strongly ionic
Figure 7-54. (a) The structure of alumina parallel to the basal plane showing two oxygen layers and the aluminum layer in between. The large arrow indicates the Burgers vector, (b) The slip steps corresponding to the dissociation of a dislocation into 4 quarter partial dislocations drawn in terms of the relative motion of two adjacent oxygen planes, (c) The motion of anions and cations during the first partial slip step showing that the two species move in different directions and thus require coordinated movement (after Kronberg, 1957).
materials with the rock salt structure, like the alkali halide salts. As mentioned, the Peierls barrier for slip in ionic materials is usually high because of electrostatic faulting. However, for rock salt materials, electrostatic faulting does not develop on the (110) [110] slip system (such as the slip system oriented at 45° in Fig. 7-53 b), and as a result, relatively pure single crystals exhibit substantial glide plasticity over a wide range of temperature. Figure 7-55 a, for example, presents room temperature stress-strain curves for NaCl which demonstrate that tensile strains in excess of 20% can be achieved in single crystals (Stokes, 1966). The conventional rule of thumb for determining slip systems in crystalline mate-
384
7 Mechanical Properties of Ceramics
NaCI room temperature
20 ' ().035mm
" •
0.07mm ,
A lO.IOmm
1b -
tri0.50mm crystal A 25mm h o / I bi-crystal IL ~2mm/l
CO
(a) a
/w-
10 .
r
LJJ
DC
5 .
jy I I
1 1j _
^ ^ \" 1 x• w
i
/i/
crystal /W ~2mm / /
j
'
bi-crystal^^Xsinglecrystal
I/VV^-^ n'
t
/ *
0 1 2 3%
If 1 II STRAIN
20
NaCI d-0.2mm
20°C 15 -96°C
(b)
~
CO CO LJJ
10
oc
0
0.5
1.0%
Figure 7-55. Tensile stress-strain curves for NaCI. (a) Room temperature data showing effects of grain size, (b) Data for fixed grain size of 0.2 mm showing effects of temperature (after Stokes, 1966).
STRAIN
rials is that slip occurs on the planes of highest packing density in the direction of the smallest unit repeat in the structure. This rule was previously applied to aA12O3, and it works well for most other ceramics, as well. However, for strongly ionic materials, the rule is sometimes broken because of the electrostatic constraint. In NaCI, for example, the planes of highest density are the (100) types, but slip at room temperature occurs predominantly on (110). While (100) slip is possible, it occurs only at higher temperatures where the electrostatic constraint is relaxed by expansion of
the lattice. Table 7-5 summarizes the slip systems of many ceramics. 7.4.2.3 Limitations on Slip and Loss of Ductility in Polycrystals The stress-strain curves for NaCI shown in Fig. 7-55 a, which include data for both single crystals and polycrystals of various grain sizes, demonstrate that the room temperature ductility exhibited by single crystals does not extend to polycrystals; in fact, all the polycrystals of grain size less than 0.50 mm are effectively brittle. This
7.4 Plasticity
385
Table 7-5. Slip systems in ceramics3. Material
A12O3 BeO C (diamond) C (graphite) CaF 2 CsBr Cu 2 O LiF KC1 MgO MgO • A12O3 NaCl PbS PbTe (3-SiC (3-Si3N4 p-SiO2 TiC TiO 2 UC UO 2 ZrB 2
Crystal structure
hexagonal hexagonal cubic (diamond) hexagonal cubic (fluorite) cubic (CsCl) cubic cubic (rock salt) cubic (rock salt) cubic (rock salt) cubic (spinel) cubic (rock salt) cubic (rock salt) cubic (rock salt) cubic (zinc blende) hexagonal hexagonal cubic (rock salt) tetragonal (rutile) cubic (rock salt) cubic (fluoride) hexagonal
Primary slip system
(0001) [1120] (0001) [1120] (l!l)[H0] (0001) [1120] (001) [110] (110) [001] (100) [001] (110)[110] (110)[lT0] (HO)[iTo] (111) [110] (110) [110] (001) [110]
Secondary slip system
several several
(110)[110]
(001) [110] (001) [110] (001) [110] (001) [110]
(ooi)[iio] (iii)[iio] (1010) [0001] (0001) [1120] (Hi)[iT0] (101) [101] (lll)[lT0] (001) [110] (0001) [1120]
(110)[110]
Number of independent slip systems
Minimum temperature for appreciable secondary slip
Primary
Secondary
2 2 5 2 3 3 3 2 2 2 5 2 3 3 5 2 2 5 4 5 3 2
2 or 3 2
- 0 . 8 Tm -0.8 T m
2
- 0 . 3 Tm
3 3 3
-0.5 Tm
3
- 0 . 5 Tm
2
~0.5T m
-0.5Tm
a
Table compiled from Davidge (1979), Evans and Langdon (1976), Kingery et al. (1976), Sprackling (1976), and Gilman (1961).
peculiar behavior, which is exhibited by many ceramics, is explained in terms of limitations on slip which don't exist in most metals. The usual explanation follows from the argument of von Mises (1928), that in order to produce an arbitrary change in shape in a crystalline material, 5 independent slip systems must operate. A slip system is indepenent if it produces slip which cannot be achieved by any combination of slip on other systems (Groves and Kelly, 1963; 1969). The basis of the argument is that an arbitrary shape change can be described by the 6 independent components of the strain tensor (three normal and three shear strains). However, since volume is con-
served during plastic deformation by slip, the normal strains must sum to zero, so that only 5 of the components are independent. Given that the shear produced by one slip system determines the value of one of the components of the strain tensor, 5 independent slip systems are needed to produce an arbitrary change in shape. The application to deformation in polycrystalline materials follows from the argument that if a grain is not free to change its shape, strain incompatibilities which develop at the boundaries with other grains will produce high local stresses and fracture. Metallic materials generally possess the 5 requisite slip systems and are thus ductile in both single crystal and polycrystalline
386
7 Mechanical Properties of Ceramics
form. However, as indicated in Table 7-5, most ceramics do not. In the case of rock salt materials like NaCl, only two of the six physically distinct (110) [110] slip systems which operate at room temperature are independent, thus explaining the loss of ductility in Fig. 7-55 a. As shown in Fig. 7-55 b, the ductility of poly crystalline NaCl increases markedly at a temperature of about 200 °C, corresponding to the activation of slip on the (001) [110] system which increases the number of independent slip systems to 5. Similar brittle-to-ductile transitions are observed in polycrystalline MgO (T=1700°C) (Day and Stokes, 1966 a; 1966 b) and polycrystalline KC1 (T = 250 °C) (Stoloff et al., 1963). The data in Fig. 7-56 for polycrystalline KC1 demonstrate how abrupt the transition can be. From a microstructural standpoint, the transition from brittle to ductile behavior is often correlated with the onset of wavy slip, that is, slip which is not confined to a single slip plane; see, for instance, Davidge (1979). In rock salt structures, wavy slip becomes possible at higher temperatures because of the activation of secondary slip systems. However, careful studies have
shown that it is not the onset of wavy slip, but rather the disappearance of all straight slip (slip confined to a narrow glide bands), which controls the transition (Stoloff et al., 1963). For example, appreciable wavy slip is observed during the deformation of polycrystalline KC1 at temperatures as low as 150°C, but straight slip persists to 250 °C, and it is the latter temperature which correlates with the marked increase in ductility (see Fig. 7-56). This suggests that ductility is limited by the nucleation of cracks by stress concentrations developed at the intersections of straight slip-bands and grain boundaries, and from this standpoint, the von Mises explanation for the loss in ductility in polycrystals is not entirely adequate. 7.4.2.4 Effects of Solutes and Impurities on Dislocation Glide Substitutional solutes and impurities, even at concentrations in the parts per million range, can have significant effects on the glide mobility of dislocations and therefore the flow stresses of ionic ceramics. Fig. 7-57, for instance, shows that the criti-
100 POLYCRYSTALLINE KCI 80
60
40
Figure 7-56. The ductility of polycrystalline KCI as a function of temperature showing a brittle-ductile transition at about 250 °C (after Stoloff et al., 1963).
20
100
200
300
TEMPERATURE (°C)
400
500
7.4 Plasticity
Q_ CO CO
ALKALI HALIDE SALTS
LU
A -
15
i <
lU
o
NaCI:Ca++
+
NaCI:Mn++
•
KCI:Sr++
X
KCl:Ba++
+o
A LiF:Mg++
•
co Q LU
8
387
A
°o
5-
-
LU
A
< O o
Figure 7-57. Effects of impurities on the critical resolved shear stress in alkali halide salts (after Dryden et al., 1965).
0
10"1
10-
10"
10"
10"'
IMPURITY CONCENTRATION (mol frac.)
cal resolved shear stress for plastic flow in alkali halide salts doped with cation impurities increases markedly for impurity levels greater than about 10 ppm (Dryden et al., 1965). The magnitue of the strengthening effect, however, is very much dependent on the valence of the impurity relative to the host. The general rule of thumb is that solutes with the same valence as the host (isovalent) are much less effective in providing solid solution strengthening than solutes with a different valence from
the host (aliovalent). The data for NaCl in Fig. 7-58, for example, demonstrate that divalent cation impurities provide much greater strengthening than univalent cation impurities (Gilman, 1961). The reason for the difference is related to the nature of the defect which forms in each of the two cases. As shown in Fig. 7-59, the extra charge carried by the addition of a divalent cation impurity to a univalent host is usually compensated by the formation of a cation vacancy. Frequently, the
NaCl Doped with Metal Chlorides
Figure 7-58. Effects of univalent and divalent cation impurities on the yield strength of NaCl (after Gilman, 1961). u.O
0.2
0.4
0.6
0.8
MOL % CHLORIDE
1.2
388
7 Mechanical Properties of Ceramics
leads to a temperature dependent strength of the form 1/2
/2
spherical distortion
tetragonal distortion
where T is the contribution to the shear yield stress due to the dislocation-defect interaction and T is the absolute temperature. The constant T 0 is the strength at 0 K given by TO =
Figure 7-59. Schematic illustration of spherical and tetragonal distortions in an ionic lattice. The tetragonal defect consists of a divalent cation impurity and a cation vacancy.
vacancy and the impurity are strongly associated, forming an asymmetric "tetragonal" lattice distortion whose elastic strain field interacts strongly with a dislocation and impedes its motion. Univalent impurities, on the other hand, produce spherically symmetric distortions (due to differences in atomic size or elastic moduli) which do not interact as strongly with dislocations. As a result, aliovalent impurities are much more effective strengtheners. It is also worth mentioning that there is an electrostatic interaction between the solute-vacancy defect complex and a dislocation (Gilman, 1974), but the strengthening provided by this interaction is not nearly as great as that due to the elastic interaction (Mitchell and Heuer, 1977). The basic theory of solid solution strenghtening by tetragonal defects was developed by Fleischer (1962; 1963). In its original form, the theory considers the interaction between a tetragonal defect and a screw dislocation as the dislocation passes within one atomic spacing of the defect. The dislocation overcomes the obstacle by stress-assisted thermal activation, which
GASC1/2/33
(7-82)
and To is a material constant T0 = GAsb3/(3.S6ak)
(7-83)
where c is the concentration of defects, G is the shear modulus, As is a measure of the tetragonality strain (formally, the difference between the longitudinal and transverse strain produced by the tetragonal distortion), b is magnitude of the Burgers vector, k is Boltzmann's constant, and oc is a numerical constant whose value is about 14. Since it was first proposed in 1962, Fleischer's theory has been modified and refined to account for numerous details like the interaction of tetragonal defects with edge dislocations; see, for instance, Mitchell and Heuer (1977); Evans and Langdon, (1976), or Sprackling (1976). While these modifications have led to some changes in the constants in Eqs. (7-81)— (7-83), the basic form of the equations has remained the same, and the theory is most often tested by comparing the theoretically predicted temperature and concentration dependencies of the flow stress with experimental data. The form of Eq. (7-81) suggests, for example, that a plot of T 1/2 VS. T1/2 should be linear. As illustrated in Fig. 7-60 for MgO doped with 150 ppm Fe 3 + (Singh and Coble, 1974) and LiF doped with 80 ppm Mg 2 + (Johnston, 1962), this is indeed the case for many ma-
7.4 Plasticity
• •
-CO
I
389
LiF, 80 ppm Mg++ MgO, 150 ppm Fe++
4 Figure 7-60. The temperature dependence of the shear flow stress for two ionic materials doped with aliovalent cations. The LiF data are from Johnston (1962), and the MgO data are from Singh and Coble (1974). 10
20
15
25
T1/2(K1/2}
terials. In addition, the c 1/2 concentration dependence of the flow stress has been observed numerous times, although occasionally an exponent between 1/2 and 1 is found (Sprackling, 1976). A critical review of the theory relative to experiment has been presented by Mitchell and Heuer (1977), in which it is concluded that modified versions of the Fleischer theory account not only for the form of the observed dependencies but the magnitudes as well.
Before concluding this section, it should be noted that the addition of solutes and impurities to ceramics can also lead to strenghtening via precipitation of a second phase. Figure 7-61 presents stress-strain curves for MgO doped with various amounts of Fe 2 O 3 (McColm, 1983) in which the increase in strength with solute conentration is due primarily to the precipitation of coherent particles of MgFe 2 O 4 in the MgO matrix.
600 •
Fe 2 O 3 -doped M g O
500 Fe = 0.55% Fe + Mg 400
— 300 CO CO LU
:/V-
Fe = 0.14% Fe + Mg
200 .
100
_
Figure 7-61. Stress-strain curves for MgO, doped with small amounts of Fe 2 O 3 , containing precipitates of MgFe 2 O 4 (after McColm, 1983).
pure MgO
0
10
20
30
40
STRAIN (arbitrary units)
50
60
390
7 Mechanical Properties of Ceramics
7.4.2.5 Charged Dislocations in Ionic Ceramics
Dislocations in ionic ceramics are often charged, and this frequently influences their behavior in significant ways. For example, the acquisition of charge reduces line tension and thus affects any plastic phenomenon in which line tension is important, such as the operation of FrankRead sources or Orowan bowing (Hirth and Lothe, 1982). Charge is also thought to enhance dislocation core diffusion and has been used in this context to explain certain unusual aspects of diffusion-controlled high temperatue creep in alkali halide salts (Frost and Ashby, 1982). In addition, the interaction between a charged dislocation and a charged defect represents another way in which solid-solution strengthening can be achieved (Mitchell et al., 1979). To understand how a dislocation can become charged, we refer to the schematic illustration of an unrelaxed (110) [110] edge dislocation in the rock salt structure in Fig. 7-62 a. To maintain a perfect crystal structure on either side of the dislocation (i.e., no electrostatic faulting), the dislocation must necessarily consist of the two extra half planes. As shown in Fig. 7-62 b, each of these half planes terminates at a row of ions in which the charges alternate between + and —. Now consider the removal of a cation of charge + e from the base of one of the extra half planes so as to create two jogs (Fig. 7-62 b). Because of the loss of a net positive charge of + e, each jog has associated with it a negative charge of — e/2. Similarly, the removal of an anion creates two jogs which carry charges of + e/2. It is thus conventional to speak of jogs in edge dislocations as being charged, and if a dislocation acquires a net imbalance of one type of jog over the other, the dislocation
[110]-
(a)
(b)
©©©©©©©©©©©©© ©©©©©©©©©©©©© ©©©©©©© ©0©© © © © © © © ©r I©©© \ / \ jog,-1
jog,-1
jog, + |
© Figure 7-62. (a) Schematic illustration of an unrelaxed (110) [110] edge dislocation in the rock salt structure, (b) Charged jogs in one of the extra half planes.
itself can be considered to be charged. It is also possible for screw dislocations to become charged (Hirth and Lothe, 1982). An edge dislocation can acquire a net imbalance of charged jogs in two fundamentally different ways. First, the free energy of formation of a cation vacancy is generally less than that of an anion vacancy. Thus, in the neighborhood of a source of vacancies, such as an edge dislocation, a surplus of cation vacancies will be formed when thermal equilibrium is achieved. Since the production of a cation vacancy at an edge dislocation occurs by the attachment of a lattice cation to a negative jog and this changes the sign of the jog from — e/2 to + e/2, a net imbalance of jogs results and the dislocation acquires a positive charge. To maintain charge neutrality, the dislocation is surrounded by an atmosphere of negatively charged cation
7.4 Plasticity
vacancies, commonly referred to as the Debye-Huckel cloud (Eshelby etal., 1958; Menezes and Nix, 1974 a). The above argument is strictly valid only for very pure materials, that is, those in which the vacancy concentrations are dominated by intrinsic (thermal) vacancies. When extrinsic vacancies are dominant, as in the case of univalent ionic solids containing divalent cation impurities, the charge on the dislocation is reversed. In simple terms, this occurs because the dislocations act as sinks for the extrinsicallystabilized cation vacancies and acquire a negative charge as the negatively charged vacancies migrate to the dislocation core and annihilate at jogs. Such dislocations are then surrounded by atmospheres of positively charged divalent cation impurities which exert drag forces on them and reduce their mobilities (Menezes and Nix, 1973). At high temperatures, the sign of the charge on the dislocation can switch as the concentration of thermally-produced intrinsic vacancies increases. The temperature at which the change in sign occurs is called the isoelectric temperature, and at the isoelectric temperature, the dislocation possesses no charge nor surrounding atmosphere. For this reason, the isoelectric temperature is often associated with anomalous mechanical behavior, such as local minima in flow stress vs. temperature curves (Eshelby et al., 1958) and unusually high stress and temperature dependencies of dislocation velocities (Menezes and Nix, 1974 b). The second way in which dislocations can acquire charge is by sweeping up vacancies during their motion (Hirth and Lothe, 1982; Sprackling, 1976). In NaCl doped with 14ppm Mn 2 + , for example, dislocations acquire a large negative charge as they move, presumably due to the sweeping up of the extrinsic cation va-
391
cancies (Huddart and Whithworth, 1973). This produces a plastically induced electrostatic field which decays away after deformation is terminated. 7.4.3 High Temperature Plasticity
To this point in the discussion, plasticity has been considered primarily in terms of dislocation glide, the predominant mechanism of plasticity in those ceramics which exhibit plastic flow at low and ambient temperatures. At high temperatures, glide is also important, but plasticity can occur by other thermally activated mechanisms which are too slow to be of any consequnce at room temperature. These include diffusion, dislocation climb, and grain boundary sliding. In this section, the mechanisms by which high temperature plasticity is produced are discussed, primarily in terms of high temperature creep. 7.4.3.1 Creep Testing
High temperature plasticity is frequently studied using the creep test. In the standard test, a tensile load is applied to a specimen, and the elongation of a portion of the gauge length is measured as a function of time. The ideal test is one in which the load is continuously varied so as to maintain conditions of constant stress as the cross sectional area of the specimen is reduced. The basic data is then a plot of the creep strain as a function of time. Figure 7-63 is a schematic representation of a typical creep curve. As shown, the curve usually exhibits three distinct stages. The first, called primary or transient creep, is usually, but not always, characterized by a decelerating creep rate. The second, called secondary or steady-state creep, is that portion of the curve in which the rate of creep is effectively constant. The third stage, or tertiary creep, is that during
392
7 Mechanical Properties of Ceramics
<
I
TIME
Figure 7-63. A typical creep curve showing primary (I), secondary (II), and tertiary (III) stages.
which the creep rate accelerates just prior to specimen failure. From a microstructural standpoint, tertiary creep is often associated with the accumulation of damage such as the nucleation and growth of internal cavities and cracks. The two parameters most often used to characterize creep behavior are the steady state creep rate, £ss, and the time to rupture, tr. One significant variation from the normal creep behavior illustrated in Fig. 7-63 is that shown in Fig. 7-64, where creep data for a single crystal of sapphire crept at
1000 °C are presented (Wachtman and Maxwell, 1954). The s-shaped curve, or "sigmoidal" behavior, is observed in many ceramic single crystals containing low initial dislocation densities. The acceleration in creep rate at the beginning of the curve is due to rapid dislocation multiplication. The simple tension test described above is the standard creep test in metals. However, in ceramics, very little tension testing is performed because of problems associated with machining and gripping specimens. As a result, the majority of ceramic creep data are acquired through compression or bend testing. However, each of these methods has its own problems. These are now briefly discussed. Compression As shown in Fig. 7-65 a, the problem in compression testing is caused by friction between the compression rams and the specimen which causes the specimen to "barrel" as it deforms. Friction can never be avoided entirely, and when friction is large, the stress state in the specimen can deviate significantly from simple uniaxial compression.
25
20
SAPPHIRE SINGLE CRYSTAL 1000°C Resolved shear stress = 39.2 MPa
15 03 a. in IU
UJ LJJ DC O
Figure 7-64. Creep curve for a sapphire single crystal exhibiting sigmoidal behavior (after Wachtman and Maxwell, 1954). 0.ue+0
5.0e+5
1.0e+6 TIME (s)
1.5e+6
2.0e+6
7.4 Plasticity
20 30 40 SHEAR
60 60
4 0
393
2b 40 60 80 HOOP
RADIAL
(a)
IDEALLY
FRICTION ACTUALLY
(b) Figure 7-65. (a) A schematic illustration of barreling during deformation in compression due to friction between the specimen and the compression rams, (b) Results of finite element analyses for the stresses developed during the uniaxial compressive deformation of cylindrical specimens of MgO. Cross hatched areas are regions of tensile stress (after Birch et al, 1976).
To illustrate this, we consider the stresses developed during the compressive deformation of cylindrical specimens of MgO, as analyzed by Birch et al. (1976). Stress contours for the shear, radial and hoop stresses in a specimen with rigidly constrained ends (i.e., very high friction) are shown in Fig. 7-65 b. The specimen was deformed to a maximum axial compressive stress of 96 MPa, and the numbers adjacent to the contours represent the magni-
tudes of the various stress components in units of MPa. Three features are worthy of note. First, the stress state is indeed quite complex and can by no means be approximated as simple uniaxial compression. Second, plastic deformation must be inhomogeneous since the shear stresses vary significantly throughout the specimen. For example, the greatly diminished shear stresses near the ends of the specimen result in the production of "dead zones" in which virtually no deformation takes place at all. Third, the radial and hoop stresses near the center of the specimen are actually tensile (the cross hatched regions in the diagram indicate tensile stress). This often leads to the production of cracks running parallel to the axis of compression and represents one of the dominant modes of failure in compression testing. Clearly, when efforts to reduce end friction are not made, compression data may be of limited value. Bending The problem encountered in bend testing is related to how meaningful creep parameters can be derived from basic test results. Referring to the 4-point bend test illustrated in Fig. 7-66 a, bend test data usually consist of a record of the load point
394
7 Mechanical Properties of Ceramics p
where J (t) is the creep compliance and, (2) that deformation in tension and compression is symmetric. The latter assumption assures that the neutral axis of the specimen does not shift during deformation. It then follows that the stresses and strains which develop in the outer fibers of the specimen in the steady state are given by
(a)
a=
3(L-a)2n
h* z
bh
, y
and S=
V
p
(7 85)
-
3n
(L-ant++al
+
l)]y-
(7 86)
"
In addition, it can be shown that
NEUTRAI^ AXIS n=5
(b) Figure 7-66. (a) The geometry of the four-point bend test, (b) The variation in the longitudinal stresses with distance from the neutral axis.
displacement, yL, as a function of time, t, after the application of a load, P. Note, as shown in the lower part of the figure, that the longitudinal stresses in the bend specimen, a, vary with the distance from the neutral axis in ways which depend on the parameter n, the stress exponent for creep. The stress exponent is just one of the material parameters which can be determined from analyses of bend test data. The most common method of data analysis is that developed by Hollenberg et al. (1971). It is based on two fundamental assumptions: (1) that the stress and time dependence of the strain, e, can be separated according to (7-84)
log foj = n log (P) + C (7-87) where the geometric parameters are shown in Fig. 7-66 a, and b is the depth of the specimen. The stress exponent for creep can thus be derived from a log-log plot of the load point displacement rate, j / L , vs. the applied load, P. The constant C is directly related to the creep compliance. The problem with this analysis is that creep in ceramics is frequently not symmetric. For example, Fig. 7-67 illustrates that a lithium disilicate glass ceramic creeps substantially faster in tension than it does in compression (Morrell and Ashbee, 1973). This behavior, which is observed in many ceramics, usually results from the fact that tensile stresses promote cavitation and cracking. Numerous alternative schemes have been developed for extracting meaningful creep parameters from bend tests in materials for which differences in tension and compression creep are known to exist (Talty and Dirks, 1978; Cohrt etal., 1984; Chuang, 1986). While some progress has been made, each of the methods has its own limitations related to the basic assumptions which make an analysis possi-
7.4 Plasticity 10"
10"
I I I I ll
I
I I 1 1 1II
I
I I I 111
LITHIUM DISILICATE GLASS CERAMIC / T = 700°C -(Morrell and Ashbee, 1973)
1 l0"5
n=6
UJ LU
395
where Q is the atomic or molecular volume, D{ is the lattice diffusivity, and d is the grain size (Nabarro, 1948; Herring, 1950). When diffusion occurs via the grain boundaries, the mechanism is called Coble creep, and the rate equation is
(T O
yaQDhS
Q I0" 6
LJ
C = 40 to 50
d*kT
!i
(7-89)
CO
5 I0"7
where Dh is the grain boundary diffusivity and S is the grain boundary thickness (Coble, 1963). Which of these two mechanisms dominates depends on the relative rates of grain boundary and lattice diffusion, and they are frequently distinguished
8 jjj io-8
I
a: UJ
5
COMPRESSION
9 I0 "
10"
I
10 STRESS (MPa)
100
i
Figure 7-67. Results of creep tests of a lithium disilicate glass-ceramic demonstrating substantially faster deformation in tension than in compression (after Morrell and Ashbee, 1973).
ble, and all require fairly tedious data analysis. For these reasons, none is yet in widespread use. 7.4.3.2 Mechanisms of Creep
The most common mechanisms of creep and high temperature deformation in ceramics are shown schematically in Fig. 7-68. Figure 7-68 a illustrates the diffusional mechanisms, in which strain is produced by the diffusional flow of atoms through or around the grains of a polycrystalline material. (See Chap. 6 of this Volume for a more comprehensive survey of diffusion in ceramics.) When the diffusional path is through the grains, the mechanism is referred to as Nabarro-Herring creep, and the tensile strain rate, e, produced by a tensile stress, a, is given by d2kT
C = 10 to 20
(7-88)
^7"
(b)
Figure 7-68. Simple creep mechanisms - (a) diffusional, (b) dislocation glide and climb.
396
7 Mechanical Properties of Ceramics
experimentally by the difference in the grain size dependence (d~2 for NabarroHerring vs. d~3 for Coble). It is important to note that diffusional creep is inherently coupled to the process of grain boundary sliding. This can be appreciated by considering the simple array of hexagonal grains shown in Fig. 7-69. As the grains elongate in the tensile direction by diffusional flow of atoms to the cross hatched areas, adjacent grains must necessarily slide over one another as indicated by the arrows in the figure. In this sense, the sliding can be said to accommodate the diffusional creep mechanism. It is also possible to view the process from the other perspective; that is, that creep strain is produced by grain boundary sliding, and the sliding is accommodated by diffusion. In fact, the processes are coupled and inseparable; see, for instance, Poirier (1985). An elegant mathematical treatment of the coupling of diffusional creep and grain boundary sliding allowing for both lattice and grain boundary diffusion has been presented by Raj and Ashby (1971). They find
the creep rate to be given by oQ 1 ^ / C~14
nSD (7-90)
Note that when Dx > Dh d, the relation reduces to the Nabarro-Herring expression, and when Dhd $> D{, the equation is equivalent to the Coble expression. In addition to diffusional and grain boundary sliding mechanisms, creep can also be produced by dislocation climb and glide. The classic mechanism of this type is that proposed by Weertman (1955), shown schematically in Fig. 7-68 b. The model is based on the glide and climb of edge dislocations produced at a source, S. As they glide, the dislocations encounter obstacles, such as sessile dislocations, which are surpassed by climb to different slip planes. Since climb and glide are sequential processes, the slower is rate controlling. Weertman's original model considers climb to be the slower process. Since climb requires the diffusion of vacancies to the core of the dislocation, creep is diffusionally controlled, and a detailed analysis leads to a rate equation of the form
AW
(7-91)
kT\E
sliding
diffusional elongation
Figure 7-69. An array of hexagonal grains deforming by diffusional creep and grain boundary sliding.
where E is the elastic modulus and n is the stress exponent for creep. Depending on the details of the assumed geometry, the stress exponent in the Weertman model is predicted to be in the range 4-5. Other important models for dislocation creep include a later Weertman model (1957) in which glide is rate limiting (as would be expected if, for example, solute atmospheres imposed drag forces on dislocations and considerably reduced their mobilities); a theory proposed by Nabarro (1967) in which creep strain is produced
7.4 Plasticity
entirely by edge dislocation climb; and the theory of Barrett and Nix (1965), in which strain is produced by the glide of screw dislocations, rate limited by the climb of jogs of edge character. All three theories predict rate equations of the same form as Eq. (7-91), with a stress exponent of 3. Thus, in general, dislocation mechanisms for creep are associated with stress exponents in the range 3 to 5.
397
10-4 CREEP OF UO,
10-5
i Q. LU LLJ 0C O LU
10-6
7.4.4 Experimental Observations of Creep in Ceramics
Most experimental work in the study of creep focuses on the stress, temperature, and grain size dependences of the steady state creep rate. Experimental data are frequently analyzed according to the semiempirical relation: 8S
=
(7-92)
where Qc is the activation energy for creep, n is the stress exponent, and m is the grain size exponent. Since the values of Qc, n, and m are useful in identifying rate controlling mechanisms, determination of these material parameters is often the principle objective of creep experiments. Typical observations for ceramics are now discussed. 7.4.4.1 Stress Dependence
The stress dependence of creep is characterized by the stress exponent, n. Its value is determined from the slope of log-log plots of sss vs. cr, such as those for polycrystalline UO 2 in Fig. 7-70 (Poteat and Yust, 1968). The UO 2 data show two linear regions, indicating a stress dependent change in mechanism. At low stresses, the stress exponent is approximately 1, indicating Nabarro-Herring or Coble creep. At higher stresses, the stress exponent changes to a value around 4.2, suggesting that creep
10" 8 10
100 STRESS (MPa)
Figure 7-70. Steady state creep data for uranium dioxide showing a stress dependent change in mechanism (after Poteat and Yust, 1968).
is controlled by dislocation climb as in the Weertman model. As will be seen shortly, stress exponents in the range 1 to 5 are commonly observed in ceramics. While not shown in Fig. 7-70, creep data at even higher stresses often swing upward and exhibit significant deviations from linearity on a log-log plot. Such behavior is referred to as power law breakdown, as a simple power law relation is not a sufficient description. Stress exponents extracted from data in the power law breakdown region are greater than those observed at lower stresses. An extensive compilation of stress exponents for ceramic materials has been assembled by Cannon and Langdon (1983; 1988). While the compilation is much too extensive to be presented here, an examination of frequency histograms of the stress exponents derived from the compilation provides valuable insight into the mecha-
398
7 Mechanical Properties of Ceramics CERAMIC STRESS EXPONENTS-SINGLE CRYSTALS
30 r
31 MATERIALS 9 7 OBSERVATIONS
DISLOCATION MECHANISMS
18 POWER LAW BREAKDOWN (?)
UJI2
o LJ
a.
HkJ
h
n
i IIm 8
m 10
J II
(a)
CERAMIC STRESS EXPONENTS - POLYCRYSTALS 40 49 MATERIALS 329 OBSERVATIONS u3
- DIFFUSIONAL
8 \ ul 16
AMORPHOUS BOUNDARY PHASE
POWER LAW BREAKDOWN OR CAVITATION
/DISLOCATION MECHANISMS H h
rti
5
6
10
J II
Figure 7-71. Frequency histograms of stress exponents for (a) ceramic single crystals, and (b) ceramic polycrystals. From data compiled by Cannon and Langdon (1983).
n
(b)
nisms of creep in ceramics. The histograms are presented in Fig. 7-71. The histogram in Fig. 7-71 a is that for the single crystal data in the compilation. It includes 97 observations from 31 separate ceramic materials. The distribution is roughly symmetric and peaked around a value of 4. This indicates the importance of dislocation mechanisms in the creep of ceramic single crystals, since stress exponents for dislocation mechanisms generally fall in the range 3 - 5 . The stress exponents greater than 5 probably result from data
obtained in the power law breakdown region. The histogram for the polycrystalline ceramics, Fig. 7-71 b, is significantly different. The distribution is not symmetric, and by far, the most frequently observed stress exponents have values close to 1, indicating the importance of diffusional mechanisms. Why diffusional mechanisms are so common in ceramic polycrystals is related to two factors. First, in many ceramics, the inherent resistance to dislocation glide is maintained even at high temperatures, so
7.4 Plasticity
mechanisms involving dislocation glide are suppressed. Second, ceramic polycrystals typically have very small grain sizes, so diffusional mechanisms are enhanced [see Eqs. (7-88) and (7-89)].
399
tailed considerations of diffusion in ceramics, and although we do not intend to treat this subject in detail, there are several points worth mentioning. Coupled Diffusion in Ionic Ceramics
7.4.4.2 Temperature Dependence The temperature dependence of creep is characterized by the activation energy, Qc. In most instances, Qc is found to be equivalent to the activation energy for diffusion, QD. This can be seen in Fig. 7-72 (Sherby and Miller, 1979), in which the two activation energies are compared for a wide variety of materials, including several ceramics (NaCl, AgBr, MgO, UO 2 , and A12O3). The reason for the equality can be appreciated by noting that all of the mechanisms discussed in Sec. 7.4.3.2, as well as many others not considered there, are rate limited by diffusion. For this reason, either the lattice or grain boundary diffusivity appears explicitly in each of the creep rate equations, Eqs. (7-88)-(7-91). An understanding the temperature dependence of creep in ceramics is thus achieved primarily through de-
In ionic ceramics, charge neutrality must be maintained as individual ionic species diffuse through the lattice (Ruoff, 1965). For the ionic compound A^jB^, this couples the diffusional fluxes, JA and JB, such that
and (7-94) where DA and DB are the diffusion coefficients for the individual species and cA and cB are their concentrations. Defining an effective diffusion coefficient, D eff , as
ACTIVATION VOLUME FOR CREEP, AVC (mm 3 /mol) ,IO 3
I04
I05
o CO3
o.i io o
0.01
0.01
I
|
I
I I I I I I
O.I ACTIVATION ENERGY FOR CREEP, Q c (MJ/mol)
I
Figure 7-72. A comparison of the activation energies for creep and diffusion in a number of metals and ceramics showing their equivalence (after Sherby and Miller, 1979).
400
7 Mechanical Properties of Ceramics
it can then be shown that the NabarroHerring equation for lattice controlled diffusional creep (Eq. (7-88)) still applies, provided Dj is replaced by Deff and Q is the volume of a molecule of AaBp. These ideas have been expanded by Gordon (1973; 1975) to account for ambipolar diffusion; that is, parallel diffusional transport through the lattice and the grain bundaries. The analysis leads to the definition of a complex diffusion coefficient
least in the temperature range where diffusion is extrinsically controlled. For example, by the law of mass action, the stabilization of cation vacancies in NaCl by divalent cation impurities such as Ca2 + leads to a suppression of the anion vacancy concentration. Since creep in NaCl is usually rate controlled by the slower diffusing Cl~, the rate of creep can be significantly reduced (Frost and Ashby, 1982). Oxygen Partial Pressure Effects in Oxide Ceramics
(7-96) 1+
-
where the subscripts refer to the diffusing species and the superscripts refer to the lattice (1) or grain boundary (b) path. The diffusional creep rate is then found by substituting Dcompiex for Db d in the Coble expression, Eq. (7-89). A close inspection of the mathematical form of the complex diffusion coefficient leads to the conclusion that creep is ratecontrolled by the species which moves slower on its fastest path. For example, when lattice diffusion is slow for both species and grain boundary diffusion is slower for species A, then the complex diffusion coefficient reduces to Dcomplex = D\ dja and creep is controlled by grain boundary diffusion of species A. Since Dcomplex is a function of both T and d, the rate limiting diffusion process may change as the temperature and grain size are varied.
The rate of creep in oxide ceramics can be influenced by oxygen partial pressure, p O2 . To illustrate this, creep data for Cu 2 O single crystals crept at various oxygen partial pressures are presented in Fig. 7-73 (Schmidt-Whitley, 1975). The rate of creep is seen to increase with pOl according to (7-97) — Po2 This dependence arises because creep is diffusionally controlled, and the slower diffusing oxygen species moves through the lattice by a neutral interstitial mechanism. In standard Kroeger-Vink notation, neutral interstitials form from the gas according to the reaction
so that the equilibrium concentration of oxygen interstitials [OJ is [OJ = Xp#22
(7-98)
where K is the equilibrium constant. The dependence of the creep rate on the square root of the oxygen partial pressure is thus understood in terms of the number of oxygen interstitials available for diffusion.
Impurity Effects on Diffusion in Ionic Ceramics
7.4.4.3 Grain Size Dependence
Creep in ionic ceramics can be influenced greatly by aliovalent impurities, at
Because of experimental difficulties in controlling grain size, the grain size depen-
401
7.4 Plasticity I
I
Cu2O SINGLE CRYSTALS 10" ~ 900°C;4.7MPa (Schmidt -Whitley, I975)
&
10"
Figure 7-73. The effects of oxygen partial pressure on the steady state creep rate of Cu 2 O single crystals (after SchmidtWhitley, 1975).
10" IO" 3
IO"2 10"' I 10 OXYGEN PARTIAL PRESSURE, p 0 (torr)
dence of the steady state creep rate, as characterized by the exponent m, has not been investigated as extensively as the stress and temperature dependencies. Nevertheless, the grain size dependence often provides important mechanistic information. For example, it is particularly useful in distinguishing between the NabarroHerring (m = 2) and Coble (m = 3) mechanisms, which, as discussed earlier, are so frequently observed in polycrystalline ceramics. As an illustration, data for relatively pure polycrystalline alumina are presented in Fig. 7-74 (Lessing and Gordon, 1975). The grain size exponent is close to m = 2, and this, in combination with a stress exponent of n = 1, suggests that creep is controlled by the Nabarro-Herring mechanism.
10-6
10-10 10
100
1000
GRAIN SIZE (|im)
Figure 7-74. The grain size dependence of the creep rate in polycrystalline alumina. The value of the grain size exponent m ~ 2 indicates Nabarro-Herring creep (after Lessing and Gordon, 1975).
7.4.4.4 Effect of Porosity Grain size is just one of several microstructural parameters which influence the rate of creep. In ceramics, two other particularly important microstructural influences are due to porosity and intergranular phases. Porosity is present in the microstructures of ceramics for many reasons, and it can have major effects on the creep resistance of the material. The data in Fig. 7-75,
10-10 0.0
0.1
0.2
0.3
0.4
0.5
POROSITY (volume fraction)
Figure 7-75. The influence of porosity on creep in polycrystalline alumina (after Kingery et al., 1976).
402
7 Mechanical Properties of Ceramics
for example, demonstrate that the rate of creep in polycrystalline alumina increases substantially with porosity (Kingery et al., 1976). The explanation for this behavior is fairly simple - as the porosity increases, the load bearing cross-sectional area of the specimen decreases, and the material creeps more rapidly. The effects of porosity are thus expected to be greater in materials for which the creep rate is more stress sensitive (i.e., higher stress exponents). 7.4.4.5 Effect of Soft Intergranular Phases
Many ceramics contain intergranular phases, the most familiar being the residual glasses which form in materials to which sintering agents (fluxes) have been added (for instance, hot pressed Si 3 N 4 , SiC and the SiAlONs). Intergranular phases are also present in the microstructures of glassceramic materials (Morrell and Ashbee, 1973) and siliconized SiC (Wiederhorn et al., 1988). The importance of the intergranular phase is that if it softens or melts at high temperatures, substantial reductions in strength and creep resistance may result. As an illustration, the flexural strength of two commercial hot-pressed Si 3 N 4 materials is plotted as a function of temperature in Fig. 7-76 (Lange, 1974). The rapid decrease in strength at about 800 °C in one material and 1200 °C in the other is due to the softening of the intergranular phase. In creep, the same effects are manifested in enhanced creep rates and shortened times to rupture (Osborne, 1975; Vaandrager and Pharr, 1989). The mechanisms by which soft intergranular phases enhance the rate of creep are shown schematically in Fig. 7-77. Strain is produced primarily by the rigid sliding of the solid grains, made possible by shearing in the soft intergranular phase.
The rate at which deformation proceeds is determined primarily by the mechanisms which accommodate the sliding at those grain interfaces which are jammed together or pulled apart as a result of the sliding. As illustrated in Fig. 7-77, numerous accommodation mechanisms are possible. The first is diffusion of the solid through the intergranular phase. This results in a mechanism which is effectively the same as Coble creep, the main difference being that diffusion takes place through the intergranular phase rather than through the grain boundary (Pharr and Ashby, 1983). A second accommodation mechanism involves percolation or "flow" of the intergranular phase, which occurs when the intergranular phase is so soft that it behaves like a liquid and flows through the structure. A third accommodation mechanism involves the nucleation and growth of cavities at those places in the microstructure where the intergranular phase is stressed in tension (Lange, 1975). Intergranular cavitation is very frequently observed in ceramics and represents the primary mecha-
120
^ IOO
1
1
I
i
I
•
h 80-
l
HS-130
•
XV
h- 6 0 cn < gc
I
HOT PRESSED Si 3 N 4 (Lange, 1974)
x
40-
« HS-llo\
• \
20 -1
200
1
1
1
I
I
I
400 600 800 1000 1200 1400 TEMPERATURE (°C)
Figure 7-76. The temperature dependence of the flexural strength of two hot-pressed silicon nitrides. The drop in strength at elevated temperatures is due to softening of the intergranular phase (after Lange, 1974).
403
7.4 Plasticity
Intergranular phase
Figure 7-77. Mechanisms of creep in ceramics containing soft intergranular phases.
nism of creep failure in materials containing soft intergranular phases (Marion et al., 1983; Thouless and Evans, 1984). Typical experimental observations are presented in Fig. 7-78 (Lange et al., 1980), in which the stress dependence of the creep rate for four different Si 3 N 4 materials alloyed with small amounts of MgO and SiO2 is shown. The alloying additions produce a glassy intergranular phase whose volume fraction, Vv can be controlled by alloying. Two types of behavior are exhibited, representing two different mechanisms of accommodation. Alloys A and C, which contain relatively small volume fractions of glass (4 and 5%, respectively), creep relatively slowly, exhibit stress exponents close to n ~ 1, and show little or no tendency toward cavity formation during creep. These observations are consistent with diffusionally accommodated sliding. Alloys B and D, which contain much larger fractions of glass (17 and 11%, respectively), creep much faster, show a much stronger stress dependence (n ~ 2), and exhibit extensive cavitation, suggesting a mechanism involving sliding accommodated by cavitation. Stress exponents with
values close to 2 are frequently reported for cavitation accommodated creep, but the mechanistic significance of this stress exponent is yet to be explained.
Si 3 N 4 -MgO ALLOYS I4OO°C (Lange et al, 1980)
10"
Alloy
Vg (%)
n
Qc (kJ/mol)
A B C D
4 17 5 II
0.9 2.0 0.9 1.9
660 1080 —
I0 2 I0 3 COMPRESSIVE STRESS.a-(MPa)
Figure 7-78. The stress dependence of the creep rate of four different Si 3 N 4 -MgO alloys. As shown in the table in the lower right hand corner of the graph, each alloy contains a different volume fraction, Fg, of the glassy intergranular phase (after Lange et al., 1980).
404
7 Mechanical Properties of Ceramics
7.5 Conclusions This chapter has examined the elastic, fracture, and plastic properties of ceramics, and has developed theoretical frameworks necessary for characterising properties in terms of atomistic or microstructural phenomena. Overall, the connections between the underlying microscopic processes and observed macroscopic behaviors are clear, and we conclude that the models forwarded are well-founded and appropriate. Examples of successful modelling include the prediction of polycrystalline Young's moduli from single crystal elastic constants, the prediction of strength using indentation tests in materials with microstructural toughening, and the prediction of the temperature dependence of flow stress for ionic solids. A common feature of the above successes is that the models are all developed for relatively "homogeneous" systems, even in the cases where microstructure introduces a degree of inhomogeneity. As ceramic materials are developed with greater microstructural refinements to make them lighter, stiffer, tougher, stronger and longer-lasting, "heterogeneous" systems will become more commonly encountered, and some of the models used here will become less effective in describing or predicting material behavior. Examples of areas in which further work needs to be done include: description of the moduli of twophase materials near percolation thresholds; description of the moduli of porous media; a priori specification of the ligamentary bridging characteristics of single and multi-phase ceramics in terms of processing variables; more rigorous connection between the toughening processes and fracture resistance variations; a priori specification of the atomistic parameters involved in non-equilibrium crack velocity
equations; and an understanding of interfacial phenomena in high temperature creep fracture. However, the underlying physical principles developed here should still provide the starting point for tackling these problems.
7.6 References Anderson, O. L. (1965), /. Geophys. Res. 70, 39513963. Anstis, G. R., Chantikul, P., Lawn, B. R., Marshall, D. B. (1981), J. Am. Ceram. Soc. 74, 533-538. Ashby, M. E, Jones, D. R. H. (1986), Engineering Materials 2: An Introduction to Microstructures, Processing and Design. Oxford: Pergamon Press. Ashcroft, N. W, Mermin, N. D. (1976), Solid State Physics. New York: Holt, Rinehart and Winston. Atkins, A. G., Mai, Y.-W. (1985), Elastic and Plastic Fracture. Chichester: Ellis Horwood Limited. Barrett, C. R., Nix, W. D. (1965), Ada Metall. 13, 1247-1258. Bateman, T. B. (1962), J. AppL Phys. 33, 3309-3312. Becher, P. F. (1981), J. Am. Ceram. Soc. 64, 37-39. Binns, D. B. (1962), Sci. Ceram. 1, 315-334. Birch, I M., Wilshire, B., Owen, D. I R., Shantaram, D. (1976), /. Mater. Sci. 11, 1817-1825. Cannon, W. R., Langdon, T. G. (1983), /. Mater. Sci. 18, 1-50. Cannon, W. R., Langdon, T. G. (1988), /. Mater. Sci. 23, 1-20. Ceramic Source (1990), Westerville: The American Ceramic Society. Chantikul, P., Anstis, G. R., Lawn, B. R., Marshall, D. B. (1981), /. Am. Ceram. Soc. 74, 539-543. Christenson, R. M. (1982), in: Mechanics of Composite Materials: Hashin, Z., Herakovich, C. T. (Eds.). New York: Pergamon Press, pp. 1-16. Chuang, T. J. (1986), J. Mater. Sci. 21, 165-175. Chung, D.-H., (1963), Phil. Mag. 8, 833-841. Coble, R. L. (1963), J. Appl. Phys. 34, 1679-1682. Cohrt, H., Grathwohl, G., Thummler, E (1984), Res. Mech. 10, 55-71. Cook, R. E (1985), Strength Characterisation of Ceramics Using Controlled Indentation Flaws, Ph.D. Thesis, Sydney: University of New South Wales. Cook, R. E, (1987), in: Advanced Structural Ceramics: Becher, P. E, Swain, M. V., Somiya, S. (Eds.). Pittsburgh: Materials Research Society, pp. 199206. Cook, R. E, (1990), Acta Metall 38, 1083-1100. Cook, R. E, Roach, D. H. (1986), J. Mater. Res. 1, 589-600.
7.6 References
Cook, R. R, Pharr, G. M. (1990), /. Am. Ceram. Soc. 73, 787-817. Cook, R. R, Lawn, B. R., Fairbanks, C. J. (1985), J. Am. Ceram. Soc. 68, 604-615. Cook, R. R, Fairbanks, C. J., Lawn, B. R., Mai, Y.-W. (1987), /. Mater. Res. 2, 345-356. Dabbs, T. P., Lawn, B. R. (1985), / Am. Ceram. Soc. 68, 563-569. Dabbs, T. P., Lawn, B. R., Kelly, P. L. (1982), Phys. Chem. Glasses 23, 58-66. Datta, S. K., Mukhopadhyay, A. K., Chakraborty, D. (1989), Ceram. Bull. 68, 2098-2102. Dauskardt, R. H., Yu, W, Ritchie, R. O. (1987), /. Am. Ceram. Soc. 70, C-248-C-252. Davidge, R. W. (1979), Mechanical Behavior of Ceramics. Cambridge: Cambridge University Press. Day, R. B., Stokes, R. J. (1966a), J. Am. Ceram. Soc. 49, 345-354. Day, R. B., Stokes, R. J. (1966b), Mater. Sci. Res. 3, 355-360. Dean, E. A., Lopez, J. A. (1983), J. Am. Ceram. Soc. 66, 366-370. Dryden, J. S., Morimoto, S., Cook, J. S., (1965), Philos. Mag. 12, 379-391. Eshelby, J. D., Newey, C. W. A., Pratt, P. L. (1958), Philos. Mag. 3, 75-89. Evans, A. G. (1990), /. Am. Ceram. Soc. 73,187-206. Evans, A. G., Langdon, T. G. (1976), Prog. Mater. Sci. 21, 171-425. Fairbanks, C. I, Lee, H. L., Hasselman, D. P. H. (1984), J. Am. Ceram. Soc. 67, C-236-C-237. Fairbanks, C. J., Lawn, B. R., Cook, R. R, Mai, Y.-W. (1986), in: Fracture Mechanics of Ceramics 8: Bradt, R. C , Evans, A. G., Hasselman, D. P. H., Lange, F. F. (Eds.). New York: Plenum Publishing Corporation, pp. 23-37. Fleischer, R. L. (1962), Ada Metall. 10, 835-842. Fleischer, R. L. (1963), J. Appl. Phys. 33, 3504-3508. Freiman, S. W., Mecholsky, J. X, Rice, R. W, Wurst, J. C. (1975), J. Am. Ceram. Soc. 58, 406-409. Freiman, S. W., White, G. S., Fuller, E. R. (1985), /. Am. Ceram. Soc. 68, 108-112. Frost, H. X, Ashby, M. R (1982), Deformation Mechanism Maps. Oxford: Pergamon Press. Fuller, E. R., (1979), in: Fracture Mechanics Applied to Brittle Materials, Freiman, S. W. (Ed.). Philadelphia: ASTM pp. 3-18. Fuller, E. R., Lawn, B. R., Cook, R. R (1983), /. Am. Ceram. Soc. 66, 314-321. Garvie, R. C , Hannink, R. H. I , Pascoe, R. T. (1975), Nature 258, 703-704. Gehrke, E., Ullner, Ch. (1988), in: Fractography of Glasses and Ceramics: Varner, J. R., Frechette, V. D. (Eds.). Westerville: American Ceramic Society, pp. 77-84. Gilman, J. J. (1961), Prog. Ceram. Sci. 1, 146-199. Gilman, J. X (1974), J. Appl. Phys. 45, 508-509. Gilman, X X, Roberts, B. W. (1961), /. Appl. Phys. 32, 1405.
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Glaesemann, G. S., Jakus, K., Ritter, X E. (1987), / Am. Ceram. Soc. 70, 441-444. Gordon, R. S. (1973), /. Am. Ceram. Soc. 56, 147152. Gordon, R. S. (1975), Mater. Sci. Res. 9, 445-464. Green, D. X, Hannink, R. H. X, Swain, M. V. (1989), Transformation Toughening of Ceramics. Boca Raton: CRC Press. Griffith, A. A. (1920), Phil. Trans. Roy. Soc. 221, 163-198. Groves, G. W, Kelly, A. (1963), Philos. Mag. 8, 877887. Groves, G. W, Kelly, A. (1969), Philos, Mag. 19, 977-986. Hashin, Z., Shtrikman, S. (1962), J. Meek. Phys. Sol. 10, 343-352. Hashin, Z., Shtrikman, S. (1963) /. Mech. Phys. Sol. 11, 127-140. Hasselman, D. P. H. (1970), J. Am. Ceram. Soc. 53, 490-495. Herring, C. (1950), /. Appl. Phys. 21, 437-445. Hertz, H. (1882), in: Miscellaneous Papers: Xones, D. E., Schott, G. A. (Trans.). London: Macmillan, pp. 163-183. Hirth, X P., Lothe, X (1982), Theory of Dislocations. New York: John Wiley and Sons. Hollenberg, G. W, Terwilliger, G. R., Gordon, R. S. (1971), J. Am. Ceram. Soc. 54, 196-199. Holloway, D. G. (1973), The Physical Properties of Glass, London: Wykeham Publications. Hu, M. S., Thouless, M. D., Evans, A. G. (1988), Ada Metall. 36, 1301 -1307. Hiibner, H., Jillek, W. (1977), /. Mater. Sci. 12, 117125. Huddart, A., Whitworth, R. W. (1973), Philos. Mag. 27, 107-119. Huntington, H. B. (1958), Sol. State. Phys. 7, 213351. Ingel, R. P., Lewis, D. (1988), /. Am. Ceram. Soc. 71, 265-271. Inglis, C. E. (1913), Trans. Inst. Nay. Arch. 55, 219241. Irwin, G. R. (1958), in: Handbuch der Physik 6. Berlin: Springer-Verlag, pp. 551-590. Johnston, W. G. (1962), J. Appl. Phys. 33,2050-2058. Kingery, W. D., Bowen, H. K., Uhlmann, D. R. (1976), Introduction to Ceramics. New York: John Wiley and Sons, p. 746. Knehans, R., Steinbrech, R. (1982), /. Mater. Sci. Letters 1, 327-329. Kronberg, M. L. (1957), Acta MetalL 5, 507-524. Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology Volume 18, Elastic, Piezoelectric, Pyroelectric, Piezooptic, Electrooptic Constants, and Nonlinear Dielectric Susceptibilities of Crystals: Hellwege, K.-H., Hellwege, A. M. (Eds.). Berlin: Springer-Verlag. Lange, R R (1974), /. Am. Ceram. Soc. 57, 84-87. Lange, F. R (1975), in: Deformation of Ceramic Materials. New York: Plenum Press, pp. 361-381.
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7 Mechanical Properties of Ceramics
Lange, F. K, Davis, B. I., Clarke, D. R. (1980), /. Mater. Sci. 15, 601-610. Lathabai, S., Mai, Y.-W, Lawn, B. R. (1989), /. Am. Ceram. Soc. 72, 1760-1763. Lawn, B. R. (1974), Mater. Sci. Eng. 13, 277-283. Lawn, B. R. (1975), /. Mater. Sci. 10, 469-480. Lawn, B. R., Evans, A. G. (1977), /. Mater. Sci. 12, 2195-2199. Lawn, B. R., Evans, A. G., Marshall, D. B. (1980), /. Am. Ceram. Soc. 63, 574-581. Lawn, B. R., Marshall, D. B. (1977), Phys. Chem. Glasses 18, 7-18. Lawn, B. R., Swain, M. V. (1975), /. Mater. Sci. 10, 113-122. Lawn, B. R., Wilshaw, T. R. (1975), Fracture of Brittle Solids. Cambridge: Cambridge University Press. Lessing, P. A., Gordon, R. S. (1975), in: Deformation of Ceramic Materials. New York: Plenum Press; pp. 271-296. Mai, Y.-W., Lawn, B. R. (1986), Ann. Rev. Mater. Sci. 16, 415-439. Marion, I E., Evans, A. G., Drory, M. D., Clarke, D. R. (1983), Ada Metall. 31, 1445-1457. Marlowe, M. O., Wilder, D. R. (1965), J. Am. Ceram. Soc. 48, 227-233. Marshall, D. B. (1986), /. Am. Ceram. Soc. 69, 173180. Marshall, D. B., Noma, T., Evans, A. G. (1982), J. Am. Ceram. Soc. 65, C-175-C-176. Marshall, D. B., Drory, M. D., Evans, A. G. (1983 a), in: Fracture Mechanics of Ceramics 6, Bradt, R. C , Evans, A. G., Hasselman, D. P. H., Lange, F. F. (Eds). New York: Plenum Publishing Corporation, pp. 289-307. Marshall, D. B., Evans, A. G., Khuri Yakub, B. T., Tien, J. W, Kino, G. S. (1983 b), Proc. Roy. Soc. Lond. A 385, 461-475. Marshall, D. B., Cox, B. N., Evans, A. G. (1985), Acta Metall. 11, 2013-2021. Material Data Sheet (1985), Golden: Coors Porcelain Co. McColm, I. J. (1983), Ceramic Science for Technologists. Glasgow: Blackie and Son, Ltd. McHenry, K. D., Yonushonis, T., Tressler, R. E. (1976), /. Am. Ceram. Soc. 58, 262-263. McMeeking, R., Evans, A. G. (1982), J. Am. Ceram. Soc. 65, 242-246. Menezes, R. A., Nix, W D. (1973), Philos. Mag. 27, 1201-1209. Menezes, R. A., Nix, W. D. (1974a), Mater. Sci. Eng. 16, 57-66. Menezes, R. A., Nix, W. D. (1974b), Mater. Sci. Eng.
16, 67-73. Michalske, T. A., Freiman, S. W (1982), Nature 295, 511-512. Mitchell, T. E., Heuer, A. H. (1977), Mater. Sci. Eng. 28, 81-97. Mitchell, T. E., Pletka, B. I , Phillips, D. S., Heuer, A. H. (1976), Philos, Mag. 34, 441-451.
Morrell, R., Ashbee, K. H. G. (1973), /. Mater. Sci. 8, 1253-1270. Mould, R. E., Southwick, R. D. (1959), /. Am. Ceram. Soc. 42, 582-592. Nabarro, F. R. N. (1948), Report of a Conference on the Strength of Solids. Physical Society of London; pp. 75-90. Nabarro, F. R. N. (1967), Philos. Mag. 16, 231-237. Nye, J. F. (1957), Physical Properties of Crystals. Oxford: Clarendon Press. Osborne, N. J. (1975), Proc. Brit. Ceram. Soc. 25, 1-30. Ostertag, C. P. (1987), J. Am. Ceram. Soc. 70, C-355C-357. Pharr, G. M., Ashby, M. F. (1983), Acta Metall. 31, 129-138. Pisarenko, G. G., Chusko, V. M., Kovalev, S. P. (1985), /. Am. Ceram. Soc. 68, 259-265. Pletka, B. J., Wiederhorn, S. M. (1982), /. Mater. Sci. 17, 1247-1268. Pokier, J. P. (1985), Creep of Crystals. Cambridge: Cambridge University Press. Pollet, J. C , Burns, S. J. (1977), Int. J. Fract. 13, 667679. Poteat, L. E., Yust, C. S. (1968), in: Ceramic Microstructures. New York: John Wiley and Sons, p. 646. Raj, R., Ashby, M. F. (1971), Metall. Trans. 2, 11131127. Readey, M. I, Heuer, A. H., Steinrech, R. W. (1987), in: Advanced Structural Ceramics: Becher, P. F , Swain, M. V., Somiya, S. (Eds.). Pittsburgh: Materials Research Society, pp. 107-120. Rice, J. R. (1968), /. Appl. Mech. 35, 379-386. Rice, J. R. (1978), /. Mech. Phys. Solids 26, 61-78. Rice, R. W, Freiman, S. W, Mecholsky, J. J. (1980), J. Am. Ceram. Soc. 63, 129-136. Roesler, F. C. (1956), Proc. Phys. Soc. B 69, 981 -992. Ruoff, A. L. (1965), / Appl. Phys. 36, 2903-2907. Shaw, R. R., Uhlmann, D. R. (1971), /. Non.-Cryst. Sol. 5, 237-263. Shaw, T. M., Shinde, S. L., Dimos, D., Cook, R. F , Duncombe, P. D., Kroll, C. (1989), J. Mater. Res. 4, 248-256. Schmidt-Whitley, R. D. (1975), /. Am. Ceram. Soc. 58, 337-338. Sherby, O. D., Miller, A. K. (1979), J. Eng. Mater. Technol. 101, 387-395. Sigl, L. S., Exner, H. E., Fischmeister, H. F. (1986), in: Science of Hard Materials: Almond, E. A., Brookes, C. A., Warren, R. (Eds.). Bristol: Adam Hilger, pp. 631-644. Singh, R. N., Coble, R. L. (1974), /. Appl. Phys. 45, 990-995. Sprackling, M. T. (1976), The Plastic Deformation of Simple Ionic Crystals. London: Academic Press. Steinbrech, R., Knehans, R., Schaarwachter, W. (1983), J. Mater. Sci. 18, 265-270. Stewart, R. L., Bradt, R. C. (1980), /. Am. Ceram. Soc. 63, 619-622.
7.6 References
Stock, A. R, Hannant, D. I, Williams, R. I. T. (1979), Mag. Cone. Res. 31, 225-234. Stokes, R. X (1966), Proc. Brit. Ceram. Soc. 6, 189207. Stoloff, N. S., Lezius, D. K., Johnston, T. L. (1963), /. Appl. Phys. 34, 3315-3322. Swain, M. V. (1981), /. Mater. Set 16, 151-158. Swain, M. V. (1985), Acta Metall. 33, 2083-2091. Swain, M. V. (1986), J. Mater. Sci. Letters 5, 13131315. Swain, M. V., Rose, L. R. F. (1986), /. Am. Ceram. Soc. 69, 511-518. Swanson, P. L., (1988), in: Fractography of Glasses and Ceramics: Varner, J. R., Frechette, V. D. (Eds.). Westerville: American Ceramic Society, pp. 135-155. Swanson, P. L., Fairbanks, C. X, Lawn, B. R., May, Y.-W., Hockey, B. X (1987), /. Am. Ceram. Soc. 70, 279-289. Tada, H., Paris, P. C , Irwin, G. R. (1973), The Stress Analysis of Cracks Handbook. St. Louis: Del Research Corporation. Talty, P. K., Dirks, R. A. (1978), J. Mater. ScL 13, 580-586. Tandon, R., Green, D. X (1990), / Am. Ceram. Soc. 73, 970-977. Thouless, M. D., Evans, A. G. (1984), J. Am. Ceram. Soc. 67, 721-727. Tillet, X P. A. (1956), Proc. Phys. Soc. B69, 47-54. Trantina, G. G. (1979), J. Am. Ceram. Soc. 62, 377380. Vaandrager, B. L., Pharr, G. M. (1989), Acta Metall. 37, 1057-1066. von Mises, R. (1928), Z. angew. Math. Mech. 8, 161166. Wachtman, J . B , Maxwell, L. H. (1954), J. Am. Ceram. Soc. 37,291-299. Wang, X C. (1984), J. Mater. Sci. 19, 809-814. Weertman, X (1955), J. Appl. Phys. 26, 1213-1217. Weertman, X (1957), /. Appl. Phys. 28, 362-364. Wiederhorn, S. M. (1967), /. Am. Ceram. Soc. 50, 407-414. Wiederhorn, S. M., Bolz, L. H. (1970), /. Am. Ceram. Soc. 53, 543-548.
407
Wiederhorn, S. M., Freiman, S. W, Fuller, E. R., Simmons, C. X (1982), J. Mater. Sci. 17, 34603478. Wiederhorn, S. M., Roberts, D. E., Chuang, T. X, Chuck, L. (1988), J. Am. Ceram. Soc. 71, 602-608. Williams, D. P., Evans, A. G. (1973), /. Testing Eval. 1, 264-270.
General Reading Atkins, A. G., Mai, Y.-W. (1985), Elastic and Plastic Fracture. Chichester: Ellis Horwood. Cannon, W. R., Langdon, T. G. (1983), "Creep of Ceramics: I - Mechanical Characteristics", J. Mater. Sci. 18, 1. Cannon, W. R., Langdon, T. G. (1988), "Creep of Ceramics: II - An Examination of Flow Mechanisms", J. Mater. Sci. 23, 1. Davidge, R. W. (1980), Mechanical Behavior of Ceramics. Cambridge: Cambridge University Press. Evans, A. G., Langdon, X G. (1976), "Structural Ceramics", Prog. Mater. Sci. 21, ill. Frost, H. X, Ashby, M. F (1982), Deformation Mechanism Maps. Oxford: Pergamon Press. Green, D. X, Hannink, R. H. X, Swain, M. V. (1989), Transformation Toughening of Ceramics. Boca Raton: CRC Press. Hirth, X P., Lothe, X (1982), Theory of Dislocations. New York: Wiley. Kanninen, M. F , Popelar, C. H. (1985), Advanced Fracture Mechanics. Oxford: Oxford University Press. Kingery, W. D., Bowen, H. K., Uhlmann, D. R. (1976), Introduction to Ceramics. New York: Wiley. Lawn, B. R., Wilshaw, T. R. (1975), Fracture of Brittle Solids. Cambridge: Cambridge University Press. McColm, I. X (1990), Ceramic Hardness. New York: Plenum Press. Nye, X F. (1979), Physical Properties of Crystals. Oxford: Oxford University Press. Sprackling, M. T. (1976), The Plastic Deformation of Simple Ionic Crystals. London: Academic Press.
8 Toughening Mechanisms in Ceramic Systems Paul F. Becher Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN, U.S.A. L. R. Francis Rose Aeronautical Research Laboratory, Defence Science and Technology Organisation, Fishermens Bend, Victoria, Australia List of 8.1 8.1.1 8.2 8.2.1 8.2.2 8.2.3 8.2.3.1 8.2.3.2 8.2.4 8.2.4.1 8.2.4.2 8.2.4.3 8.2.5 8.3 8.3.1 8.3.1.1 8.3.1.2 8.3.1.3 8.3.1.4 8.3.1.5 8.3.2 8.3.2.1 8.3.2.2 8.3.2.3 8.3.3 8.3.3.1 8.3.3.2 8.3.4 8.3.4.1 8.3.4.2 8.4 8.5 8.6
Symbols and Abbreviations Introduction Classification of Toughened Ceramics Mechanics of Toughening Measures of Toughness Phenomenology of Deformation and Fracture Transformation Toughening Transformation Criterion Approaches to Theoretical Modeling Crack Bridging Stress Analysis of Bridged Cracks Experimental Determination of the Traction Law Micromechanics of Bridging Multiple Mechanisms Toughening Mechanisms Martensitic Transformation Toughening Transformation Thermodynamics Critical Transformation Stress Transformation Toughening Contribution Zirconia Ceramics Zirconia-Toughened Ceramics Reinforcement Processes Analysis of Toughening by Whisker Reinforcement Whisker Characteristics Interfacial Characteristics Microstructural Tailoring Matrix Bridging: Grain Size Effects Matrix Bridging: Influence of Grain Geometry Coupled Toughening Responses Whisker Reinforcement - Transformation Toughening Whisker Reinforcement - Matrix Grain Bridging Summary Acknowledgements References
Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.
410 414 416 419 419 422 424 428 429 429 431 433 433 435 436 437 438 439 441 442 444 447 448 451 452 452 452 453 454 455 456 456 458 458
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List of Symbols and Abbreviations a A a0 Aa C C d D E E' Ec Ef £m £w ejj / f(d/x) F Gc Gm Go AG T AG T * AGJ.""11 h J(C) Jm A/Cb AJfb A/ gb A/ po k K Kc KF (s) KY Km Kc KR Ktip
crack half-length cross-sectional area initial crack length crack tension numerical factor contour grain size dilatational component of the transformation strain Young's modulus (of composite) function depending on Young's modulus and Poisson's ratio Young's modulus of zirconia-toughened composites Young's modulus of fiber Young's modulus of matrix phase Young's modulus of whiskers components of transformation strain tensor volume fraction of transformed material or of fiber in the bulk matrix material function describing the stress concentration force incremental or total work of fracture work of fracture for bulk matrix material intrinsic work of fracture energy consumption at tetragonal-monoclinic phase transformation increased AG T due to enhanced transformation ability at a selected temperature chemical free energy change at tetragonal-monoclinic phase transformation (steady-state) width of the transformation zone Eshelby-Rice J-integral energy dissipated by extension of a crack tip in the matrix energy dissipated by crack bridging processes energy dissipated by friction energy dissipated by matrix grain bridging frictional energy dissipated by pullout of whiskers spring constant stress intensity factor critical or steady-state fracture toughness toughness due to point forces of unit strength acting at a distance s from the crack tip applied stress intensity fracture resistance or intrinsic toughness of matrix phase steady-state toughness increment nominal stress intensity factor or crack-growth resistance local stress intensity factor
List of Symbols and Abbreviations
Ko K^ AK (Aa) AK b AKT AKUC, AKUC' AK wr / L lc /db Ze Zpo m, m* M Mb Ms Ms° P r ruc s S stj ASl^m T T(u) To Tsr u uc AU{ AUT AC7 SE V{ F gb F po VT w Wh Wp x y
411
local or matrix toughness in the absence of toughening effects nominal or far-field stress intensity factor toughness increment due to transformation toughness increment due to bridging transformation toughening contribution toughening contribution due to microcracking bridging contribution to toughness for uniaxially aligned whiskers bridged length gage length length of a fully developed zone extent of interfacial debonding initial embedded length pullout length transformation zone size constant constant martensitic start temperature for burst-type transformations martensitic transformation start temperature martensitic transformation temperature in the absence of internal stress load radius of whisker or fiber radius of the microcracked zone distance from the crack tip shear component of the transformation strain deviatoric component of stress tensor entropy change at tetragonal-monoclinic phase transformation absolute temperature bridging stress profile tetragonal-monoclinic phase transformation temperature for stress-free particle temperature below which stress is frozen in crack-opening displacement maximum crack opening displacement internal strain energy change at tetragonal-monoclinic phase transformation energy required for tetragonal-monoclinic phase transformation external strain energy required for tetragonal-monoclinic phase transformation volume fraction of whiskers or fibers volume fraction of bridging grains volume fraction of pulled-out whiskers a m o u n t of transformed zirconia specimen width work of stretching the bridging ligaments t o rupture work for pullout per unit area of fracture surface distance from stress concentrator distance from the fracture plane
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8 Toughening Mechanisms in Ceramic Systems
a aA,ac am (xfr,a[ Aa y y{ yw ylc S 5C 3C dtj <5 0 Smax A A* Ao s sc eT, sjj sj, el 9T %i X jbt v a, Gtj a <7b,<7b cra aa GC GX <7 M <7 n vu <jTEA ol (GJ)0 G"C GJ
thermal expansion coefficient crystallographic thermal expansion coefficients thermal expansion coefficient of matrix phase radial, axial thermal expansion coefficient of a fiber respectively thermal expansion coefficient mismatch shear strain interfacial fracture energy whisker (fiber) fracture energy half energy to create an increment of crack advance displacement across a single deformation band residual displacement upon unloading displacement to cause fracture Kronecker delta displacement due to formation of a transformation band maximum stretch overall load-point displacement contribution of load device to A load point displacement at failure (nominal) strain nominal failure strain transformation strain tensor, elements radial, axial strain, respectively volumetric dilatation bulk modulus of the transforming phase machine compliance friction coefficient Poisson ratio tensor describing the prevailing stress, tensor elements stress bridging stress applied tensile stress applied stress critical stress for transformation under a state of hydrostatic tension internal residual stress characteristic stress for matrix crack propagation stress acting normal to the interface applied stress at which crack extension becomes unstable thermal expansion anisotropy stress (critical) applied stress to initiate martensitic transformation stress required in the absence of internal tensile stress stress required to initiate microcracking tensile fracture strength of whiskers
G\
axial residual stress in the matrix
G0 T
maximum value of G in strain softening stress-strain curve shear stress
List of Symbols and Abbreviations
TC T i? fi x gb ¥ Qc
critical stress for transformation under a state of pure shear interfacial shear resistance frictional shear stress for grain pull out nondimensional geometrical factor critical value of interaction energy for transformation
PSZ TEA TZP ZTA ZTC
partially stabilized zirconia thermal expansion anisotropy tetragonal zirconia polycrystals zirconia-toughened alumina zirconia-toughened ceramic
413
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8 Toughening Mechanisms in Ceramic Systems
8.1 Introduction When fracture of brittle materials is accompanied by processes that dissipate a portion of the strain energy normally available for extension of the main crack, improvements in fracture toughness [Kc = (2 ylc x E)1/2] are obtained. Note that 2 ylc is the energy to create an increment of crack advance which involves the formation of two new crack surfaces, and E is the Young's modulus of the material. The extent of the increase in fracture toughness is dependent upon the effectiveness of the process(es) in depleting for the strain energy supplied by the externally applied stress. The peak fracture toughness values of metallic systems range from 10 to over 150 MPa y/m due primarily to the contribution of plastic deformation by dislocation activity in the region of the crack (Pellini, 1977). Compare this to the range of approximately 0.5 to 6 MPa ^/m for the peak fracture toughnesses that were typical for most monolithic ceramics and glasses (Kelly and Macmillan, 1986). However, one does not have to initiate plastic deformation to gain increased toughness. Alumina single crystals exhibit fracture toughness values of 2 to 3 MPa yfm for most crack plane orientations and in excess of 4 MPa y/m for basal or near basal plane orientations (Wiederhorn, 1969; Becher, 1976). Polycrystalline aluminas have toughnesses in the range of 2.5 to 5 MPa y/m depending on their microstructure characteristics (Rice et al., 1981). Recent advances in this area have led to the development of ceramics with toughnesses in the range of 10 to 20 MPa^ym, and continuous fiber reinforced composites with values that may be greater than this depending on fiber layout or architecture, crack plane orientation, and interface properties.
Among those processes or mechanisms contributing to these significant improvements in the fracture toughness are crack pinning coupled with crack deflection, crack bridging, and pullout by both dispersed particles and reinforcing brittle phases, and/or stress-induced microcracking introduced by Wei and Becher (1984), Prewo and Brennan (1980), Becher et al. (1988), Evans (1988). Both stress induced martensitic transformation toughening (Evans, 1988; Evans and Cannon, 1986; Green et al., 1989) and plasticity (Evans, 1988; Kristic et al., 1981; Sigl et al., 1988; Chermant and Osterstock, 1976; Pickens and Gurland, 1978) in dispersed phases have also been employed to enhance the fracture resistance of ceramics. For example, the fracture toughness of tungsten carbide ceramics can be increased from less than 10 MPa y/m to more than 20 MPa y/m by increasing the plastic deformation contribution due to the cobalt based binder phase through increases in binder phase content (Chermant and Osterstock, 1976; Pickens and Gurland, 1978). Why are we concerned with fracture toughness? Because in their application and development, the low fracture toughness or resistance of ceramics has proven to be a limiting feature. We can produce ceramic samples with quite high flexure strengths by very careful processing and machining, and on scaling up the size, we have succeeded in maintaining such high strengths in some cases. However in all cases, the strengths are very sensitive to flaw size as seen in the broad distributions (e.g., low Weibull moduli) of the strength values typically observed unless processing controls are maintained to minimize the introduction of defects and cracks. For example if cracks or defects are kept well below 50 micrometers by careful processing and machining, flexure strengths of
8.1 Introduction
700 MPa can be obtained in fine grained dense alumina ceramics. Even with careful processing, low-toughness ceramics lose a substantial fraction of their strength due to damage introduced during service, for example, due to static load slow crack growth, cyclic fatigue, creep damage, thermal gradients or shock, and impact or contact damage. The substantial flaw size sensitivity of the fracture strengths has often meant that ceramic components were designed (and often were limited by such designs) either to eliminate or greatly minimize in-service tensile stresses or to take advantage of only a small fraction of their potential tensile-flexure strengths. Thus, material design approaches which can impart a substantial degree of toughness to ceramics obviously can have a significant impact in their use in a very wide variety of applications. Let us briefly see how this benefits the user. As described by the Griffith relationship (Griffith, 1920), the flexure and tensile fracture strength of brittle ceramics is determined by the product of the crack-stress geometric parameter and the ratio of the toughness to the square root of the flaw size. Thus for a given fracture toughness (e.g., 5 MPa y/m), the fracture strength increases as the flaw size is decreased as shown in Fig. 8-1 a. Suppose we can only routinely detect flaws which are about 100 pm or larger in a complicated component shape. For such a material, we can only ensure that the as-inspected components will have strengths of 395 MPa assuming that only half penny surface flaws are present. Next we can see from Fig. 8-1 a that increasing the toughness from 5 to 10 and then to 20 MPa ^/m would allow for a substantial increase in the minimum strengths from 395 to 790 to 1580 MPa, respectively, for the same flaw size detection limit. With fracture toughness values
415
of 20 MPa^/m, one could also improve the production yield as larger flaw sizes could be accommodated to achieve the minimum strength requirements. For example, strengths of 790 MPa could be attained in materials with toughnesses of 20 MPa y/m with flaw sizes of up to 400 jam, allowing more components to pass inspection. Before proceeding to discuss toughening mechanisms and the influence of material and microstructural parameters on the resultant toughness, let us clarify what is meant by fracture toughness values described in this text. In the search of processes leading to high fracture toughness, test techniques are sometimes employed which do not ensure that values are obtained for a single sharp crack under known driving stress conditions. The toughness values used here are representative of the growth of a sharp crack under well-defined mode I loading conditions. We also recognize that even when such test techniques are employed, the fracture toughness values obtained may exhibit a range of values. One reason is that the material exhibits rising crack growth resistance with increase in crack length, that is R-curve behavior, which is often noted in the toughened ceramics. Here, we will limit our discussions to toughness values for extended cracks where the toughness approaches a peak or asymptotic value. The field of ceramics has benefited from substantial advances in our understanding of fracture and crack growth in brittle materials, the influence of flaws on strength, and fracture and deformation at elevated temperatures. One must, of course, be familiar with this whole area and not just toughening processes to be able to properly design materials. For those not familiar, there are a number of texts on these subjects; for a starting point, the reader
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8 Toughening Mechanisms in Ceramic Systems
4000 Surface flaw flexure stress
100 Flaw size (urn)
10 (a)
1000
Figure 8-1. Strength-toughness relationship can vary with toughening response, (a) In the fully linear elastic case, increased fracture toughness allows greater stress to be applied to the ceramic for a given flaw size. For example, if 200 um radius surface flaws can routinely be detected, ceramics with a toughness of 20 MPa y/m would exhibit strengths of nearly 900 MPa versus only slightly over 200 MPa for materials with what are considered to be conventional toughness values (5 MPa^/m). (b) However, when the size of the region contributing to the toughness becomes sufficiently large, the toughness-strength response reaches a maximum due to the strength with further toughening.
o Y-TZP+AI203
30
A Y-TZP x Ce-TZP a Mg-PSZ
20 CD
10
5
(b)
IO
15
20
Stress Intensity Factor, K c , MPa/m"
should refer to the Fracture Mechanics of Ceramics series (Bradt et al., 1974-1978, 1983, 1986) and the texts on Fracture of Brittle Solids (Lawn and Wilshaw, 1975). 8.1.1 Classification of Toughened Ceramics
Toughening mechanisms in ceramics can be divided into two broad categories, ac-
cording to whether they involve: (i) A zone of distributed inelastic deformation around the crack tip, due for example to transformation or to microcracking, or both. (ii) Bridging of the crack faces by fibers or whiskers, or unbroken ligaments of a second phase, etc.
8.1 Introduction
Mechanisms of both types may operate in a given material, and indeed a major consideration for microstructural control of properties is to determine conditions for synergistic interaction between two (or more) mechanisms. Mechanisms of the first type may be considered to increase the material's intrinsic toughness, whereas those of the second type can be regarded as reinforcement mechanisms which decrease the crack driving force by providing load transfer across the crack faces. However, a classification based on these considerations is not always clear cut and may depend largely on the length scale of interest, especially when there are multiple mechanisms operating at different microstructural length scales (Sec. 8.2). The prime example of the first type of mechanism is transformation toughening, which has so far relied almost exclusively on the stress-induced transformation of zirconia from the tetragonal to the monoclinic structure, although other ceramics (notably hafnia) which also undergo such transformations could alternatively be used, in principle. Zirconia-toughened ceramics can be divided into the following three classes, on the basis of their microstructures (Claussen, 1985): (i) Partially stabilized zirconia (PSZ) which consists of polycrystals of fully stabilized cubic zirconia containing precipitates of virtually pure tetragonal zirconia. This microstructure results from a decomposition which occurs when certain stabilizers, notably calcia or magnesia, are used at concentrations lower than would be required for full stabilization. These materials are designated as Ca-PSZ and Mg-PSZ, respectively, (ii) Tetragonal zirconia polycrystals (TZP) in which a single-phase tetragonal
417
structure is retained at room temperature due to the presence of certain solutes, for example yttria or ceria, designated as Y-TZP or Ce-TZP, respectively. (iii) Two-phase dispersions of tetragonal zirconia in a matrix of another oxide ceramic, in particular alumina. Crystallographic and other aspects of transformation toughening have been comprehensively reviewed by Green et al. (1989), Riihle and Evans (1989). The prime examples of toughening by crack bridging are fiber-reinforced ceramicmatrix composites, which have amoung the highest toughness (20 MPa ^/m) so far achieved in all-ceramic systems. The best known examples use continuous SiC (Nicalon) fibers in a glass-ceramic matrix (Prewo et al, 1986; Mah et al, 1987), and SiC-SiC composites, fabricated by chemical vapor infiltration of a fiber preform (Lamicq et al, 1986). Metal-ceramic composites can be divided into two classes depending on whether the metal or the ceramic constitutes a continuous phase. A well-known example of the former is WC-Co in which the cobalt binder forms the continuous phase (Sigl et al, 1988). A more recent example is the A1-A12O3 composite produced by the Lanxide process of continuous melt oxidation (Urquhart, 1991). In both cases, crack bridging by ductile ligaments has been observed, but the continuous metal phase also allows a zone of distributed plastic deformation to form around cracks, which can provide a major contribution to the toughness (Marshall et al, 1991). On the other hand, with the ceramic as the continuous phase and the metallic ductile phase in the form of particulates or fibers, crack bridging is the principal toughening mechanism (Deve and Maloney, 1991). Metal-ceramic composites in the form of
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8 Toughening Mechanisms in Ceramic Systems
laminates have been used in particular for the toughening of intermetallics (Deve et al., 1990; Odette et al., 1992), and this configuration appears to provide superior properties relative to a dispersion of a rodlike ductile phase (Heredia et al., 1992). Remarkably high toughnesses have been obtained by ductile-phase toughening, for example, Kc = 55 MPa^/m for TiTaAl2 reinforced with W-3Re fibers (Deve and Maloney, 1991), but Rao et al. (1992) have pointed out that the benefits can be severely degraded under cyclic loading, due to fatigue rupture of the ductile ligaments. The toughness of a y-TiAl intermetallic alloy was increased from 8 MPa
tive to initial flaw size, which is a desirable feature in that it implies damage tolerance and greater reliability in service. On the other hand, further increases in toughness are no longer translated into corresponding increases in strength. Indeed, in the case of transformation-toughened ceramics, increasing toughness can be associated with decreasing strength (Swain, 1985; Swain and Rose, 1986). The maximum strength which can be achieved depends on the value of toughness at which the transition from a "flaw-limited" regime to a "transformation-limited" regime occurs. This transitional toughness correlates with the grain size, which appears to be the most important microstructural dimension for zirconia-toughened ceramics. It is found that the microstructural requirements for optimizing strength do not generally coincide with those for optimizing toughness. This dichotomy between strength and toughness has long been recognized for metals, where the problem for microstructural design has been to increase the strength without compromising toughness. However, there is an important difference between the micromechanisms controlling strength and toughness in ceramics as opposed to metals. The toughening mechanisms in ceramics seem to be generally associated with a strain-softening response, with a major contribution to the work of fracture coming from the deformation of the softened (or damaged) material under decreasing stress. Strain softening behavior leads to strain localization into deformation bands, so that the overall strain at failure may not provide a straightforward measure of ductility: it would be necessary to note also the specimen's gauge length or the spacing between deformation bands. Another complication from the viewpoint of characterization and interpretation of toughness is an increasing tough-
8.2 Mechanics of Toughening
ness (or crack-growth resistance) as a crack extends, which is referred to as R-curve behavior. This implies that there is no longer a unique, well-defined value of fracture toughness, which can be regarded as a material constant. However, the toughness eventually reaches a plateau, and it is this steady-state toughness which is conventionally cited as the critical fracture toughness Kc. These complications require that systematic experimental studies must be combined with theoretical modeling to obtain a reliable interpretation of toughness tests. This combination is particularly important for extracting true material parameters from measurements which may be configuration dependent, and for assessing properties of direct practical interest, such as the wear or thermal shock resistance, in terms of these material parameters. Simple empirical approaches to developing advanced ceramics and composites will not suffice to unravel the influence of the properties and characteristics of the various constituents. This must be directed by a theoretical framework for characterizing the fracture resistance (toughness) response and the contributions from various toughening mechanisms. Accordingly, the existing conceptual framework for characterizing toughness and toughness mechanisms is reviewed first, in Sec. 8.2. At the same time, the researcher must consider how to utilize (and modify) theory to explore the effects of changes in composition, microstructure, material parameters, and test conditions on the toughening response associated with a particular mechanism. Some of these relationships are discussed in Sec. 8.3. For example, in transformation toughened ceramics, the ability to transform the tetragonal zirconia is a critical factor in achieving increased toughness. The materials developer can tailor the
419
grain size and/or the solute employed or both to retain the tetragonal phase. Optimization of the toughening effects requires a means of measuring the influence of changes in microstructure and composition on the transformability of the tetragonal phase. One approach is to examine how these affect the martensite start temperature Ms where the tetragonal phase begins to transform to the monoclinic phase on cooling. This can be uniquely determined in both zirconia ceramics and composites. Another is to determine the applied stress required to initiate the transformation, but in composite systems it is often not possible to detect the associated nonlinearity in the stress-strain response. However, the use of the Ms temperature requires the incorporation of transformation thermodynamics into the mechanics desription of transformation toughening, see Sec. 8.3.1. Similar use (and modification) of theory provides the means to define and test the role of material characteristics in the toughening contribution derived from crack bridging mechanisms. Indeed, the mechanics of toughening and toughening mechanisms sections present complementary approaches to both understanding and optimizing the toughening behavior of ceramic systems.
8.2 Mechanics of Toughening 8.2.1 Measures of Toughness A material's toughness is its resistance to crack growth. There are two distinct, albeit related, measures of toughness which have traditionally been used for brittle materials, namely (i) the work of fracture Gc (per unit of new crack area), and (ii) the criticalfracture toughness K c , representing the critical value of the stress intensity factor K at which crack growth proceeds unstably.
420
8 Toughening Mechanisms in Ceramic Systems
The relation between these two measures is G
= ^
(8-1 a)
E,
c
with: E =E E 1-v2
for plane stress
(8-1 b)
for plane strain
where E,v denote the material's Young's modulus and Poisson's ratio respectively (Lawn and Wilshaw, 1975). Each of these measures of toughness has its advantages: Gc can be determined entirely from experimental measurements and calibrations, whereas Kc requires a detailed stress analysis to determine K as a function of applied load, crack length, and specimen geometry. On the other hand, there are now extensive compilations of formulae for K which cover most standard specimen geometries (Tada, 1985; Murakami, 1987), so that measuring Kc experimentally has become simpler in practice than measuring Gc. Furthermore, because K depends linearly on applied load, the appropriate value of K for a combined loading system is given by a linear superposition of the separate contributions from each subsystem. In the context of brittle fracture mechanics, the fracture toughness Kc (or equivalently, the work of fracture Gc) is expected to be a material constant, independent of crack length. This simple conventional framework has proved to be inadequate for characterizing the behavior of toughened ceramics. Careful measurements, using configurations designed to promote stable quasistatic crack growth, have shown that the resistance to crack growth generally increases with crack extension when a slender saw cut is used as a starter crack. The value of the nominal stress intensity factor (i.e., the K which would be expected for the current crack length and applied load, ig-
noring the possible effects of transformation or crack bridging) is conventionally used as the measure of crack growth resistance, and is denoted by KR. KR increases monotonically with crack extension from an initial value Ko, approaching a plateau or steady-state value K c , provided that a sufficiently large specimen is used. Thus, instead of a single value Kc, a whole Rcurve (or XR-curve) is required to characterize the crack-growth resistance, as illustrated in Fig. 8-2 for Mg-PSZ (Heuer et al., 1988). Such R-curve behavior was known to occur in metals, but was first detected in ceramics by Swain (1983) in connection with Mg-PSZ, and it has since been recognized to occur even in conventional nontransforming ceramics such as polycrystalline alumina (Swain, 1986; Vekinis et al., 1990). The significance of R-curve behavior for the strength-toughness relationship is illustrated in Fig. 8-3. For test configurations involving a uniform (or approximately uniform) applied tensile stress cra, the stress intensity factor K increases as the square root of crack length a, (8-2)
1
2
3/,
AC (mm)
Figure 8-2. KR-curves for Mg-PSZ, using two specimen geometries (a), (b), showing (i) an increasing resistance to crack growth over a range of several mm, which is much larger than the gain size ( « 50 (am), and (ii) a specimen dependence of the XR-curve, which is not fully understood at present (Heuer et al., 1988).
8.2 Mechanics of Toughening
< 7 n = <Jf
a
0
Crack length a
Figure 8-3. Significance of the R-curve. The strength is the value of applied stress at which crack growth becomes unstable, which corresponds to a condition of tangency between the driving force K and the crack-growth resistance KR.
where *F is a nondimensional geometrical factor, of order unity, which depends on the crack shape and specimen geometry (Lawn and Wilshaw, 1975). Under increasing load, fracture initiates at the value of aa for which K = Ko, but this initial crack growth is generally stable, that is, the crackgrowth resistance increases faster than the crack driving force (dK/da < dKR/da\ so that the applied stress needs to be further increased to maintain crack growth. The strength au corresponds to the value of cra for which crack extension becomes unstable. This occurs when A. =
(8-3 a)
iv
and dK da
dKR da
(8-3 b)
as can be seen from Fig. 8-3. In conventional fracture mechanics, the strength would simply correspond to the condition K = Kc, that is, the strength would be determined only by the toughness Kc and the relevant initial crack length a 0 , whereas R-curve behavior leads to the additional
421
condition Eq. (8-3 b) for instability, involving the gradient of the R-curve. This becomes particularly significant when the crack extension which is required for KR to increase from the initial value Ko to the critical or steady-state value Kc is comparable with, or larger than, the intrinsic flaw size. Then, unstable fracture may occur for K closer to Ko than to Kc, so that the steady-state toughness may be largely irrelevant to the unnotched strength. In spite of this, Kc (rather than Ko) is conventionally quoted as the fracture toughness for ceramics exhibiting R-curve behavior, and although this convention will be followed in later sections, it should be appreciated that this steady-state toughness may not control the strength. To determine the R-curve experimentally, it is necessary to ensure stable, quasistatic cracking, and it is therefore desirable to use specimens where K is a decreasing function of crack length a, under the experimental loading conditions. To ensure a decreasing K with increasing a, one needs to consider the specimen's compliance relative to that of the loading device. A long initial crack will generally ensure a relatively compliant specimen, compared with the loading device, thereby approximating more closely to a displacement-conrolled test, which favors stability. It is noted that, in general, there will be two distinct R-curves (Rose and Swain, 1986), corresponding to the incremental work of fracture Gc and to the stress intensity factor KR. The usual relation, Eq. (8-1 a), holds between the steady-state values of Gc and KR, but not (in general) for the transient phase of the R-curve (Rose, 1987 a). Experimental measurements of R-curves are now almost exclusively XR-curves, because KR is usually easier to determine in practice, at least if the current crack length can be measured independently during crack exten-
422
8 Toughening Mechanisms in Ceramic Systems
sion, for example, with a traveling microscope, as opposed to methods based on monitoring the specimen's compliance. It should be noted, however, that there can be some uncertainty in locating accurately the crack tip, especially in ceramics with grain bridging, which will contribute to uncertainty in crack-length measurement, and hence in the KR-curve. It has been implicitly assumed that the R-curve determined by starting from a long initial crack represents a material property, which should therefore be independent of the initial crack length and the specimen geometry. However, there is increasing evidence of a dependence on specimen geometry, as illustrated in Fig. 8-2 for Mg-PSZ. These observations are not yet fully understood and raise the question of
Figure 8-4. The tensile surface of a Ce-TZP specimen loaded in flexure, showing the localization of deformation into bands normal to the principal stress direction (Hannink and Swain, 1989).
what should be regarded as the true material property. A plausible pragmatic approach is indicated below in Sec. 8.2.2. 8.2.2 Phenomenology of Deformation and Fracture
Toughening mechanisms can be expected to impart a degree of ductility to a material. In ceramics, however, this ductility is almost invariably associated with a strain-softening response. This leads to a tendency for the inelastic strain to become localized into deformation bands, as shown in Fig. 8-4 for Ce-TZP (Hannink and Swain, 1989). Consequently, the nominal failure strain based on the overall deformation may not constitute a useful measure of ductility. A more appropriate characterization would involve determining the stress-displacement relation across a deformation band, as illustrated in Fig. 8-5. In deriving this relation from a tensile test, or a bend test, it is necessary to take into account the relevant gage length of elastically deforming material outside the band, as well as the compliance of the loading device. This compliance can be simulated by a linear spring, whose contribution A* to the overall load-point displacement A is given by A* = AE
e=A/L
(b)
(0
(8-4)
Figure 8-5. Illustrating the relation between the stressstrain curve and the stressdisplacement curve across a deformation band. The influence on stability of gage length and machine stiffness are discussed in the text.
8.2 Mechanics of Toughening
where the load P is normalized with respect to the material's Young's modulus £, and cross-sectional area A, so that the machine compliance X has dimensions of length. Assuming that only one deformation band forms within the gage length L, the displacement across that band is given by 5=A
——
(8-5)
The relation between the stress-strain curve and the stress-displacement curve for the tensile-test configuration of Fig. 85 a can be clearly illustrated by assuming a piecewise linear response, as shown in Fig. 8-5 b, c. The nominal strain is given by A/L, if one ignores the contribution due to machine compliance, so that Fig. 8-5 b represents in effect the observed stress-strain curve. The softening portion of the deformation can be continuously monitored under load-point-displacement control only if < Or — da T~i
C
U
(o-u) V
'
Otherwise, the deformation would proceed unstably to failure once A reaches Ao, and
423
the stress-strain curve would terminate abruptly at A 0 in the manner characteristic of brittle failure. The significance of this observation is that the area under the o-d curve represents the work of transformation, and the softening range can make a significant, or even dominant, contribution to the total work, depending on the relative values of <5C and <50. The region ahead of a crack in a transformable ceramic functions in effect like a (5-controlled testing configuration which can probe the whole a-5 curve, whereas a tensile test will generally reveal only the nonsoftening portion of the response, unless the condition in Eq. (8-6) is satisfied. The tendency for strain localization which is clearly evident in Fig. 8-4 for Ce-TZP, can also be discerned in the surface-deformation patterns for Mg-PSZ under increasing tensile stress, as shown in Fig. 8-6 (Marshall and Swain, 1988). This strain localization has important implications for the characterization of transformation plasticity in ceramics. In particular, transformation parameters determined under uniaxial compression with a confining pressure, which results in a
Figure 8-6. Surface-deformation patterns for Mg-PSZ under increasing tensile stress, showing the tendency to localization into a deformation band. (A) 395 MPa, (B) 400 MPa, (C) 406 MPa. (Marshall and Swain, 1988.)
424
8 Toughening Mechanisms in Ceramic Systems
macroscopically homogeneous deformation (Chen and Reyes-Morel, 1986), may not extrapolate smoothly to tension dominated stress states, where the deformation tends to localize into bands. An analogous situation arises with glassy polymers, for which the yield locus has been found to exhibit two distinct branches corresponding to shear yielding in compression and to crazing in tension (Sternstein, 1977). The process of matrix cracking during tensile loading of ceramic-matrix composites provides a useful paradigm for dealing with localized deformation bands. The sequence of events is illustrated in Fig. 8-7 (Marshall et al., 1985). Matrix cracks propagate at a characteristic stress crM, and the density of these cracks saturates at a spacing approximately equal to twice the load-transfer length for load transfer from matrix to fibers. Each individual matrix crack, bridged by fibers, can be regarded as a deformation band whose behavior can be characterized by a o-5 curve, 8 denoting the crack opening. On the other hand, with a fixed spacing s between matrix cracks in the saturated state, the overall deformation can be characterized by a strain, which implicitly smears
the deformation uniformly over the gage length L (assumed > s). Thus, the response is adequately described by a stress-strain curve provided the relevant gage length greatly exceeds the saturation spacing s of matrix cracks. Finally, beyond the peak stress, which is determined by the fiberbundle strength, the material begins to separate into two halves under a decreasing stress, with broken fibers pulling out of the matrix blocks. Most of this pullout tends to occur across one matrix crack, so that a a-8 curve is again the appropriate characterization for the deformation in this softening range, which coincides with strain localization across one active matrix crack. 8.2.3 Transformation Toughening
There has been a considerable amount of theoretical modeling of transformation toughening in ceramics over the past decade. The principal results and underlying assumptions are summarized in this section. The main assumptions are the following: (i) The inelastic deformation around a crack tip can be homogenized, as indicated schematically in Fig. 8-8, and
Figure 8-7. Typical stress-strain curve for a fiber-reinforced ceramic-matrix composite, illustrating the localization of deformation into matrix cracks bridged by fibers.
8.2 Mechanics of Toughening
425
(iii) Crack extension is characterized by Kiip = K0
Figure 8-8. Schematic representation of a transformed zone, (a) Initial zone around starter notch, prior to crack extension, (b) Transient zone, leading to Rcurve behavior, (c) Steady-state zone (h <^a — a0).
characterized by a stress-free transformation strain / £T, where / denotes the volume fraction of transformed material, which can vary with position within the transformed zone, and £T denotes the effective transformation strain. It is emphasized that £T differs from the crystallographic (Bain) strain, because of twinning and the formation of selfaccommodating variants which substantially reduce the shear component of the net transformation strain, but not the dilatational component which remains at approximately 4% for the tetragonal to monoclinic transformation in zirconia. In fact, most theoretical work to date has assumed that £T is purely dilatational, *? = e]j = j5lJ
(8-7)
where 9T denotes the dilation strain ( « 4%) and dtj the Kronecker delta, (ii) The crack tip is characterized by a local stress intensity factor K tip , which will in general differ from the nominal (or far-field) stress intensity factor K^, due to the shielding provided by the transformed zone.
(8-8)
where Ko is regarded as the fracture resistance in the absence of any contribution from the transformation or other processes. This is independent of the current shape or size of the transformed zone and of the crack extension. In earlier work (McMeeking and Evans, 1982), Ko was taken to represent the toughness of fully transformed (overaged) material, to allow for the increased tortuosity of the crack path which accompanies transformation. More recently, the pragmatic choice has been simply to equate Ko to the initiation toughness determined experimentally (cf. Fig. 8-2). Let KR(Aa) denote the toughness (i.e., the value of the nominal stress intensity factor) after a crack extension Aa, starting from an initial saw cut simulating a sharp starter crack, and let AK(Aa) denote the toughness increment due to transformation, KR(Aa) =
AK(Aa)
(8-9)
The main theoretical results which have been derived to date can be summarized as follows: (i) The initial zone in Fig. 8-8 a provides no shielding, AK(Aa = 0) =
(8-10)
This result has been rigorously established for purely dilatational transformation (Budiansky et al., 1983), but it is likely to apply generally, at least as a first approximation (Lambropoulos, 1986), justifying the interpretation of Ko as the initiation toughness, (ii) KR approaches the steady-state value Kc over a crack extension comparable with the steady-state zone height h de-
426
8 Toughening Mechanisms in Ceramic Systems
fined in Fig. 8-8 c, (McMeeking and Evans, 1982; Stump and Budiansky, 1989), R
K (Aa>3h)^Kc
(8-11)
It is noted that experimental R-curves in Mg-PSZ generally extend over much larger distances than the observed zone height, indicating that the development of the transformed zone is not the only contribution to the Rcurve; crack bridging is also likely to contribute significantly, (iii) The steady-state zone height h for purely dilatational transformation occurring at a critical hydrostatic stress oc can be expressed in terms of the initial toughness Ko as follows (Rose, 1986 b),
_p£±£EoJ (l+v)EfBT
"•-Tor^r
(8-12 a)
<8 12b)
-
where N is a numerical factor whose value increases from 0.21 for oc > a*,
is (McMeeking and Evans, 1982) (8-13)
h = 0.21
(iv) The steady-state toughness increment can be expressed in terms of h as follows (McMeeking and Evans, 1982; Rose, 1987 a), EfdT 1+v M
= 0.21M + 1 . 0 7 - )
(8-14a) (8-14b)
where S/D denotes the ratio of the shear to the dilatational component of the (two-dimensional) transformation strain, the shear plane being assumed to be inclined at 45° to the crack plane. Experimental observations on MgPSZ and Y-TZP follow the relation in Eq. (8-14 a), as shown in Fig. 8-9, but with different slopes, which can be interpreted as indicating that different values of S/D are appropriate in Eq. (8-14 b): S/Dxl for Mg-PSZ and S/ D ^ 0 for Y-TZP (Rose, 1987 a).
Figure 8-9. Relation between steady-state toughness and zone size in two transformation-toughened ceramics (Swain and Rose, 1986).
8.2 Mechanics of Toughening
There has been considerable discussion about the correct theoretical value of M, which depends on the shape of the zone front (Evans and Cannon, 1986; Chen and Reyes-Morel, 1986; Lambropoulos, 1986; Chen, 1991). This shape in turn depends on the transformation criterion, which will be discussed in the next subsection. It is noted here that the transformation zones observed in Ce-TZP (Fig. 8-10) are strikingly different from any of the theoretical zones considered so far, and are suggestive of strain localization into deformation bands (Rose and Swain, 1988). However, the relation in Eq. (8-14 a) still holds for Ce-TZP (Yu and Shetty, 1989), albeit with M ^ 0 . 1 4 , much lower than the value for Mg-PSZ (M « 0.45) or for Y-TZP (M « 0.22). (v) The preceding results also hold for two-phase materials, such as zirconiatoughened alumina, provided that £, v are interpreted as the effective elastic constants of the two-phase material, and the dilatation 9T is replaced by 3(l-v)6> T
427
where x{ denotes the bulk modulus of the transforming phase (Rose, 1987 a; Karihaloo, 1991). Transformation in these materials is generally accompanied by microcracking (Ruhle et al., 1987;Lutzetal, 1991). The toughening due to stress-induced transformation could alternatively be characterized from an energy viewpoint as an increase in the work of failure due to the additional work of transformation, and indeed this would appear to be a much simpler approach than that based on stress analysis (Evans and Heuer, 1980; Kreher and Pompe, 1981). However, a rigorous discussion of that approach involves many subtleties which are not easily summarized (Budiansky et al., 1983; Rose, 1987 a). It is also noted that microcracking could be regarded as an energy-dissipative mechanism, analogous to transformation. Once again, a rigorous analysis is not simple (Hutchinson, 1987), although simple estimates can be formulated for the steadystate toughening which may be sufficiently accurate in practice (Kreher and Pompe, 1984). In particular, for transformation toughening, GC=GO + Wt
(8-15 a) (8-15 b)
E
where Wt represents the work of transformation per unit area of fracture surface, given by /GO
Figure 8-10. The elongated transformed zone in Ce-TZP, suggestive of strain localization (Rose and Swain, 1988).
ae(f)ej}fdf
(8-15c)
where ac (/) denotes the critical stress for transformation, which depends on the volume fraction already transformed /, which in turn varies with distance y from the fracture plane.
428
8 Toughening Mechanisms in Ceramic Systems
Using the standard notation
8.2.3.1 Transformation Criterion A definitive analysis of the energy changes which accompany a phase transformation was given by Eshelby (1957, 1961). The most important term, from the viewpoint of formulating a suitable criterion for stress-induced transformation, is the interaction-energy density CT£T, where 0 is the prevailing stress (due to both external loads and to internal sources of stress, such as already transformed material). This term constitutes the principal difference between the energy changes for a stress-induced transformation, as opposed to one which occurs spontaneously in the absence of an external stress. Consequently, a natural choice for the transformation criterion (Evans and Heuer, 1980; Rose, 1987 a) is that transformation occurs when a £T reaches a critical value Qc = QC
(8-16)
where Qc depends primarily on the volume fraction transformed, the testing temperature, the processing history, and microstructural parameters such as the grain size, as further discussed in Sec. 8.3. For the purposes of this subsection, however, Qc can be regarded as a material constant. An alternative criterion has been formulated by Chen and Reyes-Morel (1986) on the basis of their experimental measurements involving uniaxial compression under a confining pressure. This criterion is compatible with Eq. (8-16) if it is assumed (Sunetal, 1991) that (i) the shear component of £T aligns itself with the shear component of the prevailing stress
eTEE£T. = L ( 5 . . + eT
(8.17a)
a =aij = (jdij + sij
(8-17 b)
assumption (i) implies (8-18)
jj oc stj
so that Eq. (8-16) can be recast in the following form (Chen and Reyes-Morel, 1986; Chen, 1991) (8-19 a) 1 1
(8-19b) \1/2
(8-19 c)
where a c , TC can be interpreted as the critical stress for transformation under a state of hydrostatic tension or of pure shear, respectively. The appropriate choice for the transformation strain £T in Eq. (8-16) has been a point of contention, which is not yet fully resolved. The logical choice would seem to be that £T should denote the effective strain in an embryo of critical size, beyond which the transformation proceeds unstably (Cohen, 1972) that is, that the transformation criterion should involve the nucleation strain, which is not readily measured experimentally, rather than the macroscopic strain monitored by Chen and Reyes-Morel (1986). However, the experimental data conforms quite well to Eq. (8-19a-c), supporting the use of the macroscopic transformation strain for £T in Eq. (8-16) on pragmatic grounds. Another potentially more serious objection in the context of modeling transformation toughening is that the appropriate £T for tensile deformation bands, such as those in Fig. 8-4, may
8.2 Mechanics of Toughening
not be the same as the macroscopically homogeneous strain in compression dominated tests. Both of these issues require further work. 8.2.3.2 Approaches to Theoretical Modeling
Two principal approaches to modeling the toughening due to stress-induced transformation have been developed. The first approach attempts to develop constitutive equations to describe the nonlinear inelastic response, proceeding by analogy with metal plasticity (Budiansky et al., 1983; Lambropoulos, 1986). This approach is particularly effective for strain-hardening materials. The transformation criterion in Eq. (8-16) with Qc independent of/ corresponds to subcritical transformation, in the terminology of Budiansky et al. (1983), for which the mathematical character of the equations governing inelastic deformation is hyperbolic, rather than elliptic. This indicates a propensity for strain localization, which was noted, but not explored, by Budiansky et al. (1983). Strain localization, which has been extensively studied in the contexts of metal plasticity and geophysics (Cowie and Tuler, 1987), poses severe difficulties for developing a consistent computational approach to stress analysis, based, for example, on the finite element method, because of the possible sensitivity of the results to the discretization scheme which is used. The second approach models the transformation by a distribution of strain centers (Seyler et al., 1984; Rose, 1986 a, 1987 a), in keeping with the approach which is traditionally used in materials science, where distributed dislocations or dislocation pileups are used to model plastic deformation (Mura, 1982). This approach has several advantages: (i) The underlying material response is elastic, so that the principle of
429
superposition can be used, which greatly facilitates calculations; (ii) the strain centers can be lumped (in the manner of dislocation pile-ups) to simplify calculations, while retaining correctly the essential features, such as the scaling relations; (iii) microstructural interactions are more readily incorporated into the modeling; (iv) the kinematial aspects, that is, those relating to a specified distribution of strain centers, can be clearly separated from the dynamical aspects, which depend on the formulation of an appropriate criterion for transformation. These advantages are particularly significant in view of the uncertainties concerning the correct transformation criterion and the tendency for strain localization, which does not pose a problem here in the sense that the localization of transformation can be built into the model.
8.2.4 Crack Bridging
Crack bridging is most clearly evident in fiber or whisker reinforced ceramics, but it has now been recognized to contribute significantly to the toughness even in conventional polycrystalline ceramics such as A12O3. In the latter case, bridging is due to unbroken ligaments, or to frictional interlocking between mating crack faces, in the wake of a growing crack (Swanson et al., 1987; Vekinis et al., 1990). The toughening can be characterized from two viewpoints. From an energy viewpoint, the work of stretching the bridging ligaments to rupture, Wh, contributes additively to the total work of fracture Gc, GC = GC
Wh
(8-20)
where Go can be interpreted as an intrinsic work of fracture. For example, in a fiberreinforced brittle matrix, one would expect = (l-Ff)Gr
(8-21)
430
8 Toughening Mechanisms in Ceramic Systems
where Gm denotes the work of fracture for bulk matrix material, and Vi the fiber volume fraction. An alternative viewpoint is that the bridging ligaments or reinforcements transmit load across the crack faces, thereby reducing the stress intensity factor at the crack tip relative to the nominal value which would be expected for a given crack length in the absence of bridging, that is, the bridging ligaments shield the crack tip. The principal results which have been obtained from these two viewpoints are summarized in this section. To simplify calculations, the load transmitted by bridging ligaments or reinforcements is modeled by a distributed stress a acting across the crack faces. The relation between this transmitted stress a and the crack opening u (that is, the relative displacement between the crack faces) represents the fundamental material property characterizing the bridging, as noted earlier in Sec. 8.2.2. At any stage of the process of crack extension, such as that illustrated in Fig. 8-11 a, the nominal stress intensity factor can be expressed as follows, (8-22 a) AKh =
o
JKF(s)ah(s)ds
(8-22 b)
where Ko represents the intrinsic toughness (that is, Ktip = Ko during quasistatic crack growth), and the toughness increment AKh due to bridging can be expressed as an integral over the bridged zone K¥ (s), which represents the K due to point forces of unit strength acting at a distance s from the crack tip, as shown in Fig. 8-11 b, weighted by the bridging stress ah (s). Formulae for KF(s) have been compiled for several specimen geometries (Tada, 1985; Murakami, 1987). In general, K¥(s) will depend on configurational parameters such as the crack length a and specimen width
bridging
brokenJ ligaments
Figure 8-11. Configurations for bridged cracks showing (a) the bridged zone length / and crack opening u (x); (b) the point-force loading configuration used to calculate AKh; and (c) the contour C for evaluating the J-integral, which can be collapsed to C1.
w. This dependence can be ignored, as a first approximation, if the bridged length / is much smaller than all other relevant dimensions, such as a and w, corresponding to the idealization of small-scale-crack bridging, in which the crack is regarded as being semi-infinite. The appropriate K¥ (s) is then given by (Tada, 1985)
2 ns
(8-23)
8.2 Mechanics of Toughening
The bridged length / is necessarily less than or equal to the crack extension Aa, if it is assumed that cracking initiates from an unbridged saw cut, as in Fig. 8-11 a. Thus AiCb, and hence KR, will increase with crack extension Aa until the bridging ligaments or fibers rupture, resulting in R-curve behavior. Under conditions of small-scale bridging, continued crack growth would then proceed at a constant, steady-state value of KR, which will be denoted by Kc. This steady-state toughness Kc is related to the steady-state work of fracture Gc by the standard formula Eq. (8-1 a) -o
E,
It is emphasized that this relation between the incremental work of fracture GR and KR only holds for steady-state cracking, which can strictly be achieved only with small-scale bridging. In other cases, there is in general no simple relation between GR and KR which is satisfied exactly, although Eq. (8-1 a) may still hold within experimental error. In this connection it is pertinent to note that the Eshelby-Rice J-integral taken over a contour C surrounding the bridged zone, as in Fig. 8-11 c, can be evaluated by collapsing the contour onto the crack faces, because the integral is path independent (Rice, 1968), to obtain j (C) = ^
+
Um
f o (s) du (s)
Wh
=
J
du (s) —^ as
431 (8-25 b)
o (8-25 c) jj a (u) du On the oother hand, Eq. (8-20) holds for a fully developed bridged zone (that is, one in which the bridging ligaments have stretched to rupture), without the restriction to smallscale bridging, and Wh is still given by Eq. (8-25 c) which represents the area under the stress-displacement curve. A systematic study of crack bridging involves the following three complementary aspects. (i) The stress analysis of fully or partially bridged cracks for various specimen configurations, given the o-u relation, or "traction law". This would provide insights into the possible configuration dependence of the R-curve and the crack-size dependence of strength, (ii) Experimental determination of the traction law. (iii) Micromechanical models for predicting the traction law, especially the microstructural scaling relations for the maximum stress ou and the maximum crack opening uc or fiber stretch dc in Fig. 8-12. ucc
These three aspects are briefly discussed in the following subsections.
(8-24) 8.2.4.1 Stress Analysis of Bridged Cracks
This relation holds even when the bridged zone is not fully developed, and without restrictions on the zone length / compared with other dimensions such as a or w. However, J(C) can be strictly identified with the incremental work of fracture only for steady-state cracking, which implies translational invariance of the bridged zone during crack extension. In that case, ,GC = GO + Wb
(8-25 a)
The principal difficulty with the stress analysis for bridged cracks is that the bridging stresses are not known as a function of position along the crack. If they were, the toughness increment could be evaluated from Eq. (8-22 b). Instead, these stresses must be determined so as to be consistent with a given o-u relation, which requires in general the solution of a nonlinear integral equation (Marshall et al, 1985;
432
8 Toughening Mechanisms in Ceramic Systems
<5C 6
(a)
(b)
Figure 8-12. A schematic stress-displacement (cr-S) relation, or traction law, for crack bridging, (a) The area under the curve represents the work to rupture Wh. (b) Nonlinear elastic behavior.
Rose, 1987 b). However, exploratory studies suggest that the R-curve and residual strength are relatively insensitive to the precise shape of the a-u relation, provided that the area remains fixed. Consequently the analysis can be greatly simplified by assuming a constant bridging stress
= Wu
using the rupture work Wh and rupture stretch uc given by the actual G-~U relation of interest. The resulting model closely resembles the well-known Dugdale model (Lawn and Wilshaw, 1975), with the important difference that here Ktip #= 0. Formulae relating the zone length / to the maximum stretch wmax need to be modified accordingly. For small-scale bridging, one obtains ,fi 0 ~
nonlinear elastic springs. An important feature of such bridging can be appreciated by considering first the case of linear springs (Rose, 1987 b) for which G=-Eku
(8-28)
The spring constant k has dimensions (length)'1, so that the bridging law in Eq. (8-28) introduces a characteristic length fc"1. For a fully-bridged center crack, one finds two regimes of behavior, depending on the ratio of crack half-length a to /c"1. For na < /c"1, In a K t i p ^ a I—
(8-29 a)
that is, the bridging is ineffective in reducing Ktip for cracks which are short, compared with fe"1, whereas for na/2 > fc"1,
{6-11) _ W
max —
4 U
\
S
~
*) ~
~^t
The length lc of a fully developed zone can be determined from Eq. (8-27) by setting For cases where the bridging reinforcements can transmit the applied stress without failing, the bridging response under monotonic loading can be simulated by
(8-29 b) k that is, for long cracks, Ktip becomes independent of crack length, asymptoting to a value characteristic of an unbridged crack of half-length (nky1. This crack length (nky1 for the transition from the shortcrack to the long-crack regime can alternatively be regarded as the characteristic
8.2 Mechanics of Toughening
length introduced by bridging, instead of fc"1. However, micromechanical models of bridging lead more directly to the spring constant /c, which is related to the loadtransfer length to the reinforcement. Similar results also hold for nonlinear springs, in particular for the parabolic traction law which results from frictional sliding of bridging fibers relative to a brittle matrix (Sec. 8.2.4.3). An important application of the limiting value of Ktip for long cracks is for estimating the matrix cracking stress erM for continuous fiber-reinforced ceramic matrix composites, which for linear springs, would be given by
r
E = K™Ul-Vf)k— J
/2
(8-30)
on using Eqs. (8-29 b) and (8-21), £ m , Km denoting the Young's modulus and intrinsic toughness of the matrix phase, and E the modulus of the composite in the fiber direction. 8.2.4.2 Experimental Determination of the Traction Law
Two approaches can be used to determine the G-U relation directly. The first requires direct measurement of the crack opening within the bridged zone, coupled to the solution of an inverse problem of stress analysis to determine the transmitted stress corresponding to the observed crack profile (Cox and Marshall, 1991), Such detailed measurements and calculations have already been used extensively to characterize crazes in glassy polymers (Kramer, 1983; Doll, 1990). There are serious practical difficulties, both with achieving sufficient resolution for the experimental measurements and with numerical ill-conditioning for the inverse problem.
433
The second method, which is particularly appropriate for fiber-reinforced composites, is based on introducing a crack across the whole of the specimen's section, leaving the two halves held together by the bridging ligaments or reinforcements. This approach has been used for characterizing particulate rubber-phase toughening of epoxy (Kunz-Douglas et al, 1980) and more recently for ductile fiber toughening of intermetallics (Deve and Maloney, 1991) and model materials (Ashby et al., 1989). The influence of specimen gage length and machine compliance need to be taken into account in the design and interpretation of these experiments, as discussed earlier in connection with deformation bands (Sec. 8.2.2). A third approach relies on measuring parameters such as interfacial toughness or friction stress, which can be used in conjunction with a micromechanical model of bridging to generate the a-u relation. In particular, Marshall and Oliver (1987, 1990) have developed an indentation technique for measuring the frictional and residual stresses between fibers and matrix in ceramic-matrix composites. 8.2.4.3 Micromechanics of Bridging
The principal value of a micromechanical model is to provide insights into the influence of microstructural parameters (such as the fiber diameter or grain size, the interfacial toughness, frictional and residual stresses), which can be used to guide microstructural control of properties. Valuable insights can often be derived from little more than dimensional considerations (Bennison and Lawn, 1989; Campbell et al., 1990; Vekinis et al., 1990). The case of fiber reinforcement lends itself most readily to detailed .modeling (Marshall etal, 1985; Budiansky et al., 1986; Gao
434
8 Toughening Mechanisms in Ceramic Systems
etal, 1988; McCartney, 1987, 1989; Hutchinson and Jensen, 1990), and it can serve as a useful paradigm for other cases of bridging. Some of the more important results which have been obtained are summarized in this subsection. Figure 8-13 shows the principal features of the G-U curve for crack bridging by continuous fibers, based on a shear-lag analysis for a single fiber transferring load to a suitably constrained cylindrical sheath of matrix material (Gao et al., 1988; Hutchinson and Jensen, 1990). Debonding initiates at a bridging stress ai controlled primarily by (i) the interfacial fracture energy yi9 (ii) the volume fraction of fibers Vf, (iii) 2 r the fiber diameter, (iv) the residual stress in the matrix due to thermal expansion mismatch with the fibers. If it is assumed, for simplicity, that matrix and fibers have the same (isotropic) elastic constants E, v, so that the residual stress can be characterized by axial and radial strains sj, sj, corresponding to the integrated difference in expansion coefficients over the cooling range AT from
frictional sliding along full debond zone
the stress-free temperature, AT
6,%= J « z - a » ) d T
(8-31)
0
the following expression is obtained for o{ (Hutchinson and Jensen, 1990)
The bridging stress
VfEsJ
(8-33)
assuming that fiber breakage does not occur first (caseB in Fig. 8-13). The transmitted stress cannot increase beyond a0:
steady-state frictional sliding zero-friction zone
Figure 8-13. Stress-displacement curve for fiber bridging based on a shearlag analysis for a representative element shown inset (Hutchinson and Jensen, 1990).
8.2 Mechanics of Toughening
the displacement 3 increases under constant stress as the zone of friction-free slippage extends. It is noted that
(8-34)
and the work of pullout Wp, per unit area of fracture surface, is given by the wellknown relation (Kelly and Macmillan, 1986) Wp=Vfr0-
(8-35 a)
v = 4VfTor(f)2
(8-35 b)
where 4> = IJ(2 r) represents the aspect ratio of the pulled out length of fiber. For a fixed aspect ratio, Wp is proportional to the fiber diameter 2r. The estimates in Eqs. (834) and (8-35 a, b) can also be used for bridging by whiskers (Sec. 8.3.2) or frictionally interlocked grains (Vekinis et al., 1990), with obvious reinterpretations of / and r. For cases where the interfacial toughness y{ can be ignored (so that o{ « 0) and frictional sliding proceeds at a constant shear stress T 0 , bridging is characterized by a parabolic traction law (Budiansky et al., 1986) 2VfE (l-Vf)Em\
2r
(8-36 a)
where E{, £ m , E denote Young's modulus of fibers, matrix, and composite, respectively. This traction law has been widely used as a convenient approximation for the initial
435
rising portion of the o-b curve of Fig. 8-13. It leads to the following estimate for the matrix cracking stress ou (Budiansky et al., 1986)
' _ri2Vf2E2(Km)2EfT0T'3
°M~l
(1 -Vf)(Em)22r
(8-36 b) T J ^
J ~°T~E™
where crj denotes the axial residual stress in the matrix. Another widely used micromechanical model for crack bridging, and localized deformation bands generally, is a periodic crack array (Horii and Nemat-Nasser, 1986; Fleck, 1991). This model has been used to characterize crack-front interactions with obstacles (Jorgensen, 1990) and voids (Karihaloo et al., 1991). 8.2.5 Multiple Mechanisms From the viewpoint of microstructural control of properties, it is generally desirable to rely on more than one mechanism for strengthening or toughening. For example, transformation toughening operators over a limited temperature range, so that it needs to be combined with other mechanisms, such as whisker reinforcement, to produce a material with enhanced properties over a wider operating temperature range, as further discussed in Sec. 8.3. Indeed, in most practical materials failure involves multiple mechanisms, some of which may operate unintentionally as an unavoidable concomitant to the principal mechanisms. It is therefore of interest to consider the conditions for synergistic interaction between toughening mechanisms. The most important general consideration is the relative size of the failure zone associated with each mechanism. Consider in particular the combination of transformation toughening (Fig. 8-8) and crack bridging (Fig. 8-11), using the transformed zone height h and the bridged length / as
436
8 Toughening Mechanisms in Ceramic Systems
representative dimensions of the respective deformation and failure zones. If / <^ h, the contribution of bridging is effectively to increase the intrinsic toughness, which was denoted by Ko earlier in Sec. 8.2.3. The toughness increment due to transformation, given by Eq. (8-14 a) is proportional to y/h, which is in turn proportional to K o , compare Eq. (8-12 a). Consequently, in this limit, the contributions to the overall fracture toughness Kc are multiplicative, or synergistic (Amazigo and Budiansky, 1988 b; Riihle and Evans, 1989). On the other hand if / > h, which is more usually the case when crack bridging is deliberately introduced in the microstructural design (Sec. 8.3), the contributions to the overall work of fracture are additive: Wt + Wb
(8-37)
with Wx, Wh given by Eqs. (8-15 c) and (8-25 c), respectively. The extent of interaction in the intermediate range between these two limiting cases has been characterized by Amazigo and Budiansky (1988 b), assuming a constant bridging stress so as to simplify the calculations. It will be appreciated from the above that a distinction between intrinsic and extrinsic toughening mechanisms (Ritchie, 1988) is not absolute but depends on the length-scales of interest.
8.3 Toughening Mechanisms What can be done to enhance the fracture toughness of ceramics? First let us recognize that the number of mechanisms or processes are only limited by our imagination or creativity and our ability to understand how to fabricate the materials to optimize the resulting toughness. It is not the intent to cover all the possible toughening mechanisms but to focus on a few and ad-
dress what effect material properties and microstructural characteristics can have on the resultant toughness. In this way, one can form a basis for what needs to be modified in terms of processing and microstructure to be able to develop toughened ceramics based on current toughening mechanisms. Also one can modify microstructure and composition to optimize the material for the particular application and properties desired. Four general toughening mechanisms are considered here. One approach includes microstructural processes which lead to increased toughness associated with changes in matrix grain size and shape. Another involves reinforcement processes such as those introduced by the incorporation of whiskers, fibers, or platelets. In addition, nontransforming dispersed second phases can provide a moderate increase in the toughness of ceramics. The above toughening approaches involve similar processes and mechanisms such as crack bridging, deflection of the crack, crack pinning, microcracking, and pullout of grains and reinforcing phases. Another important approach is the incorporation of either dispersed metallic particles or a metallic binder phase with or in lieu of the above processes to provide improved toughness via plastic deformation in the metallic phase. Ceramics can also be toughened by those processes associated with the martensitic transformation in zirconia (and hafnia) alloys. These processes include the stress-induced martensitic tetragonalto-monoclinic phase transformation in the region surrounding the crack and stress-induced microcracking associated with the interaction of the crack tip stress field and the local stresses at the boundary of a transformed monoclinic particle. Examples of the toughening effects related to many of these processes re illustrated in
437
8.3 Toughening Mechanisms
Table 8-1. Room temperature fracture toughness values for various ceramic materials. Material
Grain size (urn)
Fracture toughness (MPa y/m)
Monolithic ceramics Dense alumina:
1-2 10-12
Polycrystalline cubic zirconia Silicon nitride Silicon carbide
2-3 3
2.5-3 4.5 3 4 3.5
Transformation-toughened ceramics Alumina-8 vol.% t-ZrO2 Alumina-20 vol.% t-ZrO 2 (1 mol% Y2O3) Alumina-20 vol.% t-ZrO 2 (12mol% CeO2) Alumina-40 vol.% t-ZrO 2 (12mol% CeO2) Polycrystalline tetragonal zirconia (TZP): 12 mol% ceria 2 mol% yttria
2 6 1.5 0.5
Partially stabilized zirconia (PSZ), 9 mol% MgO, increasing precipitate size
6 8 9.5 12.3 5 15 12 7 8 to 16
Ceramics with dispersed reinforcing phases Alumina-20 vol.% SiC whiskers Silicon carbide + 25 vol.% TiC Titania-30 vol.% A12O3 platelets Alumina-15 vol.% B4C "whiskers" Silicon nitride with elongated grains: a
1-2 2.5 la 8a
8-10 6 7 7.3 6-7 10-11
Diameter.
Table 8-1. It is obvious from these results that a wide variety of approaches can be used to toughen ceramics. 8.3.1 Martensitic Transformation Toughening
There has been extensive effort devoted to understanding the various toughening mechanisms associated with the martensitic transformation in zirconia and hafnia and the factors, for example, microstructure, alloying, matrix properties, temperature, stress state, which can influence the resultant fracture toughness and related mechanical properties. The reader is re-
ferred to very extensive reviews on this area by Evans and Cannon (1986) and by Green et al. (1989) for a more detailed review of this important field. Here we will consider some of the issues influencing the fracture toughness derived from transformation toughening in the crack tip region. The amount of increased fracture resistance achieved by the initiation of this martensitic transformation in the crack tip region can be substantial. A key determinant in the martensitic transformation toughening contribution is the magnitude of the external stress required to transform the tetragonal ZrO 2 phase to the monoclinic phase. Decreasing the applied stress
438
8 Toughening Mechanisms in Ceramic Systems
o[ required to initiate the transformation results in increasing the size h of the transformation zone generated by the crack tip stress field (see Eq. (8-13) and Evans and Heuer, 1980): (8-38) where m is a constant dependent upon the stress state and Ko is the local fracture resistance at the crack tip in the absence of the transformation. Increasing the size of the zone surrounding the crack in which the transformation occurs or increasing the amount of zirconia transformed /, or both is the basis for achieving the high fracture toughness contribution from transformation toughening. Values of fracture toughness in excess of 15 MPa^/m have been measured for PSZ ceramics (Burns and Swain, 1986; Swain and Rose, 1986; Becher etal., 1987) and polycrystalline tetragonal zirconias (Ingel etal., 1984; Tsukuma and Shimada, 1985) which represent increases of at least 5-fold over that of fully cubic zirconias, see Table 8-1. Similar increases are observed in ceramics containing dispersed zirconia particles as a second phase (zirconiatoughened ceramics, ZTCs), see Table 8-1 (Evans and Cannon, 1986; Green etal., 1989; Becher, 1986). However in systems of the same composition, the observed fracture toughness can vary tremendously. Part of this results because the amount of tetragonal zirconia transformed depends on the test temperature, the amount of tetragonal phase initially present, and how readily the transformation occurs. In order to optimize the transformation-toughening contribution, we will consider the influence of microstructural and compositional features.
8.3.1.1 Transformation Thermodynamics
Thermodynamic considerations of the transformation allow one to describe the observed transformation toughening versus temperature behavior and relate such behavior to the transformation characteristics, for example, martensitic transformation start temperatures (Ms or M b for burst-type transformations) and the critical transformation stress at a given temperature (Becher et al., 1987). In dense ceramics, the matrix constrains the tetragonal precipitates, particles, or grains from undergoing the volume expansive transformation, and the energy (AUT) required for the transformation is the sum of the chemical free energy (AGlc ~*m) which is zero at To and internal strain energy (Al/j) changes: AUT = AG^ m + AU{ = AS(T - To) + AU{ (8-39 a) where AS1 ~*m (< 0) is the entropy change for the tetragonal to monoclinic phase change, Fig. 8-14. During cooling, the tetragonal to monoclinic transformation can be initiated even though no external stress is applied. Under these conditions, the transformation starts when the temperature, T, equals M s (the martensite start temperature), and AUT equals zero so that Al/j: AC/. =
(Ms
~
- To) (8-39 b)
When T > M s , AUT > 0 so that additional energy is required to transform the tetragonal phase: (Ms-T)
(8-39 c)
For stress-induced transformations, nuclei are already present and the transformation is thermodynamically assisted by the applied stress (Patel and Cohen, 1953). One
8.3 Toughening Mechanisms EMBEDDED
FREE t-»m
< o cc
/
o
Tetragonal
LU
I
s
V
T
°
Monoclinic
UJ
£ <
TEMPERATURE
i
-*-AUSE/
t-»m
AGC
Figure 8-14. The ability to transform the tetragonal phase of zirconia increases with decrease in temperature. Tetragonal zirconia particles and grains, which are prevented from transforming by the constraining effects of the surrounding matrix, transform on cooling to the martensite start temperature, M s . At temperatures above M s , an external stress supplies the strain energy to initiate the transformation. [From Becher et al. (1988 b). Reprinted by permission of the American Ceramic Society.]
source that can supply the additional energy can be the external strain energy derived from the applied stress acting on the system. The strain energy changes associated with the transformation are the dilatation (sT) and shear (y) strains which are triggered by the tensile (taken to be equal to <ja) and shear (T) stresses. The amount of external strain energy required (A[/SE) is equal to AI7T (Patel and Cohen, 1953). 8.3.1.2 Critical Transformation Stress However, the level of AC7SE and thus the magnitude of the external applied stress required to drive the transformation can be reduced by internal tensile stresses present in the materials. There are several sources of these internal stresses including thermal
439
expansion anisotropy, and transformation stresses. In the case of MgO-PSZ ceramics, internal tensile stresses are also generated by the formation of <5-phase during lowtemperature anneals (Hannink and Swain, 1983). In tetragonal phase polycrystalline zirconias, the anisotropy in crystallographic thermal expansion coefficients, aA versus a c , provide additional local thermal expansion anisotropy (TEA) tensile stress to assist the transformation of tetragonal zirconia (Schmauder and Schubert, 1986; Ruhle and Kriven, 1983; Becher and Swain, 1992). In yttria-doped tetragonal zirconias, Aa, the thermal expansion anisotropy, and the associated TEA stresses decrease with increase in yttria content [i.e., Aa becomes zero in the cubic phase (Schmauder and Schubert, 1986; Schubert, 1986; Ruhle and Kriven, 1983)]. Thus under identical test and microstructural conditions, decreasing the yttria content would increase the internal tensile stress and diminish the external stress required to transform the polycrystalline tetragonal zirconia. Internal tensile stresses will be generated in composites when the average thermal expansion coefficient of the matrix is less than that of the zirconia [e.g., the average a value of alumina is 8.2 x 10" 6 °C~ 1 versus 13.2 x K T ^ C " 1 for t-zirconia (12mol% ceria)] (Becher et al., 1992). The martensitic transformation of tetragonal ZrO 2 to the monoclinic phase can be driven by an applied tensile stress, decreasing temperature, or both. The applied tensile stress aa required to initiate the tetragonal to monoclinic transformation can be defined from Eq. (8-39 c) by equating AUT to the applied strain energy (
=
M —T !
1V1
S
A
(8-40 a)
440
8 Toughening Mechanisms in Ceramic Systems
where AS' "*m is the entropy change (— 150 kPa/K) (Becher et al., 1987) and eT is the transformation strain (see Sec. 8.2.3) for the tetragonal to monoclinic transformation. The critical transformation stress, as shown here, approaches zero as M s is increased towards T. The measured value of trj, however, will be modified in the presence of internal residual stresses ai due to thermal expansion anisotropy (e.g., t-ZrO2) or mismatch (e.g., A12O3 vs. t-ZrO 2 ). The applied stress required is reduced in the presence of a tensile o{ component (Becher and Swain, 1992): *. = tfj = (*2)o-*i
(8-40 b)
where {ol)Q is the stress required in the absence of internal tensile stresses. The anisotropy in properties (e.g., a) of t-zirconia and in the matrix (e.g., zirconiatoughened alumina, ZTA) result in nonuniform stresses and local internal stress concentrations in the zirconia grains. The shape of the zirconia grains (e.g., in ZTA) introduces re-entrant grain corners and edges which further contribute to the local stress concentrations. The associated stress concentration profiles decay with distance x from the appropriate geometric feature (e.g., grain corner) (Ruhle and Kriven, 1983; Chiu, 1977; Rao, 1991). Here we consider the thermal expansion anisotropy or mismatch aTEA as the source of o{ and the grain corner or edge as the stress concentration feature. The approximate form of the resulting tensile stress concentration profile at a grain corner is:
In case of t-zirconia, aTEA is a function of EAaAT where AT is (Tsr - T), the difference between the temperature below which stress is frozen in, Tsr, and the temperature T that the sample is cooled to. For ZTC composites, aTEA is a function of the zirconia content as well (Hsueh, 1986; Taya et al., 1990). For example, the magnitude of the internal stress in the zirconia grains embedded in an alumina matrix will increase with decrease in zirconia content. In the absence of internal stress, the critical transformation stress becomes (trj)o: (aTc)0 = AS^m
(Ms
~
(8-42)
where M° is the transformation temperature in the absence of internal stress. Inserting Eqs. (8-41 a, b) and (8-42) into Eq. (8-40 b) and setting T equal to M s , the M s temperature can be defined as: (8-43 a) where f(d/x) is the description for the stress concentration, that is, Eq. (8-41 a) or (8-41 b). Therefore, M s should exhibit a grain size dependence. When the transformation initiates on cooling, AT equals (7^r — Ms) and Eq. (8-43 a) becomes:
Mc =
AS'"*"1 ^ ^
\x ^ M
(8-43 b)
i-O£f(i or M° — BT
(8-43 c)
(8-41 a) and 7: = <J TEA
In
(8-41 b)
from a grain edge where d is the zirconia grain size.
when p equals (sT E Aa/AS* "* m) / (d/x). To trigger an irreversible transformation simply by cooling the sample, the level of o{ imposed over a region 2Q in diameter within the grain must exceed the critical transformation stress. In the case where 2 Q
441
8.3 Toughening Mechanisms
and Tsr are constants, one sees that M s increases with increase in zirconia grain size because the internal stress scales with grain size (Becher and Swain, 1992; Becher et al., 1992; Chiu, 1977; Rao, 1991). In addition, increases in the magnitude of internal stress brought about primarily by changes in composition (e.g., increase in alumina content in ZTA) should increase the rate at which M s increases with increasing grain size, Fig. 8-15 (Becher et al, 1992). As noted by Eq. (8-40 a), increasing the M s temperature towards the test temperature, % will decrease the measured critical transformation stress. Equations (8-43 a-c) reveal that increasing the t-zirconia grain size for a given solute and zirconia content will raise the M s temperature. The continuous decrease in the measured transformation stress with increase in grain size for the polycrystalline tetragonal ZrO 2 (12 mol% CeO2) is illustrated in Fig. 8-16. In this figure, the change in the measured transformation stress with increase in grain size is compared to the transformation stress cal-
AZr0 2 (12mol% CeO2) • Al203-20vo(.%Zr02(12mol%Ce02) • Al203-A0vol.%Zr02(12mol%Ce02)
-5 300 Q_
D Calculated from [Ms-T) o Stress-strain data
5 250 in in
£ 200
k
ao
| 100 o
g 50 6 8 10 12 Grain size (pm)
U
16
Figure 8-16. The stress required to initiate the tetragonal to monoclinic transformation at 22 °C in the polycrystalline tetragonal ZrO 2 (12 mol% CeO2) ceramic decreases with increase in the grain size.
culated from Eq. (8-40 a) using the measured M s temperature for each grain size. The results indicate that the internal stress concentration model of the grain size dependent transformation behavior provides a very useful basis for microstructural design of transformation toughened materials. Thus, control of the zirconia grain size can be utilized to enhance the transformability of t-zirconia grains; the scaling of the internal tensile stresses with grain size can be a major source of the grain size effect.
300
8.3.1.3 Transformation Toughening Contribution
2
U
6
8
10
Zirconia grain size (jjm)
Figure 8-15. Predicted behavior (curves) indicates that the martensite start temperature should exhibit greater grain size sensitivity when zirconia is added to alumina, and grain size sensitivity should increase with decrease in zirconia content.
Now the related transformation toughening contribution, AKT, can be described in terms of the ability to transform the tetragonal phase. This should then provide guidelines for tailoring these materials to optimize the AKT contribution. The ability to transform the tetragonal phase increases at a selected temperature T (i.e., Ms increases towards T) and the transformation stress decreases (as shown above), the energy consumption due to the transforma-
8 Toughening Mechanisms in Ceramic Systems
442
tion AGT will increase according to (Marshall et al., 1983): AGT* = 2/£T(TJ/Z
(8-44 a)
Using Eq. (8-38) to define h, this becomes: T
T
AG * = 2fe m ^ ~ -
(8-44 b)
or by defining oJ in terms of (Ms — T), that is, Eq. (8-40 a): - T)
(8-44 c)
where AGT* is dependent on the applied stress intensity, Kl9 h the width of the transformation zone, / is the volume fraction of transforming tetragonal phase, and m equals y/3 (1 + v)2/(12n) (Evans and Heuer, 1980; see also Sec. 8.2.3). The total fracture resistance Kc is the sum of Ko, the fracture toughness of the material in the absence of the transformation, and AKT. Using these relations, the transformation toughening contribution, AKT, can be related to AGT. When AXT is very large in compari-
son to Ko (AKT>10K0\ T
AKT equals
2 1/2
[EAG /(1 - v) ] . For the case where AKT is reasonably large (i.e., AKT is 3 to 6 times Ko)9 AKT can be approximated as 0.8[£AG T /(l-v 2 )] 1 / 2 or:
T
t
m*
112
where AK * is again dependent on the applied Kj level and m* equals m/(l — v2). In order to determine the value when the transformation zone is fully developed, we must account for the crack shielding effect of AKT on the applied stress intensity to advance the crack tip. The crack tip will advance when Kx equals or exceeds the sum of Ko, the fracture resistance of the material at the crack tip (in the absence of any transformation) plus the transforma-
tion toughening component, AKT, that is, KY > Ko + AKT. Substituting this condition into Eq. (8-45) and rearrangement yields (Becher et al., 1992): AK1
Ko
(8-46)
JAT{\-col
where co equals sT (2 / m* E/AS1"" m ) 1/2 , and AT equals (Ms — T). Thus for each composition, for example, ZrO 2 content, the AKT term will increase as M s is raised towards T, the test temperature, as well as with increase in / or E.
8.3.1.4 Zirconia Ceramics
The influence of decreasing (Ms — T) on AKT can be seen for a fine-grained zirconia containing an yttria solute in Fig. 8-17. In this case the M s temperature is constant and the test temperature, T, is the variable. The included photomicrograph shows that the increase in AKT is also accompanied by an increase in the transformation zone surrounding the crack as the test temperature is decreased. A similar temperature dependence of the fracture toughness occurs in partially stabilized zirconia (PSZ ceramics exhibited a peak in the toughness versus test temperature curves. This occurs as the test temperature is decreased to just above the M s temperature for the particular PSZ ceramic. In the PSZ ceramics, the tetragonal phase is present as precipitates in a cubic phase matrix with the M s temperature increasing with increase in precipitate size. Obviously, the temperature dependence of the fracture toughness of transformation toughened ceramics must be considered in the application of such materials. One would like to tailor the ceramic so that the toughness is optimized in the temperature range of interest. This can be accomplished
8.3 Toughening Mechanisms
I
I
443
I
18 16 \
>CO
14
—
z
Q_
12 $
X
10
\
c x: O)
o
8
0 i_
3 O
co ul
—
\
>>
6 4 2
— — I
0
(a)
—
100
I
i
200 300 Temperature (K)
,\w
:
,
400
.
500
,
(b)
Figure 8-17. The fracture toughness of transformation toughened fine-grained (0.4 um) zirconia (containing 2 mol% yttria) displays a significant increase with decreasing test temperature (a) which is associated with an increase in the size of the transformation zone generated around the crack as the test temperature is decreased towards the Ms temperature (b). This zirconia also exhibits a remarkably low M s temperature <4K.
80 K rT = 9 /im
by regulating the M s temperature of the transformation-toughened ceramic so that it is below room temperature and the temperature of interest. This will maximize the amount of zirconia retained as the tetragonal phase. The M s temperature must also approach the use temperature to maximize the transformation toughening contribution; the discussion of the previous section reveals that microstructural tailoring is one approach to regulating the M s temperature as needed. When the test temperature, T, is fixed, the transformation toughening contribution for polycrystalline zirconias can be optimized by increasing the grain size, as
shown by Eq. (8-43 a-c), to increase the M s temperature such that it approaches T. The transformation toughening contribution should thus rise as the grain size is increased, for example, as shown by combining Eqs. (8-43 a-c), (8-45), and (8-46). The experimental data for polycrystalline tetragonal zirconias one containing 12 mol% ceria and the other 2 mol% yttria are in agreement with these predictions, Fig. 8-18. Thus, the analysis of the grain size dependent martensitic transformation in polycrystalline zirconias yields a basis for the microstructural design of monolithic zirconias and input to the design of composite materials.
444
8 Toughening Mechanisms in Ceramic Systems
2 U 8 Grain size (|jm)
16
Figure 8-18. The room temperature fracture toughness of TZP ceramics exhibits a strong dependence of the transformation-toughening contribution upon grain size.
As seen in Fig. 8-19, the temperature of these specific composites must be higher than 22 °C and higher than 78 K at yttria levels of 0.5 mol% and 1 mol%. This is indicated by the loss of toughness at each temperature as the yttria content of the zirconia is decreased. As prescribed by Eqs. (8-45) and (8-46), the fracture toughness of these composite systems should also increase with increase in the volume fraction of zirconia added, see Fig. 8-20 (Becher, 1986). However, the analysis specifically says that the transformation-toughening contribution increases as the volume fraction of tetragonal zirconia which transforms increases. Thus, one may observe variations in the toughness with increase in zirconia content as the zirconia can be present as either the tetrago-
8.3.1.5 Zirconia-Toughened Ceramics
As indicated earlier, other ceramics can be toughened by incorporation of tetragonal zirconia particles. Several investigators have considered such an approach to toughening alumina ceramics with fairly impressive results achieved, that is, fracture toughnesses approaching 10MPa, N /m at room temperature for aluminas containing zirconia particles with or without yttria solute (Evans and Cannon, 1986; Green et al., 1989; Becher, 1986; Garvie and Swain, 1985; Lange, 1982). The experimental observations of alumina containing 20 vol.% zirconia also reveal a decrease in fracture toughness as the test temperature is decreased from room temperature to liquid nitrogen temperature; for those composites, the M s temperature is below 78 K, Fig. 8-19. In addition, decreasing the yttria content from 3 to 1 mol% results in a greater transformation-toughening contribution at room temperature as the M s temperature is increased by reducing the yttria addition.
- 250
0
1 2 Y 2 0 3 IN ZrO2 (mol%)
3
Figure 8-19. The fracture resistance of alumina increases dramatically with the addition of zirconia particles (20 vol.%). At a given test temperature, the toughness increases with decrease in yttria content of the zirconia, i.e., as the tetragonal phase is easier to transform. However, if the yttria content is too low, much of the tetragonal phase is lost when cooling from the fabrication temperature to the test temperature. (Reprinted with permission from Becher, 1986.)
8.3 Toughening Mechanisms Alumina matrix
r=22°C
1mpl% Y2O3
-So
jl
Omol%
0
0.1 0.2 0.3 Volume fraction ZrO2
Figure 8-20. At a fixed yttria content of the zirconia, the transformation-toughening contribution in alumina-zirconia composites increases with increase in zirconia content. A maximum in the toughening effect is associated with the spontaneous transformation during postfabrication cooling with increased zirconia content. The more stable tetragonal phases those with higher yttria contents - are more resistant to such postfabrication cooling transformations but at increasing yttria content are also much less likely to transform in the crack tip stress field. (Reproduced with permission from Becher, 1986.)
nal or monoclinic phase. During processing, either more monoclinic phase or very stable (nontransforming) tetragonal phase can be produced; both of which would diminish the transformation toughening contribution. However, results do show that the toughness increases with increase in zirconia content where care is taken to control the tetragonal phase content (Becher, 1986; Becher et al, 1992). Two features that influence the ability to transform the tetragonal phase particles in these composites are the solute content of the tetragonal zirconia and the local stresses introduced by the mismatch in thermal expansion properties between the matrix and the zirconia, as discussed earlier. This latter feature is reflected in the observed maximum in the toughness with increase in zirconia content, Fig. 8-20 (Becher, 1986). As noted earlier, local tensile stresses due to thermal expansion mismatch can decrease
445
the applied stress required to initiate the transformation, for example, where the thermal expansion coefficient of the matrix is less than that of the tetragonal zirconia as in the alumina-zirconia composites. The local stresses generated in the matrix surrounding the zirconia particles begin to overlap as the particle-to-particle distance decreases, for example, as the zirconia content increases for constant particle size. Thus with increase in zirconia content, these local tensile thermal expansion mismatch stresses can become sufficient to cause spontaneous transformation of the zirconia during postfabrication cooling, decreasing the tetragonal phase content and the transformation toughening contribution. For a given solute content and particle size hence fixed critical transformation stress, this means that the toughness will go through a maximum with increase in zirconia content. The maximum toughness occurs near the volume fraction of zirconia where the local tensile stresses overlap sufficiently to initiate spontaneous transformation of a portion of the tetragonal particles, for example, zirconia-toughened alumina (Becher, 1986). The influence of increase in solute content can best be illustrated for zirconia particles containing yttria. First we should note that different solutes affect the ability to transform zirconia quite differently. For example yttria and ceria additions cause the tetragonal phase to be more stable and decrease the M s temperature while hafnia additions decrease the tetragonal stability and raise M s . Also, the relative effectiveness of solutes vary, for example, 1 mol% yttria suppresses the M s temperature far more than does 5 mol% ceria. As shown earlier (Fig. 8-15), the M s temperature increases with increase in zirconia grain size for the alumina composites containing 20 and 40 vol.% zirconia (12 mol%
446
8 Toughening Mechanisms in Ceramic Systems
ceria). However, the rate of increase in M s with increased grain size increases as the zirconia content of the composite is decreased as seen in Fig. 8-15 and predicted by Eqs. (8-43 a-c). If we simply examine the change in fracture toughness versus the M s temperature for these two composites, we would expect the composite with the greater tetragonal zirconia content to consistently exhibit the greater toughness [e.g., Eqs. (8-45) and (8-48)], see Fig. 8-21. Note however that the toughness achieved for a selected Ms temperature is obtained with a smaller-zirconia grain size in the alumina containing the lower zirconia content. Thus at a t-ZrO 2 grain size of 2 jLim, the M s about temperature of the 20 and 40 vol.% zirconia composites are about 260 K and about 150 K, respectively. Raising the grain size to approximately 3 jim increases the M s to around 260 K in the case of the 40 vol.% zirconia composite (Becher et al., 1992). One can see that simply by increasing the zirconia grain size of each composition in a controlled manner from below 0.4 jum to 1.8 jum, the fracture toughness can be increased from 4.8 to 9.7 MPa ^/m for the alumina-20 vol.% zirconia composite. Likewise increasing the zirconia grain size from about 0.6 jam to 2.8 jam resulted in raising the fracture toughness from 5.6 to 12.3 MPay/m in the alumina-40 vol.% zirconia composite. Therefore optimizing the transformation toughening contribution involves the development of a "critical" tetragonal zirconia grain size which varies with zirconia content in composites using the same matrix as well as zirconia solute content. The important issue here is to be able to optimize the toughness of these transformation-toughened ceramic monoliths and composites. It is apparent that one must keep in mind that the tetragonal phase is
a
30
AI 2 O 3 40 vol.% ZrO2(12 mol % CeC>2)
b
Zr0 2 (12mol%Ce0 2 )
c
AI 2 O 3 20 vol.% ZrO2(12 mol % CeOJ
70
110
150
|M
(a)
190
230
270
310
r| (K)
*-
• ALOo 40 vol.% Zr0 0 (12 mol c A ZrO 2 (12mol%CeO 2 ) , 20 vol.% ZrO2(12 mol % CeO2)
70
(b)
110
150 \MS~T\
190
230
270
310
(K)
Figure 8-21. Predicted transformation-toughening contribution (curves) at room temperature increases with increase in martensite start temperature, i.e., increase in tetragonal zirconia grain size (a). The observed transformation-toughening contribution exhibits a Ms temperature (and grain size) dependence similar to that predicted for the alumina-zirconia composites (b).
thermodynamically stable as the temperature is increased and thus the fracture toughness will exhibit a decrease with increase in temperature. Keeping this in mind, one can alter the ability to transform the tetragonal phase in the crack tip region and the fracture toughness by controlling the solute type and amount, the size (and
8.3 Toughening Mechanisms
447
Figure 8-22. Whisker bridging and whisker pullout are observed in the crack tip wake region of a SiC whisker reinforced alumina.
shape) of the tetragonal phase, and, in the case of composites, the matrix toughness and the mismatch in zirconia-matrix properties. 8.3.2 Reinforcement Processes There are a number of toughening processes which can be classified as part of the reinforcement approach to toughening ceramics. The name implies the use of a second phase which strengthens the matrix by carrying a portion of the applied stress, for example, as in reinforced cement which utilizes carbon steel rods as the reinforcing phase. Concrete, on the other hand, which incorporates gravel as a second phase may be reinforced or toughened by other processes. In the case of whisker-reinforced ceramics, bridging of the crack surfaces behind
the crack tip by strong whiskers imposes a closure force on the crack or a deflection of the crack tip by the whiskers or both, so that it moves out of the mode I fracture plane have been observed in the SiC whisker-reinforced aluminas (Becher et al., 1988 a; Claussen and Petzow, 1986; Becher et al., 1990; Becher, 1991). And in some instances, bridging whiskers are found to be pulled out of the matrix further behind the crack tip, Fig. 8-22. The extent of pullout, that is, the pullout length, of the whiskers is generally quite limited but still contributes to the toughness achieved. In continuous fiber-reinforced ceramics, extensive use is generally made of the fiber pullout process to attain improved fracture toughness (Evans, 1988; Marshall and Evans, 1985). While continuous fiber reinforcement will not be discussed here, various aspects of whisker bridging and pull-
448
8 Toughening Mechanisms in Ceramic Systems
out are, of course, appropriate to fiber reinforcement although the emphasis on pullout may require modifications for fiber-reinforced ceramics. For greater detail on fiber reinforcement, the reader is initially referred to earlier publications (Evans, 1988; Evans and McMeeking, 1986; Faber and Evans, 1983). Crack deflection models analyze the influence of the angular and linear displacements out of the mode I crack plane by different shaped particles using numerical analysis to define the toughness. This could be thought of as accounting for the resistance imposed by local mode II and III components of the crack and does show that geometry, for example, particle versus disk versus rod, has a significant effect as does aspect ratio consistent with experimental results (Faber and Evans, 1983). These approaches, however, do not reveal what properties of matrix, reinforcing phase, and the intervening interfaces are important. The approach to the contribution from whisker bridging analysis taken here considers the bridging effects of whiskers whose longitudinal axis are normal or near normal to the crack plane (Becher, 1990) while the real composite systems are not so highly aligned. However with the typical meandering path generally taken by the main crack through the matrix microstructure, the local crack plane may be oriented normal to a great many whiskers. One should note that the analysis obtained using the J-integral approach for whisker arrays with random texture (Krause and Fuller, 1987) arrive at the same dependence on material parameters as those predicted below. Whiskers at greater inclination to the crack plane are subject to bending stresses and act like leaf springs when they bridge the crack - a feature not addressed by current models.
8.3.2.1 Analysis of Toughening by Whisker Reinforcement
The bridging contribution to the toughness for uniaxially aligned whiskers (Becher etal, 1988 a; Becher, 1991) is: (8-47)
AKwr = Kc-K0
= [Ec(J
AJ cb )] 1/2
where Kc and Ec arc, respectively, the toughness and Young's modulus of the composite, Ko is the matrix toughness, and J m and AJcb are, respectively, the energy dissipated by extension of the crack tip in the matrix and by the crack bridging processes. One can then define in terms of the crack-opening displacement, uc, at the end of each particular zone and the bridging stress profile ah (w) within that zone: AJ c b =
\oh{u)du (8-48) o The bridging stress profile for a region where the whiskers remain intact and span the crack surfaces can be simply described as a linear increase with increase in crack opening displacement. For the present case, the maximum closure stress on the crack is defined as: ab=V(a7
(8-49)
where o™ is the tensile fracture strength of the whiskers. By equating the crack-opening displacement at the end of the bridging zone to the tensile displacement in the whisker at failure, one can define the energy dissipated by friction when intact bridging whiskers are elastically stretched while in contact with the matrix, AJfb: A/ fb =
6P,. w
31-*
(8 S0)
-
where aj, £ , r, and V{ are, respectively, the tensile strength, the Young's modulus, the radius, and the volume fraction of whiskers, and T 0 is the interfacial shear resistance. This contribution increases as more inter-
8.3 Toughening Mechanisms
facial debonding occurs to allow greater displacement for a given whisker fracture strength. The extent of interfacial debonding, /db, is defined using the analysis of Budiansky etal. (1986). Thus, a critical aspect of toughening by whisker bridging is whether or not the whisker-matrix interface debonds when the main crack tip approaches the whisker especially in the ceramic-ceramic systems where the toughness of each phase is approximately the same. The stress transferred to the whiskers increases with distance behind the crack tip, and the stress imposed on the bridging whiskers rapidly increases resulting in whisker fracture immediately behind the crack tip when no interfacial debonding occurs, Fig. 8-23. Very short elastic bridging zones are generated and measurable toughening occurs only with extremely high whisker strengths. Debonding of the interface, Fig. 8-24, occurs when the conditions are such that either the interface just ahead of the crack tip debonds or the crack tip deflects out of plane onto the interface plane. When debonding occurs, the stresses acting on the bridging whiskers is substantially reduced. The debonded length of the interface on either side of crack plane can be defined in terms of the whisker versus interface failure stresses (Hsueh and Becher, 1988) or that of the matrix (or whisker) to interface fracture energies (Budiansky et al., 1986). The bridging stress in this frictional bridging zone rises quite slowly which leads to a longer bridging zone prior to whisker fracture. Fracture of whiskers at positions away from the main crack surface can participate in the formation of a whisker pullout bridging zone and contributes additional toughening. Within the pullout zone, the bridging stress decreases as the crack-opening displacement increases behind the crack tip.
449
,- Debonded interface Crack tip
Crack opening displacement Elastic bridging
Pullout bridging cr*- Whisker failure
Distance behind crack tip X
Figure 8-23. When whisker-matrix interface debonding occurs (a), the magnitude of the bridging stress supported by the whisker is reduced, resulting in a large bridging zone length (b). Eventually the bridging stress again is sufficient to cause whiskers to fail; those failing away from the crack plane can participate in whisker pullout which further enhances the toughness. (Reproduced, with permission, from the Annual Review of Materials Science, Vol. 20. © 1990 by Annual Reviews Inc.)
Figure 8-24. Debonding-interface fracture accompanies crack propagation as observed in a SiC whiskerreinforced alumina composite.
450
8 Toughening Mechanisms in Ceramic Systems
Using the above approaches, the frictional energy dissipated by pullout of whiskers which is the most effective mechanism for dissipating energy even when the pullout lengths (/po) are only a few times the diameter of the whiskers. The pullout contribution is defined as: A/ po =
(8-51)
po
where /po is related to the debonded length of the interface and thus increases with increase in whisker diameter according to the analysis of Budiansky et al. Generally whisker-reinforced systems have moderate to high T 0 values, and thus limited pullout lengths, that is, quite different from continuous fiber-reinforced composites where T 0 values are purposely made low so that large pullout lengths are achieved. The frictional interfacial shear stress T 0 for a debonded interface will be a function of the coefficient of friction fi and the stress acting normal to the interface an (Outwater, 1956): xo = fi(jn
(8-52)
1
EO
4
-
3
-
i
The radial stress will be influenced by differential contraction induced by differences in therma expansion and elastic properties between the matrix and whisker (Angelini et al., 1987). One can calculate the magnitude of these stresses using Selsing's equations (Seising, 1961); for the alumina-SiC whisker system one finds that the radial stress acting on the interface is quite high, for example, a few hundred MPa. Using interfacial films, these stresses can be considerably reduced, for example, film must have higher thermal expansion coefficient and lower Young's modulus than alumina in this case (Hsueh et al., 1988). This latter analysis has been confirmed by X-ray studies of SiC whisker-reinforced aluminas containing uncoated and carbon coated SiC whiskers (Predecki et al., 1988). Greater toughening is predicted with increases in whisker strength, diameter, and volume content, in ease of interface debonding, and matrix thus composite Young's modulus. Experimental results, for example, Fig. 8-25, for various ceramic and glass matrix composites confirm the responses
i
i
Figure 8-25. The fracture toughness ratio (composite toughness/matrix toughness) increases with increase in SiC whisker content. Improved toughness observed in alumina, mullite, and glass matrices with addition of selected SiC whisker (radius r = 0.4 urn). (Reproduced, with permission, from the Annual Review of Materials Science, Vol. 2. © 1990 by Annual Reviews Inc.)
oQ
crfw = 10 GPa CO CO
I
r
*• 2
-
THEORY
o o — —i -
= 0.4Mm
EXP. MATRIX •
AI2O3
•
Glass
i
i
I
I
10
20
30
40
SiC WHISKER CONTENT (Volume %)
50
8.3 Toughening Mechanisms
451
Table 8-2. Toughening behavior or various whisker reinforced brittle matrix composites. Matrix
SiC whiskers (vol.%)
Fracture toughness (MPa^/m)
Reference
0 20 0
3.0-3.2 5.3 5
Becher et al. (1990)
30
7.5-8
Glass-ceramic Alumina
0 20 0 20 25 0
5.3 8.2 0.8 2.0-2.5 4.5 3
2 um grain size
20
8.5
Mullite:
0 20
2 4.7
20 20 0 20
7-8 10-11 6 8 to > 13
B4C Si 3 N 4 :
MoSi2 Glass
Mullite-20 vol.% ZrO 2 : m-ZrO2 t-ZrO 2 Zirconia-toughened alumina:
predicted by the whisker-bridging model. In fact, whisker reinforcement has been applied to a wide variety of ceramics; a portion of these are listed in Table 8-2. 8.3.2.2 Whisker Characteristics
From Eq. (8-50), it is obvious that high whisker tensile strengths impart significant toughness to the matrix at modest whisker contents. As expected from brittle-fracture behavior, internal (Nutt, 1985) and surface defects can degrade the whisker strengths. Large surface steps are also observed on some SiC whiskers. As described by Marsh (1963), surface steps or offsets can act as stress concentrators which reduce the tensile strength achieved; the magnitude of the reduction depends upon the inclination and height of the surface step and the radius at
Shaleketal. (1986) Buljan etal. (1987) Shaleketal. (1986) Buljanetal. (1987) Gac and Petrovic (1985) Gac and Petrovic (1985) Becher etal. (1988a) Becher etal. (1988a) Gadkaree and Chyung (1986) Becher etal. (1988a) Wei and Becher (1985) Becher etal. (1988a) Wei and Becher (1985) Becher and Tiegs (1987) Becher and Tiegs (1987) Becher Becher Claussen Claussen
and and and and
Tiegs (1987) Tiegs (1987) Petzow (1986) Petzow (1986)
the apex of the step (Marsh, 1963). When such defects can be minimized, very high strengths can be achieved as evidenced by average tensile strengths of approximately 8GPa and 16GPa obtained with long (> 10 mm) (Petrovic et al., 1985) and short ( < 5 m m ) (Petrovic and Hoover, 1987) 5 micrometer diameter SiC whiskers. Finally as predicted in Eqs. (8-50) and (8-51), the toughness contribution of whisker reinforcement should increase with increase in whisker diameter. Experimental measurements of fracture toughness of alumina - composites with 20 vol.% SiC whiskers - show that the toughness increased from approximately 6.5 to about 9 to about ^ M P a ^ / m for increases in mean diameter of the SiC whiskers from 0.4 to 0.75 to 1 -1.5 jam, respectively. However, mismatch in thermal expansion coef-
452
8 Toughening Mechanisms in Ceramic Systems
ficients and elastic properties between this whisker and matrix system introduces hoop and axial tensile stresses (Angelini et al., 1987) which can lead to cracking and loss of mechanical integrity with increasing whisker diameter. Therefore one must balance the expected gain in toughness for a given whisker-matrix combination accrued from increasing the whisker diameter with the effects of local stresses generated by mismatch in properties. 8.3.2.3 Interfacial Characteristics
Increasing the ratio of the whisker to interface fracture conditions [either yw/y1 or 0f7TDB (TDB i s ^ e interface strength)] also increases the extent of interface debonding and whisker pullout for a given whisker diameter. In the alumina composites containing SiC whiskers of a selected diameter, the greatest toughening effect was associated with the largest pullout lengths (/po) which were about 3-5 times the whisker radius (Becher etal., 1988 a). The Zpo and toughness values were sensitive to surface treatments given the whiskers prior to incorporating them into the composites. 8.3.3 Microstructural Tailoring
Observations show that the fracture toughness of ceramics can be influenced by microstructure, especially in noncubic ceramics, that is, aluminas (Rice and Freiman, 1981; Mussler etal., 1982; Claussen etal., 1982; Steinbrech etal., 1983; Knehans and Steinbrech, 1982). Such behavior has been attributed to microcrack generation in the crack tip region due to the interaction of the crack tip stresses and the tensile TEA stresses generated at grain boundaries due to differential crystallographic thermal contraction, the compressive TEA stresses which locally inhibit fracture to form bridging grains in the
wake of the crack tip, or combinations of these (Rice and Freiman, 1981; Swain, 1986; Swanson et al., 1987; Mai and Lawn, 1987; Wu et al., 1978). It is very likely that all these mechanisms are interrelated, for example, crack tip microcracking and local TEA compressive stresses lead to the formation of bridging grains in the crack tip wake. Most observations on grain size effects have related the occurrence of microcracking due to local residual stress intensity factors which are the product of the magnitude of the local TEA stress and the square root of the grain size (Evans and Clarke, 1980; Fu and Evans, 1982). Other studies also indicate that increased toughness in silicon nitride ceramics can be obtained by the formation of elongated grain structures (Lange, 1979). This can be understood by noting the similarity of the toughening from elongated grains with that derived from whisker reinforcement. Thus there appear to be several ways to tailor microstructure to achieve improved fracture toughness. 8.3.3.1 Matrix Bridging: Grain Size Effects
Here grain size effects on toughness are considered for the case where bridges are formed by matrix grains which are left intact behind the crack tip. Such bridges may form due to crack branching, microcracking, compressive grain boundary stresses, or combinations of these effects. The bridging stress versus the crack opening response utilized in this discussion is that where the maximum crack opening at the end of the grain bridging zone depends on the matrix grain size. In fact, the bridging component considered is simply the frictional pullout of these grains. The bridging stress is the product of the frictional shear stress t gb supported by the fracture surfaces as the grain is pulled out times the fraction
453
8.3 Toughening Mechanisms
of bridging grains Fgb. The energy contribution of the pullout of these grains can be defined through Eqs. (8-48) and (8-51) by relating the pullout length to the grain size. For the convenience of our discussion, we assume that the grain pullout length is one half the grain size d so that the maximum crack opening displacement wmax equals d/2, the energy dissipated by this process then is: ~
(8-53)
and the grain bridging toughening contribution - square root of the matrix grain size - is predicted (Becher et al., 1990). The fracture resistance Km of the matrix will then include the energy to rupture the lattice, J o , and the grain bridging contribution, AJgb: Km =
r£m ^
+
A J gb )] 1/2
(8-54)
where Em is the Young's modulus of the matrix. The Jo term is akin to the average fracture toughness value of the various crystallographic fracture planes. Indeed, one observes that the fracture toughness of alumina ceramics determined for large crack extensions increases with increasing grain size (Rice et al., 1981). A maximum is achieved due to extensive microcracking and crack linkage which diminishes the toughness above a critical grain size. Furthermore, R-curve behavior accompanies the increase in toughness due to the grain size effects (Steinbrech et al., 1983; Knehans and Steinbrech, 1982; Swain, 1986). The observations are consistent with the grain-bridging processes described above, and the fracture toughness of aluminas exhibits the predicted yjd dependence, Fig. 8-26.
1.0
2.0
3.0
U.O
5.0
Figure 8-26. Alumina ceramics and SiC whisker-reinforced aluminia exhibit greater fracture resistance with increase in matrix grain size d. Data from Becher et al. (1989). (Reproduced, with permission, from the Annual Review of Materials Science, Vol. 20. © 1990 by Annual Reviews Inc.)
8.3.3.2 Matrix Bridging: Influence of Grain Geometry
Studies of the approaches to develop more thermal shock resistant alumina ceramics revealed that the growth of platelike alumina grains in a medium sized (5-10 jam) equiaxed grained matrix yielded significant toughening (Tiegs and Becher, 1985). Fracture toughness values of 7 to 8 MPa y/m were achieved for samples containing about 25 vol.% large (up to 100300 (im wide times up to 10-30 jim thick) single crystal alumina plates. The cracks were found to be deflected along the interface between the matrix and the large platelike grains. Thus fracture around the platelike grains produces crack bridges which contribute to the toughness. While the strengths of the aluminas with such large platelike grains is reduced as they act as large flaws, these composite microstructures led to much increased thermal shock resistance. Aluminas with similar equiaxed grain sizes but without these platelike grains had toughness values of 4 to 4.5 M P a J m while very fine grained
454
8 Toughening Mechanisms in Ceramic Systems
(1-2 jim) equiaxed aluminas exhibit values below 3 MPa^/m. On a similar note, the fracture resistance of both Si 3 N 4 and SiAlON (Lewis, 1981) ceramis has been found to be substantially improved by the in situ growth of whiskerlike grains. This approach has proven to be a potent toughening process leading to fracture toughness values of Kc > lOMPa^/m (Lange, 1979; Li and Yamanis, 1989; Himsolt etal., 1979). At the same time, quite high fracture strengths (> 700 MPa) can be achieved in these materials by controlling the elongated grain dimensions. One then has whiskerlike grains which reinforce the matrix while not introducing large area defects. It should be noted that the increase in fracture toughness of these nitride ceramics is consistent with the response predicted for and observed in whisker reinforced ceramics, Eqs. (8-39 a-c), (8-47), and (8-51) (Becher, 1990). The observations indicate that the fracture resistance increases with volume content (Lange, 1979; Himsolt et al., 1979) and grain dimensions. In fact, recent results illustrate that the fracture toughness of silicon nitride containing elongated grains increases as the square root of the elongated grain diameter (Kawashima et al.? 1991). This is comparable to the increase in toughness predicted for increase in ^/whisker diameter, Eqs. (8-47), (8-50), and (8-51). The similarity in toughening response is not surprising as the fracture process in both of these classes of ceramics involve bridging of the crack surfaces by the reinforcing phase, for example, either whiskers or elongated grains, Fig. 8-27. 8.3.4 Coupled Toughening Responses
There is considerable interest in combining various toughening processes to ex-
(a)
u 12 -.10 o
•_ Si 3 N 4 + (2wt%AI°3 2 + 5 wt% Y2
L A
2 ': 0 (b)
0.5
1 2.5 1.5 [Grain diameter (pm)] 1/2
3.5
Figure 8-27. (a) Observations of the fracture path in micro structurally toughened silicon nitride ceramics reveal that the elongated grains bridge the crack much like whiskers do in reinforcement ceramics. [Reproduced, with permission, from Li and Yamanis (1989).] (b) The fracture toughness increases as the square root of the elongated grain diameter increases, as predicted for crack bridging toughness processes.
plore means to further enhance the fracture resistance of ceramic systems. In this section, only two of the many possible combinations will be addressed: whisker reinforcement and transformation toughening and whisker reinforcement and matrix microstructural-grain size effects.
8.3 Toughening Mechanisms
8.3.4.1 Whisker Reinforcement Transformation Toughening
trix toughness:
The fracture toughness of zirconia toughened composites, Kc, can be described by Kc = K
(8-55)
where Km is the matrix toughness, AKT is the contribution associated with the transformation of tetragonal ZrO 2 particles. This latter term can be defined by Eqs. (8-44 a-c), that is AKjc is proportional to AGT and hence h1/2. The size of the maximum transformation zone, /i, is a function of the ratio of the matrix toughness, Km, to the critical transformation stress, defined by Eq. (8-38). Combining these equations, one obtains:
ABll2fEc{sT)2
v
o
455
(8-56)
which indicates a strong dependence of the composite toughness upon the matrix toughness. Equation (8-56) shows that the composite toughness is significantly raised by increasing the matrix toughness as an increase in both toughness components on the right hand side of Eq. (8-56) results (Becher and Tiegs, 1987). Microcrack toughening can be associated with the presence of monoclinic ZrO 2 particles and toughness may be achieved by microcracks which are introduced by the transformation or introduced during postfabrication cooling AKUC', or those initiated by the combination of the m-ZrO 2 particle stresses and the crack tip stress AKUC. If only pre-existing microcracks contribute, then the toughness should be the sum of AXUC' and Km. On the other hand, toughness from stress-induced microcracking will also increase as the microcracked zone the main crack increases in size. The zone size, ruc, again depending on the ma-
(8-57)
2<7" c
where
1
1
1 1—
Transformation toughening Mullite 20vol% SiCw+ 20vol% ZrO2
10 20 30 1*0 Second phase content (vol%)
50
Figure 8-28. Greater fracture resistance can be achieved via coupled toughening effects - combining whisker reinforcement with zirconia toughening in a ceramic matrix. Whisker reinforcement and either microcrack toughening or transformation toughening associated with the dispersed zirconia particles were combined to raise the toughness of mullite by > 5-fold and > 3fold respectively (Becher and Tiegs, 1987). (Reprinted by permission of the American Ceramic Society.)
456
8 Toughening Mechanisms in Ceramic Systems
zirconia is approximately 1.5 as tough as the mullite matrix. The inclusion of 20 vol.% m-ZrO 2 particles to a mullite20 vol. % SiC whisker composite yields a toughness which is about 3.5-fold greater than the matrix. As noted in Fig. 8-28, these effects - whisker reinforcement, zirconia toughening, and their combined effects - appear to be additive. On the other hand, when the zirconia particles are in the tetragonal phase in a condition, for example, at a test temperature just above their M s temperature, the result of the combined toughening processes is greater than a simple additive effect, Fig. 8-28. Similar coupled toughening effects have been described by Claussen and Petzow (1986). One can see from the earlier discussion of transformation-toughened ceramics that (1) the toughness of the above composite will be a function of temperature when transformation toughening is initiated and (2) the degree of the transformation-toughening contribution will be determined, at least, by the alloy content, volume content, and size of the transformable zirconia particles. The latter factors also indicate that processing of such composites requires careful selection of compositions and advanced processing technology to achieve the desired microstructures. However, it is clear that a multiple toughening mechanism approach provides a means of obtaining substantial further increases in fracture resistance. 8.3.4.2 Whisker Reinforcement Matrix Grain Bridging
As discussed earlier, the fracture resistance of ceramics, especially, noncubic ceramics, will increase with increase in the grain size as a result of grain bridging in the wake of the crack tip. In addition, altering the matrix grain size to form whisker-
like grains can result in improved toughness due to bridging effects which are similar to those derived from whisker reinforcement. Thus the overall fracture toughness of the composite can also be influenced by the intrinsic matrix toughness, the microstructural component of the matrix toughness, especially in the case of noncubic matrices, and the whisker reinforcement contribution (Becher et al., 1991). These mechanisms may be simply additive in which case the overall composite toughness Kc will be: Kc = Km + AKgh = m
gb
= [E (J0 + AJ )]
(8-58) 1/2
c
cb 1/2
+ {E AJ )
where A J gb is the energy dissipated by matrix grain bridging, Eq. (8-53). Substitution of Eq. (8-53) into Eq. (8-58) shows that toughness of whisker-reinforced composites (also fiber-reinforced and other types of composites) with polycrystalline noncubic brittle matrices will increase with increase in matrix grain size. Experimental results for SiC whisker reinforced aluminas having various whisker contents and matrix grain sizes are in agreement with the grain size dependent toughness predicted by Eq. (8-58), Fig. 8-26. Note that these data are for samples fabricated using the sample whisker source and size. These results again illustrate how one aspect of matrix microstructure can be manipulated to enhance the fracture toughness of a composite by utilization of multiple toughening mechanisms and point to the need to control microstructure.
8.4 Summary The fracture resistance of ceramic systems can be substantially improved by a number of different approaches, and these can be combined to obtain additional
8.4 Summary
toughening effects. The successful application of these various approaches demands that attention be paid to the influence of microstructure and the chemical composition on the toughening response and how the response may be modified by the temperatures that the ceramic is exposed to. The text here has obviously not exhausted all the possible toughening mechanisms but has chosen instead to examine those of transformation toughening, whisker and related reinforcement approaches such as matrix grain size and shape, and the combined effects of these. An obvious omission which is quite similar to the above reinforcement processes is the introduction of equiaxed or platelike second phase particles or both. Dispersions of equiaxed TiC particles and TiB 2 particles can substantially increase the fracture toughness of SiC ceramics. The introduction of platelike grains has been shown to increase the toughness of alumina and recent results show that the incorporation of SiC platelets into an alumina matrix can also result in increasing the fracture resistance. These processes result in toughening behavior and fracture path characteristics which are quite similar to those for whisker and grain reinforcement effects. In the case of the use of equiaxed particles, especially for those with differing thermal expansion and mechanical properties from those of the matrix, several approaches have been proposed to describe the toughening effects. These include crack deflection, crack pinning, and crack branching and bridging. The local stresses introduced by expansion mismatch in the vicinity of second phase particles could also arrest or divert the main crack locally leading to the formation of a bridging matrix ligament. Additional attention is needed here to develop a more comprehensive model which relates mate-
457
rial properties and microstructure to the toughening response. The behavior of transforming toughening zirconias are quite well described by the existing models. Keeping account of the influence of size of the tetragonal phase particles or grains and of the solute, one can realistically design toughening zirconias. Further insight into the alloying behavior of these systems, for example, what solute characteristics influence the strength of its stabilizing effect, would be of great benefit. In the case of toughening approaches as relates to zirconia toughened ceramic composites, one can draw on the knowledge of the transformation-toughened zirconias. However, one must account for the effects of the mismatch in matrix versus zirconia particle properties and resultant local stresses on the ability to transform the tetragonal phase particles. One can ascertain how these stresses might overlap and change with increase in zirconia particle content and how this influences the transformation. While we can suggest how particle size and possible size distribution will modify the ease of transforming tetragonal zirconia particles in a ceramic matrix, this and the influence on toughness need to be systematically explored experimentally. These and matrix microstructure effects are seen as critical factors in the variability in the fracture toughness often observed in zirconiatoughened ceramics. Progress in the area of reinforced ceramics is providing a wealth of new insights into the toughening of ceramic systems. The advances in the theoretical description of the toughening response in whisker- and fiber-reinforcement ceramics provide details of how to begin to design tougher materials and directions where more insight is needed, for example, interfacial property-structure relationships. These
458
8 Toughening Mechanisms in Ceramic Systems
two systems, whisker versus fiber reinforced, cover a range of systems - those based on very weak interfaces to those utilizing quite strong interfaces and those in between - which only strengthens the need to understand interfacial phenomena and their effects on fracture resistance. In addition, the models for whisker reinforcement point to a need to develop techniques to synthesize whiskers where size and strength can be altered in a controlled manner. The use of microstructural control to toughen ceramics offers considerable potential, and along with the reinforcement approaches suggests other avenues for toughening. We need to examine the factors influencing the toughening response in systems like the silicon nitrides with elongated grain structures to determine what and how grain and interfacial-grain boundary properties alter crack propagation and the toughness. This area and the ability to combine toughening processes are exciting new fields for exploration and exploitation in the design of ceramic materials.
8,5 Acknowledgements The success of such a venture was only possible with the support and contributions of our colleagues, each of whom have contributed to this field, and our families. P.F.B. gratefully acknowledges the continued support of the Materials Sciences Division, Office of Basic Energy Sciences, U.S. Department of Energy, which has provided him with the opportunity to conduct his own research activities in this field under contract DE-AC05 840R21400 with Martin Marietta Energy Systems, Inc.
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General Reading Fracture Mechanics of Ceramics, Vol. 1-4 (19741978): Bradt, R. C , Hasselman, D. P. H., Lange, F. F. (Eds.). New York: Plenum Press. Fracture Mechanics of Ceramics, Vol. 5-8 (1983, 1986): Bradt, R. C , Hasselman, D. P. H., Evans, A. G., Lange, F. F. (Eds.). New York: Plenum Press. Green, D. X, Hannink, R. H., Swain, M. V. (1989), Transformation Toughening of Ceramics. Boca Raton, FL: CRC Press. Kelly, A. A., Macmillan, N. H. (1986), Strong Solids, 3rd ed. Oxford: Clarendon Press. Lawn, B. R., Whilshaw, T. R. (1975), Fracture of Brittle Solids. Cambridge: Cambridge University Press. Series on Science and Technology of Zirconia, Adv. Ceram. 3,12, 24. Columbus, OH: Am. Ceram. Soc.
9 Mechanical Behavior of Cellular Ceramics Rasto Brezny and David J. Green Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA, U.S.A.
List of 9.1 9.2 9.3 9.4 9.4.1 9.4.2 9.4.3 9.5 9.6 9.6.1 9.6.1.1 9.6.1.2 9.6.2 9.7 9.7.1 9.7.2 9.7.2.1 9.7.2.2 9.7.2.3 9.7.3 9.8 9.8.1 9.8.2 9.8.3 9.8.3.1 9.8.3.2 9.8.4 9.9 9.9.1 9.9.2 9.9.2.1 9.9.2.2 9.9.3 9.10
Symbols and Abbreviations Introduction Classification of Cellular Materials The Structural Role of Porous Materials Modelling Mechanical Behavior of Cellular Ceramics Structure of Foams Density-Microstructure Relationships Gibson and Ashby Model Macro- and Microstructural Characterization Elastic Behavior Open Cell Ceramics Effect of Density Effect of Cell Size Closed Cell Ceramics Fracture Toughness Theoretical Approach Experimental Work on Open Cell Ceramics Measurement of Strut Strength Effect of Density Effect of Cell Size Experimental Work on Closed Cell Ceramics Tensile Strength Theoretical Approach Specimen Size Effects Experimental Work on Open Cell Ceramics Effect of Density Effect of Cell Size Experimental Work on Closed Cell Ceramics Compressive Strength Theoretical Approach Experimental Work on Open Cell Ceramics Effect of Density Effect of Cell Size Experimental Work on Closed Cell Ceramics High Temperature Mechanical Behavior
Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.
465 467 468 469 471 472 472 473 474 475 476 476 478 479 480 480 482 482 486 489 491 492 492 494 496 496 498 500 500 500 503 504 506 508 509
464
9.10.1 9.10.2 9.11 9.12 9.13
9 Mechanical Behavior of Cellular Ceramics
Thermal Shock Behavior Creep Behavior Conclusions Acknowledgements References
509 512 513 514 515
List of Symbols and Abbreviations
465
List of Symbols and Abbreviations a A A{ B C t , . . . , C7 D E Es / G Gc, Gcs KIC Klcs L Mf n N P r rt t Tt, T 2 ATC Y
critical macroscopic flaw size constant depending on the cell geometry and solid material properties mirror and branching constants exponent related to the actual deformation mode of the unit cell geometrical constants constant characteristic of the end condition on the beam Young's modulus Young's modulus of the struts number of faces shear modulus critical strain energy release rate of the cellular and solid (strut) materials fracture toughness toughness of the solid material length of the cell edges fracture m o m e n t creep constant of the strut material number of edges per face volume fraction of porosity radius of gyration radii of the mirror-mist a n d mist-hackle boundaries thickness surface temperature of a solid critical temperature change crack geometrical constant
a ft 8 £ £Os v Q gs gt a aOs oc afc crfs
coefficient of thermal expansion Biot's modulus strain strain rate creep constant of the strut material Poisson's ratio density of the bulk material density of solid theoretical density of solid stress creep constant of the strut material compressive strut strength compressive strength of cellular solid strut strength tensile strength of cellular solid volume fraction of solid in the cell edges stress reduction factor
466
AM AZ GA HPA LEFM RD RVC SEM SENB
9 Mechanical Behavior of Cellular Ceramics
alumina-mullite alumina-zirconia Gibson-Ashby pure alumina linear elastic fracture mechanics relative density vitreous carbon scanning electron microscope single edge-notched beam geometry
9.1 Introduction
9.1 Introduction The presence of porosity in a brittle solid often significantly influences the mechanical behavior of the material. For example, although many structural ceramics are fabricated close to theoretical density, there can be remnant porosity. In some cases, these pores may be the strength-limiting defect population in the material. It has been recognized that this incomplete densification can arise from a variety of sources, e.g., differential sintering, the pyrolysis of organic impurities, etc. Pores also play an important role in the high temperature behavior of structural ceramics, as many of these materials fail by cavitational creep. Study of the mechanical behavior of porous ceramics is also a critical issue in their fabrication. Ceramics are often fabricated by the application of pressure and heat to a powder compact, and thus the densification will depend on the deformation behavior of the porous material. Even in pressureless sintering, it has been recognized that internal stresses may arise from variations in the densification rates within the porous material. Furthermore, it has been suggested that the room temperature elastic properties of powder compacts or partially-sintered materials could be used to characterize their structure and sintering behavior (Kendall et al., 1987; Green etal, 1988 and 1990). In the above examples, the presence of porosity in the material is often viewed as problematic. There are, however, many applications in which the use of porous materials can be advantageous, e.g., refractories, high temperature filters, catalytic substrates, thermal insulation, gas burner materials, etc. Although the primary function of these materials may not be structural, many of these applications require a high degree of mechanical reliability. Indeed, it is reason-
467
able to suppose that improvements in the mechanical properties of porous ceramics will open up new technological applications. The simplest classification of porous ceramics is with respect to the volume fraction (P) of the porosity. For this review, we have restricted the discussion to high porosity ceramics, i.e., materials with P > 0.70. These materials are commercially available in two broad groups: fibrous and cellular. An example of the fibrous material is shown in Fig. 9-1. This particular material is based on a bonded network of silica glass fibers and is currently used as insulation in the thermal protection system of the space shuttles. The mechanical behavior of these materials have been reviewed elsewhere (Green, 1984) and thus this chapter will be limited to cellular ceramics. As background to cellular materials and a comprehensive review of the literature, readers are encouraged to consult the recent book by Gibson and Ashby, 1988.
Figure 9-1. Microstructure of space shuttle tile, showing fibrous nature.
468
9 Mechanical Behavior of Cellular Ceramics
9.2 Classification of Cellular Materials Cellular ceramics are comprised of various arrangements of space-filling polygons (cells) and can be classified into two broad groups, honeycombs and foams. In honeycombs, such as shown in Fig. 9-2, the cells form a two-dimensional array, whereas foams are comprised of a three-dimensional array of hollow polygons. Foams are usually sub-divided into two further categories depending on whether or not the individual cells possess solid faces. If the solid of which the foam is made is contained only in cell edges, the material is termed open cell, i.e., the void space is connected through the cell faces and the material is permeable. If the cell faces are present, the foam is termed closed cell and the individual cells are isolated from each other. There is clearly the possibility that foams can be partly open and partly closed. Figure 9-3 compares the structures of an open and closed cell ceramic. There are two other related groups of high porosity ceramic materials that are worthy of mention here. The first of these groups is sintered or bonded hollow spheres. For example, glass is available in the form of hollow spheres and if one bonds these spheres together (Verweij et al, 1985), one forms a structure that has both open and closed cell features. The hollow regions within the bubbles are isolated but the pore space between the bubbles is interconnected. These glass bubbles can also be sintered together (Green, 1985). For small amounts of densification, the structure is similar to the bonded material, discussed above. On further densification, however, the structure can approach that of a (completely) closed cell material. These extremes in structure are compared in
Figure 9-2. Microstructure of ceramic honeycomb consisting of square prismatic cells.
(a)
Figure 9-3. Three dimensional cellular ceramics can be (a) open cell, like this alumina foam or (b) closed cell like foamed glass.
9.3 The Structural Role of Porous Materials
Fig. 9-4. The second group of high porosity ceramics are those that are formed by a sol-gel process. When dried, aero- or xerogels can possess "nanometer-sized" porosity in the range of volume fractions
469
we are considering in the present review (P>0.70). Although these two related groups of materials have more complicated structures than cellular materials, their mechanical behavior should possess similarities.
9.3 The Structural Role of Porous Materials Cellular structures abound in nature and although they can be complex, they are often aesthetically pleasing and intriguing. Figure 9-5 shows the cellular struc-
• I ",,,,
'-. t Mi
\•,--
(a)
(b) Figure 9-4. Macrostructure of sintered hollow glass spheres at (a) low degrees of sintering, showing both open and closed porosity (Green and Hoagland, 1985, reprinted by permission of the American Ceramic Society), and (b) high degrees of sintering exhibiting only closed porosity.
(b) Figure 9-5. Natural cellular structures found in (a) spine of sea urchin, (b) sea sponge.
470
9 Mechanical Behavior of Cellular Ceramics
tures of a sea urchin spine and natural sponge. It is reasonable to suppose natural cellular structures are not a result of random events but rather a careful evolutionary optimization process. These structures must fulfill a variety of functions but of relevance here, is the ability to withstand various types of mechanical forces. It is important, therefore, to determine whether porous materials possess some special characteristics in their mechanical behavior and if so, can man-made versions of these materials be used in structural applications. A clue to the answer to the former question can be gained from some recent calculations of Ashby (1989), in which he considers design of structures that minimize weight for a given stiffness or strength. In particular, he demonstrated the mode of loading can have a strong influence on the design process. Table 9-1 shows a few examples of these calculations, in which the weight has to be minimized for a given stiffness or brittle strength. The optimization process simply involves maximization of certain combinations of 3 parameters, E, the Young's modulus, KIC, the fracture toughness and Q, the density of the bulk material. The use of Klc, rather than strength as a brittle design parameter assumes one can specify the critical flaw size. As shown in Table 9-1, for the loading geometries considered, the minimization of weight for a given stiffness depends on maximizing the parameters, E/Q, E/Q2 and E/Q3, whereas for strength it depends on KIC/Q, KIC/Q3/2 and KIC/Q2. Thus one concludes for some loading geometries, density can play a pivotal role in producing an optimum design. In order to appreciate this effect, several materials are compared in Table 9-2, in terms of the parameters that optimize stiffness. In this table, the parameters are normalized to those of
wood, as this is the most utilized natural material for structural applications. The values used for these calculations are given in Table 9-3. There are several important observations from the data in Table 9-2. In comparing the value of E/Q for wood with dense ceramics and metals one finds wood is comparable to metals but inferior to dense ceramics. For the values of E/Q2 and E/Q3, however, wood can be substantially superior. Next, comparison of wood with data for ceramic foams (open cell alumina and closed cell glass) shows wood is only slightly better and in one case is outperformed. It should be noted that the corn-
Table 9-1. Parameters required to maximize stiffness or strength for minimum weight for selected modes of loading (after Ashby, 1989). Design parameters
Mode of loading
stiffness Rod in tension Bending of rod Bending of plate Internal pressure in cylinder
E/Q
strength KIC/Q
3I2
E/Q2
KZ/Q2 Klc/Q
E/Q
Table 9-2. Values of stiffness design parameter for various materials. Material
E/Q
E/Q2
E/Q3
Wood Steel Aluminium alloy
1 1.1 1.2
1 0.06 0.19
1 0.003 0.03
4.4 4.2 5.7 1.6
0.49 0.58 0.78 0.12
0.06 0.08 0.11 0.009
0.36 0.86
0.41 1.5
Dense ceramics Aluminum oxide Silicon nitride Silicon carbide Zirconium oxide
Cellular ceramics (10% dense) Aluminum oxide (open cell) 0.3 Glass (closed cell) 0.5
All values have been normalized to that of wood.
9.4 Modelling Mechanical Behavior of Cellular Ceramics
471
Table 9-3. Values used for design parameter calculations. Material Wood Steel Aluminum alloy
E (GPa)
e(kg/m3)
10.5 207 75
450 8000 2750
Gibson and Ashby (1988) Gibson and Ashby (1988) Gibson and Ashby (1988)
400 304 418 205
3970 3180 3210 5750
Lackey Lackey Lackey Lackey
Reference
Dense ceramics Aluminum oxide Silicon nitride Silicon carbide Zirconium oxide
et al. (1987) et al. (1987) et al. (1987) et al. (1987)
Cellular ceramics (10% dense) Aluminum oxide (open cell) Glass (closed cell)
3.0 2.9
parison of ceramic foams with a natural cellular material is a little unfair, especially as we are considering the most stiff direction of the wood. Presumably, ceramic honeycombs can give values superior to wood for the axial and transverse directions. The high values for the closed cell glass are surprising but may indicate that closed cell (crystalline) ceramics could be attractive materials for maximum stiffness with minimum weight. Unfortunately, there are very few experimental data on these types of materials. An important conclusion of the above calculations is that porous materials can offer advantages in structural applications over dense materials. Clearly, the structural design process involves more than design for maximum stiffness and one must consider many other features, such as strength, thermal shock resistance, chemical and thermal stability, etc. Moreover, there may be non-structural features involved in the design. Some of the features that could be useful in design and are present in porous ceramics include permeability (open cell), impermeability (closed cell), high surface area, low thermal conductivity, low dielectric constant, thermal and
397 255
Hagiwara (1986) Zwissler and Adams (1983)
chemical stability. Currently, cellular ceramics are not a particularly common material, unlike their polymeric counterparts, but the above discussion implies they could be used in structures. A theme of this chapter is that the mechanical behavior of currently-available cellular ceramics could be substantially improved.
9.4 Modelling Mechanical Behavior of Cellular Ceramics It clearly would be useful to derive analytical equations that relate the mechanical behavior of cellular materials to their microstructure. Such an approach is helpful in the design process as one could predict properties. It also allows the critical parameters that control the deformation process to be identified. This latter process is particularly important in the development of new materials and improved fabrication procedures. The major scientific approach that has been used to accomplish this type of theoretical analysis has been to identify a unit cell and analyze the deformation behavior of the cell. For honeycombs, unit cells that fill a plane in two
472
9 Mechanical Behavior of Cellular Ceramics
dimensions are any triangle, quadrilateral or hexagon with a center of symmetry (Gibson and Ashby, 1988). Man-made honeycombs utilize these shapes, often with a high degree of precision whereas natural honeycombs are less uniform, showing dispersion in cell shape and size (Gibson and Ashby, 1988). The uniformity of the man-made honeycombs can be analyzed in detail and a variety of deformation mechanisms have been identified (Gibson and Ashby, 1988). Analytical expressions have been put forward for the various mechanisms and confirmed by experimental data (Gibson and Ashby, 1988). In this work, we have chosen not to discuss ceramic honeycombs in detail, primarily as a result of the lack of experimental data. Such materials are expected to be elasticbrittle with creep deformation becoming important at high temperatures. The rest of the chapter will emphasize ceramic foams and the approach will be to compare theoretical expressions with experimental data. 9.4.1 Structure of Foams
Compared to honeycombs, a greater variety of space-filling, cell shapes is possible in three dimensions (foams), viz, triangular, rhombic and hexagonal prisms, rhombic dodecahedra and the tetrakaidecahedra. These types of cells have often been used as idealizations for the unit cell (Gibson and Ashby, 1988). Other geometric figures, such as tetrahedra, icosahedra and pentagonal dodecahedra have also been analyzed but these shapes fill space, only if distorted. The difficulty with the unit cell approach is that most foams do not involve a regular packing of a particular cell shape and there are variations in both shape and size, such that the cells have differing numbers of faces and edges. There are, however, topological laws that govern the connectivity of
cellular solids. For example, Euler's Law can be used to relate the average number of edges per face (n) to the number of faces (/) in an isolated cell (Gibson and Ashby, 1988), i.e., (9-1) This relationship indicates the reason most foams possess faces with 5 edges, regardless of the cell shape. For example, N is found to be 5.0, 5.14 and 5.4 for dodecahedra, tetrakaidecahedra and icosahedra respectively. Although many foam-like structures, such as grain boundaries in ceramics and metals, have / ~ 14 and N = 5.1, the topology of the foam will depend on the process by which the foam is made. For example, in man-made foams, the volume expansion during foaming is often constrained to one (rise) direction and the cells become elongated in this direction. This anisotropy in cell shape can in some cases, give significant anisotropy in mechanical properties. For this review, however, we will consider the foams to be isotropic. Gibson and Ashby (1988) have demonstrated the analysis for isotropic foams can be modified to describe anisotropy in structure or properties. 9.4.2 Density-Microstructure Relationships
An important property of a foam is its relative density, i.e., the density of the bulk foam (Q) normalized by the theoretical density of solid that forms the cell edges and faces (£t). For cellular ceramics, this definition of density does pose some problems, in that cell edges (or struts) and faces are not always theoretically dense. Indeed, as will be seen later, many open cell ceramics have struts that are hollow and even the apparently solid portion can contain fine-scale
9.4 Modelling Mechanical Behavior of Cellular Ceramics
porosity. Thus we will also define a parameter termed the normalized density of the foam, where the bulk density of the foam is normalized with respect to the density of the cell edges and faces (QS). That is, the volume used to calculate Q/QS includes the porosity within the cell edges and faces. For cases in which the cell edges and faces contain porosity or are hollow, g/gt < Q/QS. At this point, it is worth emphasizing another important point with respect to the microstructure. The microstructure should be thought of at two levels, the first we will call the macrostructure and refers to the cellular structure itself, i.e., the arrangement of the cells. The finer structure that should be considered is the structure within the cell edges and faces and we will call this the microstructure. At low densities (Q/QS < 0.2), Gibson and Ashby (1988) have shown that the normalized density can be related to the macrostructure by the following simple expressions for open and closed cell foams respectively (9-2)
473
9.4.3 Gibson and Ashby Model
The complications in defining the macrostructure of a foam and a unit cell led Gibson and Ashby (1982) to consider a simple geometry for this unit cell, as shown in Fig. 9-6 for the open cell case. As seen in this figure, deformation of the unit cell even under axial loads leads to cell edge bending and the unit cell was chosen as a result of visual observations of such bending in honeycombs and foams. Thus, provided the identification of the deformation modes is correct, it is assumed that dimensional analysis will give the correct dependence on the critical parameters that describe the deformation, and the geometric effects can be combined into a single parameter. Thus the scaling from the unit cell to the bulk properties, is incorporated into the geometric constant and presumably, the value of this parameter can be found by comparing experimental data with the theoretical expressions. By simplifying the geometry, the mechanics analysis is substantially facilitated and expressions have been derived for most of the critical mechanical properties of cellular materials. In particular for brittle cellular foams, expressions have been derived for the elastic constants, tensile
(9-3) where t is the thickness of the cell edges or faces, L is the length of the edges and C1 and C 2 are numerical constants (approximately unity) that depend on cell shape. At higher densities, these relationships become more complicated (Gibson and Ashby, 1988). Similarly, the manner in which the solid is distributed can be important. For example, collection of solid in the nodes of the struts (open cell materials) and the relative thickness of the cell faces to the cell edges (closed cell materials), will impact these relationships.
Figure 9-6. Unit cell used by Gibson and Ashby to derive mechanical relationships for open cell materials (Brezny et al., 1989, reprinted by permission of the American Ceramic Society).
474
9 Mechanical Behavior of Cellular Ceramics
and compressive strength, fracture toughness, hardness and creep rate (Gibson and Ashby, 1988). The approach in this review is to use the Gibson and Ashby model and the subsequent analytical expressions to discuss the experimental behavior found in ceramic foams. In particular, emphasis will be given to any modifications to the theory that are needed for brittle foams.
9.5 Macro- and Microstructural Characterization Following the discussion in Sec. 9.4, it is clearly important to carefully characterize both the macro- and microstructures of cellular materials. It is also advantageous to have some idea of the fabrication procedure. A common processing approach for open cell ceramics is to coat an open cell polymer foam, usually with a ceramic powder dispersed in a liquid (e.g., Lange and Miller, 1987). This approach approximately replicates the polymer and gives a rather distinctive macrostructure for the material, in that the cell struts are hollow (Fig. 9-7). The central hole represents the original shape and position of the polymer, which was removed by pyrolysis during the firing of the ceramic. Moreover, in many of these materials, the struts or faces contain microscopic porosity. Before applying any theoretical model to the mechanical properties of cellular materials, it is important to determine whether the assumed relationship between the density and macrostructure [Eqs. (9-2) and (9-3)] is valid. To keep these simple equations, it is important to determine the normalized density, i.e., the value of QS must include the total volume associated with the strut porosity. This makes the characterization process more difficult but
Figure 9-7. Fracture surface of a single strut in an open cell ceramic made by coating and burnout of polymer foam. Triangular hollow region results from polymer removal.
optical measurement of the hole size and shape and the determination of pore volume using mercury porosimetry have been used to calculate £s(Brezny and Green, 1989). Quantitative optical microscopic measurements can be used to determine the average values of t and L for a particular material. Figure 9-8 shows the logarithm of the normalized density as a function of log(t/L) for three commerciallyavailable, alumina-based, open cell ceram-
1-
0.1^r
A Q • —
yr yr yS 0.01- ^0.1
,
,
Alumina Alumina-zirconia Alumina-mullite Eq. (9-2) , ,—, , . 1
Strut thickness /length
Figure 9-8. Normalized density as a function of the thickness/length ratio of the struts in alumina materials. Solid line represents the slope predicted by Eq. (9-2) for entirely open cell material.
9.6 Elastic Behavior
ics and the solid line is that predicted by Eq. (9-2) with C± = 1 (Brezny and Green, 1989). It is clear that only one of the materials, alumina-mullite, gives good agreement with the equation. Visual observation indicated the other two materials possessed an increasing number of closed faces, as the density increased and thus one obtains materials that are partially closed. Figure 9-9 shows the type of macrostructure observed in the partially-closed cell materials. The steeper slopes for the two non-ideal materials were interpreted to be a result of the extra material being used for cell face formation rather than changing the strut dimensions (Brezny and Green, 1989). Recently, similar data was gathered by Van Voorhees (1990) for an open cell alumina with a slightly finer cell size. In this work, he found the power dependence of (t/L) on density was < 2 and this was interpreted as additional material being deposited in the nodes, where cell struts meet. Overall, it is clear that the ways in which the solid material is distributed throughout the cell (faces or nodes) can significantly impact the density-macrostructure relationships. Two other materials will be mentioned in some detail in the remainder of the chapter and it is worth briefly discussing some of their macrostructural characteristics as they were fabricated using a different procedure than discussed above. The first of these is an open cell vitreous carbon foam that is formed by pyrolysis of a polymeric foam (Sherman et al., 1991). These materials usually possess a completely open cell structure with solid struts, as shown in Fig. 9-10. The density -macrostructure data for these materials have been obtained for a single density and are consistent with Eq. (9-2), with C± = 0.75. These vitreous carbon foams are also used as the basis for a third type of fabrication ap-
475
Figure 9-9. Macrostructure of a partially closed cell material showing some face filling. Arrows indicate longitudinal strut cracks.
Figure 9-10. Macrostructure of reticulated vitreous carbon which exhibits completely open cells over a wide range of sizes.
proach, in which chemial vapor processes are used to deposit a variety of oxides, borides, nitrides and carbides onto the carbon foam (Sherman et al., 1991). Figure 9-11 shows an example of an open cell SiC material. The fractured strut shows the deposited layers of SiC and the carbon core that is used as the cellular substrate.
9.6 Elastic Behavior The initial response of cellular ceramics to stress is linear elastic and for isotropic
476
9 Mechanical Behavior of Cellular Ceramics
9.6.1 Open Cell Ceramics Using standard beam theory Gibson and Ashby (1982) determined the deflection of the cell struts in the unit cell (Fig. 9-6), and by relating the applied stress to the force acting on the struts obtained T
(a)
(9-4)
where E and £ s are the Young's moduli of the foam and the struts and C 3 is a geometric constant. By substitution of Eq. (9-2) and assuming C± = I, one can relate the modulus to the normalized density, (9-5) The analysis for the shear modulus of the foam (G) is similar and Gibson and Ashby (1982) obtained (9-6)
ip) Figure 9-11. (a) Macrostructure of SiC foam made by chemical vapor deposition of SiC onto reticulated vitreous carbon foam, (b) Fracture surface of a single strut reveals carbon core and several layers of deposited SiC.
materials, one usually requires two elastic constants, e.g., the Young's and shear moduli. Lakes (1986,1991) has suggested cellular solids may not obey classical elasticity theory. Such non-classical behavior has many ramifications (Lakes, 1991) but for this work, the cellular ceramics will be treated as being classical. Cell strut bending has been identified as the major (linear elastic) deformation mode in open cell materials (Gibson and Ashby, 1988).
Gibson and Ashby (1982) considered a variety of corrections to these simple equations but found offsetting effects and thus they suggest Eqs. (9-5) and (9-6) are valid, at least as a first approximation, for all densities. Comparing Eqs. (9-5) and (9-6) with experimental data on open cell materials, Gibson and Ashby (1988) conclude C 3 « 1 and C 4 = 0.375. As pointed out earlier, foams can show significant anisotropy and this complicates the theoretical analysis. In addition, some foams can show unusual elastic behavior, such as negative values of Poisson's ratio (Lakes, 1987, 1991). 9.6.1.1 Effect of Density Initial elastic constant measurements on open cell alumina by Hagiwara and Green (1987) showed Eqs. (9-5) and (9-6) gave
9.6 Elastic Behavior
good agreement in terms of the exponent (2) but the values of the geometric constants (C3 and C4) were less than suggested by Gibson and Ashby (1988). Clearly the choice of values of £ s and QS are critical in determining these constants. Hagiwara and Green (1987) recognized the presence of the hollow struts is a feature that would impact the theoretical analysis. From beam theory, Hagiwara and Green (1987) showed that the hollow strut would actually increase the geometric constant if one considers the variation of modulus with respect to relative density. That is, hollow struts are actually more efficient than solid, in terms of stiffness at a given relative density. This is a result of the hole significantly reducing the density but not the flexural rigidity of the struts. In order to keep the simplicity of Eqs. (9-5) and (9-6), the parameter {Q/QS) has to be interpreted as normalized density and not relative density (see Sec. 9.5). The choice of Es will be influenced by the hollow nature of the struts but as discussed above, this effect is not expected to be as critical as the density correction. It would be useful if Es could be measured directly but currently we are not aware of any such experimental technique. In order to estimate £ s , it is important to be aware of the phase content of the strut material. For example, we have recently studied an alumina-mullite (AM), open cell ceramic, the same one described in Fig. 9-8. The strut walls in these materials were found to possess ~ 25% porosity and the mullite volume fraction was 0.28. A Young's modulus for dense alumina/28% mullite of 328 GPa can be obtained from the average of the upper and lower bounds (Young's moduli of alumina and mullite are assumed to be 380 and 225 GPa respectively, Kingery et al, 1976; Wu, 1990). The value of Es must also account for the porosity and using the
477
form of the correction suggested by Davidge (1979), the value of Es was estimated to be 190 GPa. In the original work of Hagiwara and Green (1987), such a careful estimation of QS and Es was not performed and thus we have analyzed some more recent elastic constant data (Brezny, 1990; Dam, 1988; Orenstein, 1990). These data were gathered on materials from a single manufacturer, at constant cell size. The Es value of 190 GPa, as calculated above, was used for the modulus normalization (ignoring the small effect of the central hole) and the approach used by Brezny and Green (1989) was used to change relative to normalized density. Figure 9-12 shows the results of these calculations. As can be seen, the modulus data for these open cell aluminas shows considerable scatter and this was considered to be a result of material variability. The slopes of the log-log plots for the Young's and shear moduli were 1.9 and 2.2 respectively and these are in good agreement with the value of 2 predicted by Gibson and Ashby (1982). Forced fits, using a power dependence of 2, are shown in Fig. 9-12 and the values for C 3 and C 4 were 0.42 and 0.17 respectively. These values are similar to the ones origi-
Young's modulus • Shear modulus "D O •o (D N
75 E 0.01
0.001 0.1 Normalized density
Figure 9-12. Relative Young's and shear moduli of cellular alumina as a function of normalized density. Data exhibits good agreement with Eqs. (9-5) and (9-6).
478
9 Mechanical Behavior of Cellular Ceramics
nally suggested by Hagiwara (1986) and Hagiwara and Green (1987), i.e., 0.363 and 0.142 for a different open cell alumina. Overall, it appears for these open cell ceramics, the values of C 3 and C 4 are substantially less than those suggested by Gibson and Ashby (1988). Zhang and Ashby (1989) have recently refined the Gibson and Ashby model using a tetrakaidecahedron as the unit cell, obtaining values of 0.5 and 0.17 for C 3 and C 4 respectively. These latter values are in good agreement with the data on the open cell alumina (C 3 = 0.42 and C 4 = 0.17) shown in Fig. 9-12. It is important to note that the AM material discussed here, was found to agree with Eq. (9-2) (see Fig. 9-8). Cellular materials that are partially-closed, such as the other materials shown in Fig. 9-8 would not be expected to satisfy Eqs. (9-5) and (9-6) and this was confirmed by Dam (1988).
8000 CO CL
o RD = 0.11 • RD = 0.16
6000
3
o
4000
?
2000
0
1
2
3
4
5
Cell size (mm)
Figure 9-13. Relative Young's modulus of an alumina mullite material increases with cell size, for two different relative densities (RD).
9.6.1.2 Effect of Cell Size According to Eqs. (9-5) and (9-6), one does not expect any variation of the elastic constants with cell size. In the AM material discussed above, it appeared initially there may be a cell size effect. For example, Fig. 9-13 shows data for 3 different cell sizes (Dam, 1988). Macrostructural observation showed the materials with the finest cell size often contained longitudinal strut cracks, Fig. 9-14 a. Clearly, this would be expected to reduce Es for these materials. In order to gain more detailed insight into the effect of cell size, elastic constant measurements were made on vitreous carbon, open cell foams (Brezny and Green, 1990 a). These materials possess solid struts and do not appear to have the complications of partial cell closure or cracked struts. The data are shown in Fig. 9-15 and there is no significant influence of cell size. Another interesting aspect of the carbon foam is the
(a)
(b) Figure 9-14. Microstructure of fine cell alumina mullite foam exhibited (a) an increase in the number of longitudinal strut cracks (marked by arrows) and (b) fracture of this material occurred primarily by strut splitting.
9.6 Elastic Behavior
4Pa)
140 120-
jng's modulu
100-
O
80-
6040-
I
i
I ••
*-
2000
1
2
3
4
5
Cell size (mm)
Figure 9-15. Young's modulus of RVC exhibits no cell size dependence in agreement with Eq. (9-5).
low material variability, especially compared to the open cell aluminas. For the data in Fig. 9-15, 20 specimens were tested for each cell size and the point to point variability was considered to be related to variations in Es (Brezny and Green, 1990 a). 9.6.2 Closed Cell Ceramics
Gibson and Ashby (1988) have derived analytical equations for the elastic constants of closed cell materials, recognizing some faces must be placed in tension in either tensile or compressive loading. Another contribution that can be important in some circumstances is the compression of any liquid or gas that is present within the cells. Ignoring this latter effect, the analysis gave
479
C 4 = C 4 = 0.375. These equations show a transition in density exponent from 1 to 2 as 4> increases from 0 to 1, i.e., as the faces become thinner. The limiting condition, (/> = 1, gives the equations for open cell materials, i.e., Eqs. (9-5) and (9-6). Equations (9-7) and (9-8) predict the lower the value of (/>, the higher the modulus at a given density, thus it appears the cell faces can substantially increase the foam stiffness. Using a comparison with prior experimental data, Gibson and Ashby (1988) suggest $ may be in the range 0.6 to 0.8 for many closed cell foams. For these values, cell edge bending no longer appears to be the dominant deformation mechanism as it is being constrained by the attached faces. There is very little data on the elastic behavior of closed cell ceramic foams. Zwissler and Adams (1983) and Morgan et al. (1981) have studied foamed glasses and their Young's modulus data are shown in Fig. 9-16. The data, show the predicted decrease in the power dependence of the relative density compared to open cell ceramics and the values of E/Es are substantially higher (see Fig. 9-12). The implication is that the elastic constants of closed cell, polycrystalline ceramics may be in the
B Zwissler and Adams • Morgan et al. 0.1
-ct>)U)
(9-7)
Uj
0.01
and ^
(9-8)
0.001 0.01
where C 3 and C4 are geometric constants and (j) is the volume fraction of solid in the cell edges. Gibson and Ashby (1988) suggest values of C 3 = C 3 = 1 and
0.1 Relative density
Figure 9-16. Young's modulus of closed cell foamed glass material after Zwissler and Adams (1983) and Morgan et al. (1981).
480
9 Mechanical Behavior of Cellular Ceramics
range of one-tenth to one-fiftieth of the modulus of the dense materials, making their specific stiffness values very attractive for structural applications. Ashkin et al. (1990) have compared their data on gel-derived, porous silica to Eq. (9-4) and found density exponents > 2 and similar to the work on the open cell alumina discussed in Sec. 9.6.1.1, the geometric constants was < 1. Similarly, in studies on the mechanical behavior of sintered hollow glass spheres (Green and Hoagland, 1985), deviations were also seen from the Gibson and Ashby predictions. Green and Hoagland (1985) suggested the elastic constants would be very sensitive to the size of the sintered contact areas in the initial stage of sintering and demonstrated this could explain the higher density exponent. Thus although Eq. (9-4) gives a reasonable approximation to the work on other high porosity systems, such as sintered gels, there can be deviations in the region where the materials are approaching a powder, i.e., with little or no connectivity between the particles.
9.7 Fracture Toughness Ceramics that are considered for high temperature applications are often elasticbrittle at temperatures below ~1000°C. In this temperature range, the initial tensile response of ceramics is linear elastic until at a maximum load, a crack propagates through the material. For this type of behavior, one expects the strength to be determined by the fracture toughness of the material and the size of the flaws within the material. For some porous materials, it has been suggested that failure can be more appropriately described by a cumulative damage type of analysis (Meiser and Tressler, 1981). For this review, we will
consider the fracture toughness approach at least for tensile stresses, as this is the type of behavior we have observed in open cell ceramics. 9.7.1 Theoretical Approach
The fracture toughness of brittle foams was originally discussed by Maiti et al. (1984 a) using two types of analyses. Both approaches are based on the unit cell considered by Gibson and Ashby (1982). The first was derived from a linear elastic fracture mechanics argument whereas the other was a simple energy balance approach. The fracture mechanics approach initially treats the foam as a linear-elastic continuum and determines the forces acting ahead of a crack tip. The discrete nature of the macrostructure is then introduced by considering the action of these forces on an array of unit cells. The crack is considered to advance when the moment on the struts at the crack tip exceeds their fracture moment, Mf =
= C,<7fs
(
nL\ —
Q^2
(9-9)
The geometric constant (C5) was determined empirically as 0.65 for a variety of materials (Maiti etal., 1984 a), however, this constant could be very sensitive to the assumed values for
9.7 Fracture Toughness
is really only valid for crack lengths substantially greater than the cell size (factor of 10). This assertion was backed up with finite element calculations on honeycombs and experimental data on a brittle foam. Equation (9-9) predicts a square root dependence on cell size, if the other variables in the equation remain independent of this parameter, and indicates that a large cell material may give maximum toughness. Such an effect may, however, be offset by the increase in strength that is often found in materials as one decreases the dimensions of the item that fails. For example, ceramic fibers can approach their theoretical cleavage strength as their diameter is decreased, an effect that is often exploited in fiber composites. A similar effect in open cell ceramics would give an increase in strut strength with decreasing cell size. Huang and Gibson (1990) have recently shown the dependence of fracture toughness on cell size will depend on the dispersion of strut strengths. For materials in which strut strength obeys a Weibull distribution (volume flaws), the toughness will increase or decrease with cell size, depending on whether the Weibull modulus is greater or smaller than 6. The energy balance approach to the toughness of cellular materials equated the energy required to fracture a cell to that required to fracture a single strut (Maiti etal., 1984 a). In an open cell material, a crack advancing over a one cell area, fractures on average, a solid area equal to one strut and therefore GcL2 = Gcst2
(9-10)
where Gc and Gcs are the critical strain energy release rates of the cellular and solid (strut) materials respectively. This can be written in terms of the fracture toughness by substituting the relationships Klc = ^/EGC
481
(9-11) The subscript (s) refers to the properties of the solid making up the struts. This approach does not predict a cell size effect but rather a dependence on the toughness of the solid material {Klcs). In comparing Eqs. (9-9) and (9-11), there is no reason, a priori, to suppose that Klcs should be proportional tO <7fs yjh. In the original presentation, the arguments for open cell foams were repeated for closed cell materials by considering the deformation of plates. The only change involved a square dependence on relative density for both approaches (Maiti et al., 1984 a). The authors did, however, suggest that faces are often very thin in the closed cell materials and thus, they expected the closed cell materials to follow the 1.5 power dependence. A more recent analysis has modified the fracture energy approach for closed cell foams to include the contribution of the cell faces based on the fraction of material distributed within the faces (Gibson and Ashby, 1988). The result of this analysis gave (9-12) Although the two analytical approaches [Eqs. (9-9) and (9-11)] predict a similar density dependence for open cell materials, their dependence on the strut properties are sufficiently different that they impact the philosophy one would use to tailor improved materials. Equation (9-9) implies that to maximize the properties of the bulk cellular foam, one should use a large cell material having a high strut strength. This may be done through improved processing to remove microscopic defects, such as
482
9 Mechanical Behavior of Cellular Ceramics
pores, cracks or inclusions within the struts, thereby increasing afs. An increase in the toughness of the material within the struts, for a given critical flaw size, would also increase afs. On the other hand, Eqs. (9-11) and (9-12) suggest that flaw and cell sizes are not important and one must concentrate on fabricating the foam from a solid having a high fracture toughness. Alternatively one may want to increase the toughness of the struts by utilizing techniques commonly used in dense ceramics, such as introducing crack deflection, shielding or bridging mechanisms into the fracture process. Thus, in addition to their slightly contrary form, the two analytical approaches imply distinctly different routes that one should use in the design of these materials to optimize the properties. As will be shown later, however, Eq. (9-9) and not Eq. (9-11) describes the toughness of brittle open cell materials (see Sec. 9.7.3.2). It should be noted that these theoretical developments usually consider strut strength to be single-valued, but as will be clear in this work, it can be highly varied. This dispersion of strut strength may have serious implications for the fracture behavior of cellular solids, but as yet, this has not been fully analyzed or understood. 9.7.2 Experimental Work on Open Cell Ceramics
It is clear from the expressions proposed by Gibson and Ashby (1988), to describe the mechanical behavior of porous, cellular solids, the strength of the individual struts may control the strength and toughness of the bulk cellular material. In the analysis of experimental data, this property is often assumed constant and equal to the strength of the bulk solid making up the struts. This assumption of constant afs may not be valid for extremely flaw sensitive
materials like ceramics, as the probability of finding a flaw of a given size often depends on the size of the specimen being tested. As the relative density or cell size decreases in a cellular solid, the strut volume, as well as, the strut surface area decreases and thus could influence strut strength. Moreover, there are a variety of microstructural defects that can influence strength, e.g., pores, inclusions, cracks, etc., and if these change with density or cell size so will afs. Indeed, even for a given dense, monolithic ceramic, strengths may be highly dependent on the processing approach and for a given technique show high variability. Thus, in order to critically evaluate the theoretical analyses that have been put forward, it is important to find techniques for measuring afs. 9.7.2.1 Measurement of Strut Strength
Brezny et al. (1989) measured the strut strength of several cellular ceramics using a simple technique. The approach involved a thin steel wire being threaded underneath the strut and connected to a tensile load cell. The load needed to break an individual strut in bending was then used to estimate the strut strength. The strut was analyzed as a rigidly fixed beam under the action of a central point force. This technique is useful for relatively large cell materials (> 1 mm) but becomes impractical as the cell size becomes smaller. This approach was applied by Brezny et al. (1989) to the analysis of alumina-based materials fabricated by the coating of a polymer foam substrate as these were tested at a relatively large cell size (2 mm). The strut strength as a function of density for two alumina-based, open cell ceramics is shown in Fig. 9-17. The error bars in the figure represent the range of strengths measured. Several conclusions
9.7 Fracture Toughness 2000
S. 1500 -
E Alumina • Alumina-zirconia
1000 -
lid
1
0.1
0.2
0.3
Relative density
Figure 9-17. Strut strength as a function of density for two alumina materials showing average and range of values.
were drawn from these results. The first is that strut strength in these specimens was independent of relative density. This was attributed to the processing of these materials. As the relative density increased, the strut volume did not change as predicted by Eq. (9-2) but rather, material was incorporated into filling of cells or cell faces at higher densities (see Sec. 9.5). Specimens were also tested having the same relative density but smaller cell size and these exhibited a much higher strut strength (Brezny et al., 1989). The strut strength values ranged over an order of magnitude between the weakest and strongest struts, at a given density. This was attributed to a wide distribution of microscopic flaws within the struts. Fractographic observation of the struts revealed a variety of failure origins. These included pores or inclusions in the solid portion of the strut, as well as, cracks resulting from the drying of the alumina slurry or burnout of the polymer substrate (Fig. 9-18). The longitudinal cracks are similar to those discussed previously (see Sec. 9.6.1.2, Fig. 9-14 a). Finally, the strut strength data indicate a large difference between the average strut strength of the two materials. This was explained
483
(Brezny et al., 1989) in terms of the high degree of cracking within the struts of the alumina-zirconia material and the higher sintered density of the alumina struts (~95% theoretical). These results imply that the strut strength can be significantly improved, if changes to the processing, that lead to higher strut densities and reduced flaw sizes, are made. Table 9-4 compares strength data obtained by the direct mechanical technique for several different materials. For these materials, the fracture toughness values for the dense strut mate-
(b) Figure 9-18. Fracture surfaces of struts in alumina materials indicating failure origins, (a) Lateral cracks and sharp corner in the Al 2 O 3 -ZrO 2 material, (b) Failed strut in the A12O3 sample indicating the thin walls at the corners of the triangular pore and inclusion within the strut wall (marked by arrow) (Brezny et al., 1989, reprinted by permission of the American Ceramic Society).
484
9 Mechanical Behavior of Cellular Ceramics
Table 9-4. Strut strength of cellular ceramics as determined by direct measurement Material
Relative density
Al 2 O 3 a Al 2 O 3 -ZrO 2 a Al 2 O 3 -Al 6 Si 2 O 13 b SiCc Brezny et al. (1989);
0.13 0.12 0.13 0.12 b
Cell size (mm) 1.6 2.3 4.0 3.8
Strut strength (MPa) Average
Standard deviation
315 122 75 453
148 74 26 184
Brezny and Green (1989); c Price (1990).
rials are probably of the same order and yet, as shown, the average strengths show a very wide range. In several of these materials, some strut strength values exceeded 1 GPa, indicating substantial improvements to the mean and the standard deviation of the strength can be made. The direct measurement technique described above is limited to large cell materials, as well as, strut geometries amenable to loading through a wire. In addition, it was found that struts with low hardness would be crushed by the wire. Several alternative methods for estimating the strength of the struts have been introduced (Brezny and Green, 1990a, 1991). One approach consists of using an analytical equation that has been verified for a specific mechanical property and particular material. The most attractive property for this approach is the uniaxial compressive strength of the bulk cellular foam. The theoretical expression for crushing strength depends only on the geometric constant, the relative density and the strut strength. One can rearrange the theoretical expression for the crushing stength of the foam [Eq. (9-19)] to calculate the strut strength. The accuracy of this method depends on knowing the value of the geometric constant (C7). In their original analysis, Maiti et al., (1984 a) obtained C 7 = 0.65, with a fit to prior experimental data. Zhang and
Ashby (1989) have predicted a value of 0.16 for isotropic foams consisting of tetrakaidecahedral unit cells. Thus there is a need to calibrate the value of C 7 for a particular material by using an independent means for measuring strut strength. Experimental work on an open cell vitreous carbon foam has suggested a value of 0.11 as giving the best fit to the data (Brezny and Green, 1990 a). The value calculated for the alumina-mullite open cell foam was very similar (0.14). Non-ideal microstructural features of open cell ceramics, such as closed faces or split struts, can complicate strut strength estimation by this technique, as they may result in deviation of the power dependence on the relative density from that predicted by theory. Such deviations have been observed in the compressive strength behavior of some open cell ceramics (see Sec. 9.9.2). As a result of the low hardness of the struts in the open cell, vitreous carbon, strut strength could not be directly measured by the mechanical technique outlined earlier. In addition, a value of the geometric constant was not available to allow strut strength to be determined from compressive strength. Thus an alternate method for estimating the strut strength was required. An indirect technique based on fractographic analysis of strut fracture surfaces was used, (Brezny and Green,
9.7 Fracture Toughness
1990 a, 1991). As a crack propagates through an open cell material, it does so by fracturing individual struts. This process results in characteristic fracture markings, radiating from the failure origin, on each strut (Fig. 9-19). These are known as the mirror region (smooth region nearest the flaw), the mist region (slightly dimpled region outside of the mirror) and the hackle region (rough surface where portions of the crack deviate from the original plane of fracture). Beyond the hackle region, the entire crack departs from the original fracture plane and this is referred to as macroscopic crack branching. It has been shown that the position of the boundaries for a given material, (i.e., mirror-mist and misthackle) can be used to estimate fracture stress (Mecholsky et al., 1976). Thus for open cell ceramics, one can use these markings to estimate the fracture stress of individual struts. The radii (rf) of the mirrormist and mist-hackle boundaries, measured from the failure origin, are related to the fracture stress by the simple relationship o-fs = AJy/r^ where A% are the mirror and branching constants (Mecholsky et al., 1976). For cases in which the critical flaw size (c) can be observed on the fracture surface, a third estimate of the fracture stress can be made, provided the fracture toughness of the strut material is known, as crfs = Klcs/(Yy/c). The geometric constant, Y, for the appropriate crack shape and loading geometries needs to be known. If possible, it is useful to compare the stresses calculated from the 3 different fractographic features to obtain a reliable estimate of the failure stress. Although the inclusion or pore leading to failure in the vitreous carbon was often easily identified, it was difficult to determine if the entire inclusion or some smaller crack around the defect was responsible for catastrophic failure. This uncertainty makes it difficult to
485
|2Qi)m I
(c)
Figure 9-19. (a) Fracture surface of a single strut in RVC material showing the triangular strut shape and characteristic fracture markings; (b) typical failure origin on a corner of a strut clearly showing the mirror, mist and hackle regions; (c) failure occurring from volume flaw (Brezny and Green, 1991, reprinted by permission of the American Ceramic Society).
486
9 Mechanical Behavior of Cellular Ceramics
choose the appropriate value of Y, as the exact flaw geometry is not known. In general, the hackle boundary is easily identified and is visible on many fracture surfaces and thus may provide the best estimate of the fracture stress for these struts. The fractographic observations in the open cell carbon supported the basic idea that strut bending is the primary type of deformation. Strut fracture surfaces usually showed the compressive lip that is typical of bending failures (Fig. 9-19 a). As the stresses are highest at the strut surfaces, failure was found to originate from flaws at or near the surface. Occasionally, the failure origin was observed to be near the strut center (Fig. 9-19 c) and along with the presence of a circular mirror indicates substantial axial stresses can be present for certain strut orientations. Table 9-5 shows strut strength data obtained on the vitreous carbon as a function of cell size. For this material strut strength increases with decreasing cell size and values > 1 GPa are common, especially at the smaller cell sizes. These data clearly demonstrate the danger involved in assuming strut strength is constant, for a particular open cell material. Huang and Gibson (1990) have recently shown a similar variation in strut strength with cell size in a vitreous carbon foam. The magnitude of their strength values
were, however, substantially less than those given in Table 9-5. This was primarily a result of using C 5 = 0.65 in Eq. (9-9) to calculate strut strength, rather than attempting to estimate strut strength by some independent means. 9.7.2.2 Effect of Density The study of the density effect on the toughness of cellular ceramics has concentrated on materials made by replicating a reticulated (open cell) polymer substrate, by coating it with a ceramic slurry. Three alumina-based, open cell materials were tested; pure alumina (HPA), alumina-mullite (AM) and alumina-zirconia (AZ). The micro- and macrostructural characteristics of these materials have been discussed previously (see Sec. 9-5 and Brezny and Green, 1989; Brezny et al., 1989). It was concluded that the AM material exhibited the best macrostructural agreement with the Gibson and Ashby model. The other two materials contained macrostructural features such as filled cells or closed faces which result in a deviation from a truly open cell structure. Prior to an analysis of the toughness behavior, a brief discussion of the fracture process in these materials is necessary. A crack propagating in an open cell material
Table 9-5. Estimation of strut strength by fractographic analysis (after Brezny and Green, 1990 a). Cell size (mm) 4.19 2.55 2.10 1.41 0.98 0.68 0.49
Strut surface area (mm2) 1.38 0.62 0.36 0.25 0.10 0.05 0.03
Strut strength (MPa)
Strut volume (mm3) 0.07222 0.02365 0.00978 0.00607 0.00149 0.00064 0.00027
Flaw size
Mirror radius
Hackle radius
627 770 882 897 1166 1436 1105
420 573 543 710 870 872 934
592 674 792 871 1224 1222 1277
9.7 Fracture Toughness
usually passes from cell to cell by successively fracturing individual struts. This type of fracture behavior was observed in the AM material (Fig. 9-20 a). One distinguishing feature of the AZ samples was that cracks propagated by splitting the struts lengthwise as the main crack linked the longitudinal cracks already present within the struts (Fig. 9-20 b). In the longitudinal fracture process, the crack travels within the solid material throughout the fracture process and is deflected along the edges of the cells. This contrasts sharply with the discrete fracture processes associated with the AM material. In the theoretical analysis of Maiti et al., (1984 a), the transverse fracture process was assumed to occur and not the splitting process. The HPA samples, which were relatively open at lower densities, exhibited localized dense regions at higher densities, consisting of completely filled cells. The crack interacted with these dense regions by deviating from the original plane of propagation in order to avoid them. In the event that the notch originated at or near a dense region, a higher critical stress intensity factor was required to initiate crack advance (Brezny and Green, 1989). The fracture toughness of these 3 open cell ceramics was measured as a function of density using the single edge-notched beam geometry (SENB) specimens in three point loading (Brezny and Green, 1989). The results could be simply plotted as the measured fracture toughness versus the relative density, however, it is important to realize that this type of plot does not take into account any variation in strut strength or microstructure with density (Brezny and Green, 1989). It was discussed earlier that as a result of macrostructural inhomogeneities, not all materials agree with the density relationships suggested for open cell materials [Eq. (9-2)]. This does not im-
487
(a)
(b) Figure 9-20. Fracture surfaces showing two types of failure in open cell alumina, (a) transverse fracture in the AM material evidenced by the large number of triangular holes exposed in the center of the struts, (b) longitudinal fracture characterized primarily by struts split along their length (AZ).
ply, however, that the failure mechanisms are different in these materials, as this is derived from the mechanics of the unit cell. If bending of the struts is the mode of failure, combining Eqs. (9-2) and (9-9) implies that the fracture toughness should increase as (t/L)3. Thus, the fracture toughness was normalized with the strut strength and cell size at each corresponding density and plotted against t/L in Fig. 9-21. This plot is independent of the density versus strut geometry relationship [Eq. (9-2)], and is a more precise test of the failure model. The slope of the AM data is in good agreement
488
J2
9 Mechanical Behavior of Cellular Ceramics
A H • —
0.1
Alumina Alumina-zirconia Alumina-mullite GA model
0.01 -.
0.001 0.1 Strut thickness/length
Figure 9-21. Plot of the normalized fracture toughness KIC/[o-fs(7iL)1/2] versus the ratio of the strut dimensions in open cell alumina materials as well as the theoretical line given by the GA model.
It was observed that the three materials used in the above study (Brezny and Green, 1989) had different strut strengths and these directly affected the fracture toughness of the bulk ceramic foam. Normalizing the toughness of all three different materials by a{sy/L9 as suggested by Eq. (9-9), gave a reasonable fit to a single line (Fig. 9-23). This suggests that even though there are some deviations from the density-macrostructure relationship for two of the materials, one can predict the fracture toughness behavior of these materials
0.1 i
with a slope of 3 predicted by the model. The other two materials exhibit a rapid increase in toughness with little or no change in strut dimensions. Other factors are contributing to the increased toughness in these materials. This behavior may be due to the longitudinal splitting fracture process in the AZ material or the high concentration of closed faces and dense regions observed in both the AZ and HPA materials (Brezny and Green, 1989). The AM material most closely resembles an open cell ceramic, as visualized in the theoretical model. The data for this material was normalized by the strut strength and cell size at each density and plotted in Fig. 9-22. The theoretical model assumes that the struts are solid, however, as discussed earlier, the struts in these coated materials contain a large triangular hole, as well as, fine porosity within the strut wall (Fig. 9-18). The relative density was normalized to account for the varying pore fraction in the struts, i.e., the normalized density. The slope of the data in Fig. 9-22 (1.46) is in excellent agreement with the model of Gibson and Ashby which predicts a power of 1.5 on the normalized density [Eqs. (9-9) and (9-11)].
0.01 -
o
0.001 -
0.0001 Normalized density
Figure 9-22. Normalized fracture toughness Klc/ [(Tfs(nL)1/2] versus normalized density in the AM material showing agreement of the data with the GA model.
0.1 -a
£
0.01 -
CO
• Alumina • Alumina-zirconia • Alumina-mullite 0.001 0.1
1 Normalized density
Figure 9-23. Normalized fracture toughness plotted against the normalized density for all three open cell aluminas.
489
9.7 Fracture Toughness
reasonably well using Eq. (9-9), at least to a first approximation. The inconsistency of the data points at the highest densities may be a result of the significant deviations from an open cell structure in two of the materials at the highest densities, as discussed earlier (see Sec. 9.5 and Fig. 9-8).
0.3
• RD = 0.11
i
C D)
0.1 -
5
i (a)
9.7.2.3 Effect of Cell Size
•
2
One of the theoretical relationships proposed for the fracture toughness of brittle cellular solids predicts a cell size dependence [Eq. (9-9)]. Until recently the fracture toughness relationships have never been critically evaluated as a function of cell size. Brezny and Green (1990 a) examined the cell size contribution to the fracture toughness in several materials in order to fully understand the effect of this important parameter. In addition, it was hoped to distinguish between the two fracture toughness approaches discussed in Sec. 9.7.1 [i.e., Eqs. (9-9) and (9-11)]. The cellular alumina materials (AM and AZ) were tested at a constant relative density and three different cell sizes ranging from 0.3 to 3.5 mm (Brezny and Green, 1990 a). The results are shown in Fig. 9-24, and indicate that the AM material exhibits almost an order of magnitude increase in toughness over a four fold increase in cell size. This behavior was observed at two different densities and is in agreement with elastic modulus and crushing strength results presented by Dam (1988) on the same lot of material (see Sees. 9.6.1, 9.9.2.2 and Figs. 9-13 and 9-38). This behavior was explained by the strut cracks which were observed in the smallest cell material (Fig. 9-14 a). It was also observed that the small cell size material failed by longitudinal splitting of the struts (Fig. 9-14 b), whereas, the large cell material failed predominantly by transverse strut failure. It is important
l
0.2 -
i
•
3
Cell size (mm) 0.25
p
0.20 •
Q_
0.15 0.10 -
i2
0.05 •
1.0
1.5
2.0
Cell size (mm)
Figure 9-24. (a) Fracture toughness (Klc) increases with increasing cell size in a cellular alumina-mullite material due to a change in the strut microstructure. (b) Alumina-zirconia material shows no cell size dependence as failure occurred by strut splitting at all cell sizes.
to note the toughness data for the open cell AM material cannot be explained by Eq. (9-11), as the fracture toughness of the solid material is not expected to vary significantly with cell size. For Eq. (9-9), however, the data can be explained in terms of a variation of strut strength with cell size, i.e., the strut cracks effectively reduce the strut strength. In contrast, the AZ material showed no significant variation of toughness with cell size (Fig. 9-24 b), as this material exhibited strut cracks at all cell sizes. The toughness variation with cell size in the alumina materials proved to be incon-
490
9 Mechanical Behavior of Cellular Ceramics
elusive as the microstructural variability with cell size complicated the interpretation of the data. Thus toughness measurements were made on the open cell, vitreous carbon (RVC) material at a relative density of 0.035 and seven cell sizes ranging from 0.43-4.5 mm (Brezny and Green, 1990 a). This material was selected because of its open macrostructure at all cell sizes and the solid nature of the struts. The measured fracture toughness was independent of cell size (Fig. 9-25), apparently in agreement with the fracture energy approach [Eq. (9-11)]. This did not, however, rule out the possibility that the strut strength increased with decreasing cell size, allowing the toughness predicted by Eq. (9-9) to also be independent of cell size. Thus, it is again critical to obtain measurement of the strut strength and for the vitreous carbon this was accomplished using quantitative fractography. The fracture surfaces of the vitreous carbon foam were examined using a scanning electron microscope (SEM) in order to estimate the strut strength from the fracture surfaces of the individual struts. The results estimated by fractography were given in Table 9-5. In most cases three estimates of strut strength were possible (critical flaw 0.10
1
2
3
4
5
Cell size (mm)
Figure 9-25. The fracture toughness (Klc) appears independent of cell size in RVC.
size, mist and hackle boundaries) as described in Sec. 9.7.2.1, and gave reasonable agreement with each other. The hackle boundary was the easiest to identify and was used as the best estimate of the fracture stress for the struts (Brezny and Green, 1990 a). As shown in Table 9-5, the average strut strength increases with decreasing cell size. Using the Weibull probability function to describe the strength distribution (Weibull, 1951), the range of strengths observed in these struts was best described by failure from surface flaws (Brezny and Green, 1990 a). In order to accurately evaluate the fracture mechanics approach [Eq. (9-9)], the fracture toughness should be normalized by all of the parameters on the right hand side of the equation. If this procedure results in a constant value at all cell sizes, the data are consistent with Eq. (9-9). The result of this normalization is shown graphically in Fig. 9-26 and when compared to Fig. 9-25, indicates that both theoretical approaches [Eq. (9-9) and (9-11)] appear to describe the toughness of these materials. The results of Fig. 9-26 imply that the term
9.7 Fracture Toughness
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toughness of glassy carbon struts but the presence of the pits should reduce the strut strength. A three fold reduction in the fracture toughness and crushing strength of the bulk carbon foam was observed as a result of this treatment. As shown later, the crushing strength is predicted to be directly proportional to strut strength (see Sec. 9.9) and as the fracture toughness shows the same change as the crushing strength with the oxidation treatment, the two properties should have the same dependence on strut strength. This is in agreement with the fracture mechanics approach [Eq. (9-9)] and not the energy balance approach [Eq. (9-11)]. Fractographic analysis supported the bulk property measurements and indicated a decrease in the strut strength as a result of the oxidation (Brezny and Green, 1991). Consequently, it was concluded the fracture mechanics approach [Eq. (9-9)] seems to provide an accurate description of the fracture toughness of brittle open cell materials as a function of density and cell size. This approach implies that one must maximize the strength of the individual struts in order to achieve maximum toughness in the foam. As will be seen later, the strut
491
strength is not only important in the toughness of open cell ceramics but it also influences a number of other mechanical properties. As pointed out earlier, Huang and Gibson (1990) have suggested that Eq. (9-9) is really only valid for crack lengths substantially greater than the cell size and will tend to overestimate the toughness for small cracks. The difference in the behavior between the vitreous carbon and alumina-mullite materials emphasizes the importance of understanding the strut microstructure of the material in order to be able to interpret the results. In both cases, it was demonstrated the strut strength can vary as a function of cell size in brittle cellular materials. In the vitreous carbon foam, the microstructure and degree of openness within the macrostructure did not change with cell size but the strut strength was found to increase with decreasing cell size. In the alumina-based foam, however, the strut strength apparently decreased at the smallest cell size. This probably reflects the experimental difficulties in using the coating technique for the fabrication of materials with fine cell sizes and in particular, can lead to the strut cracks observed in the slurry-coated, open cell ceramics. 9.7.3 Experimental Work on Closed Cell Ceramics
Zwissler and Adams (1983) studied the effect of relative density on the fracture toughness of foamed glass. The critical stress intensity factor was determined from testing standard single edge notched beam specimens in four point bending. They oberved the toughness to be directly proportional to the relative density and the data could be linearly extrapolated to give reasonable values for dense glass, Fig. 9-27. The toughness of the foam has been nor-
492
9 Mechanical Behavior of Cellular Ceramics
0.20
0.15-
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0.15
Figure 9-27. Relative toughness as a function of relative density in closed cell foamed glass material (Zwissler and Adams, 1983).
malized by the toughness of dense glass in this figure. Such behavior is apparently in disagreement with the density exponents of 1.5 [Eqs. (9-9), (9-11) or (9-12)] or 2 as alternatively suggested by Maiti et al. (1984 a). It appears the theoretical understanding of the fracture toughness of closed cell ceramics is in need of further development. Certainly, as discussed in this work, Eqs. (9-12) cannot be used for open cell foams, i.e., when 0 = 1. The data in Fig. 9-27 indicates the values of Klc/g for the closed cell foam are very similar to that of dense glass. If such behavior is also found in polycrystalline, closed cell ceramics, it would make such materials of great interest to structural designs that require minimum weight (see Sec. 9.3). Additionally, recognizing that dense alumina-based materials typically have fracture toughness values in the range 3 to 5 MPa ^/m, comparison of the data in Figs. 9-24 and 9-27 indicates the relative toughness of the closed cell ceramic is higher than the open cell. A slightly different approach was used by Green and Hoagland (1985) to model "closed" cell materials made by the sintering of hollow glass spheres. They modeled the behavior using shell theory applied to
a thin walled hollow sphere. As the spheres sinter their centers approach and the contact area increases. The fracture toughness was analyzed by considering both bending and tension of the cell wall. The model predicts a dependence of fracture toughness on density, cell size and the strength of the cell wall material, i.e., it involved the same parameters as Eq. (9-9) but the density exponent was larger. The analysis gave reasonably good agreement at low densities, where the materials failed at the contact regions between spheres. At the higher relative densities (> 0.15), however, the experimental data exhibited a slope similar to Zwissler and Adams (1983), becoming less sensitive to changes in density. For these materials, the fracture path had changed to one through the spheres, rather than between.
9.8 Tensile Strength 9.8.1 Theoretical Approach
The earliest attempts to model the strength behavior of foams was accomplished using a pentagonal dodecahedron unit cell geometry (Chan and Nakamura, 1969; Patel and Finnie, 1970; Menges and Knipschild, 1975). It was suggested that this unit cell gives an accurate description of a foam where cells consist of a network of triangular columns and pentagonal plates (Chan and Nakamura, 1969). To describe the strength, the models assume failure due to axial stresses and buckling only. An orientation factor was included in the analysis to define the contribution of those struts oriented at some angle to the applied load (Chan and Nakamura, 1969; Lederman, 1970; Menges and Knipschild, 1975). Under tensile stresses, the struts oriented in the direction of the load are assumed to
9.8 Tensile Strength
fail first and are therefore responsible for the strength of the foam. The tensile strength was shown to depend on the strength of the solid material within the struts and linearly on the density (Menges and Knipschild, 1975). The random orientation of the struts, with respect to applied stresses in the real materials, makes it very unlikely for purely axial loading to ever occur. Although an axial component of the load will be present, it is the bending component which is most likely to result in failure in the highest fraction of the struts. Patel and Finnie (1970) recognized the important contribution of strut bending to the mechanical properties of closed cell materials. An important distinction between the approach of Patel and Finnie and the other models is in their treatment of cell faces. Based on typical dimensions of struts and faces, they calculated the relative contribution of each to the strength of the foam in tension and compression. They found that under tensile loading, even a very thin membrane within the face can support a significant fraction of the load. In tension, the struts support about 10 times the load carried by the faces, whereas in compressive loading, this ratio was much higher. Patel and Finie (1970) suggest the cell walls are likely to rupture first, because of their reduced cross section, resulting in load transfer to the adjacent struts which will fail shortly after. To calculate the strength of the foam as a function of density Patel and Finnie (1970) considered a column supported by an elastic foundation (the cell wall). The tensile strength (aft) was described as a function of foam density by the relation:
493
the exponent B is related to the actual deformation mode of the unit cell. Patel and Finnie suggested a test of the various proposed models should be based on the agreement of this exponent with experimental results. With their theoretical approach, they obtained good agreement with experimental data on a closed cell polyurethane, suggesting that E ~ 1 . 0 . Patel and Finnie also suggested that for tensile loading, the deformation phenomenon is the same for open and closed cell materials because the cell walls will rupture first, leaving the struts to carry the load. Based on these assumptions, they ignore the cell wall contribution to the tensile strength of closed cell foams in their analysis. This approach predicted no cell size effect on the tensile strength of polymer foams but indicated the distribution of solid between faces and edges could influence strength. Based on our knowledge of the flaw sensitivity of ceramics to tensile stresses, it may be more appropriate to use a fracture mechanics approach to tensile strength rather than the load-bearing arguments of Patel and Finnie (1970). In this approach, once an equation has been derived for fracture toughness it is straightforward to determine the relationship with the fracture stress, as L) is given by (9-14)
(9-13) The constant A depends on the cell geometry and solid material properties, whereas
It is interesting to note that if the cellular structure is completely intact (a = L), the tensile strength of the cellular material is
494
9 Mechanical Behavior of Cellular Ceramics
predicted to be given by (9-15) Huang and Gibson (1990) have, however, suggested that Eq. (9-9) is not valid for crack sizes of the order of the cell size. Equation (9-15) has the same form as that for compressive strength [Eq. (9-19)], and thus for cellular materials the tensile and compressive strengths are often very similar. This is a sharp contrast to dense ceramics, in which compressive strengths are typically an order of magnitude greater than tensile strengths. Equation (9-14) indicates tensile strengths at a given density can be improved by reducing the flaw size (a) to the cell size but further strength increases require improvements in
K
(
1.
(9-16)
a but such an approach remains to be tested. The density exponent in Eqs. (9-14) to (9-16) is different from that predicted and measured by Patel and Finnie (1970), their exponent was ~ 1.0. In addition, one would expect that the presence of faces in cellular ceramics would constrain cell edge bending, especially as strut buckling is expected to be very difficult (see Sec. 9.9.1). Although not discussed in this chapter, the load carrying capability of porous ceramics can be substantially enhanced when used as a component in composite materials. For example, Van Voorhees (1990) has studied a simple ceramic sandwich (laminate) composite, in which a cellular core is bonded to dense face plates. This system resulted in a substantial increase in the
load-carrying capability of the core material and allows stiffness and strength to be further maximized with respect to weight. Presumably porous ceramic matrices could also be exploited in fiber reinforced composites, taking advantage of the large differences in stiffness to obtain a modulus strengthening effect. 9.8.2 Specimen Size Effects Specimen size effects stem from the large scale macrostructure of most cellular materials and become important at small specimen size to cell size ratios. It has been postulated that edge effects are a result of a poorly-connected, outer surface region (Brezny and Green, 1990 b). Cutting, machining or other forms of surface damage of these materials could enhance this damaged region. These outer cells are included in the specimen dimensions, however, they contribute little to the properties of the sample. The way in which this layer of cells affects the mechanical properties depends on the loading geometry used in the test. For example, under axial loads this outer layer of cells will result in a reduction in the effective load-carrying cross sectional area of the sample. Under bending stresses, on the other hand, this layer of cells results in a decrease in the effective moment of inertia of the beam. At small specimen to cell size ratios, the surface cells constitute a large fraction of the specimen cross section and it is in these specimens that edge effects dominate the test errors. These effects may play a significant role in all property measurements which rely on the sample dimensions to obtain the stressed volume of material. In cellular solids, particularly at small specimen sizes, this outer layer of poorly connected cells makes it very difficult to accurately obtain the stressed volume (Brezny and Green, 1990 b).
495
9.8 Tensile Strength
Specimen size effects exhibited a significant influence on the elastic modulus and bend strength of open cell vitreous carbon. The relative strength is plotted as a function of the cell size/specimen size ratio in Fig. 9-28. The specimen size was taken as the width or height of the beam (square cross-section). The relative strength is the ratio of the calculated strength to that of the material where no specimen size effects are observed, i.e., at large specimen sizes. The calculated values of the strength are dramatically reduced for the small specimen sizes, as shown in Fig. 9-28, and this is due to both a reduction in the effective moment of inertia, as well as, a change in the location of the point of maximum stress within the beam. On the basis of these observations, a simple model was proposed to predict and correct these effects. This model treated the rectangular bend specimen as a composite beam made up of a low modulus outer layer, representing the region of poorlyconnected cells, surrounding a higher modulus core of undamaged cellular material. When calculating the strength from the sample dimensions of such a specimen, one is unaware of the effective dimensions and
1.2
thus the effective moment of inertia of the beam. An expression describing the moment of inertia of the composite beam was derived by applying the parallel axis theorem to a beam of equivalent stiffness but made up of a single material. The approach used in the study was to estimate the effective moment of inertia from beam deflection data and to use this value in calculating strength. Such an approach proved to be a useful means of correcting for the size effects and could be useful, if strength testing of large specimens is not practical (Brezny and Green, 1990 b). The measured strength values (Fig. 9-28) for all the specimen sizes have been treated using this model and are plotted in Fig. 9-29. Correcting for the specimen size effects has resulted in a dramatic reduction in the variability of the strength values over those plotted in Fig. 9-28 and shows that the strength is relatively independent of specimen size over the range of sizes tested. The variability has been reduced from an order of magnitude to a factor of 2. The remaining variability may be related to the uncertainty in estimating the stressed volume in small specimens (Brezny and Green, 1990b).
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Figure 9-29. Experimental values of the strength (given in Fig. 9-28) corrected for edge effects and plotted against cell size to sample size ratio.
496
9 Mechanical Behavior of Cellular Ceramics
These specimen size effects can result in a dramatic underestimation of the magnitudes of the material properties and the data also showed an overestimation of the width of their distributions when calculated using standard beam equations. This is important to realize when using laboratory specimens to generate reliability data. It was observed that samples which are tested in bending must have at least 20 cells along the base and height in order to minimize these effects. Lakes (1986, 1991) has also suggested that size effects in cellular solids can be due to non-classical elastic behavior. Indeed, Lakes has used size effects as a means of determining the elastic constants of cellular materials, treated as Cosserat elastic solids. 9.8.3 Experimental Work on Open Cell Ceramics The bend strength of open cell aluminas has been measured as a function of relative density and cell size in three point bending (Brezny and Green, 1989, 1990 a). As discussed in previous sections (see Sees. 9.5, 9.6, 9.7), the microstructure, elastic and fracture behavior of an alumina mullite,
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Relative density
Figure 9-30. Bend strength versus relative density in the AM material.
open cell material was well described by Eqs. (9-2), (9-5) and (9-9). It has been discussed in the literature that one can apply linear elastic fracture mechanics (LEFM) to describe the strength to flaw size relationships of brittle polymer foams (Fowlkes, 1974; Anderton, 1975; Mclntyre and Anderton, 1975; Hobbs, 1977). This relationship appears to hold for cellular ceramics as well (Brezny, 1990) and therefore experimental data were analyzed in terms of Eq. (9-14). 9.8.3.1 Effect of Density The bend strength data of the aluminamullite material are shown in Fig. 9-30. As this material exhibited good agreement with the exponent on the relative density term in expression Eq. (9-9), the same agreement was observed in the bend strength. This is not surprising as LEFM was used in both deriving Eq. (9-14) and calculating the macroscopic flaw size in the material. Assuming Eq. (9-14) accurately describes this material, the geometric factor C6 was estimated from the data as 0.19 which is in good agreement with the theoretical value of 0.18 suggested by Zhang, (1989) for an isotropic foam. The average values of fracture toughness and bend strength taken from 20-30 specimens are summarized in Table 9-6. The bend strength results were fitted to a twoparameter Weibull equation to estimate a value of the Weibull modulus (Table 9-6). The values of Weibull modulus are low, indicating a wide macroscopic flaw size distribution. The strut strengths were also analyzed using a two-parameter Weibull function and a Weibull modulus of 2 - 3 was estimated, indicating high variability in strength and critical flaw size. Examples of typical flaws observed in the struts of the open cell alumina and vitreous carbon ma-
9.8 Tensile Strength
4y/
Table 9-6. Strength and toughness measurements. Material
Q/QS
Cell size (mm)
Toughness (kPa m1/2)
Bend strength (kPa)
Weibull modulus
Flaw size (mm)
AM a
0.08 0.11 0.11 0.10 0.17 0.17 0.16 0.23
3.00 4.02 3.43 1.06 4.33 3.33 1.09 3.04
40.0 97.0 60.0 11.6 181.1 120.0 43.1 200.0
840 1778 1070 296 3153 1930 838 3710
6.6 7.0 6.7 4.6 6.2 7.6 5.7 7.3
1.2 2.4 2.0 1.0 2.5 2.6 2.0 2.2
RVCb
0.03 0.03 0.04 0.04 0.03 0.04 0.04
4.19 2.55 2.10 1.41 0.98 0.68 0.49
47.1 42.0 56.4 66.9 47.3 72.7 60.3
534 677 1016 1067 967 1560 1230
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5.4 2.7 2.2 2.5 1.8 1.6 1.8
1
Brezny and Green (1989);
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Brezny and Green (1990 a).
terials were shown earlier in Figs. 9-18 and 9-19. One would expect a higher Weibull modulus for the bulk samples than the individual struts as the weak struts are distributed throughout the structure and their effect on the final fracture process would be somewhat "smoothed-out". It would also be expected that the variability in strut strength would be an important aspect of the failure process in brittle foams. For example, highly variable strut strength would be expected to promote the possibility of damage occurring throughout a cellular material. For brittle crack propagation, one would expect strut strength variability to lead to some degree of stable crack growth. It is important to realize that these materials can contain both microscopic and macroscopic flaws. The microscopic flaws consist of pores or cracks within the strut walls whereas the macroscopic flaws are broken cell struts and other imperfections in the structure (Brezny and Green, 1989,
1990 a). These flaws can be present in the polymer foam used in processing or can form during burnout or carbonization of the polymer. Experimental values of the bend strength and fracture toughness were used with the LEFM strength equation [Eq. (9-14)] to estimate the size of the macroscopic flaws assuming a half penny surface flaw geometry (Table 9-6). The average flaw sizes in the AM material are of similar magnitude to the cell size. Although the average flaw size implies a perfect macrostructure composed of cells which are completely intact, the large strength variability in this material indicates that in fact there is a distribution of flaw sizes many of which may be larger than the cell size. Broken struts are often observed in these materials which supports this result. The microscopic flaw sizes within the struts can be estimated from the strut strength data and the toughness of the material within .the struts and were found to be ~ 60 \im. For the particular
498
9 Mechanical Behavior of Cellular Ceramics
material tested this represented about onequarter of the strut diameter. It is reasonable to conclude that reduction of flaw size in these struts should be possible and would substantially improve strut strength and hence the toughness and strength of the bulk foams.
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The alumina-mullite and alumina-zirconia materials were also tested as a function of cell size at a given density. The AM material exhibited higher strengths at larger cell sizes (Fig. 9-31 a). Equation (9-15) predicts a square root increase with cell size, as long as the flaw size and strut strength do not vary. The bend strength of this material exhibited a much stronger dependence. This behavior with cell size is similar to that of fracture toughness already discussed for the AM material (see Sec. 9.7.2.3). This was explained in terms of a change in fracture mode with cell size (Brezny and Green, 1990 a). Due to the difficulty in processing the finest cell material, it exhibits a larger degree of strut cracking, primarily longitudinal strut cracks (Fig. 9-14). The results follow the same trend as the elastic modulus and crushing strength data discussed by Dam (1988). These measurements further support the observation that both the macro- and microstructure may vary with cell size in cellular ceramics. The AZ material, on the other hand, exhibited no cell size dependence (Fig. 9-31 b), as a high degree of longitudinal strut cracks were present at all cell sizes. A comparison of these two materials made by the same general technique indicates that one must understand the effect of the macrostructure within the foam and the microstructure within the struts in order to be able to predict and understand their behavior.
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The bend strength of the open cell carbon (RVC) material was measured at one density and seven cell sizes (Brezny and Green, 1990 a). The results are given in Table 9-6 and Fig. 9-32 where they exhibit an increase in strength with decreasing cell size. This is similar to that reported for foamed glass (Morgan et al., 1981) but the power dependence on cell size was —0.25 for the RVC foam and not —0.5, as theoretically suggested by Morgan et al. (1981). If one assumes a half penny surface flaw in the bulk cellular material, it is possible to estimate a macroscopic flaw size using the
9.8 Tensile Strength
experimental data in Table 9-6. The flaw size is approximately equal to the cell size in the large cell materials (4.19 — 2.1 mm) but becomes 2 - 4 times greater than the cell size in the fine cell samples (0.98 — 0.49 mm). The average flaw size in the smallest cell samples is still less then half the size of the largest cell material. It is clear one cannot simply assume the flaw size is proportional to the cell size in these materials. For the RVC, the increasing strength with decreasing cell size is thus a result of the combination of increasing strut strength and decreasing cell to flaw size ratio. Thus, in considering the bend strength of brittle open cell materials, one should understand the strut strength and macroscopic flaw size changes, both of which can vary with cell size. The strut strength, cell size, flaw size and relative density measured for the RVC material was used to calculate the geometric constant C6 that best described the cell geometry of this foam (Brezny and Green, 1990 a). The calculated value of 0.2 is slightly larger then the theoretical value of 0.18 proposed by Zhang (1989) which was based on a tetrakaidecahedron unit cell.
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Figure 9-32. The bend strength increases with decreasing cell size in the RVC samples, due to the higher strut strength, as well as a smaller critical flaw size in the finer cell foams.
499
The Weibull moduli estimated for the RVC samples are given in Table 9-6. The values exhibit a very wide range and no correlation with cell size. The Weibull modulus of the RVC samples is on average, significantly higher then the materials made by the polymer coating process. This may be a result of the processing of this material resulting in a narrower distribution of macroscopic and microscopic flaws. The RVC struts remain solid and the flaws consist of inclusions or pores which form during carbonization (Brezny and Green, 1990 a). The processing of the alumina materials includes a burnout of the polymer substrate prior to sintering of the ceramic which often introduces cracks into the struts, as shown in Figs. 9-9, 9-18. Although the average macroscopic flaw size is not much larger than the cell size in both materials, the range of sizes is much larger in the alumina materials. A comparison of the experimental results obtained for the RVC material and the cellular alumina makes an important point when working with brittle cellular solids. The models developed to describe the behavior of these materials are very general and show only the basic relationships between the parameters in the model. When working with materials whose properties are extremely sensitive to the microstructure (like ceramics), one must be careful when using these simple models to predict the mechanical behavior. To make accurate predictions, one must thoroughly understand the type of microstructural variability which can develop in the samples as a result of processing, and for improved materials, one should tailor this microstructure to achieve the desired behavior and properties.
500
9 Mechanical Behavior of Cellular Ceramics
9.8.4 Experimental Work on Closed Cell Ceramics
The earliest experimental work which studied the tensile behavior of brittle foams was done using foamed glass (Morgan et al., 1981; Zwissler and Adams, 1983) and foamed cements (Meiser and Tressler, 1981; Hengst and Tressler, 1983). Work on foamed low density cements concluded that the strength was linearly related to the relative density (Meiser and Tressler, 1981). Acoustic emission analysis indicated that a change in failure mode from cumulative damage to Griffith type failure occurred from low density to higher density materials (Meiser and Tressler, 1981). In specimens where Griffith failure controls fracture, the strength dominating parameter was suggested as the maximum pore diameter (Hengst and Tressler, 1983). Morgan et al. (1981) studied foamed glasses with relative density of 0.055, and varying cell size, to determine the dependence of the strength. They suggested that strength was proportional to the inverse square root of the cell size in these materials. If the flaw size is linearly proportional to cell size and the toughness of the foam was independent of cell size, this is the behavior to be expected. This can be seen by considering Eq. (9-16), but it is inconsistent with Eq. (9-14) unless oH^/L is constant. Zwissler and Adams (1983) in their work on foamed glass showed that both strength and toughness values had approximately a linear dependence on relative density (Figs. 9-27, 9-33), which is difficult to understand on the basis of Eq. (9-16). If one compares the relative values of the bend strength for open cell polycrystalline materials and closed cell glasses (Figs. 9-30 and 9-33), they have similar strengths. One would expect that closed cell, polycrystalline ceramics could be made higher
CO Q_
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T3 C (D CD
1-
Relative density
Figure 9-33. Bend strength showing an approximately linear increase with increasing relative density in foamed glass (Zwissler and Adams, 1983).
strength than a material based on glass, which has low fracture toughness in the dense form. Thus it appears the reinforcing influence of the cell faces not only significantly impacts the elastic (see Sec. 9.6.2) and fracture toughness behavior (see Sec. 9.7.3) but also the tensile strength of cellular ceramics.
9.9 Compressive Strength 9.9.1 Theoretical Approach
The earliest theoretical models to predict the behavior of cellular materials considered only axial stresses as being important to the stiffness of polymer foams. One model consisted of a simple unit cell geometry based on a cubic network of struts rigidly connected at the intersections (Gent and Thomas, 1959). The tensile modulus was derived assuming the deformation occurred by pure axial tension and the compressive modulus was described by Euler buckling. Lederman (1970) compared this model to experimental data on a variety of foams, in order to obtain a fitting parameter, that takes into account variations in
9.9 Compressive Strength
foam geometry. Matonis (1964) developed a model to describe the behavior of closed cell foams based on the assumption that the cell faces were loaded in pure axial tension or compression. Later researchers criticized these models for their simplistic geometry which was not characteristic of actual foams (Chan and Nakamura, 1969; Patel and Finnie, 1970; Menges and Knipschild, 1975). These various researchers suggested that a pentagonal dodecahedron gives a more accurate description of a foam where cells consist of a network of triangular columns and pentagonal plates. To describe the strength, only axial stresses and buckling were considered, and therefore, an orientation factor was included to define the contribution of those struts at some angle to the applied load. Observation showed the first struts to fail in compression were those oriented in the direction of the load. Under shear stresses, the struts oriented at angles of 45° to the load failed first. The compressive and shear strengths were assumed to occur by Euler buckling and both of these properties where shown to depend on the elastic modulus of the solid and the square of the density (Menges and Knipschild, 1975). Under compression and shear loading the cell walls buckled and folded whereas under tension they fractured. Based on this observation, it was concluded that the struts and not the faces were the supporting members (Menges and Knipschild, 1975). One criticism of these early models is the assumption of buckling as the deformation mode. The criteria for Euler buckling is given by (Stevens, 1979):
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Dn2E ~.
an
(9-17)
where E is the Young's modulus,
501
of the column and r is the radius of gyration. The quantity L/r is called the slenderness ratio and D is a constant characteristic of the end conditions on the beam. To a first approximation, the struts can be considered as a beam rigidly fixed at both ends and a value of D = 4 is appropriate for this situation. Solving Eq. (9-17) for a typical ceramic gives a minimum slenderness ratio required for buckling of approximately 60. Typical L/r values for the strut dimensions in cellular ceramics are less than 10. In this range, columns would undergo compressive failure under axial loads rather then buckling. The random orientation of the struts in the real materials makes it very unlikely for purely axial loading to ever occur. Although an axial component of the load will be present, it is the bending component which is most likely to result in failure of the struts in ceramics where compressive strut strengths are expected to be very high. Patel and Finnie (1970) recognized the important contribution of strut bending to the mechanical properties of closed cell materials. An important distinction between the model of Patel and Finnie and all of the other models is in their treatment of cell faces. In both applied tension and compression, some of the cell faces will be placed in tension. It was assumed that cell walls will buckle in compression allowing struts to bend but tension in a face will constrain strut bending. Compressive failure or yielding, was assumed to occur by rupture of the cell wall due to tensile stresses and simultaneous buckling of the attached struts. To calculate the strength of the foam as a function of density Patel and Finnie (1970) modeled the compressive strength by considering a column supported by an elastic foundation (the cell wall). They pointed out that under compressive loads the strut will move to put
502
9 Mechanical Behavior of Cellular Ceramics
some walls in tension. Following tensile failure of the cell wall, the buckling of the struts was considered to be the principal deformation mechanism in compression. The compressive strength (afc) was described as a function of foam density by an equation of the same form as Eq. (9-13), i.e., (9-18) Patel and Finnie (1970) predicted different values of the density exponent [B in Eq. (9-18)] for open and closed cell foams under compressive loading due to the differing contribution of the faces, i.e., B increased from 1.45 to 2.06 as the volume fraction of solid in the faces decreased. It is not clear that this approach can be applied to cellular ceramics, as shown earlier, the cell edges are less likely to buckle in compression. In these materials, the bending of the cell struts will be more difficult as a result of the restraint of the attached faces but once the faces fail, strut bending should become predominant. The model proposed by Gibson and Ashby (1982) for cellular materials was extended to consider compressive behavior by Maiti et al. (1984 b). Compressive failure of the foam was assumed to occur when the bending moment being applied to the struts reaches the fracture moment (Mf), which depends on the strength (afs) of the individual struts. The maximum moment acting on a strut can be related to the stress (a) being applied to the bulk structure and is found to be proportional to a I?. Combining these relationships, the crushing strength equation is given by: (9-19) where C 7 is a geometric constant that can be determined from experimental data. For
these cases, fracture is initiated by flexural failure of individual cell struts. Using limited data, Maiti et al. (1984 b) calculated the constant C 7 to be equal to 0.65, however, this constant, as well as, the density exponent could be very sensitive to the assumed values for
Qs
where 0 is the volume fraction of the solid contained in the cell edges and (1-0) is that within the faces. For an open cell foam (1 — 4>) is equal to zero and Eq. (9-20) reduces to Eq. (9-19). In contrast to the earlier suggestion by Ashby (1983) that the presence of faces does not influence the
9.9 Compressive Strength
compressive strength. Eq. (9-20) predicts the density exponent will decrease from 1.5 to 1 as the volume fraction of solid in the faces increases. The expressions for the compressive strength of open and closed cell foams [Eqs. (9-19) and (9-20)] predict no dependence on cell size as long as the strength of the solid (a{s) remains independent of this parameter. Maiti et al. (1984 b) have defined and formulated equations to describe the compressive behavior of cellular foams in terms of deformation-mode and energy absorption maps. In compression of a cellular material, the initial response is linear elastic; this is followed with a plateau region in which the cells collapse. In the plateau region, the stress is assumed to be independent of the strain as part of the structure collapses, while other parts of the structure remain elastic. The type of deformation that occurs in the plateau region depends on the mechanical behavior of the strut material. For a brittle ceramic material, the mode is expected to involve brittle fracture of the struts. When most of the cell walls have collapsed and begin to press against each other, densification of the material can occur. This final region is where the stress rises sharply and the foam approaches the theoretical packing density of the material. Figure 9-34 shows the idealized stress-strain behavior of cellular materials as suggested by Ashby (1983). Deformation maps for cellular materials have axes of normalized compressive stress (o"/£s) and the compressive strain (e), where Es is Young's modulus of the strut material. The three distinct regions (linear-elastic, non-linear elastic or plateau, and densification) are divided by two boundary lines. The densification boundary line is defined as the region where the foam reaches one third of its theoretical density. A theoretical deformation map for a cellular ceramic
503
Densification Elastic Plateau Buckling, crushing or yielding
Strain
Figure 9-34. Idealized stress-strain behavior for cellular materials (Ashby, 1983).
is shown in Fig. 9-35, using values of (jfs = 150 MPa and Es = 325 GPa; typical values for a commercial open cell alumina. The experimental data available on the crushing behavior of brittle foams is very limited. The earliest work involved glassy carbon foams (Schmitt, 1970; McLaughlin and Kite, 1970), and more recently, studies on foamed glass (Morgan et al., 1981) and open cell ceramics (Dam et al., 1990) have been published. The results of these studies will be compared, if possible, in the following sections with the theoretical equations. 9.9.2 Experimental Work on Open Cell Ceramics
Schmitt (1970) studied the compressive failure of open and closed cell carbon foams. For the open cell carbon, the material gradually crumbled during the compressive testing. The failure was localized to the regions adjacent to the loading platens such that layers of cells successively fractured. McLaughlin and Kite (1970) compiled the experimental data on the open cell carbon but this data is insufficient to compare with the theoretical equation [Eq. (9-19)]. Schmitt (1970) mentioned two experimental concerns when testing carbon foams in compression; the importance of parallel loading surfaces and whether
504
9 Mechanical Behavior of Cellular Ceramics 1000
100
~x10 D 10
Crushing region 0
0.1
0.2
0.3
0.4
(a) 0.5
0.6
0.7
0.8
0.9
1.0
0.20
Figure 9-35. (a) Theoretical deformation-mode map generated for a brittle foam using typical values, Es = 325 GPa and
the specimens were bonded to platens. Bonding to steel discs increased the loadcarrying capability but rather than a gradual crushing, the onset of failure was distinguished by a sudden load drop as a crack propagation event occurred. McLaughlin and Kite (1970) discussed a variety of problems involved in trying to uniformly load brittle foams. 9.9.2.1 Effect of Density The crushing behavior of a commercial alumina-mullite open cell foam was studied by Dam et al. (1990) as a function of
relative density and cell size. Cube-shaped samples with axial dimensions of approximately 22.2 mm were loaded to failure in compression between SiC plates. The crushing strength was determined by extracting the point from the chart recorder where the load reached its maximum value prior to the onset of substantial crushing. A typical stress-strain plot is shown in Fig. 9-36. This figure has been smoothed considerably from the actual experimental output, in which the load variations are much larger. In comparison to the idealized version of Fig. 9-34, one sees a rather more complicated pattern of behavior. Compression tests were videotaped in order to identify details of the fracture process. As the stress is increased, it was observed that struts were failing prior to attaining the maximum stress. The struts that failed were sometimes in the contact area and indicates the difficulty in uniformly loading these materials. In addition, strut failure was observed within the body and these 2000
810
1215
1620
2025
Time (s)
Figure 9-36. Typical crushing test data for a constrained open cell alumina specimen. Region 1 is the specimen and loading fixture alignment. Region 2 corresponds to the elastic region and can involve strut fracture, either in the contact region or internally. At the crushing point (3), macroscopic cracks propagate, with an associated load drop (Region 4). Additional deformation of the fractured material occurs in region 5 until finally densification occurs (Region 6).
9.9 Compressive Strength
were presumably weaker struts or struts that are aligned in favorable positions for maximum stress. The failure of these struts is accompanied by slight drops in the stress/strain curve as the load increases. The stress continued to rise as the damage was accumulating until a large macroscopic crack or multiple cracks propagated through the sample. At this point portions of the sample separated from the main body creating sharp drops in load. In order to observe the densification region, it was necessary to contain the sample fragments. The crushing strength data, normalized by the mean strut strengths are shown in Fig. 9-37 as a function of normalized density. Using linear regression, the experimental data were found to fit 2.2
(9-21) It is clear that there is substantial disagreement between the experimental data and that predicted by Eq. (9-19). As indicated in the direct observations of the failure process, the crushing strength was not associated with the failure of a single strut, as assumed in the theoretical analysis but rather with a crack propagation event after the accumulation of a certain amount of damage has been attained. Thus one possible reason for the discrepancy between Eqs. (9-19) and (9-21) is the manner in which the crushing points were determined. The stresses which were designated as the crushing points in this study are actually the points when a crack or multiple cracks propagate through the sample and this may not be initiated by the failure of a single strut. The other possible reason for the discrepancy between the theory and the experimental data could be the difficulty in uniformly loading these porous cellular materials, as mentioned at the start of this section.
505
Normalized density
Figure 9-37. Normalized crushing strength as a function of normalized density in the AM material (1.3 mm cell size).
In indentation on brittle cellular materials, Gibson and Ashby (1988) have pointed out, there is a difficulty in uniformly loading the struts present in the contact area. Their analysis shows that when a noncompliant face is used to load a cellular material, one must account for the probability of the loading surface contacting a strut. Their analysis shows the probability of loading a given fraction of struts decreases with increasing indenter area and the indentation hardness can be substantially less than the crushing strength (an order of magnitude or more), as a result of this effect. Presumably, the same effect can occur in a compression test, i.e., the crushing strength will depend on specimen size and one can severely underestimate the true crushing strength if non-compliant loading rams are used. For the tests discussed earlier, the specimens were loaded via SiC plates and this should make uniform loading difficult. To observe the effect of load distribution on the behavior of brittle foam, a compliant polymeric layer (3 mm thickness neoprene) was used between the loading rams and the specimens. It was found that the crushing strength dependence on normalized density was dif-
506
9 Mechanical Behavior of Cellular Ceramics
ferent than discussed earlier. Linear regression of the data gave the following equation 1.7
(9-22) The 95% confidence intervals on the power for the normalized density were (1.6, 1.9). It was postulated that the change in density dependence was a result of the use of compliant rams (Dam et al. 1990). These rams also led to a substantial reduction in the experimental scatter and a change in the failure event. Rather than accumulation of damage during loading, failure occurred by a more pronounced crack propagation event. In comparing Eqs. (9-21) and (9-22), the use of compliant rams did not substantially change the magnitude of the crushing stress over the density range studied. For these tests, the specimens had been manufactured to net shape and no machinery was required. Thus, the specimens had relatively smooth loading surfaces in which the probability of strut contact was high, even for non-compliant loading rams. The agreement between Eqs. (9-19) and Eq. (9-22) is reasonably good and appears to support the approach by Gibson and Ashby for the theoretical crushing strength relationship. The dependence of the uniformity of loading on the agreement between experimental results and the theoretical relationships is an important issue that has yet to be totally resolved. Recent work (Brezny, 1990) has shown the method of loading specimens in compression can significantly influence the density exponent. In addition, it was shown by visual observation and acoustic emission, that substantial damage occurs prior to maximum load in open cell ceramics, an effect that is not really considered in the development of Eq. (9-19).
9.9.2.2 Effect of Cell Size The theoretical relationship presented by Gibson and Ashby [Eq. (9-19)] suggests that the cell size should have no effect on the crushing behavior provided the strut strength does not vary with cell size. As discussed in Sec. 9.7.2.1, this is often found not to be the case in cellular ceramics. The effect of cell size on the crushing strength has been evaluated for both the aluminamullite (Dam et al., 1990) and glassy carbon (Brezny and Green, 1990 a), open cell foams. The crushing strength of the aluminamullite (AM) material increased dramatically with increasing cell size as shown in Fig. 9-38. The crushing strength was found to be substantially lower for the smallest cell size material. Two possible explanations were considered for this cell size effect. Firstly there may be a specimen size effect in that a larger number of struts are being tested as the cell size decreases and there is therefore, an increasing probability of low strength struts being present (the test specimens were constant volume). Secondly, there may be microstructural differences at the smallest cell size. Strut
0 RD = 0.16 • RD = 0.11 3 -
T
I
2 -
I
1
i
Cell size (mm)
Figure 9-38. Crushing strength as a function of cell size for the alumina mullite material with relative densities of 0.11 and 0.16.
507
9.9 Compressive Strength
Q.
0.8i_
CD > CO
r
0.6 -
to
J
I
i g
0.4 -
i
i
w
CD
iduu
strength data could not be obtained for the finest cell size material but as discussed in Sec. 9.6.1, this material was found to contain more strut cracks and fracture involved more strut splitting (Fig. 9-14). The results of fracture toughness, bend strength and Young's modulus (Figs. 9-24 a, 9-31 a and 9-13) measured as a function of cell size in the AM material all suggest an increase in the degree of strut cracking with decreasing cell size (Brezny and Green, 1989; Dam et al., 1990). The complexity and variability in the strut microstructures with cell size in the AM material made it difficult to interpret the crushing strength results as a function of cell size. The crushing strength of the RVC material exhibited very different behavior (Fig. 9-39). There is a strong cell size dependence of the crushing strength in the RVC which is opposite to that found in the AM material, i.e., the crushing strength increased with decreasing cell size. As shown in Sec. 9.7.2.1, strut strength was found to increase in a similar fashion and thus the experimental behavior (Brezny and Green, 1990 a) was consistent with the theoretical equation [Eq. (9-19)]. From the fractographic measurements of strut strength, a geometric constant for the carbon foam material was calculated (C7 = 0.11). Once such an equation has been established for a material, a simple crushing test can be
0.2 -
o
o
0 -
1
2
3
Cell size (mm)
Figure 9-39. The crushing strength decreases with increasing cell size in RVC indicating a decrease in strut strength with increasing strut size.
used to quickly evaluate strut strength and the impact of processing improvements on this parameter. Table 9-7 presents a comparison of the various predicted geometric constants and density exponents (Gibson and Ashby, 1988; Zhang and Ashby, 1989; Zhang, 1989) with the experimental data on open cell ceramics for all the properties discussed in this chapter. A deformation-mode map was constructed, for the AM material, using the average of three principal points: crushing point, lowest stress point, and densification point. As indicated in the above discussion, the compressive behavior of brittle foams is rather erratic, especially following the elastic loading region. It does appear, how-
Table 9-7. Theoretical and experimental values for equation constants (after Brezny and Green, 1990 a).
Zhang Relative density (9-2) Young's modulus (9-5) Shear modulus (9-6) Crushing strength (9-19) Fracture toughness (9-9) Tensile strength (9-14)
Density exponent
Geometric constant (C,)
Property (Eq.)
1.06 0.5 0.17 0.16 0.18 0.18
GA «1 ft? 1
^0.38 0.65 0.65 0.65
A12O3
RVC
GA
0.65 0.36 0.22 0.14 0.13 0.19
0.75 1.5 — 0.11 0.14 0.2
2 2 2 1.5 1.5 1.5
Exper. 1.9 1.9 2.2 «2 1.46 1.47
508
9 Mechanical Behavior of Cellular Ceramics
ever, the elastic and compressive strength behavior is reasonably well described by the theory based on the Gibson and Ashby unit cell. Figure 9-40 shows the experimental deformation-mode map for the AM material for the elastic region and the crushing boundary. In comparing this figure to Fig. 9-35 b, the experimental data appear to follow reasonably well the theoretical ideas proposed by Maiti et al. (1984 b) though as discussed above cell size effects can appear in the actual compressive behavior. The crushing and densification regions are not included in this figure as the crushing behavior of the poly crystalline ceramic foams is very chaotic, with sudden and wide load variations. Indeed, fragments of the specimen are scattered away from the test specimen, making it difficult to reach densification. This contrasts strongly with the crushing behavior of the open cell vitreous carbon, which approaches the idealized behavior of Fig. 9-34. 9.9.3 Experimental Work on Closed Cell Ceramics
McLaughlin and Kite, (1970) studied the effect of density on the crushing strength of a carbon foam. Analysis of the data (Fig. 9-41) showed the density exponent to be in the range 2.2 to 2.5, substantially larger than the theoretical value of 1.5 [Eq. (9-19)]. Without further information, it is difficult to assess the source of this incompatibility. There was also substantial strength anisotropy in the compressive strength of the carbon foam, with the maximum strength when the loading is parallel to the rise direction. Gibson and Ashby (1988) have shown their various theoretical analyses can be modified to predict the effect of cell anisotropy. The crushing behavior of foamed glass was studied by Morgan et al. (1981) as a
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
e (%)
Figure 9-40. Experimental deformation-mode map for the alumina mullite open cell material, showing elastic and crushing regions.
function of cell size. In this work, they showed the tensile,flexuraland compressive strengths increased with decreasing cell size, although there were some density variations from specimen to specimen that complicated the interpretation. The strength was found to depend on the stress state, with the strengths increasing in the order; tension, flexure and compression. The strength values were also shown to depend on stress rate and this was interpreted in terms of sub-critical crack growth. The
20
Perpendicular
0.07
0.17
0.27
Density (g/cm3)
Figure 9-41. Compressive strength as a function of cell size for a closed cell glassy carbon foam (Schmitt, 1970).
9.10 High Temperature Mechanical Behavior
stress corrosion behavior of foamed glass has also been discussed by Zwissler and Adams (1983). In these experiments, they noted a substantial difference between the behavior in foamed glass as compared to dense glass. They interpreted this difference in terms of the substantially different diffusion path for water, which is the active corrosive agent, in porous compared to dense glasses.
9.10 High Temperature Mechanical Behavior As ceramics are often utilized at high temperatures (> 1000 °C), their mechanical properties in this regime is often critical in determining their lifetime. Moreover, their low thermal conductivity and fracture toughness can often lead to severe thermal stress damage. This section will consider briefly some theoretical considerations and recent studies concerning this high temperature behavior.
509
thermal expansion, v is Poisson's ratio and AT = Tx — T2. The stress reduction factor is a parameter that takes into account the rate of heat transfer and is directly related to the Biot's modulus (/?), which in turn depends on the thermal conductivity of the material, the surface heat transfer coefficient and the material dimensions. For extremely rapid temperature changes, 3> can approach unity. The onset of thermal failure is often represented by a critical temperature change (ATC) that causes damage. This parameter is often estimated by setting a = oiv For the case when
Ea
Gibson and Ashby (1988) used the equations derived for E and ou [Eqs. (9-5) and (9-15)] to predict the effect of density on the thermal shock resistance of an open cell material and obtained AT = c
0.65 AT, 1/2
(9-25)
9.10.1 Thermal Shock Behavior
When the surface temperature of a solid is suddenly changed from T± to T2, thermal stresses occur in the body as a result of the dimensional changes that occur with temperature. Thus a temperature gradient in a body usually gives rise to a stress gradient. In many ceramic materials, these stresses result in fracture events and the (retained) mechanical properties can be severely degraded. The thermal stress (a) that occurs at the surface of a plate when it is subjected to such a temperature change is given by a =
(9-23)
where $ is a stress reduction factor, E is Young's modulus, a is the coefficient of
where ATCS = <xfs/[£sas], the thermal shock resistance of a fully dense material. This equation assumes the strut strength is equivalent to the strength of the dense material and from our earlier discussions, this is clearly not necessarily true. Equation (9-25) predicts cellular ceramics (Q/QS < 0.3) will have a better thermal shock resistance than a fully dense material and that the thermal shock resistance, as denoted by ATC, increases with decreasing relative density. As indicated earlier, we have shown crfs can depend on density and cell size in some materials and this would need to be included in an exact analysis. The above derivation also does not account for the important heat transfer effects, especially
510
9 Mechanical Behavior of Cellular Ceramics
the thermal conductivity of the foam, which one would suspect may be a critical item. For example, the thermal conductivity of a foam is often substantially less than that of a fully dense material and this would increase the value of 3> in Eq. (9-23) for the foam relative to the dense material. As pointed out by Gibson and Ashby (1988), the thermal conductivity of a foam depends on a variety of factors, e.g., cell size, density, gas conductivity, etc. Clearly, inclusion of these effects will complicate the simple ideas put forward in Eq. (9-25). An important distinction is expected to occur between open and closed cell materials. For an open cell material, one expects convective flow of the quenching medium to be very important, as the medium (gas or liquid) can flow into the center of the material. In particular, if this flow is rapid, it will allow the bulk temperature gradient, from the outside of the foam to the interior, to be rapidly reduced. For a closed cell material, such flow between cells is much more difficult such that radiation effects and conductivity through the gas and solid become more important than convection (Gibson and Ashby, 1988). A recent study has considered the thermal shock resistance of an alumina-mullite, open cell ceramic (Orenstein, 1990, Orenstein and Green, 1991). Initial experiments considered the change in compressive and flexural strength for specimens quenched into water. The intent was to simulate very rapid temperature changes. Figure 9-42 shows the results of these experiments and indicates a gradual loss in strength with increasing AT, rather than an abrupt change. Such behavior is often observed in ceramics as one increases the amount of porosity (Davidge, 1979). This implies a damage accumulation process rather than the rapid extension of a few flaws. The latter process is usually ob-
O)
Q.
O
O
200
400
600
800
600
800
A7-(°C)
0 200
400
A7TC) Figure 9-42. Strength shows a gradual decrease with increasing degrees of thermal shock in an open cell alumina mullite material: (a) compressive strength and (b) bend strength as a function of quenching temperature difference.
served in dense ceramics and there is an associated sudden drop in strength at the critical condition. The onset of damage for the cellular ceramics appeared to occur in the range AT = 200 to 300 °C. This damage initiation is somewhat difficult to define as the strength has substantial variability and the reduction in strength occurs gradually. Calculation of ATC, using Eq. (9-24), gave values of ~80°C, and thus it appears that 0 < 1.
511
9.10 High Temperature Mechanical Behavior
Figure 9-43, shows the type of damage incurred in the thermal shock and it involves struts cracking, where the number of cracks was found to increase with increasing severity of thermal shock (Orenstein, 1990). The morphology of these cracks suggest they are a result of a temperature gradient across a strut rather than across the bulk of the material. Such a situation can clearly occur in an open cell material, as the quenching medium (e.g., water) flows into the material. Measurement of the Young's and shear modulus, showed these parameters were also changing as a result of the thermal shock, Fig. 9-44. Such behavior is expected as the strut elastic constant (£s) will be effectively reduced by strut cracking [see Eqs. (9-5) and (9-6)]. Thus, for these materials, elastic modulus measurements can be used to assess the damage. Such an approach is attractive, in that the measurement is nondestructive, allowing the effect of stress and thermal fatigue to be assessed, and there is typically less scatter in the experimental data. To assess the thermal shock damage in the open cell ceramics, Young's modulus measurements were made before and after thermal shock (Orenstein, 1990, Orenstein
2.5
^
-•- Young's modulus -*•- Shear modulus
2.0 p
03
S »
1.5 1.0
0.5
200
400
600
800
A 7" (°C)
Figure 9-44. Young's and shear moduli exhibit a decrease with higher degrees of thermal shock as further damage is introduced into the struts.
and Green, 1991). For these experiments the onset of significant damage was defined as the value of AT when the modulus is reduced by 10% and is termed AT10. The values of AT10 for both oil and water quenches are shown in Table 9-8 for materials with a variety of densities and cell sizes. The experimental data show the thermal shock resistance is strongly dependent on cell size (increasing with increasing cell size) and weakly on density (increasing with increasing density). The change with density is opposite to that predicted by
Table 9-8. Thermal shock resistance of open cell, alumina-mullite materials quenched in water or oil. Relative density * (%)
Figure 9-43. Micrograph showing typical damage to the struts resulting from thermal shock (Orenstein and Green, 1991, reprinted by permission of the American Ceramic Society).
11 16 8 11 16 22 11 16
Cell size*
AT10(°C)
(mm)
Water
Oil
3.6 3.6 1.3 1.3 1.3 1.3 0.4 0.4
321 + 14 379 + 35 287 + 36 288 + 43 299 + 10 304 + 35 231 + 11 240 ±14
1096 + 157 1120+174 525+ 57 560+ 68 739 + 122 830+ 68 333+ 53 354+ 43
* Nominal values from manufacturer.
512
9 Mechanical Behavior of Cellular Ceramics
Eq. (9-25) and there is a strong effect of the choice of quenching medium. From the damage observations and the magnitudes of the AT10 values, it is clear that the ideas used to derive Eq. (9-24) need to be re-evaluated. Initial calculations indicated the water will reach the specimen center prior to any significant reduction in the temperature of the struts, thus removing the bulk temperature gradient before a thermal stress develops across the struts (Orenstein, 1990). It was assumed initially the thermal shock resistance of these materials could be considered by simply considering the quenching of the struts. This allows Eq. (9-23) to be written as (9-26) The removal of the bulk temperature gradient has an important effect on reducing the value Biot's modulus as the specimen dimension of concern in the modulus is that of the strut rather than the bulk sample. Unfortunately this approach does not explain the trend of the data in Table 9-8. The parameter 0 used in Eq. (9-23) is retained in Eq. (9-26) as it is likely to be less than unity even for a rapid water quench as a result of the reduced /? associated with a strut. For example, one expects /? to increase (decreases d>) with increasing density and cell size; an effect that is opposite to the data trend in Table 9-8. It was suspected that another source of thermal stress existed and it was postulated that the quenching medium undergoes heating as it infiltrates the specimens. For the fine cell material, the flow is expected to be more difficult giving more chance for the fluid to heat. For increasing density, the volume of the quenching liquid that can infiltrate the foam decreases, and the thermal mass of the solid is higher, both of which would tend to increase the heat transferred to the
quench liquid. Temperature measurements made at the specimen centers confirmed this was the observed trend (Orenstein, 1990). Thus, it was concluded that the thermal stresses arose from two sources; the temperature difference across the struts and the bulk temperature gradient that occurred as the quenching medium was heated (Orenstein, 1990). Comparison of the predicted and experimental retained elastic modulus for a given quench temperature difference showed fair agreement. The heating of the quench media explained the dependence of the thermal shock resistance on cell size but the source of the density dependence was less clear. For example, although it was found that E and the quench media heating increased with increasing density, this was offset by the increases in foam strength and decreases in Poisson's ratio. 9.10.2 Creep Behavior
Gibson and Ashby (1988) have put forward equations to describe the creep behavior of cellular materials. The steady state creep behavior of the struts was assumed to follow the power law behavior observed in most materials, i.e., 8 = 8 Os
(9-27) ;
0s,
where s and a are the strain rate and stress associated with a strut and n, 80s and aOs are creep constants of the strut material. By a similar approach to the derivation of the elastic constants, the unit cell can be analyzed to determine the relationship between the bulk and microscopic stresses and strain rates. For open cell materials this analysis gives (9-28)
Os
9.11 Conclusions
The value of n depends on the particular mechanism of creep that is predominating in some particular stress and temperature range. Equation (9-28) shows creep strain rate for the foam has the same stress dependence as the strut material but the dependence on relative density involves n. For example, diffusional creep that is often found in ceramics, has n = 1. For this situation, the strain rate of the foam will be linearly dependent on stress and on (Q/QS)2. Thus the cellular structure will amplify the strain rate compared to the dense strut material but one would expect rather large creep rupture strains for these materials. Goretta et al. (1990) showed the strength and fracture toughness of an open cell alumina-mullite material degraded above 1200 °C, as creep mechanisms became important. Creep testing showed deformation mechanisms which were apparently linear viscous at the lower stresses, consistent with stress-assisted diffusional processes that are typical of creep in dense polycrystalline alumina (n = 1). On a rather limited data set, the density exponent was estimated to be 1.8, slightly less than that obtained by using n = 1 in Eq. (9-28). An in-
Figure9-45. The open cell ceramic exhibited creep cracks at high levels of strain, the morphology of the cracks supports a bending deformation within the struts even under axial loads.
513
crease in strain rate was observed at the higher stresses and this was associated with the creep cracks formed in the struts. An example of this cracking is shown in Fig. 9-45 and is reminiscent of the damage that occurs when dense ceramics undergo creep in flexure.
9,11 Conclusions For a variety of scientific and technological reasons, there is a need to understand the physical properties of porous ceramics and this chapter has considered one group of such materials: cellular ceramics. These materials can be obtained in the form of open and closed cell, solid foams as well as honeycombs. Cellular ceramics possess a variety of attributes that make them attractive in non-structural applications but, as indicated in this chapter, they could also be used in structural applications. For cases when maximum stiffness or strength for minimum weight are required, porous ceramics can lead to an efficient design and for some modes of loading can outperform their theoretically dense counterparts. This advantage could be further exploited if these porous ceramics were used as a component in composite systems, such as cores for sandwich laminates or as a matrix in a fiber-reinforced material. The work of Gibson and Ashby has laid a strong foundation for understanding the mechanical behavior of cellular ceramics. This approach considers a simple unit cell that attempts to mimic the expected deformation processes in the bulk cellular solid. The approach also assumes the complex geometry can be scaled by geometric constants in a simple fashion. Recent experimental studies on the elastic, toughness and tensile strength behavior of open cell ceramics have been found to be in reason-
514
9 Mechanical Behavior of Cellular Ceramics
able agreement with the theory, especially their dependence on density. Measured values of the geometric constants for open cell ceramics were, however, substantially less than suggested by Gibson and Ashby. In order to apply the theoretical analyses to cellular ceramics, it is critical to have a detailed understanding of the macro- and microstructure of the foams and the physical properties of the individual struts that compose the reticulated macrostructure. Thus, it is important to measure the structures of these materials quantitatively, especially the way in which they change with density and cell size. In some cases, the presence of non-ideal structural features, such as strut cracks, or cell faces in open cell materials can significantly influence the macroscopic mechanical properties. A critical assessment of the theoretical framework is only possible with measurement of the strut properties. Strut strength is a key item in determining the toughness and tensile strength behavior of brittle, open cell foams, and techniques have been introduced to measure this property. For brittle open cell materials, it is found that strut strength may increase or decrease with cell size. Experimental data on closed cell ceramics is extremely sparse but analysis of the data on closed cell glasses indicates closed cell ceramics may have a structural advantage over their open cell counterparts. The tensile strength of a brittle cellular foam is sensitive to the presence of flaws at both a macroscopic and microscopic level. Macroscopic flaws in commercial, open cell ceramics are often close to their theoretical limit (i.e., the cell size), but at a microstructural level it is believed substantial improvements could be made. Analysis of the strut strength data indicates strength > 1 GPa should be easily feasible and this would increase the strength and toughness of the bulk open cell ceram-
ics by a factor of at least 2, but in some cases by an order of magnitude. Such improvements represent a strong challenge to the scientists involved in the processing of ceramics. Although brittle crack propagation in response to applied tensile stresses is a key feature of cellular ceramics, damage accumulation can occur in these materials. In compressive loading some degree of damage occurs prior to reaching the maximum load. The behavior in compression is also sensitive to the uniformity of loading and, in some cases, the theoretical analysis does not clearly describe the measured properties. It is clear the effect of strut strength variability on the fracture process and the behavior of small cracks (~ cell size) are areas that are yet to be fully understood. Damage mechanisms are also important in thermal shock and at high temperatures, where extensive creep cracking can occur. For thermal stresses, it appears that open cell ceramics may possess a distinct advantage over the closed version. This advantage is a result of the convective heat flow that occurs when the pore space is interconnected, allowing bulk temperature gradients to be rapidly reduced.
9.12 Acknowledgements This work is supported by the National Science Foundation under Grant No. DMR-8818908. The authors wish to acknowledge the students and staff of the Materials Science and Engineering Department who assisted in this study. Special thanks are extended to Chuong Dam, Ken Goretta, Bob Orenstein, Hiroshi Hagiwara, Dave Price, Sam Salamone and Eric Van Voorhees for their technical contributions and many helpful discussions regarding this work.
9.13 References
9.13 References Anderton, G. E. (1975), /. Appl. Polym. Sci. 19, 3355-3359. Ashby, M. F. (1983), Metall Trans. A14 A, 17551769. Ashby, M. F. (1989), Ada Metall 37, 5, 1273-1293. Ashkin, D., Haber, R. A., Wachtman, J. B. Jr. (1990), /. Am. Ceram. Soc. 73, 3376-3381. Brezny, R. (1990), PhD Thesis, The Pennsylvania State University. Brezny, R., Green, D. J. (1989), /. Am. Ceram. Soc. 72, 1145-1152. Brezny, R., Green, D. J. (1990a), Ada Metall Mater. 38, 2517-2526. Brezny, R., Green, D. I, (1990 b), J. Mater Sci. 25, 4571-4578. Brezny, R., Green, D. J. (1991), /. Am. Ceram. Soc. 74, 1061-1065. Brezny, R., Green, D. I, Dam, C. Q. (1989), J. Ceram. Soc. 72, 885-889. Chan, R., Nakamura, M. (1969), /. Cell. Plast. 5,112. Dam, C. Q. (1988), M.S. Thesis, The Pennsylvania State University. Dam, C. Q., Brezny, R., Green, D. J. (1990), /. Mater. Res. 5, 163-171. Davidge, R. W. (1979), Mechanical Behavior of Ceramics. Cambridge: Harvard University Press, pp. 118-131. Fowlkes, C. W. (1974), Intl. J. of Fract. Mech. 10, 99-108. Gent, A. N., Thomas, A. G. (1959), J. Appl Polym. Sci. 1, 107-113. Gibson, L. X, Ashby, M. F. (1982), Proc. R. Soc. London, Ser. A 382, 43-59. Gibson, L. X, Ashby, M. F. (1988), Cellular Solids: Structure and Properties. New York: Pergamon Press. Goretta, K. C , Brezny, R., Dam, C. Q., Green, D. X, De Arellano-Lopez, A. R., Dominguez-Rodriguez, A. (1990), Mater. Sci. Eng. A124, 151-158. Green, D. X (1984), Industrial Materials Science & Engineering: Murr, L. E. (Ed.). New York: Marcel Dekker, Inc., pp. 123-143. Green, D. X (1985), /. Am. Ceram. Soc. 68, 403-409. Green, D. X, Hoagland, R. G. (1985), J. Am. Ceram. Soc. 68, 395-398. Green, D. X, Brezny, R., Nader, C. (1988), Mat. Res. Soc. Symp. Proc. v. 119, Pittsburgh, pp. 43-48. Green, D. X, Nader, C , Brezny, R. (1990), Sintering of Advanced Ceramics: Handwerker, C. A. et al. (Eds.). Westerville, OH: American Ceramic Society, pp. 347-356. Hagiwara, H. (1986), M.S. Thesis, The Pennslyvania State University. Hagiwara, H., Green, D. X (1987), /. Am. Ceram. Soc. 70, 811-815. Hengst, R. R., Tressler, R. E. (1983), Chem. and Concrete Res. 13, 127-134.
515
Hobbs, S. Y. (1977), J. Appl. Phys. 48, 4052-4057. Huang, X S., Gibson, L. X (1990), submitted to Ada Metall Mater. Kendall, K., Alford, N. McN., Birchall, X D. (1987), Proc. R. Soc. London A412, 269-283. Kingery, W. D., Bowen, H. K., Uhlman, D. R. (1976), Introduction to Ceramics. New York: John Wiley & Sons, p. 777. Lackey, W. X, Stinton, D. P., Cerny, G. A., Schaffhauser, A. C , Fehrenbacher, L. L. (1987), Adv. Ceram. Mater. 2, 24-30. Lakes, R. S. (1986), Int. J. Solids Structs. 22, 55-63. Lakes, R. S. (1987), Science 235, 1038-1040. Lakes, R. S. (1991), Trans. ASME, J. Engg. Mater. Tech. 113, 148-155. Lange, F. R, Miller, K. T. (1987), Adv. Ceram. Mater. 2, 827-831. Lederman, X M. (1970), /. Appl Polym. Sci. 15, 693703. Maiti, S. K., Ashby, M. F., Gibson, L. X (1984a), Scripta Metall 18, 213-217. Maiti, S. K., Ashby, M. F., Gibson, L. X (1984b), Acta Metall. 32, 1963-1975. Matonis, V. A. (1964), SPE Journal, 1024-1030. Mecholsky, X X, Freiman, S. W, Rice, R. W. (1976), J. Mater. Sci. 11, 1310-1319. Meiser, M. D., Tressler, R. E. (1981), Am. Ceram. Soc. Bull 60, 901-905. Menges, G., Knipschild, F. (1975), Polym. Eng. Sci. 15, 623-627. Morgan, X S., Wood, X L., Bradt, R. C. (1981), Mater. Sci. Eng. 47, 37-42. Mclntyre, A., Anderton, G. E. (1975), Polymers 20, 247-253. McLaughlin, L. M., Kite, H. T (1970), Oak Ridge Document # Y-SB-10 (Rev. 1). Orenstein, R. M. (1990), M.S. Thesis, The Pennsylvania State University. Orenstein, R. M., Green, D. X (1991), submitted to /. Am. Ceram. Soc. Patel, M. R., Finnie, I. (1970), /. Mater. 5, 909-932. Price, D. A. (1990), M.S. Thesis, The Pennsylvania State University. Schmitt, C. R. (1970), Materials Research and Standards 10, 26-28. Sherman, A. X, Tuffias, R. H., Kaplan, R. B. (1990), Bull Am. Ceram. Soc. 70, 1025-1029. Stevens, K. K. (1979), Statics and Strength of Materials, Prentice-Hall Inc., NJ. Van Yoorhees, E. X (1990), M.S. Thesis, The Pennsylvania State University. Verweij, H., deWith, G., Keeneman, D. (1985), J. Mater. Sci. 20, 1069-1078. Weibull, W. (1951), /. Appl. Mech. 18, 293-297. Wu, M. (1990), PhD. Thesis, The Pennsylvania State University. Zhang, X (1989), Private Communication. Zhang, X, Ashby, M. F. (1989), Cambridge University Engineering Department Report #CUED/CMATS/TR 158.
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Zwissler, X G., Adams, M. A. (1983), in: Fracture Mechanics of Ceramics, Vol. 6: Bradt, R. C , Evans, A. G., Hasselman, D. P. H., Lange, F. F. (Eds.). New York: Plenum Press, pp. 211-241.
General Reading Cellular Materials Almgren, Jr. F. X, Taylor, J. E. (1976), Sci. Am. 235, 1, 82. Ashby, M. F. (1983), Metall Trans. A 14A, 17551769. Gibson, L. X, Ashby, M. F. (1988), Cellular Solids: Structure and Properties. New York: Pergamon Press. Sieradzki, K., Green, D.X, Gibson, L. X (Eds.) (1991), Mechanical Properties of Porous and Cellular Materials, Materials Research Symposium Pro-
ceedings, Vol. 207, edited by Materials Research Society. Stevens, P. S. (1974), Patterns in Nature. Boston, MA: Little and Brown. Thompson, D. W. (1961), On Growth and Form, abridged edition: Bonner, X T. (Ed.). Cambridge: Harvard University Press. Wainwright, S. A., Biggs, W. D., Curry, I D , Gosline, X M. (1976), Mechanical Design in Organisms. Princeton, NJ: Princeton University Press. Fracture of Brittle Materials Davidge, R. W. (1979), Mechanical Behavior of Ceramics. Cambridge: Harvard University Press. Evans, A. G. (1990), /. Am. Ceram. Soc. 73, 2, 187206. Gordon, X E. (1978), Structures or Why Things Don't Fall Down. New York: Plenum Press. Lawn, B. R., Wilshaw, T. R. (1975), Fracture of Brittle Solids. Cambridge: Harvard University Press.
10 High Temperature Engineering Ceramics Katsutoshi Komeya Department of Materials Chemistry, Yokohama National University, Yokohama, Japan Minoru Matsui Materials Research Laboratory, Research and Development Laboratories, NGK Insulators Ltd., Nagoya, Japan List of Symbols and Abbreviations 518 10.1 Introduction 520 10.2 Material Property Requirements 520 10.3 Mechanical Properties of Ceramics 522 10.4 Oxides 523 10.4.1 Oxide Ceramics for High Temperature Engineering Applications 523 10.4.2 Alumina Ceramics 524 10.4.3 Zirconia Ceramics 526 10.4.4 Mullite Ceramics 527 10.4.5 Low Thermal Expansion Coefficient Ceramics 528 10.5 Non-oxide Ceramics 530 10.5.1 Non-oxide Ceramics for High Temperature Engineering Applications .. . 530 10.5.2 Silicon Nitride Ceramics 531 10.5.2.1 The Intrinsic Character of Silicon Nitride 531 10.5.2.2 Synthesis of Silicon Nitride Powder 531 10.5.2.3 Progress in Sintered Silicon Nitride 533 10.5.2.4 Practical Applications of Silicon Nitride Ceramics 543 10.5.3 Silicon Carbide Ceramics 544 10.5.3.1 The Intrinsic Character of Silicon Carbide 544 10.5.3.2 Synthesis of Silicon Carbide Powder 545 10.5.3.3 Progress in Sintered Silicon Carbide 546 10.5.3.4 Practical Applications of Silicon Carbide Ceramics 549 10.5.4 Evaluation of Silicon-Based Ceramics 549 10.5.4.1 Fast Fracture Strength and Its Dependence on Volume 549 10.5.4.2 Fatigue Strength 550 10.6 Ceramic Matrix Composites 557 10.6.1 Definition and Classification 557 10.6.2 Dispersants for Composites 557 10.6.3 Ceramic Matrix Composites 559 10.6.3.1 Ceramic Nanocomposites 559 10.6.3.2 Whisker Dispersed Composites 561 10.6.3.3 Long Fiber Reinforced Composites 562 10.7 Acknowledgements 563 10.8 References 563 Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.
518
10 High Temperature Engineering Ceramics
List of Symbols and Abbreviations A a a0 C
Y
constant flaw size atomic radius half the length of an interior crack constant Young's modulus Weibull distribution function frequency enthalpy stress intensity factor fracture toughness or critical stress intensity factor Weibull modulus constant number of cycles to failure L a r s o n - M i l l e r parameter stress ratio absolute temperature thermal shock resistance temperature static fatigue lifetime or equivalent time time to failure time to creep rupture lifetime effective volume geometrical factor
y 7 gb y{ ysv a aa cre <7f crg o{ <jm amax (js
thermodynamic surface energy grain boundary energy fracture energy surface energy between the solid and the vapor stress at an arbitrary point in the material applied stress; stress amplitude alternating fatigue stress/strength fracture strength strength derived from Griffith model inert strength of initial flaws mean stress maximum stress static fatigue strength tensile strength theoretical strength location parameter Weibull scale p a r a m e t e r
cs
E F
f H K
i
Klc m n N P R T Tc teq tt tT ts
K
List of Symbols and Abbreviations
CMC CVD CVI FGM FRC FRM FRP GPS HIP LPG MAS PAN PLS PLZT PSZ PZT RT SEM TEM TZP ZTA
ceramic matrix composite chemical vapor deposition chemical vapor infiltration functionally gradient material fiber reinforced ceramic fiber reinforced metal fiber reinforced plastic gas pressure sintering hot isostatic pressing liquefied petroleum gas magnesium aluminosilicate poly(acrylonitrile) pressureless sintering (Pb, La) (Zr, Ti) O 3 partially stabilized zirconia Pb(Zr,Ti)O 3 room temperature scanning electron microscope transmission electron microscope tetragonal zirconia polycrystal zirconia toughened alumina
519
520
10 High Temperature Engineering Ceramics
10.1 Introduction In general, ceramics have properties superior to metals in the areas of thermal stability, corrosion and wear resistance. But until recently they have only been used as structural parts in application areas with static atmospheres, because of their brittleness. High temperature engineering ceramics are defined as ceramics which can be used at medium to high temperatures, low to higher stresses and highly oxidizing and corrosive atmospheres. Each material has many important and superior characteristics which result from the atomic combination and chemical bonding structures of these ceramics. Engineering ceramics are divided into oxides and non-oxides, as shown in Table 10-1. In the table typical oxides for engineering applications are alumina (A12O3), zirconia (ZrO2), mullite (3A12O3 -2 SiO2), cordierite and aluminum titanate (Al2TiO5). On the other hand, non-oxide ceramics consist of carbon (C), boron nitride (BN), aluminum nitride (A1N), silicon nitride (Si3N4) including sialon, silicon carbide (SiC) and some borides. Ceramic matrix composites (CMCs) have recently been extensively developed. They are reinforced by ultrafine ceramic powders, ceramic whiskers and ceramic long fibers (see also Chap. 5 of Vol. 13 of this series). Figure 10-1 demonstrates the current and future classification of engineering ceramics, in which the newer functionally gradient materials (FGMs) and their technology are raising critical processing and analysis issues to be developed. In this chapter, property requirements are described initially, then oxides, non-oxides and composites are introduced. Silicon based ceramics such as silicon nitride and silicon carbide are discussed in detail in this chapter as they are currently consid-
Table 10-1. Engineering ceramics. Oxides
Properties
A12O3
Heat resistance, corrosion resistance, wear resistance High fracture toughness, thermal insulation Low thermal expansion coeff., thermal insulation, excellent thermal shock resistance Low thermal expansion coeff., thermal insulation, excellent thermal shock resistance Heat resistance, corrosion resistance High fracture toughness, high strength
ZrO 2 Cordierite
Al 2 TiO 5
Mullite Composites Non-oxides Si 3 N 4
BN (hexagonal) BN (cubic) A1N SiC
c
(graphite) C (diamond) Composites
High fracture toughness, high strength, excellent thermal shock resistance, wear resistance Corrosion resistance, excellent lubrication, excellent thermal shock resistance Very high hardness, excellent thermal conductivity Heat resistance, high thermal conductivity Heat resistance, corrosion resistance, wear resistance, high thermal conductivity Heat resistance, corrosion resistance, excellent lubrication Very high hardness, excellent thermal conductivity High fracture toughness, high strength
ered to be the best materials for high temperature structural applications.
10.2 Material Property Requirements Property requirements for engineering ceramics are primarily determined by the operating temperature, applied stress and environment. Thermal shock resistance and fracture toughness are also important
10.2 Material Property Requirements i—General ceramics r— Monolithic
'— Toughened ceramics (R-curve) I— Particle dispersion (Macro-micro-nano)
Engineering ceramics
— Composite
-Whisker reinforced-
521
Al 2 0 3 , SiC Mullite, MAS Si,N, PSZ, TZP
More reliable in situ composite Cost reduction
AI 2 0 3 -Zr0 2 (P) Si 3 N r SiC (P) MgO-SiC (P) AI203-SiC (W) SiC-SiC (W)
— Fiber reinforced-
C/C composite CVI (SiC-SiC (F))
I— New materials-
Lanxide
P: Particle W: Whisker F: Fiber
- Functionally gradient material (FGM) -Surface strengthened
parameters. It is essential that these properties are simultaneously satisfied. Additional critical conditions include the forming, shaping and joining of materials, as well as processing cost reduction. For example, in the case of the fabrication of turbocharger rotors, strength, toughness and oxidation in the temperature range around 1000 °C, forming ceramics into a complicated shape, and the lowest possible costs are the main specifications required. In particular, molding techniques for the rotor must be developed. Operating tern-
SiC CD
era
D
Qi
~1300°C Si3N4 SiC
Si 3 N t
O)
r ' ^ *o ~900°C sZrO 2 Si3N4 Qi a. o Metals > Ceramics \ Applied stress
Figure 10-2. Candidate materials for particular operating conditions.
Figure 10.1. Engineering ceramics.
peratures and stresses and the various materials that satisfy them are shown in Fig. 10-2. There are a large variety of applications which require different fabrication processes. This can be compared with other classes of materials such as electroceramics, magnetoceramics, and so on. There are different kinds of manufacturing processes, e.g., turbocharger rotors are fabricated by injection molding and slip casting methods, whereas antifriction ball bearings are made by die-pressing. This situation is quite different from that for electronic ceramics such as substrates and packages, which are fabricated mainly by tape casting or extruding methods. The large variety of potential applications for engineering ceramics make the development strategies for these materials very complicated. Each application needs much development engineering and requires considerable funding. Another problem is brittleness, which must be understood and overcome, which dictates that fracture strength and reliability are very important properties. As is well known, the strength depends on the microstructure. Ifflawslike pores, cracks, defects, inclusions and so on exist in the ma-
522
10 High Temperature Engineering Ceramics
Table 10-2. Properties evaluated for engineering ce-
Elastic properties Thermal properties
Young's modulus [R-1602(RT), R-1605 (HT)]a, Poisson's ratio, shear modulus Thermal expansion coefficient, thermal conductivity [R-1611]a, specific heat [R-1611]a, emissivity, softening temperature Strength Bending strength [R-1601 (RT), R-1604 (HT)]a, tensile strength [R-1606]a, compressive strength [R-1608 (RT)]a, shear strength, fracture toughness [R-1607(RT)]a, fracture energy, impact strength, thermal shock resistance, bonding strength, statistical evaluation Fatigue Fatigue life, slow crack growth, creep [R-1612] Friction Hardness [R-1610 (RT)]a, friction coeffiand wear cient, wear resistance [R-1613]a, erosion, machinability Corrosion Oxidation [R-1609]a, corrosion [R-1614] Others Nondestructive evaluation, residual stress, surface roughness, chemical analysis of silicon nitride powder [R-1603]a a
[R
(- -)]: [JIS No. (temperature)]
terial, they will act as points of fracture. The consequent range of strength values depends on the flaw distribution parameters, and is a result of the processing including the raw powder characteristics. For engineering ceramics establishment of the processing conditions for minimal scatter in the mechanical properties is particularly important. There are also many other properties that require evaluation for the fabrication and application of engineering ceramics. Table 10-2 lists a number of the properties evaluated for engineering ceramics, for which fourteen Japanese standards have been determined in the last ten years.
10.3 Mechanical Properties of Ceramics To better understand the mechanical properties of ceramics, the difference between those of metals and ceramics is shown in Table 10-3. The intrinsic difference in the mechanical properties is due to the chemical bonding. Namely most metals have metallic bonds, while ceramics generally have ionic and/or covalent bonds. For instance, alumina and zirconia are principally ionic structures, whereas silicon nitride and silicon carbide are typically covalent structures. Consequently ceramics exhibit brittle fracture without plastic deformation up to temperatures of half the melting point. Plastic deformation at low temperatures is not expected as dislocation multiplication and motion is very restricted in ceramics due to the complicated crystal structure (large Burgers vector) and a large Peierls stress (caused by the covalent/ionic bonding), see Chap. 2 of Volume 6. It must be remembered that the fracture of ceramics is very sensitive to microflaws such as pores, cracks, machining Table 10-3. Differences in properties between metals and ceramics3. Property Density Young's modulus Thermal expansion coeff. Hardness Room temp, strength High temp, strength Deformation Impact strength Fracture toughness Heat resistance Oxidation/corrosion Wear resistance Machinability L>M>S>SS
Ceramics
Metals
S L S L M-L M SS
L S L S L S L L L S-M S-M S L
s s
L L L S
10.4 Oxides
flaws and residual stress. A more detailed account of the effect of these flaws on the strength and why it is much lower than the theoretical stress of these materials is given in Chap. 7 of this Volume. The fracture strength of an ideal solid is essentially determined by the nature of the bonding and its arrangement. That is, the theoretical strength (crth) is given by the following equation, which relates the strain energy release rate for the bonding fracture to the energy to create two new fracture surfaces; (10-1) where y is the thermodynamic surface energy, E is Young's modulus, and a0 is an atomic radius. A theoretical strength of about 5000 MPa for alumina can be calculated by using a surface energy of 100 Jm~ 2 , which is about 1/10 of the Young's modulus. This value is compared with 200300 MPa for practical usable alumina ceramics. This decrease in the strength of ceramics is due to the existence of flaws. This is explained by Eq. (10-2), derived from the Griffith flaw model (Griffith, 1920), namely
523
where y{ is the fracture energy (usually y{ > y), Klc is the fracture toughness or critical intensity factor, C is the flaw size and Y is a geometrical factor. In this case flaw size means not only crack size, but also the maximum size of grains, pores and inclusions. From Eq. (10-4) it can be seen that ceramics with higher Klc are less sensitive to the flaw size. Mechanical property requirements for engineering ceramics depend upon the intended applications, as described above. Namely, a turbocharger rotor requires a high strength and toughness, excellent thermal shock resistance for the materials, as well as a higher level of shaping and joining technology. Anti-friction bearing parts also require excellent wear resistance, minimization of flaws and excellent machining and lapping ability. It should in particular be remembered that engineering ceramics require different characteristics and different shaping technologies but with costs competitive to metals, unlike other ceramic components like substrates and ferrites. It has recently been found that some monolithic ceramics such as silicon nitrides show nonlinear fracture behavior. Therefore nonlinear fracture mechanics has been developed in recent years (see Chap. 6 of this Volume).
(10-2) where C is half the length of an interior crack. However, the strength (
°'-Y(^¥T 1
(10 3)
-
If
(10-4)
10.4 Oxides 10.4.1 Oxide Ceramics for High Temperature Engineering Applications
Oxide ceramics have higher stability in a normal atmosphere and are easy to fabricate into components compared to nonoxide ceramics. Thus oxides are advantageous to commercialize and, as is well known, most traditional ceramics are oxides. Cements, glasses and refractories,
524
10 High Temperature Engineering Ceramics
Table 10-4. Properties of oxide ceramics. Property Density Young's modulus Bending strength Thermal conductivity Thermal expansion coeff. Electrical resistivity
Units
BeO
MgO
g/cm^ GPa MPa W/mK 10" 6 /°C £2 cm
2.8 350 175 250 8 >10 1 4
3.56 350 140 42 13 >10 1 4
which are generally used as structural ceramics, are mainly composed of oxides (see Chap. 2 of this Volume). Oxide ceramics can also be used as high temperature engineering ceramics. Examples are alumina, zirconia, cordierite, aluminum titanate, magnesia and calcia. The fundamental properties of these oxides are shown in Table 10.4. Each of these oxides has typical characteristics, but alumina, zirconia, mullite, cordierite and aluminum titanate are listed as the most suitable high temperature engineering oxides. Alumina is the most commercially available ceramic for high temperature applications because of its higher chemical stability and acceptable cost. 10.4.2 Alumina Ceramics There are many alumina polytypes, of which oc-alumina with its hexagonal type of corundum structure (see Chapters 1 and 2 for more details) is the most stable in thermal and chemical environments. Therefore, in general, alumina means oc-alumina. Alumina has a mixed ionic-covalent bond structure in comparison with the more covalent silicon nitride and silicon carbide, a lower formation free energy, a high melting point of 2050 °C, a specific gravity of 3.99, and its single crystals are transparent. Raw powder is generally produced from bauxite (mainly A1 2 O 3 H 2 O or
Mullite 3.6-3.9 310-390 320-500
17-31 7.0-8.5 >1014
3.1 100 180 4.2 4.4
>1014
Cordierite Zircon 2.2 100 1.5 2.8
>10 14
3.7 170 160 5 4.8
>1014
A1 2 O 3 -3H 2 O), which is dissolved in an aqueous NaOH solution in an autoclave at 170°C, and then A1(OH)3 is precipitated from a filtrate saturated with alumina. The A1(OH)3 is calcined at 1100°C to obtain a-Al 2 O 3 . In the firing temperature range of up to 900 °C y-Al 2 O 3 is formed, and over 1000 °C a-Al 2 O 3 , which has excellent stability, is formed. The alumina powder so obtained can be pulverized to finer grains and refined to higher purity. Recently new processes have been developed to prepare very high purity and ultra-fine grained alumina from aluminum alkoxide or aluminum organic compounds, which are useful for higher grade components and films where higher costs can be tolerated. Since alumina is intrinsically a sinterable material because of its higher ionicity, full densification can be achieved by pressureless sintering. However, grain growth occurs simultaneously, which can be inhibited by the addition of a very small amount of MgO dopant. Figure 10-3 shows the effect of an addition of 0.1 wt.% MgO on the densification of alumina (Jorgenson, 1965). Table 10-5 summarizes the typical properties of alumina ceramics. The superior characteristics of alumina are thermal resistivity, electrical insulation, hardness, chemical stability, producibility and economical cost. Consequently, an extremely wide range of applications
525
10.4 Oxides
0.01 r
0.001 100
1000
Time (s)
Figure 10-3. Densification curves for the sintering of alumina at 1535°C: (A) A12O3, (B) Al 2 O 3 -0.1 wt.% MgO.
Table 10-5. Typical properties of alumina ceramics. Property
Sintered, Single hot crystal pressed
Units
Purity % g/cm2 Density Porosity % GPa Young's modulus Poisson's ratio Bending strength RT MPa 1000°C Knoop hardness GPa Thermal conductivity W/mK Thermal expansion io~ 6 / o c coefficient Specific heat kcal/kg°C Qcm Electrical resistivity
99.5-99.9 100 3.9-3.98 3.99 <0.1 0 380-400 420 0.22 0.25 70 250-550 380 23 22 35 36 7.8-8.1 5.3 0.2 10 14
0.18 1016
have been developed during the last 50 years. In the high temperature engineering applications, there are pipes, plates and jigs for high temperature uses, transparent tubes for sodium lamps, wear resistant parts like wire guides and nozzles, mechanical seals and cutting tools. But this material has a number of major limitations such as low toughness, poor thermal shock resistance and high temperature strength. Therefore recent development work on this material has aimed to improve its toughness by the addition of other compounds, in the form of particles or whiskers. Hot-pressed and hot isostatically pressed (hipped) Al2O3-TiC has been developed for cutting tools (Tanaka, 1973, Yamamoto, 1987). An addition of TiO 2 is used to inhibit grain growth and to improve the thermal conductivity. Typical data for commercial grades are given in Table 10-6 in comparison with alumina ceramics. Al2O3-SiC whisker composites have been developed for improved strength and toughness (Becher and Wei, 1984; Wei and Becher, 1985), and are discussed in Sec. 10.6.3. Alumina strengthened and toughened by ZrO 2 particle dispersions has been developed with typical experimental results as shown in Fig. 10-4 (Claussen et al., 1977). The increase in toughness is explained as due to absorption of elastic strain energy by the formation of micro-
Table 10-6. Properties of Al 2 O 3 and Al 2 O 3 -TiC ceramics.
A12O3 system Al 2 O 3 -TiC system
(jam)
Flexural strength MPa
Fracture toughness (MPa/m 1/2 )
Vickers hardness GPa
2-3 1-2
500-700 700-800
3.0-3.2 4.0-4.2
20 21.5
Density
Grain size
(g/cm3) 3.9-4.0 4.1-4.2
Compressive Thermal shock resistance strength MPa CC-1) 4000 4500
200 350
526
10 High Temperature Engineering Ceramics
10
cracks through phase transformation from tetragonal to monoclinic. The particle size dependence for toughening observed in the figure is interesting. At present a threepoint bending strength of 1000 MPa and a Klc of 10 MPa m 1/2 have been achieved. Current research activities are growing in the area of such nanocomposites. 0
U 8 12 16 20 ZrO2 volume percent in A12O3 matrix (%)
10.4.3 Zirconia Ceramics
Zirconia is an oxide with the formula ZrO 2 . Since it has an extremely high melting point of 2700 °C, its original potential was as a refractory material. But its use was limited because of its peculiar transformations. These transformations proceed in three stages: monoclinic <
> tetragonal 2370 < °C cubic
900 °C
(5.56 g/cm 3 ) ZrO2 volume percent in Al 2 0 3 matrix (%)
Figure 10-4. Effect of ZrO 2 content on the strength and fracture toughness of Al 2 O 3 -ZrO 2 ceramics. (*) ZrO 2 particle size.
2500
cub 2000 -
tet
\
\
\ \
E"1OOO
tet + CUD
\
mono+tet^ X 500 mono /
\
mono + cub 1
i
•
f
\ \ \ 1 1 1
Y203
Figure 10-5. Phase diagram of the system ZrO 2 Y 2 O 3 , where cub = cubic, tet = tetragonal, mono = monoclinic.
V
°
(6.10 g/cm 3 )
These transformations from the tetragonal to the monoclinic phase are accompanied by large changes in volume, 4.6 vol.%, and if the material is used without modification, cracks or other consequential changes arise. However, the addition of Y 2 O 3 , CaO, etc. into the crystal structure maintains the highest temperature configuration (cubic) even at low temperatures. This can be seen from the phase diagram for ZrO 2 -Y 2 O 3 , which is shown in Fig. 10-5 (Lange, 1982). Zirconia obtained using this phase relation is called "stabilized zirconia". This is an important material for solid electrolytes, since zirconia has highly ionic bonds and it has a fluorite (CaF 2 ) type, cubic crystal structure (see Chap. 14 for more details). The fluorite structure is a face-centered cubic lattice with anions in the center of each of the eight tetrahedrons it forms and a large open space within the inner octahedron (see Chap. 1 for more details of the crystal structure). Thus diffusion of the anions,
10.4 Oxides Table 10-7. Properties of PSZ ceramics. Property
Units
Density g/cm2 a Bending strength (RT ) MPa Young's modulus GPa MPam* Fracture toughness Vickers hardness GPa Thermal expansion coefio~7oc ficient (RT-1000°C) Thermal conductivity (RT) W/mK Electrical resistivity (RT) Qcm
Value 5.8-6.05 750-1300 150-220 7-14 15 8.7-11.4 1.9-3.4 >1O10
RT: room temperature.
which form a simple cube, is easy compared to that of the cations. Besides which, anion vacancies exist in greater abundance than would normally be created by additives and temperature conditions. There is also partially stabilized zirconia, better known by its acronym, PSZ (Garvie et aL, 1975). The stress induced martensite-like transformation of tetragonal ZrO 2 to monoclinic ZrO 2 absorbs energy at the crack tip, thus contribution to y{ and Klc. By using the phase transformation effectively, toughened ceramics can be developed, as shown in Table 10-7. This socalled "stress induced" phase transformation and its development are noteworthy for the development of high toughness ceramics as structural materials. The structure of PSZ is as follows. Zirconia with a stable cubic configuration is synthesized at high temperatures by the addition of CaO or Y 2 O 3 . Next, if it is annealed at temperatures at which the tetragonal configuration is stable, minute tetragonal crystals will be precipitated, and a mixture of the cubic and tetragonal configurations will be produced. Thus the mixture is partially stabilized by the part that is in the cubic configuration. The solid solution with Ca(Y) is given by the formula
527
[Zr,Ca(Y)]O2_x, because the migration of O 2 ~ ions is possible since oxygen lattice vacancies are produced. Because of this solid electrolyte capability, it is used on oxygen sensors (oxygen concentration cells) (see Chap. 7 on the toughening of ceramics). Also there are high expectations for using PSZ in engineering parts because of its high toughness. However, as discussed in Chap. 7, the temperature sensitivity of the fracture toughness of zirconia toughened ceramics limits their usefulness as engineering ceramics at elevated temperatures. TZP (tetragonal zirconia polycrystal), which consists mainly of a metastable fine grained tetragonal phase, has been developed. Another toughened ceramic, ZTA (Zirconia toughened alumina) with a very high bending strength of over 2000 MPa has also been developed. According to Eq. (10-4), strength is proportional to Klc. However, Swain (1985) proposed that in the case of toughened zirconia there is a limit to the strength obtainable by the phase transformation mechanism (Fig. 10-6). Namely, when a stress greater than the critical stress is applied to a crack tip, tetragonal-to-monoclinic (t-m) transformation occurs, and consequently the strength is limited in spite of the higher
10.4.4 Mullite Ceramics Mullite, 3Al 2 O 3 -2SiO 2 , is the only stable compound in the system Al 2 O 3 -SiO 2 (Fig. 10-7), and since it is easily formed by heating clay minerals, it has been applied in a wide range of highly refractory materials. The main characteristic properties of mullite are a melting point of 1850°C, lower thermal expansion coefficient of 5xlO~ 6 o C~ 1 , and lower elastic modulus than A12O3. Accordingly it is character-
528
10 High Temperature Engineering Ceramics
3.0 -
_ 600
a Mg PSZ * Y-TZP o Y-TZP-AI 2 O 3 /C f =10Mm
A A / \ / // / . / \
-2.0 -
S. ess
o
t_
V^s«r
o Q_
~ 500 JC
"01
/ Cf=30|jm
^300 T3 C 0) CD
100 Mm
n P"
i
i
10
15
**) Transformation-limited strength *) Flaw-limited strength Cf = Critical flaw size 6^- Critical stress to initiate the transformation Figure 10-6. Relation between strength and fracture toughness of zirconia toughened ceramics.
Wt.% A12O3 60 80 Liquid
2000 SiO2 5 1800 ~ - Liquid "^^ CL
185 Mullite Liquid
+
0 SiO2
Cor. + Mullite(ss) r-Mullite(ss)
SiO2 + Mullite i
U00 20
100
Mullite (ss) ^~* + Liquid >^Zov.~
1595°C
I 1600
1 pressureless sintered (1650°C,4h)
1000 1200 Temperature (°C)
1400
Figure 10-8. Bending strength as a function of temperature for new mullite ceramics.
*)
20
1
hot-pressed (1650°C.1h.50MPa)
S 400
/
J><
_L
1
1
40 60 Mol% AI2O3
80
100 A12O3
Figure 10-7. Phase diagram of the system A1 2 O 3 -
the alkoxides. The mullite ceramics developed have higher refractoriness and no degradation in their bending strength at high temperatures, as shown in Fig. 10-8 (Kanzaki and Tabata, 1985), which seems to be due to the absence of a glassy phase at the grain boundaries, however, this material has a low fracture toughness (1-2 MPa m 1/2 ). This new mullite has been utilized for the development of devices where low static stresses are encountered such as heat resistant parts, high temperature bending strength jigs and furnace parts. However, since mullite is superior to the non-oxide ceramics, such as Si 3 N 4 and SiC, in processing and powder costs, it is expected to be one of the most important engineering ceramics in the future. Attempts are being made to improve the strength and fracture toughness of this material. 10.4.5 Low Thermal Expansion Coefficient Ceramics
ized as a low cost, excellent thermal shock resistant and heat resistant material, and has been used for chemical resistant and furnace applications. Recently, a high quality mullite has been developed by using high purity and ultrafine powder synthesized through new chemical routes from
Oxide ceramics can be divided into three categories according to their thermal expansion coefficient as follows: low thermal expansion coefficient < 2 . 0 x l 0 ~ 6 O C 1 ; intermediate thermal expansion coefficient 2.0-8.0xlO~ 6 o C" 1 ; and high thermal expansion coefficient > 8 . 0 x l 0 ~ 6 °C~ 1 .
10.4 Oxides
529
Table 10-8. Thermal expansion of various kinds of oxide ceramics.
Table 10-9. Properties of cordierite honeycomb ceramics.
Category
Crystalline phase
Material
Thermal expansion coefficient
Main phase: cordierite Others: mullite, spinel, a-Al 2 O 3
Property High thermal expansion coefficient
MgO 13.8(20 1800°C) ZrO 2 11.4(20-1000°C) BeO 8.8 (20-1000 °C) A12O3 8.5 (20-1000 °C) MgAl 2 O 4 8.6 (20-1000 °C) Medium thermal BeAl 2 O 4 6.4 (20-1000 °C) expansion ZrSiO 4 4.1 (20-1000 °C) coefficient BaO • A12O3 • SiO2 3.4 (20-1000 °C) Zn 2 SiO 4 3.2 (20-1000 °C) 3 A12O3 • 2 SiO 2 5.0 (20-1000 °C) Low thermal 2 MgO 2A12O3 0.5-1 expansion •5SiO 2 (20-1000 °C) coefficient L i 2 O A l 2 O 3 - 4 S i O 2 1.9(20 1000 °C) 0.5(20 1000 °C) Quartz glass 0.2 (20-1000 °C) Al 2 TiO 5
Table 10-8 gives examples of materials in each of these categories. Materials which belong to the low thermal expansion coefficient category include cordierite, lithium aluminosilicate, titanium aluminate and silica glass. The thermal expansion coefficient of cordierite is different along each crystal axis. Namely, 2.5 x K T ^ C " 1 along the a axis and -0.9 x 10~ 6 °C~* along the c axis. Honeycomb ceramics for catalyst supports are fabricated by extruding plate-like grains of raw kaolin or talc powders into honeycomb shapes and reacting these compacted materials to form cordierite crystals. Consequently, directionally arranged crystalline grains of cordierite are obtained in which the thermal expansion coefficient along the extrusion direction is smaller than that in the perpendicular direction. Table 10-9 gives typical properties of cordierite honeycomb type ceramics (Banno and Asano, 1987). Excellent ther-
Units
Thermal expansion io~6/°c coefficient (RT-800°C) Specific heat (25 °C) cal/g°C Thermal conductivity (25 °C) W/mK Softening temperature °C Water absorption ratio % Total microporosity cm3/g Microporosity for > 10 urn % Mean micropore diameter |am Mechanical strength: T *\
A
S*
... --y
J± U11CUUUI1
B direction C direction
Value 0.8 0.2 1.1 1390 22 0.2 45 9
TV/fT>o
JVLFa
MPa MPa
> 1.5 > 0.15
mal shock resistance and heat resistivity are apparent from the table. Figure 10-9 shows an example of catalyst supports for purification of the exhaust gas from automobiles. Aluminum titanate also shows a similar thermal expansion anisotropy, 11.8xlO~ 6 along the a axis, 19.4xlO" 6 and - 2.6 x 1 0 " 6 o C " 1 along the b and c axes, respectively. Therefore, during cooling from the firing temperature range of 15001700°C, microcracks appear at the grain boundaries. Very small thermal expansion coefficients of 0-1 x 10" ^ C " 1 have been obtained in the sintered ceramics. Since aluminum titanate has a high melting point of 1860 °C, low elastic modulus and excellent thermal insulation as well as a low thermal expansion coefficient, it has been used in practice for extreme thermal shock situations, such as for port liners in automotive engines. -A number of problems remain to be overcome, such as
530
10 High Temperature Engineering Ceramics
Table 10-10. Properties of aluminum titanate ceramics. Property
Units
Value
Density Porosity Bending strength
g/m 3 % MPa
2.73-3.26 21.0-4.6 10-17 12-35 45-59 0.9-1.2
RT 1200°C GPa Young's modulus RT W/mK Thermal conductivity RT Thermal expansion ratio RT to 1000 °C % °C Max. operating temperature
0.08-0.05 1650
Figure 10-9. Catalyst supports for purification of the exhaust gas from automobiles. (Courtesy of NGK Insulators, Ltd.)
strength improvement and instability at around 1100°C, where Al 2 TiO 5 easily decomposes into A12O3 and TiO 2 . Table 10-10 gives the properties of aluminum titanate ceramics.
10.5 Non-oxide Ceramics 10.5.1 Non-oxide Ceramics for High Temperature Engineering Applications
Non-oxide ceramics include metal carbides, nitrides, silicides, borides, etc. In recent years, the properties required of materials cover a broad range. In the field of engineering ceramics, especially in the area of heat-resistant and high temperature engineering ceramics, the application conditions are such that the existing oxides will not survive. Hopefully materials developed in the future will be more oxidation resistant. Also it seems likely that the materials which hold the key to new technical breakthroughs will be non-oxide ceramics. Carbon materials composed of graphite and diamond, carbides such as silicon carbide, tungsten carbide, titanium carbide,
and nitrides such as silicon nitride, aluminum nitride, boron nitride, are the most prominent non-oxide ceramics, and because the degree of covalency in their bonds is large, it can be predicted that they will show a strong resistance to deformation. Both silicon carbide and silicon nitride are thought to satisfy the necessary conditions noted above. Worldwide study of these materials began in the late 1960s and early 1970s. However, it is difficult to arrive at something that can be regarded as an industrial material through the simple extension of existing materials engineering, and it is natural that new engineering works will have to be initiated. Further explanation of these industrial materials will be found in the following sections. One critically important problem they all have in common is their poor reliability. Advances in processes and evaluation methods are indispensable to progress in increasing reliability. In this section, many non-oxide ceramics will be described, but emphasis will be placed on Si 3 N 4 and SiC.
10.5 Non-oxide Ceramics
10.5.2 Silicon Nitride Ceramics
531
10.5.2.2 Synthesis of Silicon Nitride Powder
10.5.2.1 The Intrinsic Character of Silicon Nitride Silicon nitride is a typical covalent compound with an ionicity of 0.3. It has a higher formation free energy than either alumina or silica, as illustrated in Fig. 1010 (Mitomo, 1991a). Also it has no melting point under ordinary atmospheric pressure, a high vapor pressure and a very low diffusion coefficient. These intrinsic properties of silicon nitride suggest that this material has poor sinterability to full density. Therefore special sintering technologies such as reaction sintering, hotpressing, gas pressure sintering and hipping have been developed for this material. It is also notable that silicon nitride is easily oxidized in an oxygen containing atmosphere. As a result, the surface of silicon nitride is always covered by a thin silica layer. Nevertheless, considerable development work on materials and components has been done because of the significant market potential of silicon nitride as an engineering ceramic, and several problems have been overcome.
There are four kinds of synthesis methods for silicon nitride raw powders, as shown in Table 10-11. These include direct nitridation, silica carbothermal reduction and nitridation, silicon imide decomposition and vapor phase reaction. Of these, direct nitridation was widely used originally. Today the first three methods are available for industrial production, in which the selection of the raw powder is dependent on the specification of customers. Outlines and characteristics of the above methods are now described. Direct Nitridation of Silicon Silicon nitride powder is synthesized by direct nitradation of silicon powder heated in an N 2 gas stream. However, since the reaction is exothermic 3Si(s) + 2N 2 (g) -> Si 3 N 4 (s) AH =-175
kcal/mol
(1)
(1600 K)
careful temperature control is necessary in order to obtain a higher content of a-phase silicon nitride.
Table 10-11. Synthesis methods for silicon nitride powders. £-50
Synthesis method
-
Silicon direct nitridation method Silica reduction and nitridation method Imide decomposition method
£ -100 in
_a JO
CD
-150 1500
2000 2500 Temperature (K)
Figure 10-10. Formation free energies.
3000
Gas phase synthesis method
Reaction formula 3Si + 2 N 2 ^ S i 3 N 4 3 S i O 2 + 6 C + 2N 2 -» Si 3 N 4 + 6CO SiCl 4 +6NH 3 ^Si(NH) 2 + 4NH4C1 3 Si(NH)2 -+ Si 3 N 4 + 2 NH 3 3SiCl4 + 16NH 3 -+Si 3 N 4 + 12NH 4 Cl
532
10 High Temperature Engineering Ceramics
• ' ,.
'**
f-i
2a(CuKa)
Figure 10-11. SEM micrographs of silicon nitride powders synthesized by the silica reduction and nitridation method: (A) SiO 2 -C-N 2 , (B) SiO 2 -C-Si 3 N 4 -N 2 (bar = 10 urn). Electron diffraction of B reveals that it is almost entirely a phase.
Pure and fine powder is produced by grinding and refining the synthesized silicon nitride block. This method produces silicon nitride powder at a lower cost compared to other methods. Silica Carbothermal Reduction and Nitridation Silicon nitride powder is formed by an endothermic reaction of the system SiO 2 -C-N 2 according to 3SiO2(s) + 6C(s) + 2N 2 (g) -+ Si 3 N 4 (s) + 6CO(g)
(2)
AH = 303 kcal/mol (1700 K) It was found that the addition of silicon nitride to the SiO 2 -C mixture strongly affected the grain morphology, as shown in Fig. 10-11, and, in consequence, more aphase particles of controlled size and shape were obtained (Inoue et al., 1982). Although the powder synthesized is of a granular type with accompanying sharp edges and shows a lower green density in molding, it is meaningful that this powder gave rise to the development of high strength silicon nitride. Recently a silicon nitride powder which exhibits good sinterability has been synthesized from a new system, the SiO 2 -
L P G - N H 3 system (LPG: liquefied petroleum gas). Silicon Imide Decomposition Amorphous silicon nitride is synthesized by the following two-step process: SiCl4 + 6NH 3 -> Si(NH)2 + 4NH 4 Cl (room temperature) (3) 3Si(NH)2(s) -+ Si3N4(s) + 2NH 3 (g) (1200-1500 °C) (4) Fine grained silicon nitride powder of high oc-form content is obtained by crystallization of the amorphous silicon nitride product, as shown in the SEM micrograph in Fig. 10-12. The powder formed by this method shows high purity, excellent sinterability, and is widely used worldwide to fabricate the highest quality silicon nitride parts (Yamada and Kotoku, 1989). The quality of silicon nitride raw powders has improved in recent years. Table 10-12 lists typical characteristics of the above three kinds of silicon nitride powder. The characteristics required for the raw powder are mainly high purity, fine grains of controlled size and shape, high oc-silicon nitride content, and so on. To achieve good densification according to
533
10.5 Non-oxide Ceramics
o Silicon imide decomposition a Silica reduction nitridation A Silicon direct nitridation
0.3 0.2
10
20 30 LQ 50 Sputter depth (nm)
60
100 300
Figure 10-12. SEM micrograph of silicon nitride powders synthesized by silicon imide decomposition.
Figure 10-13. Oxygen distribution from the surface to the inside of silicon nitride particles, measured by Auger electron spectroscopy.
Table 10-12. Typical compositions (in wt.% of the elements) and characteristics of silicon nitride powders.
able microstructures, as described later. However, there are many things to be explained, such as the role of existing oxygen, relations between raw powder characteristics and microstructures and properties of sintered products. Figure 10-13 shows some unexplained experimental results (Jenett et al., 1989), where the distribution of oxygen from the surface to the interior is different for the different synthesis methods. It is of particular note that in the powder from the imide decomposition method, the oxygen exists only as a surface silica layer. It is likely that characterization of the raw powder will remain a perennial problem until the next century. Anyway, the present status of these powder production routes is that direct nitridation is available for low cost, imide decomposition is to be used for good sinterability, and silica reduction and imide decomposition are to be used for high strength and toughness development.
Method:a
Ab
Ab
Composition Si 59.4 N 39.7 O C Al 0.06 Ca Fe 0.01 Mg <0.03 Cl
59.4 38.6 1.0 0.01 0.005 0.006 0.001 -
a(%)
91
0
Particle diameter (um) 1-3 Specific surface (m2/g) -
18
B
D
C
59.0 38.5 1.0 <3 1.9 _ 0.05 0.1 0.20 < 0.001 < 0.002 0.01 < 0.001 < 0.0006 0.01 0.005 0.01 < 0.001 < 0.002 0.03 <0.04 >98 0.7 -
97 0.6 10
57 4
a
A: Direct nitridation; B: Silica reduction; C: Imide decomposition; D: Vapor phase reaction. b From different makers.
the available sintering processing, it is particularly important that each powder has acceptable physical and chemical properties. It has been found that promotion of controlled sintering seems to bring desir-
10.5.2.3 Progress in Sintered Silicon Nitride In general, the properties of a ceramic depend on its micro structure. Therefore
534
10 High Temperature Engineering Ceramics
Table 10-13. Development steps for silicon nitride ceramics. Material
Firing technology
Materials development
a Si 3 N 4 P Si 3 N 4 a Sialon P Sialon CMC
Reaction sintering Pressureless sintering Gas pressure sintering Hot pressing HIP Very high pressure sintering
Reaction sintered Densification with sintering aids Strengthening by available additives Quality improvement by the development of raw powder and fabrication processing Improvement of high temperature strength Improvement of oxidation/corrosion Improvement of fracture toughness Machinable silicon nitride
development of the optimum microstructure has always been required for alumina ceramics, PZT [Pb(Zr,Ti)O 3 ] and PLZT [(Pb, La) (Zr, Ti) O 3] dielectric ceramics and even for refractories. However, for engineering ceramics such as silicon nitrides, more severe microstructure control is necessary. Steps in the progress of the improvement of silicon ceramics are reviewed in Table 10-13. Critical stages in the devel-
opment of silicon nitride ceramics are described below. Table 10-14 gives the characteristics of the various kinds of sintered silicon nitride ceramics including sialon, which is also described below. Reaction Sintering This method was investigated in the 1960s (Popper and Ruddesden, 1961). Re-
Table 10-14. Properties of various sintered silicon nitrides including sialon. Silicon nitride
Property
Density (g/cm3) Thermal conductivity Thermal expansion coefficient Young's modulus Poisson's ratio Bending strength
(W/mK) (10~6 C" 1 ) (GPa) (MPa) RT 1000°C 1200°C 1400°C
Fracture toughness (MPa m1/2) Critical thermal shock temperature (°C:ATC)
Sialon
Reaction sintering
Pressureless or gas-pressure sintering
Hotpressing
P
2.1-2.6 2.6-20
2.9-3.5 13-18
2.9-3.5 29-32
3.0-3.15 -
3.22 -
2.3-3.0 100-200 0.24-0.26
3.0-3.5 240-330 0.24-0.28
3.1-3.3 320 0.26
2.5-3 230 0.29
3.2 310
150-295 160-300 170-307 -
400-1000 350-1000 250-800 -
800-1050 800-1000 250-950 -
360-800 350-800 300-800
900 700 450
3-4
4-7
6-7
2-4
6.3
350-600
400-800
800-900
500-600
600
10.5 Non-oxide Ceramics
1200
-O
O
Relative density
I
100^
0 ^ ^
{
0s-
^^
1000 -
-90 -
800
or i
I
Sc
Y
i
1
80 £
600
T
1
en
Modulus of rupture
535
i
i
\
i
i
i
i
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i
i
i
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i
i
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i
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70
La Ce Pr Nd Gd Tb Dy Ho Er
Additive Figure 10-14. Densities and room temperature bending strengths of post-reaction sintered silicon nitride specimens containing rare earth additives.
action sintered Si 3 N 4 products are fabricated through direct nitridation by heating Si powder compacts in an N 2 gas stream. The products have a porosity of 25-15%, but there is no change in the dimensions before and after sintering. However, high strength cannot be attained by this method. In subsequent work (Seltzer, 1977), postreaction sintering using additives such as Y 2 O 3 -A1 2 O 3 has become an interesting processing route to obtain a densified Si 3 N 4 body with a small amount of shrinkage. Many kinds of rare earth compound additives have been tried, and have resulted in full densification, higher strength and good oxidation resistant properties being attained [Fig. 10-14 (Shimamori etal., 1988)]. Oxidation resistivity will be described later. Densification Full densification sintering of Si 3 N 4 was first performed by Deeley etal. (1961). Many kinds of additives have been investigated as densification aids using hot-pressing, and it was found that MgO was a good densification aid. MgO is thought to react with SiO2 on the surface of the Si 3 N 4 particles to form a glassy phase in the system
0 0.2 0.4 0.6 0.8 1.0 a-phase content in Si3N4 powder
Figure 10-15. Fracture toughness vs. a//? ratio in hotpressed Si 3 N 4 -MgO.
SiO2-MgO and densification is promoted by liquid phase sintering (Wild et al., 1972). The use of a-Si 3 N 4 raw powder resulted in a high room temperature strength and toughness by the development of an elongated grain structure, which is clearly shown in Fig. 10-15 (Lange, 1983). However, it has been observed that the existence of a grain boundary glass phase composed of Mg-Si-O leads to strength degradation at temperatures above 1000 °C. NCI32 material from the Norton Company is a hot-pressed silicon nitride with MgO doping that has been widely circulated around the world. A gas pressure sintering method was developed for the densification of silicon nitride by Mitomo (1976). Figure 10-16 shows the first experimental results, in which a higher gas pressure atmosphere gives effective densification promotion. This gas pressure dependence seems to be related to the higher vapor pressure of silicon nitride at sintering temperatures. Strengthening by Available Additives The most important early developments in silicon nitride ceramics are considered to be the determination of the optimum addi-
536
10 High Temperature Engineering Ceramics
60
U00 1500 1600 1700 1800 1900 2000 Temperature (°C)
Figure 10-16. Temperature dependence of densification of Si 3 N 4 -5 wt.% MgO for N 2 gas pressure sintering (GPS) and pressureless sintering (PLS).
uoo -
200
400 600 800 1000 1200 1400 Temperature (°C)
Figure 10-17. Flexural strength of hot-pressed aSi 3 N 4 with Y 2 O 3 and A12O3 addition as a function of temperature. (A) compact presintered at 1700°C in A1N powder bed; (B) compact presintered at 1700°C in Si 3 N 4 powder bed; (C) no presintering treatment. All specimens were hot-pressed at 1750°C under a pressure of 49 MPa for 90 min.
tives for the densification and strengthening of Si 3 N 4 by Komeya and Inoue (1969), and of sialon by Oyama and Kamigaito (1971), and Jack and Wilson (1972). Many different compositions were investigated. In these studies, the discovery of rare earth oxide additives leading to, for example, the systems Si 3 N 4 -Y 2 O 3 -Al 2 O3 and Si 3 N 4 Y 2 O 3 -A1 2 O 3 -A1N have had a large impact on the development of silicon nitride as an engineering ceramic. As is now well known, a more elongated grain structure and more complete densification is promoted by addition of yttria, which leads to higher strength and toughness [Figs. 10-17 (Tsuge e t a l , 1975) and 10-18 (Komeya, 1984)]. Tsuge etal. (1979) have obtained the highest fracture strength for silicon nitride with Y 2 O 3 -A1 2 O 3 additions, as shown in Fig. 10-19, for which 3-point bending strengths of 1460 MPa at room temperature and 1260 MPa at 1200°C have been achieved. The improved materials from these compositions had high strength from room temperature to 1000 °C and have recently been put to practical use in engine components. To realize practical applications of silicon nitrides much effort has been devoted to raw powder development and improvement of the powder quality, as well as molding/firing processing of the components. As a
Figure 10-18. Change in grain morphology on sintering powder compacts of a-Si 3 N 4 -Y 2 O 3 -Al 2 O 3 : (A) raw powder, (B) sintered compact. Bar = 5 um.
10.5 Non-oxide Ceramics
1500
In recent work, higher fracture toughness values have been achieved by advanced grain structure control, which is discussed in another section.
3270
Density
537
3260 3250 \
1000 3240
Improvement of High Temperature Strength and Oxidation I Corrosion Resistance
3230 Presintered (1750°C, 90min)
? 500 CD
3230 •Q
I
c
3210
Hot-pressed (1780°C, 49 MPa. 120 min)
O Q-
0
0
1
2 3 A Free SiO2 (wt.%)
3200
5
6
Figure 10-19. Effect of free silica on the strength of hot-pressed Si 3 N 4 -5wt.% Y 2 O 3 -2wt% A12O3 at room temperature (RT) and 1200°C.
99 -
(MPa) o SN1 727 90 • SN2 783 _ 80 - • SN4 719 §S 60 SN10 544
I"
m
nf
21 27
ff /fit
9.5
&<*
4-0 a 9 ^ j * a/
A
/I
2 20 Q. 10
I
li-
/
D
m
/
rr
/ i
100
200
300 400
/ i
f li
i
i
600 800 1000
Strength (MPa)
Figure 10-20. Weibull plots of bending strength for Si 3 N 4 containing (SN1) 1 mol%, (SN2) 2 mol%, (SN4)4 mol% and(SN10) 10 mol% of Y 2 O 3 -Nd 2 O 3 fired at 1900°C for 4 h.
result, highly reliable silicon nitride ceramics with a very high Weibull modulus (m), over 20, have been developed. A typical example of a Weibull plot is shown in Fig. 10-20 (Hirosaki and Mitomo, 1992).
As described above, high strength silicon nitride ceramics usable from room temperature to 1000 °C have been available for the last ten years. However, to be useful as components in advanced engines and engineering plants, improvement of the high temperature strength and oxidation/corrosion resistance of silicon nitride by means of conventional firing processes, such as pressureless sintering or gas pressure sintering, is indispensable. As an approach to high-temperature strength improvement, grain-boundary phase crystallization was developed. This method consisted of preheat-treatment of an Si 3 N 4 -Y 2 O 3 -Al 2 O 3 powder compact by placing it in an aluminum nitride powder bed in an atmosphere of nitrogen gas, and subsequently hot-pressing it (Tsuge etal., 1975; Komeya, 1984). Figure 10-21 shows the relationship between the 1200 °C bending strength and the crystalhnity of grain boundary phases; the crystalline phase is mellilite (Y2Si3O3N4) (Tsuge and Nishida, 1978). Since then, different methods for stimulating grain boundary crystallization, such as annealing sintered specimens and use of new additives for the above systems, have been studied. Figure 10-22 shows an example of the improvement of the high temperature strength caused by adding HfO2 to the Si 3 N 4 -Y 2 O 3 -AlN (Komeya etal., 1991 a). The three-point bending strengths at 1300°C were 1200 MPa for hot-pressed specimens and 900 MPa for pressureless
538
10 High Temperature Engineering Ceramics
1200
0
20 £0 60 80 100 Grain boundary phase crystallinity (%)
Figure 10-21. Effect of grain boundary crystallization on strength at 1200°C for the system Si 3 N 4 -Y 2 O 3 A1 2 O 3 (A) aRT = 1210MPa, <71200<>c=650MPa; (B) MPa, <719nnor = l020MPa.
0
200 400 600 800 1000 1200 1400 Temperature (°C) Figure 10-23. Bending strength of a 4- /? mixed sialon ceramics derived from the Si 3 N 4 -Y 2 O 3 -AlN system.
Y Pr Ce Yb Er Dy Gd Sm Nd La 100
-- 700
A
80
-600!
\
lues
- 5 0 0 J?
"
(a)
800
900 1000 1100 1200 1300 Temperature (°C)
L0
\
\
^
\
>v
^
^
AA A
A
; 5 Range of test
60
300-§
»- 2 0 0 ;
1200
20
-100
£ 1000 0 0.8
800
I
1
0.9 1.0 Ionic radius (A)
1.1
Figure 10-24. Effect of ionic radius of rare earth elements on the elevated temperature strength of Si 3 N 4 Y 2 O 3 -A1 2 O 3 .
600 400 800
900
1000 1100 1200 1300
(b) Temperature (°C) Figure 10-22. Temperature dependence of bending strengths of (a) hot-pressed and (b) pressureless sintered specimens: (A) Si 3 N 4 -Y 2 O 3 -Al 2 O 3 , (B) Si 3 N 4 -Y 2 O 3 -Al 2 O 3 -AlN, (C) Si 3 N 4 -Y 2 O 3 -AlNHfO7.
sintered ones. Ceramics consisting of oc+ p mixed sialon were developed by hot-pressing the Si 3 N 4 -Y 2 O 3 -A1N system yielding good high temperature strength, about 1000 MPa at 1300°C [Fig. 10-23 (Ukyo and Wada, 1989)].
10.5 Non-oxide Ceramics
500 1000 Temperature (°C)
1500
Figure 10-25. Temperature dependence of the bending strength of sialon ceramics (z = 0.5).
The existence of a grain boundary itself as well as grain boundary phases may degrade properties in high temperature applications. In a study on new additives, the effect of the ionic radius of rare earth elements on the eutectic melting points and elevated temperature strengths of compositions of Si3N4-MJCO);--SiO2 (M: rare earth element) was investigated, as shown in Fig. 10-24 (Anderson and Bratton, 1977). This result suggested that additions of rare earth elements with smaller ionic
2
4 6 (Oxidation time) 1 7 2 / h 1/2
539
radius have a great potential for high temperature strength improvement. It is known that P-sialon ceramics have excellent high temperature properties without the necessity of adding elements to produce grain boundary phases. The temperature dependence of the three-point bending strength of dense p-sialon ceramics is shown in Fig. 10-25 (Yamada et al., 1988). See also Chap. 3 (Sec. 3.4) of this Volume. Resistance against oxidation and corrosion should be evaluated for each application environment. As this evaluation is very difficult because of the complexity and varying nature of the application conditions, only general oxidation resistance is described in this section. The oxidation resistance of silicon nitride with grain boundary phases depends on the composition, structure and contents of the grain boundary phases. For instance, it has been reported that in the Si 3 N 4 -Y 2 O 3 -Al 2 O3 system, the weight gain due to oxidation increased with increasing content of Y 2 O 3 and of other compounds. For example, the weight gain for the three compositions
10
Figure 10-26. Weight gain by oxidation in flowing air for (a) Si 3 N 4 -Y 2 O 3 -Al 2 O 3 and (b) Si 3 N 4 -Y 2 O 3 -Al 2 O 3 -TiO 2 .
540
10 High Temperature Engineering Ceramics
4.0
s O
3.0 -
0 4
Sialon, z=0.5 Sialon, z=2.0
bo
a
2.0 bo •H 0)
In dry air flow Oxidation temperature : UOO'C
1.0 Figure 10-27. Weight gain by oxidation in flowing air for sialon. 2
4 6 8 (Oxidation time) 1 7 2 / h 1/2
800 600 "a •a
LOO
Oxidation weight gain
Sc Y La Ce Pr Nd Gd Tb Dy Ho Er
Figure 10-28. Weight gain and room temperature strength after 100 h oxidation in air at 1300°C for various post-reaction sintered specimens.
Si 3 N 4 -Y 2 O 3 -Al 2 O 3 , Si 3 N 4 -Y 2 O 3 -Al 2 O 3 TiO 2 and p-sialon (Si 6 _ z Al z O 2 N 8 _ 2 , 0 < z < 4.2) with z = 0.5, in an air flow at 1100-1400 °C, is shown in Figs. 10-26 and 10-27 (Komeya et al., 1991b). The weight gain increases with increasing temperature. Sialon shows a very low weight gain of only about 1 x 10" * mg/cm2 after 54 h
10
oxidation at 1400 °C. The temperature above which the weight gain rapidly increases is quite different when TiO 2 is added. Namely, the critical temperature with TiO 2 is 1300°C, as opposed to 1350°C without. It is also reported that oxidation is dependent on the phases present in the case of Si 3 N 4 -Y 2 O 3 -SiO 2 . A highly oxidation resistant material has recently been developed by post-reaction sintering of a starting composition of the Si-Sc 2 O 3 system. The influence of various rare earth oxides on the oxidation weight gain is shown in Fig. 10-28 (Shimamori et al., 1988). The above results suggest that further development of a highly oxidation resistant grain boundary phase is necessary. P-sialon ceramics without grain boundary phases may be suitable for higher temperature applications, if higher strength and toughness can be achieved. The use of silicon nitride ceramics in high temperature applications requires the improvement of the high temperature strength, fracture toughness and oxidation/corrosion resistance.
10.5 Non-oxide Ceramics
541
Table 10-15. Typical sintering aids for silicon nitride. Y2O3 MgO Y 2 O 3 -A1 2 O 3 A12O3 Y 2 O 3 -A1 2 O 3 -A1N MgO-Al 2 O 3 A12O3-A1N Y 2 O 3 -Al 2 O 3 -AlN-TiO : Yb 2 O 3 Y 2 O 3 -Al 2 O 3 ~MgO Y2O3-Al2O3-MgO-ZrO2 (Si-)Sc2O3 Y 2 O 3 -MgO-ZrO 2 (Si-)Sc 2 O 3 -Y 2 O 3 Y 2 O 3 -SiO 2 CeO2-MgO-SrO CeO 2 -MgO-SrO~ZrO 2 Y 2 O 3 -Cr 2 O 3 Y 2 O 3 -A1N CeO 2 -MgO-Y 2 O 3 Y 2 O 3 -AlN-HfO 2 CeO 2 -Al 2 O 3 BeAl2O4 Y 2 O 3 -AlN-ZrO 2
Development of Microstructures to Improve the Fracture Toughness It is now well known that fracture toughness can be improved by control of ceramic microstructures. Effective parameters for microstructural control in order to improve the fracture toughness are described. Many sintering aids, as listed in Table 10-15, have been studied, for which Si 3 N 3 -Y 2 O 3 is the base composition. These systems have been selected to achieve technological targets such as strengthening, toughening and oxidation/ corrosion resistance. For this purpose microstructural design and processing to obtain the optimum characteristics have been emphasized. Some of the main methods are described next. Improvement of fracture toughness of silicon nitride has been achieved by causing anisotropic grain growth. Figure 10-29 shows examples of microstructures and mechanical properties obtained for Si 3 N 4 Y 2 O 3 -A1 2 O 3 by Kawashima et al. (1991), for which a toughness of 11.3 MPa m 1/2 and a three-point bending strength of 774 MPa were obtained as a result of the formation of large elongated grains. Higher strength (1147 MPa) was attained
(b) Figure 10-29. Grain structures and mechanical prop(a) <7f = 774MPa, Klc = 11.3 MPa m 1/2 . (b) 1147 MPa, Klc= 5.7 MPam 1 / 2 .
with microstructures composed of homogeneous small grains. Figure 10-30 shows that the fracture toughness increases with the square root of the grain diameter of larger grains grown in gas pressure sintered specimens. The results indicate, that the large elongated grains contribute to the toughening (Kawashima, 1990). Nakajima (1991) also reported a toughness of 10.1 MPa m 1/2 by grain size control (Table 10-16). Mitomo (1991 b) pointed out that, in the gas pressure sintering, the a to (3 transformation is completed at the intermediate stage, and most of the densifica-
542
10 High Temperature Engineering Ceramics
1.5
2.0
2.5
(Grain diameter)
172
(|jm
3.0 1/2
)
Figure 10-30. Relation between fracture toughness and grain diameter of abnormally grown grains.
PLS
100r
15
GPS
04
50
100
50
Content Figure 10-31. Relation between densification, phase change and microstructure development with gas pressure sintering (GPS) and pressureless sintering.
Table 10-16. Fracture toughness under different firing conditions for the system Si 3 N 4 -Y 2 O 3 -Al 2 O 3 . Firing temp. (°Q
Density
1750 1800 1850 2000
3.19 3.21 3.22 3.22
(g/cm3)
3-pt bending strength (RT) (MPa) (MPa m1/2)) 880 910 800 720
7.1 9.4 10.1 10.1
Figure 10-32. Microstructure of a material from powder with nuclei added.
tion is accompanied by growth of p grains (Fig. 10-31). Consequently, a bimodal grain size distribution was obtained. He also found that a more uniform grain structure was formed using (3-silicon nitride powder, which is considered to be due to the absence of the a to p phase transformation. With an addition of 5wt.% nuclei of (3-silicon nitride to this powder, larger elongated grains appeared in the microstructure [Fig. 10-32 (Mitomo, 1991b)]. It has been confirmed that this approach can increase Klc. Urashima et al. (1992) reported microstructures with high and low Klc for silicon nitrides which were very similar, suggesting that the mechanical properties of grain boundary phases and interfacial bonding between silicon nitride grains and the grain boundary phase are also very important factors for toughening. As has been described so far, properties such as toughness, strength and oxidation resistance are very much affected by microstructures. Microstructures, in turn, are influenced by compositions, starting powders and processing conditions. Therefore, results obtained by many studies, some of which were presented here, have contributed to the improvement of properties either directly or indirectly.
10.5 Non-oxide Ceramics
10.5.2.4 Practical Applications of Silicon Nitride Ceramics Silicon nitride ceramics which have excellent properties from room temperature to 1200 °C have been developed. These properties include high strength, high thermal shock resistance, and high oxidation and corrosion resistance. As a result of the progress of critically important technologies, several kinds of practical applications have been realized. Table 10-17 shows application areas of silicon nitrides in comparison with silicon carbide and other ceramics. Applications are divided into engine components and industrial parts. The
543
silicon nitride components listed in the table, except for gas turbines, are available in practice, but, at present, each of them is only in small scale volume production, because of cost and reliability problems. However, it is significant that automotive engine components such as the glow plug, precombustion chamber, rocker arm pad, turbocharger rotor and injector link have been put to practical use. In particular, production of the ceramic turbocharger rotor has had considerable impact on the engineering ceramics fields. Antifriction bearings and cutting tools have been widely applied as industrial parts for the last ten years.
Table 10-17. Application areas for representative engineering ceramics. Application area
Components
Material
GO
CO
<
N
z PQ
Gas turbine Reciprocal engine
Wear part
Metals / semiconductors
Heat jig Others
Automotive Power generator Ignition plug Turbocharger rotor Glow plug Precombustion chamber Injector link Cam roller Valve Catalyst susceptor Port liner Antifriction bearing Cutting tool Mechanical seal Ball for grinding Other wear parts Heat-treatment for Si wafer Jigs for Al die casting Wire puller Break ring Heat-treatment jig Sport, hobby
AT: Al 2 TiO 5 ; b MAS: magnesium aluminosilicate (cordierite); c coating.
(x)c
x X
X
X
X
X
544
10 High Temperature Engineering Ceramics
Figure 10-33. Typical engineering parts in practical use. (Left) Turbocharger rotor (courtesy of Nissan Motor Co., Ltd.). (Right) Antifriction bearing (courtesy of Toshiba Corp.).
Lubricant spindle # 6 0
Steel ball 3 / 8 " , 3 p c s Test specimen 1800 cpm (No. of stress cycles) Load 400kgf Thrust type test setup
-
7.
90
S>50 / Q. 10
O LL
. A SUJ
2
Ceramics
5 10 50 100 No. of stress cycles (*106 cycles)
Figure 10-34. Rolling fatigue life of silicon nitride in comparison with SUJ2 alloy.
Typical photographs of some of the components in practical use are shown in Fig. 10-33. The realization of all of these parts has required much work on fabrication, evaluation and component testing.
For instance, the antifriction bearing has been put into practice by attainment of the attractive rolling fatigue life shown in Fig. 10-34 (Komeya and Kotani, 1986) and development of a more reliable fabrication process. Although ceramic gas turbines are under development for early next century, several projects are already well underway. 10.5.3 Silicon Carbide Ceramics 10.5.3.1 The Intrinsic Character of Silicon Carbide
Silicon carbide is an even more covalent compound than silicon nitride with an ionicity of only 0.19 and a higher decomposition temperature of about 2500 °C under atmospheric pressure. It can exist in a (hexagonal) and p (cubic) crystal structures, the a-type of which can consist of many polytypes, as shown in Table 10-18. Silicon carbide is characterized by higher hardness, excellent high temperature creep resistance, high thermal conductivity, semiconducting properties and excellent oxidation/corrosion resistance. From these characteristics, silicon carbide has applications for service at high temperatures under corrosive conditions and in areas where wear must be prevented. It is also widely used for heating elements which must operate at temperatures up to
10.5 Non-oxide Ceramics
Table 10-18. Silicon carbide polytypes and their lattice constants. Polytype
a (A)
2H 3C 4H 6H 15R
3.076 4.348 3.095 3.095 3.095
c(k) 5.048
10.09 15.17 37,95
1500°C in air. Recent progress has been made in the use of this material for high performance applications such as gas turbine and heat engine parts, ball bearings, pump seal components and so on, applications where it competes with silicon nitride. However, one of the most critical problems still to be overcome for silicon carbide ceramics is its low fracture toughness (3-4 MPa m 1/2 ), which will be discussed later.
545
ous recrystallization, polycrystalline silicon carbide ingots are produced according to SiO2(s) + 3C(s) -• SiC(s) + 2CO(g) AH= 132 kcal/mol
(5)
(2700 K)
Synthesized silicon carbides consist of octype crystals of mainly 6H and 15R polytypes. After crushing, the products are selected into several grades according to their level of quality. Higher grade silicon carbides are ground and purified so as to obtain pure and fine grains of silicon carbide powders. Low grades of silicon carbide are generally used as refractories and abrasive grits. Silicon carbide powder from the Acheson method is classed as a low cost powder. Table 10-19 compares the characteristics of the Acheson method silicon carbide powders with those from other synthesis methods. Low Temperature Carbonization of Silica
10.5.3.2 Synthesis of Silicon Carbide Powder Three kinds of synthesis methods for SiC powder have been developed: the Acheson method, low temperature carbonization of SiO2, vapor phase reaction, including direct carbonization of silicon and carbon and thermal decomposition, of which the first two are currently available. Outlines of these three methods are described below. Acheson Method The Acheson method has been carried out since the beginning of the new ceramic age. A graphite core is prepared as an electrolyte, and powder mixtures of silica and coke are placed around the core. By electrical resistance heating, the temperature is elevated to over 2500 °C. Through a carbothermal reduction reaction and continu-
The carbothermal reduction reaction of fine silica and carbon powder mixtures gives fine-grained and pure P-type silicon carbide powder, for which the reaction is carried out at 1400-1800 °C. Although the reaction is similar to the Acheson method, it is different in that the synthesizing temperature is lower and the crystal structure produced is p-type. This method is the one of choice for preparing high quality, finegrained silicon carbide powder. Typical characteristics of synthesized powders are shown in Table 10-19. Ultrafme powders of less than 100 nm in particle size have recently been developed using the sol-gel method. Vapor Phase Reaction Ultrafme silicon carbide powders are also synthesized by vapor phase reaction between SiCl4 or SiH 4 and hydrocarbons,
546
10 High Temperature Engineering Ceramics
Table 10-19. Characteristics of silicon carbide powders. Method:3 Structure: Composition (wt.%) SiC Fb-C Fb-SiO2 Fb-Si Fe Al Ca Mg Na B Cr Ni Diameter (jam) Specific surface (m2/g) 1
A a
A a
B
B
Sol-gel B
C
C
P
P
P
P
P
99 0.3 0.1 0.02 0.01 5.0 -
97 1.4 0.7 0.06 0.01 0.45 14
>98 0.4 0.3 0.04 0.03 0.27 17.5
>99 0.10 0.14 0.012 0.048 0.004 0.001 0.003 0.002 0.2-0.3 20
>99 <0.3 <0.2 <0.1 <0.02 <0.02 <0.01 < 0.001 <0.01 < 0.002 0.4 20
97.2 1.0 1.3 0.006 0.0017 0.0009 0.3 -
94.5 1.6 2.1 0.0018 0.0008 0.0004 0.032 -
A: Acheson, B: silica reduction, C: vapor phase reaction; b F = free.
as shown by the following chemical equation: (6) 7SiCl4 + C 7 H 8 + 10H 2 7SiC + 28HCl Although the powder products have higher quality than those of the methods previously discussed, it is not commercially available because of the higher cost of the vapor phase reaction process at present. This process is rather more attractive for chemical vapor deposition (CVD) of SiC coatings on a substrate such as graphite. Silicon carbide coated graphite is used as a susceptor for silicon wafer processing. 10.5.3.3 Progress in Sintered Silicon Carbide Silicon carbide is a poorly sinterable ceramic similar to silicon nitride. Sintering methods are divided into reaction sintering, pressureless sintering, hot-pressing and hipping with additives.
Reaction sintering consists of reaction bonding using SiC-C-Si mixtures and subsequently recrystallizing the silicon carbide compact. Sintered products contain over 10% porosity and, as a result, have lower strength. Densified SiC-Si materials are obtained by the infiltration of molten Si into the SiC-Si compacts at about 1650 °C (Kennedy et al., 1973). In this case the reaction sintering mechanism is achieved by the excellent wettability of SiC and carbon by molten Si resulting in high capillary pressures which draw in the liquid. The porous silicon carbide ceramics can be used for refractories and heating elements. Dense SiC-Si materials are used as key components for heat-treatment of high purity silicon wafers. However, since the high temperature strength of Si-infiltrated silicon carbide is low at temperatures above the melting temperature of silicon (1410 °C), it is not suitable for high temperature engineering applications, (Fig. 10-35; Kennedy et al., 1973). Conse-
10.5 Non-oxide Ceramics 600
200 400
600 800 1000 1200 U00 Temperature (°C)
Figure 10-35. Temperature dependence of bending strength of reaction sintered silicon carbides.
Table 10-20. (a) Effect of B and C addition on sintering silicon carbide, (b) Raw powders used in (a), (a) SiC Content (wt.%) Raw powder B C A A A B B C C C
0.4 0.4 0.4 0.0 0.4 0.0 0.6 0.6
0.0 0.0 0.6 0.9 0.9 0.0 0.0 0.9
Sinter- Shrink- Dening temp. age sity (°Q (%) (%) 2020 2100 2020 2020 2020 2100 2100 2020
5.0 5.5 18.5 15.0 2.5 14.8
71.0 72.0 98.3 59.0 94.5 49.0 53.5 84.0
(b) Raw powder
A B C
Specific surface (m2/g)
Oxygen (ppm)
Metallic impurities (ppm)
16 9 14
600 300 3000
1000 2000 500
quently, engineering applications of reaction sintered silicon carbides are limited under high stress conditions because of their poor mechanical properties. Prochazka discovered in 1973 that the addition of B and C resulted in excellent densi-
547
fication promotion during pressureless sintering of silicon carbide (Prochazka and Charles, 1973). When a silicon carbide powder compact with a small amount of B and C is sintered at around 2000°C, almost full density may be attained, as shown in Table 10-20 (Prochazka and Charles, 1973). The densification mechanism is explained as follows. The surfaces of silicon carbide particles are covered with a silica layer. The carbon addition acts to eliminate the oxide layer and increase the surface energy between the solid and the vapor (ysv). On the other hand, the B addition results in a lower grain boundary energy (ygb) in the sintering system. Since a dihedral angle of over 60° is required to attain pore shrinkage, ygh/ysv < >/3 is necessary for densification. The above thermodynamic conditions are satisfied by B and C additions because B and C cause a change in the surface and grain-boundary energies of SiC. Whether the densification is promoted by liquid phase sintering or solid state sintering is not clear, but this new development of the sintering process for a previously unsinterable ceramic is very significant. Both a and P silicon carbide powders may be sintered by this method. The sintered body has no degradation of strength, and also excellent oxidation and corrosion resistance at high temperatures. However, its relatively low fracture toughness, which leads to strengths below those of silicon nitride, is a disadvantage, which is delaying the development of applications for this material. It is known that Al compounds such as A12O3 and A1N are other additives which promote the densification of silicon carbide. Densification in the case of Al compound additives is considered to be promoted by liquid phase sintering. This seems to be due to the formation of SiO 2 -
548
10 High Temperature Engineering Ceramics 8.0
0
(U
0.8
1.2
A! (wt.%)
Figure 10-36. Changes in lattice constant of SiC with Al content in the sintering of silicon carbide.
I I I 1 room temperature (/? =
2.9
3.0 3.1 3.2 Density (g/cm3)
3.3
Figure 10-38. Fracture toughness of densified silicon carbide containing Al.
800 ^ 700 c " 600 C •o
c 500
I• T
pressureless sintered
Q) -Q
Z
j
400
/ h i p ped
"a 300 200 2.8 u_
i1
i 2.9
3.0
3.1
3.2
3.3
Density (g/cm 3 )
2.0 3.0 Aspect ratio
Figure 10-37. Bending strength of densified silicon carbide containing Al.
Figure 10-39. Relation between Klc and aspect ratio of SiC grains in sintered SiC-Al 2 O 3 .
A12O3 compounds and dissolution of Al into the silicon carbide crystals in accord with the solubility limit, as shown in Fig. 10-36 (Murata and Smoak, 1978). Since grain boundary phases exist in the sintered body, the strength decreases with increasing temperature. However, it is advantageous that the room temperature strength and fracture toughness, as shown in Figs. 10-37 (Nakatsuji etal., 1992) and 10-38 (Nakatsuji et al., 1992), are superior to those produced by B-C additions. This
improvement is seen in Fig. 10-39 (Suzuki and Sasaki, 1984), which illustrates the relationship between Klc and the aspect ratio of the plate-like SiC grains in the microstructure. Typical properties of sintered silicon carbide ceramics are illustrated in Table 10-21. The critical factors for successful silicon carbide development are the generation of higher toughness and high temperature strength at an acceptable cost. Although a number of additives have been studied,
549
10.5 Non-oxide Ceramics
Table 10-21. Properties of various silicon carbide ceramics. Property
Units
Hot-pressed
Sintered
Si-infiltrated
Recrystallized
Density Porosity Bending strength RT 1400°C
g/cm 3 % MPa
3.2 <1 770 410
3.14-3.18 2 470 440
Young's modulus Hardness Thermal conductivity Thermal expansion coeff.
GPa GPa W/mK xlO" 6 /°C
450
3.10 <1 530 200 (1450 °C) 420 25-35 84 4.3
2.6 18 100-130 130-150 (1500°C) 20
80 4.8
generally B-C and Al compounds seem to be the most effective additives. 10.5.3.4 Practical Applications of Silicon Carbide Ceramics
Sintered silicon carbide ceramics have excellent corrosion resisting properties in severe chemical conditions, as well as high strength at room temperature and higher temperatures, compared with other possible materials, especially silicon nitride ceramics. The main applications of silicon carbide ceramics are mechanical seals and heat-treatment jigs for Si wafer processing. This material has also been a candidate for high temperature gas turbines. Consequently, considerable experience in ceramic gas turbine technologies has been accumulated worldwide. Table 10-17 shows application areas for silicon carbides compared with other similar ceramics. 10.5.4 Evaluation of Silicon-Based Ceramics
Mechanical property considerations in previous sections were limited to strength and fracture toughness, which are the most important items for a material's development. However, in order to develop reli-
410 28 88 4.0
4.8
able ceramic components other properties of these materials have to be evaluated, such as fast fracture strength under bending and tensile loads, static fatigue strength, cyclic fatigue strength, thermal shock strength, thermal fatigue strength, oxidation/corrosion resistance in real environments, foreign object damage, and so on. In designing ceramic components, the most important properties are the fast fracture strength, and the static and cyclic fatigue strength. In this section, an outline of the fast fracture strength and some of the static and cyclic fatigue strengths of silicon-based ceramics, especially silicon nitride, is given. 10.5.4.1 Fast Fracture Strength and Its Dependence on Volume
The strength of ceramics depends on the dimensions of their existing flaws. Therefore the distribution of strength is dominated by the distribution and dimensions of flaws, and the Weibull statistical theory is generally used for the analysis of this distribution. The failure probability of a component under uniaxial stress is expressed by the Weibull distribution function, F= 1 - exp { - J, [{a - ou)/
550
10 High Temperature Engineering Ceramics
4-Point bendinq 1000
900 /3-Point 800 _ 700 |
Slope =
^<\
600
. JL
60 Tension
) 0 Tension
£ 500 c CD
£ 400 CO
Z. 140 Tension
SSN-A1 m = 15O .SSN-A2 /77=15 • 300 SSN-B /77=15 A SiC m-11 • 200 • 10"
• • nail
Figure 10-40. The relationship between the effective volumes and mean strengths for SSNAl, SSN-A2, SSN-B and SiC under uniaxial stress.
20 0 Tension^
. . . ..,„!
10°
\
|
101
10 2
,
i
10 3
10*
,.,i
10 5
10 6
Effective volume (mm3)
where o is the stress at an arbitrary point in the material, ou is the location parameter, (70 is the Weibull scale parameter and m is the Weibull parameter. Usually, m is called the Weibull modulus. In general, au is taken to be zero and a two-parameter Weibull distribution is applied. With the maximum stress (tfmax) on the specimen, Eq. (10-5) is transformed into F= 1 - exp [ - jv {amjao)m Ve = \v [o (x, y , z)/(jmax]m d V
Ve]
(10-6) (10-7)
where Fe is the effective volume. The strength of specimens with different effective volumes can be represented by the ratio between the effective volumes, °il°2 = lV*2lVcl}llm
strength was tested in three- and fourpoint bending according to the Japanese Industrial Standard (JIS) R1601. Under uniaxial stress, a linear relationship was observed between the effective volume and the mean strength of both silicon nitride and silicon carbide. The Weibull modulus, which can be obtained from the gradient of the line, was 15 for SSN-A1, SSN-A2 and SSN-B, and 11 for silicon carbide. These values agree with the values obtained from the Weibull plot of the four-point bending strengths of the ceramics. Therefore, the strength of the ceramics, based on the twoparameter Weibull distribution, can be estimated from the volume effect in Eq. (10-8).
(10-8)
Figure 10-40 shows the relationship between the effective volumes and mean bending and tensile strengths for typical silicon nitride and silicon carbide ceramics (Matsui etal., 1991). The difference between SSN-A and SSN-B is in the applied sintering additives. The tensile strength was tested with rod specimens of 6 to 20 mm in gauge diameter (0). Bending
10.5.4.2 Fatigue Strength Static Fatigue Strength The static fatigue lifetime of ceramics is generally predicted by the power law crack growth rate equation (Kawakubo and Komeya, 1987; Evans, 1974) (10-9)
10.5 Non-oxide Ceramics
with X , = Yo 1/2
(10-10)
where A and n are constants, a is the flaw size, Kt is the stress intensity factor, Y is a geometrical factor and aa is the applied stress. From Eqs. (10-9) and (10-10), the lifetime ts under constant stress in a static fatigue test is obtained as (10-11) —n — 2
C =
[(n-2)AY2Klcn-2]
(10-12)
where a{ is the inert strength for initial flaws. As well as the static fatigue test, a dynamic fatigue test is also used to evaluate the crack growth behavior. The fracture strength oi under a constant stress rate in a dynamic fatigue test is obtained as follows, based on Eqs. (10-9) and (10-10), (Tj + 1 =(7!+l)C 8 (t
(10-13)
The time to failure tf in a dynamic fatigue test can be converted into the static fatigue lifetime teq (hereinafter referred to as equivalent time) as follows, based on Eqs. (10-11) and (10-13), 1
(10-14)
Figure 10-41 shows the static fatigue characteristics of three types of sintered silicon nitride, with different sintering additives, under a tensile stress (Masuda etal., 1989). Figure 10-41 a shows the results of the static and dynamic fatigue tests (the relationship between the applied stress and equivalent time) for SSN-A, and Fig. 10-41 b shows those for SSN-B and SSN-C. At a high temperature, the three types of silicon nitride differ from each other in their static fatigue behavior. These differences are caused by the differences in the high temperature characteristics of their
551
grain boundary phases. While the grain boundary phases of SSN-A are glassy, those of SSN-B and SSN-C are mainly crystalline. Glassy grain boundaries start to soften at a lower temperature than crystalline grain boundaries. Furthermore, the softening of the crystalline grain boundaries is suppressed at a higher temperature in SSN-C than in SSN-B. As a result, SSN-C has excellent static fatigue characteristics at high temperatures, followed by SSN-B and then SSN-A. For SSN-A, the equivalent lifetimes for static and dynamic fatigue tests at 1000 °C are in good agreement with each other. The strength degradation was caused by slow crack growth from existing flaws. However, remarkable creep deformation occurred in SSN-A above 1100°C. For SSN-B at 1200 °C and 1400 °C, the results are divided into two stress regions. In the high stress region, it is possible to apply the power law crack growth formulation to static and dynamic fatigue data. In this region, the strength degradation was caused by slow crack growth from existing flaws. However in the low stress region, it is not possible to apply Eq. (10-9), which is based on slow crack growth from existing flaws, to the static fatigue data. In this region, SSN-B and SSN-C showed creep deformation. Therefore another lifetime prediction procedure must be used for this region. The Larson-Miller parameter P, defined by
= T(C+\ogtT)
(10-15)
is generally used to predict the lifetime of metals, where T is the absolute temperature, tr is the time to creep rupture and C is a constant. Figures 10-42 a and b show the master creep rupture curves using the LarsonMiller parameters, where values of C=44
552
10 High Temperature Engineering Ceramics
1000 900 800 700 600
Dynamic fatigue
Static fatigue SSN-A800°C A 1000°C D
:
-
•
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V> 300
< 200 \
100 90 —i i mint—i 10 -5 10"
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i
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10 101 10 10 2 10 Equivalent time to failure (h)
10c
(a) 1000 900 800 700 600 — 500 a Q_
^
SSN-B 1200 °C SSN-C 1200 °C HOOT
: "•=£: -
Static fatigue O
Dynamic fatigue
A
A
•
•
400 300 -
CL
< 200
90
" . .......I
10 -5
. .......I
10"
.
10 - 3
......I
i
^A X
\
ao a
o
\ \
D
X I
, ,..
10"
Figure 10-41. Comparison of the static and dynamic fatigue lifetimes, (a) SSN-A; (b) SSN-B and SSN-C
10"
10 L
10 1
104
10s
Equivalent time to failure (h)
(b) for SSN-B and C = 30 for SSN-C are used (Masuda et al., 1989). The fatigue data at the high temperatures that cause creep deformation can be represented by a temperature-independent straight line. Thus the Larson-Miller parameter can be applied
to the lifetime prediction in the creep deformation fracture region. While C = 20 is generally used for metals, C=20 is unsuitable for silicon nitride ceramics. As the C value gets larger, the effect of temperature on the creep rupture lifetime increases.
553
10.5 Non-oxide Ceramics 1000 900 800 700 600 500
1000 900 800 700 600 500
A A*A*-
I
•
\
M
i
a,
300
A 100CTC A HOCTC D115CTC • 1200*C 01250*C • 1300-C ©1350'C
200
100 90
(a)
•
SSN-B
CD
i
j
55
60
^
300
V
CD
200
• \ \ i
70
65 •tog tr) x10
75
-3
100 90 35
(b)
SSN-C A 1200'C D 1300'C O 1400*C
L5
50
55
60
•P=r(30 + log f r )
Figure 10-42. Larson-Miller curves, (a) SSN-B; (b) SSN-C.
The fracture surfaces of silicon nitride can be classified into two distinctive types. The fracture surfaces of samples that failed at low temperatures and high stress have pores and inclusions, and slow crack growth regions were observed around them. On the other hand, at high temperatures and low stress, relatively large regions with irregularities, which are creep deformation regions, were observed on the fracture surfaces. Such regions tended to increase with decreasing stress. In summary, static fatigue in silicon nitride is generally caused by slow crack growth or creep deformation. Thus the fracture mechanism must be identified in order to predict the failure lifetime appropriately. Cyclic Fatigue Strength This section describes examples of cyclic fatigue characteristics of sintered silicon nitride at room and elevated temperatures. Room temperature characteristics are described first.
Figure 10-43 shows the stress versus number of cycles to failure (S-N) curve for tapered cantilever beam specimens of sintered silicon nitride under alternating loads, at frequencies from 0.03 Hz to 3 kHz (Masuda et al., 1988). Figure 10-44 shows the time-to-failure data calculated from the S-N data for the tapered cantilever beam specimens. The cyclic fatigue behavior of sintered silicon nitride appears to depend principally on the number of cycles rather than on the time, because the fatigue strength at various frequencies did not show any discontinuities against the number of cycles (see Figs. 10-43 and 10-44). The solid curve in Fig. 10-43 suggests a decrease in the fatigue limit to about 40% of its initial strength. Figure 10-45 shows the mean stress/ stress amplitude diagram of sintered silicon nitrides (Masuda et al. 1990). at on the horizontal axis represents the mean tensile strength of 6 mm diameter button-head type specimens. Open circles represent the specimens that survived 107 cycles, the
554
10 High Temperature Engineering Ceramics 900 800 700 600
Cantilever beam cyclic fatigue test
•
'500 "a.
400
SSN-A
• OO O^JLOO nDmc1 O
E a
300
Figure 10-43. S-N curve of cantilever beam specimens of sintered Si 3 N 4 under alternating load, at frequencies from 0.03 Hz to 3 kHz.
o • A
200
J
10°
3kHz 2OHz 0.3Hz 0.03Hz ....J . .....J . .....ul .......J . .......I ........1 ..... ..1 10J 10b 10' 10° Number of cycles to failure N
O-
1 ..
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1
101u 10n i l
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Cantilever beam cyclic fatigue test SSN-A
800 700 600 '.
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O
500
•
•
0
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£00
• • • £ • £9 •OCO ArbA GO B i O O
•
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5
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.
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1
102
broken line represents tensile strength. Alternating (tensile-compressive) loads decreased the strength to a larger extent than pulsating (tensile-tensile) loads. This diagram shows more clearly the safe stressstate region. The solid line from ae to ax represents a modified Goodman line, which is expressed by <*a = <7e [1 - Om/O]
(10-16)
where aa is the stress amplitude,
. ,......i
103
1
105
Figure 10-44. Time-to-failure data calculated from the S-N data for the tapered cantilever beam specimens in Fig. 10-43.
rion for metal components. The modified Goodman line agreed well with the results of the present fatigue test. The design methodology proposed for metal fatigue is applicable to the sintered silicon nitrides. To clarify the effects of volume on cyclic fatigue, cyclic fatigue tests under alternating loads were carried out, using two kinds of specimens with different volumes. Figure 10-46 shows the results of cyclic fatigue tests at room temperature, in which tensile specimens and tapered cantilever beam specimens of sintered silicon nitrides were used (Masuda et al., 1990). The fatigue
10.5 Non-oxide Ceramics
555
SSN-A at 107 cycles •
Failed
O Survived
100
200 300 £00 500 Mean stress <Jm (MPa)
600
Figure 10-45. Mean stress versus stress amplitude for fatigue failure in sintered Si3N4 at 107 cycles measured at room temperature.
700
1000 -f
900 f.
SSN-B
800 700 i 600 : 500
• #-
LOO T3
£
300 Figure 10-46. The effect of
a
200 • Cantilever beam specimen • Tensile specimen 100 10°
101
102
103 10* 105 106 107 108 Number of cycles to failure N
limit of both specimens with different volumes seem to be the same. Cyclic fatigue strength at elevated temperatures is described next. Data for sintered silicon nitrides with a glassy grain boundary phase at 1000 °C and room temperature were plotted on a log-log plot of stress versus number of cycles to failure, as shown in Fig. 10-47. The mean tensile strengths of 6 mm diameter button-head
109
1010
1011
volume on cyclic fatigue at room temperature. Cantilever beam specimens and tensile specimens of sintered Si 3 N 4 were used; the former have a smaller volume than the latter.
type specimens at room temperature, 800 and 1000 °C were 585, 560 and 360 MPa, respectively. The arrow pointing to the left indicates that the specimen failed at the onset of loading, and the ones pointing to the right indicate that the specimens survived that cycle without failure. There was a large scatter, but the fatigue life of the specimens greatly increased as the stress amplitude decreased.
556
10 High Temperature Engineering Ceramics
800 700
SSN-A O
500 LOO
300
E
200
1 x o 100 90 80 10°
Ten-Comp (R=-1) O RT f=20Hz # 1000°C f=20Hz A 1000°C f=1Hz • 1000°C f=O.O1Hz
101
102
Ten-Ten (R=0) 3 1000*C f=20Hz
103 10* 105 106 107 Number of cycles to failure
At room temperature the fatigue strength at 107 cycles was about 60% of the strength. The cyclic fatigue degradation at 1000 °C with a stress ratio of — 1 at a frequency/of 20 Hz was smaller than at room temperature. In contrast to cyclic fatigue behavior at room temperature, the onset of the fatigue life at 1000 °C de-
108
109
10,10
Figure 10-47. S-N diagram of sintered Si 3 N 4 under tension-compression alternate loading at room temperature and 1000 °C. The symbol on the vertical axis represents the tensile strength of the material used.
pended on the frequency, as shown in Fig. 10-47. At elevated temperatures, the lower the frequency, the less the fatigue resistance. Low cycle fatigue at elevated temperatures was dominated by time-dependent fatigue. The effect of mean tensile stress and static fatigue on the cyclic fatigue of sin-
/?=0 Tensile strength
Cyclic fatigue at 10 cycles 20Hz Failed Survived
Static fatigue 10OOh
0
100
700 200 300 £00 500 600 Mean stress
10.6 Ceramic Matrix Composites
tered silicon nitride with a crystalline grain boundary phase at elevated temperatures is shown in Fig. 10-48. These results were obtained under load control at a constant frequency of 20 Hz. The vertical axis represents a fully reversed fatigue condition and the horizontal axis represents the static fatigue strength and the tensile strength. As the temperature is increased, the static fatigue strength decreases. The boundary within which the stress may be safely applied tends to become elliptical as the temperature is increased. An approximation for the mean stress effect is given in Eq. (10-17) for elevated temperatures. Namely
557
Table 10-22. Construction of composites. Element Matrix
Material and features r
Metals Plastics Ceramics-j-Oxides (A12O3, MgO • • •) L Non-oxides (SiC, Si3N4 • • •)
Dispersant - j - Metals V- Plastics L Ceramics -p Particle I Flake [-Whisker (SiC, A12O3---) L Fiber (C, SiC, A1 2 O 3 --)
10.6 Ceramic Matrix Composites
posites using long fibers are classified by their matrices into FRP (fiber reinforced plastics), FRM (fiber reinforced metals) and FRC (fiber reinforced ceramics). It is well known that biomaterials are naturally occurring composites. Human bone is an example of such a composite. Artificial composites, such as FRP, are used increasingly for engineering applications. The progress in carbon fiber technology applied to FRPs has brought rapid advancement in sports goods such as fishing rods and golf club shafts and in main panels and wings in automotive and aircraft components. Other recent developments include the synthesis of long fibers of silicon carbide and their processing for applications. In the next section recent advances in CMCs (ceramic matrix composites) are described (see also Chap. 5 of Volume 13).
10.6.1 Definition and Classification
10.6.2 Dispersants for Composites
Composites are defined as materials composed of at least two kinds of material, and can be classified as shown in Table 10-22. In general these consist of polymer, metal or ceramic matrices reinforced by dispersants in the form of particles, whiskers, platelets or long fibers. Corn-
Characteristics of typical whiskers and fibers are shown in Table 10-23, see also Chapter 2 of Volume 13 of this Series. Alumina fiber is fabricated by spinning and then heating A12(OH)5C1 aqueous solution. Carbon fibers consist of PAN (polyacrylonitrile) type and pitch type,
(10-17) where
558
10 High Temperature Engineering Ceramics
Table 10-23. Properties of various inorganic fibers (Hayami, 1992). Material
Diameter (urn)
Density (g/cm3)
Tensile strength (MPa)
Elastic modulus (GPa)
Glass
E-glass S-glass Silica glass
10 10 1-15
2.52-2.65 2.45-2.49 2.19
3800 (25°C) 4500 (25°C) 6000
75(25°C) 85(25°C) 75
Polycrystal
C, high strength C, high elastic modulus C, low elastic modulus C, pitch high strength SiC (NICALON) A12O3
7-8 5-9
1.70-1.82 1.81-2.1 1.5-1.7 2.1 2.55 3.9
2500-4500 1900-2500 700-1000 2100 2400 1400
190-250 440-700 40-100 700 190 380
21000 14000 19000-21000 15 500-21000
490-700 380 500-700 430-530
Single crystal
11 10-15 20
SiC Si 3 N 4 Graphite A12O3
3-10
3.18 3.18 1.66 3.96
Multitype
B/W B/C SiC/B/W SiC/W
140 140 107 140
2.46 2.27 2.65 3.30
3700 3320 2500 3400
400 390 410 430
Whisker
SiC
0.05-1.5 x 5-200
3.18
20600
481
3.9 3.18
21000 13 700
430 378
1.7 7.9
19000 13 300
710 210
A12O3 Si 3 N 4
1-3
0.1-1.6 x 5-200
Graphite Fe
which are produced by the decomposition and graphitization of polylacrylonitrile and petroleum pitch. The fiber characteristics such as elastic modulus and strength can be controlled by the selection of optimum heat-treatment conditions. Two types of commercially available silicon carbide long fibers have been developed at present. One is synthesized chemically as a coating on tungsten or carbon wires. Another, called NICALON commercially, is made by the decomposition of polycarbosilane fiber to silicon carbide. Table 10-24 gives the properties of
NICALON (Nippon carbon, 1990). In spite of excellent mechanical properties at lower temperatures, it shows strength degradation at high temperatures. This degradation results from the nanocomposite structure of p-SiC, glassy carbon and amorphous silica. Synthesis of a low oxygen content silicon carbide fiber has been investigated. Since these ceramic fibers are stil at the development stage, further advancements in high temperature FRC are expected in the future. Whiskers are defined as needle-like single crystals and are characterized as having
10.6 Ceramic Matrix Composites
Table 10-24. Characteristics of NICALON fiber. Property
NL-200 NL-400 NL-500
Diameter (jim) Density (gem3) Specific resistance (Ocm) Tensile strength (GPa) Elastic modulus (GPa) Thermal expansion coefficient (xlO~7°C)
14 2.55
14 2.30
14 2.4-2.6
103 2.94 196
106 2.94 176
0.5-5.0 2.94 186
3.1
-
-
very high strength. Whiskers are usually synthesized by sequential vaporization, decomposition and vapor phase reaction of the source materials. Silicon carbide whiskers, which are widely used for CMC construction, are produced by the reaction between silica and carbon sources in a carbon crucible. Fine particles such as alumina, zirconia and silicon carbide are also suitable for the fabrication of particle dispersion composites, especially micro and nanocomposites. 10.6.3 Ceramic Matrix Composites Two kinds of disperants, metals and ceramics, have been used for the reinforcement of ceramics. The former promote relaxation of the stress at a crack tip by plastic deformation of the metal phase in the ceramic matrix. A typical example is a WC-Co alloy in which the Co addition brings both densification by liquid phase sintering and high toughness, > 20 MPa m 1/2 , by energy absorption. However, recent sustained research has focused on CMCs using ceramic dispersants such as particles, whiskers and long fibers. In this section, typical ceramic composites such as nanocomposites, whisker reinforced composites and long fiber reinforced composites are briefly introduced.
559
10.6.3.1 Ceramic Nanocomposites Ceramic nanocomposites have been vigorously investigated by Niihara and coworkers (Niihara, 1991 a, b; Niihara and Nakahira, 1991). Ceramic composites can be divided into two types, microcomposites and nanocomposites. In the microcomposites, micrometer-size second phases such as particles, platelets, whiskers and fibers are dispersed at the grain boundaries of the matrix. The main purpose of these composites is to improve the fracture toughness. On the other hand, nanocomposites can be grouped into three types; intergranular, intragranular and nano/ nano-composites, as shown in Fig. 10-49 (Niihara, 1991b). In the intra- and intergranular nanocomposites [Fig. 10-49 (c)], nano-size particles are dispersed mainly within the matrix grains or at the grain boundaries of the matrix, respectively. As described later, these systems lead to an improvement in the mechanical properties such as hardness, fast fracture strength,
Inter-type
(c)Intra/inter-type (d)Nano/nano-type
Figure 10-49. The classification of ceramic nanocomposites.
560
10 High Temperature Engineering Ceramics
fracture toughness, creep resistance and fatigue strength, from room temperature to high temperatures. On the other hand, the nano/nanocomposites are composed of nanometer-sized dispersoids and matrix grains. The primary purpose of the nano/ nanocomposite is to add new properties to ceramics, such as machinability and superplasticity, that are usually associated with metals. At the initial stage, ceramic nanocomposites were successfully prepared by CVD. It is, however, recognized that the powder metallurgical processes are more promising for engineering ceramics, since components of complex shape are required. Many kinds of nanocomposites, such as Al 2 O 3 /SiC, Al 2 O 3 /Si 3 N 4 , A12O3/ TiC, mullite/SiC, B 4 C/TiB 2 , SiC/amorphous SiC and Si3N4/SiC, have been successfully prepared by the usual powder metallurgical techniques such as pressureless sintering, hot pressing, and HIPping. Figure 10-50 (Niihara, 1989 b) shows an example of a transmission electron microscope (TEM) picture of an Al 2 O 3 /5 vol. %
Figure 10-50. Transmission electron micrograph of the Al 2 O 3 -5 vol.% SiC nanocomposite. Arrows identify the SiC particles.
CL
annealed. 1300°C, 1h £ 1000
2 500^ 6 0
10 20 30 40 SiC content (vol.%) Figure 10-51. The improvement of fracture strength by a nano-size SiC dispersion for the Al 2 O 3 -SiC nanocomposites.
SiC nanocomposite. Most of the finer SiC particles, typically less than 0.2 jam, were predominantly dispersed within the matrix grains with some larger SiC particles at the grain boundaries. Similar observations of second phase dispersion were also made for the MgO/SiC, Al 2 O 3 /Si 3 N 4 and natural mullite/SiC composites. The above observations were confined to the intragranular-type nanocomposites, in which the nano-size particles were predominantly dispersed within the matrix grains. The intra/inter-type nanocomposites [Fig. 1049 (c)] have also been fabricated by controlling the sintering conditions. Mechanical properties such as fracture strength and toughness were greatly improved by the addition of nano-size SiC and Si 3 N 4 dispersions to the matrix grains. Figure 10-51 (Niihara and Nakahira, 1991) illustrates the variation of fracture strength with SiC content for the Al2O3/SiC nanocomposite. The strength of A12O3 is increased almost three times by the dispersion of only 5 vol.% of nano-size SiC particles. A further improvement in the strength of up to 1550 MPa was also obtained by annealing at 1300°C for 1 h in either air or an inert
561
10.6 Ceramic Matrix Composites
Table 10-25. Improvements in the mechanical properties observed for ceramic nanocomposites. Composite system
Al2O3/SiC Al 2 O 3 /Si 3 N 4 MgO/SiC Si3N4/SiC
Toughness (MPa m1/2) 3.5 ^ 4 . 8 3.5 ^ 4 . 7 1.2 ^ 4 . 5 4.5 - • 7 . 5
Strength (MPa) 350-> 350^ 340-> 850-+
atmosphere. Significant improvements of the fracture strength were also found for other nanocomposites, as summarized in Table 10-25 (Niihara, 1990). The extreme increase in the fracture toughness is also apparent from the table. The high temperature strength was also significantly improved by the nano-size particle dispersion. Figure 10-52 (Niihara, 1989 a) shows the variation of fracture strength with temperature for A12O3 and MgO based nanocomposites. Monolithic A12O3 and MgO exhibit low strength at room and high temperatures, whereas the Al2O3/SiC and MgO/SiC nanocomposites give an impressive improvement in strength to well over 1000 °C. The greatest
1520 850 700 1550
Max. operating temperature (°C) 800^ 800-^ 600^ 1200^
1200 1300 1400 1400
improvement in high temperature strength was observed for the MgO/SiC nanocomposite. Even in the temperature range from 1000°C to 1400°C, the MgO/30 vol.% SiC nanocomposite exhibits higher strength than the monolithic MgO ceramic. The high temperature strength degradation in oxide ceramics occurs through grain boundary sliding, cavitation formation and/or diffusional creep. However, the nano-size particle dispersion within the matrix grains promotes transgranular, rather than intergranular, fracture, as shown by Niihara (1991c). This phenomenon was also observed at temperatures above 1000 °C. Thus it may be concluded that the increase in high temperature strength is mainly due to the prohibitation of grain boundary sliding, cavitation and creep deformation by dislocation pinning, which is produced by the dispersion within the matrix grains. In summary, mechanical properties of nanocomposites were substantially improved by the particle dispersion. Nanoparticle dispersion has excellent potential for increasing the fracture strength and toughness of a wide range of ceramics. 10.6.3.2 Whisker Dispersed Composites
500 1000 Temperature (°C)
1500
Figure 10-52. Temperature dependence of the fracture strength for the Al 2 O 3 -5 vol.% SiC and M g O 30 vol.% SiC nanocomposites.
Many studies of whisker dispersed composites have been carried out in recent years. The most impressive results have been achieved for A12O3 and mullite com-
562
10 High Temperature Engineering Ceramics
Table 10-26. Properties of Al 2 O 3 /20 vol.% SiC, mullite/20 vol.% SiC whisker reinforced composites. KIcat 25 °C (MPam 1/2 )
Bending strength (MPa) At25°C
CR-10 A12O3 composite Linde-A A12O3 composite A12O3 Mullite composite Mullite
9.0
805
Atl200°C
520
Q_
-C
ing ;5trei
Material
1200-
TJ CD
8.6 4.6 4.6 2.2
600
450
438
posites reinforced by SiC whiskers, research that was conducted at Oak Ridge National Laboratory (ORNL) (Tiegs and Becher, 1987) (see Chap. 8 of this Volume). It was reported that the bending strength and the fracture toughness were significantly improved by these additions, as shown in Table 10-26 (Becher and Wei, 1984; Wei and Becher, 1985). These composites also showed excellent creep resistance. A thermal shock resistance of Ar c = 900°C for a Al 2 O 3 /20 vol.%SiC(W) composite was obtained, which is a much higher than that for monolithic A12O3 (ATC < 400 °C). This composite has found considerable practical use as a cutting tool. Figure 10-53 (Tiegs and Becher, 1987) shows the results of experiments that determined the bending strength and fracture toughness as a function of SiC whisker content. An improvement in these mechanical properties was observed when whiskers were added. Other whisker dispersed composites have been reported for mullite/SiC, ZrO2/SiC, MgO/SiC and Si 3 N 4 /SiC, but the main processing was by hot-pressing. More commercially viable processing such
0 5
10
15
20
25
30
Whisker content (vol.%) Figure 10-53. Bending strength and fracture toughness of Al 2 O 3 /SiC whisker composites.
as pressureless and gas pressure sintering is necessary for cost effective production of shaped components. The mechanisms of strengthening and toughening are thought to be crack pinning, crack deflection and pull out of the whiskers behind the crack tip. These aspects are mentioned in more detail in Chap. 8 of this Volume. 10.6.3.3 Long Fiber Reinforced Composites
As is well known, C/C composites are typical commercialized long fiber reinforced composites. These composites are fabricated by chemical vapor infiltration (CVI) (Stinton et al., 1986), in which a hydrocarbon precursor is infiltrated into the shaped component woven from the carbon fiber, and is burned out during a carbonization step. Research on fiber reinforced ceramics (FRCs) was accelerated after NICALON fiber was developed. Various types of composites were fabricated using both carbon and SiC fibers by means of hot-pressing processes. Table 10-27 (Niihara, 1989 c) shows the fracture strength and toughness of typical fiber
10.8 References
Table 10-27. Properties of ceramic fiber reinforced composites. Composite
Klc Fracture strength (MPa) (MPam 1/2 ) At At At RT 1000 °C 1200 °C
LAS/SiC fiber
1.2-• 24
850
820
SiC/SiC fiber SiC/carbon fiber Si3 N 4 /carbon fiber
3.5 ^ 33
300
400
280
3.5 -+ 36
500
700
700
4.6 ^ 2 9
481
443
563
posite, which was produced by the chemical vapor infiltration of an SiC precursor into a shaped SiC fiber compact. Table 1028 (SEP, 1988) shows physical and mechanical properties of some SiC/SiC composites. Although this material is very expensive at present, it has attractive fracture toughness and high temperature properties. New processing methods that contribute to cost reduction of these composites would constitute a major breakthrough.
10.7 Acknowledgements Table 10-28. Properties of an SiC/SiC fiber composite with NICALON fiber reinforcement in two directions2. Fiber content: 40% Density: 2.6 g/cm3 Porosity: 8-15% Temperature (°C)
23
1000
1400
Tensile strength (MPa) Young's modulus (GPa) Bending strength (MPa) Compressive strengtha (MPa)
200 230 300
200 200 400
150 170 280
|| 580 1 420
480
380
300 250
30
30
5 2
5 2
Fracture toughness (MPa m1/2) 30 Thermal diffusivitya x 10" 6 (m2/s) II 1 2 1 6 Thermal expansion II
II 1
'X
-^ 2.5
a
||, parallel to a direction of fiber reinforcement; _L, perpendicular to the directions of fiber reinforcement.
reinforced composites. Remarkable improvements in the mechanical properties, especially fracture toughness, were attained. An interesting example of fiber reinforced composites is the SiC/SiC com-
The authors thank Prof. M. V. Swain, University of Sidney, Dr. M. Mitomo, NIRIM, and Prof. K. Niihara, Osaka University, for their kind advice and for making information available.
10.8 References Anderson, C. A., Bratton, R. (1977) Ceramic Materials for High Temperature Turbines, Final Report, U.S. Energy Res. Dev. Adm. Contract No. EY-76C-05-5210, Aug. 1977. Banno, H., Asano, Y. (1987), Ceramics for Automobiles. Tokyo: Sankaido, p. 163. Becher, P.F., Wei, G.C. (1984), /. Am. Ceram. Soc. 67, C-267. Claussen, N., Steeb, J., Pabst, R. F. (1977), Am. Ceram. Soc. Bull. 56, 559. Davidge, R. W, Evans, A. G. (1970), Mater. Sci. Eng. 6, 281. Deeley, G.G., Herbert, J.M., Noore, N.C. (1961), Powder Metall. 8, 145. Evans, A.G. (1974), Int. J. Fract. 10, 251. Garvie, R. C , Hannink, R. H., Pascoe, R. T. (1975), Nature 258, 703. Griffith, A. A. (1920), Phil. Trans. R. Soc. 221, 163. Hayami, R. (1992), Silicon Carbide, Silicon Nitride and Fiber Reinforced Ceramics. Osaka: TIC, p. 399. Hirosaki, N., Mitomo, M. (1992), Preprint of 63rd Meeting, 124th Committee of Japanese Academy, p.l. Inoue, H., Komeya, K., Tsuge, A. (1982), J. Am. Ceram. Soc. 65, C-205. Jack, K.H., Wilson, W.I. (1972), Nature (London), Phys. Sci. 238, 28.
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10 High Temperature Engineering Ceramics
Jenett, H., Bubert, H., Grallath, E. (1989), Fresenius Z. Anal. Chem. 333, 502. Jorgensen, P. I (1965), J. Am. Ceram. Soc. 48, 207. Kanzaki, S., Tabata, H. (1985), in: New Material Series: Mullite: Somiya, S. (Ed.). Tokyo: Uchida Rokakuho, p. 51. Kawakubo, T., Komeya, K. (1987), /. Am. Ceram. Soc. 70, 400. Kawashima, T. (1990), in: Silicon Nitride Ceramics 2: Mitomo, M., Somiya, S. (Eds.). Tokyo: Uchida Rokakuho, p. 135. Kawashima, K., Okamoto, H., Yamamoto, H., Kitamura, A. (1991), /. Ceram. Soc. Jpn. 99, 320. Kennedy, P., Shennan, J. V., Braiden, P., McLaren, I, Davidge, R.W. (1973), Proc. Br. Ceram. Soc. 22, 67. Komeya, K. (1984), Am. Ceram. Soc. Bull. 63, 1193. Komeya, K., Inoue, H. (1969), Japanese Patent No. 703 695. Komeya, K., Kotani, H. (1986), JSAE Rev. 7(3), 72. Komeya, K., Komatsu, M., Kameda, T., Goto, Y, Tsuge, A. (1991a), J. Mater. Sci. 26, 5513. Komeya, K., Meguro, X, Asayama, M., Kameda, T., Umebayashi, M. (1991b), in: Proc. 1st Int. Symp. on the Science of Engineering Ceramics, Kimura, S., Niihara, K. (Eds.). Tokyo: The Ceramic Society of Japan, p. 205. Lange, F. F. (1982), J. Mater. Sci. 17, 247. Lange, F. F. (1983), Am. Ceram. Soc. Bull. 62, 1369. Masuda, M., Soma, X, Matsui, M., Oda, I. (1988), /. Ceram. Soc. Jpn. 96, 277. Masuda, M., Yamada, N., Soma, T., Matsui, M., Oda, I. (1989), J. Ceram. Soc. Jpn. 97(5) 520. Masuda, M., Soma, T., Matsui, M. (1990), J Eur. Ceram. Soc. 6, 253. Matsui, M., Masuda, M., Nakatsuji, Y (1991), in: Proc. 1st Int. Symp. on the Science of Engineering Ceramics: Kimura, S., Niihara, K. (Eds.). Tokyo: The Ceramic Society of Japan, p. 177. Mitomo, M. (1976), J. Mater. Sci. 11, 1103. Mitomo, M. (1991a), Prepr. of Symp. on Oxidation Non-oxide Ceram., Metall. Soc. Jpn., Tokyo, p. 1. Mitomo, M. (1991b), in: Proc. 1st Int. Symp. on the Science of Engineering Ceramics, Kimura, S., Niihara, K. (Eds.). Tokyo: The Ceramic Society of Japan, p. 101. Murata, Y, Smoak, R. H. (1978), in: Proc. Int. Symp. on Factors in Densification and Sintering of Oxide and Non-oxide Ceramics: Hakone, p. 545. Nakajima, M. (1991), in: Proc. 9th Fine Ceram. Symp.: Engineering Research Association for High Performance Ceramics, Tokyo, p. 121. Nakatsuji, Y, Yamada, N., Tsuruta, H., Masuda, M., Matsui, M. (1992), in: Fracture Mechanics of Ceramics: Bradt, R.C., Hasselman, D.P.H., Munz, D., Sakai, M., Shevchenko, V.Ya. (Eds.). New York: Plenum, Vol. 10, p. 211. Niihara, K. (1989 a), in: Proc. 1st Jpn. Int. SAMPE Symp.: Igata, N., Kinbara, I., Kishi, T., Nakata,
E., Okura, A., Urya, T. (Eds.). Tokyo: Nikkan Kogyo Shinbun, p. 1120. Niihara, K. (1989 b), Proc. MRS Int. Meeting on Advanced Materials, Vol. 4: Hamano, Y, Kamigaito, O., Kishi, T., Sakai, M. (Eds.). Pittsburgh, PA: Mater. Res. Soc, p. 129. Niihara, K. (1989c), in: Fine Ceramics: Okuda, H., Izeki, T., Komeya, K., Niihara, K. (Eds.). Tokyo: Japan Standardization Association, p. 61. Niihara, K. (1990), /. Jpn. Soc. Powder Powder Metall. 37, 348. Niihara, K. (1991a), Ann. Chim. (Paris), 16, 479. Niihara, K. (1991 b), /. Ceram. Soc. Jpn. 99(10), 914. Niihara, K., Nakahira, A. (1991), in: Advanced Structural Inorganic Composites: Vincenzini, P. (Ed.). Amsterdam: Elsevier, p. 637. Nippon Carbon (1990), NICALON Catalog. Oyama, Y, Kamigaito, O. (1971), Jpn. J. Appl. Phys. 10, 1637. Popper, P., Ruddesden, S. N. (1961), Trans. Br. Ceram. Soc. 60, 603. Prochazka, S., Charles, R. J. (1973), Am. Ceram. Soc. Bull. 52, 885. Seltzer, M. S. (1977), Am. Ceram. Soc. Bull. 56, 418. SEP (1988), CERSEP Catalog. Shimamori, T., Kato, X, Matsuo, Y (1988), Progress in Fine Ceramics in Next Generation Research: Engineering Research Association for High Performance Ceramics, Tokyo, p. 115. Stinton, D.P., Capto, A.J., Lowder, R.D. (1986), Am. Ceram. Soc. Bull. 65, 347. Suzuki, K., Sasaki, M. (1984), presented at US-Japan Seminar on Fundamental Structural Ceramics, Seattle. Swain, M. V. (1985), Ada Metall. 33, 2083. Tanaka, H. (1973), Seimitsukikai 39, 917. Tiegs, T.N., Becher, P.F. (1987), Am. Ceram. Soc. Bull. 66, 339. Xsuge, A., Nishida, K. (1978), Am. Ceram. Soc. Bull. 57, 424. Xsuge, A., Nishida, K., Komatsu, M. (1975), / Am. Ceram. Soc. 58, 323. Xsuge, A., Inoue, H., Komeya, K. (1979), presented at 81st Annual Meeting, Am. Ceram. Soc, April. UBE (1989), UBE-E10 Catalog. Ukyo, Y, Wada, S. (1989), J Ceram. Soc. Jpn. 97, 872. Urashima, K., Xajima, Y, Watanabe, M. (1992), in: Fracture Mechanics of Ceramics: Bradt, R. C , Hasselman, D. P. H., Munz, D., Sakai, M., Shevchenko, V. Ya. (Eds.). New York: Plenum, p. 235. Wei, G.C., Becher, P.F. (1985), Am. Ceram. Soc. Bull. 64, 298. Wild, S., Grieveson, P., Jack, K. H. (1972), Special Ceramics 5, Popper, P. (Ed.). Stoke on Xrent, UK: British Ceramic Research Association, p. 377. Yamada, K., Nishio, H., Okamoto, H., Umebayashi, S., Kishi, K. (1989), presented at 3rd Int. Symp.
10.8 References
Ceramic Materials and Components for Engines, Las Vegas, Nov. 1988. Yamada, T., Kotoku, Y. (1989), Jpn. Chem. Ind. Assoc. Mon. 42, 8. Yamamoto, Y. (1992), in: Silicon Carbide, Silicon Nitride and Fiber Reinforced Ceramics: Osaka: TIC, p. 399.
General Reading Bradt, R. C , Evans, A. G., Hasselman, D. P. H., Lange, F. F. (Eds.) (1974-1986), Fracture Mechanics of Ceramics, Vol. 1-8. New York: Plenum. Chen, L-W., Becher, P. R, Mitomo, M., Petzow, G., Yen, T.-S. (Eds.) (1992), Silicon Nitride Ceramics, Scientific and Technical Advances, MRS Symp. Ser., Vol. 287. Pittsburgh, PA: Materials Research Society.
565
Davidge, R. W. (1979), Mechanical Behavior of Ceramics. New York: Cambridge University Press. Hampshire, S. (1986), Non-oxide Technical Engineering Ceramics. Amsterdam: Elsevier. Kimura, S., Niihara, K. (Eds.) (1991), Proc. 1st Int. Symp. on the Science of Engineering Ceramics. Tokyo: Ceramic Society of Japan. Kingery, W. D., Bowen, H. K., Uhlmann, D. R. (1976), Introduction to Ceramics. New York: Wiley. Richerson, D. W. (1982), Modern Ceramic Engineering. New York: Marcel Dekker. Riley, F. L. (Ed.) (1977), Nitrogen Ceramics. Leyden: Noordhoff Int. Riley, F. L. (Ed.) (1983), Progress in Nitrogen Ceramics. Boston: Martinus Nijhoff. Tressler, R. E., McNallan, M. (Eds.) (1990), Corrosion and Corrosive Degradation of Ceramics. Westerville, OH: American Ceramic Society.
11 Ceramic Superionic Conductors Sukhvinder P. S. Badwal CSIRO Division of Materials Science and Technology, Clayton, Victoria, Australia
List of 11.1 11.2 11.3
Symbols and Abbreviations Introduction Basic Theory of Superionic Conduction Techniques for Studying Transport and Kinetic Properties in Superionic Conductors 11.3.1 Conductivity Measurements 11.3.1.1 DC Techniques 11.3.1.2 AC Techniques 11.3.2 Transport Number Determination 11.3.3 Thermodynamic Measurements 11.3.4 Kinetic Measurements 11.3.4.1 Impedance Spectroscopy 11.3.4.2 Galvanostatic Current Interruption 11.3.4.3 Other Transient Techniques 11.4 Types of Ceramic Superionic Conductors 11.4.1 Oxygen-Ion Conductors 11.4.1.1 Zirconia Based Materials 11.4.1.2 Ceria Based Materials 11.4.1.3 Thoria and Hafnia Based Materials 11.4.1.4 Bismuth Oxide Based Materials 11.4.1.5 Pyrochlores and Other Oxides 11.4.2 Beta-Aluminas 11.4.3 Proton Conductors 11.5 Microstructure and Transport Properties 11.6 Devices Based on Ceramic Superionic Conductors 11.6.1 Sensors 11.6.2 Electrochemical Reactors 11.6.3 Electrochemical Pumps 11.6.4 Hydrogen Production 11.6.5 Fuel Cells 11.6.6 Batteries 11.6.7 Miscellaneous Applications 11.7 Acknowledgements 11.8 References Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.
568 570 571 573 574 574 575 577 579 582 583 586 587 588 588 589 596 599 601 604 606 609 610 617 617 621 622 622 623 625 626 626 627
568
11 Ceramic Superionic Conductors
List of Symbols and Abbreviations A A{ ao C
c{ c dl cg c gb D\ e E Em Eocy F Fo
f fo AG AGm HR AHm AH I
h k L n No Po2 P®
R R Rgh R \ A
<Sm
T t{ t\w V V [Vo]
z
area of cross section preexponential term in Arrhenius relationship oxygen activity capacitance concentration of ionic defects double layer capacitance geometric capacitance grain boundary capacitance ionic diffusion coefficient tracer diffusion coefficient electronic charge activation energy for conduction electromotive force open circuit voltage Faraday constant relaxation frequency in impedance arcs correlation factor jump attempt frequency free energy of reaction Gibbs free energy for ion jump Haven ratio enthalpy of ion migration heat of reaction current jump distance Boltzmann constant distance between potentials probes number of electrons involved in an electrode reaction number of anion sites per unit volume oxygen partial pressure oxygen partial pressure at which t{ = 0.5 gas constant resistance grain boundary resistivity lattice resistivity entropy of ion migration temperature ionic transport number average ionic transport-number voltage overpotential concentration of vacancies nuclear charge
List of Symbols and Abbreviations
569
Ze Zo Z'o ZQ
charge on ionic charge carriers impedance real part of the impedance imaginary part of the impedance
a a TT/2 y fi{ HQ2
distribution parameter in Cole-Cole plots angle of depression of the impedance arc geometric factor ionic mobility oxygen chemical potential standard oxygen chemical potential electronic conductivity ionic conductivity total conductivity time constant associated with the electrode or electrolyte arc in the impedance plane fuel/electric efficiency angular frequency
JUQ2
cre G{ (j T T0 (pF co
B
AC DC DTA EMF IR NMR PSZ SOFC TEM TGA XPS
alternating current direct current differential thermal analysis electromotive force ohmic potential losses in an electrochemical cell nuclear magnetic resonance partially stabilized zirconia solid oxide fuel cell transmission electron microscopy thermo-gravimetric analysis X-ray photoelectron spectroscopy
570
11 Ceramic Superionic Conductors
11.1 Introduction Superionic conductors (or fast ionic conductors) is a loosely used term to describe a class of materials which may be crystalline, glassy, or polymeric through which transport of ions is fast (cr>10" 4 Q" 1 cm~ 1 at the device operating temperature), electronic conductivity is insignificant, and on application of an applied electric field, material transport can take place. These materials are electrolytes in the true sense which have ionic conductivity in the solid state as opposed to the molten or the liquid state. Unlike in liquid electrolytes, the conductivity in solids is selective and there is usually one mobile ionic species. Such materials have been known for several decades. For example, Nernst (1899) demonstrated that the electrical conduction through ZrO 2 -Y 2 O 3 at elevated temperatures was mainly due to mobile oxygen ions. Often in solid electrolytes the ionic conductivity is defined in terms of electrolytic domain. This is the region of conduction with respect to temperature and the chemical potential of the electroactive species over which the ionic transport number is > 0.99 (Patterson, 1971, 1974; Heyne, 1977). Ionic conductors can be divided into three main classes of materials. These are: (i) crystalline compounds e.g. oxygen-ion conductors such as zirconia, ceria, thoria and bismuth oxide based materials, cation conductors such as Na + , and substituted (Li + , K + , Ag + , NH+, H 3 O + )p(p>aluminas; Agl; RbAg 4 I 5 ; Li3N; Nasicon and several others, (ii) amorphous materials such as glasses (Na + , Li + and K + conductors) and (iii) polymers (ion exchanged or solvated with alkali metal salts, e.g. Nafion and polyethylene oxide). The ceramic superionic conductors covered in this chapter fall into the first category of materials.
Ceramics are insulators, electronic conductors (metallic or semiconduction) or ionic conductors. The mode of conduction depends in general on the crystal structure of the material, the concentration of each type of charge carrier [ionic and electronic (n or p-type)], temperature and the band gap. In crystalline compounds the ionic conduction occurs in a well defined host lattice whose composition and structure play a major role in determining the level of ionic conductivity at any given temperature. At room temperature many materials are insulators or poor conductors but with increasing temperature they become good conductors (e.g., ZrO 2 based electrolytes). The majority are mixed conductors i.e. transport takes place by simultaneous motion of electronic and ionic defects. However, for a material to qualify as an electrolyte, the concentration of electronic charge carriers must be several orders of magnitude smaller than that of ionic defects. Ever growing global population and the associated increasing demand for energy in both developing and developed countries has put an unsustainable pressure on our environment. Therefore, if we are to preserve the environment for future generations and improve and/or sustain living standards, then new technologies have to be developed which contribute to the reduction of pollution, greenhouse gases and assist in preserving the limited resources available. It is in this area that superionic conductors have the potential to play an increasingly important role. Superionic materials are already been used in sensors, batteries and fuel cells and are playing an ever increasing role in pollution monitoring and control, energy conservation and conversion. Several different types of technologies based on superionic conductors are commercially available and
11.2 Basic Theory of Superionic Conduction
others are currently under development. Gas sensors based on fast ionic conductors are in use in the chemical and metallurgical industries for process or quality control, in small to medium size boilers and thermal power plants for improving combustion efficiency, in automobiles for increased fuel efficiency and reduced emission and in general for pollution control and monitoring. Significant advances have been made on secondary batteries based on beta alumina or other similar electrolytes for vehicle traction and stationary energy storage. Earlier versions of solid oxide or ceramic (also known as the third generation) fuel cells with combined heat and power generation capability are undergoing extensive trials and high power density cell designs are under development. This chapter has been planned as follows. Initially a brief outline of the basic theory behind superionic conduction is given. This is followed by description of various techniques used to study transport, thermodynamic and kinetic properties of superionic conductors. The galvanic cells utilizing ceramic superionic conductors are inherently accurate in providing reproducible thermodynamic data. The section on thermodynamic properties also discusses applications of the galvanic cells for determining the free energy of formation of binary and ternary metal oxides, fluorides and carbides, the activity of an electrochemical species in solid or molten mass (e.g., oxygen activity in molten metals, alloys or nonstoichiometric oxides). Next a number of classes of materials are described, with emphasis on two main types of materials of great technological significance. These are the oxygen-ion conductors (zirconia, ceria, bismuth oxide, thoria) and Na + or substituted (Ag + , K + , H 3 O + , NH^, etc.) beta 0 , p'O-aluminas. A section is devoted to the relationship between
571
the ceramic microstructure and transport properties. Finally, applications of ceramic superionic conductors in new technology areas and several devices based on them are described.
11.2 Basic Theory of Superionic Conduction In this section a brief account of the basic theory behind superionic conduction is given. A detailed discussion on the relationship between the nature and formation of point defects responsible for ionic conduction, crystal structure and lattice disordering, and transport mechanisms is not within the scope of this chapter and readers should consult some excellent books and articles written on the subjet (Geller, 1977; Glasser, 1973; Hagenmuller and Van Gool, 1978; Hladik, 1972; Mahan and Roth, 1976; Mitoff, 1966; Seltzer and Jeffee, 1973; Sorensen, 1981, Subbarao, 1980; Tallan, 1974; Van Gool, 1973; Vashishta et al., 1979; Wheat et al, 1983). In superionic conductors, the point defects, whose concentration is fixed by the composition, are responsible for the high ionic conduction. In general, the concentration of ionic defects is much larger than that of electronic defects and solids behave almost like pure ionic conductors. However, distinction must be made between low point defect concentration (or dilute) solids such as alkali metal halides, AgBr etc., which in the solid state have very low conductivity and high activation energy for ionic transport and those with high concentration of point defects [e.g., doped zirconia - vacant lattice sites in the anion sublattice (Etsell and Flengas, 1970)] or high cation disordered sublattice (e.g., (3 or |3"-alumina, RbAg4I5) (Heyne, 1977;
572
11 Ceramic Superionic Conductors
Kasper, 1978; Kennedy, 1977; Powers and Mittof, 1978). Often cations with different valence (aliovalent) are added to create large concentrations of defects. These cations may substitute for an ion in the normal lattice site or alternatively enter an interstitial site. Anion conduction results from anions being present at interstitial sites or from anion vacancies. The cation conduction may arise due to the presence of interstitial cations or cation vacancies. For example in fluorite-related solid solutions of zirconia (ZrO2), ceria (CeO2) or thoria (ThO2) with dopants such as CaO, MgO, Y 2 O 3 , Sc 2 O 3 , Yb 2 O 3 , the dopant cation occupies a normal lattice site. To preserve charge neutrality, vacancies are created in the oxygen sublattice to compensate for the charge difference between Zr 4+ and the lower-valent dopant cation. These vacancies are randomly distributed in the crystal lattice and are responsible for the high ionic conduction. In Na + beta ((3, |3")-alumina, the Na + is the disordered cation present in crystallographic loose layers. The number of available sites in the layer for Na + to occupy are larger than the number of Na + ions. The Na + ions are therefore distributed over a large number of sites. Many solid electrolytes (e.g., oxygen-ion conductors, substituted beta aluminas, CaF2) are poor conductors at room temperature but become good conductors at higher temperatures with increasing disorder in the sublattice but without any phase transition. Other materials such as Bi 2 O 3 and some silver and copper salts (Takahashi and Iwahara, 1973; Wiedersich and Geller, 1970) undergo a first order transition from a poor conduction state at low temperature to a high conducting state at elevated temperature. Nevertheless, in the superionic conductors, from a structural point of view, there are clear pathways for ions to migrate with more avail-
able sites for them to occupy than the number of mobile ions. The ionic conductivity and transport of material results from hopping of ionic defects into adjacent available sites under the influence of an applied electric field and is given by: er^C^ZeJft
(11-1)
where [i{ is the ionic mobility Cx is the concentration of ionic defects or conducting ions per unit volume and Z e is the charge on the ionic charge carriers. Typically in a solid, the mobility of electronic defects is several orders of magnitude higher than that of the ionic defects. Therefore for a material to be a predominantly ionic conductor, the defect concentration for ions must be significantly high (in the percent range) and that of electronic charge carriers should be negligible. The dependence of ionic conductivity on temperature is usually expressed in the form of the Arrhenius relationship:
where A{ is the pre-exponential term and is independent of the temperature, E is the activation energy, k is the Boltzmann constant and T is the temperature. Kilner and Steele (1981) have given the following general equation for anion mobility in oxygenion conducting solid electrolytes: tt
= [Z e/(fc T)] 3j /o y exp [- AGJ(k T)] (11-3)
where J d is the jump distance, f0 is the jump attempt frequency, y is a geometric factor and AGm is the Gibbs free energy for the jump. Similar expressions are used for other ionic conductors (Goodenough, 1983). For dilute solid solutions (low dopant concentration), substituting for the concentration of vacancies ([Fo]), the number of anion sites per unit volume, JV0, and the
573
11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors
mobility term in Eq. (11-1) the following expression can be written for the ionic conductivity (Kilner and Steele, 1981):
•exp(ASm//c)exp[-Atfm/(/cT)] = A{exp[-AHJ(kT)]
(11-5)
where AHm is the enthalpy of ion migration. A plot of log (conductivity x T) versus reciprocal temperature should be a straight line whose slope gives the enthalpy for ion migration and intercept the preexponential term. However, it is common to observe a continuous change in the slope of the Arrhenius plots towards a lower activation energy with increasing temperature (Abelard and Baumard, 1982; Adham and Hammou, 1983; Badwal, 1984; Badwal and Swain, 1985; Baumard and Abelard, 1984; Casselton, 1970; Ioffe et al, 1975). In the case of fluorite-type oxide solid electrolytes this has been attributed to the formation of complexes of varying degree between vacancies and dopant cations at low temperatures and their increasing dissociation as the temperature rises (Baumard and Abelard, 1984; Hohnke, 1981; Kilner, 1983; Kilner and Faktor, 1983; Kilner and Waters, 1982; Nakamura and Wagner, 1980, 1986; Schmalzried, 1977; Wang et al., 1981). Several of these authors have discussed the formation of neutral complexes for divalent and charged complexes in the case of trivalent dopant cations. In the dilute solid solution range simple associates and for concentrated solid solutions higher order complexes (involving several nearest neighbors) between dopant cations and vacancies and ordering of vacancies have been considered. At low temperatures the activation energy term in Eq. (11-2) consists of the enthalpy for defect formation as well as
enthalpy for migration of vacancies. In the high temperature range when clusters are completely dissociated the activation energy equals the enthalpy of vacancy migration. The binding energy for associate formation depends on the type of the dopant and ionic charge on the dopant cation and its size. The conductivity is also related to the diffusion coefficient (DJ by the Nernst-Einstein relationship:
The correlation factor (/) should be included if Eq. (11-6) is to be applied to isotopic diffusion (Dt) and is given by: Dt
(11-7)
The correlation factor is usually between 0.5 and 1, depends on the transport mechanism and is often written as the Haven ratio, HR (Compaan and Haven, 1956; Haven, 1978; LeClaire, 1973).
11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors Several techniques are commonly used to study transport, kinetic and thermodynamic properties of superionic conductors or solid electrolyte cells based on these materials. These techniques have been described below. The electrical or electrochemical measurements alone are not sufficient to fully understand the transport mechanism. It is necessary to combine these measurements with characterization techniques such as X-ray diffraction, neutron diffraction, scanning and transmission electron microscopy, DTA/TGA, optical microscopy, NMR, infra-red and Raman
574
11 Ceramic Superionic Conductors
spectroscopy. Often there is a complex relationship between the transport properties, crystal structure and the ceramic microstructure (phase assemblage, grain size distribution, porosity, surface area, grain boundary density and impurity segregation) of the system under study. Powder synthesis, ceramic fabrication techniques and sintering conditions also play a major role in influencing kinetic and transport properties. Measurements only on fully characterized systems are valuable in understanding the nature of transport processes.
Power supply/ Current source/ Measurement
Electrolyte
Voltmeter
Electrode
Electrolyte
Electrode
11.3.1 Conductivity Measurements 1,2 Current probes 3,4 Potential probes
11.3.1.1 DC Techniques
In solid electrolyte cells, major contributions to the total cell resistance come from the electrolyte resistance (in the case of polycrystalline materials both the grain boundary and the lattice resistivity) and the electrode resistance at the cathode/ electrolyte and anode/electrolyte interfaces. The cell resistance can be determined from a simple relationship between the current flowing through the cell and the steady state potential difference between a pair of electrodes reversible to the charge carrying species. The two-probe DC technique has been used in the past to determine the electrolyte resistivity. The circuit for this method is shown in Fig. 11-1. The electrolyte conductivity, cr, for a specimen of length L and cross sectional area A is given by: a = (I/V)(L/A)
(11-8)
where / is the current flowing through the cell and V is the voltage drop between the pair of electrodes. This is the simplest technique requiring a minimum of instrumentation but it is one of the most error prone methods of measuring conductivity of su-
Figure 11-1. An equivalent circuit and cell arrangement for a two-probe conductivity technique.
perionic conductors. A simple two-probe DC method may be adequate to give a reasonable estimate of electrolyte resistance provided that there is good contact between the electrode and the electrolyte, that the electrodes maintain a constant composition during the measurement and that the electrode resistance is negligible compared with the electrolyte resistance. It is difficult to attain a near perfect contact between the electrolyte and electrodes. Furthermore in a solid electrolyte cell, the contribution of the electrode resistance is often too significant to be ignored. All these parameters change with temperature and the measurement procedure in a different fashion. Let alone measuring the true electrolyte conductivity, the two-probe DC technique can not be relied upon to even furnish reproducible results as a function of temperature. In order to eliminate the contribution from the electrode/electrolyte interface, a
11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors
four-probe technique, in which the current passes through two current probes and the potential drop is measured with a high input impedance voltmeter across another two probes, should be used. The equivalent circuit of a four-probe technique is shown in Fig. 11-2. In this technique all the four probes are physically isolated and when measuring the ionic conductivity, must also be reversible to the charge carrying species within the material. L in Eq. (11-8) is now the distance between the potential probes. With proper considerations to the positioning of the probes and selection of the probe material, the technique is capable of providing accurate information about the electrolyte conductivity. The technique can be surface sensitive especially if the composition of the material is not uniform and is affected by the temperature and the gas environments. The major drawback, however, is that although very useful for single crystals, it is incapable of
Power supply/ Current source/ Measurement
Electrolyte
T Voltmeter
Electrode
Electrolyte
Electrode
h/wv 1,2 Current probes 3,4 Potential probes Figure 11-2. An equivalent circuit and cell assembly for the four-probe technique.
575
distinguishing between intergrain (grain boundary) and intragrain (lattice resistivity) in polycrystalline materials. Nevertheless, the four-probe technique is fast, extremely useful in providing information about the total conductivity over a much wider temperature range and is very accurate for studying time dependent conductivity (ageing-phase decomposition or precipitation) behaviour at a constant temperature. Information about phase transformation and/or phase precipitation can be easily obtained as shown by some examples in Figs. 11-3, 11-4. 11.3.1.2 AC Techniques
Several different AC techniques are used for measuring the conductivity of superionic conductors. These include measuring the current voltage response at a constant frequency of between 1 to 10 kHz using a two or a four-probe cell arrangement discussed above. The underlying assumption in this approach is that at all measurement temperatures the electrode processes must relax below this constant measurement frequency to allow only electrolyte resistance to be measured. Both these methods give erroneous results as with increasing temperature the time constant of various electrode and electrolyte processes increases and the frequency response of each shifts to a high frequency region. Moreover, these vary with the type of the electrode or the electrolyte material used, the cell geometry, nature of the transport processes and the gas concentration. Figure 11-5 compares the results of electrolyte resistivity obtained using fixed frequencies of 1 and 10 kHz with the total and lattice resistivity values determined using impedance spectroscopy for a Pt/ZrO 2 -Y 2 O 3 /Pt cell. The error inherent in measuring electrolyte resistance at a constant frequency is quite
U.UDO
(a) 3mol% Y 2 0 3 -Zr0 2
1000°C
0.056 \ 7 E
0.054
o
£ 0.052
0.050
(a) 0048
1000
2000 3000 Time in min
(b) 7.8mol% Sc 2 0 3 -Zr0 2
4000
5000
1000°C
0.30 0.28
T
E CJ0.26 .S b 0.24
Figure 11-3. Ageing behaviour studied by the four-probe DC conductivity technique at 1000 °C in (a) 3 mol% Y 2 O 3 -ZrO 2 and (b)7.8mol% Sc 2 O 3 -ZrO 2 .
0.22
(b) 0.20 1000
2000 3000 Time in min
4000
5000
Figure 11-4. Arrhenius plots for two Sc 2 O 3 -ZrO 2 specimens with different amounts of monoclinic zirconia investigated by the four-probe DC conductivity technique. The jumps occur due to the transformation of monoclinic (present as twinned regions in the microstructure-inset) to tetragonal zirconia on heating (D) and the reverse transformation on cooling (o).
-4.0
a— Heating cycle o - Cooling cycle -5.0
75
9.0
10.5 12.0 Temperature in 10AK"1
13.5
15.0
11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors
577
Figure 11-5. Arrhenius plots for a Pt/3 mol% Y 2 O 3 -ZrO 2 /Pt cell showing the effect of measurement technique on the measured electrolyte resistance. At 500 °C the contributions of the grain boundary and the volume resistivity are equal, o - At 1 kHz, A - a t 10kHz, • - total (grain boundary and lattice) resistivity, o - lattice resistivity. 12.0
13.0
U.O
15.0
16.0
17.0
Temperature in 104-K"1
clear. Impedance spectroscopy (described below) in which the response of the cell is studied over a wide frequency range, is obviously a more versatile technique and therefore is most commonly used. It is a powerful technique for separating the contributions of various processes in a solid electrolyte cell in the frequency domain and offers considerable advantage over other techniques. Recent advances in instrumentation and data analyses have further contributed to its versatility. For polycrystalline electrolyte materials it can separately provide information about migration of charge carrying species within the grains (intragrain or lattice resistivity) and across grain boundaries (intergrain or grain boundary resistivity) and is an excellent technique for studying the effect of impurity segregation at grain boundaries. For studying transport properties of superionic conductors with AC methods, the use of reversible electrodes is not necessary. 11.3.2 Transport Number Determination
Transport (transference) number of mobile species is an important factor in estab-
lishing the suitability of a conductor as an electrolyte. High ionic conductivity and an ionic (anionic or cationic) transport number close to unity over wide cell operating conditions are some of the criteria which must be fulfilled by a material to be a good electrolyte. Many materials are mixed conductors and the ionic transport number varies with the cell operating conditions. Even small electronic conductivity can limit the use of a material as an electrolyte. The ionic conduction in a solid electrolyte is characterized by the ionic transport number t{ which is the ionic fraction of the total current (anionic, cationic and electronic charge) flowing through the system. (11-9) and aT = ai + ae (11-10) Several different techniques are available for separating the ionic and electronic contributions to the total conductivity in solid electrolytes and the most common ones are described below (Etsell and Flengas, 1970; Goto and Pluschkell, 1972; Heyne, 1977; Sequeira, 1985).
578
11 Ceramic Superionic Conductors
(i) A sample can be electrolyzed between a pair of electrodes reversible to the mobile ionic species for a period of time and composition at the anode and cathode sides of the specimen measured and compared to the quantity of the charge passed (Bottelberghs, 1978). Alternatively the specimen can be electrolyzed between two or more pellets of materials reversible to the charge carrying species. The transport numbers can be determined by comparing the weight change of the pellets with the amount of charge passed. This method is named after Tubandt who first introduced it and can furnish information about both cation and anion transport numbers at the same time. (ii) The more commonly used and simple technique for determining transport numbers is the EMF method. In this, the material under investigation is placed between two reversible electrodes which define the chemical potential for the mobile component of the material at each electrode/electrolyte interface. If both interfaces are at a different chemical potential then the EMF signal across the cell, for example for an oxygen concentration cell, is given by (Wagner, 1933): \
equal to some average value t\w then Eq. (11-12) can be approximated to: (11-13) The ionic transport number nevertheless varies with the composition and the need to have a different chemical potential on either side of the cell means that the ionic transport number will not be constant throughout the material. Thus it is not possible to integrate Eq. (11-12) and the ionic transport number can not be taken in front of the integral. However, Eq. (11-13) may be a reasonable approximation provided that the chemical potential gradient across the electrolyte is kept very small and the ionic transport number then equals the ratio of the measured to the theoretical values of the electromotive force. In order to overcome this problem Schmalzried (1962, 1963) derived the following expression for the ionic transport number t{ in oxygen-ion conducting solid electrolytes by assuming n-type and ionic conductivity and a (p O2 )~ 1/4 ^ aw f° r e^ec" tronic conductivity variation as a function of oxygen partial pressure:
ln/io
(11-11) where n'Ol and y!'O2 are the chemical potentials of oxygen on either side of the specimen, F is the Faraday constant and n is the number of electrons required to complete the electrode reaction. Since fiO2 = fio2 + R Tlnp O 2 , the above equation can be written as: RT
(11-12)
If the ionic transport number can be assumed to be constant in the material and
where p& is the oxygen partial pressure at which t{ = 0.5 (or o{ = cre). This expression can be used to determine the ionic transport number by substituting Eq. (11-14) in Eq. (11-12). Goto and Pluschkell (1972) have discussed the various limiting cases under which these expressions are valid. One serious problem with this EMF technique is that if the electronic transport number is appreciable (te > 0) then material transport takes place from one electrode to the other due to internal short circuiting of the cell. This has the effect of altering the oxygen concentration at the
11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors
electrode/electrolyte interface. Also both electrodes become polarized due to passage of current as the electrode reactions take place at finite rates. These effects cause deviation from the true equilibrium chemical potential. The measured EMF signal falls below the actual value causing overestimation of the electronic transport number. The technique is most suitable when the material is mainly an ionic conductor and has been widely used for determining the electrolytic domain of various materials (Etsell and Flengas, 1970; Goto and Pluschkell, 1972). (iii) Another method is to study the conductivity of a mixed conductor as a function of the partial pressure of a component related to the mobile ionic species in the mixed conductor under study. This technique has commonly been used in oxygenion conducting solid electrolytes such as stabilized zirconia, doped thoria and doped ceria to determine the electrolytic domain. In these materials the ionic defect concentration is controlled by the dopant concentration and ionic conductivity is essentially independent of oxygen partial pressure. However, the number of electronic defects" is markedly influenced by small deviations from stoichiometry and therefore the electron or hole conductivity varies significantly with oxygen partial pressure. Thus the ionic transport number can be determined by analyzing curves of conductivity versus oxygen partial pressure. (iv) A most direct way of determining small electronic transport numbers is the polarization technique. This technique has been used quite extensively and involves the use of one reference electrode and one electronically or ionically blocking electrode (Fig. 11-6). A small DC voltage signal is applied to the cell to set up a chemical potential gradient between the reference and the blocking electrode. In the case
Reversible electrode
579
Ion or electron blocking electrode
Figure 11-6. A schematic of the DC polarization technique (with ion or electron blocking electrode) for determining electronic or ionic conductivity in a mixed conductor. 3, 4 are potential probes reversible to ionic or electronic charge.
of the ionic blocking electrode no ionic current and in the case of the electronic blocking electrode no electronic current flows under steady state conditions. With the use of two additional probes positioned on the specimen, reversible only to the electronic or ionic current, electronic or ionic conductivity can be measured. The polarization method has been discussed in detail by a number of authors (Dudley et al, 1980; Heyne, 1977; Mizusaki and Fueki, 1982; Sequeira, 1985; Wagner, 1957,1975) and successfully employed in a number of systems. In the case of oxygenion conductors it has limited application as the interference from electrode reactions involving oxygen in the gas phase can not be completely eliminated. 11.3.3 Thermodynamic Measurements
Since the work of Kiukkola and Wagner (1957 a, 1957 b), who reiterated interest in the usefulness of galvanic cells for studying thermodynamics of solid state reactions,
580
11 Ceramic Superionic Conductors
considerable advances have been made. Solid electrolyte cells have been and are frequently used for determining the solubility of oxygen in molten metals and alloys, thermodynamic stability (or free energy of formation) of binary and ternary compounds and chemical potential of various species in solids, molten metals, alloys, and nonstoichiometric oxides. One of the most commonly used applications of galvanic cells is in relation to determining the free energy of formation of binary or ternary compounds. For example for the cell, reference electrode (aro) |O 2 ~ conductor | M - MO (a£), provided that the ionic transport number is unity and constant throughout the electrolyte, the free energy of formation for the metal oxide (M +1/2 O 2 -> MO) is given by: AG°= -
aro/a%) (11-15)
where aro and a^ are the oxygen activities at the reference and test electrodes respectively. The EMF technique is inherently accurate for obtaining thermodynamic information from a reversible galvanic cell. The measurements of EMF signal are made in the open circuit mode with respect to a reference electrode with a voltmeter with sufficiently high input impedance to avoid electrode polarization. The technique is simple, requiring a minimum of instrumentation. The main limitation is the availability of suitable reference electrode materials over the desired temperature range. Many extensive review articles have been written describing the applications of solid electrolytes for thermodynamic measurements, on the theoretical treatment of galvanic cells and limitations of the technique (Alcock, 1968; Chandrasekharaiah etal, 1980; Goto and Pluschkell, 1972; Kubashewski and Alcock, 1979; Markin et al., 1967; Seetharaman and Abraham,
1980; Shores and Rapp, 1971; Steele, 1968; Steele and Alcock, 1965; Steele and Shaw, 1978). Oxygen-ion conducting solid electrolytes such as stabilized zirconia, doped thoria and doped ceria are most commonly used for determining the free energy of formation of binary and ternary metal oxides, binary intermetallics, and oxygen activity in molten metals and nonstoichiometric oxides. In these galvanic cells the reference electrodes used include Pt (air), (U,M)O 2±:c (air), Ni/NiO, Fe/Fe x O, Cu/Cu 2 O, Cr/ Cr 2 O 3 , Nb/NbO and Ta/Ta 2 O 5 (Bannister, 1984; Etsell and Flengas, 1970; Goto and Pluschkell, 1972; Hladik, 1972 b; Patterson et al., 1967; Steele and Alcock, 1965; Worrell and Iskoe, 1973; Yuill and Cater, 1967). Other electrolytes employed include metal fluorides (e.g., CaF 2 , BaF 2 , SrF2) and metal-ion conducting beta alumina (Na + , Ag + ). Metal fluorides have been used for determining the free energy of formation of metal oxides, fluorides and carbides in addition to thermodynamic information on the activity of a metal in binary alloys. However, their use is somewhat restricted because of the limited and less reliable free energy data available on reference metal fluorides and their high volatility. Beta alumina electrolytes have been used for determining metal (Na, Ag) or sulfur activity. Table 11-1 lists some examples of galvanic cells used for obtaining different types of thermodynamic data. Recent review articles (Chandrasekharaiah et al., 1980; Seetharaman and Abraham, 1980; Steele and Shaw, 1978) give more detailed accounts of various systems studied by the galvanic cell technique. The simplicity of the galvanic method can be deceptive and extreme care needs to be given to the selection of the reference electrode and electrolyte materials and
11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors
581
Table 11-1. Some examples of thermodynamic measurements with galvanic cells. Type of measurement
System
Electrolyte
Free energy of formation
binary and ternary metal oxides, silicates, spinels intermetallic compounds (TiPt3, HfPt3, ZrPt 3 , Co3W) metal fluorides, carbides molten glasses, silicates, metal slags binary intermetallics (Co-W, Fe-Nb, Zr-Pt, U-Co) binary liquid alloys
zirconia or thoria based, metal fluorides zirconia or thoria based
UO 2 + J B ,CeO 2 _,,Nb 2 O 5 _,, (U,Pu)O 2±;c , TiO 2 _ x , (U,Zr)O 2+x , VO 2 _ X ,WO 3 _ X Cu, Pb, Sn, Ag, Fe, Na Na-Pb, Na-Hg, Ag, Ag-compounds, metal sulfides
zirconia or thoria based
Free energy of formation Free energy of formation Oxygen activity Metal activity
Nonstoichiometry in oxides
Oxygen dissolved in molten metals metal or sulfur activity
various physical parameters in designing experiments. A brief account of the important factors which should be considered when designing galvanic cells for obtaining thermodynamic data, is given below. The selection of a suitable electrolyte and reference electrode materials is of utmost importance as these together put limits on the accuracy of the thermodynamic data and the range over which measurements can be made. The electrolyte must be free of cracks and connecting pores to avoid molecular transfer of gas from one side of the cell to the other as this will have an effect on the equilibrium EMF signal. This is not a serious problem as with the modern ceramic powder and fabrication techniques it is possible to obtain high density crack free electrolytes with a built in strenghtening and toughening mechanism (Green et al., 1989). Also for accurate thermodynamic measurements both electrode compartments should be hermetically sealed to avoid gas phase transfer of the electroactive species between the two electrodes.
CaF 2 zirconia or thoria based zirconia or thoria based CaF 9
zirconia or thoria based beta-alumina
Over the experimental chemical potential and temperature ranges, the electrolyte used in the galvanic cell should have an ionic transport number close to unity with a minimum of interference from secondary phases and the omnipresent impurities at grain boundaries in polycrystalline ceramics. As discussed previously, even small electronic conductivity can lead to internal short circuiting, transport of mass from one electrode to the other and polarization of the electrodes. This has the effect of disturbing the local chemical equilibrium especially if the electrode kinetics are slow. Therefore it is necessary to study only those systems and use reference electrodes which do not impose chemical potentials at the electrode/electrolyte interface beyond the ionic stability domain of the electrolyte (t{ > 0.99) (Heyne, 1977; Patterson, 1971, 1974). The selection of the reference electrode is to some degree dictated by the experimental conditions over which thermodynamic data are required. However, the reference electrode must be capable of maintaining
582
11 Ceramic Superionic Conductors
accurately the chemical potential at the electrode/electrolyte interface. Electrodes with fast kinetics (high exchange current density) are desirable. It has been indicated that the Cu/Cu 2 O reference electrode can more easily adjust to small perturbations than Fe/Fe x O and Ni/NiO electrodes (Worrell, 1977), the latter having most difficulty in maintaining appropriate chemical potential at the electrode/electrolyte interface. Kinetic data on solid electrolyte systems is not extensive and for a given system under study it is advisable to check for the reversibility of the cell (both reference and test electrodes). This can be easily done by perturbing the system from its equilibrium position in both directions by superimposing a small voltage signal or passing a small current for a short period and observing restoration of the previous EMF signal with time. Inert atmosphere is maintained over the metal/metal oxide reference electrode to minimize gas phase interference and to avoid mixed potentials arising from electrode reactions involving the gas phase especially in cells based on oxygen ion conducting solid electrolytes. Purification of the gas is desirable to remove traces of oxygen. Titanium or copper gettering furnaces are normally used to achieve this. The effect of gas flow rate on the stability of the EMF signal, provided there is no cooling of the cell by fast gas flow rates, can be used to check for the gas phase interference. Alternatively the use of vacuum or a sealed reference electrode compartment may be more satisfactory. The system under study must be thermodynamically well defined and there should not be any chemical reactions between the electrode and electrolyte components. Any new phases formed at the electrode/electrolyte interface can establish
their own chemical potentials and give misleading results. Thermal EMF's due to temperature gradients across the galvanic cells (thermoelectric effect) is another major source of error in obtaining thermodynamic information. A mere 1 °C difference in the temperature of two electrode/electrolyte interfaces can produce about 0.5 mV signal (Goto and Pluschkell, 1972). It is either added on or subtracted from the isothermal EMF due to the true chemical potential gradients characteristic of the system under study. The temperature gradient on the same side of the cell but across the electrolyte can lead to mixed potentials due to the thermoelectric effects (Goto and Pluschkell, 1972). Care should be taken in designing experiments to minimize such temperature gradients. Finally errors inherent in the thermodynamic data for reference electrodes can not be avoided and the accuracy of the information obtained from such cells should reflect this additional source of error. In the absence of all the sources of error discussed above and proper designing of the cell, the reproducibility of the galvanic cell technique for obtaining thermodynamic data is acceptably high. 11.3.4 Kinetic Measurements
Several techniques are used to separate the contributions of various polarization processes in solid electrolyte cells and to study the kinetics of electrode reactions in the time or frequency domain. Numerous books and review articles have been written describing various theoretical and experimental aspects of these transient techniques (Gabrielli, 1980; Gileadi et al, 1975; Koryta and Dvorak, 1987; Macdonald, 1977; Sequeira, 1985; Vetter, 1967; Yeager and Salkind, 1972). Only an overview of
11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors
some techniques more relevant to studying solid electrolyte systems will be described here. In any given study, the use of a technique is dictated by the information required, the accuracy, experimental parameters and limitations imposed by the cell design. A combination of techniques may be necessary to satisfactorily understand the mechanism of charge transfer processes in a solid electrolyte system. Often kinetic parameters are related to the physical state of the electrode (microstructure-grain size, porosity and surface area, etc.) which may also need to be investigated. The impedance technique is extremely versatile for determining the contribution of electrode or electrolyte processes as the detail contained in an impedance spectrum can be quite significant. A single impedance spectrum can provide information about diffusion, charge transfer and adsorption/dissociation processes at the electrode/electrolyte interface as well as about the grain conductivity (intragrain) and grain boundary (intergrain) blocking in polycrystalline electrolytes. Impedance studies are usually carried out in the linear region under an applied signal of low magnitude when the system is near equilibrium. However, in order to study the use of superionic conductors in devices such as batteries, fuel cells, electrochemical reactors, etc. it is essential to study the current carrying capabilities of electrode/electrolyte interfaces. In principle, it is possible and the instrumentation is available to make impedance studies in the dynamic mode when the cell is perturbed from its equilibrium position either in the potentiostatic mode (constant applied DC potential) or in the galvanostatic mode (constant current). However, the technique is slow and limited in supplying information about currentpotential behaviour of solid electrolyte cells. Moreover, accurate measurements
583
can be made only for those systems which are sufficiently stable over the time required to collect several impedance spectra. The galvanostatic current interruption technique is beneficial for studying polarization events in solid electrolyte systems where ohmic losses are significant. This method is fast, and accurate irrespective of the size of the ohmic potential and no prior model assumptions are necessary about the nature of the electrode polarization processes. Potentiostatic methods are used extensively in solution electrochemistry and are useful when ohmic losses in a cell are small. For solid electrolyte systems these techniques have limited applications because of the significant ohmic contribution and have been used mainly to study charge/discharge characteristics of batteries. 11.3.4.1 Impedance Spectroscopy
The impedance spectroscopy technique involves applying an AC signal (sinusoidal) of varying frequency to the solid electrolyte cell and comparison of the input and output signals to get information about the phase shift and the impedance modulus. A sine wave is used because for a sinusoidal signal applied to a linear system the input and output have the same form and at a specific frequency there is a linear relationship between them. The impedance of the cell is the ratio of the voltage to current as Ohm's law holds in the time domain. The resultant response of a solid electrolyte cell can be displayed in the complex plane either in the more commonly used impedance or admittance formulations. Each electrode (diffusion, charge transfer, or adsorption/dissociation) and electrolyte (grain boundary or lattice) process has a different time constant and therefore relaxes over a
584
11 Ceramic Superionic Conductors
different frequency range. If the frequency range is large enough, then the contribution of each process can be separated in the frequency domain. In general, the time constant associated with each process decreases with increasing temperature and the response of the cell shifts to a higher frequency spectrum. In the simplest form, a solid electrolyte cell can be represented by a series combination of several resistance (R) and capacitance (C) elements (subcircuit) in parallel as shown in Fig. 11-7, each corresponding to a different electrode or electrolyte process characterized by a different time constant. The resistor in the subcircuit corresponds to the flux flow for the relevant process and the capacitor represents the space charge effects. The simulated response of the circuit of Fig. 11-7 is shown in Fig. 11-8 and is somewhat similar to that observed for solid electrolyte cells using polycrystalline electrolytes. From impedance circuit theory, it can be shown that the response of each subcircuit (a resistor in parallel with a capacitor) is a semicircle in the complex impedance plane with its origin on the real impedance axis (Badwal, 1988). The difference of intercepts of the semicircle on the real axis gives the value of the resistor, and the value of the capacitor can be obtained from the apex frequency [T0 = l/coo = RC =
l/(2nF0)].
Impedance spectroscopy has been used extensively for a number of years to investigate the kinetic processes in aqueous electrochemistry and several review articles have been written describing both experimental and theoretical aspects of this technique (Archer and Armstrong, 1980; De Bruin and Badwal, 1978; Gabrielli, 1980; Macdonald, 1987; Sluyters-Rehbach and Sluyters, 1970). It is only in the last 1 5 20 years that this technique has been ap-
Hh
Hh
Hh
Hh
Figure 11-7. A simple equivalent circuit of a solid electrolyte cell.
Frequency
Figure 11-8. Response of the circuit shown in Fig. 11-7 in the complex impedance plane. T1S t gb and rel are relaxation times and Rl9 Rgh and # e l are resistivities associated with electrolyte bulk (intragrain), grain boundary (intergrain) and electrode processes respectively.
plied to study the electrical and electrochemical properties of solid electrolyte cells (Macdonald, 1987). Impedance spectroscopy is useful in providing information about the nature of various rate limiting processes at the electrode/electrolyte interface and within the solid electrolyte, on the grain boundary blocking effects by the grain boundary phases and the lattice resistivity. It is an extremely sensitive technique for studying how various ceramic processing variables (sintering temperature, time, heating and cooling rates), post-sinter treatments and impurities in the starting powders have an effect on the nature and segregation sites for the grain boundary phase and precipitation of secondary phases (in the bulk of the grain or at grain boundaries).
11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors
In general, in solid electrolyte cells, arc I in Fig. 11-8 arises from charging of the electrode/electrolyte interface and electrode reactions occurring at or near the interface. It may consist of two or more overlapping relaxations and may include contributions from diffusion, charge transfer and adsorption/dissociation processes. It is usually observed at low frequencies (<10kHz). The grain boundary arc (II) due to partial or complete blocking of charge carriers is observed at intermediate frequencies (1-100 kHz). The third arc [also known as the geometric arc (III)] from which the lattice electrolyte resistivity and the dielectric constant of the material can be determined is observed at higher frequencies (>10kHz) and is influenced by the geometric dimensions of the specimen. For single crystals, the intermediate grain boundary arc is not observed. The frequency domain over which each process relaxes varies with temperature, the cell geometry and the nature of the transport processes at the electrode/electrolyte interface and within the solid electrolyte. Each process has a different dependence on temperature, gas concentration, and the electrode and electrolyte type and microstructure. In real electrochemical systems each electrode or electrolyte process can not be represented by a simple resistor-capacitor (in parallel) subcircuit as described previously and which gives rise to a perfect semicircular arc in the complex impedance plane. The arcs are usually depressed below the real impedance axis. Such a behaviour in general indicates a distribution of time constants and heterogeneity in the system. The symmetric distribution of relaxation times can be represented by ColeCole relationships for the real (Z'o) and imaginary (ZQ) parts of the impedance given by (Bottcher and Bordewijk, 1978):
Z'
585
(11-16)
" 1 + 2 (cy t o ) 1 ' a sin (a TC/2) +(co T 0 ) 2(1 " a) Z'o (H-17) _ R(coxo)1'cc cos (an/2) ~ 1 +2(coT o ) 1 - a sin(a7r/2) + (a;T o ) 2(1 - a) where a is a distribution parameter and a n/2 is the angle of depression of the semicircle below the real impedance axis. In general the impedance response of a polycrystalline electrolyte is simple and can be represented by two Cole-Cole type distributions. Various models describing impurity segregation in solid electrolytes and their relationship to the grain boundary resistivity have been discussed in detail by Badwal et al. (1991). The electrode behaviour is often complex and is affected by both the physical and chemical nature of the electrode and electrolyte materials. A prior knowledge of various physical processes is necessary to delineate impedance spectra. The equivalent circuit approach, in which the circuit is constructed on the basis of previous understanding of the system, is simple and therefore more commonly used to analyze impedance data. Nonlinear least squares techniques for fitting experimental data to analytical expressions for the impedance of a plausible equivalent circuit are extremely useful. Macdonald (1989) has developed versatile nonlinear least squares programs for this purpose which allow for fitting of the experimental data to a range of equivalent circuits consisting of both ideal and distributed elements. The details of cell designs, instrumentation and data analyses techniques have been reviewed elsewhere (Badwal, 1988; De Bruin and Badwal, 1978; Dickinson and Whitfield, 1977; Gabrielli, 1980; Macdonald, 1987; Schouler, 1985; Spinolo et al., 1988; Tsai and Whitmore, 1982).
586
11 Ceramic Superionic Conductors
11.3.4.2 Gal vanostatic Current Interruption
The galvanostatic current interruption technique involves passing a constant current through a two or a three electrode cell for a sufficiently long time to achieve steady state potential. The current is then interrupted with a fast electronic switch and the potential-time transient is recorded with a fast storage oscilloscope or a transient recorder within microseconds of current interruption. The voltage decays almost instantaneously across the electrolyte for the ohmic (IR) potential losses (usually less than 1 JIS) and no trace on the oscilloscope or data on the transient recorder is recorded. The slow part of the transient corresponds to polarization losses at the electrode/electrolyte interface as shown in Fig. 11-9. The principle of operation of the galvanostatic current interruption technique can be easily understood in terms of an equivalent circuit (Fig. 11-10) representing the basic polarization processes in the solid electrolyte cell. In this circuit Z o is the nonlinear faradaic impedance associated with the electrode (anode and cathode) reac-
Current on
tions, Cdl is the double layer capacitance, Rl and Rgh are respectively the lattice and grain boundary resistance in the solid electrolyte, Cg is the geometric capacitance of the cell and Cgb is the grain boundary capacitance associated with blocking of mobile charge carriers at grain boundaries in polycrystalline materials. For each resistorcapacitor subcircuit, at the instance the current pulse is applied, it is divided between two parallel paths. Initially most of the current goes towards charging of the capacitor and little current flows through the resistor. However, the current through the capacitor path decreases rapidly with time. Under steady state conditions when the capacitor is completely charged all the current flows through the resistor. The reverse of this occurs when the current is switched off. In general Cg and Cgb (Cgb > Cg) in solid electrolyte cells are several orders of magnitude smaller than the interfacial double layer capacitance (Cdl). Thus the time constants associated with the electrolyte processes are much lower than that for the electrode process and charging and discharging of the electrode/ electrolyte is a much slower process. The
Current switch off
Figure 11-9. Transient response of the solid electrolyte cell to switching on or off of a constant current.
Zero Time
11.3 Techniques for Studying Transport and Kinetic Properties in Superionic Conductors
587
Figure 11-10. A schematic of the galvanostatic current interruption technique along with the three electrode cell arrangement. WE is the working electrode, CE is the counter electrode, and RE the reference electrode.
(a) Anode
WEI1I
777/777/////////, Solid electrolyte
\
Y77/77/A CE(3)
V7/7A RE(2)
galvanostatic technique allows for separation of the electrode and electrolyte contributions in the time domain. With the two electrode assembly, the electrode contribution includes overpotential losses at both the cathode/electrolyte and anode/electrolyte interfaces. However, as shown in Fig. 11-10, with the use of a third (reference) electrode through which no current passes, it is possible to separately study anodic or cathodic polarization processes. A versatile computer controlled current interruption technique for studying polarization processes in solid electrolytes has been described by Nardella et al. (1988). 11.3.4.3 Other Transient Techniques
Potentiostatic techniques commonly used in liquid electrolyte systems essentially involve controlling the potential be-
tween a working or test electrode and a reference electrode and allowing the current to vary between the test and a counter electrode in a three cell configuration. These techniques have limited application in solid electrolyte systems as ohmic losses can be significant and can cause distortion of the polarization curves. The Luggin probe approach used commonly in liquid electrolyte cells to reduce IR or ohmic potential drop across the electrolyte is not always feasible. Moreover, it does not completely eliminate ohmic losses. Several methods are available to compensate for the electrolyte resistance. These include, built in electronic circuitry in the potentiostats, galvanostatic current interruption and impedance spectroscopy or AC bridge methods. Linear potential sweep and cyclic voltammetry are the common and most versatile potentiostatic techniques used in the study of solid state battery system (Sequeira, 1985). Both methods involve imposing a linear voltage ramp between working and reference electrodes and measuring the current response between working and counter electrodes. The voltage ramp rates can vary from a few mVh" 1 to several V h" 1 and the voltage scan range is
588
11 Ceramic Superior!ic Conductors
usually within ± 3 V. In the linear potential sweep the voltage ramp is applied only in one direction from a rest potential whereas in cyclic voltammetry the direction of sweep is reversed frequently and the whole procedure repeated several times. In a sequence of measurements, as the applied voltage nears the standard potential for the electrode process, the current begins to flow the magnitude of which increases rapidly, but once the applied potential exceeds the standard potential for the electrode process the current starts decreasing. The general characteristics of a cyclic voltammetry curve are shown in Fig. 11-11. The technique is useful for studying charge/discharge behaviour and cycle life in battery systems as the areas under the peaks correspond to the charge or discharge capacity of the battery. It is not unusual to observe more than one peak for oxidation or reduction sweeps if the solid electrolyte system contains more than one electroactive species and their oxidation or reduction potentials are sufficiently separated. The other less frequently used techniques in solid electrolyte systems to study electrode kinetics are chronopotentiome-Ve
Potential over time
Figure 11-11. Cyclic voltammograrn of a cell with reversible electrodes.
try and chronoamperometry. In the former the potential is monitored as a function of time for a system under constant current control. In the latter, the current response of a system to a potential step perturbation is investigated as a function of time. Both these techniques have been extensively used in solid electrolyte cells especially those based on oxygen-ion conductivity for studying diffusion of oxygen in metals (both in the solid and molten states), for determining chemical diffusion of oxygen in nonstoichiometric oxides and diffusion/ solubility product in metals (Hladik, 1972 c; Tare et al, 1980).
11.4 Types of Ceramic Superionic Conductors 11.4.1 Oxygen-Ion Conductors
The use of oxygen-ion conducting materials in solid electrolyte devices and as a tool for studying thermodynamic and kinetic properties is wide spread. A majority of solid electrolytes which are fast oxygenion conductors have either the face centered cubic (fluorite-type) or the distorted face centered cubic structure (see Ch. 1, Sec. 1.2.3 for structure model of fluorite lattice). These materials contain a large number of vacancies created by the incorporation of lower valent cations into the fluorite lattice (extrinsic defects). In the fluoritetype structure, cations are grouped in a face centered cubic arrangement with oxygen ions occupying all the tetrahedral sites. The lower valency dopant cation substitutes on a zirconium lattice site thus creating vacancies in the oxygen sublattice for charge compensation. Oxygen-ion vacancies have been confirmed to be the dominant defects by X-ray and density measure-
11.4 Types of Ceramic Superionic Conductors
ments. One anion vacancy is introduced for one divalent cation or two trivalent cations substituted in the host cation sublattice. The ionic conductivity in the fluorite-type structure is isotropic in nature and results from migration of oxygen-ion vacancies distributed randomly in the oxygen sublattice. There is a rather large scatter in the conductivity and activation energy data reported in the literature. This can be attributed to different preparation techniques used and to the level of impurities in the materials all of which affect the total conductivity, to different measurement techniques used by various authors all of which do not furnish the same information, and to incomplete characterization of the ceramics. In addition, the contribution from the grain boundary resistivity, the level of interaction between vacancies and between dopant cations and vacancies are a function of the temperature. Unless the role of each process is fully appreciated and its contribution to the total conductivity is isolated, the interpretation of the data can be subjective. 11.4.1.1 Zirconia Based Materials Pure zirconia (ZrO2) exists in three polymorphs. The monoclinic (m) phase is the stable form at room temperature but is mainly an electronic conductor with a very low value for conductivity (Kumar et al., 1972; Nasrallah and Douglas, 1974). It undergoes phase transformation to the tetragonal (t) modification on heating at 1170°C which itself transforms to the cubic phase at 2370 °C. The cubic phase is stable up to the melting point of zirconia (2680 °C). On cooling the reverse transformations take place. These phase transformations are martensitic in nature. The tetragonal to monoclinic phase transformation is
589
accompanied by about 3 - 5 % volume change which is enough to cause severe cracks in the ceramic. The t -> m transformation can be avoided and the high temperature cubic and tetragonal phases can be stabilized at lower temperature by the addition of a number of metal oxides (CaO, MgO, Y 2 O 3 , Sc 2 O 3 and rare earth oxides). These metal oxides form solid solutions with zirconia and stabilize the tetragonal and the cubic phases in addition to introducing vacancies in the anion sublattice which are responsible for the observed high ionic conduction. The phase diagrams for ZrO 2 based materials are complex and there is a considerable disagreement in the literature as to the exact location of the phase boundaries. Methods of powder and ceramic fabrication also have a significant influence on the phase assemblage. The existence of metastable phases, ordering and precipitation as a function of heat treatments further add to the complexity of the system. For technological applications CaO, MgO, Y 2 O 3 , Sc 2 O 3 and Yb 2 O 3 systems have been more widely studied and as superionic conductors the tetragonal and the cubic phases of stabilized zirconia are of main interest. The composition range over which these phases exist is narrow and is temperature dependent. The amount of the dopant required to fully stabilize the cubic phase is about 8 mol% Y 2 O 3 (Scott, 1975; Yoshimura, 1988), corresponding to about 3.75% vacancy concentration, 8-9mol% Yb 2 O 3 (Perez y Jorba, 1962), 8 mol% Sc 2 O 3 (Ruh etal, 1977; Thornber et al., 1970), and 12-13 mol% CaO (6-6.5% vacancy concentration) (Stubican and Hellmann, 1981). The amount of other rare earth oxide (Dy 2 O 3 , Sm 2 O 3 , Gd 2 O 3 , Nd 2 O 3 ) required to stabilize the cubic phase varies between 8-12 mol% (Col-
590
11 Ceramic Superionic Conductors
longues et al., 1961; Etsell and Flengas, 1970). The cubic phase range varies with the temperature and it exists over 8 to 50mol% Y 2 O 3 at 1600 °C (Scott, 1975), 12-13 to 20 mol% CaO at 1500 °C (Etsell and Flengas, 1970; Stubican and Hellmann, 1981) and 8-12 to 40-50 mol% rare earth oxides at 1000 °C (Collongues etal, 1961; Etsell and Flengas, 1970). In the Sc 2 O 3 -ZrO 2 system, the cubic phase exists only over the composition range of &9 to 15mol% Sc 2 O 3 at 1200°C but in compositions containing more than about 10 mol% Sc 2 O 3 , a low conducting rhombohedral (P) phase usually coexists with the cubic phase (Bannister and Skilton, 1983; Ruh et al, 1977). In the ZrO 2 -MgO system, the cubic solid solutions are stable only at higher temperatures and decompose below about 1300 °C (Grain, 1967). If the stabilizer content is insufficient then the structure of the material consists of two or more phases which may be in the metastable form depending on the thermal history of the ceramic. Such materials are known as partially stabilized zirconia (PSZ). Although some of these properties have been exploited to advantage in MgO and CaO-ZrO 2 systems and materials with high strength, toughness and thermal shock resistance have been developed (Garvie et al., 1975; Green et al., 1989), they nevertheless have serious consequences for ion transport properties. In the ZrO 2 -Y 2 O 3 system, the phase assemblage between 2 - 3 and 8.5 mol% Y 2 O 3 consists of a mixture of cubic, tetragonal and sometimes monoclinic phases. At about 2 - 3 mol% Y 2 O 3 a low-dopant tetragonal (t) phase is formed. This phase has a fine grain size, has extremely high strength and toughness and transforms to monoclinic zirconia under stress (Nettleship and Stevens, 1987). The lattice conductivity of this phase is higher than that of
fully stabilized zirconia, below about 600700 °C (Badwal and Swain, 1985). A metastable dopant-rich tetragonal phase known as the t'-phase has also been reported in ZrO 2 -Y 2 O 3 and ZrO 2 -Sc 2 O 3 systems. This phase does not transform under a stress field but slowly decomposes with time at elevated temperatures to a cubic phase and tetragonal ZrO 2 precipitates (Heuer et al., 1988). The transformation of the t'-phase is diffusion controlled, leading to a decrease of the ionic conductivity (Ciacchi, 1990). In the ZrO 2 -Y 2 O 3 system, the t'-phase is formed by quenching the ceramic from a temperature in the cubic phase field (Y2O3 < 7 mol%). In the ZrO 2 -Sc 2 O 3 system, the t'-phase is formed under normal sintering conditions (quenching is not necessary) between 4.58mol% Sc 2 O 3 . For detailed discussion of the phase diagram work, fabrication techniques, thermal and mechanical properties readers should refer to several review papers and articles written on various aspects (Claussen etal., 1984; Green et al., 1989; Heuer and Hobbs, 1981; Heuer, 1987; Koehler, 1984; Somiya et al., 1988; Stevens 1986; Stubican and Hellmann, 1981; Swain, 1989; Yoshimura, 1988). There seems to be some correlation between the minimum amount of the dopant required to fully stabilize the cubic phase and the conductivity maximum observed as a function of the dopant concentration (12-13 mol% CaO, 8-9 mol% Y 2 O 3 , 8-9mol% Yb 2 O 3 and 8-12 mol% other rare earth oxides) (Dixon et al., 1963; Etsell and Flengas, 1970; Schmalzried, 1977; Strickler and Carlson, 1965; Takahashi, 1972; Tannenberger et al., 1966). In the cubic phase field, the conductivity decreases rapidly with increasing dopant concentration. Such a behaviour is shown in Figs. 11-12 and 11-13 for a number of
11.4 Types of Ceramic Superionic Conductors
591
-075
Figure 11-12. Conductivity as a function of dopant content in zirconia based systems. The data for Yb 2 O 3 (o), CaO (D) and Gd 2 O 3 (A) from Tannenberger et al. (1966). Sc 2 O 3 data (o) from author's laboratory.
-3.25 m o l % M 2 0 3 (MO)
-0.75 O Single grain # Polycrystalline
1000°C
0.90 o c b o)-1.20
-1.35 -1.50
(a) -3.70
-3.90 T
-4.10
-A.50
Figure 11-13. Variation of conductivity as a function of Y 2 O 3 concentration in the ZrO 2 -Y 2 O 3 system at (a)1000°C(total)and(b) 400 °C (lattice resistivity), o - Single grain; • - polycrystalline specimens.
O Single crystal • Polycrystalline
-4.70 13
1
(b)
mol% Y203
592
11 Ceramic Superionic Conductors
ZrO2-based system. The trend, however, is different at higher and lower temperatures as shown in Fig. 11-13 for the more extensively studied ZrO 2 -Y 2 O 3 system. At 400 °C there is no sharp maximum as observed at 1000 °C. In fact there is little change in the lattice conductivity up to about 8 mol% Y 2 O 3 above which conductivity decreases rapidly with increasing dopant concentration. A maximum in the conductivity at 1000 °C has also been observed for doped CeO 2 and ThO 2 systems at about the same vacancy concentration (see below). Both CeO 2 and ThO 2 in the pure form have the cubic structure and the dopant is added only to increase the concentration of extrinsic defects (vacancies). Thus the relationship between the conductivity maximum and the minimum amount of the stabilizer required to fully stabilize the cubic phase in zirconia is somewhat ambiguous unless the conditions which require the crystal lattice to be fully stabilized in the cubic structure also give rise to a maximum conductivity. In zirconia based electrolytes if conductivity measurements are made over a wide temperature range (300-1100 °C), a continuous change in the slope of the Arrhenius plots is observed (Abelard and Baumard, 1982; Badwal, 1984; Badwal and Swain, 1985; Casselton, 1970; Ioffe et al., 1975). This behaviour is obvious in both single crystals (or grains) and high purity materials and is not due to the higher contribution of the grain boundary impedance at lower temperatures. The activation energy decreases monotonically with increasing temperature. The activation energies reported in the literature are for different temperature ranges and some caution is necessary in directly comparing values reported by different authors. In general, an increase in the activation energy with in-
crease in the dopant concentration has been reported (Dixon et al., 1963; Etsell and Flengas, 1970; Ioffe et al, 1978; Strickler and Carlson, 1965). However, the change in the slope of the Arrhenius plots with temperature as well as the activation energy over a given temperature range are functions of the dopant concentration. In both Y 2 O 3 and Sc 2 O 3 systems the curvature in the Arrhenius plots is less marked as the dopant concentration decreases (Badwal, 1987; Badwal and Ciacchi, 1990) and is shown in Fig. 11-14 for the Z r O 2 Y 2 O 3 system. The isothermal change in the conductivity with the dopant concentration and the conductivity behaviour as a function of temperature for different dopant contents have been discussed by several authors (Hohnke, 1979, 1981; Kilner, 1983; Kilner and Waters, 1982; Nakamura and Wagner, 1980, 1986; Schmalzried, 1977). Models with varying degrees of interactions and nearest neighbours involving dopant cations and vacancies and ordering of vacancies have been considered. In general, over the entire temperature range, two broad regions for ionic conduction exist for fluorite-type ionic conductors. At the low temperature end (below 600-700 °C), simple associates form between dopant cations and vacancies for dilute solutions and the activation energy consists of the energy for defect pair association and the enthalpy for vacancy migration. With increasing temperature the defect pairs begin to dissociate and at higher temperatures, as vacancies become free, the conductivity is determined mainly by the concentration of charge carrying defects and the activation energy equals the enthalpy for vacancy migration. The transition between the two regions occurs over a very broad temperature range. For concentrated solutions, complexes involving several near neigh-
11.4 Types of Ceramic Superionic Conductors
593
2.0 E
i
1.0
Log
jo 0.0
-1.0
-2.0 7.5
o3mol% A8mol% Di2mol% Y 2 0 3 -Zr0 2
9.0
10.5 12.0 Temperature in 10*K~1
bours can form. Moreover, interactions between vacancies can lead to ordering of vacancies. This may explain the observed rapid decrease in the conductivity with increasing dopant content for concentrated solutions. However, in the dilute solution range the phase assemblage in zirconia based materials, below the minimum amount of dopant required to fully stabilize the cubic phase, may consist of two or more phases in addition to variants of the same phase with varying degrees of solute distributions. As a result interpretation of the data in the dilute solid solution range is somewhat obscured. In Z r O 2 - M 2 O 3 systems, in general, an increase in the conductivity and decrease in the activation energy with decreasing ionic radius of the dopant cation is observed (Kilner and Brook, 1982; Stafford etal., 1989; Strickler and Carlson, 1965; Takahashi, 1972). This behaviour has been explained in terms of the steric blocking effect of the dopant cation and binding energy between the dopant cation and vacancies. Larger ions are more effective in blocking vacancy migration. Also the binding energy, which is a combination of coulombic and strain (caused by different Zr 4 +
L ^
13.5
^*^
Figure 11-14. Arrhenius conductivity plots as a function of the stabilizer content, o - 3 mol%, A 8 mol% and n - 12 mol% Y 2 O 3 -ZrO 2 .
15.0
and dopant cation size) factors, is affected by the dopant cation size (Kilner and Brook, 1982; Stafford et al., 1989). Conductivity studies in Sc 2 O 3 -Y 2 O 3 -ZrO 2 (Ciacchi, 1990) and Yb 2 O 3 -Y 2 O 3 -ZrO 2 (Corman and Stubican, 1985) at a constant dopant concentration (8 or 10 mol%) but as a function of Sc 2 O 3 (Yb 2 O 3 )/Y 2 O 3 ratio clearly demonstrate that the dopant cation size has an effect. The ionic radius of both Sc 3+ and Yb 3 + is close to that of Zr 4 + but smaller than that of Y3 + and in both systems conductivity increased with increasing Sc 2 O 3 or Yb 2 O 3 content. In the high temperature region (850-1000 °C) where most of the vacancies are expected to be dissociated and free to migrate, the activation energy has been reported to increase with increase in the Y 2 O 3 content in the Sc 2 O 3 -Y 2 O 3 -ZrO 2 system. Figure 11-15 compares the conductivity behaviour over a large temperature range for several zirconia based electrolytes. Amongst various zirconia based electrolytes, the maximum conductivity has been observed for Sc 2 O 3 stabilizer (smallest cation size) followed by Yb 2 O 3 , Gd 2 O 3 and Y 2 O 3 . Table 11-2 gives conductivity and activation energy data for several compositions.
594
11 Ceramic Superionic Conductors
Figure 11-15. Arrhenius plots for various stabilized zirconia electrolytes, o - 13mol% CaO (Tien and Subbarao, 1963), A - 10mol% Y 2 O 3 , n - 8 mol% Sc 2 O 3 (author's data).
0.0 o I
-1.0
-2.01— 7.5
• 8mol% Sc2O3 A 10mol% Y 2 0 3 O 13mol% CaO 9.0
10.5 12.0 Temperature in 10^-K"1
A larger number of materials show a continuous change in the conductivity with time (ageing) at higher temperatures (800-1200 °C) (Badwal, 1987; Ciacchi, 1990; Etsell and Flengas, 1970; Vlasov and Perfiliev, 1987). The conductivity deterioTable 11-2. Ionic conductivity and activation energy data for zirconia based electrolytes. Composition
(ZrO 2 ) 0 . 88 (Y 2 O 3 ) 0 . 12 a (ZrO2)0.90(Y2O3)0.10a (ZrO 2 ) 0 . 92 (Y 2 O 3 ) 0 . 08 a (ZrO 2 ) 0 . 97 (Y 2 O 3 ) 0 . 03 a (ZrO2)0.92(Sc2O3)0.08a (ZrO2)0.87(CaO)0.13b (ZrO 2 ) 0 . 92 (Yb 2 O 3 ) 0 . 08 c (Zr0 2 )o. 90 (Gd 2 0 3 ) 0 . 10 d (ZrO 2 ) 0 . 81 (In 2 O 3 ) 0 . 19 e a
G in Q^cm"1 (1000 °C)
E in kJmol" 1 (±3) (Temperature range in °C)
0.11
95(850-1000) 115(400-550) 0.12 88(850-1000) 105 (350-500) 0.15 75(850-1000) 100(300-425) 0.055 72(850-1000) 88 (300-450) 0.18-0.31 75(850-1000) 130(400-500) 0.06 115(750-1000) 0.2 80(600-1000) 0.02 (800) 0.04 (800) 146 (400-800)
Data from Author'sJ laboratory; b Dixon etal. (1963); c Yamamoto et al. (1989); d Tannenberger et al. (1966); e Hohnke (1980).
13.5
15.0
rates continuously over a long period (usually rapidly in the first few hours and then more slowly) when the sintered materials are annealed as shown previously in Fig. 11-3 for a ZrO 2 -Y 2 O 3 and a ZrO 2 -Sc 2 O 3 composition. The rate of conductivity deterioration is a function of the annealing temperature, previous thermal history, the type and concentration of dopant and is determined by thermodynamics and kinetics of phase equilibrium reactions. For each system or composition there is usually an upper and a lower temperature beyond which no ageing and deterioration in the conductivity occurs. In most of these systems the ageing can be reversed by heating the materials to higher temperatures. The ageing in single crystals and within the grains of polycrystalline ceramics occurs as a result of slow decomposition of the metastable phases, formation and growth of precipitates of low conducting phases and ordering of cation or anion sublattices (Allpress and Rossell, 1975; Baukal, 1969; Etsell and Flengas, 1970; Green et al., 1989; Hannink, 1978; Rossell, 1981; Stubican and Ray, 1977; Stubican etal., 1977; Subbarao and Sutter, 1964; Tien and Subbarao, 1963; Vlasov and Per-
11.4 Types of Ceramic Superionic Conductors
filiev, 1987). These processes require diffusion and rearrangement of cations and, therefore, are limited by the slow cation migration at the annealing temperatures and often proceed through the formation of intermediate metastable phases. Even materials whose phase assemblage consists of a single phase may not be in thermodynamic equilibrium at the annealing temperatures. The existence of short or long range ordering in cubic solid solutions on annealing has been observed in zirconia based systems (Allpress and Rossell, 1975; Stubican and Ray, 1977; Stubican et al., 1977). The strongest evidence for the formation and growth of microdomains or ordered compounds on annealing exists in the ZrO 2 -CaO system (Allpress and Rossell, 1975; Stubican and Ray, 1977) and the observed decrease in the conductivity with time in the vicinity of 1000 °C for higher dopant concentrations (18-20mol% CaO) has been attributed to an order/disorder transition (Subbarao and Sutter, 1964; Tien and Subbarao, 1963). In the single phase ZrO 2 -Y 2 O 3 compositions, the effect of ordering on the conductivity has not been quantified and in any case appears to be relatively small (Etsell and Flengas, 1970). No ageing occurs for the 10mol% Y 2 O 3 composition at 1000 °C (Badwal, 1984). In the ZrO 2 -Sc 2 O 3 system all compositions between 4.5 and 8 mol% Sc 2 O 3 are essentially single phase materials in the as-sintered form but show a decrease in conductivity with time at 1000 °C. This results mainly from the slow disproportionation of the dopant-rich metastable t'-phase present in the sintered materials into a cubic phase matrix and tetragonal (low dopant level) precipitates (Badwal, 1987; Ciacchi, 1990). For 7.8mol% Sc 2 O 3 -ZrO 2 , the maximum conductivity deterioration occurred at 900 °C (Fig. 11-16) (Ciacchi, 1990).
595
150
600
700 800 900 1000 Annealing temperature in °C
1100
Figure 11-16. Percentage resistivity increase in 7,8 mol% Sc 2 O 3 -ZrO 2 at different annealing temperatures after 9500 min.
In the two phase ceramics, the phase assemblage in the sintered materials is usually not in thermodynamic equilibrium, and a significant deterioration in the conductivity occurs with time in all partially stabilized zirconias in the vicinity of 1000 °C as a result of solute partitioning and precipitation and in the growth of low conducting phases. In ZrO 2 -Y 2 O 3 , at 1000 °C, conductivity deterioration has been observed for all compositions (2-8 mol% Y2O3) in the two phase (cubic and tetragonal) field (Badwal and Ciacchi, 1990). The conductivity of both MgO and CaO-PSZ deteriorates even more rapidly with time in the vicinity of 1000 °C (Fig. 11-17). In MgO-PSZ, ageing below the sub-eutectoid temperature leads to the transformation of the tetragonal precipitates to monoclinic zirconia, development of fine monoclinic structure within tetragonal zirconia precipitates and the formation of an ordered anion vacancy phase Mg 2 Zr 5 O 1 2 within the grains (Hannink and Garvie, 1982). Also increased precipitation of monoclinic zirconia takes place at the grain boundaries. Similarly precipitation and coarsening of low conducting phases also occur in CaO-PSZ during annealing (Hannink et al., 1981).
596
11 Ceramic Superionic Conductors
-2.0 3.Awt.% MgO —PSZ
1000°C
E -2.1 o C
b o-2.2 Figure 11-17. Ageing be-2.3
haviour of 3.4wt.% MgOPSZ at 1000 °C. 1000
2000 3000 Time in min
In polycrystalline materials, apart from a change in the conductivity in the bulk of the grains, increase in the grain boundary resistivity due to annealing has also been reported (Ciacchi, 1990; Kleitz et al., 1981; Vlasov and Perfiliev, 1987). In addition to the ageing behaviour discussed above, phase transformations during heating or cooling of zirconia ceramic can lead to sudden changes in conductivity. For example the presence of monoclinic zirconia (due to incomplete phase reaction or formed as a result of phase decomposition) leads to jumps in the Arrhenius plots for the conductivity and hysteresis effects as shown above in Fig. 11-4. Such phase transformations are accompanied by a volume change, leading to microcracking and deterioration in the conductivity on thermal cycling (Badwal, 1983). The conductivity of zirconia based electrolytes is independent of oxygen partial pressure over a wide range of temperatures and oxygen partial pressures with oxygenion transport number close to unity (Etsell and Flengas, 1970). Despite considerable scatter attributable to the techniques used for determining the ionic transport number, the electrolyte domain at 1000 °C extends at least from 1 to 10~ 20 atm oxygen
4000
5000
partial pressure. It narrows with increasing and widens with decreasing temperature. At lower oxygen partial pressures the mode of conduction is n-type. In zirconia-based ceramics segregation of low conducting impurities during sintering and subsequent heat treatments considerably modifies the total conductivity. The contribution to the total resistivity from grain boundaries is a function of the powder and ceramic processing procedures used. The effect of grain boundary resistivity is more marked in small grain size ceramics with a large grain boundary surface area such as yttria tetragonal zirconia (Badwal, 1990). This subject will be discussed in more detail in Sec. 11.5 on "Microstructure and Transport Properties". 11.4.1.2 Ceria Based Materials Pure ceria (CeO2 _x) exists in the fluorite structure over a wide temperature and oxygen partial pressure range (x « 0.3, Bevan and Kordis, 1964). For small values of x9 ceria is a mixed conductor but the electronic (n-type) conductivity dominates with increasing degree of nonstoichiometry (VanHandel and Blumenthal, 1974). In pure ceria both oxygen vacancies and
597
11.4 Types of Ceramic Superionic Conductors
cerium interstitials have been reported as the nonstoichiometric defects although most of the data point to an oxygen-ion vacancy model (Blumenthal and Hofmaier, 1974; Panlener et al., 1975). On addition of low valence dopants (CaO, Y 2 O 3 , Gd 2 O 3 , Nd 2 O 3 , Yb 2 O 3 , La 2 O 3 , etc.), the concentration of oxygen vacancies increases well above that of electronic defects and the material becomes a predominantly ionic conductor. The solubility of the added oxides is quite high (Bevan etal., 1965 a, 1965 b; Etsell and Flengas, 1970) and the solid solutions with the fluorite-type structure exist over a wide dopant concentration range. In doped ceria, oxygen vacancies are the main charge compensating defects (Blumenthal etal., 1973). In the CeO 2 -CaO system, the maximum in the conductivity between 500 and 1000 °C has been reported at 11 -12 mol% CaO (5.5-6% vacancy concentration) by Adham and Hammou (1983) and Blumenthal etal. (1973) whereas No wick etal. (1979) observed no such maximum. The activation energy does not change significantly with the dopant content between 3 and 14mol% CaO. In the CeO 2 -Y 2 O 3 system, Wang et al. (1981) have studied the effect of Y 2 O 3 content over a large concentration range (0.05-40 mol%) and observed a sharp maximum at 182 °C in the conductivity [Fig. 11-18 (a)] and a minimum in the activation energy at 4 mol% Y 2 O 3 . With further increase in the dopant concentration to 40 mol%, the conductivity decreased by more than four orders of magnitude at 182°C. However, Adham and Hammou (1983) observed a conductivity maximum at 8 mol% Y 2 O 3 (500600 °C). A careful examination of the data reported by Wang etal. (1981) at 560°C also revealed a broad maximum above 6mol% Y 2 O 3 [Fig. ll-18(b)]. Like with zirconia based materials, the Arrhenius
plots of ionic conductivity show a change in slope towards lower activation energy with increasing temperature. Wang et al. (1981), Kilner (1983) and Hohnke (1981) have interpreted the conductivity behaviour in doped CeO 2 in terms of interactions between vacancies and dopant cations at low temperatures as discussed previously for the zirconia based electrolytes. The effect of dopant cation type and its concentration is more meaningful in ceria based systems in the dilute solid solution range as the same fluorite structure is maintained throughout. Amongst various CeO2-based electrolytes the maximum conductivity has been reported for Gd 2 O 3 doped CeO 2 (Gerhardt-Anderson and No wick, 1981; Gerhardt and No wick, 1986; Kudo and Obayashi, 1975). Table 11-3 gives values for ionic conductivity and activation energy for various doped CeO 2 compositions. Some ambiguity results from different temperature ranges over which the activation energy data has been reported.
Table 11-3. Conductivity and activation energy data for doped ceria electrolytes Composites
(CeO2)0.92(Y2O3)0.08a (CeO2)0.95(Y2O3)0.05b (CeO2)0.90(CaO)0.10b (CeO2)0 90 (Gd 2 O 3 ) 0 1OC (CeO 2 ) 0 . 82 (Gd 2 O 3 ) 0 . 18 d (CeO 2 ) 0 . 82 (Nd 2 O 3 ) 0 . 18 d (CeO2)0.82(La2O3)0.18d a
a in
E in
(T in °C)
(temperature range in °C)
0.0091 (600) 0.003 (500) 0.145 (1000) 0.10 (1000) 0.0064 (600) 0.25 (1000) 0.235 (1000) 0.23 (1000) 0.154(1000)
68 (450-700) 73 (400-1000) 88(400-1000) 72 (450-700) 68 (700-1000) 81 (700-1000) 78 (700-1000) 78 (700-1000)
Adham and Hammou (1983); b Tuller and Nowick (1975); c Reiss etal. (1981); d Kudo and Obayashi (1975).
11 Ceramic Superionic Conductors
-2.0
Figure 11-18. Variation of conductivity with Y 2 O 3 content in the CeO 2 -Y 2 O 3 system, (a) 182°C(Wang etal., 1981). (b) n - 5 6 0 ° C (Wang et al., 1981); o 600 °C, A - 500 °C (Adham and Hammou, 1983).
Grain boundary resistivity in ceriabased materials makes a major contribution to the total resistivity and has been reported to be dependent on the type and concentration of dopant in addition to impurities (Adham and Hammou, 1983; Gerhardt and No wick, 1986; Tanaka etal., 1987; Wang and No wick, 1980). In general, higher grain boundary resistivity has been observed for low dopant content. The origin of grain boundary resistivity is similar to that in zirconia based electrolytes. Impurities segregate at grain boundaries
and have been suggested to form a continuous glassy film surrounding each grain or aggregates of grains (Gerhardt et al., 1986; Tanaka et al., 1987). The ionic conductivity regime is narrow in ceria based electrolytes and is a function of the dopant concentration. These materials easily develop n-type electronic conduction in low oxygen partial pressures and at high temperatures (Adham and Hammou, 1983; Blumenthal etal., 1973; Hurley and Hohnke, 1980; Tuller and No wick, 1975). For example for
11.4 Types of Ceramic Superionic Conductors
(CeO2)0 95 (Y 2 O 3 ) 0 0 5 , Tuller and Nowick (1975) have reported that the electrolyte domain (t{ > 0.99) extended to 10" 1 3 atm at 600 °C and only to about 10 " 6 atm oxygen partial pressure at 1000 °C. Doped ceria electrolytes have limited application in low oxygen concentration environments and at high temperatures despite their high ionic conductivity compared with zirconia based materials. 11.4.1.3 Thoria and Hafnia Based Materials
Thoria (ThO2) exists in the cubic fluorite-type structure and in the pure form exhibits p-type conductivity (Bauerle, 1966; Etsell and Flengas, 1970; Lasker and Rapp, 1966). In high oxygen partial pressures, the predominant defects are electron holes (h) and interstitial anions Of~. Oxygen dissolves in the lattice according to the reaction: O 2 (g) = 2Of~ + 4 h \ Any variation in the oxygen partial pressure changes the relative concentration of ionic and electron defects. Dopants such as CaO, MgO, Y 2 O 3 , Gd 2 O 3 , Yb 2 O 3 are added to introduce anion vacancies and thus to increase the concentration of ionic defects over electronic charge carriers. The solubility of the added oxide varies considerably with the dopant-type and with temperature; the solubility limit increases with temperature. Around 1700 °C a solubility of about 10 and 20 mol% for CaO and Y 2 O 3 dopants respectively have been reported (Curtis and Johnson, 1957; Hund and Metzger, 1952; Mehrotra et al., 1973; Mobius, 1964; Subbarao et al., 1965). In doped thoria, p-type conductivity is a function of temperature and the electrolyte composition. For example, in ThO 2 -Y 2 O 3 , both ionic and p-type conductivity as well as the ionic transport number increase with Y 2 O 3 content (Hammou, 1975; Lasker and Rapp, 1966). In general, for Y 2 O 3 and
599
CaO dopants, for oxygen partial pressures less than about 10" 6 atm and at 1000 °C, the conductivity is predominantly ionic. Lasker and Rapp (1966) and Steele and Alcock (1965) have reported that the total conductivity of thoria-yttria solid solutions is independent of oxygen partial pressure over the range 10~ 6 -10~ 2 8 atm. The p-type conductivity in pure and doped thoria follows a (Po2)1/4 law (Lasker and Rapp, 1966). Amongst thoria based materials, most of the electrical conductivity studies have concentrated on ThO 2 -Y 2 O 3 and ThO 2 -CaO systems. The ionic conductivity occurs by migration of oxygen ions. A comparison of the measured and theoretical densities strongly points to an anion vacancy model for the fluorite-type solid solution (Subbarao etal., 1965; Wimmer et al., 1967). The maximum in the conductivity has been observed at about 8 mol% Y 2 O 3 (3.75% anion vacancy concentration) (Hammou, 1975; Lasker and Rapp, 1966) and 5 10mol% CaO (Steele and Alcock, 1965; Maiti and Subbarao, 1976). It is worth mentioning here that the solubility of CaO in ThO 2 is much lower than that in ZrO 2 and CeO 2 . The conductivity of ThO 2 -CaO compositions is about an order of magnitude lower than that of ThO 2 -Y 2 O 3 . The ionic conductivity in doped thoria materials is one to two orders of magnitude lower than that in corresponding zirconia based materials of similar compositions (Fig. 11-19). Table 11-4 lists conductivity and activation energy values for several ThO 2 -Y 2 O 3 (CaO) compositions. The electrolytic conductivity domain extends to much lower oxygen partial pressures in doped thoria. From DC polarization experiments on the ThO 2 -Y 2 O 3 system, Patterson etal. (1967) have estimated t{ to be > 0.99 at 1000 °C for oxygen
600
11 Ceramic Superionic Conductors
Figure 11-19. Arrhenius plots for various solid electrolytes all doped with 8mol% Y 2 O 3 . o - Z r O 2 , A-HfO 2 , n - T h O 9 .
-2.0
9.0
10.5
12.0
13.5
15.0
Temperature in 10A-K"1
Table 11-4. Ionic conductivity and activation energy data for doped thoria and stabilized hafnia electrolytes. Composition
o in Q 1 cm {T in °C)
1
(ThO2)0 92 (Y 2 O 3 ) 0 08 a (ThO 2 ) 0 . 92 (Y 2 O 3 ) 0 . 08 b (ThO 2 ) 0 . 92 (Y 2 O 3 ) 0 . 08 c (ThO2)0.93(CaO)0.07d (ThO2)0.95(CaO)0.05e (HfO 2 ) 092 (Y 2 O 3 ) 008 f (HfO2)0.80(Y2O3)0.20f
0.018(1045) 0.013(1000) 0.0075 (1000) 0.002(1000) 4.5 x l 0 ~ 4 (1000) 0.025 (1000) 0.0053 (1000)
Ein (temperature range in °C) 106(1045-1400)
112(1000-1300) 70(800-1000) 128(800-1000)
a
Hammou (1975); b Bauerle (1966);c Lasker and Rapp (1966); d Maiti and Subbarao (1976);e Steele and Alcock (1965);f Schieltz et al. (1971).
partial pressures down to 10 34 atm. Other authors have also reported similarly high ionic transport numbers at very low oxygen partial pressures (Etsell and Flengas, 1970; Hammou, 1975; Lasker and Rapp, 1966; Wimmer et al., 1967). There is general consensus that for ThO 2 -Y 2 O 3 at 1000 °C, the electrolyte conductivity domain is at least between 10~ 6 and 10~25 atm oxygen partial pressure. The ionic conductivity domain decreases with increasing temperature, a behaviour similar to that observed for zirconia based materials. The major advantage of doped thoria electrolytes compared with zirconia based materials is their
high stability in extremely reducing environments. For this reason these materials are more attractive for use in galvanic cells for measuring low oxygen concentrations, for example in liquid metals (Chandrasekharaiah et al., 1980; Jagannathan et al., 1980). These electrolytes are not serious contenders for use in fuel cells and oxygen gauges because of their low ionic conductivity and the presence of p-type conductivity at high oxygen partial pressures. Pure hafnia (HfO2) undergoes several polymorphic transformations with temperature and does not exists in the fluoritetype phase at low temperatures. The cubic
11.4 Types of Ceramic Superionic Conductors
structure has to be stabilized by the addition of dopants such as Y 2 O 3 , La 2 O 3 , Gd 2 O 3 , and CaO (Etsell and Flengas, 1970; Komissarova et al., 1964; Spiridinov etal, 1968). HfO 2 -CaO cubic solid solutions are not stable below 1450 °C and decompose to monoclinic HfO2 and CaHf 4 O 9 (Delamarre and Perez y Jorba, 1965). In HfO 2 -Y 2 O 3? the most extensively studied electrolyte amongst the HfO2 based systems, 7-8mol% Y 2 O 3 is required to fully stabilize the fluorite phase. The fluorite phase at 1500°C is stable for Y 2 O 3 additions up to about 50mol% (Spiridinov etal., 1969). Besson et al. (1966) and Schieltz et al. (1971) have studied the electrolytic behaviour of this system. The defect structure consists of a filled cation sublattice and anion vacancies. The maximum in the conductivity was observed at 8 mol% Y 2 O 3 . In the fluorite phase, the activation energy for conduction increases with increase in the dopant concentration. A maximum in the activation energy and minimum in the conductivity (1000 °C) have been reported at 33.3 mol% Y 2 O 3 . At this composition the existence of a compound Y2Hf2O7 was postulated (Caillet et al., 1967). Below this composition, the conductivity behaviour has been attributed to increasing anion vacancy ordering as the Y 2 O 3 content increased in the fluorite lattice (Schieltz et al., 1971). More recently Saly et al. (1989) have reported the conductivity of several rare earth doped (15 mol% Ln 2 O 3 ) - HfO2 single crystals and observed an order of magnitude higher conductivity for Sc 2 O 3 dopant compared with other rare earth oxides. The ionic conductivity of HfO 2 based materials is low compared with stabilized zirconia (Fig. 11-19) and the electrolytic conductivity regime is narrow (1 to 10 ~ 16 atm oxygen partial pressure at 1000°C) (Schieltz etal., 1971). Therefore
601
these materials offer no significant advantages over either zirconia or thoria based electrolytes. 11.4.1.4 Bismuth Oxide Based Materials Bi 2 O 3 exists in the stable monoclinic form (oc-phase) at room temperature. On heating the a-phase transforms to the fluorite-type 8-phase at around 730 °C. The monoclinic a-phase is a predominantly electronic conductor whereas the 8-phase is mainly an oxygen-ion conductor. The Arrhenius plot of the conductivity shows a large jump (about three orders of magnitude increase in the conductivity) around 730 °C during the heating cycle (Fig. 11-20). The oxygen-ion conductivity arises from the large vacancy concentration in the defect fluorite-type structure. It is the best oxygen ion conductor known with up to about two orders of magnitude higher conductivity than that of fully stabilized zirconia in the same temperature range (Fig. 11-20). However, the 5-phase is stable only in the narrow temperature range (730-825 °C) up to the melting point of bismuth oxide. On cooling, the 8-phase persists as a metastable phase and transforms to the tetragonal p-phase at about 650 °C or to the body centered cubic yphase at about 640 °C which in turn transfers to the a-phase below 640 °C (Cahen, 1980; Harwig, 1977; Takahashi and Iwahara, 1973; Verkerk, 1982). All the phase transformations may or may not occur at the temperatures given above depending on the cooling rate. Different stability regimes for both the P and the y-phases dependent on the cooling rates have been reported. Both p and y-phases have several orders of magnitude lower ionic conductivity than the 8-phase (Cahen, 1980; Harwig, 1977; Verkerk, 1982; Verkerk and Burggraaf, 1981). All the phase transformations
602
11 Ceramic Superionic Conductors
Figure 11-20. A comparison of the conductivity of some bismuth oxide and zirconia based electrolytes. 1 Bi 2 O 3 ; 2-(Bi 2 O 3 ) 0 8 (Er 2 O 3 ) 0 2 ; 3-(Bi 2 O 3 ) 0 . 75 (Y 2 O 3 ) 0 . 25 ; 4-(Bi 2 0 3 ) 0 . 715 (Dy 2 0 3 )o. 285 ; 5-(ZrO 2 ) 0 . 92 (Sc 2 O 3 ) 0>08 ; 6-(ZrO 2 ) 0 . 9 (Y 2 O 3 ) 0 . 1 .The data for Bi 2 O 3 electrolytes as per Table 11-5.
-5.0 10.5 12.0 Temperature in 10*-K
9.0
required to fully stabilize the fluorite-type phase at room temperature is 25-32 to 43 mol% Y 2 O 3 , 28.5 to 50mol% Dy 2 O 3 , 35 to 50mol% Gd 2 O 3 , 17.5 to 45 mol% Er 2 O 3 , 22-28 mol% WO 3 , 15-25 mol% Nb 2 O 5 , 18-25 mol% Ta 2 O 5 (Kruidhof et al., 1990; Takahashi and Iwahara, 1973; Takahashi et al., 1975; Takahashi et al., 1977; Verkerk etal., 1980; Verkerk and Burggraaf, 1981; Verkerk, 1982). The phase assemblage in Bi 2 O 3 -M 2 O 3 systems is quite complex and is dependent upon the prethermal history (for example
are accompanied by a large volume change. The high oxygen-ion conducting face centered cubic (f.c.c) 5-phase can be stabilized to much lower (and even room) temperatures by the addition of a number of other metal oxides such as Y 2 O 3 , Dy 2 O 3 , Er 2 O3,Nb 2 O 5 ,Ta 2 O 5 ,WO 3 ,andGd 2 O 3 . Verkerk and Burggraaf (1981) have discussed the effect of ionic radius of the dopant cation on the minimum amount of the dopant required to stabilize the cubic phase. This correlation is shown in Fig. 11-21. The amount of the stabilizer
Doped-Bi 2 0 3 OYb
Gd3-
3+
• 0.3
Dy3* O
o 0.2
15.0
13.5
/
o
y^
Figure 11-21. A correlation between the minimum amount of dopant (Dmin) required to stabilize the face centered cubic phase in Bi 2 O 3 and the dopant cation size, o - After Verkerk et al. (1981), • -more recent data for Y 2 O 3 .
o
\
X
\ o
0.1 0.097
0.099
0.101 0.103 Ionic radius in nm
0.105
0.107
603
11.4 Types of Ceramic Superionic Conductors
the cooling rate from the sintering temperature and subsequent heat treatments) of the specimens. Figure 11-22 summarizes the overall phase assemblage detected in various Bi 2 O 3 -M 2 O 3 systems. The cubic phase exists in the metastable form (at low temperatures) in compositions containing up to about 5-10 mol% lower stabilizer than that required to fully stabilize the cubic f.c.c phase. However, on extended annealing, the f.c.c phase slowly transforms to the hexagonal or the rhombohedral phase (e). This phase has been reported to have a much lower conductivity than the 5-phase. In the Bi 2 O 3 -Gd 2 O 3 system, Takahashi et al. (1975) reported that for Gd 2 O 3 compositions below 30 mol%, the fluorite phase was the high temperature phase which transformed to the tetragonal (for lower stabilizer content) or the rhombohedral (higher stabilizer content) phase at lower temperatures. In the system Bi 2 O 3 -Y 2 O 3 , Kruidhof et al. (1990) have reported that as-prepared compositions between 22 and 32.5 mol% Y 2 O 3 had a face centered cubic structure but on annealing at 650 °C a sluggish phase transformation took place from cubic to the hexagonal structure; the amount of the hexagonal phase decreases with increasing Y 2 O 3 content. At 31.8 mol% Y 2 O 3 only cubic and at 22 mol% Y 2 O 3 only the hexagonal phase existed. Somewhat similar behaviour was also observed in the Bi 2 O 3 -Dy 2 O 3 and Bi 2 O 3 -Er 2 O 3 systems (Kruidhof et al., 1988; Verkerk and Burggraaf, 1981). Watanabe and Kikuchi (1986) have reported that while cubic to hexagonal phase transformation is very sluggish, the reverse transformation from hexagonal to cubic phase is fast. Joshi et al. (1990) for 25 mol% Y 2 O 3 in Bi 2 O 3 also reported a slow decomposition of the 5-phase with time between 600 and 700 °C. These reports are contrary to the expectation of the phase
Low temp, range
High temp, range
600°-700°C M203 + 6
+(15-25)%
£
M203 + 6
6
6
(M203)m -(5-10)%
6 {metastable) or
(6+
£•)
6
'
5-10% 0
a
+ <5 + £
a +ft+ e*
P
* May be present in small quantities
Figure 11-22. A summary of the phase assemblage reported in the literature for Bi 2 O 3 -M 2 O 3 . 5-Face centered cubic, a-monoclinic, p-tetragonal, e-hexagonal or rhombohedral.
diagram proposed by Datta and Meehan (1971). For very low concentration of M 2 O 3 (<5-10mol%), the tetragonal and/or oc-phases are present in the phase assemblage. All these phase transformations on thermal cycling are accompanied by a large increase (during the heating) or decrease (during the cooling cycle) in the conductivity. Amongst all the Bi 2 O 3 systems studied, the maximum conductivity has been reported in the Bi 2 O 3 -Er 2 O 3 system for the (Bi 2 O 3 ) a8 (Er 2 O 3 ) 0 2 composition [0.023 fi1 cm" 1 at 500 °C'and 0.37 Q"1.cm" 1 at 700°C, Verkerk et al. (1980)], and it is about two orders of magnitude higher than that of (ZrO 2 ) 0 . 9 (Y 2 O 3 ) 0il (Fig. 11-20). The ionic transport number for the stabilized f.c.c phase of Bi 2 O 3 is unity but these materials are reduced easily and develop
604
11 Ceramic Superionic Conductors
electronic conductivity in low oxygen partial pressures. For the f.c.c. phase, for compositions containing 5-10 mol% stabilizer above the minimum required to fully stabilize the f.c.c. phase, a sharp change in the slope (knee) of Arrhenius plots is observed around 600-670 °C towards a lower activation energy at higher temperatures (Fig. 11-23). This change in the slope is not associated with any phase transformation. For higher compositions no change in the activation energy is observed and the slope of the Arrhenius plots is about the same as that observed in the low temperature range for compositions showing a knee (Fig. 11-23). Verkerk and Burggraaf (1981) report that above the knee, the activation energy increases with stabilizer content whereas the pre-exponential term remains constant. For compositions showing no knee (and those with a knee but in the low temperature range), the activation energy is independent of the stabilizer content but the pre-exponential term decreases linearly with increasing stabilizer content. Table 11-5 gives conductivity and activation energy values for several compositions.
Verkerk et al. (1982) from neutron diffraction studies on the Bi 2 O 3 -Er 2 O3 system observed no long range ordering of vacancies but a small change in the lattice parameter of the cubic phase near the knee temperature (Verkerk et al., 1980). From diffuse scattering they postulated the existence of short range ordering at low temperatures. On heating above the knee temperature (600-670 °C) the lattice disorders giving a defect structure similar to that of Bi 2 O 3 . In general, in Bi 2 O 3 based electrolytes the contribution of the grain boundary resistivity is negligible. The mechanical properties of bismuth oxide based electrolytes are extremely poor and they undergo considerable creep at temperatures as low as 800-900 °C. This along with the ease with which these materials develop electronic conductivity in reducing atmospheres restricts their use in solid state electrochemical devices especially in solid oxide fuel cells. 11.4.1.5 Pyrochlores and Other Oxides
Oxygen-ion conduction is not limited to the fluorite structure. A number of other
-0.5
-5.5
Figure 11-23. Arrhenius plots for Bi 2 O 3 -Dy 2 O 3 as a function of composition. Dy 2 O 3 content: • - 25, o - 28.5, A - 35, • - 40, o - 4 5 , v-50mol%. 11.0
13.0 Temperature in
15.0
17.0
11.4 Types of Ceramic Superionic Conductors
605
Table 11-5. Conductivity and activation energy for the face centered cubic phase of pure and doped bismuth oxide and some pyrochlores. Composition
a in Q x cm (700 °C)
(Bi2O3)0.80(Er2O3)02<)b-
3.1 (800 °C) 0.37
(Bi 2 O 3 ) 0 . 65 (Er 2 O 3 ) 0 . 35 b (Bi 2 O 3 ) 0 . 65 (Gd 2 O 3 V 35 a (Bi 2 O 3 ) 0 . 715 (Dy 2 O 3 ) 0 . 285 c
0.07 0.10 0.15
(Bi2O3)0.50(Dy2O3)0.50c (Bi2O3)0.70(Y2O3)0.30d
0.011 0.14
(Bi 2 O 3 ) 085 (Nb 2 O 5 ) 0 . 15 e Nd 2 Zr 2 O 7 f Gd 2 Zr 2 O 7 f
0.19 4xlO~ 5 (727°C) 0.0068 (727 °C)
EinkJmor1(±3) (temperature range in °C)
62(>600) 115(<550) 109 (250-750) 73(>600) 108 (< 600) 109(325-775) 71(>650) 110 (< 625) 85(400-850) 67 82
a
Takahashi et al. (1975);b Verkerk et al. (1980);c Verkerk and Burggraaf (1981);d Author's data; e Takahashi et al. (1977);f Van Dijk et al. (1984).
oxides with other crystal structures (e.g., pyrochlores, perovskites and rare earth oxides) also exhibit oxygen-ion conductivity over a limited temperature and oxygen partial pressure ranges. Pyrochlores with the general formula (A 3+ ) 2 (B 4+ ) 2 O 7 have been known for some time to be oxygen-ion conductors (see Ch. 1, Sec. 1.6.1 of this volume for typical structure models of pyrochlores). Most of the conductivity studies have been restricted to materials for which A = Ln and B = Zr or Ti. Both the pyrochlore and the fluorite structures are closely related although unlike in the fluorite structure, both the cation and anion sublattices in a perfect pyrochlore are ordered. This, however, is not true of all pyrochlores. For example in Ln 2 Zr 2 O 7 both the cation and anion sublattices show a degree of disorder which increases as the size of Ln 3 + approaches that of Zr 4 + . Evidence for this has come from infra-red, Raman and neutron diffraction studies (Klee and Weitz, 1969; Scheetz and White, 1979;
van Dijk et al., 1980 a). In this series Gd 3 + is the smallest rare earth ion for which the pyrochlore order is observed. The detailed conductivity investigations have been made on Ln 2 Zr 2 O 7 and Ln 2 Ti 2 O 7 (Ln = Nd, Sm, Gd, Tb, Er) pyrochlores and their solid solutions (Burggraaf et al. 1981; van Dijk etal, 1980 b; van Dijk, 1981; van Dijk et al., 1984; van Dijk, 1985). These authors have reported an order-disorder (fluorite -> pyrochlore) transition at high temperatures. For Gd 2 Zr 2 O 7 , this occurs at 1550°C. Materials quenched from above the transition temperature had the fluorite structure. Both cation and anion sublattice order are related. Cation order lowers the activation energy and anion order lowers the pre-exponential term. Increase in the Ln 3 + size and the associated cation order therefore not only reduces the activation energy for ionic conduction but the ionic conductivity as well. Thus it is difficult to achieve an overall better conductor by changing the degree of order or disorder. In general, pyrochlores have
606
11 Ceramic Superionic Conductors
lower oxygen-ion conductivity than zirconia, ceria or bismuth oxide electrolytes (Table 11-5). Some doped or undoped rare earth oxides, Sc 2 O 3 , Y 2 O 3 and some perovskites have been reported to possess good oxygenion conductivity but only over limited oxygen partial pressure or temperature ranges (Etsell and Flengas, 1970; Dell and Hooper, 1978; Steele, 1989). In fact (La2O3)0.95(SrO)0.o5 has higher conductivity than fully stabilized yttria-zirconia below about 600 °C but these materials degrade in moist air (Steele, 1989). Such materials are useful only in selected applications, have least technological importance as superionic conductors and are mainly of academic interest. 11.4.2 Beta-Aluminas
The term beta-alumina refers to a group of sodium aluminates whose structure and composition are closely related. In terms of transport properties, two important sodium aluminates are Na + P-alumina and Na + p"alumina with nominal compositions of N a 2 O - l l A l 2 O 3 and Na 2 O-5Al 2 O 3 respectively. Neither P or P"-alumina are stoichiometric and both exhibit a variable composition. The Na + p-alumina contains much higher amounts of soda than indicated by the stoichiometric formula whereas p"-alumina is sodium deficient. The structure and properties of beta-aluminas have been reviewed by several authors (Collongues etal., 1978; Kennedy, 1977; Kummer, 1972; Powers and Mitoff, 1978; Stevens and Binner, 1984; Whittingham and Huggins, 1972). The crystal structure for beta-alumina consists of Al 3+ and O2~ packed in spinel blocks in a similar manner to that in MgAl 2 O 4 (Al 3+ occupying both octahedral and tetrahedral sites) (see Ch. 1, Sec.
1.3.7 of this volume for typical structure models of P-alumina). Two dimensional loosely packed layers containing Na + and O 2 " separate the so-called spinel blocks. The major difference between P- and p"alumina is the sequence in which the spinel blocks are stacked. In p"-alumina the stacking arrangement is repeated every three spinel blocks whereas in P-alumina the conduction plane acts as a mirror for two spinel blocks. p"-alumina has one less Al3 + per unit cell and the charge is compensated by the presence of three additional Na + in the loose conduction layers. The structure for p-alumina is hexagonal and it is rhombohedral for P"-alumina. The Na + p"-alumina structure between the binary oxides (Na 2 O and A12O3) is unstable because of the cation vacancy in the spinel block, and needs to be stabilized by the addition of MgO or Li 2 O (Bugden and Duncan, 1977; Imai and Harata, 1972; Kummer, 1972). Mg 2 + or Li + occupy the vacant lattice site in the spinel block and the charge is compensated by Na + ions in the conduction plane. The addition of stabilizing oxides also has an effect on the sodium content as well as the resistivity of the material (Imai and Harata, 1972; Kennedy and Sammells, 1972, 1973). The conduction of Na + takes place in the loosely packed layers and is limited to these two dimensional planes. Conduction along the oaxis is extremely difficult. The high sodium ion conductivity in Na + beta (p, p")-alumina results from the large number of available sites for conduction and the low activation energy for ion migration (15-30 kJ mor1) (Hooper, 1977; Kennedy, 1977; Whittingham and Huggins, 1972). The ionic transport number in p or p"-alumina electrolytes is near unity with negligible contribution from electronic conductivity (Galli et al., 1973; Whittingham and Huggins, 1972).
11.4 Types of Ceramic Superionic Conductors
One of the useful properties of beta-aluminas is their ability to replace Na + ions with other cations by an ion exchange reaction in the molten salt (200-800 °C), or in an aqueous solution. Only monovalent and some divalent cations exchange easily with Na + in P-alumina whereas the sodium content of P"-alumina can be exchanged (partially or completely) with a number of monovalent, divalent and even trivalent cations (Li + , K + , Ag + , Rb + , Tl + , C u \ NH^ and H 3 O + , Ca 2 + , Sr2 + , P b 2 + , Hg 2 + , Cd2 + , Gd 3 + , Nd 3 + etc.) (Collongues et al., 1978; Farrington and Briant, 1979; Farrington et al., 1989; Frase et al., 1986; Kaneda et al., 1979; Kennedy, 1977; Kummer, 1972). In many cases direct substitution may not take place and the sodium has to be substituted by an intermediate cation. The replacement of Na + by other ions leads to change in the unit cell dimensions. |3"-alumina decomposes to (3-alumina and NaAlO 2 at about 1450 °C, but the addition of MgO or Li 2 O raises the decomposition temperature. This is useful for obtaining high density ceramics or single crystals at higher temperatures. P-alumina is stable up to 1600-1800 °C although some loss of Na 2 O may occur during sintering of the material at such higher temperatures because of the high equilibrium vapour pressure of Na 2 O. Special attention needs to be paid to the preparation procedure especially for polycrystalline materials. The phase assemblage of the ceramic is a function of the fabrication techniques and the sintering conditions used. During preparation of P and |3"-alumina a mixture of one or both along with oc-alumina or NaAlO 2 has been observed depending on the preparation method (Kummer, 1972; McDonough et al., 1978; Ray and Subbarao, 1975; Virkar et al., 1974). p-alumina is the main phase formed at
607
high sintering temperatures (> 1500 °C) whereas P"-alumina can be a major product on sintering or annealing around 1400 °C. Both p- and p"-alumina are sensitive to moisture and uptake of water leads to a decrease in the conductivity. Moisture sensitivity is higher for P"-alumina and is a function of the size of the monovalent mobile cation (Zu-Xiang, 1989). The transport properties of sodium and substituted beta-aluminas have been reported in a number of review articles and conference proceedings (Bates and Farrington 1981; Boyce etal., 1986; Collongues et al., 1978; Farrington and Briant, 1979; Kennedy, 1977; Kummer, 1972; Stevens and Binner, 1984; Van Gool, 1973; Vashishta, 1979; Weppner and Schulz, 1988; Zu-Xiang, 1989). The conductivity of beta-alumina electrolytes is sensitive to the sodium content, relative proportion of p and P"-phases in the ceramic and composition of each phase (nonstoichiometry). In polycrystalline materials, in addition, the total resistivity is influenced by the grain size and orientation, porosity and the presence of impurities commonly added as sintering aids. In Table 11-6 conductivity data at 25 and 300 °C along with activation energy values of single crystals of P and P"-phases have been given. Figure 11-24 shows Arrhenius plots for single crystals of Na + p, Ag + substituted P and Na + P"-alumina. Substitution of Na + by other cations has a significant effect on the conductivity (Collongues et al., 1978; Farrington and Briant, 1979; Whittingham and Huggins, 1972) as shown in Table 11-6. In P or P"-alumina electrolytes, the highest conductivity is observed for the sodium cation and has been attributed to its ideal size (Kennedy, 1977). The mobility of divalent and trivalent cations is considerably lower compared to the monovalent cations (Farrington et al.,
608
11 Ceramic Superionic Conductors
3.25 2.75
1=2.25 o
Figure 11-24. Conductivity plots for o - Na + P (Whittingham and Huggins, 1971a), A-Ag + p(Whittingham and Huggins, 1971b), n - N a + p " (Farrington and Briant, 1979) alumina single crystals.
.S 1.75 •Si.25 0.75
O Na* /3-alumina A Ag*/?-alumina • Na*/3"- alumina
0.25 8.0
16.0
12.0
28.0 20.0 24.0 Temperature in 10A-K~1
1988, 1989). The conductivity of stabilized Na + P"-alumina (Li2O or MgO) single crystals is significantly higher (by a factor of 3 - 5) than that of p-alumina (Table 11 -6). This may be associated with the difference in their crystal structure, higher concentra-
Table 11-6. Ionic conductivity and activation energy data for P, P"-alumina single crystals. p, p"-alumina
or in Q * cm
1
E in
kJmor 1 (±2) 25°C
300°C
(temperature range in °C)
0.152 0.087
NH+p b Na + p" c
0.014 0.0067 6.5xl0~ 5 2.2xlO~ 6 1.3 x l 0 ~ 4 1.0xl0~ 6 0.16
0.001 1.7
K + p" c
0.13
0.54
Ag+pLi + P" c
3.8xl0~ 3 0.073 5xlO~ 3 lxlO"4
15.8 (to 820) 16.5 (to 800) 28.4 (to 820) 34.3 (to 800) 18.0 (to 180) 48 (100-300) 21.2 (<25) 11.6 (to 400) 20.3 (< 25) 9.7 (> 100) 18.4 (to 600) 29 (to 160) 29 (to 190)
Na+pa Ag + P a K+pa Tl+pa Li+pa
NH+,H 3 O + P" C a
Whittingham and Huggins (1972); b Frase et al. (1984); c Farrington and Briant (1979), MgO stabilized single crystals.
32.0
36.0
tion of Na + in the conduction planes and the high mobility of Na + in p"-alumina (Kennedy, 1977). Also all the sites for Na + occupation are equivalent in |3"-alumina and channels along conduction paths are more open. The activation energy for ionic conduction for various beta-aluminas varies between 15-30 kJmol" 1 (Hooper, 1977; Kennedy, 1977; Whittingham and Huggins, 1972). In polycrystalline materials, commonly used in technological applications, the total resistivity is considerably higher (up to an order of magnitude) than that in single crystals (Hooper, 1977; Kennedy, 1977). The scatter in the reported values for the total resistivity is rather larger and is partly associated with different porosity, impurity levels, grain orientation and relative proportions of p and P"-phases in the ceramic (Stevens and Binner, 1984; Youngblood et al., 1977; Youngblood and Gordon, 1978). Moreover, because of the anisotropic nature of the material, the lattice conductivity is lower than that in single crystals of the same composition. In polycrystalline materials, grains are randomly distributed and the total resistivity is not a simple addition of the resistance of individual grains
11.4 Types of Ceramic Superionic Conductors
and the grain boundary resistivity. Since the conduction takes place only in two dimensional planes perpendicular to the oaxis, the relative orientation of each grain with respect to its neighboring grains plays a significant role. The tortuosity effect (increased path length for ion migration between the two electrodes), is the ratio of lattice resistivity in polycrystalline materials and the single crystal resistivity perpendicular to the c-axis, and is greater than one in beta-aluminas (Kennedy, 1977; Powers and Mitoff, 1978). The tortuosity effect has been shown to be somewhat dependent on the ceramic fabrication procedure (Ohta et al., 1976; Virkar et al, 1974; Youngblood and Gordon, 1978). The conductivity differences observed in single crystals of p- and p"-alumina phases are also reflected in polycrystalline ceramics. Nearly theoretically dense polycrystalline ceramics with a large proportion of the P"phase give lower values for resistivity. In general, the activation energy for the lattice resistivity in polycrystalline materials is similar to that observed for the single crystal resistivity. Impurities such as SiO2 and CaO added as sintering aids form blocking glassy phases which segregate at the interfaces between grains and at triple points and significantly alter the grain boundary resistivity (Buechele and De Jonghe, 1979; Hsieh and de Jonghe, 1978). However, because of the large activation energy associated with the grain boundary resistivity ( ^ 3 5 - 4 0 k J m o l " 1 ) compared to that for the lattice resistivity (^15-25 kJ mol" 1 ), the contribution of the grain boundary resistivity to the total resistivity above about 200 °C is usually small (Hooper, 1977; Jakubowski and Whitmore, 1979; Kennedy et al., 1979). Na + beta-alumina electrolytes are known to degrade during current passage
609
and during use in the sodium/sulfur battery. The common modes of degradation include an increase in the electrolyte resistivity, crack initiation, growth and failure of the ceramic, and partial reduction leading to the development of electronic conductivity. Ansell (1986) has reviewed different modes of degradation in commercially produced polycrystalline materials. The major applications of p- and p"-alumina electrolytes are in probes for determining metal activity, and in high density batteries for vehicle traction and stationary energy storage. The use of proton conducting beta-alumina electrolytes for hydrogen production and in electrochemical reactors has also been considered (Nicholson et al., 1985; Munshi and Nicholson, 1990). 11.4.3 Proton Conductors
Several types of proton conductors with high ionic conductivity such as Nation, HUO 2 PO 4 • 4H 2 O (HUP), protonic (H 3 O + , NH4) beta-aluminas and Nasicon have been reported for use in environmental and energy related technologies (Chandra, 1988; Canaday etal, 1989; Goodenough et al., 1983; Goodenough etal., 1985; Jensen and Kleitz, 1982; Poulsen, 1989). Materials such as hydrogen-ion conducting beta-alumina and Nasicon can be prepared by ion exchange of their sodium analogue but hydrogen-ion conductivity is some orders of magnitude lower (Canaday et al., 1989; Frase and Farrington, 1984; Frase et al., 1986). The useful operating temperature range for most of these hydrogen-ion conducting electrolytes is below 400 °C because at higher temperatures they are unstable. Iwahara etal. (1981, 1988, 1989) have reported proton-ion conductivity in materials based on SrCeO 3 and BaCeO 3 in
610
11 Ceramic Superionic Conductors
which trivalent cations (Y 3+ , Yb 3 + , Nd 3 + , etc.) are partially substituted for cerium. Typical dopant concentration is around 5%. These materials are normally electronic (p-type) conductors. However, they rapidly develop proton-ion conductivity at high temperatures (800-1000 °C) in the presence of a hydrogen containing atmosphere (pure H 2 or H 2 /H 2 O). The hole conductivity decreases and in pure hydrogen atmosphere, the materials become virtually pure proton-ion conductors [a(H + ) = 10" 2 Q" 1 cm" 1 at 1000°C]. Iwahara and Uchida (1983) confirmed proton conduction in these materials by hydrogen permeation experiments. However, the proton conductivity is an order of magnitude lower than that of oxygen-ions in zirconia-based electrolytes. Proton conductivity has also been observed in ThO 2 (Shores and Rapp, 1972) and KTaO 3 (Wing-Kit and No wick, 1986) based materials but was much lower than observed in systems based on SrCeO 3 and BaCeO 3 . Proton conductivity in SrCeO 3 and BaCeO 3 based materials is a complex function of hydrogen, water and oxygen partial pressures but Iwahara (1988) has proposed the following possible reaction equilibrium for hydrogen incorporation into the oxide lattice: H 2 (g) + 2h' = 2H'
(11-18)
or H 2 O(g) + 2h' = 2H + 1/2 O 2
(11-19)
Applications of these high temperature proton conductors in sensors, fuel cells, hydrogen pumps and electrochemical reactors have been discussed at length by Iwahara (1988, 1989).
11.5 Microstructure and Transport Properties The transport properties of ceramic superionic conductors are considerably affected by the microstructure. The phase assemblage, grain size and its distribution, and the presence and location of impurities all have an influence on the total ionic conductivity. The role of microstructue can be divided broadly into bulk and grain boundary effects. In general, precipitation and growth of secondary phases within the grains of the ceramic influences bulk transport properties whereas precipitation of such phases or segregation of impurity phases at or near the grain boundaries have an effect on the grain boundary resistivity. Since most oxygen-ion conducting solid electrolytes have the fluorite-related structure, the conductivity is mainly isotropic in nature, the tortuosity factor is near unity and for single phase materials the microstructure plays little role in determining the lattice or volume resistivity. However, in anisotropic materials such as beta-aluminas in which ions can migrate only along certain planes, the tortuosity factor is greater than one and the total resistivity depends on the alignment of the grains and is not a simple combination of the grain boundary resistivity and the resistivity of individual grains. In such materials the lattice resistivity is expected to be higher because of the increased path length for ion migration between the two measuring electrodes (Kennedy, 1977). The total conductivity in beta-aluminas depends considerably on the ceramic processing routes used as they affect the grain size and its orientation (Ohta et al., 1976; Youngblood and Gordon, 1978). Increased path length can also occur in isotropic materials due to the presence or the precipitation of low con-
11.5 Microstructure and Transport Properties
ducting phases within the grains. The role of the microstructure in modifying transport properties has been illustrated below by taking some specific examples although the subject has been discussed to some degree in the relevant sections on various ceramic superionic conductors. Figure 11-25 shows micrographs of 7.8 mol% Sc 2 O 3 doped ZrO 2 in the as-sintered form (a) and after annealing at 1000 °C for 672 h (b). The twinned morphology in the as-sintered ceramic microstructure is due to the presence of t'phase. This phase is formed by martensitic transformation on cooling the ceramic from the sintering temperature at which it has a cubic symmetry. On annealing, the metastable t'-phase slowly disproportionates into the cubic phase and tetragonal ZrO 2 precipitates (Fig. ll-25b) leading to substantial reduction in the lattice conductivity (Figure 11-3). In the ZrO 2 -Y 2 O 3 system, all compositions between 2 and 8 mol% Y 2 O 3 show conductivity deterioration when they are annealed in the two (tetragonal + cubic) phase field. Badwal et al. (1990 a), in a systematic study on a high purity 3 mol% Y 2 O 3 -ZrO 2 composition report an increase in the lattice resistivity as a result of annealing between 600 and 1500°C (Fig. 11-26). The maximum increase occurred at the annealing temperature of 1100°C. Transmission electron microscopy showed a complex substructure within the grains (Fig. 11-27). It consisted of large yttrium concentration gradients, tetragonal phase variants with respect to solute and regions of monoclinic phase. Energy dispersive analysis by X-rays gave a clear indication of solute partitioning. The degree of this substructure was most intense for specimens annealed at 1100°C. Both CaO and MgO-PSZ have very good thermomechanical properties. These
611
(b) Figure 11-25. Transmission electron micrographs of 7.8 mol% Sc 2 O 3 -ZrO 2 ; (a) as-sintered and (b) after annealing at 1000 °C for 672 h. Micrographs courtesy of J. Drennan.
612
11 Ceramic Superionic Conductors
37500
35000
Figure 11-26. Lattice resistivity of 3 mol% Y 2 O 3 -ZrO 2 as a function of the annealing temperature. Annealing time: 50 h at each temperature.
25000 300
500
700 900 T (anneal) in °C
1100
ceramics are sintered in the cubic phase field followed by heat treatment in the 1100-1400 °C range to coarsen the tetragonal zirconia particles to achieve the desired thermomechanical properties. However, the electrical properties deteriorate quite considerably as a result of annealing. Figure 11-28 shows the microstructure of 3.4 wt% MgO-ZrO 2 before (a) and after (b) annealing at the modest temperature of 1000 °C for 110 h. A small increase in the m-ZrO 2 especially at grain boundaries due to the decomposition of PSZ (clearly visible as white areas in Fig. 11-28 b) leads to a large increase in both the lattice (minor) and the grain boundary (major) resistivity (Fig. 11-29). Numerous papers have been published describing the role segregated impurities play in modifying the grain boundary and the total resistivity of ceramic superionic conductors (Badwal, 1990; Badwal and Drennan, 1990; Buechele and De Jonghe, 1979; Gerhardt et al, 1986; Hsieh and De Jonghe, 1978; Kleitz et al., 1981; Rajendran et al, 1987; Tanaka et al, 1987; Wang and No wick, 1980). Impurities are often added as sintering aids to obtain higher density and/or to lower the sintering temperature of the ceramic. Alternatively impurities
1300
1500
may be present in the starting materials or are incorporated during powder processing and ceramic fabrication. These impurities form amorphous or glassy phases during sintering and or subsequent treatments, and have a tendency to segregate to the external surface and within the ceramic at triple grain junctions and at interfaces between grains. The mechanism by which these phases form is complex and the exact composition of the grain boundary phase is difficult to determine when it is present as a thin intergranular layer. Quantitative analysis is available only when they are present in large quantities at one place such as at triple points and the external surface of the ceramic (Badwal et al., 1988, 1991). The glassy phases have the potential to alter the composition of the bulk phase especially in the near interface region. In oxygen-ion conducting solid electrolytes silicon is the most commonly detected impurity along with segregation of one or more components of the bulk phase. Figure 11-30 shows an energy dispersive Xray spectrum taken from the triple grain junction of a ZrO 2 -Y 2 O 3 ceramic. It clearly shows the presence of Si along with enhanced segregation of Y. The physical and chemical nature of the segregated
11.5 Microstructure and Transport Properties
613
Figure 11-27. Transmission electron micrograph showing substructure within the grains of a 3 mol% Y 2 O 3 ZrO 2 specimen annealed at 1000°Cfor 50 h. (a) Bright field (central white area monoclinic zirconia precipitates) and (b) dark field image. Micrographs courtesy of R. H. J. Hannink.
Figure 11-28. Optical micrographs of 3.4 wt.% MgO-PSZ (a) as-sintered, (b) after ageing at 1000 °C for 110 h. Micrographs courtesy of J. Drennan. (a)
(b)
As fired
Aged 1000°C for 110h
300000 450°C
10k cs c
100k
1k
150000
Figure 11-29. Impedance spectra at 450 °C for 3.4 wt% MgO-PSZ (o) assintered and (•) after ageing at 1000 °C for HOh.
TS grade o as fired . aged at 1000°C (110 h)
150000
300000
450000
Z' in Qcm
600000
750000
614
11 Ceramic Superionic Conductors
Figure 11-30. Energy dispersive X-ray spectrum of (a) a triple point and (b) an adjoining grain in a Y 2 O 3 -ZrO 2 ceramic showing silicon and enhanced yttrium segregation at triple grain junction. Courtesy of J. Drennan.
phases and their location within the ceramic determine the contribution to the grain boundary resistivity. Impurities phases in general have low ionic conductivity and those which wet the grains better are likely to be more effective in blocking charge carrying species. Badwal et al. (1991) have discussed various models proposed in the literature to describe the mechanism of ion transport across grain boundaries in oxygen-ion conducting solid electrolytes. These models are based on either a continuous grain boundary layer surrounding each single grain or an aggregate of grains, or a discontinuous grain boundary layer. Evidence for both continuous and discontinuous grain boundary layers has been provided based on the transmission electron microscopy work (Badwal et al., 1991; Gerhardt et al., 1986; McCartney, 1987; Ruhle
etal, 1984; Tanaka et al., 1987). Figure 11-31 a shows the existence of a more continuous grain boundary phase in a ceramic containing a large amount of impurities. The impedance behaviour is shown in Fig. 11-32 a. Figure 11-31 b is a high resolution transmission electron micrograph showing direct grain to grain contact and the absence of a grain boundary phase at grain boundaries. The micrograph was taken from high purity (SiO2 content is 20 ppm) 3 mol% Y 2 O 3 tetragonal ZrO 2 ceramic the impedance' behaviour of which is shown in Fig. 11-32 b. As expected the grain boundary resistivity in the ceramic with the more continuous grain boundary layer is significantly higher. Although it is possible to have two extremes of clean grain boundaries or a continuous grain boundary layer, no single model based either on continuous or partially covering
11.5 Microstructure and Transport Properties
(a)
615
(b)
Figure 11-31. Transmission electron micrographs of 3 mol% Y 2 O 3 -ZrO 2 ceramics; (a) more continuous grain boundary phase and (b) clean grain boundary. Micrographs courtesy of I Drennan and R. H. J. Hannink.
300000 - (a)
350°C
°°°
o°° o o
150000
f
X
& o o o
E o c; c
0.
0000
D
300000
600000 350°C
(b)
o° ° • " " ° ' " \
10000 cP (P
V
o0ooo0
QO
0
20000
40000 ZA in ft cm
Figure 11-32. Impedance spectra at 350 °C as per Fig. 11-31; for the ceramic with (a) more continuous grain boundary phase, (b) relatively clean grain boundaries.
616
11 Ceramic Superionic Conductors
grain boundary layers, or in the absence of impurities, on intrinsic effects (such as space charge layers resulting from lattice irregularities, imperfect contact between grains, nano- or micro-cracks) alone can describe the grain boundary behaviour for all ceramics. The magnitude of the grain boundary resistivity varies significantly with the level and type of impurities in the ceramic, the grain boundary density or surface area and the nature and location of the grain boundary phase. In addition the nature and location of the grain boundary impurity phase(s) can be altered by the ceramic processing conditions such as sintering temperature, heating and cooling rates, post-sinter heat treatments, and mechanical loading of the ceramic at high temperatures (Badwal and Drennan, 1989; Badwal, 1990; Badwal et al., 1990 b; Badwal and Drennan, 1990). Migration of the grain boundary phase (s) to the external surface during post-sinter heat treatments also affects the grain boundary resistivity (Hughes and Badwal, 1990). In general, materials with high levels of glassy impurities have high grain boundary resistivity and the measured grain boundary resistivity (macroscopic value
105000
o-1300°C
D-1500°C
without allowing for unit dimensions of the grain boundary layer) usually decreases with increasing grain size or the sintering temperature (Fig. 11-33). Often the appearance of an inflection (Badwal and Drennan, 1987) or initially an increase (Badwal, 1990) in the grain boundary resistivity as a function of the sintering temperature has been observed as shown in Fig. 11-34 for a 3 mol% Y 2 O 3 -ZrO 2 composition. This behaviour has been attributed to the dynamic nature of the grain boundary phase. Transmission electron microscopy, and Xray photoelectron spectroscopy of the fractured surfaces of specimens sintered at different temperatures indicated maximum spreading (wetting) of the grain boundary phase at the peak or the inflection temperature (Hughes and Sexton, 1989; Badwal et al., 1988). Above this temperature, the grain boundary phase gets relocated to the external surface and triple grain junctions (Badwal and Drennan, 1990; Hughes and Badwal, 1990). Additions of silica based impurities and materials such as Li 2 O and SrO lead to an increase in the grain boundary resistivity (Badwal, 1990) but the addition of alumina has been reported to be beneficial. In fact,
A-1700°C
E 70000
o G c
Figure 11-33. Effect of increasing sintering temperature (and grain growth) on the grain boundary resistivity of a 3 mol% Y 2 O 3 -ZrO 2 ceramic at 350 °C.
35000
175000
11.6 Devices Based on Ceramic Superionic Conductors
617
60000 -
10000
1150
Figure 11-34. Variation of the grain boundary (o) and the lattice (•) resistivity at 375 °C as a function of the sintering temperature. 1250
1350
U50 1550 Temperature in °C
Rajendran etal. (1987) observed a reduction in the grain boundary resistivity by a factor of six on addition of 10wt.% alumina to 2.5 mol% Y 2 O 3 -ZrO 2 . Transmission electron microscopy of these materials (accumulations of the grain boundary phase near alumina grains) and the work of Drennan and Butler (1984) and Hughes and Rajendran (1989) strongly suggests that alumina reacts with the grain boundary phase and effectively removes it from the conduction paths. In order to understand the complex nature of grain boundary segregation, a systematic study involving impedance spectroscopy, analytical electron microscopy techniques and surface analysis (Auger, XPS) techniques combined with controlled ceramic processing conditions is necessary.
11.6 Devices Based on Ceramic Superionic Conductors 11.6.1 Sensors Sensors based on superionic conductors have been in use for several years for pollution and safety monitoring, control and
1650
1750
automation of industrial processes and energy conservation. Their use has already resulted in considerable reductions in fuel consumption and in the emission of toxic gases to the atmosphere. A number of different types of sensors have been developed and several are commercially available (Aucouturier et al., 1986; Badwal et al, 1987; Kleitz et al, 1990; Moseley and Tofield, 1987; Seiyama etal, 1983; Williams and McGeehin, 1984). The more commonly used potentiometric sensor consists of an impervious electrolyte membrane and two electrodes which equilibrate the electroactive species in the gas phase with conducting ions in the solid electrolyte (Fig. 11-35). Both electrode compartments are hermetically sealed from each other. The EMF signal is established by the difference in the concentration of the electroactive species at each electrode/electrolyte interface and is given by Eq. (11-13) with t\w = unity. The concentration on one side of the cell is fixed by a reference gas/ electrode. For cells based on an oxygen-ion conducting solid electrolyte, an inert electrode and air or a sealed metal/metal oxide composite with well defined thermodynamic potential is used to fix the oxygen concentration on one side of the cell.
618
11 Ceramic Superionic Conductors Electrolyte Unknown atmosphere
Reference gas
•
Electrode (Glass or metal/ceramic seal) Glass,metal or ceramic ~ tube
High grade_ alumina tube
\W\\W
WWWW
Reference gas
W
1
Electrode
Ceramic weld seal Reference gas
Electrolyte
Reference gas
Glass seal
-Electrode
Electrolyte ^-Electrode
Wire
Unknown atmosphere
Figure 11-35. Schematics of various designs for the potentiometric sensors.
Ceramic plug
Potentiometric sensors based on fully or partially stabilized zirconia have been developed for a variety of applications and cover a wide temperature (300-1600 °C) and oxygen partial pressure (1 - 1 0 " 2 5 atm) ranges. The major application areas are the monitoring of oxygen in molten metals, air/fuel radio control in automotive exhausts, monitoring and control of atmospheres in heat treatment furnaces and combustion control in boilers. Oxygen sensors are currently in use in automotive exhausts for effective and efficient performance of the three-way catalytic converters near the stoichiometric air/ fuel ratio (McGeehin, 1981). A three-way catalytic converter is used to reduce harmful emissions of NO^, CO and hydrocarbons (Young, 1983). The use of the sensor for this operation is relatively straightfor-
ward. An oxygen sensor located in the exhaust manifold is used as a switch to monitor fuel rich or fuel lean environments. The EMF signal of the potentiometric sensor changes by several hundreds of mV near the stoichiometric air/fuel ratio due to a large change in the oxygen partial pressure (Fig. 11-36) and is used in the controlled loop feed back mode to control the air/fuel ratio. High accuracy is not required from the sensor output although fast response times (typically in the vicinity of 100 ms range) are a prerequisite. Better fuel economy and low emission levels can be achieved when the engine is running in the lean fuel regime. However, for this operation a precise control of air/ fuel ratio is required (Takeuchi, 1986). Unfortunately in the lean burn range, the output signal from a potentiometric sensor is
11.6 Devices Based on Ceramic Superionic Conductors
small and it does not change significantly with change in the oxygen concentration because of the logarithmic relationship between the EMF signal and the oxygen partial pressure. Moreover, potentiometric sensors are not accurate especially when the cell operating temperature is below 500-600 °C because of the difficulty in establishing equilibrium at the electrode/electrolyte interface and interference from hydrocarbons in the exhaust gases. For lean burn operation of the car engine a number of sensors operating on the oxygen pumping principle have been or are currently under development and have been discussed in detail by Kleitz et al. (1990), Maskell (1987), Takeuchi (1986), and Williams and McGeehin (1984). Such sensors consist of a single zirconia cell with a diffusion barrier or cavity constructed on the cathode side or two zirconia cells Stoichiometric Rich *
I
•Lean
1200
10:1
12:1
tt:1 Air/fuel ratio
16:1
18:1
Figure 11-36. A change in the output of a potentiometric oxygen sensor as a function of the air/fuel ratio (McGeehin, 1981).
619
joined back to back and held a fixed distance apart with a spacer and may or may not have a diffusion capillary connecting the fixed volume to the unknown atmosphere (Fig. 11-37). In one mode of operation, oxygen is electrochemically pumped out from the cavity until the voltage rises rapidly corresponding to a very low oxygen partial pressure at the cathode. The voltage signal is measured with the same cell (single cell) or with the second cell (in a two cell assembly) operating in the potentiometric mode. The current is then reversed and from the charge required to achieve the same partial pressure on the inside and outside of the cavity, the oxygen partial pressure of the unknown gas can be determined by applying Faraday's law. Such time measuring devices are accurate and simple. In another mode of operation, on pumping oxygen out at a certain predetermined rate, a diffusion barrier is set up and the current is then proportional to the diffusion flux (Kleitz et al., 1990; Maskell, 1987). One major advantage of the current mode sensing devices is that they provide a linear relationship between current and oxygen partial pressure on application of an external bias (Takeuchi, 1986). In metal manufacture, a precise control of temperature and oxygen partial pressure in various oxidation and reduction processes, is important to the quality of the final refined product. Oxygen either dissolved or in the form of an oxide plays a significant role in deciding the properties of the metal. For this reason sensors are used for monitoring oxygen in the exhaust gases as well as in molten metals. The sensors for use in molten metal are directly dipped into the molten mass and therefore are constructed from materials with high thermal shock resistance such as partially stabilized zirconia. Considerable advances have been made in developing sensors for
620
11 Ceramic Superionic Conductors Porous ceramic Diffusion barrier
Electrolyte . Electrode Leak aperture
Electrolyte
Electrode Electrolyte —•
• Pump cell
Spacer Sensor cell
"Pump cell Leak aperture Electrolyte -
^—Spacer (V) Sensor cell
use in molten steel (operating temperature around 1600 °C) and several different types are commercially available (Goto and Nagata, 1988). These sensors, however, have a short life of 1 - 5 min and are expendable. Attempts have been made to improve the life of these sensors by improved sensor design (Worrell and Liu, 1986). The use of oxygen sensors in molten metal have been described by a number of authors (Deo and Tare, 1971; Etsell and Flengas, 1972; Foroulis and Smeltzer, 1975; Goto and Nagata, 1988; Jagannathan et al., 1980; Janke, 1981). Other oxygen sensors developed and utilizing an O 2 ~ conducting solid electrolyte include a miniature probe, essen-
Figure 11-37. Schematics of various electrochemial pumping type oxygen sensors.
tially a potentiometric sensor using a sealed Pd/PdO reference electrode (Vitter et al., 1983), and a sensor based on the corrosion properties of Pd (de Bruin and Badwal, 1980; de Bruin et al., 1982). The latter authors have shown that the formation of PdO at the electrode/electrolyte interface, which is a function of temperature and oxygen partial pressure, is accompanied by orders of magnitude increase in the electrode resistance. Thus the existence or absence of PdO can be detected'and related to oxygen partial pressure by monitoring the impedance (at a low frequency) as a function of temperature or alternatively at a constant temperature by applying a DC voltage ramp.
11.6 Devices Based on Ceramic Superionic Conductors
A number of other sensors for monitoring gaseous and molten systems have been discussed (Aucouturier et al, 1986; Seiyama et al., 1983). For example sensors based on H + , NH^, and H 3 O + conducting solid electrolytes have been suggested for monitoring hydrogen concentrations in gases. Sodium beta-alumina has been used for determining sodium activity in sodium based alloys and in silicate melts, Ag substituted beta-alumina has been used for determining Ag activity in silver alloys (Barker et al., 1983). Metal substituted beta aluminas have also been considered for monitoring sulfur activity in metal sulfides.
oxide, sulfur dioxide to sulfur trioxide, ammonia to nitric oxide, for decomposition of nitric oxide, for the production of hydrogen cyanide and for the study of numerous oxidation reduction reactions (Di Cosimo etal., 1986; Gellings et al., 1988; Kiratzis and Stoukides, 1987; Lintz and Vayenas, 1989; Michaels and Vayenas, 1984; Stoukides, 1988). Proton conductors can also be used in heterogeneous catalysis for hydrogenation and dehydrogenation reactions. Iwahara (1988) has discussed the use of high temperature proton conductors based on SrCeO 3 for dehydrogenation reactions such as ethane to ethylene. The principle of an electrochemical reactor is demonstrated in Fig. 11-38 taking the example of an oxygen-ion conducting solid electrolyte. One side of the cell (cathode) is exposed to air or oxygen and the other side to a reaction mixture or the chemical to be oxidized. The activity of oxygen on the anode side of the cell can be substantially increased by application of a DC bias or shorting the cell through a load. The selectivity to partial oxidation/ reduction reactions and enhancement of reaction rates can be achieved by the suitable choice of a catalytic electrode or electrode/catalyst mixture and by the careful
11.6.2 Electrochemical Reactors
Interest in electrochemical reactors stems from the fact that solid electrolyte cells can be used to produce industrially important chemicals by the partial oxidation or reduction of organic or inorganic compounds in a controlled fashion. Most of the studies so far have concentrated on oxygenion or proton conductors. Solid electrolyte cells based on oxygen-ion conductors have already been used to convert ethyl benzene to styrene, propylene to propylene oxide, butene to butadiene, ethylene to ethylene
Cathode
621
Anode
•-
CH A +NH 3 +30 2 "
Electrolyte
o2- —
(Ethylbenzene)
(Styrene)
C 3 H 6 + O 2 -—-C 3 H 6 CU2e 2
2NH 3 + 5 0 ~ — - 2N0 + 3H 2 0 + 10e CH3OH + 0"2' — - HCHO + H 2 0 + 2e
Electrode/catalyst
Figure 11-38. Operating principle of an electrochemical reactor based on a oxygen-ion conducting solid electrolyte.
622
11 Ceramic Superionic Conductors
control of ion migration through the solid electrolyte. In fact considerable enhancement in the catalytic rates for the electrode materials appears to occur under an applied potential. These rates are well above what can be accounted for by the oxygenion transport rates. This phenomenon has been reported and discussed by Gellings et al. (1988) and Vayenas et al. (1989). Many cells, in principle, can be used in the combined electrochemical reactor/fuel cell mode to cogenerate chemicals as well as electricity although considerable work needs to be done before such systems are commercially viable. 11.6.3 Electrochemical Pumps
Solid electrolytes can also be used for gas separation because of their selectivity to only one type of charge carrying species. As an example, only oxygen ions can migrate in zirconia based electrolytes. Thus on application of an electric field across the cell pure oxygen can be generated at the anode. Such devices have a bifunctional role and can be used to electrochemically pump oxygen in or out of a stationary or a dynamic system. Their major applications are in controlled atmosphere heat treatment furnaces and in the preparation of calibration gases. They may also find applications in the food packaging industry or in the medical area if the cells can be made to economically produce large quantities of oxygen for low energy consumption. Using proton conducting solid electrolytes, hydrogen can be extracted from gases such as ethane or a mixture of steam and carbon monoxide on one side of the cell and generated on the other side (Iwahara, 1988).
11.6.4 Hydrogen Production
Hydrogen is a gas of considerable commercial importance. It is a clean fuel of the future but no cheap way of producing hydrogen in large quantities is economically viable. Hydrogen burnt in a fuel cell produces no greenhouse gases or pollutants such as SO^ or NO X . In this regard medium to high temperature solid electrolyte cells based on O 2 ~, H + and H 3 O + have been proposed for the electrolysis of steam (Doenitz and Schmidberger, 1982; Iwahara, 1988; Nicholson, 1988). Bockris (1975) has shown that the high temperature steam electrolysis can be carried out quite efficiently provided that the cell was absorbing heat from an external source (e.g., solar heat or waste heat from a nuclear power plant) because of the endothermic nature of the water dissociation reaction. At 1000 °C about 46% of the energy required to dissociate water could be supplied as heat to the cell from an external source. The operating principles of three different types of hydrogen production cells are shown in Fig. 11-39. In the first cell which utilizes an oxygenion conducting solid electrolyte and operates at 800-1000 °C, steam is converted to hydrogen and O 2 ~ at the cathode. Pure oxygen is generated at the anode and hydrogen and excess steam comes from the cathode compartment. The concept, design, advantages and limitations of high temperature steam electrolysis have been discussed by several authors (Doenitz and Schmidberger, 1982; Isaacs, 1981; Spacil and Tedmon, 1969). The second type of hydrogen production cells using SrCeO 3 or BaCeO 3 based materials have been considered by Iwahara (1988). At the anode, steam is converted to protons and oxygen, and pure hydrogen is generated at the cathode. These cells operate in the vicinity
11.6 Devices Based on Ceramic Superionic Conductors
623
a) High temperature Battery Anode
Cathode
H20 + 2e — H2
--—1/20 2 + 2e (Air)
b) High temperature
Battery
Anode
Cathode
C0 + H 2 0 — C0 2 + 2H* + 2e • C2H6 —C 2 H 4 + 2H%2
Electrolyte |
H20 —-0 2 + 2H%2
c) Low temperature Anode
Battery Cathode
Figure 11-39. Operating principles H20 -*• 2H+ + 1 / 2 0 2 3H2O
of 800 °C. The steam electrolysis cells based on H 3 O and NH4 beta-alumina electrolytes (operating temperature around 200 °C) have been discussed by Nicholson (1988) and Munshi and Nicholson (1990). The ionic conductivity of H 3 O + betaalumina is much lower than that of NH4 beta-alumina but the latter is stable only up to 200 °C. Most of these cells are of an experimental nature and several practical problems remain to be solved before they can be seriously considered for hydrogen production. If economically developed, cells of this type are attractive not only for hydrogen production but also for load leveling purposes. They can be electrically driven to
of three different types of solid electrolyte steam electrolysis cells.
produce hydrogen during off-peak load hours by consuming excess electricity. During peak load hours they can be used in the fuel cell mode (see below) to convert hydrogen back to electricity. 11.6.5 Fuel Cells A fuel cell is an electrochemical cell which converts the chemical energy of a fuel oxidation reaction to electricity with high efficiency. The efficiency of a fuel cell is not limited by the Carnot cycle, and fuel/ electric efficiencies up to 60% are achievable for high temperature (solid oxide and molten carbonate) fuel cells without heat recovery. The overall fuel conversion effi-
624
11 Ceramic Superionic Conductors
ciency can be further enhanced by heat recovery to about 80%. Fuel cells are a low polluting technology. The SOX and NO X emissions from a fuel cell are expected to be at least an order of magnitude lower than the competing conventional combustion engine technologies. Also because of the inherent high efficiency of fuel cells, the amount of carbon dioxide produced per unit energy generated is low. Fuel cells are likely to compete in the near future with conventional power generation technologies and several different types of fuel cells are currently under development for dispersed (at load centers) and central station power generation (Lovering, 1989). The third generation (solid oxide or ceramic) fuel cell has been pioneered by Westinghouse Electric Corporation and is based on the oxygen-ion conducting solid electrolyte Y 2 O 3 -ZrO 2 . The principle of operation of the cell is shown in Fig. 11-40. The open circuit voltage signal (£ocv) across the electrolyte membrane is established by the presence of a fuel environment (low oxygen partial pressure) on one side and air (oxidant) on the other and can be calculated from the free energy (AG) of the fuel combustion reaction at the cell operating temperature or from the difference in the oxygen partial pressure on both sides of the fuel cell: £ O C V =-AG/(4F) = RT/(4F)]n(p'oJp"oJ
Cathode
(11-20)
When the cell is shorted through an external load, oxygen at the cathode is reduced to oxygen-ions which migrate through the electrolyte under the potential gradient and react with the fuel at the anode. The fuel/electric efficiency ((pFiE) is about 60% and at the cell operating temperature is given by: (pF,E = (AG/AH)(E/EoJ = -4EF/AH
(11-21)
and E = Eocy-IR-V
(11-22)
where IR is the resistive voltage loss within the cell and V is the combined overpotential loss at both electrode/electrolyte interfaces. The solid oxide fuel cell (SOFC) operates at 1000 °C and one of the by-products is high quality heat which can be recovered in the form of electricity (combined cycle) or used for space heating or in industrial processes. Thus the overall efficiency of the solid oxide fuel cell with heat recovery can be close to 75-80%. The SOFC is fuel flexible and can operate on a large number of gaseous fuels. Because of its high operating temperature both direct and indirect in-situ reforming of natural gas may be possible. Direct oxidation of natural gas is particularly attractive for combined heat and power generation at load centers as extensive gas distribution grids exist in
Anode
— H 2 0 + 2e (Air)
Figure 11-40. Operating principle of the solid oxide fuel cell.
11.6 Devices Based on Ceramic Superionic Conductors
many countries. However, to achieve this suitable catalytic electrodes need to be developed to avoid carbon deposition. Westinghouse has already tested 3-5 kW SOFC prototypes of tubular design and construction of 25-100 kW prototype units appears possible in the near future (Dollard, 1989). These fuel cells utilize Y 2 O 3 stabilized ZrO 2 as the electrolyte, Ni/ZrO 2 cermet as anode, Sr doped LaMnO 3 as cathode and doped LaCrO 3 as the interconnection material. The power density for this tubular design is low and fabrication costs somewhat high. For this reason planar and monolithic cell designs, which potentially offer high power density (> 1 MW/m3) and low fabrication costs, are currently under investigation. However, the high operating temperature of the SOFC puts severe constraints on the materials and considerable research and development effort is required (Singhal, 1989; SOFC-Nagoya, 1989). Other types of ceramic fuel cells mentioned in the literature are those based on perovskite materials such as SrCeO 3 , BaCeO 3 discussed earlier (Iwahara, 1988, 1989). However, proton conductivity in these materials is developed only in the presence of pure hydrogen, and is an order of magnitude lower than the oxygen-ion conductivity in ZrO 2 -Y 2 O 3 electrolytes. Moreover, fabrication of these materials is not an easy process. No significant progress has been made on such fuel cells. 11.6.6 Batteries A number of solid state high energy density storage batteries based on ceramic superionic conductors are currently under development for utility load leveling and vehicle traction application in the USA, Japan and Europe (Fischer, 1989; Kennedy, 1977; Linden, 1984; Scholtens and van
625
Gool, 1978). The first sodium/sulfur battery utilizing sodium beta-alumina electrolyte was proposed by Weber and Kummer (1967) some 23 years ago. Both anode (sodium) and cathode (sulfur) are in the molten state. The beta-alumina is fabricated either as flat plates or in the form of closed end tubes and separates both electrodes. During discharge molten sodium held for example in a beta-alumina tube is converted to Na + at the anode. Sodium ions migrate through the electrolyte and react with sulfur held in an outer stainless steel container. The overall cell reaction is: 2Na + x S = Na2SJC
(11-23)
with theoretical energy density of 760 Wh/kg. The discharge takes place through a number of intermediate steps but is a stopped at Na2"S3 to avoid solidification of polysulfide. The battery must be operated above 285 °C to keep the electrodes and reaction products formed during the discharge in the molten state. The normal operating temperature is between 300-350 °C. Although prototypes ranging in capacity up to 400 kWh have been manufactured (Takahashi, 1988), the battery still suffers from long term degradation associated mainly with the electrolyte stability and corrosion of the battery construction materials (Ansell, 1986). Also, because of the reactive nature of both the electrode materials used in this battery system, special fabrication and handling procedures are required. A further development is the so-called "Zebra" battery (Coetzer, 1986). This battery utilizes two Na + conductors, NaAlCl4 in the cathode compartment and Na + beta alumina electrolyte as a separator between anode and cathode compartments. The use of NaAlCl4 allows the battery operating temperature to be -much lower (250260 °C). The molten sulfur cathode of the
626
11 Ceramic Superionic Conductors
sodium/sulfur battery is replaced by FeCl 2 , molten NaAlCl4 electrolyte and a metallic iron current collector. A small amount of nickel chloride is added to control over charge of the battery. The open circuit voltage of the battery is slightly higher (2.35 V for Fe and 2.59 V for Ni) than that of the Na/S battery (2.08 V). The theoretical energy density is around 700 Wh/kg. The battery is assembled in the discharged state [NaCl and metallic Fe (Ni) in the cathode compartment]. The sodium electrode is generated by electrolysis during the charge cycle (2 NaCl + Fe -> FeCl2 + 2Na). Many of the chemical corrosion, operational and fabrication problems associated with the sodium/sulfur battery are significantly reduced in the Zebra battery. This battery is well thought out and has the potential to replace the sodium/sulfur battery. 11.6.7 Miscellaneous Applications
Apart from the use of superionic conductors in applications discussed above these materials have been tried in several other devices such as timers, capacitors, coulometers, heating elements for furnaces and thermoelectric convertors. With the appropriate selection of electrodes, the charging characteristics of an electrode/ electrolyte interface and hence the capacitance can be changed. Such devices have high capacitance and can be used to store energy temporarily. The major drawback is their low decomposition voltage. The cells of the type, reversible electrode/electrolyte reversible electrode-blocking electrode have been suggested as timers. On application of a constant current, the material is transported from the right side of the cell to the left. Once the reversible electrode has been exhausted no further current can flow and the voltage rises sharply. By controlling the value of the constant
current and the amount of the reversible electrode on the right hand side of the cell, timers of duration ranging up to several months can be made. A coulometer works in a similar fashion to the timer except that the charge passed is determined by measuring the amount of the material transported through the cell from the Faraday law. Furnaces utilizing zirconia-based solid electrolyte as the heating elements and capable of operating in oxidizing environments up to 2000 °C are now commercially available. The alkali metal thermoelectric convertor or the sodium heat engine based on Na + beta-alumina electrolyte is under development (Prasad et al., 1983; Takahashi, 1988) for direct conversion of heat to electricity (efficiency around 20-25%). The thermoelectric convertor is a sodium concentration cell in which electric power is obtained from heat by generating different sodium vapour pressures on either side of the electrolyte.
11.7 Acknowledgements The author is thankful to Drs. K. Foger and M. J. Bannister for reviewing this manuscript.
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Subbarao, E. C , Sutter, P. H., Hrizo, X (1965), /. Am. Ceram. Soc. 48, 443-446. Suzuki, Y, Takahashi, T., Nagae, N. (1981), Solid State Ionics 3/4,483-487. Swain, M. V. (1989), Materials Forum 13, 237-253. Takahashi, T. (1972), in: Physics of Solid Electrolytes, Vol. 2: Hladik, J. (Ed.). London: Academic Press, pp. 989-1049. Takahashi, T. (1988), in: Proc. Solid State Ionic Devices, July 18-23, Singapore: Chowdari, B. V. R., Radhakrishna, S. (Eds.). Singapore: World Scientific, pp. 95-103. Takahashi, T, Iwahara, H. (1973), /. Appl Electrochem. 3, 65-72. Takahashi, T., Esaka, X, Iwahara, H. (1975), /. Appl. Electrochem. 2, 197-202. Takahashi, T, Iwahara, H., Esaka, T. (1977), /. Electrochem. Soc. 124, 1563-1569. Takeuchi, T. (1986), in: Proc. 2. International Meeting on Chemical Sensors, July 7—10, Bordeaux: Aucouturier, X-L., Cauhape, X-S., Destriau, M., Hagenmuller, P., Lucat, C , Menil, R, Portier, X, Salardenne, X (Eds.). Bordeaux, pp. 69-78. Tallan, N. M. (1974), in: Electrical Conductivity in Ceramic and Glasses, Parts A and B. New York: Marcel Dekker Inc. Tanaka, X, Baumard, X R, Abelard, P. (1987), / Am. Ceram. Soc. 70, 637-643. Tannenberger, H., Schachner, H., Kovacs, P. (1966), Revue Energie Primaire 2, 19—26. Tare, V. B., Ramana Rao, A. V., Ramanarayanan, T. A. (1980), in: Solid Electrolytes and their Applications, Subbarao, E. C. (Ed.). New York: Plenum Press, pp. 165-199. Thornber, M. R., Bevan, D. X M., Summerville, E. (1970), J. Solid State Chem. 1, 545-553. Tien, T. Y, Subbarao, E. C. (1963), /. Chem. Phys. 39, 1041-1047. Tsai, Y X, Whitmore, D. H. (1982), Solid State Ionics 7, 129-139. Tuller, H. L., Nowick, A. S. (1975), /. Electrochem. Soc. 257, 255-259. van Dijk, T. (1981), Thesis, Twente University of Technology, Enschede, Netherlands. van Dijk, T., Helmholdt, R. B., Burggraaf, A. X (1980 a), Phys. Stat. Sol. (b) 101, 765-774. van Dijk, T, de Vries, K. X, Burggraaf, A. X (1980 b), Phys. Stat. Sol (a) 58, 115-125. van Dijk, M. P. (1985), Thesis, Twente University of Technology, Enschede, Netherlands. van Dijk, M. P., ter Maat, J . H . H , Roelofs, G., Bosch, H., van de Velde, G. M. H., Gelling, P. X, Burggraaf, A. X (1984), Mat. Res. Bull. 19, 11491156. van Gool, W. (1973), in: Fast Ion Transport in Solids. Amsterdam: North Holland Publishing Company. Van Handel, G. X, Blumenthal, R. N. (1974), /. Electrochem. Soc. 121, 1198-1202.
Vashishta, P., Mundy, J. N., Shenoy, G. K. (1979) (Eds.), in: Fast Ion Transport in Solids, Electrodes and Electrolytes. New York: North Holland. Vayenas, C. G., Bebelis, S., Neophytides, S., Yentekakis, I. V. (1989), Appl. Phys. A 49, 95-103. Verkerk, M. X (1982), Thesis, Twente University of Technology, Enschede, Netherlands. Verkerk, M. X, Burggraaf, A. X (1981), J. Electrochem. Soc. 128, 75-82. Verkerk, M. X, Keizer, K., Burggraaf, A. X (1980), /. Appl. Electrochem. 10, 81-90. Verkerk, M. X, Van de Valde, G. M. H., Burggraaf, A. X (1982), J. Phys. Chem. Solids. 43, 1129-1136. Vetter, K. X (1967), in: Electrochemical Kinetics, Theoretical and Experimental Aspects. New York: Academic Press. Virkar, A. V, Tennenhouse, G. X, Gordon, R. S. (1974), /. Am. Ceram. Soc. 57, 508. Vitter, G., Foster, P., Lahlou, M., Gutierrez Monreal, RX (1983), Solid State Ionics 9110, 12731276. Vlasov, A. N., Perfiliev, M. V. (1987), Solid State Ionics 25, 245-253. Wagner, C. (1933), Z. Phys. Chem. B21, 25-41. Wagner, C. (1957), in: Proc. Int. Committee Electrochem. Thermodyn. Kinetics (CITEC) 7, 361377. Wagner, C. (1975), Progr. Solid State Chem. 10, 3-16. Wang, Da Yu, Nowick, A. S. (1980), /. Solid State Chem. 35, 325-333. Wang, Da Yu, Park, D. S., Griffith, X, Nowick, A. S. (1981), Solid State Ionics 2, 95-105. Watanabe, A., Kikuchi, T. (1986), Solid State Ionics 21, 287-291. Weber, N., Kummer, X T. (1967), Proc. Annu. Power Sources Conf. 21, 37-39. Weppner, W, Schulz, H. (1988), in: Solid State Ionics - 87 Confr. Proc. Amsterdam: North Holland. Wheat, T. A., Ahmad, A., Kuriakose, A. K. (1983) (Eds.), in: Progress in Solid Electrolytes, Energy Mines and Resources: Wheat, T. A., Ahmad, A., Kuriahose, A. K. (Eds.). Ottawa: Erp/MSL 83-94 (TR). Whittingham, M.S., Huggins, R. A. (1971a), J Chem. Phys. 54, 414-416. Whittingham, M. S., Huggins, R. A. (1971 b), /. Electrochem. Soc. 118, 1-6. Whittingham, M.S., Huggins, R. A. (1972), NBS Special Publication 364, Solid State Chemistry, Proc. 5th Mater. Res. Symp., 139-154. Wiedersich, H., Geller, S. (1970), in: The Chemistry of Extended Defects in Non-metallic Solids: Eyring, L., O'Keefe, M. (Eds.). Amsterdam: North Holland, pp. 629-650. Wimmer, X M., Bidwell, L. R., Tallan, N. M. (1967), /. Am. Ceram. Soc. 50, 198-201. Wing-Kit, L., Nowick, A. S. (1986), Solid State Ionics 18/19, 989-993.
11.8 References
Williams, D. E., McGeehin, P. (1984), Electrochemistry 9, 246-290. Worrell, W. L. (1977), Solid Electrolytes: Geller, S. (Ed.). New York: Springer-Verlag, pp. 143-168. Worrell, W. L., Iskoe, J. L. (1973), in: Fast Ion Transport in Solids: Van Gool, W. (Ed.). Amsterdam: North Holland Publishing Company, pp. 513-521. Worrell, W. L., Liu, Q. G. (1986), US patent No. 4, 627, 892. Yamamoto, O., Takeda, Y, Kanno, R., Kohno, K., Kamiharai, T. (1989), J. Mater. Sci. Lett. 8, 198 — 200. Yeager, E., Salkind, A. J. (1972), in: Techniques of Electrochemistry, Vol. 1. New York: Wiley Interscience. Young, C. T. (1983), in: Progress in Solid Electrolytes, Energy Mines and Resources: Wheat, T. A., Ahmad, A., Kuriakose, A. K. (Eds.). Ottawa: Erp/MSL 8394 (TR), pp. 549-580. Youngblood, G. E., Gordon, R. S. (1978), Ceramurgia International 4, 93-98. Youngblood, G. E., Virkar, A. V, Cannon, W. R., Gordon, R. S. (1977), Am. Ceram. Bull. 56, 206210, 212. Yoshimura, M. (1988), Am. Ceram. Soc. Bull. 67, 1950-1955. Yuill, W. A., Cater, E. D. (1967), J. Phys. Chem. 71, 1436-1441. Zu-Xiang, L. (1989), in: High Conductivity Solid Ionic Conductors, Recent Trends and Applications: Takahashi, T. (Ed.). Singapore: World Scientific, pp. 223-241.
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General Reading Adham, K. EL, Hammou, A. (1983), Progress in Solid Electrolytes, Energy Mines and Resources: Wheat, T. A., Ahmad, A., Kuriakose, A. K. (Eds.). Ottawa: Erp/MSL 83-94 (TR), pp. 313-345. Bates, X, Farrington, G. C. (1981) (Eds.), in: Fast Ionic Transport in Solids. Amsterdam: North Holland. Chandra, S. (1981), Superionic Solids. Amsterdam: North Holland. Chowdari, B. V. R., Radhakrishna, S. (1988) (Eds.), in: Solid State Ionic Devices. Singapore: World Scientific. Green, D. X, Hannink, R. H. X, Swain, M. V. (1989), in: Transformation Toughening of Ceramics. Boca Raton: CRC Press Inc. Hagenmuller, P., van Gool, W. (1978) (Eds.), in: Solid Electrolytes, General Principles, Characterization, Materials, Applications. New York: Academic Press. Hladik, X (1972) (Ed.), in: Physics of Solid Electrolytes, Volumes 1 and 2. London: Academic Press. Macdonald, X R. (1987) (Ed.), in: Impedance Spectroscopy. New York: John Wiley & Sons. Subbarao, E. C. (1980) (Ed.), in: Solid Electrolytes and their Applications. New York: Plenum Press. Takahashi, T. (1989) (Ed.), in: High Conductivity Solid Ionic Conductors, Recent Trends and Applications. Singapore: World Scientific.
12 Ferroelectric Ceramics Kenji Uchino Materials Research Laboratory, Pennsylvania State University, University Park, PA, U.S.A.
List of Symbols and Abbreviations 12.1 General View of Ferroelectrics 12.1.1 Crystal Structure and Ferroelectricity 12.1.2 Origin of Spontaneous Polarization 12.1.3 Origin of Field Induced Strain 12.1.4 Electrooptic Effect 12.1.5 Example of a Ferroelectric 12.1.6 Applications of Ferroelectrics 12.2 High-Permittivity Dielectrics 12.2.1 Relaxor Ferroelectrics 12.2.2 Multilayered Capacitors (MLC) 12.3 Pyroelectric Devices 12.3.1 Temperature/Infrared-Light Sensors 12.3.2 Infrared Image Sensors 12.4 Piezoelectric Devices 12.4.1 Piezoelectric Materials 12.4.2 Piezoelectric Resonance 12.4.3 Piezoelectric Transformers 12.4.4 Piezoelectric Vibrators 12.4.5 Ultrasonic Transducers 12.4.6 Surface Acoustic Wave Devices 12.4.7 Piezoelectric Actuators 12.4.7.1 Deformable Mirrors 12.4.7.2 Impact Dot-Matrix Printers 12.4.7.3 Ultrasonic Motors 12.5 Electrooptic Devices 12.5.1 Transparent Electrooptic Ceramics 12.5.2 Bulk Electrooptic Devices 12.5.3 Waveguide Modulators 12.6 Positive Temperature Coefficient (PTC) Materials 12.6.1 The PTC Phenomenon 12.6.2 PTC Thermistors 12.6.3 Grain Boundary Layer Capacitors 12.7 Conclusions 12.8 Appendix 1: Tensor Representation of Physical Properties Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.
637 639 639 640 642 643 644 645 646 646 648 649 649 650 651 651 654 657 658 658 658 659 661 661 662 664 664 665 666 668 668 669 669 670 670
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12.8.1 12.8.2 12.8.3 12.9 12.9.1 12.9.1.1 12.9.1.2 12.9.2 12.9.2.1 12.9.2.2 12.10
12 Ferroelectric Ceramics
Tensor Representation Crystal Symmetry and Tensor Form Reduction of the Tensor (Matrix Notation) Appendix 2: Phenomenology of Ferroelectricity Landau Theory of the Phase Transition Second-Order Transition First-Order Transition Phenomenology of Electrostriction Case I: X = 0 Case II: X 4= 0 References
670 671 673 674 674 674 674 675 675 676 676
List of Symbols and Abbreviations
List of Symbols and Abbreviations C
P
cd D E /A
fR F
9
I k k,k' L M n P P Ps Q QM
r s To
Tc u
U V
wdip Welas X
xs X a y
r
specific heat Curie-Weiss constant piezoelectric coefficient electric displacement electric field antiresonance frequency resonance frequency Landau free energy piezoelectric coefficient, secondary electrooptic coefficient light intensity electromechanical coupling factor force constants optical pathlength electrostrictive coefficient refractive index pyroelectric coefficient dielectric polarization spontaneous polarization electrostrictive coefficient mechanical quality factor primary electrooptic coefficient, voltage rise ratio of a piezoelectric transformer elastic compliance Curie-Weiss temperature Curie temperature displacement of an ion from the equilibrium position energy sound velocity energy of the dipole moment elastic energy of displacement strain spontaneous strain stress ionic polarizability Lorentz factor Dhase retardation relative permittivity vacuum permittivity dipole moment of the unit cell of a crystal barrier height of the Schottky barrier
637
638
D-TGS GBL MLC OA PLZT PMN PTC PTCR PVFD PZT rpm SAW VTR
12 Ferroelectric Ceramics
deuterated triglycine sulphate grain boundary layer multilayered capacitor office automation (Pb,La)(Zr,Ti)O 3 lead magnesium niobate positive temperature coefficient positive temperature coefficient of resistivity polyvinylidene fluoride lead zirconate titanate revolutions per minute surface acoustic wave video tape recorder
12.1 General View of Ferroelectrics
12,1 General View of Ferroelectrics 12.1.1 Crystal Structure and Ferroelectricity
In so-called dielectric materials, the constituent atoms are considered to be ionized to a certain degree and are either positively or negatively charged. In such ionic crystals, when an electric field is applied, cations are attracted to the cathode and anions to the anode due to electrostatic interaction. The electron clouds also deform, causing electric dipoles. This phenomenon is called the electric polarization of the dielectrics, and the polarization is expressed quantitatively as the sum of the electric dipoles per unit volume (C/m2). Figure 12-1 shows schematically the origin of the electric polarization. There are three kinds; electron, ion and dipole reorientation-related polarizations. Compared with vacuum capacitors, dielectric capacitors can store more electric charge due to the dielectric polarization P as shown in Fig. 12-2. The physical quantity corresponding to the stored electric charge per unit area is called the electric displacement Z>, and is related to the electric field by the following expression: (12-1)
= 80E+P=8 80
639
Here, s0 is the vacuum permittivity (= 8.854 x 10" 12 F/m), £ is the material's relative permittivity (also simply called permittivity or dielectric constant, and in general it is a tensor). Depending on the crystal structure, in some crystal lattices, the centers of the positive and negative charges do not coincide even without the application of external electric field. In this case, it is said that there exists spontaneous polarization in the crystal, and, especially when the polarization of the dielectric can be altered by an electric field, it is called ferroelectric. Not every dielectric can be a ferroelectric. Crystals can be classified into 32 point groups according to their crystallographic symmetry, and these point groups can be divided largely into two classes, one with a center of symmetry and the other without. There are 21 point groups which do not have a center of symmetry. In crystals belonging to 20 of these point groups [except for the point group (432)], positive and negative charges appear on surfaces when stresses are applied. These materials are known as piezoelectrics. Pyroelectricity is the phenomenon in which, because of the temperature dependence of the spontaneous polarization, as the temperature of the crystal is changed, electric charges cor-
Electronic polarization <
0
Ionic polarization
Dipole reorientation
Figure 12-1. Microscopic origins of the electric polarization.
640
12 Ferroelectric Ceramics
terial and experimentally ascertain the polarization reversal. Table 12-1 shows the classification of the point groups. 12.1.2 Origin of Spontaneous Polarization
Electric field
Why is it that crystals which, from a consideration of the elastic energy, should be stable by being non-polar, still experience the shifting of cations and anions and become spontaneously polarized? The reason is briefly explained below. For simplicity, let us assume that dipole moments result from the displacement of one kind of ion A (electric charge q) relative to the crystal lattice. Consider the case in which the polarization is caused by all the A ions being displaced equally in a lattice. It follows that, on any individual A ion, there exists a local field from the surrounding polarization P, even if there is no external field. The concept of the local field is shown schematically in Fig. 12-3. It can be shown that:
of: Free charge ob : Bound charge a,: True charge
Figure 12-2. Electric charge accumulation in a dielectric capacitor.
responding to the change of the spontaneous polarization appear on the surface of the crystal. Among the pyroelectric crystals, those whose spontaneous polarization can be reversed by an electric field (not exceeding the breakdown limit of the crystal) are called ferroelectrics. There is some ambiguity in this definition. In order to establish ferroelectricity, it is necessary to apply an electric field on a pyroelectric ma-
(12-2)
Table 12-1. Crystallographic classification with respect to crystal centrosymmetry and polarity.a Polarity
Nonpolar (22)
Centrosymmetry
Number of point Cubic groups
O (11)
11
Crystal class Hexagonal
Tetragonal
Rhombo- OrthoMono- Trihedral rhombic clinic clinic
m3m Oh
m3 Th
6/mmm 6/m D6h C6h
4/mmm DAh
4/m CAh
3m D3d
3 mmm C 3 , D2h
432 0
23
622 D6
6
422 D4
4
32
222
6m2
C3h
42m
S4
D3
D2
3m
2/m C2h
T Ct
2 C2
1
11 43m Td
x
T
E>3*
D2d
(21) Polar (pyro) (10) a
10
6mm
6
4mm
4
Qt,
C
C
C
6
4v
Ar
Piezoelectric crystals are those in the area enclosed by the thick line.
C
3v
3 C
3
2mm C
2v
m
C
l
641
12.1 General View of Ferroelectrics
Figure 12-3. Concept of the local field. Eloc is given by
4neorf
This is the driving force of the ion shift. Here y is called the Lorentz factor. For an isotropic and a cubic system, it is known that y = 1 (Kittel, 1966). e0 is the permittivity in vacuum and is equal to 8.854 x 10" 1 2 F/m. If the ionic polarizability of ion A is a, then the dipole moment of the unit cell of this crystal is:
trics, k! plays an important role in determining the magnitude of the dipole moment. By rewriting Eq. (12-6) using: P = Nqu (q is the electric charge) (12-7) Combining with Eq. (12-5), the total energy can be expressed as follows (see Fig. 12-4):
(12-3)
= [ay/(3fio)]P
The energy of this dipole moment (dipoledipole coupling) is c
2
2
Wdip = - /i • £'° = - [a y /{9 e )] P
2
(12-4)
Per unit volume, it is: WW = N w dip = -[Na
y2/(9 s2)] P2
(12-5)
On the other hand, when the A ions are displaced from their nonpolar equilibrium positions, the elastic energy also increases. If the displacement is u, and the force constants k and k\ then the increase of the elastic energy per unit volume can be expressed as: (12-6) Here, k' (> 0) is the higher-order force constant. It should be noted that in pyroelec-
(12-8) :
Nay 9s2
k!
4N33q v*
From this, one can see that if the coefficient of the harmonic term of the elastic energy is equal or greater than the coefficient of the dipole-dipole coupling, then P = 0, i.e., the A ions are stable and remain at their non-polar equilibrium positions. Otherwise, a shift from the equilibrium position {P2 = [2Nay2/(982)-k/(Nq2)]/[kf/(N3qAn is stable. In the perovskite-type crystal structure (as in barium titanate) as described in the next section, it is thought that because of the occurrence of a larger Lorentz factor y ( « 10) (Kinase et al., 1969) than found for other crystal structures, spontaneous polarization can occur more easily.
642
12 Ferroelectric Ceramics
(a)
Dipole interaction
two types of strain (defined by the ratio AL/L: the amount of deformation with respect to the original length) that may be induced by an electric field depending on the nature of the interaction "springs" between the ions which is, in turn, determined by the crystal structure (Uchino et al., 1983). As shown in Fig. 12-5 a, in crystals where there is no centrosymmetry, strain, x, is generated in proportion to the electric field E. This is the converse piezoelectric effect, and the tensor quantity, d, defined by the relationship x = 6E
Elastic energy
(c)
\y Figure 12-4. Energy explanation of the origin of spontaneous polarization. (a) Dipole interaction Wiip =
-[Nocy2/(9e20)]P2
(b) Elastic energy W
_ e l a s
p2
~
(c) Total energy
12.1.3 Origin of Field Induced Strain With the application of an electric field, the dielectric material inevitably induces strain or crystal deformation. There are
(12-9)
is referred to as the piezoelectric coefficient. On the other hand, in centrosymmetric crystals, as shown in Fig. 12-5 b, the expansion and contraction of the "spring" are such that the net response is nearly zero. However, the anharmonic nature of the "spring" motion will still bring about a small induced strain that is proportional to the square of the electric field E. This is referred to as the electrostriction effect which is expressed in terms of the strain, x, the applied electric field, E, and the electrostriction coefficient, M, as:
x = ME2
(12-10)
The system pictured in Fig. 12-5 a also possesses a spontaneous bias of electrical charge, or a spontaneous polarization. When a large reverse bias electric field is applied to a crystal that has a spontaneous polarization in a particular polar direction, a transition "phase" is formed which is another stable crystal state in which the relative positions of the ions are reversed (in terms of an untwinned single crystal, this is equivalent to rotating the crystal 180° about an axis perpendicular to its polar axis). This transition, referred to as polarization reversal, also causes a remarkable change in strain. This particular class of
643
12.1 General View of Ferroelectrics x=(6 2 -6 1 )/a 0 =dE
Ion pair potential energy
Ion pair potential energy
\\
// /
\
(a) Piezoelectric strain
\ \ \v
/
^
/
(b) Electrostriction
Figure 12-5. Diagrammatic explanation of the origins of piezoelectric strain (a) and electrostriction (b).
substances are referred to as ferroelectrics, as mentioned in Sec. 12.1.1. Generally, what is actually observed as a field-induced strain, is a complicated combination of the three basic effects just described. 12.1.4 Electrooptic Effect Since light is an alternating electromagnetic wave with electric and magnetic field directions crossing each other, it induces electric polarization in a dielectric crystal and the light itself is influenced by the crystal. The alternating frequency of the light is so high ( ^ 1 0 1 5 H z ) that only the electronic polarization should follow the field change, and the relative permittivity of the crystal is small, not exceeding 10. The permittivity 8 at this high frequency is related to the refractive index n by the following equation: e=n
(12-11)
When an external electric field is applied to the crystal, ion shift is induced, deforming the shape of the electron cloud, and consequently the refractive index is changed. This phenomenon is called the electrooptic effect. Generally, refractive indices are symmetrical 2-R tensor quantities and represented by using a refractive indicatrix (Eq. 12-12), where n^,n2 and n3 are principal refractive indices. _
n\
+
£L + _
n\
=
i
(12-12)
n\
With the application of an electric field, the change in refractive index is given by an expansion expression:
(12-13)
644
12 Ferroelectric Ceramics
Here rijk is a primary electrooptic coefficient {PockeVs effect) and gijkl is a secondary coefficient (Kerr effect). Considering a paraelectric phase of a perovskite crystal (m3m) as an example, the Kerr coefficients are represented in the following matrix: 011
012
012
012
011
012
012
012
011
0 0 0
0 0 0
0 0 0
0 0 0 044
0 0
0 0 0 0 044
0 0 0 0 0
0
044
(12-16) This is the principle of a light shutter/ valve, and the voltage required for the first intensity maximum (i.e., Fy = n) is essential and called the half-wavelength voltage.
Then, the refractive indicatrix under the electric field applied along z-direction can be expressed as: 2
2
x +y n [l~(n2/2)g12E2] 2
2i2
= 1
d is the electrode gap and L is the optical path length (see Fig. 12-6). Putting a crystal between crossed polarizers arranged at the 45° direction with respect to z-axis, the output light intensity can be modulated as a function of applied voltage in the following way:
(12-14)
When light is transmitted along the ^-direction, the phase retardation Fy between an ordinary and an extraordinary light is given by: (12-15)
12.1.5 Example of a Ferroelectric A typical ceramic ferroelectric is barium titanate, which is used here as an example to illustrate some properties of the ferroelectrics. As shown in Fig. 12-7, BaTiO 3 has a perovskite crystal structure. (See also Chap. 1, Sees. 1.3.3 and 1.6.2 of this Volume for a more complete description of the crystal structures of perovskites.) In the high-temperature paraelectric phase (nonpolar phase) there is no spontaneous polarization (the symmetry is O h — m3m). Below the transition temperature T c called the
Unpolarized light
Polarizer Crystal
Polarizer
Figure 12-6. Optical phase retardation through an electrooptic crystal. Notice the crossed polarizer configuration.
645
12.1 General View of Ferroelectrics
(a) Ba2
T>TC 4+
• Ti
T
@ Ba
2
O O-
Tc : Curie temperature
Curie temperature (about 120 °C), spontaneous polarization occurs, and the crystal structure becomes slightly elongated, that is, tetragonal (C4v — 4mm). Figure 12-8 shows schematically the temperature dependence of the spontaneous polarization Ps and permittivity s. Ps decreases with increasing temperature and vanishes at the Curie point, while e tends to diverge near Tc. Also, the reciprocal permittivity 1/e is known to be linear with respect to the temperature in a wide range in the paraelectric phase (so-called Curie- Weiss law), =
C/(T-T0)
(12-17)
Here C is the Curie- Weiss constant and To the Curie- Weiss temperature. To is slightly lower than exact transition temperature It is also known that the spontaneous polarization Ps and the spontaneous strain xs follow the relationship: xs = QPs2
Figure 12-7. Structure of BaTiO3
12.1.6 Applications of Ferroelectrics
Ferroelectric materials, especially polycrystalline ceramics, are very promising for varieties of application fields such as highpermittivity capacitors, pyroelectric sensors, piezoelectric I electrostrictive transducers, electrooptic devices and PTC thermistors. For capacitor dielectrics, the peak dielectric constant around the transition (Curie) temperature is utilized, while the strong temperature dependence of the spontaneous polarization below Tc is applied for pyroelectric sensors. Piezoelectric materials are applicable in sensors and actuators. Pressure and acceleration sensors
Spontaneous polarization
\ \ \ \\
Inverse permittivity
/
Me
/
(12-18)
xs decreases almost linearly with increasing temperature. In the case of BaTiO 3 , in the ferroelectric phase, it exhibits the piezoelectric effect, while in the paraelectric phase, it is non-piezoelectric and exhibits the electrostrictive effect.
/
Tc Curie point
v N
Permittivity
Temperature
Figure 12-8. Temperature dependence of the spontaneous polarization Ps and permittivity s.
646
12 Ferroelectric Ceramics
are now commercially available in addition to conventional piezo-vibrators. Precision positioners and pulse drive linear motors have already been installed in precision lathe machines, semiconductor manufacturing apparatus and OA equipment etc. Recent topical development is found in ultrasonic motors. Electrooptic materials will become future key components in displays and optical-communication systems. For thermistor applications, semiconductive ferroelectric ceramics with a positive temperature coefficient (PTC) of resistivity due to a junction effect have been developed from barium-titanate-based materials.
12.2 High-Permittivity Dielectrics 12.2.1 Relaxor Ferroelectrics There are two classes of ceramic capacitors: one is used for the thermal compensation of electrical circuits, using a TiO2-based material, and the other is a high-permittivity capacitor with BaTiO 3 - or Pb(Zr,Ti)O3-based materials. Recently relaxor ferroelectrics such as Pb(Mg 1/3 Nb 2/ 3)O 3 and Pb(Zn 1/3 Nb 2/3 )O 3 have been developed for very compact chip capacitors. The reasons why these complex perovskites have been investigated intensively for capacitor applications are: (1) their very high permittivity, and (2) their temperature-insensitive characteristics (i.e., diffuse phase transition) in comparison with the normal perovskite solid solutions. An intuitive crystallographic model has been proposed to explain the high permittivity of the disordered perovskites (Uchino, 1980). Figures 12-9 a and 12-9b show the ordered and disordered structures for an A(B I1/2 B II1/2 )O 3 perovskite crystal. As-
suming a rigid-ion model, a large "rattling" space is expected for the smaller B ions in the disordered structure because the large B ions prop open the lattice framework. Much less "rattling" space is expected in the ordered arrangement where neighboring atoms collapse systematically around the small B ions. When an electric field is applied to a disordered perovskite, the B ions with a large rattling space can shift easily without distorting the oxygen framework. A larger polarization can be expected per unit magnitude of electric field. In other words, larger dielectric constants and larger CurieWeiss constants. On the other hand, in ordered perovskites with a very small rattling space, the B ions cannot move easily without distorting the octahedron. A smaller permittivity and Curie-Weiss constant are expected. The reason why the phase transition becomes diffuse in the relaxor ferroelectrics has not yet been clarified, although the "microscopic composition fluctuation" model is the most widely accepted (Kanzig, 1951; Rolov, 1963, Uchino etal, 1981). Considering the Kanzig region (the minimum size region in order to cause a cooperative phenomenon, ferroelectricity) to be in the range of 100-1000 A, disordered perovskites such as Pb(Mg 1/3 Nb 2/3 )O 3 reveal a local fluctuation of the distribution (b)
Figure 12-9. Crystal structure models of the A(BI1/2BII1/2)O3 type perovskite: (a) ordered structure with a small rattling space and (b) disordered structure with a large rattling space (Q =Bl and • = Bn).
12.2 High-Permittivity Dielectrics
647
Ordered
o•o» o o • o • o • © • o » o « o » ofo • 6~« <3" • o*o « o • o« o • o«o •{•o • o • o # o * o * o * o « o « o « ojo j •o • o •o«o#o*o*o«oo«*o«o« o o o « ojo • o • o •o«o*o+o«o«o«o••o•o• O • O • O * O « O « O « O •jOO o*{«o«o«o* o#o#o#o«o» o • ] • o • o • o • o • o «o • ojcnr oV6io • o • o • o • o • o • o •(• o«o«o*o*o*o*o
20
-10
0.3 0.4 0.50.6 0.7 Fraction of •
-20
0.3 0.40.5 0.6 0.7 Fraction of •
tOOOOOIfttlOOttOOtO*
Disordered
o • o • • o • •o«»oooooo#oo • •••ooo* toottoooit** tot«*tto«oot«oo*tooo ooootoooioo«o#tooo«o toototoo*oooo«too«o« o«oo«otoo»ootototo«« •o*oo»o»oo»«oo#•oo»o •oo«too#ooo«ooooio*o ooo#o»toooototo»«ooo
-20
-10
• • o o o oooo*otitoiootoooooo
••oo«oo«o«oto*ooto ooto«ooo«*o«ootto*
tot«ooi*ooot«tioo
of Mg 2 + and N b 5 + ions. Figure 12-10 shows a computer simulation of the composition fluctuation in the A(B I1/2 B II1/2 )O 3 type crystal calculated for various degrees of the ionic ordering. The fluctuation of the Bj/Bn fraction x obeys a Gaussian error distribution. H. B. Krause reported observing the short-range ionic ordering of Pb(Mg 1/3 Nb2/3)O 3 by electron microscopy (Krause et al, 1979). The high-resolution image in Fig. 12-11 reveals somewhat
0.3 0.4 0.5 0.6 0.7 Fraction of •
Figure 12-10. Computer simulation of the composition fluctuation in the A(B I1/2 B ni/2 )O 3 -type calculated for the varying degrees of the ionic ordering (Kanzig region size: 4 x 4).
ordered (ion-ordered) islands in the range of 20-50 A, each of which may have a slightly different transition temperature. Another significant characteristic of these "relaxor" ferroelectrics is dielectric relaxation (frequency dependence of permittivity) from which their name originates. Temperature dependence of the permittivity in Pb(Mg 1/3 Nb2/3)O 3 is plotted in Fig. 12-12 for various measuring frequencies (Smolensky et al., 1961). With in-
648
12 Ferroelectric Ceramics
creasing measuring frequency, the permittivity in the low-temperature (ferroelectric) phase decreases and the peak temperature shifts towards the higher frequency; this contrasts with normal ferroelectrics such as BaTiO3 where the peak temperature hardly changes with frequency. This is probably caused by shallow multipotential-wells in a locally distorted perovskite cell due to the disordered ionic arrangement (Skanavitype dielectric relaxation) (Skanavi et al., 1958), in addition to a ferroelectric phase transition phenomenon. Figure 12-11. High resolution electron-microscope image of the Pb(Mg 1/3 Nb 2/ 3)O 3 single crystal ((110) plane). Note ion-ordered islands in the range of 2 0 -
Multilayer structures have been developed as part of capacitor manufacturing aimed at the integration of electrical circuit components. Figure 12-13 schematically shows a multilayer capacitor chip. Thin sheets made by the tape casting technique, starting from a slurry of the dielectric powder and organic solvents, are coated with Pt or Ag-Pd paste to form electrodes, then several tens of sheets are stacked together and sintered. Finally, external electrodes, used to connect the chip with the circuit, are painted on.
50 A.
-12000
-10000
- 8000
- 6000
12.2.2 Multilayered Capacitors (MLC)
o.
0.20 - 4000
External electrode -
0.15 -
0.10 -
0.05
-200
-150
-100
-50 0 Temperature (°C)
50
100
150
Figure 12-12. Temperature dependence of the permittivity and tan S in Pb(Mg 1/3 Nb 2/ 3)O 3 for the various measuring frequencies (kHz): (1) 0.4, (2) 1, (3) 45, (4)450,(5) 1500,(6)4500.
Internal electrode Figure 12-13. Structure of a multilayer capacitor chip.
649
12.3 Pyroelectric Devices
12.3 Pyroelectric Devices
1
(a)
12.3.1 Temperature/Infrared-Light Sensors Practical applications of the pyroelectric effect in temperature sensors and infraredlight detectors have gradually been promoted, providing, together with uses in piezoelectric resonators, of the commercial market for dielectric ceramics. The merits of pyrosensors compared to other infrared-sensor materials such as semiconductors are summarized as follows: (a) Wide range of response frequency (b) Use at room temperature (c) Quick response in comparison with other temperature sensors (d) High-grade quality (optical-grade homogeneity etc.) of ceramic pyrosensors is unnecessary. The principle on which the pyroelectric effect is based is the measurement of the charge generation associated with the spontaneous polarization change with temperature: (12-19) j = dPJdt = (dPJdT)(dT/dt) = p(dT/dt) Here, p is denoted as a pyroelectric coefficient. Two typical electrode arrangements for pyrosensors are illustrated in Fig. 12-14: (a) face electrodes with the polarization direction parallel to the infrared irradiation,
Radiation
p 1 w
1
L-J
Figure 12-14 Typical geometric configurations for pyroelectric detectors: (a) face electrodes; (b) edge electrodes.
and (b) edge electrodes with the polarization direction perpendicular to the irradiation. The former type has higher efficiency, but requires a sophisticated fabrication process of transparent uniform electrodes for infrared light. The pyroelectric sensor is a device transducing optical/thermal energy to electrical energy, and its efficiency or figure of merit is evaluated in several ways; p, p/cp or p/(cpe) (cp: specific heat). This is because the temperature change of the sample is larger for the smaller cp material under constant heating, and the voltage generated by a certain amount of pyrocharge becomes larger for the smaller 8 (permittivity) material. Table 12-2 lists the figures of merit of several pyroelectric materials. Improvement of the characteristics has been attempted by using composites of
Table 12-2. Room-temperature properties of various pyroelectric detector materials and some "figures of merit" for their detector operation. Material
TGS LiTaO3 Sr 1/2 Ba 1/2 Nb 2 O 6 PLZT (6/80/20) PVF 2
V (nCcm^K"1) 30 19 60 76 3
e'/s0
50 46 400 1000
11
C
P
1 -7 3 19 2-34 2 - 57
2-4
P/CP
(nAcmW1) 17-8 60 25-6 29-9 1 -3
p/(cps)
(Vcm-2!-1) 4000 1470 720 340 1290
650
12 Ferroelectric Ceramics
pyro-ceramics and polymers (Bhalla et al., 1981). In addition to the primary pyroelectric effect, a secondary effect is superimposed, i.e., the stress due to the thermal expansion a difference between the ceramic and polymer generates electric charge through the piezoelectric effect. Figure 12-15 shows a typical structure of a polymer used in pyroelectric infrared sensors. In practical usage, a pyro-sensor requires an infrared-light (thermal-ray) chop-
per, because the electrical signal can be detected only at the transient stage of light illumination or shut off. An electromagnetic motor was conventionally used as a light-chopper mechanism, and recently a piezoelectric bimorph chopper has been developed by Y. Kuwano etal. (Shibata et al., 1985), which prompted miniaturization of the pyrosensors (Fig. 12-16). 12.3.2 Infrared Image Sensors
In Fig. 12-17 the visualization of a thermal-distribution image is exemplified by a pyro-vidicon tube (Taylor et al., 1973). The light emitted from an object is filtered with a germanium lens producing an infrared beam which is focused onto the pyroelectric target through an optical chopper. The temperature distribution of the object is represented on the target as a voltage distribution. This is monitored from the back surface of the target by electron-beam scanning using a conventional TV tube. One of disadvantages of the pyro-vidicon is the degradation of the image over a long period of usage due to thermal diffusion on the target. Pedder et al. proposed a segmented target design in order to solve the diffusion problem (Warner et al., 1981). Figure 12-18 shows the microscopic struc-
Cushion ring Silicon window Pyro-film ring
Ground ring Reflector
Figure 12-15. A polymer-based pyroelectric infrared
Infrared ray (Input) Case. s
) Room-temperature * detector
K Piezoelectric bimorph
Figure 12-16. Swing-type pyroelectric temperature Infrared detector
12.4 Piezoelectric Devices Germanium lens Target
Mesh
Focus and scan coils
Wall anode
/
/
651
/
.
Grid
'///y///////////f///////////////7////A
Chopper
Electron beam Germanium window
First anode
Target e lement capacitance C t Beam mpedance Cathode (b)
Signal plate
Z i
V
= j Input capacitance C f
ture of a D-TGS (deuterated triglycine sulphate, (ND 2 CD 2 COOD) 3 D 2 SO 4 ) target, and Fig. 12-19 is an example of a picture taken in darkness.
Figure 12-17. Pyro-vidicon tube (a) and its equivalent circuit (b).
ples of these ternary compositions are; Pb(Mg 1/3 Nb 2/ 3)O 3 , Pb(Mn 1/3 Sb 2/3 )O 3 , Pb(Co 1/3 Nb 2/3 )O 3 , Pb(Mn 1/3 Nb 2/3 )O 3 , Pb(Ni 1/3 Nb 2/3 )O 3 , Pb(Sb 1/2 Sn 1/2 )O 3 , Pb(Co 1/2 W 1/2 )O 3 , Pb(M g l / 2 W 1 / 2 )O 3 .
12.4 Piezoelectric Devices 12.4.1 Piezoelectric Materials In the early 1950s, barium titanate (BaTiO3) began to be utilized in Langevintype piezoelectric vibrators. Later, at the National Bureau of Standards (NBS) in the USA (now NIST), PZT (Pb(Zr,Ti)O3) was found to exhibit piezoelectric constants twice as large as those of BaTiO 3 around the morphotropic phase boundary between the rhombohedral-tetragonal phases (Fig. 12-20); (Jaffe et al., 1955). Subsequently, PZT modified by doping, and a ternary solid solution with a different perovskite have been intensively investigated. Exam-
Figure 12-18. Infrared image target with divided fine segments (19 jam width, 16 \\m depth, 25 jam pitch).
652
12 Ferroelectric Ceramics
Piezoelectric data for PZT ceramics are summarized in Table 12-3. In polycrystalline piezoelectric ceramics, a poling process (applying a strong DC electric field) is required to rearrange the spontaneous polarization. After being poled, the ceramic can exhibit the piezoelectric effect just as single crystals do (Fig. 12-21). Piezoelectricity is also found in polymers (Kawai, 1969). Figure 12-22 shows an example polyvinylidenefluoride (PVDF).
0.40
1600
Composition [mol %]
Figure 12-19. Images taken by a pyro-vidicon on a dark night. 1 E=0
2E=EC
4 .3
7 5 £=0
2
E
Figure 12-20. Permittivity and the planar coupling factor in PbZrO 3 -PbTiO 3 ceramics.
4E=EC
I Figure 12-21. Illustration of the strain change associated with the domain reversal in a ferroelectric ceramic.
653
12.4 Piezoelectric Devices
Piezoelectric polymers have the following characteristics: (a) small piezoelectric d constants (for actuators) and large g constants (for sensors). (b) Lightweight and high elasticity, leading to good acoustic impedance matching to water or the human body. (c) Low mechanical quality factor QM, giving a wide frequency band resonance.
Figure 12-22. Structure of polyvinylidene difluoride (PVDF); O: fluorine, : carbon, # : hydrogen.
Table 12-3. Electromechanical parameters in PZT-PMN ceramics.2 PCM-5A
PCM-33
PCM-4B
PCM-67
PCM-80
0.65 0.38 0.71 0.70 0.50
0.65 0.39 0.74
0.70 0.43 0.72 0.63 0.50
0.32 0.19 0.48 0.37 0.40
0.58 0.35 0.69 0.64 0.47
Electromechanical coupling factors
K k33
fe15
K Piezoelectric constants d31
0.50
-247 xlO" 1 2 490 xlO" 1 2 599 xlO" 1 2 -11.8x10" 3 20.6x10" 3 29.7x10" 3
- 4 2 xlO" 1 2 109 xlO" 1 2 131 xlO~ 1 2 -7.7 xlO~ 3 19.8 x l O " 3 24.7 x 10" 3
-122 xlO" 1 2 273 xlO" 1 2 412 xlO" 1 2 -11.3x10" 3 25.5x10" 31.9x10" 3
3530 2740
2380 2280
620 600
1210 1460
1.50
2.30
1.40
0.64
0.64
6.2 x 10 10 5.5 x l O 1 0 2.0 x l O 1 0
6.9 x l O 1 0 5.2 x l O 1 0
6.3 x 10 10 5.1 x 10 10 2.2 x 10 10
ll.Ox 10 10 10.8 x 10 1 0 4.2 x 1O10
8.8 x 10 10 6.8 x 10 1 0 3.1 x 10 io
Density Q
7.7
7.7
7.8
7.7
7.9
Mechanical quality factor QM
60
50
64
3130
2080
Curie temperature (°C)
326
182
264
340
283
d33
d15 931 933 015
-186 xlO" 1 2 375 x10" 1 2 579 xlO" 1 2 -12.3x10- 3 -25.7x10- 3 33.9x10" 3
-263 x l O " 1 2 575 x l 0 ~ 1 2
1710 1830
-8.4xlO"3 18.4 x l O - 3
3
Permittivity e
ii/ e o
Loss tangent D Elastic constants E
Vs 22
a
Elastic constant 1/s: N/m2; piezoelectric constants d: m/V, g: V • m/N; loss tangent D: %; density Q: 103 kg/m3.
654
12 Ferroelectric Ceramics
Recent development in the field of composites of piezoceramics and polymers is remarkable (Klicker, 1981), superior piezoelectric response being achieved while still maintaining the mechanical flexibility of the polymers. 12.4.2 Piezoelectric Resonance When an electric field is applied to a piezoelectric material, deformation (AL) or strain (AL/L) arises. When the field is alternating, mechanical vibration is caused, and if the drive frequency is adjusted to a mechanical resonance frequency of the device, large resonating strain is generated. This phenomenon can be understood as a strain magnification due to accumulating input energy, and is called piezoelectric resonance. The piezoelectric resonance is very useful for realizing energy trap devices, actuators etc. The theoretical treatment is described in the following. If the applied electric field and the generated stress are not large, the stress x and the dielectric displacement D can be represented by the following equation: (ij = 1,2,..., 6; m,fc = 1,2,3) (12-20) Dm^dmiXi^slkEk
(12-21)
These are called piezoelectric equations. The numbers of independent parameters for a lowest symmetry trigonal crystal are 21 for sfj9 18 for dmi and 6 for s*fc. The number of independent parameters decreases with increasing crystallographic symmetry. Concerning the polycrystalline ceramics, the poled axis is usually denoted as the z-axis and the ceramic is isotropic with respect to this z-axis (point group Coov(oom)). The number of non-zero matrix elements is 10 (sfl9 sf2, sf3, sf3, sf4, d3l9d33,d !, and ef3).
Next, let us introduce an electromechanical coupling factor k, which corresponds to the efficiency of an electro-mechanical transducer. The internal energy of a piezoelectric vibrator is given by summation of the mechanical energy UM (= J x dX) and the electrical energy UE (= J D dE). U is calculated as follows, when linear relations Eqs. (12-20) and (12-21) are applicable: U = UM+UE =
(12-22)
1 2ij
' k,m
The s and e terms represent purely mechanical and electrical energies (UMM and UEE\ respectively, and the d term denotes the energy transducer from electrical to mechanical energy or vice versa through the piezoelectric effect. The coupling factor k is defined by: K
— UME/V
U
MM
U
EE
yiA-Z3)
The k value varies with the vibrational mode (even in the same ceramic sample), and can have a positive or negative value (see Table 12-4). Let us consider the transverse mechanical vibration of a piezo-ceramic plate as shown in Fig. 12-23. If the polarization is
1 Figure 12-23. Transverse vibration in a rectangular plate.
12.4 Piezoelectric Devices
655
Table 12-4. Several shapes of the resonator and their electromechanical coupling factors. Coupling factor
Elastic conditions
Shape of the resonator
x1 4= o, x2 = x3 = o
v\
4= 0, x2 4= 0, x3 4= 0
Xl
Definition
Xx = X2 = 0, X3 4= 0 Xl = x2 4= 0, x 3 4= 0 X x = X 2 # 0, X 3 = 0 Xl = x 2 4= 0, x 3 4= 0
x
= X 2 4= 0, X3 # 0
X x = X 2 4= 0, X3 4= 0 ! = x 2 4= 0, x 3 = 0
Xj 4= 0, X2 4= 0, X 3 = 0 l 4= 0, x2 = 0, x 3 + 0 Xi 4= 0, X 2 = 0, X 3 4= 0 Xl 4: 0, x 2 4= 0, x 3 = 0
Y.
Xt 4= 0, X 2 4= 0, X3 4= 0 X l 4= 0, x 2 = 0, x 3 = 0
l-/c| 1 -(/c 3 1 -Bfe 3 3 ) 2 i
j
fe'33
k
— k 2A ~ *15
K
*i*0,
X2 = 0, X3 4= 0 x 2 4= 0, x 3 4= 0
Bfe 31
<—' /
/
x1 = x 2 = X3 = o,x 4 *o
Jd-fcL) d15
x1=x2 = x 3 = 0, x 4 4= 0
/eX
s£
V 5 33V S 1
in the z-direction and the x-y planes are the planes of the electrodes, the extentional vibration in the x-direction is represented by the following dynamic equation: (d2u/dt2) = F =
/8x) + (dX12/dy) + (6X 1 3 /8 Z ),
(12-24)
u is the displacement of the small volume element in the ceramic plate in the x-direction. The relations between stress, electric field (only Ez exists) and the induced strain are given by: Xl
= sf, X,
sE12 X2
sf 3
•d31
Ez
656
12 Ferroelectric Ceramics
Using Eq. (12-28), the admittance for the mechanically free sample is calculated as:
i "I" =
S
13
13
(12-25)
1
(12-31)
V d231
— s12)X6
When the plate is very long and thin, X2 and X3 may be set equal to zero through the plate. Since shear stress will not be generated by the electric field Ez, Eq. (12-25) is reduced to: 1
=
xJsE1-(d31/sE11)Ez
w is the width, L the length, t the thickness of the sample, and Fis the applied voltage, sff is the permittivity in a longitudinally clamped sample, and is given by: pLC — PX — (A2 / c £ ^
(12-26)
33 —
d2u/dx2
\
(\ 1J\7\
31/ 11/
V
/
The piezoelectric resonance is achieved where the admittance becomes infinite or the impedance is zero. The resonance frequency / R is calculated from Eq. (12-31), and the fundamental frequency is given by:
Introducing Eq. (12-26) into Eq. (12-24), and allowing for x± = du/dx and dEJdx = 0 (due to the equal potential on each electrode), leads to a harmonic vibration equation: — co2 QSE1U
33
(12-27)
(12-33)
co is the angular frequency of the drive field, and Q is the density. Substituting a general solution u = u±(x)ejcot + u2(x)e~j(Ot into Eq. (12-26), and with the boundary condition X1 = 0 at x = 0 and L (sample length), the following solution can be obtained:
On the other hand, the antiresonance state is generated for zero admittance or infinite impedance: (12-34)
du/dx = xx = d31 Ez [sin co(L — x)/v +
The final transformation is provided by the definition:
=
+ sin (co x/v)]/sin (co L/v)
2v
(12-28)
cot
Here, v is the sound velocity in the piezoceramics and is given by
L
0
o
ef3 -
f1 P
\^7~\
pLC
E
2
— kK31
The resonance and antiresonance states are described by the following intuitive model. In a high electromechanical coupling material with k« 1, the resonance or antiresonance states appear for tan [co L/(2 v)] = 00 or 0, i.e., co L/(2 v) = (m — 1/2)n or mn (m: integer), respectively. The strain amplitude xx distribution for each state [calculated using Eq. (12-28)] is
When the specimen is utilized as an electrical component such as a filter or a vibrator, the electrical impedance [(applied voltage/induced current) ratio] plays an important role. The current flow into the specimen is described by the surface charge increment, i.e., 9D3/9t, and the total current is given by: L
2v
(12-35)
(12-29)
i=jcowiD3dx=ja)w
k231
p
Xi
\\JLX
(12-30)
657
12.4 Piezoelectric Devices Resonance
Antiresonance Low coupling
m=1
High coupling m=1
^^ I
m=2
m=2
Figure 12-24. Strain generation in the resonant or antiresonant state.
K—A illustrated in Fig. 12-24. In the resonance state, large strain amplitudes and large capacitance changes are induced, and the current can easily flow into the device. On the contrary, at the antiresonance, the strain induced in the device compensates in total, not causing the capacitance change, and the current can not flow easily into the sample. In the usual case, where k31 ^ 0 . 3 , the antiresonance state varies from the abovementioned mode and becomes closer to the resonance mode. The low-coupling material exhibits an antiresonance mode where capacitance change due to the size change is compensated completely by the current required to charge up the static capacitance. In general, the sound velocity v of the specimen is first obtained from the resonance frequency / R , then the electromechanical coupling factor fe31 is calculated from the v value and the antiresonance frequency fA using Eq. (12-34). Especially in low-coupling piezoelectric materials, the following approximate equation is available:
k31/(l-k23l)
very high voltage generated in a piezoelectric ceramic under applied mechanical stress can cause sparking and ignite the gas (Fig. 12-25). There are two means to apply the mechanical force; sudden application and continuous increase. When input and output terminals are fabricated on a piezo-device and input/output voltage is changed through the vibration energy transfer, the device is called a piezoelectric transformer. Proposed by C. A. Rosen et al. (Rosen, 1957), there have been a variety of such transformers investigated: Fig. 12-26 shows a fundamental structure where two differently-poled parts coexist in one piezoelectric plate. A standing wave with a wavelength equal to the sample length is generated, a half wavelength portion of the wave existing on both (a)
= -(Af/f1d (12-36)
Electrode
12.4.3 Piezoelectric Transformers One of the very basic applications of piezoelectric ceramics is a gas igniter. The
20
w
40
Time [\is]
Figure 12-25. (a) Gas igniter and (b) output voltage.
658
12 Ferroelectric Ceramics
t Polarization
w
Polarization-
\ Piezo-ceramic (a) Piezoelectric transformer
Load
are a bimorph consisting of two piezo-ceramic plates bonded together, and a piezoelectric fork consisting of a piezo-device and a metal fork. A piezoelectric buzzer is shown in Fig. 12-27, which has merits such as high electric power efficiency, compact size and long life. 12.4.5 Ultrasonic Transducers
(b)
Figure 12-26. Piezoelectric transformer.
the input (/x) and output (/2) parts of the sample. The voltage rise ratio r is given for the unloaded condition by Eq. (12-37). The r ratio is increased with an increase of (l2/t). (12-37) S
33/ S 11
Piezoelectric transformers were previously used in color TVs because of their compact size in comparison with the conventional electromagnetic coil-type transformers. 12.4.4 Piezoelectric Vibrators
In the use of mechanical vibration devices such as filters or oscillators, the size and shape of a device is very important, and both the vibration mode and the ceramic material must be considered. The resonance frequency of the bending mode in a cm-size sample ranges from 100-1000 Hz, which is much lower than that of the thickness mode (100 kHz). For these vibrator applications the piezo-ceramic should have a high mechanical quality factor (QM) rather than a large piezoelectric coefficient d; i.e., hard-type piezoelectric ceramics are preferable. For speakers or buzzers, audible for humans, devices with a rather low resonance frequency are used (kHz range): Examples
Ultrasonic waves are now used in various fields. The sound source is made of piezoelectric ceramics as well as of magnetostrictive materials. Piezoceramics are generally superior in efficiency and in size to magnetostrictive materials. Especially hard-type piezoelectric materials with a high QM are preferable. A liquid medium is usually used for sound energy transfer. Ultrasonic washers and ultrasonic microphones for short-distance remote control are widely used in factories, and ultrasonic scanning detectors are useful in medical electronics. 12.4.6 Surface Acoustic Wave Devices
Surface acoustic wave (SAW) filters have been widely used for the intermediate frequency image transfer signal in color TVs, because of their excellent time delay characteristics. The fundamental structure of the SAW filter is illustrated in Fig. 12-28, where a pair of interdigital electrodes are fabricated on the piezoelectric crystal. A
Figure 12-27. Piezoelectric buzzer.
659
12.4 Piezoelectric Devices
Load
Figure 12-28. Fundamental structure of a SAW filter.
surface wave generated at the input-side electrode is transferred and picked up at the output-side as an electric signal. The device is very useful as a high-frequency filter. There are four materials at present used for SAW devices, Pb(Zr,Ti)O 3 (PZT)based ceramics, ZnO thin films, LiNbO 3 and LiTaO3 single crystals, whose characteristics are summarized in Table 12-5. A small temperature coefficient of the frequency is preferable, which is determined by the summation of the temperature coefficient of the sound velocity and the thermal expansion coefficient of the ceramic. When a polycrystalline material is used, it must be pore-free and homogeneous. Samples must be highly reproducible, and require advanced fine ceramic preparation technology. 12.4.7 Piezoelectric Actuators
In recent years, the need for new displacement elements, in particular, in such fields as optics, precision machinery and small
motors, has been rapidly increasing. The requirements for the processing accuracy of optical devices such as lasers and cameras, along with the positioning accuracy required in the processing of semiconductor chips are now typically of the order of micron and submicron levels. The need for a reliable micro-scale positioner has motivated a new surge of activity in the development of ceramic actuators which operate on the principle of electric-field-induced strain. For actuator applications, large electric fields ( « 1 kV/mm) are applied to the material, thereby generating large stresses ( ^ l O M P a ) and strains (A///^10~ 3 ). Therefore, in addition to an adequate electrostrictive response, electrical insulation strength and mechanical toughness are necessary material characteristics. Lead zirconate titanate (PZT)-based ceramics are currently the primary materials for piezoelectric applications (Furuta et al, 1986). The(Pb,La)(Zr,Ti)O 3 (PLZT) (7/62/38) compound is one such material. The strain curves for this composition are shown in Fig. 12-29 a. When the applied electric field is small, the induced strain is nearly proportional to the electric field. As the field becomes larger (i.e., greater than about 100 V/mm), however, the strain curve deviates from this linear trend and a significant hysteresis is exhibited due to polarization reversal. This limits the use of
Table 12-5. Characteristics of SAW filter substrate materials.
SAW velocity (m/s) Coupling factor (/c2, %) Temperature coefficient of frequency (ppm/°C) Permittivity (es) Curie point (Tc, °C) Pb(Mn 1/3 Nb 2/3 )O 3 PbZrO 3 -PbTiO 3 .
LiTaO3 (X-112°Y)
LiNbO 3 (128 °Y)
PZT a
ZnO
3295 0.7 -31 47.9 618
3960 6.0 -78 67.2 1210
2430 2.9 -17 350 300
3150 0.6 -15 8.84 1200
660
12 Ferroelectric Ceramics
-10
-5 0 5 10 Electric field (kV/cm)
-10
-5 0 5 10 Electric field (kV/cm)
the material in actuator applications that require a linear, non-hysteresis response. Previously, electrostriction, a second-order phenomenon of electromechanical coupling, was considered to be a negligible effect and, therefore, was not studied from a practical point of view. Recent research and development on PMN [lead magnesium niobate, Pb(Mg 1/3 Nb 2/ 3)O 3 ]-based ceramics (Cross et al., 1980), however, have kindled new interest in the use of such electrostrictive materials in this area. PMNbased ceramics exhibit significant strains up to 0.1 % (i.e., a 1 cm sample can elongate Displacement u sed Driving method
Figure 12-29. Field-induced strain in ceramics, (a) Piezo-electric material PLZT (7/62/38). (b) Electrostrictive material 0.9Pb(Mg 1/3 Nb 2/ 3)O 3 O.lPbTiO,.
by as much as 10 jim). Another attractive feature of these materials is the near absence of hysteresis (Fig. 12-29b). Piezoelectric/electrostrictive actuators may be classified into two categories based on the type of driving field applied to the device and the nature of the strain induced by that field (Fig. 12-30): (1) Rigid displacement devices for which the strain is induced unidirectionally by an applied DC field, and (2) resonating strain devices for which the mechanical resonance is excited by an AC field. The first can be further divided into two categories: (1) Servo disName
Servo drive Eb
Servo displacement transducer
0
Rigid displacement
Material
Bias field Electrostrictive materials (PMN-based)
E Em Pulse field On/Off drive 0
OFF
E
Strain x
Pulse drive motor _
Soft piezoelectric materials (PZT-based)
Ultrasonic motor
Hard piezoelectric materials
Sinusoidal field
Resonating displacement- Alternating drive
r\ Time t
Figure 12-30. Classification of piezoelectric/electrostrictive actuators; E: electric field, x: strain.
12.4 Piezoelectric Devices
placement transducers controlled by a feedback system through a position-detection signal, and (2) pulse-drive motors that operate in a simple ON/OFF switching mode (Uchino, 1986). Very recently, an actuator referred to as a flight actuator has been proposed which hits a steel ball strongly by means of an ON/OFF piezoelectric unit similar to that found in a pinball machine (Ota et al., 1985). The material requirements for the three classes of devices are somewhat different and hence, certain compounds will be better suited to particular applications. The ultrasonic motor, for instance, requires almost the conventional hard-type piezoelectric with a high mechanical Q. The servodisplacement transducer suffers most from strain hysteresis and, therefore, a PMN electrostrictor is used for this device. The pulse-drive motor requires a low-permittivity material aiming at a quick response rather than a small hysteresis so that soft-PZT piezoelectrics are most suitable for this application. In the sections to follow, three typical application examples will be taken up for examination and discussion. 12A.lA Deformable Mirrors In the field of optical information processing, deformable mirrors have been proposed to control the phase of the incident light wave. The deformable mirror can be made more convex or concave as necessary. This type of mirror, which finds application as an accessory device on observatory telescopes, effectively corrects for image distortions resulting from fluctuating airflow. An example of a deformable mirror is a multilayered two-dimensional bimorph type like that shown in Fig. 12-31 (Sato et al., 1982). The operation of this mirror is
661
similar in principle to a "bi-metal" device which consists of two metal plates, with different thermal expansion coefficients, bonded together. The plates will bend with a change in temperature. When three layers of thin electrostrictive ceramic (PMN) plates are bonded to the elastic plate of a glass mirror, the mirror surface is deformed in various ways corresponding to the strain induced in the PMN-layer. The nature of the deformation is determined by the electrode configuration and the distribution of the applied electric field. Trial units have been designed such that the first layer, with a uniform electrode pattern, produces a spherical deformation (i.e., refocusing), while the second layer with an electrode pattern of six minute divisions corrects for coma aberration. 12.4.7.2 Impact Dot-Matrix Printers Among the various types of printing devices currently in use, dot-matrix printers are routinely employed. Each character formed by such a printer is initially composed of a 9 x 9 dot matrix. A printing ribbon is subsequently impacted by a multiwire array. A sketch of the printer appears in Fig. 12-32 a (Yano et al., 1984). The basic actuator assumes a multilayer configuration in which roughly 100 thin piezoelectric ceramic sheets are stacked. The advantages of using a multilayer-type actuator for this particular application include a low driving voltage, large displacement, and a high electromechanical conversion efficiency. This actuator is installed in a specially designed displacement magnification unit (Fig. 12-32 b) to drive the top printer pins. This unique magnification unit is based on a monolithic hinge lever with a magnification of 30 and realizes an amplified displacement of 300 |im and an energy transfer efficiency greater than 50%.
662
12 Ferroelectric Ceramics
(a) Layer
Electrode configuration
1st Layer 1
2nd Layer
(b) Aberration
1
T
Vv + 2
Interference fringe pattern of desired wavefront
PMN v. Electrostrictive y material Glass plate
Interference fringe pattern of generated wavefront
Refocusing
Coma aberration x 3 +xy 2
Refocusing + coma aberration C y9 (x 3 +xy 2 ) + C,(x 3 +xy 2 )
The merits of the piezoelectric impact printer compared with the conventional electromagnetic type are: (1) higher printing speed by an order of magnitude, (2) lower energy consumption by an order of magnitude, and (3) reduced printing noise since a complete sound shield may be employed with the heatless drive. 12.4.7.3 Ultrasonic Motors Efforts have been made to develop highpower ultrasonic vibrators as replacements for conventional electromagnetic motors. Two actuators, in particular, are currently being investigated for this application: A
Figure 12-31. (a) Structure of a multilayer bimorph deformable mirror, (b) The actual control of wavefront.
vibratory-coupler type and a surface-wave type (Akiyama, 1986). The basic design of the vibratory coupler is pictured in Fig. 12-33. The Langevintype piezoelectric vibrator generates a flatelliptical movement at the tip of the vibratory piece. When contacting a rotor at a slight angle, the vibratory piece generates a rotational torque. This simple design, however, has several drawbacks. Defacement of the rotor caused by mechanical friction at the contact point and lack of control in both the clockwise and counter-clockwise directions are two of the most serious problems associated with this unit. The problem of
12.4 Piezoelectric Devices (b)
663
Lever 1
\
Head element
Force point Supporting point
Lever 3 Lever 2 Wire
4- Piezoelectric actuator ^Wire
Wire guide
Figure 12-32. (a) Structure of printer head and (b) differential type piezoelectric printer head element.
Oscillator
Figure 12-33. Basic structure of a vibratory couplertype ultrasonic motor.
Propeller.etc.
friction is alleviated by securely pressurefitting the vibratory reed and rotor together in order to restrict, as much as possible, sliding during operation. The model picture in Fig. 12-34 is one such modified unit (Kumada, 1985). At a rotational speed of 600 rpm, this motor has performance characteristics that surpass normal electromagnetic motors with a rotational torque of 13kgf-cm (^1.3Nm) and an energy conversion efficiency of 80%. The other type of motor utilizes surface wave vibrations. The operating principle of
(b)
Torsion coupler Aluminum horn
Piezo electric element
Spacing adjustment plate
Aluminum ring
Figure 12-34. Ultrasonic motor using a torsion coupler (a) and rough sketch of the torsion vibration coupler (b).
664
12 Ferroelectric Ceramics
ability to rotate in both directions and its thin design which makes it suitable for installation in video (VTR) or movie cameras as an automatic focusing device. w
\ \ .
Direction of wave travel
12.5 Electrooptic Devices
Figure 12-35. Operating principle of a surface wave linear motor (transverse propagating wave being excited on an elastic body).
this device is illustrated in Fig. 12-35. By means of the traveling elastic wave induced by the piezoelectric, a slider in contact with the "rippled" surface of the elastic body is driven in the direction indicated. Both linear and rotational-type motors of this type are possible. The structure of a surfacewave rotational-type motor is pictured in Fig. 12-36. Although the energy transformation efficiency (30%) and rotational torque (0.5 kgf • cm) of the surface wave device are rather low as compared to the vibratory-coupler type, its merit lies in its -Rotor -Slider -Elastic ring -Piezoelectric ring Surface
In the 1960s the nonlinear polarizability of ferroelectrics was discovered and various electrooptic and optical parametric devices have been investigated. However, problems still remaining are the difficulty of preparing high-grade optically-homogeneous single crystals, and the correspondingly high cost for a given level of performance. 12.5.1 Transparent Electrooptic Ceramics
Even with a polycrystalline microstructure, a ferroelectric ceramic can exhibit the electrooptic effect if it is sintered to a porefree state to make it transparent. The bestknown material is the (Pb,La)(Zr,Ti)O 3 system (PLZT), which has good transparency in a wavelength range from visual to infrared, and exhibits an optical anisotropy
Direction of polarization
LLJ
0.5/
S
6.5
0.5 2.5
Unit: mm
Figure 12-36. Structural example of a surface wave rotational motor.
665
12.5 Electrooptic Devices PbZrO3 100
[mol %] PbZrO3 90
80
70
60
50
40
PbTiQ, 20
10
0
Material
P 1 E
Figure 12-37. Relation between PLZT composition and structure and electrooptic application.
under applied electric voltage. Displays and light valves are promising applications. Figure 12-37 shows the phase diagram of the (Pb 1 _ x La J C )(Zr 1 _,Tg i _ x / 4 O 3 system and the corresponding possible applications. The PLZT solid solution exhibits both the Pockels' and Kerr electrooptic effects, depending on the composition. Some examples are shown in Fig. 12-38. The electrooptic coefficients of the PLZT system are much larger than the values in conventional crystals such as LiNbO 3 and (Sr,Ba)Nb 2 O 6 (SBN) (see Table 12-6), which means that the voltage required for the electrooptic shutter is much less in the PLZT
PLZT 9/65/35 (2nd)
PLZT 7/62/38 (1st)
1
y -10
An 1 E
y. . V y
-20 -10 0 10 20 -20 -10 0 10 Electric field Electric field E [kV/cm] E [kV/cm]
20
Figure 12-38. Polarization P and birefringence An as a function of electric field E in PLZT ceramics.
12.5.2 Bulk Electrooptic Devices
PLZT eye glasses for stereo TV have been fabricated using the light shutter function (Kumada et al., 1977). Lenses consist of a pair of optically isotropic PLZT (9/65/35) discs sandwiched by two crossed polarizers. When zero voltage is applied on the electrode, the light will not be transmitted. The transmitted light intensity in-
Table 12-6. Pockels' (1st) and Kerr (2nd) electrooptic coefficients for various materials. Materials 1st electrooptic coefficient
LiNbO 3 Ba 2 (K 0 . 9 Na 0 . 1 )Nb 5 O 15 KH 2 PO 4 (Sr0,5Ba0,5)Nb2O6 PLZT 8/65/35 (GS = 10 \un) PLZT 8/65/35 (GS = 3 \im)
r(xlO~ l o m/V) 0.17 0.52 0.52 2.10 5.23 6.12 #(xlO- 1 6 rn 2 /V 2 )
2nd electrooptic coefficient PLZT 9/65/35 (GS = 2 urn) PLZT 10/65/35 (GS = 2 jim)
5.30 9.12 1.07
666
12 Ferroelectric Ceramics
creases with increasing applied voltage, and reaches a maximum when the phase difference (retardation) of 180° is induced in the PLZT disc. The voltage required for the maximum intensity is denoted as a half-wavelength voltage. The stereo TV image of an object is taken by two video cameras corresponding to the two eyes and the signal from each camera is mixed alternately to make a frame for the right- and left eyes. When viewing, the right and left PLZT shutters are triggered synchronously for each image frame, resulting in a stereo image. Recent progress with high-definition TVs is remarkable, and several systems have been proposed. One of the promising devices is a projection-type TV utilizing two-dimensional PLZT displays (Ohmura, 1989). Electrooptic characteristics in PLZT ceramics are generally much superior in response speed and contrast ratio to those in liquid crystals. Moreover, the durability of ceramics under strong light illumination is excellent. However, the most significant problems in PLZT devices, which have prohibited their actual commercialization, are the high driving voltage and the cost. Therefore the development of a simple, mass-production process and the design of
electrode configurations with a narrow gap are the key factors for PLZT displays. A recently developed design for a 2-dimensional display as shown in Fig. 12-39 presents a very bright image with no crosstalk-related problems and is easy to produce. The fabrication process of the 2-dimensional PLZT light valve array is outlined in Fig. 12-40. Wet-chemically prepared (coprecipitated) PLZT 9/65/35 powders were mixed with organic solvent and binder and formed into a green sheet. The sheets were printed with electrodes and then laminated and sintered in an atmosphere with a controlled oxygen content. A transmittance of 62% could be obtained by atmosphere-controlled sintering, comparing well with a value of 63% for the ideal sample prepared by hot-pressing. Finally, the external connecting electrodes were applied to make vertical and horizontal addressing possible. The construction of the PLZT color image projector is shown in Fig. 12-41. Three light fluxes, red, green and blue, are obtained by separating light from a xenon lamp with dichroic mirrors, and passing each through identical PLZT shutter. Then, the fluxes are superimposed to make a color image. 12.5.3 Waveguide Modulators
Light
Figure 12-39. Newly developed design of a 2-dimensional display.
Light waveguides can be fabricated by depositing a high-refractive-index layer on a substrate. The principle of the waveguide is shown schematically in Fig. 12-42. Nbdiffused LiNbO 3 single crystals are commonly used; Fig. 12-43 a and 12-43b show typical planar- and ridge-type electrooptic waveguides (Kaminow, 1975). The transmitted light intensity is easily modulated by applying a relatively low voltage. Phase modulation by 1 radian can be achieved by applying a voltage of 0.3 V with power consumption of several jiW/MHz.
12.5 Electrooptic Devices
667
Fabrication process
electrode (vertical)
I
C |
electrode (horizontal)
Doctor blade casting
PLZT green sheet
Green sheet Electrode printing Lamination
AI2O3 crucible
L
Firing
(
Multilayer PLZT
O2gas j
Cutting Polishing | (
External electroding
PLZT sample Atmosphere powder
2 - D Display ~~"
Figure 12-40. Fabrication process of the newly developed 2-D display.
-Mirror
Dichroic mirror (Green Ret.)
Dichroic mirror (Red Ref.)
Figure 12-41. Construction of the PLZT color image projector.
668
12 Ferroelectric Ceramics TE1 TE0 n3 Superstrate
n 2 Substrate
(b)
/ >
Figure 12-42. Diagrams of (a) slab and (b) graded-index waveguides. The wavefunctions for the TE 0 and TEX modes are shown in the refractive-index profiles.
12.6 Positive Temperature Coefficient (PTC) Materials 12.6.1 The PTC Phenomenon When barium titanate (BaTiO3) is doped with a low concentration of lanthanide ions (0.3 at.%) the ceramic becomes semiconductive with a resistivity in the range of 10-10 3 Q • cm. Moreover, the resistivity is Electrode
Guided light beam
Electrode
LiNbO3 crystal
Figure 12-43. Electrooptic waveguides, (a) Planar-type and (b) ridge-type.
drastically increased by 3-5 orders of magnitude with increasing temperature around the Curie point. This phenomenon was discovered in 1954, and denoted as the PTC (positive temperature coefficient of resistivity) effect, since then it has been investigated intensively by many researchers (Andrich, 1965; Heywang, 1964). The PTC dopant is an ionic species with a larger ionic valence such as La, Sm, Ce or Gd, and replaces the Ba ions and Nb, Ta, Bi in the Ti sites. Since the temperature at which the resistivity anomaly occurs is closely related with the Curie point, the temperature coefficient can easily be designed by choosing the solid solution on the basis of BaTiO 3 . Fig. 12-44 shows some varieties of the PTCR curves. The theory for the PTC effect has not been established completely. The most acceptable model is illustrated in Fig. 12-45, which was initially proposed by H. Heywang et al. (Heywang, 1964). When the two semiconductive (n-type) ceramic particles are in contact through a grain boundary, an electron energy barrier (Schottky barrier) is generated and the barrier height is given by the following equation: cj) = eNs2/(2s08Nd)
(12-38)
JVd is the concentration of donor atoms and Ns is the surface density of negatively
12.6 Positive Temperature Coefficient (PTC) Materials
100 M
Mn 0.127
1M
100 k
Cr 0.37
No addition '% 10 k DC
Si 1.0
1k
100
10
tial barrier due to the increase in permittivity as the temperature falls to Tc. = C/(T-T0)
10M
100 200 Temperature (°C)
300
Figure 12-44. Resistivity vs. temperature behavior of PTCR BaTiO3 ceramics. Modifiers and additive concentrations are indicated.
charged acceptors (here assumed to be confined to the surface due to Ba vacancies). Note that the permittivity s obeys the Curie-Weiss law (Eq. (12-39)) above Tc, and that the low resistance at Tc is thus accounted for by the lowering of the poten-
669
(12-39)
Below Tc the permittivity falls, but the spontaneous polarization appears and controls the electron concentration to reduce the barrier height. This keeps the resistivity in a rather low range. 12.6.2 PTC Thermistors
PTC thermistors are applicable not only for temperature-change detection but also for active current controllers. The thermistor, when self-heated, causes a decrease in the current owing to the drastic increase of resistivity. Practical applications are found in over-current/voltage protectors, starting switches for motors and automatic demagnetization circuits for color TVs. "Ceramic heaters" have also been widely commercialized in panel heaters, electronic thermos bottles and hair dryers. 12.6.3 Grain Boundary Layer Capacitors
When a semiconductive BaTiO3 ceramic is oxidized to make a resistive surface layer, it can be used as a high-capacitance condenser. The capacitance is adjustable in the range of 0.4-0.5 jiF/cm2.
Figure 12-45. Energy-level diagram near a grain boundary of the PTCR BaTiO3.
670
12 Ferroelectric Ceramics
Figure 12-46. Model of the grain boundary layer condensers.
A new type of grain boundary layer (GBL) condensers has been developed by using electrically resistive grain boundaries. The model is illustrated in Fig. 12-46. (See also Chap. 14 of this Volume for a more detailed analysis of grain boundary semiconducting effects.) In practice, CeO 2 or Bi 2 O 3 is coated on a semiconductive ceramic and diffused into the grain boundaries by thermal treatment so as to make the boundary layer highly-resistive. The resistive grain boundary layers of 1 |im thickness are fully connected in the ceramics with grains of 10 Jim in size. This type exhibit excellent frequency characteristics and can be used as wide-band pass condensers up to several GHz.
12.7 Conclusions We have described the fundamentals and applications of ferroelectrics, including: high-permittivity dielectrics pyroelectric devices piezoelectric devices electrooptic devices PTC materials From a viewpoint of commercialization, capacitor dielectrics account for most of
the sales at present, and piezoelectric vibrators such as buzzers and speakers hold the second position. The sales concerned with the other applications are negligibly small. What does the future hold for ferroelectric devices? Ferroelectrics can be utilized in various devices but until now have failed to reach commercialization in most cases. In the light sensor, for example, semiconductive materials are superior to ferroelectrics in response speed and sensitivity. Magnetic devices are much more popular in the memory field, and liquid crystals are typically used for optical displays. Ferroelectric devices often fail to be developed in the cases where competitive materials exist. Therefore, it can be said that ferroelectrics are strong candidates for application only in those fields where no viable alternative materials exists. It is the author's opinion that the following will be promising areas: electromechanical devices (piezoelectric actuators, ultrasonic motors) thin-film hybrid sensors (pyro-, pressure, acceleration sensors) electrooptic devices (light waveguides, thinfilm hybrid displays)
12.8 Appendix 1: Tensor Representation of Physical Properties 12.8.1 Tensor Representation
Let us first consider an example of tensor conductivity. The conductivity is defined so as to correlate an applied electric field E and the induced current density y as follows: j = aE
(Al)
671
12.8 Appendix 1: Tensor Representation of Physical Properties
Since both the electric field and the current density are first rank tensors (i.e., vector) quantities, the conductivity should have a second rank tensor representation (i.e., with two suffixes); this is described as '12
(A2) '32
or (A3) A third-rank tensor is exemplified by piezoelectric coefficients, providing a relation between the applied field and the induced strain x: x = AE
12.8.2 Crystal Symmetry and Tensor Form
When we measure a physical property along two different directions, the two values measured must be equal if these two directions are crystallographically equivalent to each other. This consideration sometimes reduces the number of the independent tensor components representing the above property. Let us again take conductivity as an example of a second-rank tensor. If the current density) in an (x9y,z) coordinate system is described in an (x\y\ z') system a s / , j and / are related using a unitary matrix x as follows: H2
(A 4)
Since the E and x are first-rank and second-rank tensors, respectively, the d should have a third-rank tensor form represented as X (A 5) jk — The d tensor is composed of three layers of the symmetrical matrices.
(A 7)
*22
The electric field is transformed in the same way: (A 8) or (A9)
Mil
1st layer (i = 1)
M23
*131 " 1 3 2 11
^212
1
^213\
A unitary matrix without an imaginary part has the following relation:
2nd layer (i = 2) ( d221 d222 d223 J (A6) \d231
^232
"12
^233/
11
^312
^313
3rd layer (i = 3) ( d321 \d33l
d322 d332
d323 d333/
Generally speaking, if two physical properties are represented using tensors of prank and g-rank, the quantity which combines the two properties in a linear relation is also represented by a tensor of (p +.q)rank.
"13
\
«22
«23 )
a
a
32
/
"11
"21
"31
\
= ( *12 ^22 %2 I \ fl 13
33/
a
23
a
33/
For centro-symmetry, the transformation matrix is written as
and for rotation about a principal axis,
(
cos 0
-sinfl 0
sin 9 ()\
cosO 0 J 0
1/
672
12 Ferroelectric Ceramics
Then, we can calculate the corresponding a' tensor defined by (A 10)
As far as a third-rank tensor such as piezoelectric tensor is concerned, the transformation on change of the coordinate system is represented as =
Z l,m,n
(A 15)
a
ilajmakndimn
When the crystal has a 4-fold axis along the z-axis, the transformation matrix is given by
When the crystal has a 2-fold axis along the z-axis, the conductivity tensor should have the same components for the transformation of
In consideration of the tensor symmetry with m and n such as d123 = d132 and d213 = d231 (each matrix of the zth layer of the d tensor is symmetrical), we can obtain the relations:
— ^221 — ^212 — ^122 — ^331
= d313 = d133 = d332 = d323 = d233 = d312 = d321 = 0 From the condition '11 '21
^31
(A 16)
^333*0 ^311
=
dii^
= di^ti
11j
^32
123
^322 lol
= d?7? = dsyrti ZZJ
ZJZ
*231
N
'11
'12
'21
*22
-1 00 0 - 1 0 J(A13)
we can induce the relations: 31
13
32
23
(A 14) (A 17) It is very important to note that most of the physical constants have a symmetric tensor form (the proof involves thermodynamical considerations and is beyond the scope of this article).
12.8 Appendix 1: Tensor Representation of Physical Properties
the following change in the notation for the strain components (A 19)
12.8.3 Reduction of the Tensor (Matrix Notation)
A general third-rank tensor has 3 3 = 27 independent components. Since dijk is symmetrical in j and k some of the coefficients can be eliminated, leaving 18 independent dijk; it also facilitates the use of the matrix notation. So far all the equations have been developed in full tensor notation. But when calculating actual properties, it is advantageous to reduce the number of suffixes as much as possible. This is done by defining new symbols, for instance, d21 — d211 and d14_ = 2d 1 2 3 : The second and third suffixes in the full tensor notation are replaced by a single suffix 1 to 6 in matrix notation, as follows: tensor notation 11 22 33 23,32 31,13 12,21 matrix notation
1 2
3
4
673
5
v
ll
-*12
C
12
• X 22
C
31
X
2^
The reason for the | s in the substitution (A 19) is due to the cancellation with | s in (A 18). Then, we have ,A o m E,
\J\2\)) (i = l,2,3;./ = 1,2,....6)
or
22,
x5
^33
d14r
d24
dt<
d 25
U
d26
d3
(A21)
3
Concerning the stress components, the | s are unnecessary. (A 22^
6
In terms of these new symbols the array (A 6) is rewritten as:
The matrix notation has the advantage of compactness over the tensor notation, and it makes it easy to display the coefficients on a plane diagram. However, it must be remembered that in spite of their form, the d(js do not transform like the components of a second-rank tensor. An example of a piezoelectric matrix for the point group 4 is written as (A23)
(A 18)
The last two suffixes in the tensor notation correspond to those of the strain components; therefore, for consistency, we make
674
12 Ferroelectric Ceramics
12.9 Appendix 2: Phenomenology of Ferroelectricity 12.9.1 Landau Theory of the Phase Transition
A thermodynamical theory explaining the behavior of a ferroelectric crystal can be obtained by considering the form of the expansion of the energy as a function of the polarization P. We assume that the Landau free energy F in one dimension should be represented formally as: (A24) The coefficients a, /?, y depend on the temperature in general. Note that the series does not contain terms in odd powers of P because the free energy of the crystal will not change by the polarization reversal (P -> — P). The phenomenological formulation should be applied for all the temperature range through paraelectric and ferroelectric states. The equilibrium polarization in an electric field E satisfies: dF
(A25)
To obtain the ferroelectric state, the coefficient of the term in P2 must be negative, in which the polarized state is stable, while in a paraelectric state it must be positive passing through zero at some temperature To (Curie-Weiss temperature):
« = (T-r o )/(8 O -c)
(A 26)
C is taken as a positive constant and To is equal to or lower than the actual transition temperature Tc (Curie temperature). The variation of a with temperature is explained microscopically by thermal expansion and other effects of anharmonic lattice interactions.
12.9.1.1 Second-Order Transition
When P is positive, the y is often neglected because nothing special is added by this term. The polarization for zero applied field (A 27) is obtained from (A 25) so that either Ps = 0 or P2 = (To - T)/(jff e0 C).
T-To z0C
(A27)
For T > To, the unique solution Ps = 0 is obtained. For T < TQ the minimum of the Landau free energy is obtained at: >C)
(A 28)
The phase transition occurs at Tc = To and the polarization goes continuously to zero at this temperature; this is called a secondorder transition. Relative permittivity e is calculated as: 1/8 = so/(dP/dE) = 80 (a + 3 p P2)
(A 29)
Then, £
=
(C/(T- T0) \C/[2(T0-T)]
(T > To) (To < T)
(A 30)
Figure 12-A1 shows the variations of Ps and 8 with temperature. It is notable that the permittivity becomes infinite at the transition temperature. Triglycine sulphate is an example exhibiting the second-order transition. 12.9.1.2 First-Order Transition
When /? is negative in Eq. (A 24) and y is taken positive, the transition becomes first order. The equilibrium condition for E = 0 (A 31) leads to either Ps = 0 or (A 32).
(T-To).
(A31)
l(2y) (A 32)
675
12.9 Appendix 2: Phenomenology of Ferroelectricity
1i 1 i i
\
j /
Spontaneous ^ v polarization Ps \J\
I il
1 I \ \
i
\
Permittivity t
/
y
Spontaneous polarization Ps
/ /
;
Permittivity e
Inverse permittivity l/e
Inverse permittivity l/e , —- *"" TQ
Temperature
TQ
(Curie Temp.)
Temperature
(Curie Temp.)
Figure 12-A1. Second-order transition in a ferroelectric.
Figure 12-A 2. First-order transition in a ferroelectric.
The transition temperature 7^ is obtained from the condition that the free energies of the paraelectric and ferroelectric phases are equal: i.e., F = 0, or:
the elastic compliance and the electrostrictive coefficient. Note that the piezoelectric coupling term PX is omitted and the electrostrictive coupling term P2 X is introduced when the paraelectric phase has centrosymmetry (non-piezoelectric). This leads toEq.(A36)and(A37).
(A 33) Therefore:
E = (dGJdP) = aP + pP3 + yP5 -2QPX
(A 34)
16(
(A36) 2
x= - {dGJdX) = s i + QP .
Note that the Curie Temperature Tc is slightly higher than the Curie-Weiss temperature T09 and that the discrete jump of the Ps appears at Tc. Also, the permittivity exhibits a finite maximum at Tc for a first-order transition (Fig. 12-A 2). Barium titanate is a good example.
12.9.2.1 CaseI:J*T=0 When an external stress is zero, the following equations are derived: (A38) x = QP2
(A39) 2
12.9.2 Phenomenology of Electrostriction Let us assume that the elastic Gibbs energy should be expanded in a one-dimensional form: G±(P,X, T) = |aP 2 + y 2
2
-\sX -QP X,
\
[a = (T-T0)/(e0Q]
P, X, T are polarization, stress and temperature, respectively, and s and Q are called
(A37)
l/e o e = a + 3/3P + 5yP*
(A40)
If the external electric field is equal to zero (E = 0), two different states are derived; P = 0 and P2 = {^Jp2-4ay - P)/(2y). (I) Paraelectric phase: Ps = 0 or P = eosE (under small E) Permittivity: e = C/(T - To) (Curie-Weiss law)
(A41)
676
12 Ferroelectric Ceramics
Electrostriction: Q8282E2
X=
(A42)
(8T0/6p) = (8Tc/8p) = - 2 Q s0 C
(II) Ferroelectric phase:
Ps2 = (yJP2 — 4ay-
2s08QPsE+Qs2e2E2
(A43)
Spontaneous strain:
12.10 References (A 44)
Piezoelectric constant: (A 45)
d = 2sosQPs
Piezoelectricity is equivalent to the electrostrictive phenomenon biased by the spontaneous polarization. Temperature dependence of the spontaneous strain and the piezoelectric constant is plotted in Fig. 12-A3.
Piezoelectric constant d Spontaneous
ti
T c Temperature (Curie Temp.)
Figure 12-A 3. Temperature dependence of spontaneous strain and piezoelectric constant.
12.9.2.2 Case II: X * 0 When a hydrostatic pressure p (X = — p) is applied, the inverse permittivity is changed in proportion to p: l/808 =
(A48)
In general, the ferroelectric Curie temperature is decreased with increasing hydrostatic pressure.
(under small E) +
Therefore, the pressure dependence of the Curie-Weiss temperature To or the transition temperature Tc is derived as follows:
Akiyama, Y. (1986), Ultrasonic Motors/Actuators. Tokyo: Triceps. Andrich, E. (1965-66), Electr. Appl. 26, 123. Bhalla, A. S., Newnham, R. E., Cross, L. E., Schulze, W. A., Dongherty, I P., Smith, W. A. (1981), Ferroelectrics 33, 139. Cross, L. E., Jang, S. I , Newnham, R. E., Nomura, S., Uchino, K. (1980), Ferroelectrics 23, 187. Furuta, K., Uchino, K. (1986), Advanced Ceram. Mater. 1, 61. Heywang, W. (1964), /. Am. Cer am. Soc. 47, 484. Jaffe, B., Roth, R. S., Marzullo, S. (1955), /. Res. Nat. Bur. Stds. 55, 239. Kaminow, I. P. (1975), Trans. IEEE, M.T.T. 23, 57. Kanzig, W. (1951), Helv. Phys. Ada 24, 175. Kawai, H. (1969), Jpn. J. Appl. Phys. 8, 975. Kinase, W, Uemura, Y, Kikuchi, M. (1969), /. Phys. Chem. Solids 30, 441. Kittel, C. (1966), Introduction to Solid State Physics. New York: John Wiley & Sons, Inc. Klicker, K. A., Biggers, X V., Newnham, R. E. (1981), J. Amer. Ceram. Soc. 64, 5. Krause, H. B., Cowley, J. M., Wheatley, J. (1979), Acta Cryst. A 35, 1015. Kumada, A. (1985), Jpn. J Appl. Phys. 24, Suppl. 24-2, 739. Kumada, A., Kitta, K., Kato, K., Komata, T. (1977), Proc. Ferroelectric Mater. & Appl. -2, p. 205. Nikkei Mechanical (1983), Feb. 28 Ed., p. 44. Ohmura, K., Murai, Y, Uchino, K., Giniewitcz, J. (1989), Interaction. Display Research Confer., Proc, IEEE, p. 138. Ota, T., Uchikawa, T., Mizutani, T. (1985), Jpn. J. Appl. Phys. 24, Suppl. 24-3, 193. Rolov, B. N. (1963), Fiz. Tverdogo Tela 6, 2128. Rosen, C. A. (1957), Proc. Electronic Component Symp., p. 205. Sato, T., Ichikawa, H., Ikeda, O., Nomura, S., Uchino, K. (1982), Appl. Optics 21, 3669.
(Ferroelectric) 5yP* + 2Qp (T -T0 + 2Qs0Cp)/(80 C) (Paraelectric)
(A46) (A47)
12.10 References
Shibata, K., Takeuchi, K., Tanaka, T., Yokoo, S., Nakano, S., Kuwano, Y (1985), Jpn. J Appl. Phys. 24, suppl. 24-3, 181. Skanavi, G. I., Ksendzov, I. M., Trigubenko, V. A., Prokhvatilov, V. G. (1958), Soviet Phys. - JETP 6, 250. Smolensky, G. A., Isupov, V. A., Agranovskaya, A. I., Popov, S. N. (1961), Sov. Phys. - Solid State 2, 2584. Taylor, R. G. R, Boot, H. A. H. (1973), Contemporary Phys. 14, 55. Uchino, K. (1986), Bull. Amer. Ceram. Soc. 65, 647. Uchino, K., Cross, L. E., Newnham, R. E., Nomura, S. (1980), /. Phase Transition 1, 333. Uchino, K., Kuwata, X, Nomura, S., Cross, L. E., Newnham, R. E. (1981), Jpn. J. Appl. Phys. 20, Suppl. 20-4, 171. Uchino, K., Nomura, S. (1983), Oyo Butsuri 52, 575. Warner, D. J., Pedder, D. X, Moody, I. S., Burrage, X (1981), Ferroelectrics 33, 249. Yano, T., Fukui, L, Sato, E., Inui, O., Miyazaki, Y (1984), Electr. & Commun. Soc, Proc. 1-156.
677
General Reading Herbert, X M. (1982), Ferroelectric Transducers and Sensors. New York: Gordon and Breach. Jaffe, B., Cook, W. R., Jaffe, H. (1971), Piezoelectric Ceramics. New York: Academic Press. Jona, K, Shirane, G. (1962), Ferroelectric Crystals. Oxford: Pergamon Press. Levinson, L. M. (1988), Electronic Ceramics. New York: Dekker. Nowotny, X (1992), Electronic Ceramic Materials. Brookfield: TransTech Publ. Nye, X F. (1969), Physical Properties of Crystals. Oxford: Oxford University Press. Smolenskii, G. A. (1984), Ferroelectrics and Related Materials. New York: Gordon and Breach. Uchino, K. (1986), Piezoelectric/Electrostrictive Actuators. Tokyo: Morikita PubL Uchino, K. (1991), Piezoelectric Actuators - Problem Solving. Tokyo: Morikita Publ.
13 Ferrimagnetic Ceramics Bhaskar B. Ghate AT&T Bell Laboratories, Mesquite, TX, U.S.A. Alex Goldman Ferrite Technology Worldwide, Pittsburgh, PA, U.S.A.
List of Symbols and Abbreviations 13.1 Introduction 13.2 Historical 13.3 Basic Concepts 13.3.1 Atomic Magnetic Moments 13.3.2 Ferrimagnetism 13.3.3 Saturation Magnetization and Curie Temperature 13.3.4 Domains and Bloch Walls 13.3.5 The Hysteresis (B-H) Loop 13.4 Ferrite Crystal Structures 13.4.1 The Spinel Structure 13.4.2 The Hexagonal Ferrite Structure 13.4.3 The Garnet Structure 13.5 Intrinsic and Extrinsic Properties 13.5.1 Magnetization of Zn-Substituted MnZn Ferrite 13.5.2 Magnetic Anisotropy 13.5.3 Magnetostriction 13.5.4 Types of Hysteresis Loops 13.6 Ferrite Processing 13.6.1 Introduction 13.6.2 Powder Preparation 13.6.2.1 Conventional Processing 13.6.2.2 Nonconventional Processing 13.6.2.3 Calcining 13.6.2.4 Milling 13.6.2.5 Organic Binders and Additives 13.6.2.6 Spray Drying 13.6.3 Challenges in Pressing 13.6.4 Sintering 13.6.4.1 Ferrite Kilns 13.6.4.2 Sintering Cycles 13.6.4.3 Fast Firing Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.
681 683 684 684 684 685 687 687 688 689 690 691 691 692 693 693 694 695 696 696 696 696 700 700 701 701 702 702 702 703 704 706
680
13.6.5 13.6.6 13.7 13.7.1 13.7.2 13.7.3 13.8 13.9 13.10 13.11 13.12
13 Ferrimagnetic Ceramics
Vacuum Sintering, Hot Pressing, and Hot Isostatic Pressing Machining, Lapping, and Tumbling Case Studies High Permeability Ferrites Ferrites for High Frequency Power Supplies Ferrites for Recording Heads Hard Ferrites Microstmcture and Grain Boundary Chemistry Recent Developments Future Prospects References
707 709 711 711 717 720 722 723 725 725 726
List of Symbols and Abbreviations
681
List of Symbols and Abbreviations a A, B b B Bm BT £ s , Bsat Bmax d DCT Ea / H Hc k K K09Ki9K2
atmosphere parameter ion sublattices constant magnitude of magnetic induction or flux density magnitude of peak induction or flux density magnitude of remanent magnetization magnitude of saturation magnetization magnitude of maximum usable flux density density; minimum dimension normal to flux direction critical diameter anisotropy energy frequency magnitude of magnetic field strength magnitude of coercive field proportionality constant proportionality constant magnetocrystalline anisotropy constants referring to the zero, first, a n d second orders of the E a series L inductance m, n exponents M molecular weight MA,MB saturation moments of A, B site ions Ms saturation magnetization N Avogadro or Loschmidt number nB number of Bohr magnetons Pe power loss due t o eddy currents Ph hysteresis loss PO2 equilibrium oxygen pressure Ptot total power loss due to eddy currents Q quality factor R resistance Rp high core loss resistivity r oct>rtet radius of octahedral, tetrahedral sites T absolute temperature Tc Curie temperature T o (A), To (B) temperatures at which the S M P occurs for two concentrations (A a n d B) of F e 2 + ions x, y stoichiometric variables alJa2,a3 y d X
direction cosines of the ion moment relative to the three crystal directions stoichiometric variable loss angle magnetostriction coefficient
682
II', II"
,A
13 Ferrimagnetic Ceramics
saturation magnetostriction coefficient magnetostriction coefficients in the cube-edge and cube-diagonal directions permeability of a material real and imaginary (loss) components of permeability Bohr magneton initial, maximum permeability parallel permeability
/*0
aosoiuie permeaoiiiiy 01 iree space
Q
electrical resistivity
AC AES E, EP, Q EMI ESCA HDTV HIP HPF HRTEM MIG MOSFET OD PVA SEM SIMS SMD SMPS SMP SMT TEM VCR VHS YIG
alternating current Auger electron spectroscopy different shapes of ferrite cores electromagnetic interference electron spectroscopy for chemical analysis high-definition television hot isostatic press hot pressed ferrite high-resolution transmission electron microscopy metal-in-gap metal-oxide semiconductor field-effect transistor outside diameter polyvinyl alcohol scanning electron microscopy secondary ion mass spectrometry surface mount device switched mode power supply secondary maximum in permeability surface mount technology transmission electron microscopy video cassette recorder video home system yttrium - iron - garnet
683
13.1 Introduction
13.1 Introduction Oxide ceramics which exhibit ferrimagnetic behavior play an important role in the electronics industry and are commonly known as ferrites. Today's technology of high frequency recording, power supplies, telecommunications, television and entertainment electronics would have been very different were it not for the many useful properties of ferrites. Ferrites are the mixed metal oxides containing iron oxide as their main component. There are three important classes of commercial ferrites, each one having a specific crystal structure: (1) Soft ferrites with the cubic spinel structure such as NiZn-, MnZn-, and MgMnZn ferrites; (2) soft ferrites with the garnet structure such as the microwave ferrites, for example, yttrium iron garnets; and (3) hard ferrites with the magnetoplumbite (hexagonal) structure such as Ba and Sr hexaferrites.
Like ferromagnetic materials, ferrimagnetic ceramics exhibit spontaneous magnetization in the absence of an external field, consist of self saturated domains, and show the characteristic hysteresis behavior (Cullity, 1972 a; Smit and Wijn, 1959 b; Heck, 1974 b). The major difference between these two classes of materials, one primarily metals and the other ceramics, is that the resistivity of ferrites, depending on composition, is at least six to twelve orders of magnitude higher than that of ferromagnetic materials such as permalloys and silicon irons. This has given ferrites a distinct advantage as magnetic materials of choice in high frequency applications, although their saturation magnetization is approximately one fifth to one eighth that of silicon irons (Table 13-1). In addition, the crystal structures of ferrites are tolerant to numerous variations in their chemical compositions, giving the technologist access to a wide range of properties.
Table 13-1. Saturation flux density Bs, resistivity Q and Curie temperature Tc for several magnetic materials'1. Material
Iron (100% Fe) Silicon-Iron (4% Si) Cobalt (99.95% Co) Nickel (99.6% Ni) FeO • Fe 2 O 3 MnO • Fe 2 O 3 NiO • Fe 2 O 3 CuO • Fe 2 O 3 MgO • Fe 2 O 3 MnZn Ferrite NiZn Ferrite MgMn Ferrite MgZn Ferrite Zn Ferrite BaO-6Fe 2 O 3 5Fe 2 O 3 -3Y 2 O 3 (YIG)
Q
(T)
(Ocm)
(°Q
2.158 2.00 1.9 0.608 0.60 0.52 0.35 0.17 0.14 0.4-0.63 0.3-0.4 0.06-0.22 0.24-0.27 0 0.41 0.17
9.6 xlO" 6 60xl0"6 6.3 x l 0 ~ 6 8.7xlO~ 6 4xlO~ 3 104 8xl05 105 107 0.1-10 106 10 4 -10 6 10 7 -10 8 (4.5-8) xlO 3 10 4 -10 5 10 10 -10 12
770 730 1121 358 563-590 295-303 575-597 410-490 325-440 90-300 100-500 120-350 150-160 — 450 275
a Data from various sources including Heck (1974 b), Landolt-Bornstein (1970). The high value of Bs for MnZn ferrites is quoted from Kugimiya and Hirota (1989).
684
13 Ferrimagnetic Ceramics
Ceramic processing techniques allow the economic fabrication of devices in various shapes and sizes. Depending on their coercivity (Hc), ferrites are said to be either soft (Hc< 10 A/ cm) or hard (Hc > 100 A/cm) (for an explanation of Hc refer to Sec. 13.3.5). Soft ferrites may be subdivided further into two categories, one suitable for nonmicrowave applications (f< 100 MHz), and the other suitable for microwave applications (/MOOMHz). In this chapter, we will focus primarily on soft ferrites used in devices typically operating in the frequency range of 4 kHz (voice frequency) to 50 MHz. A few basic concepts necessary to understand the behavior of magnetic materials and their applications will be described, followed by an examination of the relation between composition, processing and microstructure, and resulting properties of ferrites. We will then elaborate on processing of three major product families of the technologically important MnZn spinel ferrites. The reader is also referred to Chap. 8 by Guillot (Magnetic Properties of Spinel Ferrite), Chap. 14 by Boll (Soft Magnetic Materials and Alloys), and Chap. 15 by Buschow (Permanent Magnet Materials) in Vol. 3 B of this Series. They cover the basic physics of ferro- and ferrimagnetism and materials science of garnets in particular, and some aspects of hexaferrite magnetic ceramics.
13.2 Historical Ferrites came into prominence at the end of the Second World War. The early work on ferrimagnetic materials was done in Japan by Kato and Takei (1933), and Kawai (1934), and in the Netherlands by Snoek (1936). It was Snoek and his coworker, Six, who realized that the most
important property of an inductor core material is not tan <5 (tangent of the loss angle) but the ratio of tan d/fi (fi being the permeability of the material), which functions as the correct loss factor (Wijn, 1971). This led directly to the development of MnZn ferrites with the highest permeability then attainable, while simultaneously ensuring a low loss factor. By 1945 Snoek had laid the foundations of the science and technology of ferrites and a new industry was born (Snoek, 1947). An excellent historical perspective on the research and development of ferrites is given by Wijn (1971) and Hoshino (1981). For a broader perspective on developments in Magnetism, the reader will find the issue of IEEE Transactions on Magnetics (1984) to be of special interest. It is filled with several interesting contributions. The industrial importance of ferrites becomes apparent when one examines the diversity of their applications (Table 13-2). The 1990 estimated annual world output of soft and hard ferrites (Ruthner, 1989) is shown in Table 13-3, and is valued at 1.7 billion dollars (Warlimont, 1990; Yamamoto, 1990). Through the years, not only the demand in terms of tonnage has steadily increased but also the specific applications of ferrites have changed remarkably and kept pace with the developments in electronic technologies. At this time, the TV industry remains the largest user of ferrites with approximately 1 kg of ferrites per TV set. We will discuss future trends towards the end of this chapter.
13.3 Basic Concepts 13.3.1 Atomic Magnetic Moments The magnetic properties of solids have their origin in the two types of electron motion, orbital and spin. Each has a
13.3 Basic Concepts
685
Table 13-2. Applications of ferrites. Class
Primary characteristics
Applications
NiZn
high \i Qa, high resistivity
antenna rods (< 15 MHz)
MnZn
high nQ, high Bs, high stability with time, temperature and dc bias
loading coils
MnZn, NiZn
high p.i9 high JJLQ, high stability with time and temperature
filter inductors, and transformers for audio, TV, and telecommunication (MnZn to 1 MHz, NiZn to 100 MHz)
MnZn, NiZn
high /ij, low eddy current losses
pulse and wideband (telecommunications) transformers (up to 500 MHz)
MnZn, NiZn
high /z, high Bs, low hysteresis and eddy current losses
power converters (MnZn to 1 MHz, NiZn to 10 MHz)
MnZn
high ft, high Bs
TV deflection yokes
MnZn, NiZn
mod. high fi, high hysteresis losses, high B,
suppression beads, choke coils (up to 250 MHz)
MnZn, NiZn
high JI, high density, high Bs, high wear resistance, very low loss at high frequencies
recording heads (up to 10 MHz)
MgMn, MgMnZn, and MgMnCd
high Br/Bs, low Hc
memory cores (historical)
Ba, Sr
high He, high (BH)max, high Q
inexpensive permanent magnets for automotive motors and in consumer products
y-Fe 2 O 3 and Ba hexaferrite
high Bs, high Hc in particle form
YIG
high £, narrow resonance line width
a
recording media for tapes and disks microwave isolators and gyrators
fi Q is figure of merit.
magnetic moment associated with it. The fundamental quantity, the Bohr magneton jiiB, is a measure of the magnetic moment caused by the spin of the electron, and is equal to 1.1654 x 10~ 29 Vs m (or 0.927 x 10" 2 0 erg/Oe) (Cullity, 1972b). The magnetic moment associated with orbital and spin motion is a vector quantity, parallel to the axis of spin and normal to the plane of orbit, respectively. The net magnetic moment of the atom, therefore, is the vector sum of all its electronic moments. In most magnetic materials containing elements of the first group of transition metals the resultant orbital moment
of electrons is much smaller than the spin moment. A comparison between the calculated and experimental values of the net magnetic moments for several divalent and trivalent metal ions of interest is shown in Table 13-4. In arriving at the calculated values, it was assumed that the orbital moments were not there or they were "quenched". 13.3.2 Ferrimagnetism
In metals such as iron, nickel, and cobalt (transition metals) having unfilled subvalence shells, the magnetic moments of the
686
13 Ferrimagnetic Ceramics
Table 13-3. Estimated world output (metric tons per year) of soft and hard ferritesa. Soft ferrites
Country
Japan South Korea Germany (East & West) C.LS. (USSR) Taiwan China (PRC) U.S.A. France Other nations Total (40 nations)
Hard ferrites
40000 18000 15000 15 000 14000 12000 10000 8000 28000
140000 20000 24000 30000 20000 15 000 75 000 13 500 94000
210000
431 000
a
Source: Ruthner (1989), some rounding of numbers is done. Table 13-4. Effective Bohr magneton numbers for mostly divalent and trivalent ions of the iron group. Ion Ti 3 + , V 4 + y3 + Cr 3 + • , v 2 +
Mn 3 + , Cr2 + 2+ Fe 3 + , Mn Fe 2 + Co 2 "h Ni 2 +
Configuration
Calculateda
Experimental
3d 1 3d 2 3d 3 3d 4 3d 5 3d 6 3d 7 3d 8
1.73 2.83 3.87 4.9 5.92 4.90 3.8 2.83
1.8 2.8 3.8 4.9 5.9 5.4 4.8 2.8
a Note: Values calculated as if the orbital moments were not there, Kittel (1969).
inner shell (the d shell) electrons remain uncompensated. This results in each atom acting as a small magnet. In addition, within each crystal the atoms are sufficiently close and the magnetic moments of individual atoms are sufficiently strong. This leads to strong positive quantum-mechanical exchange interaction and long range ordering of magnetic moments which manifests itself as ferromagnetism. Heck (1974 c) lists the three conditions that must be met simultaneously before a sub-
stance shows ferromagnetic behavior. They are as follows: (1) There must be an unfilled electron shell within the atom. (2) There must be uncompensated electronic spins in this unfilled inner shell. (3) The ions of the atoms must form a crystal lattice having a lattice constant at least three times the radius of the unfilled electron shell. If the adjacent moments are aligned antiparallel (Fig. 13-1) as a result of strong negative interaction, and only one type of magnetic moment is present, the neighboring atomic moments cancel each other resulting in net zero magnetization. The material is then said to exhibit antiferromagnetism. This situation can be interpreted as the result of simultaneous existence of two sublattices. A sublattice is a collection of all of the magnetic sites in a crystal with identical behavior, with all moments parallel to one another and pointing in the same direction, which are spontaneously magnetized and have the same intensity. Typical examples of antiferromagnetic materials are the metals Cr and oc-Mn. Sublattices (two or more) can also have spontaneous magnetizations in opposite directions but with different intensities. For instance, when a material contains magnetic ions of different species and magnetic moments, or of the same species occupying crystallographically inequivalent sites, the resultant moments of the sublattices lie parallel or antiparallel to one another and the dominant exchange interaction is mediated by the neighboring nonmagnetic ions. Such materials have a spontaneous magnetization which is weaker than in materials whose magnetic moments are oriented in the same direction, and yet strong enough to be of technological significance. These materials are said to exhibit ferr imagnetism, a term coined by Neel (1948). Lodestone or magnetite, FeO.
13.3 Basic Concepts
TTTTTT TltlTl TiUT Ferromagnetism
Antiferromagnetism
Ferrimagnetism
Fe 2 O 3 , which was recognized by navigators centuries ago for its magnetic behavior, is an example of a naturally occurring ferrimagnetic substance. For a schematic representation of the three forms of magnetism, refer to Fig. 13-1. 13.3.3 Saturation Magnetization and Curie Temperature
Saturation magnetization or saturation polarization refers to the net magnetic moment per unit volume of a given material and is given by the expression M.
d M
where nB is the number of Bohr magnetons per atom or ion, /iB is one Bohr magneton (1.1654 x 10~ 29 Vsm), N is the Avogadro or Loschmidt number (6.025 x 10 23 atoms per mole or molecules per mole), M is the molecular weight, and d is the density. The units of M s are Vs/m2 (or tesla, T). Althouth the SI system is increasingly coming into use, much current usage related to ferro- and ferrimagnetic substances of technical importance is based on the CGS system of units, where the use of the term magnetic flux density or magnetic induction is prevalent. Magnetic induction (B) is the response of the medium to the magnetic field (H) that has been generated in a medium by a current, in accordance with Ampere's law. Thus a flux density of 1 Wb/m 2 (10000 G), where Wb is the unit "weber", is identical to a magnetic induction of 1 T. We might also add
687
Figure 13-1. Schematic representation of magnetic moments.
that the field strength H (see Sec. 13.3.5) is expressed in the SI system of units as A/m and is related to the CGS unit oersted: lOe = 79.577 A/m. Ms is maximum at 0 K. In materials with two or more sublattices, the net saturation magnetization is equal to the vector sum of the net moments of each sublattice. Thus with two sublattices A and B, it will be M s = | M A — M B |. With rise in temperature, increasing thermal agitation weakens the strong directionality of the moments and there is a steady decrease in the net magnetic moment. Above a certain temperature, the spontaneous magnetization associated with ferro-, antiferro-, and ferrimagnetic substances totally disappears, and the material behaves as if it were paramagnetic (very weak form of magnetism). This temperature is called the Curie temperature. The transition from the ferro- or the ferri-magnetic to the paramagnetic state may not be sharp but may occur over a narrow temperature range of 5 to 10 °C (see Table 13-1). 13.3.4 Domains and Bloch Walls
The Weiss molecular field theory of ferromagnetism (Weiss, ,1907) predicted the existence of small, spontaneously magnetized regions, called domains, in a ferromagnetic substance. These are small regions, on the order of 10~ 4 cm, containing about 1012 to 1015 atoms, and where all the resultant moments are aligned in some specific direction. The direction of these moments changes from one domain to the
688
13 Ferrimagnetic Ceramics
next such that the net magnetization for the solid is zero. However, application of a relatively weak field often results in aligning the moments in the direction of the field, thereby achieving large magnetization, which is the characteristic of ferroand ferrimagnetic substances. Domains are separated by transition zones called domain walls or Bloch walls, which are regions of high energy, and are typically 100 nm wide. They are analogous to grain boundaries in polycrystalline materials. Since two adjacent domains which are separated by a wall have different directions of magnetization, a domain wall becomes the region of directional accommodation, and the magnetization within the wall gradually changes (Fig. 13-2). Domains and domain walls originate in an effort to lower the magnetic energy of the crystal. They exist only up to the Curie temperature. 13.3.5 The Hysteresis (B-H) Loop When a ferro- or a ferrimagnetic substance has not been previously subjected to any external field, we say the substance is Domain A
Domain B
Domain wall
mi I I I ! i
in "virgin state". On application of even a very small field, its domains and the domain walls are perturbed from their equilibrium positions., The magnetic moments begin to line up in the direction of the field and the substance which was nonmagnetic becomes magnetic. With increase in the externally applied field, there is increasing alignment of the moments through a complex process where some domains grow, others disappear, the domain walls move, and domains rotate. This process continues until all moments are lined up in the direction of the field. At this point, the substance exhibits its characteristic saturation magnetization (more commonly referred to as saturation induction) for that temperature. The curve showing this relation between induction (B) and the applied field (H) until the sample has reached its saturation point (Bsai) is called the initial magnetization curve. If the specimen is cyclically demagnetized and magnetized, the resulting curve is the hysteresis loop or the B-H loop of the substance. This is due to the fact that the process of domain wall displacement and rotation is generally irreversible. The B-H loop is the most outstanding characteristic of any technically useful magnetic material. Figure 13-3 illustrates a typical hysteresis loop for ferrites. The initial magnetization curve establishes several important characteristics of the material such as the initial permeability ju{, maximum permeability fim, and saturation flux density (Bsai or Bs). Among these, ^ and Bsai are probably the most quoted. The equation which defines initial permeability is ft = —
Expanded view
Figure 13-2. Gradual change in direction of moments inside a domain wall (Bloch wall).
lim
(|)
(13-1)
where ii0 is the absolute permeability of free space, and is also referred to as the magnetic field constant [An x 10 " 7 Vs/
13.4 Ferrite Crystal Structures
5 5
sat< max
689
^t
Remanent induction \ ^
fir- Normal / / 11
fir
magnetization curve
fl 7 ' Coercive force \
1 Maximum permeability / UnrB/H at knee of / magnetization curve / ^ — Initial permeability ^^f HfB/H for very / small H+
/ /
H
Hc
y
f-
H
Hysteresis loop area is a measure of hysteresis loss per cycle Figure 13-3. Characteristic hysteresis loop for a magnetic material.
(Am)], B is the magnetic induction or flux density in Wb/m 2 , and H is the applied field in A/m. In addition to these parameters, the shape of the B-H loop, the area of the loop, coercivity (Hc), remanence (J5r), and maximum usable flux density (Bmax) are also technologically very important parameters. The shape of this curve depends on the intrinsic properties of the material such as crystal anisotropy (Sec. 13.5.2), magnetostriction (Sec. 13.5.3), magnetostatic energy and domain wall energy, and on extrinsic parameters such as pores, inclusions, and the nature of grain boundaries. The area inside the loop represents the hysteresis loss. Remanence is the residual magnetization when the applied field has been reduced to zero. Coercivity corresponds to the field that has to be applied in the opposite direction to bring the magnetization to zero. In addition, there are two other parameters, (BH)max and the square-
ness ratio (BJBS) which are of special interest in dealing with hard ferrites and memory cores, respectively. For further details, please refer to Heck (1974d). Also refer to Table 13-2 to appreciate the connection between specific applications and magnetic parameters that are identified by the B-H loop. We will postpone the discussion on various types of hysteresis loops (isoperm, perminvar, and square loop) to a later section.
13.4 Ferrite Crystal Structures As mentioned earlier, ferrites crystallize in three different crystal types: the spinel, the garnet, and the magnetoplumbite (Table 13-5). The materials of interest to us are mixed metal oxides with iron oxide as their main component. A knowledge of the distribution of the cations in the crystal lattice, their valences, radii, and site prefer-
690
13 Ferrimagnetic Ceramics
Table 13-5. Crystal types of ferrites. Structure
General formula
Example
Spinel
cubic
1 MeO • 1 Fe 2 O 3
Me = Ni, Mn, Co, Cu, Mg, Zn e.g., MnO • Fe 2 O 3
Garnet
cubic
3Me 2 O 3 -5Fe 2 O 3
Me = Y, Sm, Eu, Gd, Dy, Ho, Er, Lu e.g., 3Y 2 O 3 -5Fe 2 O 3
hexagonal
!MeO-6Fe2O3
Me = Ba, Sr, Pb, Ca e.g., BaO-6Fe 2 O 3
Type
Magnetoplumbite
ences, etc., is necessary to understand the magnetic behavior of these materials and to tailor their properties to suit specific applications. 13.4.1 The Spinel Structure
Refer to Fig. 13-4. Named after the mineral spinel MgAl 2 O 4 , the spinel structure contains a basic pattern of face centered cubic oxygen ions with a large unit cell containing eight formula units or "molecules", AB 2 O 4 , for a total of (7x8 = )56 ions per unit cell. A and B refer to the divalent and the trivalent metal ions, respectively. Within stacked arrays of
B
O2-
Figure 13-4. Two octants of the spinel unit cell. A ions are on tetrahedral sites and B ions on octahedral sites of the O 2 ~ anion packing.
large oxygen ions, two types of interstices are found: one formed by four oxygen ions at the vertices of a tetrahedron and the other by six oxygen ions at the vertices of an octahedron. These interstices are commonly referred to as the tetrahedral, or A sites, and the octahedral, or B sites. In each unit cell there are a total of 96 interstitial sites (64 A sites and 32 B sites), of which only 8 A sites and 16 B sites are occupied by the metal ions. These 24 cations are located in specific patterns and with the possibility of some intermediate gradations, which make the spinel structure very interesting. In the mineral spinel, crystallographically called the normal spinel, Mg 2 + ions are on A sites and the Al 3 + ions occupy B sites in a symmetrical fashion. Both zinc and cadmium ferrites have this structure, and they both are nonmagnetic. In an inverse spinel, all the divalent ions are on B sites and the trivalent ions are split between the A and B sites. The ferrospinels of interest to us have the inverse spinel structure. Thus 8 Fe 3 + ions occupy A sites and the rest of the di- and trivalent ions occupy B sites. The formula for an inverse spinel is written as Fe 3 + (Me2 + Fe 3 + ) 2 O 4 where Me could be a divalent metal ion such as Fe 2 + , Mn, Ni, Co, Zn, Cu, or Mg. As mentioned earlier, intermediate arrangements are also possible. Thus the
13.4 Ferrite Crystal Structures
691
Table 13-6. Cation distribution for simple spinel ferritesa.
Ferrite
Metal ion distribution A site
Fe 3 O 4 MnFe 2 O 4
NiZnFe 2 O 4 a
0.8Mn
2+
B site
it Zn 2 +
Z n 2 + F e 3 + ft
F e 3 + ^\ F e 2 + || 0 . 2 M n 2 + || 1.8 Fe 3 F e 3 + UI F e 3 + || N i 2 + U; F e 3 + || N i 2 + Jli F e 3 + II
Source: Smit and Wijn (1959 a).
range of possible distributions can be represented by the general formula Me x Fef*JMe 1 _ x Fei+ x ]0 4 where the ions inside the brackets are located on octahedral sites, and the ions on the outside are on the tetrahedral sites. For a completely random distribution x = l/3; for a normal spinel x = 1, and for an inverse spinel x = 0. Typically, the radii of the tetrahedral and octahdral sites are: 0.058 < r t e t < 0.067 nm and 0.070
toplumbite, a mineral of the approximate composition PbFe 7 5 Mn 3 5A1O 5 Ti 0 5 O 1 9 . Typical compositions of the hexaferrites are BaFe 1 2 O 1 9 , SrFe 1 2 O 1 9 , and PbFe 1 2 O 1 9 (or B a O 6 F e 2 0 3 , SrO-6Fe 2 O 3 , and PbO • 6Fe 2 O 3 ) (see Table 13-5). The crystal structure is much more complex than spinel. One obvious feature of this structure is the large difference in the axes of this crystal. The axial ratio c:a is 2.32 nm: 0.588 nm or roughly 4:1. The hexagonal elementary cell consists of 10 oxygen layers schematically shown in Fig. 13-5. The crystal lattice is again a close packed oxygen structure consisting of both cubic and hexagonal close packing. In an elementary cell each layer contains four large ions. There are four successive layers of four oxygens followed by a fifth layer containing three oxygens and a barium ion. In contrast with spinels, the ferric ions in a hexaferrite are distributed in three different kinds of interstitial sites, the tetrahedral, the octahedral, and a third kind which is surrounded by 5 oxygen ions. For further details of this complex structure and its variations the reader is referred to Smit and Wijn (1959d). 13.4.3 The Garnet Structure
13.4.2 The Hexagonal Ferrite Structure
The commercially important hexagonal ferrites have the same structure as magne-
Garnet, which is a semiprecious stone, has a complex cubic structure. A typical composition is 3MnO" A1 2 O 3 ' 3SiO, or
692
13 Ferrimagnetic Ceramics
13.5 Intrinsic and Extrinsic Properties
B C A C A C B A B A
Cubic
(feo)
Hexagonal Cubic
to
Hexagonal
Figure 13-5. Schematic representation of the barium ferrite structure (Smit and Wijn, 1959 a; Cullity, 1972).
Mn 3 Al 2 Si3O 12 . It is possible to substitute certain trivalent ions such as Y and Gd for a mixture of divalent (Mn 2 + ) and tetravalent (Si 4+ ) ions in natural garnet and make it silicon free. This gives rise to the important class of microwave ferrites having the general formula M | + Fe5 + O 1 2 where M 3 + is a rare earth or yttrium ion. Since Garnets are covered in detail by Guillot (Vol. 3 A, Chap. 8 of this Series), it is sufficient to note that the cubic unit cell is large with a lattice parameter of more than 1.2 nm and it contains 160 atoms. The ferric ions are distributed in the tetrahedral and octahedral positions in 3:2 proportion giving rise to two antiparallel sublattices. The M 3 + ions, because of their larger size cannot be accommodated in the octahedral sites. As a result they form a third sublattice of dodecahedral sites in which each M 3 + is rather irregularly surrounded by eight oxygen ions (Smit and Wijn, 1959e).
The realization of optimum properties of ferrimagnetic ceramics requires a clear understanding of the distinction between the intrinsic and extrinsic properties of magnetic materials. As the term implies, intrinsic properties are those which are insensitive to variations in microstructure. Specifically, saturation magnetization, Curie temperature, crystalline anisotropy, and resonant frequency are independent of microstructure once we fix the chemical composition of a material at the basic molecular unit. We determine these properties in a defect-free single crystal. Extrinsic properties are those which are highly microstructure-sensitive. Prime among these are permeability, hysteresis loop, resonance line width, and magnetic losses (hysteresis, eddy current, and residual). These are influenced by the way the material is processed, the chemical homogeneity, crystallite or grain size, sintered density, and the presence of nonmagnetic inclusions including pores, pore size and pore distribution (see Table 13-7). Thus, it is futile to attempt to change Curie temperature by adjusting the microstructure, and
Table 13-7. Intrinsic and extrinsic (microstructure dependent) properties of ferrites. Intrinsic
Extrinsic
Saturation magnetization permeability Crystal anisotropy magnetic loss Magnetostriction hysteresis loop Curie temperature energy product Ferromagnetic resonance (FMR) FMR line width Lattice resistivity bulk resistivity Thermal expansion bending strength Elastic modulus grain size Source: Bradley (1971), Smit and Wijn (1959 a).
693
13.5 Intrinsic and Extrinsic Properties
conversely to develop correct permeability or control magnetic losses by merely adjusting the basic chemical composition of the material while ignoring the gross microstructure. For a detailed description of the intrinsic and extrinsic properties the reader may refer to Tebble and Craik (1969 a) and Bradley (1971). We will only discuss a few basics of magnetization, anisotropies, magnetostriction, and the hysteresis loop. 13.5.1 Magnetization of Zn-Substituted MnZn Ferrite Spinel ferrites with cations distributed between the tetrahedral (A) sites and the octahedral (B) sites give rise to three types of magnetic interactions through the mediating O 2 ~ ions, namely, A-A, B-B, and A-B. Of the three, A - B interactions are predominant, giving rise to two oppositely magnetized sublattices, A and B. The resultant magnetic moment M s equals the difference between the saturation magnetic moments, MA and MB, of A and B site ions. Again, the saturation moment for the B sublattice is greater than that of the A sublattice, and the net saturation magnetization Ms = | MB — MA |. Theoretically predicted and experimentally observed values of saturation magnetization for a few simple ferrites are given in Table 13-8 (Smit and Wijn, 1959 e). It was noted earlier that the spinel crystal is capable of accommodating a wide range of chemical variations and substitutions of ions on the A and B sites. This gives rise to a range of Ms values. An interesting and technologically useful example, typical of ferrimagnetism, is exhibited by the mixed zinc ferrites where divalent nonmagnetic zinc ions are substituted for divalent magnetic ions such as manganese or nickel. Zinc ions having a
Table 13-8. Magnetic moments of simple ferrites in Bohr magnetons at 0K a . Ferrite MnFe 2 O 4 FeFe 2 O 4 CoFe 2 O 4 NiFe 2 O 4 CuFe 2 O 4 MgFe 2 O 4 a
Calculated
Observed
5 4 3 2 1 0
4.6 4.1 3.7 2.3 1.3 1.1
Source: Smit and Wijn (1959 a).
strong preference for A sites will replace a proportionate number of the magnetic Fe 3 + ions, which will then be forced to occupy B sites. The magnetization of the A sublattice is expected to decrease and that of the B sublattice to increase with a net increase in the magnetization of the mixed ferrite at the absolute zero point. Although theoretically the saturation should increase linearly with increasing zinc content, beyond a certain point the antiferromagnetic coupling begins to diminish and the ions on the B lattice will begin to align themselves antiparallel to one another. The net magnetization of the ferrite will diminish as shown in Fig. 13-6 (Guillaud, 1951). An additional consequence of the weakening interactions is that there is a steady drop in the Curie temperature. 13.5.2 Magnetic Anisotropy Magnetic anisotropy simply means that the magnetic properties exhibit directional dependency. In crystalline materials, the magnetic moments tend to align more readily along certain crystallographic axes called directions of easy magnetization or directions of minimum anisotropy energy. For example, a single crystal of iron tends to magnetize in the directions of the cube edges [100] whereas nickel exhibits easy magnetization along the body diagonal
694
13 Ferrimagnetic Ceramics
Figure 13-6. Variation of spontaneous magnetization of spinel ferrites MFe 2 O 4 with zinc substitution for M (Guillaud, 1951).
[111]. In most of the spinel ferrites the body diagonal [111] is the easy direction except for cobalt ferrite which exhibits an easy direction of magnetization along the cube edges [100]. If the magnetization vector has to be moved out of an easy direction into a more difficult direction, energy must be supplied by an external magnetic field. A measure of this energy is given by the anisotropy constant, K. The anisotropy energy Ea in a cubic crystal is given by Ea = Ko
(OL\
a?) (13-2)
where K± and K2 are the first and second order magnetocrystalline anisotropic constants, for a particular material, in the [110] and [111] directions, respectively, and are expressed in erg/cm3 or J/m 3 in the SI system. a l5 a2, and a 3 are the direction cosines of the moment of the ion relative to the three crystal directions. K2 is very small relative to Kt in the temperature range of practical interest (-40 to 80 °C) and can be ignored. It should be empha-
sized that magnetocrystalline anisotropy is solely a function of crystal structure and chemical composition, and is independent of microstructure. Extensive studies of the crystalline anisotropy of ferrites (Yosida and Tachiki, 1957; Wolf, 1961) suggest that in most cases "single ion" effects predominate, and are functions of both the specific ion and the site it occupies in the spinel lattice. "Single ion" effects depend strongly on the magnetization of the specific sublattice which in turn is highly temperature dependent. Thus the total anisotropy is very temperature dependent. We will further refer to this in Sec. 13.7.1. In addition to the crystalline anisotropy intrinsic to the material, there are other types of anisotropies: shape anisotropy; stress anisotropy; and anisotropy induced by magnetic annealing and plastic deformation. Refer to Cullity (1972 c) and Heck (1974e) for further details. An understanding of anisotropy and magnetostriction is very important in designing materials for diverse magnetic functions. 13.5.3 Magnetostriction Upon magnetization almost all magnetic materials undergo a volume change. In addition to the isotropic change, the crystal will display length changes along the direction of applied field. The change could be positive or negative, and up to some limit its magnitude is proportional to the field strength, beyond which there is no change. This phenomena was first reported in 1842 by Joule and later confirmed by Webster (1925). Joule observed that when a piece of iron was magnetized, it elongated in the direction of magnetization and contracted transversely. This behavior is termed magnetostrictive behavior or magnetostriction. The fractional change in
13.5 Intrinsic and Extrinsic Properties
695
length per unit length associated with a change in magnetization from zero to saturation is known as the magnetostriction. It is usually represented by the symbol A, instead of s which is strain caused due to applied mechanical stress. All ferrites except ferrous ferrite show negative magnetostriction, that is, a decrease in length in the direction of magnetization. Ferrous ferrite is positively magnetostrictive. Thus in a solid solution of mixed ferrites, it is possible to adjust the net magnetostriction to zero. For polycrystalline spinel ferrites with crystallites oriented at random, the average saturation magnetostriction or deformation, As, is given by 2
3
T^ioo) + 7-
(13-3) Perminvar
where A (100) and A ( 1 1 1 ) are the magne-
tostriction coefficients in the cube-edge and cube-diagonal directions (Tebble and Craik, 1969b). 13.5.4 Types of Hysteresis Loops Figure 13-7 (a-d) illustrates four different types of hysteresis loops that one encounters when dealing with ferrites. These are: (1) The normal loop; (2) the isoperm loop; (3) the perminvar loop; and (4) the rectangular or square loop (Heck, 1974f). The normal loop appears in materials composed of randomly oriented crystals where the magnetostriction energy is greater than the magnetocrystalline anisotropy. It is seen in ferrites of moderate permeability and higher losses. The BJBS ratio is about 0.5 to 0.75. The isoperm loop occurs in MnZn ferrites containing about 52 to 54 mol% iron oxide (Ross, 1971 a) which is the composition region where both K± and ls are very small and approach zero (Ohta, 1963). Ross also mentions that isoperm loop is
Rectangular
Figure 13-7. Different types of hysteresis loops.
only realized in a structure of homogeneous pore-free crystallites. In these structures, domain walls are highly mobile and their movement is largely reversible. Isoperm means constant permeability. Thus the peak permeability is attained readily when only a small field is applied, and it changes very little with increasing field strength. BJBS is appreciably below 0.5. The very narrow loop is indicative of very low hysteresis losses. This loop is characteristic of high permeability ferrites. The perminvar loop is characterized by low and constant permeability and near zero hysteresis losses at low field strengths. Above a particular field strength, known as the critical field or the stabilization field, the permeability no longer remains constant but begins to increase sharply. As the field is cycled between increasingly larger limits, the B-H line progressively opens up into a loop but with essentially zero remanence and coercive force (Cullity, 1972 c).
696
13 Ferrimagnetic Ceramics
Finally, if the material is taken to saturation, the original domain structure is completely destroyed with the loop changing from the characteristic perminvar loop as seen in Fig. 13-7c to a normal loop as in Fig. 13-7 a. Perminvar loop occurs in materials which have been subjected to an annealing process. Annealing is expected to produce some sort of internal ordering of ions and vacancies, or ordering through diffusion of dislocations or holes. Consequently, there is induced anisotropy and the domain walls tend to be stabilized in the positions they occupied during anneal. Therefore, at low external fields, the domain walls which are in deep energy wells are only elastically deformed, and snap back to their original position when the field is removed. However, under the influence of large fields, the internal order is disturbed irreversibly and the perminvar effect disappears. The perminvar effect occurs more frequently in ferrites with iron contents around 60 mol% (Ross, 1959,1971 a). It is favored by the presence of cobalt. Excess oxygen also seems to favor the formation of the perminvar loop. In MnZn and NiZn ferrites of low iron content, perminvar loop is observed at very low temperatures (— 45 to — 80 °C) and close to the Curie temperature. Because of their instability over time, MnZn ferrites with the perminvar loop have found limited applications, if any (Ross, 1971a; Slick, 1971; Dixon etal., 1977). The rectangular or square loop usually implies a hysteresis loop having a remanence ratio (BJBS) between 0.8 and 1.0. There are two types of rectangularity. Spontaneous rectangularity is generally attributed to excessive crystal anisotropy. Induced rectangularity is due to magnetostrictive effect. Square loop ferrites came into prominence because of their use in
information storage and retrieval (memory cores). Today this field is of academic significance only, and the reader may refer to Tebble and Craik (1969c), Heck (1974a), and Slick (1980) for further information.
13.6 Ferrite Processing 13.6.1 Introduction Ferrite manufacturing is very capital intensive. Therefore the ferrite manufacturer has to adjust the process steps to suit the equipment. The overall processing can be divided into four major steps: (1) Powder preparation, (2) pressing powder into a core (desired physical shape and size), (3) sintering, and (4) finishing or machining. Each step has to be carefully optimized to build upon the results achieved in the prior step. Figure 13-8 a is a representative flow chart showing various steps in a conventional processing scheme for soft ferrites. Figure 13-8b depicts nonconventional powder processing schemes primarily used in research and pilot facilities. For a fuller understanding of ceramic processing, the readers may refer to Processing of Ceramics, Vol. 17 in this Series. For extensive details on ferrite processing, refer to Goldman (1991), Parker (1990), and to Proc. Int. Conf. on Ferrites (1971, 1976, 1981, 1985, and 1989). 13.6.2 Powder Preparation 13.6.2.1 Conventional Processing Raw Materials Selection The following factors are usually considered in the choice of raw materials: (1) Purity, (2) particle size, (3) surface area, (4) blending, (5) milling, and (6) cost. In common with other advanced electronic ce-
697
13.6 Ferrite Processing
ramies, ferrite raw materials with the practically feasible, highest reactivity are chosen. Generally, the finer the particles going into the thermal treatment, the more reactive the powder will be and more homogeneous the final product. For MnZn powders Choi etal. (1968) and Choi and Aubaile (1971) devised a "reactivity index". For Fe 2 O 3 , the index was measured by the temperature of the first appearance of zinc ferrite. For manganese oxide, it was the temperature of the dissolution of Mn into Zn ferrite. Cost is often an important consideration especially in consumer-oriented applications. Ferrites used in low price-tag consumer items use inexpensive raw materials which often include natural or beneficiated iron oxides. Iron oxides roasted from unpurified steel mill pickle liquors are better and are used for medium quality applications. For high permeability MnZn ferrites, the utmost in purity is needed. Table 13-9 gives a range of several impurities in some commercial iron oxides including
high purity types. Of all electronic ceramic materials, ferrite costs are the lowest when calculated in dollar value of component per kg of ceramic material (Ross, 1982). Impurities and Additives Many of the useful properties of ferrites are the result of carefully planned deviations from a pure metal ferrite such as MnFe 2 O 4 or NiFe 2 O 4 . Earlier, we saw the beneficial effect of including ZnO in the Mn ferrite lattice. In this section we are concerned primarily with impurites and additives in quantities of a few ppm to less than 2 weight percent of the gross chemical compostion of the ferrite. CaO and SiO2 are two components which commonly appear as impurities and need to be checked. The same components are also incorporated in a ferrite mix as additives for their beneficial effects. The early impetus to the study of additives came from an observation by Guillaud (1957) that CaO present as an impurity, lowered the eddy current
Table 13-9. Assays of commercial iron oxides showing major impurities. Vendor 1. 2. 3. 4. 5. 6. 7. 8. 9.
Natural ore Beneficiated ore Grinding swarf Lurgi Ruthner Ruthner Ruthner Ruthner Roast copperas
%Fe 2 O 3
%SiO 2
%CaO
%C1
S.S.A/
97-98 99.6 98 99.4 99.3 98.7 99.2 99.3 99.5
1-2 0.2 0.11 0.1 0.025 0.02 O.O15-O.O5 0.01-0.02 0.015
0.3-0.4 0.02-0.05 — 0.1 0.04 0.05 0.02-0.06 0.01-0.02 0.02
— — 0.05 0.05-0.2 0.15 0.1 0.15 -
coarse 2.7 d = 53 urn coarse 3-4 3 2.6 2.6 8.3
0.07 — — -
5-6 5-6 5-6 16-20
High purity iron oxides 1. 2. 3. 4.
99.3 99.3 99.4 99.5 Specific surface area (m2/g).
0.006 0.006 0.003 0.001
0.008 0.001 0.001 0.001
698
13 Ferrimagnetic Ceramics
]
Major Constituents Iron Oxide
Additives
L
Titania Vanadia Tin Oxide
Zinc Oxide
Manganous Carbonate or Oxide I
Weigh and Mix
Dry Mixing Mix Mulling Moisten if Needed
| Wet Milling in Deionized Water
Granulate
I Granulate | Calcine 800 -1000 C Calcium Carbonate, Silica
2nd Milling in Deionized Water
Analyze Milled Slurry
Deflocculant Organic Binder Internal Lubricant Add Fe2O3 or MnO2 as Needed
[Spray Dry 130 - 150°C |
U | Add External Lubricant and Screen | | Press Parts | Burn off Binders 300 - 500 C | Sinter T-t-P0o 1150-1400°C 4-12 Hours Varying O 2 |
(a)
| Final Check and Pack |
losses significantly. It was noted that Ca segregated at the grain boundaries creating an electrically insulating layer between the grains. CaO has been also known to enhance the mechanical properties in most ferrites (Johnson etal., 1981; Akashi, 1961). SiO2 is another nagging impurity whose level must be controlled. In con-
Figure 13-8. (a) Conventional processing of soft ferrites. (b) Nonconventional powder processing schemes.
junction with CaO it is beneficial in maximizing grain boundary resistivity, and thus lowering high frequency losses at least up to 100 kHz, as shown in Fig. 13-9 (Akashi, 1961). TiO 2 , SnO2, and other oxides have been used to reduce losses and control temperature variations of permeability (Stijntjes etal., 1971). Over the years, a
13.6 Ferrite Processing Iron Constituent
Manganese Constituent
699
Zinc Constituent
1 Blend in Desired Ratio
| Aqueous Solution [
Add Precipftant
Co-Spray Roast
U Precipitates
|
Alcohol Solution
Spray into Cold Solvent
Add Organic Precipitant
Dried Salt Spheres
OrganoMetal Derivatives
Fuse in Molten Salt Ji Hydrolyze
Jl CoRoasted Oxides
Metal Alkoxides
Oxides in Molten Salt
li Decompose and Calcine Analyze ] | Adjust Composition | *
(b)
Finish as in Conventional Processing * In spray-roasting process only iron and manganese constituents are included at the start and zinc constituent (ZnO) is added at this stage.
20 0.07
37
0.1
27
0.2
0.3
0.4
0.5
CaO content (mol.%)
0.6
0.7
Figure 13-9. Influence of SiO2 and CaO additions on the resistivity of a Mn 0 . 6 8 Zn 0 2 1 Fe 2 t l O 4 ferrite at 100 kHz (Akashi, 1961).
700
13 Ferrimagnetic Ceramics
variety of additives have been examined and are being used to achieve one or more of the following objectives: (1) as aids in sintering and densification; (2) as grain boundary modifiers to control electrical and mechanical properties; and (3) to modify the properties of the host lattice. For a fuller understanding of the role of additives, the reader is referred to Guillaud (1957), Lescroel and Pierrot (1960), Konig (1974), Ghate (1977), and Johnson and Ghate (1985). Blending Blending of raw materials can be accomplished by a number of methods, some of which involve size reduction. Blending can also be classified as wet, semi-wet, or dry. Table 13-10 lists several blending methods with their advantages and disadvantages. 13.6.2.2 Nonconventional Processing Several nonconventional powder processing schemes have been developed to achieve one or more of the following: (1) Chemically homogeneous powders, (2) reactive powders, (3) closely controlled Table 13-10. Conventional process blending methods. Type of blending
Equipment
Drying method
Wet Wet Wet
ball mill ball mill ball mill
Wet Wet Semi-wet
attritor high shear mix muller
Semi-wet
Blender
Dry
high shear
spray dryer pan dryer pressure or vacuum filtration followed by belt or oven drying pan or spray dryer pan dryer blender belt or other continuous dryer batch oven or rotary calciner pelletizer no drying needed
chemical compositions, (4) enhanced purity, and (5) controlled particle size and shape. Some of the more important forms of soft ferrite nonconventional processing schemes are: (1) coprecipitation (Goldman, 1977; Bo and Leyi, 1981); (2) cospray roasting (Ruthner et al, 1971; Wagner, 1980); (3) freeze drying (Schnettler and Johnson, 1971), and sol-gel synthesis (Regazzoni and Matijevic, 1983; Sainamthip and Amarakoon, 1987); (4) molten salt synthesis (Kimura et al., 1983; Wickham, 1971); and (5) organic precursors (Wickham, 1960). Only two of these have seen limited commercial utilization. Small quantities of coprecipitated material are being used for demanding custom applications such as recording heads. Co-spray roasting has seen more commercial usage. At present there are two large ferrite manufacturers who are using this method of making powder for their internal usage. Spray roasting process permits tight control over the desired chemistry. It reduces compositional variability within a given batch. Okutani and Mori (1989) compared the variability in chemistry of powders made by the conventional and spray roasted processes. They observed that in a MnZn ferrite composition, Fe:Mn ratio was 4.133 ±1.521 for the conventional process and 3.327 + 0.271 for the spray roasted process. Likewise, the Zn:Mn ratio was 0.4808 ±0.076 for the conventional and 0.412 + 0.032 for the spray roasted process. 13.6.2.3 Calcining The mixed powder batch consisting of oxides, carbonates, or spray roasted oxides, etc., whether prepared by conventional or nonconventional methods, in most cases, is unsuitable for pressing into parts. Calcination is a step in which such a raw
13.6 Ferrite Processing
batch or the "red mix" (the color imparted by the red iron oxide) is heated to a temperature between 800 and 1000 °C, generally in ambient air, to convert it to the spinel phase. Calcination achieves three objectives: (1) Raw materials such as carbonates decompose, and oxides react to form spinel; (2) improves the density of the powder and reduces subsequent shrinkage during final sintering (firing); and (3) renders the powder pressable after additional process steps. A series of chemical reactions outlining the formation of ferrite are shown in Table 13-11. 13.6.2.4 Milling The calcined ferrite mix is fairly coarse. The hard aggregates may range in size from 0.5 mm to 2 cm and they must be broken up by a milling operation. During milling the calcined particles are broken up to expose their centers whose new surfaces are either unreacted or less reacted than the original external surfaces. These new surfaces will provide the reactivity or driving force during sintering of the pressed part. For certain applications where chemical homogeneity is critical, such as in
701
garnets for microwave applications, the milling step may be followed by a second calcination and additional milling. 13.6.2.5 Organic Binders and Additives
Certain additives, primarily organic and identified as deflocculants, binders, plasticizers, and lubricants, are incorporated in the milled powder mostly during milling, and in some cases after the milled slurry has been dried. The primary purpose of the binders, etc. is to create freely flowing powder which can be readily pressed into complex shapes which can then be transported for further processing without breaking. The most common binder for ferrites today is polyvinyl alcohol or PVA which is available in several grades depending on the molecular weight and resultant viscosity. The PVA, when dried, creates a hard shell around the particle aggregates which may be difficult to crush in the pressing operation. Therefore, a plasticizer such as polyethylene glycol which softens the particles is often used. Glycerin can also be used. Another additive which is used as a powder lubricant is zinc stearate powder which can be added during ball
Table 13-11. Representative reactions occurring during ferrite formation. 1. Decomposition of carbonates, etc.
M n C O 3 ^ M n O + CO 2
500- 700 °C
2. Formation of zinc ferrite
ZnO + Fe 2 O 3 => ZnFe 2 O 4
670- 850 °C
3. Formation of manganese ferrite
MnO + Fe 2 O 3 => MnFe 2 O 4 1/3 Mn 3 O 4 + Fe 2 O 3 => MnFe 2 O 4 +1/6 O 2
650- 850 °C 800-1000 °C
4. Formation of MnZn ferrite
MnFe 2 O 4 + ZnFe 2 O 4 => MnZnFe 2 O 4
700-1000 °C
5. Formation of ferrous ferrite. Solid solution of ferrous ferrite with MnZn ferrite
3/2 Fe 2 O 3 => FeFe 2 O 4 +1/4 O 2
950-1200 °C
6. Oxidation of ferrites during sintering and cooling if equilibrium cooling is not achieved
Mn 2 ^FerOj; x/4 O 2 ^Mn 2 i x Fei:j]O 4+x/ '2
702
13 Ferrimagnetic Ceramics
milling as an internal lubricant, or added to the dried powder as an external or die lubricant to aid in pressing. 13.6.2.6 Spray Drying The spray drying operation converts the milled slurry (wet mix) into free flowing powder of well formed, compact spheres. The process consists of spraying the slurry in a tall stainless steel chamber (approximate dimensions: 1 to 5 m diameter, 4 to 20 m tall) in controlled droplet size against a counterflowing current of hot air (110 to 300 °C). The spray drying conditions are adjusted in such a way that most spraydried powder typically falls in the —120 + 220 mesh (U.S. sieves). Dry lubricant such as zinc stearate powder (1/4 wt.%) is blended in, which will act as an external lubricant during the pressing operation. 13.6.3 Challenges in Pressing One of the advantages that ferrites possess over the metallic strip magnetic components is the wide variety of shapes into which ferrites can be formed (Fig. 13-10). The designer of magnetic components is interested in a size and shape of the magnetic core which will result in maximum flux containment and a well behaved magnetic circuit. He is equally concerned with the ease in assembly of the structure which includes a bobbin assembly containing the winding. Towards this end, ferrite suppliers have developed several shapes which include pot-cores, E cores, EP cores, Q cores, toroids, and so on. These structures are realized by first die pressing the spraydried powder into "green" parts and firing (sintering) them close to their desired final shape and dimensions. The dimensions of the fired part will be determined by the green density of the pressed compact, the shrinkage during firing, and the dimen-
Figure 13-10. Representative ferrite (courtesy of Tokin Corp.).
core shapes
sions of the die. These three variables must be coordinated by careful planning. The green density is determined by the ferrite chemistry, the powder characteristics, the binder content, and the pressing pressure. The shrinkage during firing depends on the reactivity of the milled powder, the binder content and the firing conditions (temperature, time, and atmosphere). Linear shrinkages during firing may vary from 12 to 20%, primarily between 14 and 17%. Incorrect die design or press set-up, or improper powder preparation may result in several problems with the finished part. They include: (1) Incorrect dimensions, (2) warpage of the part, (3) cracking of the part, (4) internal porosity, (5) die pullout and rough surfaces, and (6) laminated parts. 13.6.4 Sintering Sintering is by far the most critical and an expensive process step. If carefully executed, it yields the required crystal structure, oxidation state, microstructure, and physical condition of the ferrite core. For
13.6 Ferrite Processing
a general background on sintering of oxides and sintering of ferrites the reader may refer to the following: Coble and Burke (1964), Blank (1961), Reijnen (1968), Kuczynski (1971), Stuijts (1971), Paulus (1971), Morineau and Paulus (1975), and Yan and Johnson (1981). The influence of zinc loss on the permeability of MnZn ferrits has been discussed by Gallagher et al. (1978). Different product applications may have different magnetic specifications requiring specific sintering cycles. However, there are a few common elements of sintering which apply to all applications. They are: (1) Complete formation of the spinel lattice, (2) attainment of chemical homogeneity, and (3) attainment of uniform microstructure. Using the example of a MnZn ferrite, representative reactions leading to the ferrite formation are listed in Table 13-10. The variable objectives that depend on the application are those that optimize the following parameters: (1) Average grain size and size distribution, (2) porosity and location of pores (inter or intragranular), (3) density, (4) metal ion valency (Fe2 + , Mn 3 + , etc.), and (5) grain boundary conditions (chemistry and thickness of the boundary layer). In general, for high permeability applications, the most dense structure with the highest purity and the largest uniform grain size is desirable. Any porosity that exists should be intergranular and the grain boundaries thin so that domain walls may cross them without impediment. For high-frequency low-loss applications the grain size is preferably small and the grain boundaries thicker and more pronounced. Microstructures typical of high permeability ferrites and low-loss (telecommunication grade) ferrites are shown in Fig. 13l l a and b, respectively.
703
(a)
• fc-v :• r /-1 ;J... Vf+AlXS.
•« (b) Figure 13-11. Representative microstructures of two ferrites: (a) High permeability (ft«23 000) MnZn ferrite (300 x). (b) Low loss (fiQ at 100 kHz of 650 000) MnZn ferrite (750 x ).
13.6.4.1 Ferrite Kilns
Ferrite kilns or furnaces may be classified as either batch (or periodic) or continuous types. Batch kilns have been used mostly for firing low tonnage quantities of smaller size, higher quality or custommade cores which command a higher price per unit weight. In addition, they may be used for very large parts which require very long firing cycles (one week or more). With batch kilns, firing costs have general-
704
13 Ferrimagnetic Ceramics
profiles will also change correspondingly. We shall see later, that sintering cycles may vary for different types of ferrites (MnZn and NiZn) and also for different applications (e.g., power versus high permeability). The sintering cycle for a ferrite includes four clearly defined zones: (1) Binder burn off zone, (2) heat up zone, (3) high heat and soak zone, and (4) cooling zone. Typical firing cycles for a medium permeability (5000 n{) MnZn ferrite and a high density power ferrite are shown in Fig. 13-
ly been higher because of the longer firing times and labor involved in loading and unloading the ferrite product. Large production quantities of standard telecommunication and power ferrite cores are generally fired in continuous (tunnel) kilns for economic reasons. 13.6.4.2 Sintering Cycles Since the objectives in firing vary with the application, the sintering conditions including the temperature and atmosphere Soak
—
Equilibrium cool
*Too%op
1300 "",
/
Air (21%0 2 )
G 1100 —
1 __
2 900 — o
—
g.700
—
; \
1
0
$
\
\ i \ ; \
3|
/ /
^
i
/
K
500 — / 300
Heat up
100
1
Room
8
temp. 0
(a)
uoo 1200
2 800 — o g-600
i
16
20
\ 10C °C/h
50°C/h>^
o in o o o p
/250°C/h
"~ / — / ^-+—Air
—5%0 r E ° - £
WoO°C/h \
S cT
(nominal)
\
LU UO
200 Room temp.
(b)
//
N2
\ N
•7
r
i
Soak-1350°C 2h /——v
— "~
i
12 Time (hours)
i
[
8
12 16 Time (hours)
1
20
Figure 13-12. Conceptual firing cycle for: (a) medium permeability ferrite, (b) high density power ferrite. Binder burned off in a separate cycle (Tanaka, 1978; Ishino and Nuriyama, 1987).
13.6 Ferrite Processing
705
Isocomposition lines .Phase boundaries
100
10
0)
sz a. (/> o 0.1
0.01
Figure 13-13. Equilibrium weight changes as a function of atmospheric oxygen content and temperature for the system: (MnO)0 268 (ZnO) 0183 (Fe 2 O 3 ) 0 549 (courtesy of P. I. Slick, 1971).
Relative weight change (AW/HMOO)
0.001 U00 1300
1200
1100 1000 Temperature (°C)
900
12 a and b, respectively, and the equilibrium atmosphere cooling diagram (Slick, 1971) is shown in Fig. 13-13. Binder burn-off: The first step in any ferrite sintering process is the removal of the binder which was originally introduced to facilitate pressing. Conventional binder burn-off temperatures range from 350 to 500 °C. Care must be taken not to burn off the binder too rapidly as there is a danger of evolution of copious amounts of combustion gases and cracking of large parts. The time of burn off can vary from 4 to 8 hours depending on the core size. If burnoff is incomplete, the residual elemental carbon may cause reduction of some of the oxides at high temperatures. Ghate (1981) suggested a sequentially burning binder combination of several binders and whose constituents did not leave a residue (clean burning), in order to reduce the rate of evolution of combustion gases and prevent core cracking or forming microcracks. Also refer to Harvey (1980). Whether a
850
pressed part (core) visibly cracks, disintegrates, develops fine microfissures, or remains in tact depends on the density of the "green" part, the rate of heating and whether all the combustion gases from the binder burn-out evolve at one temperature or over a temperature range. Heatup section: The heatup section usually contains several temperature control zones, in which the temperature increases from the maximum in the burn off zone (500 °C) to the soak or hold temperature. When there are no atmosphere changes such as in Ni or NiZn ferrites or in simple telecommunication cores, the heatup is linear. The overall heating rate may be on the order of 100 to 250 °C per hour. In many cases, the atmosphere is air. Microstructurally, there may be some densification and grain growth at the last stages of heat-up. Recently there have been attempts to help control the final grain size and density by inserting an intermediate temperature hold or slowdown close to the
706
13 Ferrimagnetic Ceramics
peak temperature often accompanied by an atmosphere change. Ishino and Nuriyama (1987) have shown that using this method, some densification was accomplished without much grain growth. High heat section: The peak temperature in the high heat section may vary from 1150°C to about 1450°C. In a continuous kiln, the time at the hold or soak temperature can vary from about 4 to 8 hours. In a batch kiln, the times may be much longer. In some cases they may extend to weeks. Very long firing times, especially in continuous kilns, lead to problems of contamination from the atmosphere and refractories. Another serious problem is the possible loss of zinc, especially in firings at very high temperatures and low oxygen levels. While NiZn ferrites require no atmosphere control in the high heat section, in the case of MnZn ferrites, much care must be taken to establish the required Fe 2 + content. Blank (1961), Slick (1971) and others have given the relationship between equilibrium oxygen partial pressure and temperature for various Fe 2 + contents in MnZn ferrites. These curves are for equilibrium conditions and in general are adhered to for many standard ferrites. However, because of potential zinc loss, high temperature firing employed for high permeability ferrites is done at very high oxygen levels, often in pure oxygen. In the case of very low loss ferrites, some deviation from equilibrium firing may be made for the sake of producing oxidized grain boundaries. An attempt to equilibrate the lattice may be made during the cool. For high frequency power materials, if equilibrium firing is used, high permeability is attained but the losses may also be high. Cooling section: Blank (1961) has established the correlation between temperature and equilibrium oxygen atmosphere in
MnZn ferrites. Correlation of these variables becomes especially important as the temperature is lowered in the cooling section of the furnace. The cooling part of the cycle is the most important step in the firing process. Any desirable properties that may have been developed in the previous operations may be damaged during cooling unless proper atmosphere control is used. In the sintering of high permeability cores, the oxygen level may be high during the hold or soak section but just before the cool, the oxygen level is dropped rapidly to an equilibrium level and cooled according to the equilibrium curve. For low-loss power cores, Rikukawa (Rikukawa and Sasaki, 1985) has recommended using the expression logPO2 = a - ~
(13-4)
where PO2 is the equilibrium oxygen pressure in atm, a the atmosphere parameter (intercept), and b a constant. Rikukawa recommends a value of 14 540 for b as used by Morineau (Morineau and Paulus, 1975) and the use of a as a variable atmosphere parameter. Often the rate of cooling is more rapid at the early stages of the cool to prevent reoxidation of the ferrite lattice. In the case of MgMn ferrites or Cu ferrites, the desired properties are obtained if the cores are rapidly quenched after firing. This is done to freeze the high temperature ion distribution. Slow cooling will result in poor properties. Quenching was the standard method of making the early MgMn ferrite memory cores. 13.6.4.3 Fast Firing For many years, ferrite cores were fired in extremely long cycles which largely contributed to their cost. When ferrite usage
13.6 Ferrite Processing
increased during the 1970's and prices became quite competitive, steps were taken to reduce firing times. This led to the studies of fast firing. Morell and Hermosin (1980) have shown that in the case of both MnZn and NiZn ferrites, firing could be done in a very short time compared to the standard practice. For MnZn ferrite cores, Morell used times of 16 minutes as compared to conventional times of 15 to 20 hours. For NiZn ferrites, the corresponding values were 12 to 47 minutes and 15 to 20 hours, respectively. Although the cores were relatively small, this experiment showed that to form the lattice and microstructure, extended time was not needed. Part of the need for long firing times in production kilns involves heating up refractories as well as the cores. Morell used a thin Ptwire mesh belt to carry the cores in the furnace. Faster firing has also been achieved by the use of clean burning binders and higher temperatures (Dixon et al., 1981). Pot cores (cylindrical potlike cores, 22 mm OD x 11 mm height) were fully fired in a door to door cycle of 6 hours with satisfactory magnetic properties while maintaining the structural integrity of the parts. Judicious use of lower melting oxides such as GeO 2 , CuO and V 2 O 5 and in some instances SiO2 also may cause densification at lower temperatures. Advances in powder preparation have also reduced the firing time. More efficient design of kilns and recycling of hot gases have contributed to better kiln utilization. The various techniques listed above have reduced firing times in continuous kilns to a cycle time of 24 hours or less.
707
13.6.5 Vacuum Sintering, Hot Pressing, and Hot Isostatic Pressing
Traditionally these three sintering techniques are employed when the conventional techniques do not result in near theoretical densities or there is excessive porosity and grain growth which adversely affect mechanical and other properties. These unconventional techniques are generally reserved for realizing premium grade materials for exotic applications such as windows for space vehicles or lenses for night vision telescopes or special armor materials. In such cases, the applications are not dictated by consumer driven cost targets but by strategic interests. For large scale applications of ferrites such as TV deflection yokes and ferrite cores for switched mode power supplies, the densities and other associated properties obtained by conventional sintering are quite adequate. However, the early need for pore-free ferrites with superior mechanical properties was felt when MnZn ferrites were seen to satisfy the needs of the magnetic recording heads better than NiZn ferrites. MnZn ferrites held the promise of higher Bsat and ^. The magnetic recording head industry has been the prime driver for successive developments of the three sintering processes as applied to ferrites. Vacuum sintering at 1200 to 1300°C followed by normal sintering at 1250 to 1400 °C in equilibrium atmosphere was used by Shichijo and Takama (1971) to make the polycrystals stoichiometric and to promote grain growth. The samples were then cooled in vacuum. This process produced MnZn ferrites of near theoretical densities (5140 kg/ m 3 ) and & at 1 kHz of 23 000. Long head life, less wear and good frequency response in hot pressed ferrite (HPF) heads was reported by Ikeda et al. (1971). Precompact-
708
13 Ferrimagnetic Ceramics
ed disks were hot pressed in silicon nitride dies in an electric furnace at 1000 to 1380°C in air under a pressure of 30 MPa. Initial permeabilities of 30000 having a large grain diameter and density of 5.11 g/ cm3 were reported. It was also noticed that the presence of wavy or snaky grain boundaries, as against straight boundaries, led to a lowering of permeability (see Table 13-12, and Fig. 13-14). It was theorized that snaky boundaries were regions of high energy. Hot pressing techniques were also used to densify NiZn-, CuZn-, MnZn-, 1000pm Table 13-12. Effect of wavy boundaries of hot pressed ferrite (HPF). Density, grain size, and permeability data of HPF and conventionally sintered MnZn ferrites.
Figure 13-14. Microstructure of a dense, large grain ferrite showing wavy boundaries.
Density (g/cm3)
and Ba ferrites with mixed results. Several references to various aspects of hot pressing of MnZn ferrites such as purity of starting powders, particle size and effects of precalcining, mechanical properties of sintered ferrites, etc. are also available in Russian literature (Paschenko et al., 1983; Glotov etal., 1983; Ostafiichuk etal., 1989; Pakhomova etal., 1989). An interesting variation of the standard hot pressing is the technique of continuous hot pressing, which was developed at Philips Laboratories (Oudemans, 1968). The two salient features of this process are: (1) A hexagonal alumina die system held under compression, and (2) a powder feed mechanism which permitted continuous flow of the material through the die. The system operated under the extreme conditions of high temperatures between 900 and 1450 °C, and pressures on the order of 100 MPa. Fully dense materials with a grain size of 0.5 |im were reported for a microwave ferrite. Hot pressing of MnZn ferrite was later superseded by hot isostatic pressing
Grain size (urn)
Permeability
% Balancing (straight) boundaries
HPF samplesa 5.11 5.11 5.11 5.11 5.11 5.11 5.11
370 90 27 51 49 61 60
4500 12100 14000 16200 18000 23000 30000
2 27 26 32 24 31 35
Conventionally sintered samples b 4.97 5.04 5.06 5.01
10 22 27 38
5000 12000 15000 20000
Conventionally sintered samplesc 4.55 4.70 4.88 4.95 5.04 5.05 a
11 14 19 21 27 30
6 500 10000 14000 16000 21500 25000
Ikeda etal. (1971); b Ross (1971a); c Perduijn and Peloschek (1968).
13.6 Ferrite Processing
(HIPing) using argon gas (Takama and Ito, 1979). High purity raw materials with total impurities less than 0.01 wt.% were mixed, calcined in air at 850 °C for 3 h, and ball milled to 1 [im. The powder was pressed into green compacts and sintered by the conventional method at 1100 to 1300 °C in 2% oxygen, with care taken to avoid excessive grain growth. The presintered specimens (with densities 95% of theoretical) were HIPed for one hour in argon at 100 MPa at 1100°C, and at 30 MPa at 1200 °C. Uniform grain size and pore-free microstructure were attained only when the HIPing was performed at a temperature lower than the presinter temperature. Shinohara and Murakami (1981) reported on a similar procedure and explained the densification during HIPing as due to compression of the pores and pore migration by grain growth. They noticed that during post HIP annealing, there was pore enlargement. Rui-yun et al. (1989) studied the densification of LiZn ferrite by HIPing. They observed that desired results with respect to pore free samples are possible only when presintered material had no open porosity. Most recently, a HIP has been very effectively used to press high purity MnZn and BaZn hexaferrites to near theoretical densities (Fig. 13-15 a and b, respectively). The latter were preconditioned to provide highly oriented particles. The green powder compacts were isostatically pressed at 280 MPa prior to HIPing in Ar at 175 MPa. This resulted in a theoretically dense and a robust sample of highly oriented polycrystalline ferroxplana ferrite, as shown in Fig. 13-15b (West etal., 1991). However, its desired performance as a high frequency recording head material was less than satisfactory. Hahn (1991) observed that when a NiZn ferrite was HIPed, although the resulting structure was pore free, the grain size of the exterior layer was
709
much smaller than in the interior regions. See Fig. 13-15. No explanation for this phenomenon was given. These observations lead us to believe that the so called unconventional techniques are on their way to being accepted widely, and will be commercially used for sophisticated, high tech products. 13.6.6 Machining, Lapping, and Tumbling
The sintered parts coming out of a furnace are normally within 1 to 2% of the user-required dimensions. Depending on the part's complexity, its size and shape, and the method by which the green part was formed, the part may have suffered differential shrinkages and consequently could have been warped. The parallelism between the two outer legs of an E core could be lost giving rise to what is commonly referred to the "flower pot" effect, the base dimension being shorter than the dimension at the open ends. The fired surfaces would have undergone a change in chemistry (zinc loss). For these and several other reasons, the sintered parts are subjected to a mechanical finishing operation or operations. They include cutting, coarse grinding, machining, centerless grinding, gapping, polishing, lapping, and tumbling. Some of these operations may cause additional chipping, cracking, and grain pull outs rendering the parts useless. In addition many of these operations are quite expensive (e.g., diamond machining and lapping) and labor intensive. Therefore, they have to be chosen carefully to suit the parts and customer requirements. Also, the electrical requirements (for example, inductance) are critically dependent on how well these operations are conducted. For instance, in order to develop a high permeability part, if all care has been exercised to select the correct composition,
710
13 Ferrimagnetic Ceramics
(a)
20 /mi
(b) •f > « •
Vv
i.
•
&
•' *-
.
<
Figure 13-15. Microstructures of hot isostatic pressed ferrites: (a) MnZn ferrite (400 x), (b) barium hexaferrite (1000 x) (courtesy of B. D. West, Eastman Kodak Co.).
right raw materials, most appropriate pressing, and correct sintering to produce the part, and not enough care in the finishing operation, a 10000 permeability part will be quickly reduced to a 5000 permeability part or much worse; similarly a lowloss material would become a lossy material. As an example, Fig. 13-16 shows the variation in effective permeability of an EP13 (an industry standard shape) core pair caused by different lapping methods. Finishing operations introduce surface
stresses. Thus extreme care is needed in completing this step. For further details, the readers may refer to Knowles (1970, 1975), Brose van Groenou (1975) and Brose van Groenou et al. (1976). Once the parts are machined, they are thoroughly cleaned, dried, and packed with minimum handling. Extreme care is needed to avoid even finger prints or fine dust, cigarette smoke, or contamination from the packaging material since these would ruin the quality of the finished mating surfaces.
13.7 Case Studies
13.7 Case Studies In this section we will illustrate the applications of materials science and processing concepts to the development of MnZn ferrites of three types: (1) High permeability ferrites for broad-band transformers. (2) High Bs and low loss ferrites for switching power supplies. (3) High density recording heads. 13.7.1 High Permeability Ferrites
With the introduction of pulse code modulation, the demand for broad-band transformers has significantly increased in the past few years. The band width of these transformers is extended to broader frequency ranges creating the need for very high permeability ferrites which also show high core loss resistivity (Rp). Also, the parallel permeability (ji'p) has to be stable within a broad frequency range extending to several MHz. The term parallel permeability refers to the real part of permeabil25 EP13 core pair /
- 2 0 --
y^
gap <^\ Lapped mating s surface ^
E 15-
c
B
A
5 -_
I
i
i
I
5 10 15 20 /ij, Material permeability (x103)
25
Figure 13-16. Effect of machining on permeability of MnZn ferrites (Dixon, 1979): (a) 500 grit diamond grind or 1 micrometer alumina (free abrasive), (b) 3 micrometer diamond lap. (c) 0.25 micrometer diamond lap.
711
ity in a parallel equivalent circuit, when one treats permeability as a complex quantity consisting of a real and an imaginary part (Snelling, 1988). There have been numerous literature references to the study of high permeability ferrites (Guillaud and Paulus, 1956; Ross etal., 1964; Shichijo etal. 1964; Beer and Schwarz, 1966; Perduijn and Peloschek, 1968; Ross 1971a). All these studies point to the following: There is a direct linear relation between mean grain size and permeability. High permeabilities necessitate large grain sizes, and the domains must be highly mobile. Therefore, any disturbance that can impede domain wall motion should be avoided. To achieve high permeability, in addition to selecting the correct composition, it is necessary to develop a fairly dense and homogeneous microstructure made up of pore-free, uniformly large grains, and pores located at the grain boundaries. More recent studies by Tanaka (1978, 1981) point to the effects of oxygen nonstoichiometry on the domain structure and the initial permeability in MnZn ferrites. Venkatramani and Srivastava (1987) concluded that for high permeability, in addition to microstructural requirements, it is necessary to have small oxygen non-stoichiometry which leads to the incorporation of Fe 2 + ions in the doubly degenerate orbital ground state (Smit, 1971). MnZn ferrites with high initial permeabilities in the range of 10000 to 18 000 and the Curie temperatures between 100 and 130°C are now commercially available, with the higher permeabilities limited to small toroids. Attaining such high permeabilities on a commercial scale has been a technological challenge. Essentially, three requirements must be met: (1) proper composition, (2) adequate purity of raw materials, and (3) a well defined and controllable manufactur-
712
13 Ferrimagnetic Ceramics
ing process. Let us examine each of these in detail. Composition: Figure 13-17 shows the compositional dependence of crystal anisotropy and magnetostriction constants (refer to Sec. 13.5.2 and 13.5.3) in the mixed oxide system (MnZnFe)Fe 2 O 4 (Ohta, 1963). Shown in this figure are regions of small anisotropy Kl9 ^ (11 i) and ^(ioo) along with lines where ^ = 0 and /ls = 0 for the case where both Zn 2 + and Fe 2 + substitutions are incorporated into a Mn ferrite host lattice. This is probably the diagram most referred to by ferrite technologists. To attain high permeability, the crystal anisotropy (K±) and the magnetostriction (yls) must be near zero. These conditions are met in a narrow composition and temperature range (see Fig. 1325, Sec. 13.7.2). A plot of permeability (jij) versus temperature of such a material (Fig. 13-18 a) will show a peak in permeability, known as the secondary maximum in permeability (SMP), at this temperature. The permeability drops off sharply on both sides of this peak. Figures 13-18 a and b together illustrate another important concept of anisotropy compensation and adjustment (within reason) of the temperature at which the SMP occurs. For most high permeability ferrites this peak is set betweeen 15 and 25 °C. It turns out that the contribution of most magnetic ions to the crystal anisotropy and magnetostriction is negative whereas, the crystal anisotropy of Fe 2 + can be positive in some cases, and that of Co 2 + is always positive. Also, Fe 2 + shows a strong positive magnetostriction. Thus it is possible in a MnZn ferrite composition with a slight excess of Fe 2 + ions to adjust zero anisotropy at the temperature of choice. Figure 13-18 b depicts K± as a function of temperature for a MnZn ferrite host lattice without Fe 2 + marked host and the "single ion contribu-
0 A100
10
20
30 ZnO
50 ZnFe20A
Figure 13-17. Compositional dependence of crystal anisotropy and magnetostriction constants in the mixed oxide system (MnZnFe)-Fe 2 O 4 at 20 °C (Ohta, 1963).
r 0 (B)
To (A)
T Figure 13-18. Anisotropy compensation and shift in SMP with change in Fe2 + content: (a) Note the secondary maximum in permeability (SMP). (b) Note that SMP occurs when Kx is zero (Stijntjes et al., 1971).
13.7 Case Studies
tion" (Smit et al., 1962) to K± at two concentrations of Fe 2 + , marked Fe 2 + (A), and Fe 2 + (B). The resultant or total Kx for the two compositions is shown as dashed lines. The successful use of these concepts, and the use of pure raw materials and carefully controlled sintering conditions by Beer and Schwarz (1966) and Ross (1966, 1971a) resulted in a maximum peak permeability of 40 000. These concepts are now well established, and most commercial high permeability materials are made in the composition range Fe 2 O 3 = 52.0-53.0 mol%, MnO = 25.0-27.0 mol% with the balance being ZnO (Ross, 1989). The use of very pure materials and a composition within the narrow region of zero crystalline anisotropy and zero magnetostriction when processed under very carefully controlled conditions results in a very sharp peak in the \i-T curve. From a practical point of view, very steep rises and steep drops in permeability within a very narrow temperature range are not desirable. Instead, one needs a reasonably high and uniform permeability over a broad temperature range of, say, 20 to 60 °C. So the next task is to find a way to spread the peak over a wider temperature regime. This is achieved by introducing small chemical inhomogeneities. It needs to be pointed out that although Kx reaches a zero value, there is still the contribution due to K2 and higher order constants. Recognizing the contribution of Fe 2 + to anisotropy, sintering, and cooling conditions may have to be adjusted so as to create a small chemical gradient within the crystallites (controlled oxidation) just enough to suppress the sharp peak and to spread it over a wider temperature range of 10 to 20 °C (Smit, 1971). The temperature difference between the SMP and the primary peak at the Curie temperature also influences the steep fall and the catenary
713
commonly observed between the two peaks. In some instances, compositions which show a second maximum in permeability between the first SMP and the Curie temperature are selected to adjust the temperature characteristics. Purity of raw materials and additives: It is necessary to maintain a high level of purity in the raw materials. Total impurity content should be well below 0.1 wt.%. The following impurities are likely to enter in the ferrite mix formulation due to impure raw materials, impure water, binders such as gum arabic and halowax, and cross contamination in the local plant environment: Na + , K + , SO 4 2 ~, Cl~, Si4 + , Ge 4 + , Ca2 + , Bi3 + , Pb 2 + , Hg 2 + , Cr 3 + , and Co 3 + . Their presence, in some cases as low as a few ppm, can lead to discontinuous grain growth, unwanted precipitates, and in general enhanced anisotropy and lattice strain which could drastically decrease the peak permeability. As an example of the problem arising due to unclean processing equipment^ consider the case where the equipment has been first used for making a NiZn ferrite mix containing a small amount of cobalt oxide or carbonate. If this equipment is nominally washed and then used to mix a high permeability MnZn ferrite composition, the few ppm of Co still lingering in the equipment can get into the MnZn ferrite mix, and will play havoc with the desired results. The damaging effects of trace amounts of chlorine entering the formulation via Halowax binder, and impurities in the gum arabic binder have been shown to drastically degrade permeability as seen in Fig. 13-19. Note that it is customary to compare \i-T curves^rather than look at ja at any one temperature. It should also be noted that the presence of very small amounts (< 300 ppm) of Ca2 + may be desirable to improve Rp. However, cost permitting, it is
714
13 Ferrimagnetic Ceramics
20 Clean burning
16
£ 15 o
12
-50
-10
30 70 110 Temperature (°C)
150
Figure 13-19. Effect of binders on temperature dependence of permeability of (MnO)22 6 (ZnO) 24 7 (Fe 2 O 3 ) 52 7. Note the large differences resulting from the use of three different binders (Dixon and Pass, 1978).
preferable to start out with the purest obtainable raw material, and then introduce controlled amounts of additives. Manufacturing process: Once we have selected the correct chemistry and suitable raw materials, understanding the subtleties of processing and maintaining proper control over the process is critical. We will elaborate on a few of the process steps with specific examples. Calcining: Dixon and Pass (1978) divided a batch (red mix) in two portions. One portion was calcined in ambient air and the other in an atmosphere of nitrogen. Both powders were then identically processed into sintered toroids. They observed that parts prepared from nitrogen-calcined powder had a denser microstructure with less pronounced intergranular porosity but the permeability at the SMP was considerably lower than for parts prepared from air-calcined powder. A second heat treatment of the parts (of nitrogen calcined
powder) designed to duplicate the microstructure of part prepared from air-calcined powder was successful, but the permeability did not improve. The microstructure did not provide any clues for the observed discrepancy. Empirically, it was deduced that calcining should be done in air. Sintering: Sintering of high permeability MnZn ferrite green bodies poses at least four challenges: (1) Attaining highest density with maximum uniform grain size, (2) avoiding any trapped porosity within the grain interiors, (3) suppressing zinc volatilization, and (4) achieving correct stoichiometry in the spinel phase (Fe2 + /Fe 3 + , and oxygen content). If it were not for challenges (3) and (4), sintering of ferrites would have been much more straightforward. In addition to the factors discussed under Ferrite Processing (Sec. 13.6), factors which can help in meeting the first two challenges are: (1) Choice of correct binders, plasticizers, and lubricants in preparing powders for pressing; (2) pressed (green) compact of uniform density which is not too high and not too low, a density of 2900 kg/m3 is typical; (3) good understanding of the initial and intermediate stages of sintering for the powder compact on hand. Most of the porosity and trapped gasses within the pressed compact must be expelled from the compact when the pore structure is still continuous, and significant grain growth has not commenced. Let us examine ways to address the third and fourth challenges. Refer to the equilibrium cooling diagram (Fig. 13-13). To attain high density and large grain size, it is necessary to fire the parts at a high temperature and for long times. A soak at 1370 °C for 8 hours is not uncommon. To achieve high permeability it is necessary to equilibrate the sample in a carefully chosen POi, and typically the atmosphere (a mixture of
13.7 Case Studies
N 2 and 0 2 ) in the sintering zone is adjusted between 0.4 and 1% oxygen. Under these conditions, zinc volatilization from the ferrite is excessive. So, as mentioned earlier in Sec. 13.6, the common practice is to conduct most high temperature sintering in an atmosphere rich in oxygen, and then switch the atmosphere to the desired low oxygen content to achieve correct equilibrium. High oxygen sintering suppresses zinc volatilization and aids in sweeping the pores from the interior to the grain boundaries where they coalesce into larger pores (Carpay, 1977 a, b). Once densification and grain growth have been achieved, equilibration is relatively easy. In spite of this approach, some zinc volatilization is inevitable. Figure 13-20 shows concentration gradient of zinc from the surface to the interior of a high permeability MnZn ferrite. And every ferrite manufacturer has its own tricks to minimize this effect. Among these may be mentioned the following: (1) Maintain an almost stagnant atmosphere which is rich in oxygen until ready to carry out the equilibration step; (2) cover the parts with coarse, sintered ferrite powder of similar composition; (3) set the parts to be sintered on plates of ferrites of similar composition; (4) saturate the kiln with zinc by adjusting the load with an uneven proportion of noncritical
Z.
715
parts with high permeability parts; (5) creatively load the parts so that most of the parts except the ones on the perimeter of the saggar exchange zinc amongst themselves. Dixon and Pass (1978) studied the effect of sintering toroidal samples which were placed in small unfired coffins (enclosures) of MnZn ferrites. The results of firing ferrite samples of varying zinc content in a ferrite enclosure with a fixed content of 21.3 mol% ZnO are shown in Fig. 13-21. It was observed that the highest permeability was obtained for the sample whose zinc content matched that of the enclosure. On etching the samples in hot HC1, samples which had ZnO content higher than that of the coffin were void of any surface cracks. However, samples which had a lower zinc content than the enclosure material revealed subsurface cracks. This observation is consistent with the development of a compressive stress in the surface layer caused by the reduced lattice parameter on absorption of zinc from the enclosure. The counter balancing tensile stress in the interior causes the subsurface cracks which were revealed after etching away the surface compressive layer. An additional firing was performed in which samples of varying zinc content were enclosed in coffins of the same material as the toroidal
I.UU
Nominal ZnO value
20.00
/
Figure 13-20. Zinc concentration vs. depth in a medium permeability (5000 ^{) ferrite of nominal starting composition: (MnO) 27 . 0 (ZnO) 20i6 (Fe 2 O 3 ) 5 2 4 (courtesy of Magnetics, Inc., Butler, PA).
19.50
19 00
i
0.2
i
i
i
i
i
0.4 0.6 0.8 Depth below surface (mm)
i
1.0
716
13 Ferrimagnetic Ceramics
22
* •
_ — —
40 r
^20 o
Auto enclaved
V \ \
;
1210-
20
as fired
a> a. N
/
i
i
22
/j \
]
A
A/
I10
26.36 mol.% MnO Enclosure < 21.36 mol.% ZnO 52.28 mol.% Fe2O3 21
/fn\ o
U Q.
\ 10 mil etch
\
O
o
IS)
16-
— 30 meabiliity 1
I 18
Fe 2 0 3 • 52.0 mol.% o 52.5 mol.% o 53.0 mol.%
I
0 -50
23
mol.% ZnO
Figure 13-21. Influence of zinc loss on the secondary peak permeability (Dixon and Pass, 1978). * Denotes the permeability of a sample toroid fired in an enclosure mode at the same composition as the toroid.
i 150
Figure 13-22. Shift in SMP as a function of iron oxide content of a MnZn ferrite.
25 o
samples. It was noticed that this procedure gave permeabilities comparable to the maximum achieved by etching. These results point to the need for suppressing zinc loss from the sample as well as minimizing zinc absorption by the sample from the ambient. In Fig. 13-22 and 13-23, are shown the effects of varying the iron oxide content while maintaining a constant MnO:ZnO ratio, and varying the oxygen content of the atmosphere in which the samples were equilibrated at the highest sintering temperature and then cooled along the corresponding isocomposition lines. The remarkable shifts in secondary peaks in each case amplify the need to maintain a tight control over these factors. These effects also suggest the flexibility that is afforded in processing which permits controlling the secondary maximum in permeability within a temperature region.
I i 50 100 Temperature (°C)
Fe203= 53.0 mol.% MnO =25.5 mol.% ZnO =21.5 mol.%
-20
I 15 Q) Q.
Legend 1.0 % 0 2 0.6 % 0 2 0.2 % 0 2 0.02 % 0 2
10
-40
-20
0 20 Temperature (°C)
40
60
Figure 13-23. Shift in SMP as a function of oxygen partial pressure during soak.
Typical microstructures of two commercially available high permeability ferrites with comparable permeabilities ( / i ^ l l 000) are shown in Fig. 13-24a and 13-24b. Note the remarkable differences in the grain size, uniformity of grain size, and pore size. Sample in Fig. 13-24 a has generally larger grains and also a mixture of large and small grains. Sample in Fig. 13-
13.7 Case Studies
-.-.Ivr.
Figure 13-24. Micro structures of two commercial high permeability (fa «11 000) ferrites showing vastly different microstructures (150 x ).
24 b has a much smaller and a uniform grain size. The differences in the microstructures are most likely due to the starting powders (impurities, chemical homogeneity, particle size) and also to the type of kilns and firing cycles employed to produce these parts. Thus grain size alone is not a sufficient criterion to determine the outcome. 13.7.2 Ferrites for High Frequency Power Supplies
In the last ten years significant advances in fast bipolar transistors and high power
717
MOSFETs have created a need for a new class of ferrites specifically designed for high frequency power conversion applications (switched mode power supplies or simply SMPSs). The demand for the new power ferrites is expanding rapidly along with a need for vastly improved materials for use at higher and higher frequencies. For example, in the early 80's, high frequency power conversion typically implied 40 kHz. Today, switching frequencies of 200 to 300 kHz are common practice, and leading edge designs call for power conversions at 1 MHz. This has given a strong incentive to understand loss mechanisms, and to develop improved processing and newer chemistries to meet the SMPS designers' technical requirements. Thus far, MnZn ferrites containing certain additives have steadily met the challenge. Steady improvements in core loss of power ferrites have been achieved in the past thirty years. For example, core losses measured at 25 kHz and 200 mT have been reduced from 160mW/cm 3 in 1960 to less than 50 mW/cm3 by 1983 (Ochiai and Okutani, 1985). In addition to improving materials, the ferrite manufacturers have also been keenly aware of the need to develop more efficient core structures and other associated transformer components. We will examine some of the more recent developments which have contributed to vastly improved materials. The desirable properties of power magnetic materials for SMPS transformers are: (1) High saturation flux density, Bsat, to provide a large flux excursion using a minimum number of secondary turns. (2) High amplitude permeability implying that saturation should occur at relatively low field strengths to keep low magnetizing currents. This also means fewer primary turns.
718
13 Ferrimagnetic Ceramics
(3) Low core losses (hysteresis and eddy current) at high flux densities and high operating frequencies. To avoid overheating, core loss should decrease with increasing temperature in the vicinity of the operating temperature, which could be between 80 and 100 °C. (4) The thermal conductivity of ferrite should be high. This also implies that the core shape should promote rapid heat dissipation. (5) High Curie temperature (>220°C) to retain the magnetic properties at operating temperatures 80 to 120 °C. For a good understanding of the SMPS circuits, the reader is referred to Snelling (1988) and Pressman (1991). High Bsat: The literature on MnZn ferrites suggests a possible Bmax of 0.56 T at room temperature and 0.4 T at 100 °C (Smit and Wijn, 1959 a). Shinohara and Murakami (1981) reported Bsat of 0.59 T for a composition MnO 36mol%, ZnO 9 mol% and Fe 2 O 3 55 mol%. This unusually high value was obtained from measurements on a hot isostatically pressed sample. The sample density was 5080 kg/ m 3 compared with the theoretical value of 5120 kg/m3. Better commercial materials have a Bsat of 0.50 to 0.51 T at room temperature and 0.37 to 0.39 T at 100 °C, and their compositions lie somewhere within the following limits: MnO 33-37 mol%, ZnO 9-13 mol% and Fe 2 O 3 53.554.5 mol%. High i?sat is not the only requirement of a power ferrite material. A compromise has to be struck between saturation and core losses to attain the lowest core losses at the elevated operating temperatures. Figure 13-25 shows the region on the M n O - Z n O - F e 2 O 3 miscibility diagram where compositions desirable for SMPS applications are situated (Ochiai and Okutani, 1985; Konig, 1975). Also shown on
30
A—7^
0
10
?\—A—A70
20 ZnO
30
40
-
Figure 13-25. Portion of the miscibility diagram showing regions suitable for: (A) high permeability, (B) power materials, (C) newer i?sat materials.
this diagram are the lines K± = 0 and Xs = 0 (Ohta, 1963). Compare the composition region (B) to the region (A) suited for high permeability ferrites. Note that the composition region of high permeability ferrites is much smaller than that of power ferrites primarily because high permeability (ji{ of 10000) is only attainable in the proximity of zero crystal anisotropy and zero magnetostriction. However, high Bsat and high Curie temperatures are attainable over a wider composition range. Thus, our challenge becomes one of striking the right compromise among all parameters. Core losses: Much of the early discussion on this subject centered on losses when the core was subjected to vanishingly small fields (Heck, 1974b). The [iQ product (a figure of merit commonly used by electrical engineers where Q is the quality factor and is equal to 2 nfL/R at the operating frequency) gave a clear indication of the suitability of the core. However, in power applications, the problem is somewhat more difficult (Wilson, 1985; Stijntjes and Roelofsma, 1985; Sano et al., 1988). The total losses can be partitioned in three ways: (a) Eddy current loss, (b) hysteresis loss, and (c) residual loss. Of these, the first two are significant contributors to the total loss, and the contribution of the residual loss is not quite clear (Snelling, 1989).
13.7 Case Studies
By eddy current loss we mean power loss of magnetic materials in alternating fields due to induced currents in the material. In contrast, hysteresis loss is the energy dissipated in tracing a B-H loop which is essentially the energy needed to move the domain walls during each cycle. The general expression for eddy current loss in magnetic materials is
Pe = {constant) Bif2—
(13-5)
Q
where Pe is the power loss due to eddy currents in W/kg, Bm the peak induction flux in Vs/m 2 ,/the frequency in Hz, Jthe minimum dimension normal to flux direction, and Q the electrical resistivity in Qm. Thus to keep the eddy current losses constant as the switching frequency rises, the resistivity of the material must improve in proportion to the square of the frequency. Also, d should decrease within reason. Disproportionate decrease in d may adversely affect the permeability and also increase coercivity. Since for ferrites the resistivity is frequency- and temperature-dependent, the relevant values of resistivity must be used. It was mentioned under Sec. 13.1 that ferrites are attractive over metals because of their high resistivities. However, when Fe 2 + is introduced by way of excess iron (compositions containing over 50 mol% iron oxide) to reduce crystal anisotropy, the resistivity decreases due to the electron hopping mechanism between Fe 2 + and Fe 3 + . Thus pure MnZn ferrites can have resistivities as low as 0.1 Qm, which makes them unattractive for high frequency use. Guillaud (1957) demonstrated that the resistivity of ferrites can be increased with the addition of Ca to a ferrite composition (MnO) 0>28 (ZnO) 0 . 19 (Fe 2 O 3 ) 0 . 5 3. The Ca segregated at the grain boundary creating a highly resistive coating on the grains.
719
Further improvement in resistivity was shown by Akashi (1961) with the simultaneous addition of CaO and SiO2 (Fig. 139). He further observed that the resistivity was also a function of the oxygen content of the sintering or annealing atmosphere. For instance, a sample of MnZn ferrite containing CaO and SiO2 when sintered in nitrogen (3 ppm O2) showed a resistivity of 0.81 fim, and when it was sintered in nitrogen containing 5% O 2 the resistivity increased to 2000 fim. Such a phenomenal increase in resistivity was attributed to the presence of a boundary phase, a solid solution represented by ( C a - ^ S i . O ^ . ^ f e r r i t e V Paulus (1971) noted that slow cooling rates gave high resistivity. He concluded that in ferrite with no calcium, resistivity increases due to oxidation of the boundary. When calcium is present, it segregates at the boundaries and modifies the reduction-oxidation equilibrium thus depleting the ferrous ions in the boundary. This causes a highly insulating thin boundary layer. In effect, this thin layer is capacitive, and therefore the resistivity of the ferrite becomes highly frequency dependent (Koops, 1951; Stijntjes, 1989). With increasing frequency, the AC resistivity due to the boundary layer vanishes and only the intrinsic resistivity of the material remains. The hysteresis loss is related to frequency and flux density by the expression
= kfmBn
(13-6)
where Ph is hysteresis loss in W/m 3 , k a proportionality constant, / the frequency in Hz, and B the peak flux density in T. Exponents m and n are experimentally derived values. If the magnetic loss were simply due to hysteresis, then the exponent of/would be unity. Typically it is 1.3 and it rises further as the frequency increases
720
13 Ferrimagnetic Ceramics
beyond 100 kHz. Exponent n is typically 3. An often quoted empirical equation for total losses is rtoi = KJ
ny
\\D-I)
where x varies between 1.3 and 1.6, and y between 2.2 and 2.7. For further discussion, please refer to Snelling (1988). The factors governing the hysteresis loss are: (1) Magnetocrystalline anisotropy; (2) magnetostriction, k\ (3) internal and external stresses; (4) volume fraction of pores, inclusions, dislocations, cavities; and (5) saturation magnetization. For low hysteresis losses all other factors except Ms should be low. Kl9 2, and M s are mainly dependent on chemical composition. K± is also adjustable by the mechanism of crystalline anisotropy compensation, for example by substituting different ions such as Ti 4 + , Co 2 + (Stijntjes etal., 1971; Giles and Westendorp, 1977). If the microstructure is controlled, stress and volume fraction of pores, etc. can be minimized. It is suggested that besides chemical composition, microstructure governs the hysteresis loss. The ideal high frequency power ferrite will minimize loss by minimizing and balancing hysteresis and eddy current losses. Sano et al. (1989) presented the following model to achieve an ideal microstructure in a ferrite for use at high frequencies: (1) The higher the frequency, the smaller should be the grain size. (2) The composition of grains should be uniform. (3) The grains should be coated with a high resistivity boundary, and the boundary should be as thin as possible. (4) The grain minus the boundary should be homogeneous and free of voids or porosity. (5) The sintered density should be as high as possible. They applied these concepts with good success in the development of the H7F material which shows very low losses at high fre-
quencies. The starting powder was a sprayroasted high purity material to which known amounts of CaO, SiO2? and TiO2 were added. Use of a specially designed sintering cycle in which atmosphere and heating rate from 900 to 1100°C were adjusted resulted in a dense compact with small grain size. Figure 13-26 shows microstructures of two power ferrites, PC44 and PC50 (H7F). Note the differences in grain size and core losses. 13.7.3 Ferrites for Recording Heads
Magnetic recording technologies play a key role as today's most important information recording technology. The rate of progress in magnetic recording is keyed to the areal memory density, which has been doubling for about every two years for the last three decades (Kugiyama and Hirota, 1989; Hoagland, 1985). The parameter pacing this progress has been the head to medium spacing and the ability to continually reduce its value from more than 25 |iim to 0.3 jim. The technical developments in the VHS-VCRs and computer disk drives are very fascinating to follow. R & D on high-definition TV (HDTV) and other developments in digital technology are challenging recording head manufacturers. Recording head technology has made significant progress in keeping pace with the progress in the recording media (from yiron oxide to metal particle tapes to Ba-ferrite and Co-CoO films). NiZn ferrite heads of earlier years have been replaced by polycrystalline MnZn ferrite heads, and then by single crystal MnZn ferrite heads. These in turn were replaced by composite heads of single and polycrystalline materials including the most recent development of metal-in-gap or MIG heads, thin film heads and planar hybrid heads (Kugiyama and Hirota, 1989; Kajiwara etal., 1990;
13.7 Case Studies
Figure 13-26. Microstructures of two power ferrites showing different grain sizes (test conditions: 500 kHz; 50 mT; 80 °C): (a) PC40 material-core loss: 200 kW/m3, (b) PC50 material-core loss: 60 kW/m3.
Ichinose and Aronoff, 1990; West et al., 1991; Coutellier et al., 1989). MnZn ferrite heads have enjoyed a certain popularity and are expected to see a fair market share for the next few years where the operational frequencies are less than 10 MHz. The technical requirements for a recording head material are: (1) High Bsat (£>0.6T); (2) high ii' (>700 at 10 MHz) [for a definition of// and fi" refer to Smit (1971)]; (3) small grain size (5 jim), < 1 % porosity, high wear resistance; (4)
721
very low rubbing noise or high signal to noise ratio; (5) high hardness (700 on the Vicker's scale); and (6) high mechanical strength. These are some of the primary material requirements. In addition, there are factors such as better tribological nature, machinability, bondability, and reliability. The high points to be noted in terms of the focus of this chapter are: (1) Attempts to increase Bsat have led to additional investigations of compositions containing 60-65 mol% Fe 2 O 3 along the second ^ = 0 line (Kugimiya and Hirota, 1989) with excellent results. Although Xs was > 0, a /i of 950 at 10 MHz and B (800 A/m) of 0.63 T were achieved; (2) chemically prepared high purity materials and carefully designed sintering conditions including the use of hot pressing, hot isostatic pressing, and annealing resulted in the material of choice; (3) single crystal MnZn ferrite technology has been effectively exploited. The effects of proper crystal orientation on the head output are well understood and the heads designed accordingly; (4) mechanical properties of MnZn ferrites have been carefully researched in reference to processing conditions; (5) refined techniques of lapping the heads with micropolycrystalline diamond powder have resulted in shortened lapping times, scratch free surfaces with finishes of 0.002 pm AA (0.05 jim peak to peak) and no adverse effects on permeability (Bailey and Dexter, 1985). Recording head technology has stimulated the new developments in the science of high permeability and high saturation MnZn ferrites in an unconventional way. It remains to be seen whether the traditional large scale ferrite manufacturers will take advantage of this new knowledge to develop improved materials for "traditional" applications such as wide-band and
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13 Ferrimagnetic Ceramics
pulse transformers and high frequency power ferrites.
13.8 Hard Ferrites Most commercial hard ferrites are the hexaferrites with the general formula MO • 6 Fe 2 O 3 where M is Ba or Sr. Barium ferrites have held a dominant position since they were first introduced in 1952. The reasons for success of Ba and Sr ferrites are: (1) The raw materials are inexpensive and nonstrategic, (2) they are produced by ceramic techniques, (3) they are light weight, and (4) they exhibit sufficient coercive force and reasonable induction to be of use in many applications such as small motors for automotives and loudspeakers. According to Stuijts (1964), the most straightforward relation between microstructure and properties is found in the permanent magnet materials based on single domain behavior of their constituent particles. Permanent magnet materials are gauged by two parameters: High i/ c , and high M m a x within the temperature limits of operation (Fig. 13-27). BHmax is a measure of the magnetic energy which can be stored in the external field of the magnet. The high coercivity of hard ferrites is due to the large magnetocrystalline anisotropy (Kt ^0.3 MJ/m 3 ) with the preferred direction of magnetization parallel to the oaxis combined with low saturation induction (i? s ^0.47 T). The high coercivity can be realized only when Hc is of the same order of magnitude as the anisotropy energy, Ea. This is possible in single domain particles where we eliminate the formation of the domain walls. The object is to make it as difficult as possible for rotation of the magnetization vector. For Ba hexaferrites
400 200 -H (kA/m) Figure 13-27. Demagnetization curves for a few hard magnetic materials (MG: Megagauss).
800
600
the critical diameter, Z)cr, below which no lowering of the magnetostatic energy occurs by creation of domains inside a particle, has been calculated to be about 1 jim (Went e t a l , 1952). The other quantity, BHmax, calls for a high induction. Since B in polycrystalline materials is directly proportional to the apparent density of the material, suitable sintering aids may have to be used to achieve the density and avoid grain size above the Dcr. Figure 13-28 shows parts of hysteresis loops of a material when fired optimally and when overtired causing excessive grain growth and thus lowering Hc. Another way to achieve high density without detrimental grain growth was suggested by Van Den Broek and Stuijts (1977) while working with Sr hexaferrites. They noticed that steadily lowering the Fe 2 O 3 : SrO ratio permitted achieving almost 5000 kg/m3 density and a lowering of the sintering temperature by 150°C. Maintaining this ratio for Ba fer-
13.9 Microstructure and Grain Boundary Chemistry
1: Fired 5 min at 1250°C 2: Fired 5 min at 1350°C
-3
-2
0 1 2 /-/ {106 A/m) —
Figure 13-28. Effect of overfiring on the shape of upper half of B-H curve for Ba hexaferrite (Stuijts, 1963).
rites as well is now a common industry practice (Goldman, 1991). Processing of hexaferrites is almost similar to that of spinel ferrites except for these points: the calcined powder particle size and the grain size of the sintered material must be held below Dcr; air firing is required instead of controlled oxygen equilibrium cooling; and preorientation of particles during pressing in case anisotropic grade ferrites are needed. The hexagonal platelike particles of calcined and milled powders can be aligned in the slurry format (wet mix) in the presence of a strong externally applied field, and then pressed into shapes by squeezing out the liquid vehicle (van den Broek and Stuijts, 1977; Fischer, 1978; Parker 1990).
13.9 Microstructure and Grain Boundary Chemistry The significance of tailoring the microstructure to meet specific properties, such as high permeability, low loss, frac-
723
ture toughness, and high coercivity, has been emphasized in several places in this chapter. In this section, we will attempt to summarize some of the major findings pertaining primarily to the grain boundary region, and microstructures in general. The analytical tools which have been used by various investigators have included Auger electron spectroscopy (AES), photon electron spectroscopy (ESCA), secondary ion mass spectrometry (SIMS), high-resolution transmission electron microscopy (HRTEM), and measuring X-ray line broadening. Optical microscopy in the 200 x to 1000 x range, scanning electron microscopy (SEM), and electron microprobe analysis have also been extensively used to study microstructures of the as-sintered and fractured surfaces. Collectively these studies have resulted in a wealth of information and have provided much guidance in developing improved materials. However, there is still no definitive understanding between variations in magnetic properties and microstructural data. In addition, unlike in metals observation of domains and domain wall motion in ferrites is very difficult (Knowles, 1961; Tebble and Craik, 1969 c) and thus the magnetic behavior as a function of microstructure is for the most part hypothesized. The two most widely studied topics pertain to MnZn ferrites are: (1) Segregation of impurities, particularly Ca and Si, at the grain boundaries; and (2) the effects of sintering atmospheres on the oxidation and zinc depletion in the grain boundary region. Another general topic that has been widely studied is the influence of gross features such as grain size and porosity, and whether the porosity is inter- or intragranular. Since this topic has been discussed in previous sections, we will address the first two topics only.
724
13 Ferrimagnetic Ceramics
Most studies have resulted in the finding that calcium and silicon primarily segregate at the boundaries. Franken and Stacey (1980) suggested that Ca 2 + segregates to the boundary during slow cooling, whereas Lin etal. (1982) observed Ca 2 + segregation in samples fractured at 1300°C. They also observed a Ca-rich liquid phase at 1250° to 1320°C. Tsunekawa et al. (1979) revealed the presence of a thin layer, 3-5 nm wide, of a nanocrystalline phase at the boundary containing Ca and Si and noted that the lattice parameter increased rapidly as one approached the amorphous phase at the boundary from the grain interior. Using photoelectron X-ray spectroscopy and TEM, den Broeder and Franken (1981) studied the effects of silica additions in Sr hexaferrites and they observed that the SiO2 segregates to the grain boundaries, much as in the spinel ferrites. The addition of SiO2 served to minimize grain size, possibly due to an impurity drag mechanism. In high permeability MnZn ferrites, a strong correlation between zinc depletion at the grain boundary and permeability degradation was confirmed by AES by Sundahl etal. (1981). The lowest permeability materials exhibited a 20 % zinc depletion, while the best ferrites exhibited only a 10% depletion. Also refer to Fig. 13-20. Significant increases in grain boundary Fe levels (measured as Fe/O signal ratio) were also observed for ferrites with high permeability. Gradients in composition set in by zinc depletion, change in Fe 2 + /Fe 3 + ratio, or due to other additives with limited solubility in the lattice will give rise to a range of K± (crystalline anisotropy) value and result in local microstresses, as substantiated by X-ray line broadening measurements.
More recent studies by Nakata etal. (1985) of the grain boundary region in MnZn ferrites of widely differing permeabilities have revealed that each grain consists of many small regions of 5-10 nm in size. The crystallographic orientation of each region was seen to be different from each other in the order of 0.1 to 0.4°. They also observed a significant enhancement in the Fe/O ratio at the boundary in high permeability ferrites as did Sundahl et al. (1981). Although gross micro structures as observed by optical or scanning electron microscopy, may appear to be clean and having comparable average grain sizes, TEM studies of high permeability MnZn ferrites have revealed varying degress of deposits within the pores and at grain boundaries giving rise to largely differing permeabilities, as seen in Fig. 13-19 (Ghate, 1981). In one instance, there was evidence to conclude that the chlorine trapped during the burning of an halogenated organic binder (Halowax) reacted with iron to form very fine fibrous crystallites of iron chloride in the pore region which gave rise to local microstresses and resulted in significant permeability degradation. Excess oxidation of NiZnCo ferrites during annealing at 550 °C very likely resulted in the formation of hematite at the grain boundary, and caused a sharp drop in resistivity of the annealed sample. However, controlled oxidation of Fe 2 + , primarily near the grain boundary, resulted in enhanced resistivity (Dixon etal., 1977). For further details on grain boundaries and microstructures in ferrites, the readers may also refer to Livingston (1975), Ghate (1981), Okazaki (1981), and Bongers and Franken (1981).
13.11 Future Prospects
13.10. Recent Developments Developments in ferrites and ferrite processing are keyed to the progress in electronic technology. Surface mount technology, high frequency power supplies, high frequency recording heads, high definition TV, increased emphasis on electromagnetic interference (EMI) suppression, efficient lighting, and automotive electronics have been the catalysts for much of the recent progress in the science and technology of ferrites. Surface mount technology (SMT) poses specific challenges (Oyama, 1991) with respect to creating low profile components, improved heat dissipation, chemical durability and compatibility to operations such as reflow soldering and flux cleaning. One must also be aware of the consequences of stressing components during encapsulation. The biggest challenge thus far in SMT has been the creation of miniaturized components. In a recently developed process (Okutani and Mori, 1989) screen printing is used to alternate layers of a ferrite paste and half turns of a conductive paste to construct a totally shielded inductor. The process is similar to that used to build multilayer chip capacitors. The ferrite powder is prepared by conventional methods and then formed into a paste with suitable binders. The ferrite paste and a half turn of winding conductive silver paste are printed alternately by screen printing. The initial and final ferrite layers are up to 300 Jim thick, and the intervening layers are about 40 jam thick. The printed thick film is cut into green chips, followed by binder burn out and sintering. The sintered parts are ground and finished to dimensions and suitable electrodes are attached. The finished product is less than 1.5 mm in height. Finding a suitable ferrite composition
725
(NiCuZn ferrite) which will have enough inductance, resistivity, and that can be sintered at low temperatures (<900°C) was a key factor in the successful development of this product. An extension of the chip inductor technology (Okutani and Mori, 1989) is the integration of a number of inductive and capacitive elements in a single cofired multilayer chip component, 4.5 mm x 3.2 mm x 1.3 mm, to create an electronic wide band filter for TV. Major challenges in fabricating such a device include matching thermal expansions of the inductor with the capacitor and avoiding reaction between TiO 2 of the capacitor and the ferrite. Besides chip inductors and superior recording heads, the large tonnage ferrite industry has been moving towards the use of high purity raw materials, new chemistries which will yield high BsaV low core losses, high permeabilities, more efficient kilns, and improved quality (tighter tolerances, consistently reproducible electrical and mechanical properties, and fewer visual defects).
13.11 Future Prospects If one examines the trends in magnetic materials as a whole, ferrites will continue to play a unique role by virtue of their high electrical resistivity, ease of fabrication into a multitude of shapes having widely divergent properties, light weight and cost effectiveness. As Watanabe (1991) pointed out, the key words to heed are "digital, down-sizing, and SMD (or SMT)". Accordingly, it is expected that development of future process technologies will be evolutionary. Goldman (1991) predicts that future developments will include (1) new
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13 Ferrimagnetic Ceramics
MnZn ferrite compositions for use in SMPSs up to 2 MHz, (2) increased use of co-spray roasted ferrite powders, (3) solgel processing to produce special powders or coated powders, (4) increased use of new types of batch kilns for improved throughputs and high quality products, (5) new core shapes to suit SMD which will challenge the manufacturers (uniform density and microstructure, suppression of zinc loss, and efficient kiln utilization), and (6) producing zero defect parts in the shortest cycle times. The technological developments in ferrites have been basically evolutionary rather than revolutionary. Materials science and technology has been steadily applied to improve properties as well as new products. However, the highly capital intensive nature of ferrite processing makes it that much more difficult to readily implement changes, especially in products used in large quantities or requiring a large volume of material. With greater emphasis on surface mount technology and miniaturization, there will be increasing demand for materials which will be mechanically strong and chemically resistant to operations such as wave soldering and cleaning, shock and vibration, humidity-temperature aging, etc., performed on printed wiring boards. Sugimoto (1985) gave a long sighted view of ferrites as advanced ceramics and presented a long list of potential new developments. Some of them have already materialized, such as perpendicular magnetic recording media, and composite materials such as a combination of single and poly crystalline ferrite heads. Considering other competing materials, primarily the amorphous or ultrafine grain materials such as Finemet of Hitachi Metals, it appears that there will be increasing activity in exploring amorphous ferrites (Sugimoto, 1989).
13.12 References Akashi, T. (1961), Trans. Jap. Inst. Met. 2, 171. Bailey, N. R, Dexter, D. D. (1985), in: Advances in Ceramics, Vol. 15, Fourth Int. Conf. on Ferrites. Columbus, OH: Am. Ceram. Soc, pp. 413-419. Beer, A., Schwarz, I (1966), IEEE Trans. Magn. MAG-2, 470. Blank, J. M. (1961), /. Appl. Phys. 32, 378-79S. Also see U.S. Patents 3 027327 (issued March 27,1962), and 2960 744 (issued November 22, 1960). Bo, L., Leyi, Z. (1981), IEEE Trans. Magn. MAG-17, 3144. Bongers, P. R, Franken, P. E. C. (1981), in: Advances in Ceramics, Vol. 1: Levinson, L. M. (Ed.). Columbus, OH: Am. Ceram. Soc, pp. 38-52. Bradley, R N. (1971), in: Materials for Magnetic Functions. New York: Hayden Book Company, p. 56. Broese van Groenou, A. (1975), IEEE Trans. Magn. MAG-11, 1446. Broese van Groenou, A., Veldkamp, J. D. B., Snip, D. (1976), J. Phys. Colloq. Cl, Suppl. to No. 4 (4), 285. Carpay, R M. S. (1977 a), in: Ceramic Microstructures '76: Fulrath, R. M., Pask, J. A. (Eds.). Boudler, CO: Westview Press, pp. 261-275. Carpay, R M. S. (1977b), /. Am. Ceram. Soc. 60, 82. Choi, G., Aubaile, J. P. (1971), in: Ferrites, Proc. Int. Conf., July 1970, Japan. Tokyo: Univ. of Tokyo Press, pp. 243-248. Choi, G., Damay, R, Auradon, G. P., Strivens, M. A. (1968), Electrical Comm. 43, 265. Coble, R. L., Burke, J. E. (1964), in: 4th Int. Symp. Reactivity of Solids, 1960, Amsterdam. Amsterdam: Elsevier, pp. 38-51. Coutellier, J. M., Lehureau, I C , Machui, J., Meunier, P. L. (1989), in: Advances in Ferrites, Proc. ICF-5, 1989, India. New Delhi: Oxford and IBH Publ. Co., pp. 863-868. Cullity, B. D. (1972a), Introduction to Magnetic Materials. Reading, MA: Addison-Wesley, pp. 117203. Cullity, B. D. (1972 b), Introduction to Magnetic Materials. Reading, MA: Addison-Wesley, p. 86. Cullity, B. D. (1972c), Introduction to Magnetic Materials. Reading, MA: Addison-Wesley, pp. 207247. Cullity, B. D. (1972d), Introduction to Magnetic Materials. Reading, MA: Addison-Wesley, pp. 367368. den Broeder, F. J. A., Franken, P. E. C. (1981), in: Advances in Ceramics, Vol. 1: Levinson, L. M. (Ed.). Columbus, OH: Am. Ceram. Soc, pp. 494501. Dixon, M. (1979), Ann. Mtg. Am. Cer. Soc, Paper 82-E-79, May 1979, Cincinnati, OH. Dixon, M., Pass, C. E. (1978), Fall Mtg. Am. Ceram. Soc, Paper 12-E-78F, Sept. 1978, Dallas, TX.
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Hoagland, A. S. (1985), in: Advances in Ceramics, Vol. 16, Fourth Int. Conf on Ferrites. Columbus, OH: Am. Ceram. Soc, pp. 263-271. Hoshino, Y (1981), in: Ferrites: Proc. Int. Conf, Sept.-Oct. 1980, Japan. Center Acad. Publ. Jpn. (CAPJ), pp. XXXI-XXXV. Ichinose, M., Aronoff, M. (1990), IEEE Trans. Magn. MAG-26, 2972-2977. IEEE Trans. Magn. Mag-20, 5, Sept. (1984). Ikeda, A., Satomi, M., Chiba, H., Hirota, E. (1971), in: Ferrites: Proc. Int. Conf, July 1970, Japan. Tokyo: Univ. of Tokyo Press, pp. 337-339. Ishino, K., Nurimiya, Y. (1987), Ceram. Bull. 66, 1469. Johnson, D. W, Vogel, E. M., Ghate, B. B. (1981), in Ferrites: Proc. Int. Conf, Sept.-Oct. 1980, Japan: Center Acad. Publ. Jpn., pp. 285-291. Johnson, D. W, Ghate, B. B. (1985), in: Advances in Ceramics, Vol. 15. Columbus, OH: Am. Ceram. Soc, pp. 27-38. Kajiwara, K., Hayakawa, M., Kunito, Y, Ikeda, Y, Hayashi, K., Aso, K., Ishida, T. (1990), IEEE Trans. Magn. MAG-26, 2978-2982. Kato, V, Takei, T. (1933), J. Inst. Elect. Engrs. 53, 408. Kawai, M. (1934), J. Soc. Chem. Ind. Jpn. 37, 392. Kimura, T., Takahashi, T, Yamaguchi, T. (1983), in: Solid State Chemistry, Vol. 3: Metselaar, R., Heijligers, H. J. M., Schoonman, J. (Eds.). Amsterdam: Elsevier, p. 391. Kittel, C. (1969), Solid State Physics. New York: John Wiley and Sons, p. 438. Knowles, X E. (1961), Proc. Phys. Soc. 78, 233-238. Knowles, X E. (1970), /. Phys. D: Appl Phys. 3,1346. Knowles, X E. (1974), Philips Res. Rep. 29, 93. Knowles, X E. (1975), IEEE Trans. Magn. MAG-11, 44. Koops, C. G. (1951), Phys. Rev. 83, 121-124. Konig, U. (1974), Appl. Phys. 4, 237. Konig, U. (1975), IEEE Trans. Magn. Mag-11,13061308. Kuczynski, G. C. (1971), in: Ferrites, Proc. Int. Conf, July 1970, Japan. Tokyo: Univ. of Tokyo Press, pp. 87-95. Kugimiya, K., Hirota, K. (1989), in: Advances in Ferrites, Proc. ICF-5,1989, India. New Delhi: Oxford and IBH Publ. Co., pp. 853-860. Landolt-Bornstein (1970), Magnetic and Other Properties of Oxides and Related Compounds, Vol. 4: Hellwege, K. H., Hellwege, A. M. (Eds.) New York: Springer, pp. 50-340. Lescroel, Y, Pierrot, A. (1960), Cables and Transm. 14, 220. Lin, I-Nan, Misra, R., Thomas, G. (1982), IEEE Trans. Magn. MAG-18, 1544. Morell, A., Hermosin, A. (1980), Ceram. Bull. 59, 627. Morineau, R., Paulus, M. (1975), IEEE Trans. Magn. MAG-11, 1312-1314.
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Nakata, A., Chihara, H., Sasaki, A. (1985), /. Appl. Phys. 57, 4177-4179. Neel, L. (1948), Annales de Physique 3, 137-198. Ochiai, T., Okutani, K. (1985), Advances in Ceramics, Vol. 16, Fourth Int. Conf. on Ferrites. Columbus, OH: Am. Ceram. Soc, pp. 447-456. Ohta, K. (1963), J. Phys. Soc. Jpn. 18, 685. Okazaki, K. (1981), in: Advances in Ceramics, Vol. 1. Columbus, OH: Am. Ceram. Soc, pp. 23-37. Okazaki, K., Igarashi, H. (1971), in: Ferrites, Proceedings of the Int. Conf, July 1970, Japan. Tokyo: Univ. of Tokyo Press, pp. 131-133. Okutani, K., Mori, T. (1989), in: Ferrite Processing and Manufacturing, Tutorial Session: Recent Topics in Soft Ferrites, ICF-5, IIT-Powai: Srivastava, C. M. (Ed.). Bombay, India: Convener Ostafiichuk, B. K., Mikharskii, B. K., Fedoriv, V. D., Gorskii, V. V, Garmash, V Y, Arsenich, I. I. (1989), Neorganicheskie Materialy 25, 1815-1819. Oudemans, G. J. (1968), Philips Tech. Rev. 29, 45. Oyama, S. (1991), Soft Ferrites '91, Sept. 1991, San Diego, CA, Conf. Rep. Falmouth, ME: Falmouth Associates, Inc. Pakhomova, N. L., Zalyaletdinov, R. K., Dzerzhkovich, N. B., Kasimenko, L. M., Kozlov, V. A., Semenov, V. I. (1989), Neorganicheskie Materialy 25, 1719-1722. Parker, R. J. (1990), in: Advances in Permanent Magnetism. New York: John Wiley and Sons, pp. 8081. Paschenko, V. P., Andrev, A. Y, Mikharskii, S. N., Nesterov, A. M., Ganin, V V, Pimkin, A. Y. (1983), Poroshkovaya Metallurgiya 8, 82-85. Paulus, M. (1971), in: Ferrites, Proc. Int. Conf, July 1970, Japan. Tokyo: Univ. of Tokyo Press, pp. 114-120. Perduijn, D. J., Peloschek, H. P. (1968), Proc. Brit. Cer. Soc. 10, 2636. Pressman, A. L. (1991), Switching Power Supply Design. New York: McGraw-Hill, p. 542. Proc. 1st Int. Conf on Ferrites (1971): Hoshino, Y, Iida, S., Sugimoto, M. (Eds.). Tokyo: University of Tokyo Press. Also: Baltimore, MD: University Park Press. Proc. 2nd Int. Conf on Ferrites (1977), /. de Phys., Colloq. Cl, Suppl. A, 38 C-l. Proc. 3rd Int. Conf on Ferrites (1981): Watanabe, H., Iida, S., Sugimoto, M. (Eds.). Tokyo: Center for Academic Publications, Japan (CAPJ). Proc. 4th Int. Conf. on Ferrites (1985), Advances in Ceramics, Vols. 15,16: Wang, F. F. Y. (Ed.). Columbus, OH: Am. Ceram. Soc. Proc. 5th Int. Conf. on Ferrites (1989), Advances in Ferrites, Vols. 1, 2: Srivastava, C. M., Patni, M. J. (Eds.). New Delhi: Oxford and IBH Publ. Co. Regazzoni, A. E., Matijevic, E. (1983), Colloids and Surfaces 6, 189. Reijnen, P. (1968), in: Science of Ceramics, Vol. 4. London: Academic Press, pp. 169-188.
Rikukawa, H., Sasaki, I. (1985), in: Advances in Ceramics, Vol. 15, Fourth Int. Conf. on Ferrites. Columbus, OH: Am. Ceram. Soc, pp. 215-219. Ross, E. (1959), Naturwiss. 46, 65. Ross, E. (1966), Electronic Components Bull. 1, 136. Ross, E. (1971a), in: Ferrites, Proc. Int. Conf, July 1970, Japan. Tokyo: Univ. of Tokyo Press, pp. 203-209. Ross, E. (1971b), in: Ferrites, Proc. Int. Conf, July 1970, Japan, Tokyo: Univ. of Tokyo Press, pp. 187-189. Ross, E. (1982), IEEE Trans. Magn. Mag-18, 1529. Ross, E. (1989), in: Advances in Ferrites, Proc. ICF-5, 1989, India. New Delhi: Oxford and IBH Publ. Co., pp. 129-136. Ross, E., Hanke, I., Moser, E. (1964), Z. Angew. Phys. 17, 59. Rui-Yun, H., Xiao-Li, C , Shu-Xiang, L. (1989), in: Advances in Ferrites, Proc. ICF-5,1989, India. New Delhi: Oxford and IBH Publ. Co., pp. 177-181. Ruthner, M. J. (1989), in: Advances in Ferrites, Proc. ICF-5, 1989, India. New Delhi: Oxford and IBH Publ. Co., pp. 23-34. Ruthner, M. I , Richter, H. G., Steiner, I. L. (1971), in: Ferrites, Proc. Int. Conf, July 1970, Japan. Tokyo: Univ. of Tokyo Press, pp. 75-78. Sainamthip, P., Amarakoon, V. R. W. (1987), Abstract 78-E-87, Am. Cer. Soc. Bull. Sano, T, Morita, A., Matsukawa, A. (1988), Proc. Third Ann. High Frequency Power Conversion Conf, San Diego, CA. Sano, T, Morita, A., Matsukawa, A. (1989), in: Advances in Ferrites, Proc. ICF-5, 1989, India. New Delhi: Oxford and IBH Publ. Co., pp. 595-604. Schnettler, F. X, Johnson, D. W. (1971), in: Ferrites, Proc. Int. Conf, July 1970. Japan. Tokyo: University of Tokyo Press, pp. 121-124. Shichijo, Y, Takama, E. (1971), in: Ferrites, Proc. Int. Conf, July 1970, Japan. Tokyo: Univ. of Tokyo Press, pp. 210-213. Shichijo, Y, Asano, G., Takama, E. (1964), /. Appl Phys. 35, 1646. Shinohara, T, Murakami, S. (1981), in: Ferrites, Proc. Int. Conf, Sept.-Oct., 1980, Japan. Cent. Acad. Publ. Jpn. (CAPJ), pp. 321-323. Slick, P. I. (1971), in: Ferrites, Proc. Int. Conf, July 1970, Japan. Tokyo: Univ. of Tokyo Press, pp. 81 83. Also see U.S. Patent 3 609 083. Slick, P. I. (1980), in: Ferromagnetic Materials: Wohlfarth, E. P. (Ed.). Amsterdam: North-Holland Phys. Publ. Co., pp. 190-241. Smit, J. (1971), in: Magnetic Properties of Materials', Smit, J. (Ed.). New York: McGraw-Hill Book Co., pp. 1-19. Smit, I , Wijn, H. P. J. (1959a), in: Ferrites. New York: John Wiley and Sons. Smit, X, Wijn, H. P. X (1959 b), in: Ferrites. New York: John Wiley and Sons, pp. 15-42. Smit, X, Wijn, H. P. X (1959c), in: Ferrites. New York: John Wiley and Sons, p. 140.
13.12 References
Smit, J. Wijn, H. P. J. (1959d), in: Ferrites. New York: John Wiley and Sons, pp. 179-190. Smit, I , Wijn, H. P. J. (1959 e), in: Ferrites. New York: John Wiley and Sons, p. 212. Smit, I , Lotgering, F. K., van Stapele, R. P. (1962), /. Phys. Soc. of Japan, 17, Suppl B-l, 268-272. Snelling, E. C. (1988), in: Soft Ferrites. London: Butterworths, pp. 201-231. Snelling, E. C. (1989), in: Advances in Ferrites, Proc. ICF-5, 1989, India. New Delhi: Oxford and IBH Publ. Co., pp. 579-586. Snoek, J. L. (1936), Physica 3, 463. Snoek, J. L. (1947), New Developments in Ferromagnetic Materials. New York, Amsterdam: Elsevier. Stijntjes, T. G. W. (1970), Philips Res. Rep. 25, 9 5 107. Stijntjes, T. G. W. (1989), in: Advances in Ferrites, Vol. 1: Srivastava, C. M., Patni, M. J. (Eds.). New Delhi: Oxford and IBH Publ. Co. Stijntjes, T. G. W, Roelofsma, J. J. (1985), in: Advances in Ceramics, Vol. 16, Fourth Int. Conf. on Ferrites. Columbus, OH: The Am. Ceram. Soc, pp. 493-506. Stijntjes, T. G. W, Klerk, X, Rooymans, C. J. M., Broese van Groenou, A., Pearson, R. F., Knowles, G. E., Rankin, P. (1971), in: Ferrites, Proc. Int. Conf. July 1970, Japan. Tokyo: Univ. of Tokyo Press, pp. 191-193. Stuijts, A. J. (1964), in: Microstructure of Ceramic Materials, Proc, NBS Miscellaneous Publication 257. Available from U.S. Govt. Printing Office, Washington, DC. Stuijts, A. J. (1971), in: Ferrites, Proc. Int. Conf, July 1970, Japan. Tokyo: Univ. of Tokyo Press, pp. 108-113. Sugimoto, M. (1985), in: Advances in Ceramics, Vol. 15, Fourth Int. Conf on Ferrites. Columbus, OH: Am. Ceram. Soc pp. 5-10. Sugimoto, M. (1989), in: Advances in Ferrites, Proc. ICF-5, 1989, India. New Delhi: Oxford and IBH Publ. Co., pp. 3-12. Sundahl, R. C , Ghate, B. B., Holmes, R. X, Pass, C. E., Johnson, D. W. (1981), in: Advances in Ceramics, Vol. 1. Columbus, OH: Am. Ceram. Soc, pp. 502-511. Takama, E., Ito, M. (1979), IEEE Trans. Magn. Mag15, 1858-1860. Tanaka, T. (1978), Jpn. J Appl. Phys. 17, 349-354. Tanaka, T. (1981), J. Am. Cer. Soc. 64, 419-421.
729
Tebble, R. S., Craik, D. X (1969 a), in: Magnetic Materials. London: Wiley-Interscience, pp. 562-602. Tebble, R. S., Craik, D. X (1969b), in: Magnetic Materials. London: Wiley-Interscience, pp. 656-713. Tebble, R. S., Craik, D. X (1969c), in: Magnetic Materials. London: Wiley-Interscience, p. 577. Tsunekawa, H., Nakata, A., Kamijo, T, Okutani, K., Mishra, R. K. Thomas, G. (1979), IEE Trans. Magn. Mag-15, 1855. van den Broek, C. A. M., Stuijts, A. L. (1977), Philips Tech. Rev. 37, 157. Venkataramani, N., Srivastava, C. M. (1987), IEEE Trans. Magn. Mag-23, 2221-2223. Visvanathan, B., Murthy, V. R. K. (1990), Ferrite Materials. New Delhi: Narosa Publishing House and Springer-Verlag. Wagner, U. (1980), J. Magn. Magn. Mater. 19, 99. Warlimont, H. (1990), IEEE Trans. Magn. Mag. 26, 1313-1320. Watanabe, T. (1991), Soft Ferrites '91, Sept. 1991, San Diego, CA, Proc. conf. Falmouth, ME: Falmouth Associates, Inc. Webster, W L. (1925), Proc. Royal Soc. (A) 109, 570-584. Weiss, P. (1907), J. Physique 6, 661-690. Went, X X, Rathenau, G. W, Gorter, E. W, van Oosterhout (1952), Philips Tech. Rev. 13, 194-208. West. B., Yang, D., Jeffers, F. (1991), J. Appl. Phys. 69, 5637-5639. Wickham, D. G. (1960), J. Inorg. andNucl. Chem. 14, 217. Wickham, D. G. (1971), in: Ferrites, Proc. Int. Conf, July 1970, Japan. Tokyo: Univ. of Tokyo Press, pp. 105-107. Wijn, H. P. X (1971), in: Ferrites, Proc. Int. Conf, July 1970, Japan. Tokyo: Univ. of Tokyo Press, pp. XIX-XXIII. Wilson, T. G. (1985), in: Advances in Ceramics, Vol. 16, Fourth Int. Conf. on Ferrites. Columbus, OH: Am. Ceram. Soc, pp. 433-456. Wolf, W P. (1961), Ferrimagnetism, Reports on Prog, in Physics. 24, 212-303. Yamamoto, T. (1990), in: Elecronic Components Sector-Industry Report. Morgan Stanley and Co., Table II, 4. Yan, M. F , Johnson, Jr. D. W. (1981), /. Am. Ceram. Soc. 61, 342-349. Yosida, K., Tachiki, M. (1957), Prog. Theor. Phys. 17, 331.
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13 Ferrimagnetic Ceramics
General Reading Bates, L. F. (1961), Modern Magnetism, 4th ed. Cambridge: Harvard University Press. Chikazumi, S. (1964), Physics of Magnetism. New York: John Wiley & Sons. Cullity, B. D. (1972), Introduction to Magnetic Materials. Reading, MA: Addison-Wesley. Goldman, A. (1990), Modern Ferrite Technology. New York: Van Nostrand Reinhold. Heck, C. (1974), Magnetic Materials and their Applications. New York: Crane, Russack Co.
Jiles, D. (1991), Introduction to Magnetism and Magnetic Materials. New York: Chapman and Hall. Kittel, C. (1986), Introduction to Solid State Physics, 6th ed. New York: Wiley. Parker, R. J. (1990), Advances in Permanent Magnetism. New York: Wiley. Smit, J., Wijn, H. P. J. (1959), Ferrites. New York: John Wiley & Sons. Snelling, E. C. (1988), Soft Ferrites, 2nd ed. Boston, MA: Butterworths. Standley, K. J. (1962), Oxide Magnetic Materials. Oxford: Clarendon Press.
14 Semiconducting Polycrystalline Ceramics Gordon E. Pike Electronic Ceramics Department, Sandia National Laboratories, Albuquerque, NM, U.S.A.
List of Symbols and Abbreviations 14.1 Introduction 14.2 Grain Boundary Effects 14.3 Electrostatic Barriers and Transport Properties 14.3.1 Equilibrium 14.3.2 Steady State 14.3.3 Harmonic Response 14.3.3.1 Harmonic Response at Equilibrium 14.3.3.2 Harmonic Response in Steady State 14.4 Multi-Grain Effects 14.5 Intergranular Second Phases 14.6 Summary 14.7 References
Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.
732 734 737 739 739 741 746 747 749 750 751 752 752
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14 Semiconducting Polycrystalline Ceramics
List of Symbols and Abbreviations A b c C CD CL,R C^ d D dXx e Ec EF EFn Eg eh, eth EY e V1 F(x) G GL R G dc J ^dc,i,q Jlbbl, Jrbbr J over k 1, r Nd nt(E) nt0 Pb <2 b T V(t) Ko *dc YLR
Richardson constant boundary (subscript) captured current fraction capacitance per unit area Debye capacitance factor capacitance per unit area of left, right depletion region high frequency capacitance depletion width ceramic grain size thickness of the left-, right-hand depletion layer electron charge conduction band energy minimum Fermi level neutral Fermi level gap energy hot, thermalized electron valence band energy maximum Fermi level for trapped carriers in the boundary electric field conductance per unit area conductance per unit area of left, right depletion region dc conductance per unit area net current density across grain boundary dc, in-phase, quadrature current components current density components of carrier exchange between bulk and grain boundary current density over grain boundary barrier Boltzmann constant left-, right-hand grain (subscript) density of donor sites energy distribution of grain boundary trap states areal density of trapped electrons at the grain boundary (at equilibrium) notation for a dangling bond defect in Si excess charge density (areal) at grain boundary absolute temperature total time dependent applied voltage ac > dc components of V(t) admittance per unit area of left, right depletion region
a 8 g0 C
coefficient of nonlinearity relative permittivity permittivity of free space Fermi level separation from Ec in bulk
List of Symbols and Abbreviations
T 4>B (/> B0 co
time constant potential barrier height potential barrier height at equilibrium frequency
PTC TEM XPS
positive temperature coefficient transmission electron micrograph X-ray photoemission spectroscopy
733
734
14 Semiconducting Polycrystalline Ceramics
14.1 Introduction Semiconducting polycrystalline ceramics are a special subset of the semiconductor materials covered more generally in Vol. 4 of this Series. The basic ceramic materials have the same general characteristics of all semiconductors. They have a valence band and conduction band separated in energy by a forbidden gap, the bandgap. They can be doped with donors or acceptors to provide free carriers in the bands, a process which produces increased, extrinsic conductivity. However, unlike the textbook examples of semiconductors, typical ceramic bodies are complicated by the fact that they are not pure, nor stoichiometric, nor single crystalline (see Fig. 14-1). These deviations from ideality provide semiconducting polycrystalline ceramics with characteristics both different from simple semiconductors and difficult to accurately control in fabrication processes. By current standards of semiconductor purity, ceramic bodies are quite impure. Silicon for microelectronics contains maximum impurity amounts in the parts per million range, usually added as a desirable dopant. But within the individual crystallites of polycrystalline ceramics, there are frequently much higher levels (0.01 to 10%) of chemical impurities. Some are added deliberately to achieve desirable microstructures or electrical properties, while others result from impure ingredient materials (powders, mainly) and processing conditions (e.g., powder milling). A high level of non-stoichiometry within the crystallites may result from defects, typically interstitial cations or anion vacancies even in relatively pure materials. Their density is usually sensitive to oxidation/reduction conditions during processing. These defects frequently have small ionization energies so that they act as shal-
(b) Figure 14-1. Transmission electron micrograph (TEM) of a ceramic semiconductor, (a) This is a TEM of a ZnO varistor illustrating its polycrystalline structure and phase separation of y-Bi2O3 at several triple points, (b) This is a higher magnification view of one of the triple points in part (a). (Courtesy of C. R. Hills, Sandia National Laboratories.)
low, self-dopants at room temperature. When this occurs, the ceramic is said to be defect doped. The defect dopants can have a profound effect on the electrical conductivity; the prototypical example being rutile (TiO 2 -J in which the conductivity at 500 °C can be varied from 10" 7 S/cm to 10~ 3 S/cm just by altering the ambient partial pressure of oxygen (Logothetis and Hetrick, 1979). Figure 14-2 shows this effect at several temperatures.
14.1 Introduction \\j
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Figure 14-2. Influence of ambient oxidation conditions on resistivity. The partial pressure of oxygen, Po 2 , surrounding nominal TiO 2 determines the density of lattice defects (oxygen vacancies or Ti interstitials) in equilibrium. These defects are donors, and thus their density determines the free electron density and the electrical resistivity. [From Logothetis and Hetrick (1979); courtesy of E. M. Logothetis; copyright 1979, reproduced by permission of Pergamon Press plc.l
In addition to the crystallites of the primary ceramic semiconductors, there are the regions between them. Frequently this region contains one or more ceramic phases of different composition, see Fig. 14-3 a. The constituents of these second phases may be added to control the microstructure development during processing such as grain (crystallite) size and distribution. The second phase may also be added to develop a desired electrical property; the most common such property is insulation between adjacent grains. How-
735
ever many semiconducting ceramics have only infrequent second phases in the boundaries between adjacent grains, see Fig. 14-3 b. Even in this case in which the grains are directly joined, the grain boundaries are often of dominant importance to the electronic properties of semiconducting polycrystalline ceramics. The reason for this is the ability of the grain boundaries to capture and trap majority carriers from the grains. The boundaries then contain two dimensional sheets of charge which repel other carriers of their type when they approach the boundary from adjacent grains, thus making conduction between grains, and across the entire ceramic body, difficult. This effect lowers the conductivity of the semiconducting polycrystalline ceramic relative to its single crystal form, in some cases by many orders of magnitude. The existence of grain boundaries capable of greatly suppressing the dc conductivity is the principal distinguishing feature between semiconducting polycrystalline ceramics and the more common semiconducting materials. Indeed, the technological uses of semiconducting polycrystalline ceramics tend to exploit and utilize this and related effects, whereas most other semiconductor technologies try to negate or passivate them. Several examples of applications are given in Table 14-1. The functional characteristics which make the listed ceramics useful are all based on electrical properties of the grain boundaries. Because of the importance of resistive grain boundaries the rest of this chapter will concentrate on those ceramic materials which possess this property. For ceramics prepared such that their dc conductivity is little different from equivalently doped, single crystal samples, their properties are adequately described in Vol. 4 of this Series.
736
14 Semiconducting Polycrystalline Ceramics
Figure 14-3. Grain boundaries with and without second phases in ceramic SrTiO 3 . Shown are two high-resolution transmission electron micrographs of grain boundaries in ceramic SrTiO 3 . Part (a) illustrates a boundary with an amorphous intergranular phase rich in sodium which has been diffused into the previously sintered SrTiO3 from a coating of Na 2 O. Part (b) illustrates a similar boundary free of any second phase. [From Fujimoto et al. (1985); courtesy of M. E. Fujimoto; copyright 1985, reproduced with permission of the American Ceramic Society.] (b)
In this chapter it will be presumed that the individual grains of the primary ceramie material are semiconducting; issues of atomic bonding, band structure, and what makes a particular ceramic material a
semiconductor are not addressed here, Again, the reader interested in these issues should see Vol. 4 of this Series. Instead the effects of grain boundaries and intergranular phases will be described. The in-
14.2 Grain Boundary Effects
737
Table 14-1. Example applications of polycrystalline semiconducting ceramics. Application
Functional characteristic b
barrier layer capacitors
large effective dielectric constant
varistors, suppresses voltage transients and regulates voltages
electrical insulator at low electric fields, but switches to conductor at high fields
BaTiO3
temperature sensor, positive temperature coefficient
resistance increases significantly with increasing temperature
Mn 0 8 Ni 0 2 O
temperature sensor, negative temperature coefficient
resistance decreases significantly with increasing temperature
oxygen sensor
resistance changes with oxygen partial pressure at high temperatures
self-regulating heater
resistance increases sharply at high temperature to limit current
Principal constituenta SrTiO3 ZnO
TiO 2 Bai_PbxTiO3 a
The principal constituents are given only to show their variety; b the functional characteristics usually depend strongly on other chemical additives in percent amounts.
fluence of impurities, defects, and non-stoichiometries is mainly on the details of the electrostatic potential barriers which form at the grain boundaries. Microstructure is principally manifest through the grain size, or number of grain boundaries per unit thickness of material.
14.2 Grain Boundary Effects The simplest models for semiconducting polycrystalline ceramics are those for which the individual grains of the primary ceramic are completely homogeneous in their chemical composition and defect microstructure and have a random crystallographic orientation. All important electronic properties of semiconducting polycrystalline ceramics may be derived from these simple models. Deviations from such a simple model affect only the quantitative aspects of these properties. Of course, for technological applications, consideration of quantitative values is important, for
these determine the performance of the material. Although the individual ceramic grains may be homogeneous, the boundary regions of adjacent grains are typically quite different. Due to the random crystallographic orientation of powder particles in bulk, sintered specimens, or of nucleated islands in deposited thin films, there will be atom position mismatches in regions of direct contact, see Fig. 14-3 b. These atomic scale mismatches are accommodated by the formation of point and extended defects within and near (several atomic spacings) the two-dimensional grain boundary. Some of these defects have electronic energy levels within the bandgap of the semiconducting ceramic, and thus may act as carrier trapping sites. A well-studied example of such grain boundary defects and their trapping properties is the silicon dangling bond (Pb center) in polycrystalline silicon (Seager and Ginley, 1979; Johnson et al., 1983). If, as in pure polycrystalline Si, these defects were the only source of charge
738
14 Semiconducting Polycrystalline Ceramics
nearly six orders of magnitude difference in grain boundary conductance due to a 10° tilt angle. Not only is the low voltage conductance vastly different, but also the functional variation of current on voltage is qualitatively different. These differences are all attributable to the differing densities and energy distributions of electronic traps in the grain boundaries from the indicated crystallographic mismatches. Another common difference between the bulk and grain boundary regions in polycrystalline ceramics is the segregation of various chemical impurities, both intentional and unintentional, at the boundary. Because of the ill-defined boundary microstructure, little attempt has been made to determine details of the electronic energy levels of impurities in grain boundaries. However, it is known in some cases
trapping, then the electronic characteristics of each grain boundary would be widely variable due to the differing degrees of mismatch of adjacent grains. This wide variability has been observed experimentally in polycrystalline silicon (Redfield, 1981; Seager and Ginley, 1981; Seager et al., 1982). An outstanding example of the variability due to mismatch alone is found in the systematic study of oriented bicrystals of GaAs (Salerno et al., 1984). Figure 14-4 shows the current density as a function of voltage across single tilt boundaries in GaAs (Salerno et al., 1984). For the bicrystal with a carrier density of 2.5 x 1015 cm" 3 the conductivity is highest with no mismatch (0° tilt). Tilt angles about a [110] axis within the grain boundary of 2.5, 5, and 10° produce progressively lower conductivities. For the data shown there is
[1101/(111) Tilt boundaries Reverse bias of (111) side a o° ^ n |1l0l = 2.5x10* cm' 3 |1l0l O 10° • 10° "]
1.0x10 : r0: jn.no,=1.
15
crrT3 10
11
Voltage (V)
Figure 14-4. Effect of crystallographic mismatch on electrical properties of grain boundaries. These data are for several GaAs bicrystals grown with selected relative orientations between the two crystallites. The grain boundary in the "reference" crystallite is always a (111) plane. The grain boundary in the rotated crystallite is an off-(lll) plane achieved by rotation from the reference orientation about a [110] axis within the grain boundary plane. This produces a pure tilt boundary. The tilt angles produced experimentally are indicated in the figure. The large variations in the absolute conductance values and the current-voltage relationships are due to the different potential barriers caused by different charge trapping at grain boundary mismatch defects. [From Salerno et al. (1984); courtesy of J. P. Salerno and reproduced with his permission.]
14.3 Electrostatic Barriers and Transport Properties
739
Figure 14-5. Continuous second phase at a ceramic grain boundary. This is a transmission electron micrograph of a grain boundary in ceramic SrTiO 3 . After sintering the titanate at high temperature, Bi 2 O 3 has been diffused into the material during a second firing step. An amorphous, Bi-rich second phase about 10 nm thick is visible as the darkest band. Asymmetrically surrounding this is a lighter band which results from Bi diffusion into the titanate from the second phase material. The amount of Bi in these diffusion layers is estimated at 2% or less, and the width is highly variable depending on the crystallographic orientation of the grains. [After Franken and Viegers (1981); courtesy of P. E. C. Franken and D. R. Clarke; reproduced with permission of J. Materials Science.]
and is plausible in others, that some of these impurities can also act as charge trapping sites within the grain boundaries. The trapping of charge carriers by defects and impurities at grain boundaries is sufficient to dramatically change the electronic properties of semiconducting polycrystalline ceramics relative to those of single crystals, and to impart new and technologically useful characteristics. This is true even in the absence of second crystallographic phases. While continuous second phases exist at grain boundaries in some ceramic materials, see Fig. 14-5, their effects on the electronic properties of grain boundaries is qualitatively different from trapped charge alone and thus they will be treated separately at the end of this chapter. To describe the electrical properties of semiconducting polycrystalline ceramics, the characteristics of individual boundaries, or bicrystals, will be considered first,
and in considerable detail. Just as most effects of all semiconducting polycrystalline ceramics are found in ideal, homogeneous models of the materials, most effects of the homogeneous models are exhibited by single grain boundaries. The effects of multiple boundaries as found in real ceramic bodies will be addressed as one of the last sections in this chapter.
14.3 Electrostatic Barriers and Transport Properties 14.3.1 Equilibrium
Figure 14-6 schematically illustrates the formation of the equilibrium band structure in an ideal bicrystal. Consider two crystallites (1 + r) of an n-type ceramic semiconductor which are electrically neutral and separated in space as shown in Fig. 14-6 a. The energy level of the valence band
740
14 Semiconducting Polycrystafline Ceramics
(a)
Grain boundary material
Impurities +Defects
(b)
Figure 14-6. Schematic diagram of a separated bicrystal. (a) Left- and right-side single crystal grains of an w-type semiconductor are shown in an energy diagram with a thin, disordered, and impure sheet of the same semiconductor. The latter material will generally have a different neutral Fermi level, EFn, than the adjacent grains, and will have electronic states within the bandgap energy region. Those above EFn will be unoccupied in the separated condition illustrated, (b) After joining the three pieces to make an actual bicrystal in equilibrium, electrons have transferred from the crystallites to the boundary to equalize the Fermi level. The resulting charge configuration of a sheet of negative charges at the boundary and compensating amounts of positive charge from ionized donors from a distance d on either side may be described by a symmetric electrostatic potential barrier of energy ^ B 0 .
maximum, £ v , the conduction band minimum, E c , and the Gibbs free energy per electron (Fermi level, EF) are shown as flat to the edge of each crystallite. A third piece of material, representing the eventual grain boundary region is also shown for conceptual purposes. It has the same chemical composition and phase as the crystallites, but contains all of the impurities and defects discussed above. Because of these latter quantities, this thin piece of material (a few atomic layers) has a different neutral Fermi level, £ F n , than the crystallites. When all three pieces are joined to form a true bicrystal, the system will change to achieve a uniform Gibbs free energy per electron. This happens by free electron trapping at the defects or impurities in the grain boundary region. Each electron trapped makes it more difficult for subsequent electrons to be trapped nearby, and equilibrium is attained when the chemical energy gained by occupying a bandgap trap state is offset by the electrostatic energy required to move an electron from the bulk to the boundary. The resulting configuration is shown in Fig. 14-6b. A two-dimensional sheet of trapped negative charge leaves behind a layer of positively charged donor sites. This is mathematically described by a potential energy barrier of
14.3 Electrostatic Barriers and Transport Properties
magnitude (height) (14-1) and depletion width
where s0 is the permittivity of free space, 8 is the relative permittivity, Nd is the density of donor sites, and nt0 is the areal density of trapped electrons at the boundary (at equilibrium). If the density of donor sites were not uniform with distance from the boundary, then Nd would be replaced with an integral. To obtain a feeling for the magnitude of the barrier height and depletion width in semiconducting ceramics, consider some typical parameters found in ZnO varistors. For JVd = 10 18 crn~ 3 , 8 = 8.5, and nt0 = 5 x l 0 1 3 c m ~ 2 , then 0BO = O.66eV and d = 250 nm. Note that most materials have ~10 1 5 atoms/cm2 on any plane surface (i.e., grain boundary), and thus only a small fraction of surface sites are needed as trap sites (nt0) to create a substantial barrier. Using the Boltzmann relative population factor, exp[ —(/>B0/(/cT)] where k is Boltzmann's constant and T is the absolute temperature, it is seen that only one conduction band electron in 10 11 has sufficient thermal energy at room temperature to surmount a barrier of this height. This explains why a small amount of charge carrier trapping makes intergrain conduction difficult in semiconducting polycrystalline ceramics. There are several experimental techniques commonly used to determine the value of 0 BO . As will be seen by Eqs. (14-14) and (14-15), measurements of the steady state conductance as a function of temperature, or the capacitance per unit area of the grain boundary at one temperature can each provide a value of (f)B0. For
741
well characterized bicrystals these techniques are easy to use and yield consistent results (Seager and Pike, 1979). However in real ceramic bodies with a huge number of inequivalent boundaries, multi-grain effects can complicate the analysis as discussed later. 14.3.2 Steady State When a steady state, or dc, voltage is applied across a bicrystal, the band structure changes as shown in Fig. 14-7. The offset of the conduction bands from left to right bulk of the bicrystal is the energy difference, eV, induced by the applied voltage *. The essential features of this distortion are governed by the quasi-Fermi level for trapped carriers at the grain boundary. In steady state, and even at equilibrium, the trapped charges are not frozen permanently into position. Rather there is a dynamic exchange of carriers between the bulk and boundary which can be described by current components
(14-3)
(14-4) 2
Jbl=cAT exp
-
kT
1 The assumption that the grain boundary region alone sustains all of the applied voltage neglects the portion of voltage dropped across the bulk of the crystallites. In most cases of practical interest, in bicrystals and in electronic ceramics, this is a good approximation. However in cases where
742
14 Semiconducting Polycrystalline Ceramics
is because the boundary continually loses charge equally to each side (J bl and J br ), but is replenished only from the left when voltages greater than 3kT make this energetically difficult to do from the righthand grain. The height of the potential barrier, B, depends on the amount of charge trapped there. The quantitative relation is calculated from two expressions for this areal charge density (Pike and Seager, 1979). The excess charge density is related to the number of trap states nt(E) filled above the neutral Fermi energy £ F n shown in Fig. 14-6 a: Ec
Figure 14-7. Bicrystal energy diagram for an applied voltage. When a voltage, V, is applied across a bicrystal with a potential barrier, the energy and charge occupation levels change. Generally more charge is trapped at the boundary, the combined depletion width (d{ + dT) grows larger, and cj)B decreases, e Vx is the difference in quasi-Fermi level between the boundary and the more negatively biased grain.
where c is the fraction of current incident on the grain boundary which is captured into trap states, A is the Richardson constant (Sze, 1969), and 1, r, and b subscripts denote the left- and right-hand grains and the boundary, respectively. The quantity e V± is the separation of the Fermi level for trapped carriers in the boundary from that in the more negatively biased (higher electron energy) grain, see Fig. 14-7. In steady state the value of e V1 is determined by the condition that the net current into the boundary is zero which yields:
,£ F )- •f(E,EFn)]dE (14-6) It may also be obtained from the requirement that the bicrystal is net neutral, and that the number of charges in the grain boundary must equal the number of charges in the depletion layers
H2b = «J
(14-7) Equating these two expressions yields an equation implicit in 0 B ; this is usually solved numerically. Rather than show several solutions for B(V)9 the results are taken one step further by calculating the current density over the potential barrier. To do this it is assumed that the current passes between grains by thermionic emission over the barrier 2: j=
• exp for eV>kT
(14-5)
Thus the Fermi level at the grain boundary becomes pinned close to the level in the more negative voltage grain. This special relationship to the more negative, left grain
(14-8)
i-;
- kT
2 Carrier drift and diffusion may also be used to model the transport over the barrier. The essential features of the results are little changed by this alternate treatment (Stratton, 1956).
14.3 Electrostatic Barriers and Transport Properties
According to the integral in Eq. (14-6) the variation of 4>B(V), and hence J{V\ will depend on just how the trap states above E¥n are distributed in energy. Figure 14-8 illustrates the current-voltage curves resulting from four different forms for nx(E\ but all with the same total area density (cm" 2 ) of traps above E Fn and the same fraction of those filled at equilibrium. For later reference the maximum slopes on this log-log plot, a = AlogJ/AlogT^ are shown as well. This calculation may be reversed; that is, a known set of currentvoltage values for a bicrystal may be deconvoluted to determine the density and energy distribution of grain boundary states (Pike and Seager, 1979). There have been a few attempts to experimentally determine nt(E) by this process, but again because of multi-grain effects, they have been most successful on bicrystals (Seager et al., 1979; Rossinelli et al., 1989). Thus far in this chapter the description of electrical properties has been essentially theoretical. However there are many experimental manifestations of the phenomena discussed. Various electrical and structural phenomena are created or emphasized by the presence of chemical impurities in the sintered ceramic body; a brief summary of selected effects for ZnO varistors is given in Table 14-2. Two examples from Table 14-2 are discussed in more detail below to illustrate the degree of electrical property variation achievable through small chemical additions to the ceramic. Figure 14-9 shows current density versus electric field for three ceramic specimens with ZnO as the primary semiconductor (~99%). The dashed curve represents results for sintered ZnO (1200°C, 16 hours) without deliberate additions of other chemical species. The material is quite conductive, ~ 10 S/cm, and ohmic (JocF). The solid curve results when 0.5 mole percent
Curve
10c
1
743
nt(E) N 0 exp(E/0.5)
10" 10-
3.10" 10" 10" 10" 0.1
1.0 V (volts)
10.0
Figure 14-8. Current voltage characteristics of ideal bicrystals. The four curves are calculated current density versus voltage applied across a bicrystal with a potential barrier at the boundary, as in Fig. 14-7. To illustrate the effect of grain boundary trap states distributed differently in energy above £ F n , each curve has a different assumed energy distribution: (1) density increasing exponentially toward E c ; (2) density uniform in energy; (3) density decreasing exponentially toward Ec; (4) all states at one energy. All other parameters of the bicrystal are the same. The a values are the maximum slopes of the curves on this log-log plot (from Pike and Seager, 1979).
Table 14-2. Roles of selected additives in ZnO varistors. Role
Additives
Produce grain boundary trap states to establish (pB
Bi, Ba, Pr, Pb
Increase nonlinearity via enhanced impact ionization
Co, Mn
Increase grain conductivity for high current operation Increase stability against electrical degradation
Al, In Cr, Ni, Sb, Na
Inhibit grain growth
Al, Si, Sb
Promote grain growth
Be, Ti, Sn
744
14 Semiconducting Polycrystalline Ceramics -—ZnO
-—ZnO:Bi +0.2% Co
2,
ZnO:Bi
0 /
o
•
E -6 en
O
0
o
-10 .
-12
0
1
:-
—r"
2
3 Log(E) (V/cm)
• 4
5
Figure 14-9. Current voltage curves for ZnO ceramics. Three experimental curves of current density versus electric field are shown for ZnO ceramics of three different chemical compositions. The dashed curve is for nominally pure, sintered ZnO. The solid curve is for sintered ZnO plus 0.5 mol.% Bi 2 O 3 . The dot-dash curve is for the second composition plus 0.2 mol.% CoO. The maximum a values for these curves, respectively, are 1 (ohmic), 7, and 37.
of Bi 2 O 3 is added to the ZnO powder prior to sintering (1100°C, 16 hours). Two striking effects are seen. At low fields or small voltages per grain boundary the conductivity has decreased nearly 12 orders of magnitude. This change is due to large potential barriers at the ZnO grain boundaries which result from Bi-related, electron trapping sites. It is known that Bi is not soluble in ZnO, and that Bi 2 O 3 will leave the sintered ZnO boundary region on slow cooling. At room temperature most of the Bi-rich oxide is found in triple-point interstices of the ceramic body, see Fig. 14-1. Only small amounts remain within the boundary, but the remnant density is sufficient to dramatically increase the trapping there. The second striking effect of the Bi addition is to cause a pronounced nonlinearity in the current-voltage characteristic. The coefficient of nonlinearity, a, reaches a maximum of about 7, which is comparable to those calculated for distrib-
uted nt(E) in Fig. 14-8. Similar results have been for ceramic TiO 2 (Yan and Rhodes, 1982), SrTiO 3 (Gaucher et al., 1988), and BaTiO 3 (Heywang, 1971; Ihrig and Puschert, 1977) systems. These steady state results are characteristic of semiconducting polycrystalline ceramics in which only majority carriers are important in determining the potential barrier height as a function of voltage, (j)B{V). The dot-dash curve in Fig. 14-9 shows the effect of adding one more chemical species, cobalt, to the ZnO: Bi ceramic. Unlike Bi, the Co (and other 3d transition metals) is soluble in ZnO, with the Co 2 + substitutional for the Zn 2 + (Hausmann, 1969; Fichou et al., 1985). The low field conductivity has decreased further, undoubtedly from additional trapping induced by the Co at the boundary. But more remarkable is the rather sharp onset of a highly nonlinear region with a~37 near 104 V/cm. This switching behavior, from an insulator to a high differential conductor, has made this material commercially useful as a voltage limiter in much the same way Zener diodes are used. The differences between the ZnO varistor (variable resistor) and the Zener are that the former is polarity independent and will operate at much higher voltages. Aside from chemical additions to the ceramic, thermal processing conditions can also have a large effect on electrical properties. Since most semiconducting ceramics are oxides, and since oxygen vacancies and cation interstitials act as self-dopants, it is not surprising that sintering and annealing temperatures and ambient oxidizing or reducing atmospheres do affect the properties. Empirical studies of these effects abound, but careful fundamental research is generally lacking. An exception to this is the recent attention to grain boundary oxygen concentration in ZnO varistors. X-ray photoemission spectroscopy (XPS)
14.3 Electrostatic Barriers and Transport Properties
and positron annihilation spectroscopy have been used to demonstrate the role of oxygen and its variation with annealing temperature (Gupta et al., 1989; Stucki and Greuter, 1990). Many models have been proposed to explain the large a characteristic observed in ZnO varistors. It has been recognized for years now that its occurrence at 3 to 4 volts per grain boundary could not be explained by the relatively simple model of Figs. 14-7 and 14-8 (Bernasconi et al., 1976). Several groups introduced the concept that minority carriers (holes for ZnO) might become important at these values of grain boundary voltage (Mahan et al., 1979; Pike, 1982). Although the room temperature population of holes in ZnO, with its 3.2 eV bandgap is completely negligible from thermal processes, they can be created in the non-equilibrium process of impact ionization illustrated in Fig. 14-10.
745
Most electrons which cross the potential barrier lose excess energy rapidly by the emission of optical phonons and remain near the local conduction band minimum, Ec; these are labelled as eth in Fig. 14-10. However a small fraction of electrons do not lose their energy by this route, but instead are accelerated to a large kinetic energy. These hot electrons, eh in Fig. 14-10, can lose energy by a new mechanism once the threshold condition, e F + B>£g, is exceeded. As shown in Fig. 14-10, the hot electrons can collide with valence band electrons to impact ionize them into the conduction band. More important for the conduction process is the positively charged hole created in the valence band. The hole is strongly attracted to the electrons trapped at the boundary, and rapidly moves there. This process reduces the net trapped charge which reduces the potential barrier. The value of B decreases until the
Figure 14-10. Hole creation near a grain boundary. This energy diagram schematically illustrates the mechanism of impact ionization by hot electrons. Most electrons crossing the potential barrier thermalize quickly by emission of optical phonons; these are shown as e th . A few electrons escape this process and become "hot", or high energy. When their kinetic energy becomes larger than the bandgap, they can lose energy by impact ionizing electrons from the valance band. The remaining positively charged hole moves rapidly to the electrons trapped at the boundary, and reduces the net charge there (from Pike et al., 1985).
746
14 Semiconducting Polycrystalline Ceramics
boundary can capture enough additional electron current to equal the hole current, and thus establish a new steady state condition. The change of B with applied voltage, with and without the hole mechanism, has been calculated for typical ZnO parameters and is shown in Fig. 14-11. Since by Eq. (14-8) the current density is exponentially dependent on ^ B , the increase of nonlinearity with the onset of the hole mechanism is apparent. A direct confirmation that holes are indeed created in the highly nonlinear conduction region has been accomplished by measurement of characteristic energy, bandgap photons created by the recombination of the holes with the thermalized electrons, eth (Pike et al., 1985). Another manifestation of the presence of holes is the so called negative capacitance discussed in the next section. The unusual steady state conduction behavior described above was due to changes in applied voltage. If the semiconducting ceramic is also ferroelectric, then another unusual conduction phenomenon occurs due to changes in temperature. Again the key parameter is the barrier height, B. Equation (14-1) shows that the barrier height is inversely proportional to the rela-
0.6
(U-
0.2-• Effect of minority carriers produced by impact ionization
2 3 Voltage in V
tive permittivity, s. Above the Curie temperature of a ferroelectric £ decreases substantially with increasing temperature according to the Curie-Weiss law. This causes 4>B to increase, and by Eq. (14-8) the conductivity decreases exponentially (Heywang, 1971; Mader et al., 1984). An example of the temperature dependence of resistivity is given in Fig. 14-12 for BaTiO 3 and a series of related compounds containing Sr or Pb (Andrich, 1969). This effect has been widely utilized to produce "positive temperature coefficient" (PTC) resistors for temperature sensors (thermistors) and selfcontrolled heating elements (Hill and Tuller, 1986). For the latter applications the PTC element is placed in series with the heater. Regulation is achieved by Joule heating within the element; an increase in current raises the temperature and the resistance which tends to reduce the current again. 14.3.3 Harmonic Response
When a ceramic grain boundary with an electrostatic potential barrier formed by trapped carriers is subjected to a harmonic voltage in addition to any steady state Figure 14-11. Effect of hole generation on barrier height. This graph plots calculated curves of barrier height versus voltage for a bicrystal with grain boundary trap states all at one energy. The solid curve considers the effect of majority carriers alone; cj)B decreases slowly towards zero above five volts. When the effect of impact ionization above the bandgap energy threshold is added, the dashed curve is generated; <j)B decreases more rapidly with applied voltage which yields a much higher nonlinearity in the current-voltage relationship (from Pike et al., 1985).
14.3 Electrostatic Barriers and Transport Properties
747
io 7 y=o.7.
o
_
C3 I O 3
IO1
10"
-100
100 200 TEMPERATURE (°C)
300
400
Figure 14-12. Resistivity versus temperature for polycrystalline, ferroelectric semiconductors. These are the measured variations of resistivity with temperature for sintered ceramics of n-type BaTiO 3 and related compounds in which Sr or Pb is substituted for the Ba. These substitutions cause the Curie temperature to change relative to that of BaTiO 3 which is at 120°C. The inclusion of 0.3 mol.% of LaTiO3 makes these mixed titanates semiconducting. Above the Curie temperature of each compound the effect of the decreasing dielectric constant on increasing the barrier height, B, and the resistivity is seen. [Fr6m Andrich (1969); courtesy of D. Clarke; published with permission of Philips Technical Review.]
voltage, several interesting phenomena are observed. For simplicity this section will consider ceramic grains with only one, shallow donor species. However, effects for multiple donor species have been observed, and their explanation has been treated extensively (Blatter and Greuter, 1986; Greuter et al., 1986). In particular deep donors, additional to the shallow donors, are a source of dispersion in single bicrystals even at equilibrium in contradistinction to the simple example presented below. The general response of a charge trapping grain boundary to an applied dc plus harmonic voltage of frequency co, V(t) = Vdc + Fac sin co t
(14-9)
laxation forms: (14-10)
l+C0 2 T 2
(14-11)
where in the absence of deep donors Gdc is the dc conductance, C^ is the high frequency capacitance, i is a time constant associated with the bulk/boundary exchange of charge, and CD is a complex function of the barrier parameters which vanishes for Vdc = 0; i.e., at equilibrium. This case will be treated first, then followed by the response in the presence of a nonzero steady state voltage.
has been studied by several groups for the 14.3.3.1 Harmonic Response case of e Vac < k T (Seager and Pike, 1980; at Equilibrium Pike, 1984; Blatter and Greuter, 1986). The conductance and capacitance per unit area Even without a detailed solution it can of boundary are found to have Debye rebe shown from symmetry arguments that
748
14 Semiconducting Polycrystalline Ceramics
the conductance and capacitance of a simple, and symmetric, grain boundary barrier as depicted in Fig. 14-6b are independent of the harmonic frequency. A simple model of the grain boundary electrical admittance, which will also be useful in a later section, may be used to demonstrate this frequency independence. In Fig. 14-13 the grain boundary is schematically illustrated as the center node connected to the conductive bulk of each adjacent crystallite by a parallel conductance-capacitance network representing the depletion region. The admittance of the left (right) depletion region is given by: *I (U\ — ^T (R\ + 1 CO C i /m
(14-12)
By the assumed symmetry at equilibrium, G L =G R = 2G and C L = C R = 2C. As in a metal-semiconductor contact, neither G nor C has a frequency dependence. The series combination of the two depletion layer networks has an admittance of Y=G + icoC
(14-13)
which shows that the net double layer structure, at equilibrium, does not intro-
n/WHi Figure 14-13. Schematic diagram of grain boundary admittance. The depletion layers at semiconductor grain boundaries are represented by parallel conductance, G, and capacitance, C, networks. The grain boundary, shaded region, acts as an electrical node between the two depletion layers. The outer edges of the depletion layers are the highly conductive bulks of the crystallites, and represent the input to each network.
duce a frequency dependence for either the capacitance or conductance. At equilibrium the conductance and capacitance, per unit area of grain boundary, are given by (Seager and Pike, 1980; Pike, 1984): / c\eA ( kT (14-14) (14-15)
Thus the capacitance is essentially that of a parallel plate capacitor whose electrodes are separated by the width of the depletion region, 2d. A practical application of this result is that a thin capacitor dielectric can be obtained in a strong mechanical structure. If the ceramic grain size is D^>2d, then the apparent, or effective, dielectric constant for the ceramic body is e e0 D/(2 d). This is a geometric enhancement of the dielectric constant which is commonly the basis of the so called ceramic boundary layer capacitors (Goodman, 1986). Notice that the enhancement is greater when the grain conductivity is high [large Nd and thus small d by Eq. (14-2)], and when an intergrain second phase is absent (smaller effective d). Practical ceramic capacitors with large capacitance can be made with semiconducting ceramics which are also ferroelectric (see Chap. 9 of this Volume). For ferroelectrics the local value of & within the material depends on the local dc electric field. However, since there is a variable electric field F(x) within the depletion layer near the grain boundary, the effective value of a for the ceramic body is not easily calculated. Also the local value of e depends strongly on the temperature, and thus these types of capacitors are used where an enhanced, effective & is needed only over a small temperature range (Goodman, 1986).
14.3 Electrostatic Barriers and Transport Properties
14.3.3.2 Harmonic Response in Steady State
Application of a steady state voltage, F dc , in addition to the harmonic voltage causes the potential barrier to become asymmetric (see Fig. 14-7). This broken symmetry permits several interesting, and qualitatively unusual, harmonic phenomena to occur. Figure 14-14 illustrates several of these phenomena observed in a
Ge, low field
40
10*1 \ -
T=296K
-
10 Hz
UL
0 .
phase separation technique • • HP-4270 Bridge
(
-20 •
-40
i
i
i
100 F in V/cm
polycrystalline ZnO varistor material. The capacitance of this material is plotted as a function of the dc voltage. At low voltages it decreases slightly, followed by a region of substantial increase, and finally a maximum and a plunge to negative values. The increase and negative value of capacitance has been documented on well characterized bicrystals as well (Seager and Pike, 1980; Pike et al., 1983). To understand this behavior it is first necessary to understand how the capacitance is measured. A harmonic voltage is impressed across the sample, and the resultant harmonic current flow is measured. For the voltage of Eq. (14-9), the current is generally of the form: J =J
+ J^coscot
(14-16)
dc
20
c
749
i
200
Figure 14-14 Capacitance versus eleptric field for a commercially available low field (General Electric, Type V22ZA3) ceramic ZnO varistor. This graph shows the small signal capacitance of a ZnO varistor measured as a function of the dc electric field across the sample. The frequency range of 10 to 104 Hz was spanned using two techniques (points and solid curves) which overlapped at 103 Hz. All curves decrease slightly from their value at zero bias. At low frequencies, less than 104 Hz, the curves then increase in the range of 100 to 200 V/cm. At 102 and 103 Hz the measured capacitance reaches a maximum value significantly above C (F = 0), and then plunges to large, negative values. The curve at 104 Hz also becomes negative (from Pike, 1982).
where subscripts i and q denote in-phase and quadrature currents. The capacitance per unit area is defined as Jq/(co Vac\ where J q is generally a function of co, Vdc, and T. Reference to Fig. 14-15 will help understand the response of a charge-trapping grain boundary to the applied voltage. As for equilibrium, one component of the capacitance results from displacement currents at the edge of the depletion regions. It is this component which represents stored charge and is expected. As Vdc is increased, the combined thickness (dx -h dr) of the depletion layer grows (see Fig. 14-7) and this component, C^, decreases slightly. This is the effect seen at low voltages in Fig. 14-14. The anomalous capacitance results from the modulation of real current, J over , crossing the boundary. Because there is a time constant T governing the exchange of charge between bulk and boundary, the charge in the boundary cannot achieve its equilibrium value corresponding to the instantaneous value of applied voltage. This causes (j)B (t) to be slightly out of phase with V(t), and since Jocexp[-(/> B (£)/(& T)], the
750
14 Semiconducting Polycrystalline Ceramics
£=-=0
==qB
Figure 14-15. Schematic diagram for anomalous capacitance. The anomalous capacitance is due entirely to self-modulation of the current passing over the potential barrier in a bicrystal. Under steady state conditions this current would be the dc current; but when V(t) contains a harmonic variation, Jover does also. The trapped charge in the grain boundary obeys a rate equation with a time constant T. The finite value of T causes ^B* and Jover to develop harmonic components 90° out of phase with the applied voltage. The latter, Jq [Eq. (14-16)], yields the anomalous capacitance.
current develops an out-of-phase (quadrature) component. It is this part of the quadrature current J q which yields the anomalous capacitance. Detailed calculations (Seager and Pike, 1980) show that when only majority carriers are important in the barrier charge trapping, the anomalous capacitance always augments the normal capacitance [C D >0, cf. Eq. (14-11)]. However, when minority carriers are also involved, it is possible to have the sign of the effect reverse (CD < 0), and thus have the apparent capacitance become negative (Pike, 1982). Notice that the anomalous component, of either sign, is not capacitance as normally conceptualized. It is not a reversible storage of energy (as is C^), but rather a self-induced modulation of overbarrier, Joule heating current.
14.4 Multi-Grain Effects Although electrical results on real, multi-grain ceramic materials have been used to illustrate various phenomena in semiconducting polycrystalline ceramics, the explanations thus far have been in terms of bicrystal (single grain boundary)
phenomena. These can indeed account for the major features. However, all grain boundaries are not identical; see Fig. 14-4 for extreme examples of electrical differences. A difference in the density of charge trapping sites within the boundaries will lead to a distribution of potential barrier heights, (f)B, throughout the ceramic. This means that the temperature dependence of conductance for different grain boundaries will be different. Since current paths across the polycrystalline ceramic will include many grain boundaries, the macroscopic conductivity of the ceramic body is frequently not Arrhenius as would be predicted from Eq. (14-14). In some cases the intergrain, thermionic emission across the boundaries might also be acting in parallel with conductance laterally along neighboring boundaries. This also yields nonArrhenius behavior. The frequency dependence of capacitance is another property affected by differing boundaries. Even when each separate grain boundary at equilibrium is expected to be symmetric and without a frequency dependence, the collection of different boundaries within the multi-grain ceramic forms an admittance network (see Fig.
14.5 Intergranular Second Phases
14-16) in which the macroscopic conductance and capacitance is indeed frequency dependent (Pike, 1982). Thus zero-bias dispersion in the bulk dielectric constant of the ceramic is commonly seen (Smith et al., 1989). An example of dispersion at zero and finite bias is shown in Fig. 14-17 for a commercial ZnO varistor. Since small differences in the grain boundary barrier heights have little effect on the boundary capacitance, but an exponential effect on the boundary conductance, it is primarily the latter which is expected to cause the dispersion. If the variations in barrier height were due solely to crystallographic mismatches as in Fig. 14-4, then the dispersion would be very large. However, in ceramics the impurities at the grain boundaries usually are predominantly responsible for the charge trapping. Since these impurities are distributed with near uni-
Inter-Grain admittance
\
100 F in V/cm
751
200
Figure 14-17. Capacitive dispersion in a ZnO varistor. ("Ge, low field" means "General Electric, Type V22ZA3 low field varistor".) This is the measured capacitance as a function of voltage at several frequencies of a commercial ZnO varistor. The temperature was 405 K. There is nearly a factor of three difference in capacitance between 10 and 105 Hz at zero bias where individual grain boundaries are expected to have no dispersion. At other voltages the dispersion persists, but other factors discussed in Sec. 14.3.3.2 contribute as well (from Pike, 1982).
formity, the barrier height variations are smaller than for pure polycrystalline Si or GaAs.
14.5 Intergranular Second Phases Grain boundaries
Figure 14-16. Schematic diagram of the admittance network formed in an multi-grain ceramic. Each grain boundary has a net electrical admittance due to its electrostatic potential barrier. Since small variations in the barrier height can yield large differences in inter-grain conductance, the network is an inhomogeneous collection of admittances. This inhomogeneity causes dispersion in the capacitance of the macroscopic network (from Pike, 1982).
There are some semiconducting polycrystalline ceramics for which an intergranular second phase at the boundary is a key feature to their electrical properties. The most technologically important of these are ceramic capacitors which use the second phase as the main dielectric layer rather than the grain boundary potential barrier. An example of this is SrTiO 3 which is first sintered as a solid body, and
752
14 Semiconducting Polycrystalline Ceramics
then reheated while surrounded by Bi 2 O 3 and PbO. The Bi and Pb rapidly diffuse along the grain boundaries and become incorporated as a second oxide phase (Wernicke, 1981; Burn and Neirman, 1982). An example of this microstructure is seen in Fig. 14-5. With an analysis of the enhancement of the effective dielectric constant similar to that presented in Sec. 14.3.3.1, it is easy to see how a uniform second phase 10 to 50 nm thick could yield technologically useful properties. Another reason for creating these second phases at the boundaries is to provide a carrier blocking layer so that the resultant dielectric material has a low dissipation loss factor, and can be used at high voltages without switching "on" like a varistor.
14.6 Summary The electrical properties of semiconducting polycrystalline ceramics are frequently dominated by electrostatic potential barriers which form around the grain boundaries. These barriers are due to charge trapping at the grain boundaries, and this charge trapping is usually induced or enhanced deliberately by processing to add chemical impurities or structural defects. The purpose is to exploit some of the resultant properties of large barriers for technological advantage. In some ceramics such as ZnO these barriers act as switches which turn-on at a well defined electric field. In ferroelectric ceramics based on BaTiO 3 the strong change in dielectric constant with temperature induces orders of magnitude change in conductance which is used as the basis for sensors and current limiters. The potential barriers also provide an enhanced, effective dielectric constant which is used in ceramic capacitor technology. Finally, although it is not
technologically useful, the voltage dependence of the dielectric constant is peculiar with anomalous increases and sometimes negative values as a direct consequence of these barriers.
14.7 References Andrich, E. (1969), Philips Tech. Rev. 30, 170-177. Bernasconi, X, Klein, H. P., Knecht, B., Strassler, S. (1976), J. Elect. Mat. 5, 473-495. Blatter, G., Greuter, F. (1986), Phys. Rev. B33, 39523966. Burn, I., Neirman, S. (1982), J. Mater. Sci. 17, 35103520. Fichou, D., Pouliquen, X, Kossanyi, X, Jakani, M., Campet, G., Claverie, X (1985), J. Electroanal. Chem. 188, 167-187. Franken, P. E. C , Viegers, M. P. A. (1981), J. Mat. Sci. 16, 2003-2004. Fujimoto, M. E., Chiang, Y.-M., Roshko, A., Kingery, W. D. (1985), /. Am. Ceram. Soc. 68, C-300-C-303. Gaudier, P., Perrier, R. L., Ganne, X P. (1988), Adv. Ceramic Mat. 3, 273-277. Goodman, G. (1986), Ceramic Materials for Electronics: Buchanan, R. C. (Ed.). New York: Marcel Dekker, Chap. 2. Greuter, R, Blatter, G., Rossinelli, M., Schmuckle, F. (1986), Defects in Semiconductors, Mat. Sci. For., Vol. 10-12: v. Bardeleben, H. X (Ed.). Switzerland: Trans. Tech., pp. 235-240. Gupta, T. K., Straub, W. D., Ramanachalam, M. S., Schaffer, X P., Rohatgi, A. (1989), J. Appl. Phys. 66, 6132-6137. Hausmann, A. (1969), Phys. Stat. Sol. 31, K131 -133. Heywang, W. (1971), J. Mat. Sci. 6, 1214-1224. Hill, D. C , Tuller, H. L. (1986), Ceramic Materials for Electronics: Buchanan, R. C. (Ed.). Marcel Dekker, Chap. 5. Ihrig, H., Puschert, W. (1977), /. Appl. Phys. 48, 3081-3088. Johnson, N. M., Biegelsen, D. K., Moyer, M. D. (1983), Appl. Phys. Lett. 40, 882-887. Logothetis, E. M., Hetrick, R. E. (1979), Sol. St. Comm. 31, 167-171. Mader, G., Meixner, H., Kleinschmidt, P. (1984), J. Appl. Phys. 56, 2832-2836. Mahan, G. D., Levinson, L. M., Philipp, H. R. (1979), /. Appl. Phys. 50, 2799-2812. Pike, G. E. (1982), Grain Boundaries in Semiconductors, Vol. 5. Boston: Mat. Res. Soc, Proc, pp. 369-379. Pike, G. E. (1984), Phys. Rev. B30, 795-802. Pike, G. E., Seager, C. H. (1979), /. Appl. Phys. 50, 3414-3422.
14.7 References
Pike G. E., Gourley, P. L., Kurtz, S. R. (1983), Appl. Phys. Lett. 43, 939-941. Pike, G. E., Kurtz, S. R., Gourley, P. L., Philipp, H. R., Levinson, L. M. (1985), / Appl. Phys. 57, 5512-5518. Redfield, D. (1981), Appl Phys. Lett. 38, 174-176. Rossinelli, M., Greuter, R, Schmiickle, R (1989), in: Electroceramics, Proc. No. 41. London: British Ceramic Soc, pp. 177-188. Salerno, J. P., Fan, I C. C , McClelland, R. W, Vohl, P., Mavroides, J. G., Bozler, C. O. (1984), Electronic Properties of Grain Boundaries in GaAs: A Study of Oriented Bicrystals Prepared by Epitaxial Lateral Overgrowth. Lexington (MA): Lincoln Laboratory, MIT (Tech. Rpt. 669). Seager, C. H., Ginley, D. S. (1979), Appl Phys. Lett. 34, 337-340. Seager, C. H., Ginley, D. S. (1981), J. Appl Phys. 52, 1050-1055. Seager, C. H., Pike, G. E. (1979), Appl. Phys. Lett. 35, 709-711. Seager, C. H., Pike, G. E. (1980), Appl Phys. Lett. 37, 747-749. Seager, C. H., Pike, G. E., Ginley, D. S. (1979), Phys. Rev. Lett. 43, 532-535. Seager, C. H., Sharp, D. X, Panitz, J. K. G., Hanoka, J. I. (1982), J. de Physique Cl 43, 103-116. Smith, A., Baumard, J.-R, Abelard, P., Denanot, M.-R (1989), J. Appl Phys. 65, 5119-5125. Stratton, R. (1956), Proc. Phys. Soc. London B69, 513-552.
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Stucki, R, Greuter, R (1990), Appl Phys. Lett. 57, 446-449. Sze, S. M. (1969), Physics of Semiconductor Devices. New York: Wiley-Intersci., p. 379. Wernicke, R. (1981), Adv. Ceram. 1, 261-271. Yan, M. R, Rhodes, W. W. (1982), Appl Phys. Lett. 40, 536-537.
General Reading Ceramic Materials for Electronics: Buchanan, R. C. (Ed.) (1986). New York: Marcel Dekker. Electronic Ceramics: Properties, Devices and Applications: Levinson, L. M. (Ed.) (1988). New York: Marcel Dekker. Grain Boundary Phenomena in Electronic Ceramics, in: Advances in Ceramics, Vol. 1: Levinson, L. M. (Ed.) (1981). Columbus (OH): Am. Ceram. Soc. Greuter, R, Blatter, G. (1990), Electrical Properties of Grain Boundaries in Poly crystalline Compound Semiconductors, in: Semicond. Sci. Tech. 5, 111 — 137. Grovenor, C. R. M. (1985), Grain Boundaries in Semiconductors, in: J. Phys. C18, 4079-4119. Hench, L. L., West, J. K. (1990), Principles of Electronic Ceramics. New York: Wiley and Sons. Rhoderick, E. H. (1980), Metal-Semiconducting Contacts. Oxford: Clarendon Press.
15 Oxide Superconductors David R. Clarke
Materials Department, University of California, Santa Barbara, CA, U.S.A. Manfred Daumling
Physics Department, University of Geneva, Geneva, Switzerland
List of Symbols and Abbreviations 15.1 Introduction 15.2 Crystal Structures 15.2.1 Calcium Cuprate (CaCuO2) 15.2.2 Lanthanum Strontium Cuprate (La^^Sr^CuOJ 15.2.3 Thallium Barium Calcium Cuprate (Tl 2 Ba 2 Ca w _ 1 Cu M O 4+2n ) 15.2.4 Bismuth Strontium Calcium Cuprate (Bi 2 Sr 2 Ca n _ 1 Cu n O 4 + 2n) 15.2.5 Thallium Barium Calcium Cuprate (TlBa 2 Ca n _ 1 Cu n O 3 + 2n) 15.2.6 Yttrium Barium Cuprate (YBa2Cu3O7_^) 15.2.7 Neodymium Cerium Cuprate (Nd2_3;Ce3;CuO4) 15.2.8 Barium Bismuth Lead Oxide (BaP^ -*Bi x O 3 ) 15.3 Phase Equilibria and Stability 15.3.1 Y - B a - C u - O Phase Equilibria 15.3.1.1 In Air 15.3.1.2 Effect of Oxygen Partial Pressure on Phase Stability 15.3.1.3 Oxygen-Deficient YBa 2 Cu 3 O 7 _^ 15.3.2 B i - S r - C a - C u - O Phase Equilibria 15.3.3 Crystal Growth 15.3.4 Diffusion 15.4 Single-Crystal Properties of Yttrium Barium Cuprate 15.4.1 Mechanical Properties 15.4.2 Optical Properties 15.4.3 Electromagnetic Properties in the Normal State 15.4.4 Superconducting Properties 15.4.4.1 Transition Temperature 15.4.4.2 Critical Magnetic Fields 15.4.5 Critical Current Densities 15.4.6 Flux Creep and the Irreversibility Line 15.4.7 Intra-Grain Current Densities and Flux-Pinning Mechanisms 15.4.7.1 Excess Pinning at Finite Magnetic Fields 15.4.7.2 Critical-Current Anisotropy 15.4.7.3 Pinning by Twin Planes 15.4.7.4 Pinning by Oxygen Defects Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. Allrightsreserved.
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15.4.7.5 15.4.7.6 15.5 15.5.1 15.5.2 15.5.3 15.5.4 15.5.5 15.5.6 15.6 15.6.1 15.6.2 15.6.3 15.7
15 Oxide Superconductors
Irradiation Effects Precipitate Pinning Thin Films Epitaxial Growth Growth Mechanisms Buffer Layers Multilayer Films Critical Thicknesses Surface Resistance Polycrystalline Materials Microstructural Effects Current Densities Across Single Grain Boundaries Modeling References
790 791 791 792 794 797 798 800 802 803 804 806 810 812
List of Symbols and Abbreviations
List of Symbols and Abbreviations
c D E H Hc #irr
I Jed hi.
k
h
n Q R t T Tc V
elastic constant diffusion coefficient elastic modulus magnetic field (thermodynamic) critical field lower, upper critical field irreversibility field electric current critical current depairing current density current density (of thin film) critical current density Boltzmann constant fracture resistance of a thin film critical grain size number of adjacent Cu-O planes within the unit cell radiofrequency quality factor resistance thickness of a thin film critical thickness of a thin film temperature superconducting-transition temperature (critical temperature) electrical potential thermal expansion coefficient oxygen deficiency (stoichiometry) value tilt angle (angle between magnetic field and c axis) Ginzburg-Landau parameter magnetic penetration depth; microcrack spacing effective (superconducting) coherence length
G
4>
mm stress resistivity thermodynamic (diffusion) factor
A BCS BSCCO DC GB MBE Pa PBCO RF RSJ
ampere Bardeen-Cooper-Schrieffer (superconductivity theory) Bi 2 Sr 2 CaCuO 2+<5 direct current grain boundary molecular-beam epitaxy pascal PrBa 2 Cu 3 O 7 _^ radiofrequency resistively-shunted junction
Q
757
758
SEM SNS SQUID STEM STM T TEM YBCO YSZ
15 Oxide Superconductors
scanning electron microscopy superconductor-normal-superconductor model superconducting quantum interference device scanning transmission electron microscopy scanning tunneling microscopy tesla transmission electron microscopy YBa 2 Cu 3 O 7 _ 5 yttria-stabilized zirconia (substrate)
15.2 Crystal Structures
15.1 Introduction The discovery by Bednorz and Miiller, in 1986, of superconductivity at much higher temperatures than had previously been thought possible, and in an oxide rather than a metal, initiated a rush of activity probably unprecedented in the history of materials. In the approximately five years since publication of their initial paper (Bednorz and Miiller, 1986) an enormous body of work has been performed; several new superconducting compounds have been discovered, their crystal structures determined, processes developed for growth of single crystals, thin films, ceramic shapes and wires, many of their superconducting properties have been measured and the first steps taken towards their utilization in superconducting electronics and magnet applications. Despite this intense activity, the subject of oxide superconductors is far from mature with a number of the key issues yet to be resolved. As a result, the purpose of this chapter is limited to surveying the field at this point in time, but hopefully in sufficient detail that the reader can gain an appreciation for the structure and properties of these fascinating new materials. Reflecting the fact that the bulk of the research performed so far has been devoted to the properties of the yttrium barium cuprate superconductor, the emphasis of the sections describing the superconducting properties will also be on these materials. As the literature is now so vast (estimated to be in excess of 12000 papers to date) and many advances have been made contemporaneously, no attempt is made to do more than cite appropriate articles for the reader to refer to. An invaluable inventory of the growing literature is the High-Tc Update, published bimonthly by the Ames Laboratory, Iowa State University, in both paper and e-mail
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formats. The latter is available on-line from [email protected]. While this chapter is primarily devoted to the high-temperature superconducting oxides that are based on copper oxide, referred to here as the cuprate superconductors, a small number of oxide superconductors had been known prior to Bednorz and Miiller's discovery. In each case, superconductivity was observed at low temperatures but only after an appropriate heat treatment. The first oxide found to be superconducting was strontium titanate, which had a superconducting transition temperature Tc of 0.7 K after reduction (Schooley et al., 1964). In the same year, superconductivity was reported in TiO and NbO (Hulm et al., 1965). In succeeding years, superconductivity was found to occur in a number of tungsten bronzes (Sweedler et al., 1965; Sleight et al., 1969) and in lithium titanate (Johnston etal., 1973). In 1975 Sleight and his colleagues reported that the compound BaPb1_xBi;cO3 was superconducting, with a transition temperature that was dependent on the bismuth content (Sleight et al., 1975). An intriguing feature of the BaPb x _xBi^C^ system, and one found in a number of metallic superconductors, is that superconductivity is found to occur at the boundary between the metallic and semiconducting behavior. Similar behavior has since been noted in a number of the cuprate superconductors (Bednorz and Miiller, 1986; Sleight, 1988).
15.2 Crystal Structures Although the mechanism of superconductivity in the cuprate superconductors is not known, it is increasingly clear that they all share a common structural characteristic, namely sheets of copper-oxygen
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(Cu-O) planes that are separated by planes of various other oxides and rare earth cations. The different structures, discussed in the following sections, can be distinguished by the number of adjacent Cu-O planes within the unit cell, and this has led to a short-hand notation for the structures in terms of this number n (Table 15-1). In the C u - O planes, each Cu ion is surrounded by four O ions in a square-planar arrangement. The squareplanar configuration of the copper-oxygen ions in such structures is not new, having been studied, for its own sake, prior to the discovery of the cuprate superconductors (Muller-Buschbaum, 1977). In all of the structures the separation between the individual Cu-O planes, when they are adjacent to each other is approximately constant, and has a value of about 0.32 nm, whereas the distance to the next set of adja-
cent Cu-O planes is much larger, and depends on the nature of the ions in the structure, and also its particular crystal structure. An alternative structural description can be given in terms of the stacking of defect perovskite and rocksalt blocks. This description, based in part on the fact that the earliest cuprates discovered, i.e., La2 _JSr>;CuO4 and YBa 2 Cu 3 O 7 _^, are related to the well-known K 2 NiF 4 structure, places less importance on the layered nature of the structures but emphasizes the structural similarities with other, more common oxides. An important feature of the structures of all the cuprate superconductors is the approximately constant distance between the Cu and O ions in the Cu-O planes and their much greater distance perpendicular to the Cu-O planes. The relatively short in-plane Cu-O distances suggests that the
Table 15-1. Short-hand notations used for various cuprate superconductors and a bismuth oxide superconductor. Homologous formula
TC(K)
Number of CuO layers (n)
(La 2 _ x Sr x )CuO 4 (La 2 _ x $ryCaCu 2 O 6 Tl 2 Ba 2 Cu 2 O 6 Tl 2 Ba 2 Ca€u 2 O 8 Tl 2 Ba 2 Ca : 2 Cu 3 O 10 Bi 2 Sr 2 CuO 6 Bi 2 Sr 2 CaCu 2 O 8 Bi 2 Sr 2 Ca 2 Cu 3 O 10 (Nd 2 _ x CeJCuO 4 YBa 2 Cu 3 O 7 YBa 2 Cu 4 O 8 Y 2 Ba 4 Cu 7 O 1 4 TlBa 2 CuO 5 TlBa 2 CaCu 2 O 7 TlBa 2 Ca 2 Cu 3 O 9 TlBa 2 Ca 3 Cu 4 O 11 CaCuO 2 (Nd,Ce,Sr)CuO 4 (Ba 0 . 6 K 04 )BiO 3
38 60 0-80 108 125 0-20 85 110 30 92 80 40 0-50 80 110 122 — 30 30
1 2 1 2 3 1 2 3 1 2 2 2 1 2 3 4 1 1 -
Common notations
La(w = l) La(w = 2) 2-Tl(w=l) 2-T\(n = 2) 2-H(n = 3) 2-Bi(n = l) 2-Bi(w = 2) 2-Bi(w = 3) Nd(n = l) Y123 Y124 Y247 1-Tl(w=l) 1-Tl(w = 2) 1-H(n = 3) 1-H(n = 4) n = oo — -
214 T12201 T2212 T2223 Bi2201 Bi2212 Bi2223 T YBCO — 111201 T11212 T11223 T11234 — T* BKBO
15.2 Crystal Structures
bonding in the square-planar configuration of the Cu and O atoms is covalent in character, whereas the larger, perpendicular distances correspond to a much-weaker bonding. The C u - O planes confer an anisotropy to the crystal structures and are notionally taken to represent the ab planes of the structures, with the c-axis being perpendicular to this. This structural anisotropy is manifested as a corresponding anisotropy in the properties of the cuprates, both in the physical properties as well as in the electrical properties. For example, the bismuth cuprates are easily cleaved. At the time of writing it is widely believed that both the superconducting and the normalstate electrical transport occur predominantly in the Cu-O planes. The role of the intermediate planes and chains is still a matter of considerable uncertainty, but these are believed to act as a reservoir for charge carriers. Since the oxides exhibit superconductivity and, in the normal state, an appreciable electrical conductivity, there is considerable uncertainty as to the appropriate paradigm for describing their structure and bonding. Despite this, many of the structural aspects of the oxide superconductors, for example the likelihood of particular ionic substitutions, may be understood on the basis of the application of the usual rules of crystal chemistry, based on the concepts of ionic sizes and coordination number. The difficulty arises when attempting to describe the electronic and ionic bonding, and the way in which dopant alio-valent ions (i.e., ions with a valency different from that they are replacing in the crystal structure) affect the overall electronic structure. For these reasons, the charge on the ions is taken to be the notional value rather than the effective value,
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In the following sections the principal families of oxides that have been found to be superconducting are described. (Further descriptions of the crystal structure of oxide superconductors can be found in Chapter 1 of this Volume.) In each case the nominal formula unit is presented. 15.2.1 Calcium Cuprate (CaCuO 2 )
Calcium cuprate, if it existed, would represent the simplest superconducting copper oxide consisting of infinitely repeating C u - O planes each separated by a plane of alkaline earth (e.g., Ca 2 + ) ions (Fig. 15-1). This n = oo structure, however, can be formed by substituting Sr2 + ions for some of the Ca 2 + ions. When first synthesized, this Ca 0 86 Sr 0 14 CuO 2 material was insulating (Siegrist et al., 1988), but very recent work has shown it to be superconducting when prepared at high pressures. The isostructural parent compound, SrCuO 2 , is similarly insulating but has been successfully doped to become superconducting, up to a Tc of 40 K, by the substitution of Nd 3 + for Sr 2+ (Smith et al., 1991). Interestingly,
(a) (b) Figure 15-1. The crystal structure of (a) the "infinitelayer" compound, Cax _ x Sr x CuO 2 , that forms the basis of the cuprate superconductors, and (b) the prototype perovskite, BaBiO3, that forms the basis of the bismuth-oxide superconductors. In both structures, an oxygen ion is located at the intersection of the straight lines. The infinite-layer material consists of sheets of Cu-O units, in a square-planar configuration, separated by alkaline-earth cations. The cubic perovskite is formed by corner-sharing of the Ba-O octahedra that surround a central Bi cation. Both structures become superconducting only after appropriate doping (see text for details).
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in contrast to the Sr2 + -doped CaCuO 2 , which is a hole conductor, this compound is an electron conductor. 15.2.2 Lanthanum Strontium Cuprate (La2_,Sr,CuO4) This family, based on the body-centered tetragonal, K 2 NiF 4 structure, contains single C u - O planes on mirror planes which are separated by two, staggered (by 1/2, 1/2, 0) planes of L a - O (Fig. 15-2a). The prototypical LaCuO 4 structure, which is insulating, can be doped by substituting Sr 2+ for La 3 + to become metallic, and for x > 0.05 it becomes superconducting with a maximum transition temperature of ~ 38 K. (The first copper-oxide superconductor, La 2 - J Ba 3 7 CuO 4 , discovered by Bednorz and Miiller (1986), is obtained by replacing some of the La 3 + ions by Ba2 + ions, rather than by Sr2 + ions.) Hall measurements indicate that the carriers are holes, as might be expected from substitution by a divalent ion. A very rich variety of behavior has been reported as a function of this hole doping, ranging from antiferro-
magnetic insulator behavior to superconductivity and semiconducting behavior (Fisk et al, 1989). The two-layer compound, La 2 CaCu 2 O 6 , formed by the incorporation of a second C u - O layer and stabilized by the addition of a Ca-O plane, has recently been reported to be superconducting with a transition temperature of ~ 60 K (Cava et al., 1990). As with many of the other cuprate superconductors, although the compound had been synthesized, it was not superconducting until properly doped. In the case of the two-layer lanthanum compound this was achieved by annealing under high pressure oxygen. The three-layer lanthanum compound, La 2 Ca 2 Cu 3 O 8 , has also been synthesized, but the appropriate doping to make it superconducting has yet to be found. An interesting feature of the lanthanum cuprates is that they are isostructural with the one-, two- and threelayer Ruddleston-Popper phases, Sr 2 TiO 4 , Sr 3 Ti 2 O 7 and Sr 4 Ti 3 O 1 0 , respectively. These have so far only been made as insulating compounds.
La,Sr
Figure 15-2. The crystal structure of (a) the one-layer compound La1_JCSrxCuO4, (b) the two-layer compound La 2 CaCu 2 O 6 , and (c) Nd 2 _ y Ce y CuO 4 .
15.2 Crystal Structures
(a) 2 - T I ( n = 1 )
(b) 2 - T I ( n = 2 )
(c) 2 - T I ( n = 3 )
Two distinct oxygen sites are present in these La2_3;Sr};CuO4-based structures. There are oxygen ions in the square-planar C u - O arrangement and other oxygen ions, which are termed apical oxygen ions, immediately above and below the C u - O planes. The difference between the in-plane and the out-of-plane C u - O distances suggest a distorted octahedral arrangement of the oxygen ions around the Cu ion, as depicted by the octahedron drawn around each Cu site in Fig. 15-2 a. Similarly, in the two-layer structure, where the Cu-O planes are separated by a Ca ion, the distances suggest a pyramidal arrangement of the oxygen ions around a Cu ion, as shown in Fig. 15-2 b. These polyhedra are useful for visualizing and representing the structures, but can possibly be misleading, since the character of the bonds in and out of the plane are likely to be very different.
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Figure 15-3. The crystal structures of the two-layer compounds Tl 2 Ba 2 Ca n _ 1 Cu n O 4+2n , with (a), (b), and (c) being the w - 1 , n = 2, and ft = 3, structures, respectively.
15.2.3 Thallium Barium Calcium Cuprate (Tl 2 Ba 2 Ca ft _ 1 Cu w O 4
These compounds, each containing double Tl-O layers (Fig. 15-3), are body-centered tetragonal and bear striking structural similarities to the lanthanum compounds. As in those compounds, each unit cell contains two formula units. To date, one, two and three C u - O layer compounds have been discovered with successively higher transition temperatures (see Table 15-1). In the one-layer compound the Cu-O planes are separated by a stack containing one Ba-O plane, two Tl-O planes and then one further Ba-O plane. The Ba-O and Tl-O planes are shifted by an in-plane vector of (1/2,1/2), such that the C u - O planes are mirror planes of the structure. In the n — 2 and n = 3 structures, the four, shifted Ba-O and Tl-O planes
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15 Oxide Superconductors
remain the same as in the one-layer structure, but a Ca ion is interposed between the Cu-O planes, as shown in Figs. 15-3 a and b. In these structures, there exist two further types of oxygen site in addition to those in the square-planar C u - O arrangement. The apical oxygen belongs to the Ba-O plane, and bonds to four Ba ions in this plane, one Cu ion in the C u - O plane and one Tl in an adjacent T l - O plane. The third type of oxygen site is that found in the Tl-O plane itself, and which has an approximately-octahedral coordination, being bonded to five Tl ions, four in the plane, and to one Ba ion in the adjacent Ba-O plane. Although not as extensively studied as in the bismuth analogues (see below), the two-layer thallium compounds can exist over a range of solid solutions, with Ca 2 + and Tl 3 + being able to substitute for one another (Morosin et al, 1988; Morosin etal., 1990; Cheetham et al., 1989). Similarly, Pb 2 + is also believed to substitute for Ba2 + . As might be expected, these ionic substitutions lead to variations in the lattice parameters. However, they also can give rise to a broadening of the superconducting transition, presumably as a result of compositional inhomogeneity. 15.2.4 Bismuth Strontium Calcium Cuprate (Bi 2 Sr 2 Ca^ 1 Cu l t O 4 + 2ll )
These compounds appear to be isostructural with the two-layer thallium barium calcium cuprates, but with thallium being replaced by bismuth and barium being replaced by strontium. However, it is now recognized from a number of studies, that compounds having compositions corresponding to the general formula Bi 2 Sr 2 Ca n _ 1 Cu M O 4 + 2M, do not actually exist, but rather the compounds are formed
with an apparent cation deficiency (e.g., Chippindale et al., 1988; Saggio et al., 1989; Ikeda et al., 1989). The one-layer compound is Sr-deficient compared to the ideal stoichiometry and can also contain Ca substitutions. In fact, as with the two-layer thallium cuprates, the bismuth analogues exhibit an extensive substitutional solid solution. The extent of this solid solution range, in both the one-layer and two-layer bismuth compounds, has been explored by Golden etal. (1991a, b) and their results are shown in Figs. 15-10 and 15-11 (see Sec. 15.3.2). From these data, it is seen that the two-layer phase is deficient in Sr + Ca but contains excess Bi relative to the nominal composition. This suggests that extensive exchange occurs between the Sr and Ca sites in the structure. Also, as the excess Bi is only partly compensated by the deficiency in the total of the Sr + Ca content, it suggests that there is a cation deficiency on the Sr site. This would also be consistent with suggestions that Sr-site deficiencies may be important in controlling the hole concentration in the C u - O planes (Sleight, 1988; Cheetham etal., 1988). In the Pbdoped three-layer compound, analytical electron microscopy suggests that the phase is deficient in Ca rather than Sr (Cheetham etal., 1989). Although there is evidence that the normal state resistivity and superconducting-transition temperatures are dependent on the composition within the solid solution phase field, insufficient data are available to make any significant correlations. There is, however, a tendency for the sharpness of the superconducting transition to increase with annealing, suggesting a homogenization, as seen in the thallium compounds. A feature of the two-layer bismuth compounds is that they can exhibit incommensurate modulations in the Bi-O planes (Shaw et al., 1988). Interestingly, the modu-
15.2 Crystal Structures
lations are not always present and can also vary from place to place in a crystal. Furthermore, they can be different in different crystallographic directions. The cause of these modulations is not really known, but they have been attributed to the presence of oxygen interstitials (Zanderbergen et al., 1988). Similar modulations have also been reported, from transmission-electron-microscopy (TEM) studies, in some of the two-layer thallium cuprates (van Tendeloo et al, 1989). A further feature of the two-layer bismuth structures is that the adjacent Bi-O layers are further apart (i.e., 0.32 nm) than the corresponding, adjacent Tl-O layers (i.e., 0.20 nm) in the two-layer thallium structures. One direct consequence of this, and of the lone-pair electrons on the Bi3 + , is that the bismuth structures have a pronounced micaceous cleavage. It is also believed to result in the supercurrent transport, perpendicular to the layers, having to
765
"Josephson-tunnel" from one layer to the next. One consequence of the larger interion distances is that the interplanar distance is larger and the fracture energy is lower. Indeed, the layered bismuth cuprates can be easily cleaved. This characteristic feature has proved useful in facilitating surface-analysis experiments on clean surfaces, but poses a problem in making highstrength electrical contacts. 15.2.5 Thallium Barium Calcium Cuprate (TlBa 2 Ca w _ 1 Cu M O 3 + 2w )
The one-layer thallium compounds are structurally distinct from the two-layer thallium (bismuth) compounds discussed above. In addition to having only one layer of Tl-O per unit cell, the unit cell is primitive tetragonal and contains only one formula unit. For the purposes of structural comparison with the two-layer compounds, the diagrams of Fig. 15-4 show
oTI • Ca • Ba ©Cu
(a) I - T I ( / > = 1 )
(b) l - T I ( n = 2 )
(c)l-TI(n=3)
Figure 15-4. The crystal structures of the one-layer, homologous series TlBa 2 Ca n _ 1 Cu n O 3 + 2n, forrc= l - 3 .
766
15 Oxide Superconductors
two unit cells above each other. All of the one, two, three and four C u - O layer structures have been reported to be superconducting. In each case, the n immediately adjacent C u - O planes are separated by a Ba-O, a Tl-O and then another Ba-O plane. As with the two-layer thallium compounds, when there are two or more Cu-O planes in the unit cell they are separated by a plane of calcium ions. Similarly, there are the same three types of oxygen site in the structure. Although it is expected that bismuth analogues of the structure should exist, none have been synthesized to date. 15.2.6 Yttrium Barium Cuprate (YBa 2 Cu 3 O 7 _,) The structure of yttrium barium cuprate is rather more complicated because, in contrast to the previously discussed structures, it contains two distinct four-coordinated copper sites and can exhibit a wide range of oxygen contents, ranging from YBa 2 Cu 3 O 6 to YBa 2 Cu 3 O 7 . Nevertheless, the fully oxygenated compound, YBa 2 Cu 3 O 7 , can be considered to be structurally similar to the one-thallium layer, two C u - O plane compound. Replacement of the Ca and Tl ions by Y and Cu, respectively, and shifting the O ion in the Tl-O layer so it is vertically above the other Cu ion yields the structure of YBa 2 Cu 3 O 7 . This arrangement gives an orthorhombic unit cell (Fig. 15-5). Two layers of Cu-O, having a square-planar arrangement, are separated by a layer of Y ions in the same way as they are separated by a layer of Ca ions in the one-thallium, two C u - O compound. The second type of copper site is also four coordinated with oxygen, but can be thought of as belonging to a chain lying along the b-axis of the unit cell. In both the planar and chain configurations, the Cu-O distance is small, sug-
1 Figure 15-5. (a) Schematic diagram of the crystal structure of yttrium barium cuprate. (b) Crystal structure of yttrium barium cuprate viewed along the [001] direction in a high-resolution electron micrograph. The unit cell is indicated by the square of side a. The central dark spot represents the column sites of the Ba and Y atoms, with the dark spots at the corners of the square representing the Cu atoms in the square-planar arrangement of the Cu-O units (micrograph courtesy of S. Horiuchi).
gesting covalent bonding in the chain, as well as in the Cu-O plane. It should be noted that the C u - O distance, perpendicular to the chain direction in the Cu-O plane, which has a value of ~ 0.184 nm, is,
15.2 Crystal Structures
in fact, even smaller than that along the chain, i.e., ~ 0.194 nm. The fully oxygen-deficient compound, YBa 2 Cu 3 O 6 , contains one fewer oxygen atom per unit cell. Its structure is the same as that of YBa 2 Cu 3 O 7 but with the oxygen removed from the Cu-O chains in the bdirection, so resulting in a tetragonal unit cell. This compound is not superconducting, despite the presence of the two, squareplanar Cu-O planes in the structure. As will be discussed later, the superconducting transition temperature is dependent on the oxygen stoichiometry of the yttrium barium cuprate, and steadily decreases with reduction in the oxygen content until a metal-insulator transition is reached, at a composition approximating to YBa 2 Cu 3 O 6 5 . As oxygen is taken from the compound, it is removed from the chain sites to create oxygen vacancies to give a structure intermediate between that of YBa 2 Cu 3 O 7 and YBa 2 Cu 3 O 6 . Depending on the manner in which the oxygen content is reduced the vacancies in the chain sites can form either at random or in a variety of local or long-range-ordered structures of vacancies. The degree of ordering, which can be revealed by electron diffraction studies (Beyers et al., 1989), has been found to affect the attainable superconducting-transition temperature (see Sec. 15.4.4.1). Although there has been considerable speculation concerning the possible anion substitutions for oxygen, including several reports of both fluorine and nitrogen substitutions leading to dramatic increases in the transition temperature, they have not been substantiated. Despite this, there may be a slight increase in Tc with fluorination (Cirillo etal., 1988). By contrast, cation substitutions have been well established (Beyers and Shaw, 1989). All the rare-earth ions, with the notable exception of
767
praseodymium, can completely replace the Y ion and the resulting compounds all remain superconducting. Praseodymium can fully replace Y in the structure but the resulting compound is not superconducting. However, partial replacement by this ion is possible without destroying the superconductivity. Some of the Cu ions can also be replaced by other transition ions of approximately the same size, for example Fe, Zn and Co, up to their limits of solubility. The extensive literature suggests that Fe can replace Cu in the C u - O chains but not in the C u - O planes, whereas Zn can partially replace the Cu on both sites. In each case, transition-element doping causes a reduction in the superconducting transition temperature, being especially effective when substituted on the plane sites. However, some dopants, Fe and Co, for example, reduce the difference in the a and b lattice parameters, thereby minimizing the ferroelastic distortion. Two additional superconducting compounds, YBa 2 Cu 4 O 8 and YBa 4 Cu 7 O 14 , are structurally closely related to yttrium barium cuprate. Both contain the double Cu-O planes separated by a sheet of Y ions, and also the Cu-O chain structure. The principal difference is that YBa 2 Cu 4 O 8 has a double set of edgesharing Cu-O chains along the b axis, and that in YBa 4 Cu 7 O 14 the chains alternate (in the c direction) between being single and double edge shared. In all other respects, all three structures are similar, with the interatomic distances being almost the same, as are also the a and b lattice parameters. Since both contain additional copper and oxygen in their unit cells, their stability is favored by higher oxygen pressures. Limited doping studies have been performed on the YBa 2 Cu 4 O 8 compound, and these show, for example, that Y3 + can be partially replaced by Ca 2 + , leading to
768
15 Oxide Superconductors
an increase in the superconducting transition temperature from ~ 80 K to ~ 90 K. 15.2.7 Neodymium Cerium Cuprate
In the same way as the lanthanum copper oxide structure forms the basis of a family of substitutional superconducting compounds, so too does neodymium copper oxide. It has a body-centered tetragonal structure, sometimes referred to as the T structure, which is closely related to the LaCuO 4 crystal structure (see Fig. 15-2c). Both have a single C u - O plane lying perpendicular to the c axis, with a sheet of Nd 3 + or La 3 + ions on either side, and with the ions situated directly above and below the Cu ions. The difference in the two structures is that in the neodymium cuprate the additional oxygen ions are directly above and below the oxygen ions in the square-planar C u - O plane, whereas in the lanthanum cuprate they are above the Cu ions in the C u - O plane, forming a distorted octahedral oxygen arrangement about the Cu ion. Substitution of Ce 4 + for Nd 3 + , to give a formula unit of Nd 2 _ 3; Ce ); CuO 4 , leads to electron doping and changes the compound from being insulating to superconducting. There remains considerable uncertainty about the solid-solution range over which superconductivity is observed (due to the presence of compositional inhomogeneities) but it is of interest to note that the compound can be electron doped, whereas the lanthanum cuprate can only be hole doped. A related crystal structure, known as the T* structure, is formed by co-doping onto the Nd site in the T structure. In much the same way as in the high-oxygen-pressure phases of yttrium barium cuprate, where the YBa 4 Cu 7 O 14 phase is an intermediary between YBa 2 Cu 3 O 7 and YBa 2 Cu 4 O 8 ,
the T* structure is an intermediary between the T and V phases. Its unit cell can be considered to be a composite of half of the T structure and half of the T' structure. This structure is found over a range of solid solutions of the type (La, Nd, Ce, Sr) 2 CuO 4 . As with other superconducting cuprates, the transition temperature is dependent on the precise composition. 15.2.8 Barium Bismuth Lead Oxide (BaPb 1 _ JC Bi x O 3 )
Barium lead bismuth oxide is a cubic ABO 3 perovskite (Fig. 15-1 b), in which the barium ion occupies the "A" site and the lead ions partially substitute for the bismuth ion on the "B" site. The maximum superconducting-transition temperature, i.e., ~ 13 K, is obtained at a composition of x = 0.25 and, depending on the concentration of lead, the compound can be either metallic, semiconducting or superconducting. Although doping of the "A" site by alkali ions had been attempted soon after the discovery of this compound, the renewed interest in altering the superconducting-transition temperature of the cuprates by doping provided an impetus for a re-examination of the doping behavior of the BaPb 1 _ x Bi x O 3 compound. Substitutional doping with alkali metals on the "A" site changes BaBiO3 from an insulator to a metallic superconductor, with a maximum transition temperature of ~ 30 K at a composition of K o 4 Ba 0 6 BiO 3 (Cava etal., 1988). The structure remains cubic but, by analogy with the Pb 2+ -doped BaBiO 3 , is slightly distorted and can exhibit commensurate modulations (Verwerft et al., 1991). Despite having a significantly lower transition temperature than the cuprate superconductors, the K 0 4 Ba 0 6 BiO 3 compound, being cubic, seems to avoid the difficulties of an-
15.3 Phase Equilibria and Stability
isotropy. In addition, all of the features of the tunneling data can be adequately interpretated on the basis of conventional Bardeen-Cooper-Schrieffer (BCS) superconductivity theory (Huang et al., 1990).
15.3 Phase Equilibria and Stability Detailed phase equilibria and thermodynamic information is presently only available for the most-studied systems, namely Y - B a - C u - O and B i - S r - C a - C u - O . Some limited information is also available for the N d - C e - C u - O system (Jorda and Saugier-Cohen, 1991), and a number of the phase compatibilities in the T l - B a - C a - C u - O system (Aselage et al., 1990) have been established. Determination of the phase equilibria is complicated by the fact that almost all oxide superconductors are at least quaternary systems, thus providing a large degree of freedom on the possible phases that can be present. In most instances, the systems are treated as a three- or four-component system, by fixing the oxygen partial pressure.
769
15.3.1 Y-Ba-Cu-O Phase Equilibria 15.3.1.1 In Air The principal phase compatibilities in the Y - B a - C u - O system in air at 950 °C were first identified by Frase and her coworkers (Frase et al., 1987), including the discovery of a second, but non-superconducting, perovskite, YBa 3 Cu 2 O, in addition to YBa 2 Cu 3 O 7 _ a . Later work by Roth et al. (1988) confirmed and expanded on the phase equilibria at different temperatures. A constant-temperature section of the phase diagram at 950 °C in air is reproduced in Fig. 15-6 and shows the stoichiometric (with respect to the anions) phase YBa 2 Cu 3 O 7 _ (5 to be in equilibrium with any two of the phases Y 2 BaCuO 5 , CuO or BaCuO 2 . Melting occurs within the shaded region and provides the self-flux used in crystal growth. The temperature at which liquid first forms depends sensitively on the presence of carbon dioxide. The phase relations in the barium-rich part of the phase diagram change at higher temperature (960 °C), where YBa 2 Cu 3 O 7 _a is no longer in equilibrium with both the Y 2 BaCuO 5
CuO
950°C
BaCuO2
Y 2 Cu 2 0 5
Ba 2 Cu0 2 Ba3CuO4
BaO
Ba4Y2O7
Figure 15-6. Constant-temperature (950°C) section of the C u O - B a O - Y O ^ system in air, illustrating the phase compatibilities with YBa 2 Cu 3 O 7 _ 5 (denoted as 123). The other perovskite phase, 132, has an as yet undetermined range of stoichiometry. The approximate ternary eutectic region used for self-flux crystal growth is shown shaded.
770
15 Oxide Superconductors 1500
\ ^
v
i
i
•
and BaCuO 2 , but rather with either one of these and the other perovskite, YBa 3 Cu 2 O. An important feature of the phase equilibria is that YBa 2 Cu 3 O 7 _ a decomposes peritectically into solid Y 2 BaCuO 5 and a "Y-poor" liquid phase (Lindemer et al., 1991). This is shown in the YBa 2 Cu 3 O 7 _^-CuO section in Fig. 15-7, which also indicates the currently accepted stability regimes for the YBa 2 Cu 4 O 8 and Y 2 Ba 4 Cu 7 O 14 phases. The thermodynamic relations between the constituent oxides have recently been determined by Zhou and Navrotsky (1992).
i
1553
1400
211 + CuO + L
§
Pi
OS
1200
1234 123 +CuO 247 +CuO.
Q_
1132
CD
1132 247 + 124 124 +CuO
1100 123 + 124
15.3.1.2 Effect of Oxygen Partial Pressure on Phase Stability 800
0
123
20
60
40
80
100
CuO
mol %
Figure 15-7. The YBa 2 Cu 3 O 7 _ <5 -Cu-O section of the CuO-BaO-Y 2 O 3 phase diagram at a maximum oxygen pressure of 105 Pa, as summarized by Lindemer et al. (1991). The regions of stability of the Y 2 Ba 4 Cu 7 O 14 (247) and YBa 2 Cu 4 O 8 (124) phases are indicated.
Both higher and lower oxygen partial pressures tend to alter the phase compatibilities, as reviewed by Lindemer et al. (1989), Beyers and Ahn (1991), Bormann and Nolting (1989) and Karpinski etal. (1990). A summary of the data, discussed in detail by Lindemer etal. (1991), is presented in Fig. 15-8. From this it can be seen
600
<M
,o o
Figure 15-8. Temperature-oxygen partial pressure stability regime for YBa 2 Cu 3 O 7 _ 5 (after Lindemer et al., 1991).
123
12
4
io /r
15.3 Phase Equilibria and Stability
that there exists a window of stability of YBa 2 Cu 3 O 7 _ 5 . At high oxygen pressures the YBa 2 Cu 3 O 7 _ d phase can become unstable with respect to the formation of Y 2 BaCuO 5 and Ba 2 Cu 3 O 5 . At high temperatures it melts to form a liquid plus the Y 2 BaCuO 5 phase, and at low partial pressures of oxygen it decomposes to a mixture of Y 2 BaCuO 5 , BaCu 2 O 2 and YBa 3 Cu 2 O 6 . There remains unresolved the question as to the lower temperature limit of stability of YBa 2 Cu 3 O 7 _^, and indeed whether it is thermodynamically stable at room temperature and below. However, data reported by Tetenbaum et al. (1989) indicate the possible existence of a miscibility gap at oxygen deficiencies larger than 0.2 and temperatures below 400 °C, supporting the idea that phase separation occurs at lower temperatures. This is supported by phase-diagram calculations by Cedar et al. (1991), which predicts the existence of separate ordered phases down to much lower temperatures. It is interesting to note that a comparison of the decomposition conditions, un-
10°
771
der reduced oxygen pressure, for other cuprates appears to indicate that the decomposition is dependent on the stability of the C u - O planes themselves. This suggests that the limits of stability for many of the cuprate perovskite superconductors may be similar (Mawdsley et al., 1992). Figure 15-8 does not show the phase diagrams for the YBa 4 Cu 7 O 14 and YBa 2 Cu 4 O 8 phases. These form, as indicated in Fig. 15-7, in the presence of excess CuO and cannot form by the decomposition of stoichiometric YBa2Cu3O7_<5. Stability diagrams for these Cu-O-excess compositions are also presented by Lindemer et al. (1991).
15.3.1.3 Oxygen-Deficient YBa 2 Cu 3 O 7 _ 45
The stoichiometry of YBa 2 Cu 3 O 7 _ d depends on both the oxygen partial pressure and the temperature, as indicated by the data shown in Fig. 15-9, obtained from the work of Specht et al. (1988). This, and other data obtained over a wider range of
YBa2Cu3Ox
Figure 15-9. Oxygen stoichiometry of the YBa2Cu3O7_,5 system as a function of the oxygen partial pressure and the temperature. The contours correspond to lines of constant oxygen content, and the orthorhombic-to-tetragonal phase boundary is shown as a dashed line (after Specht et al. 1988). 600
700
Temperature (°C)
800
900
772
15 Oxide Superconductors
conditions, has been reviewed by Lindemer et al. (1989). An important feature of Fig. 15-9, shows that fully-stoichiometric material, YBa 2 Cu 3 O 7 , can only be obtained by oxygenation at temperatures below about 400 °C in an atmosphere of oxygen. The phase boundary between the orthorhombic and tetragonal forms of yttrium barium cuprate is also indicated on this figure, where it can be seen that the transformation temperature is dependent on the oxygen partial pressure. The oxygen deficiency in YBa2Cu3O7_<5 is accommodated by oxygen vacancies formed principally on the chain sites. Experimentally, oxygen ordering has been observed both by electron diffraction (Beyers et al., 1989; Levine and Daumling, 1992) and by X-ray scattering (Zeiske et al., 1991). Oxygen-vacancy ordering has been studied by statistical-mechanics methods (deFontaine et al., 1990), as has the ordering transformation by using the concentration-wave approach (Khachaturyan and Morris, 1990). For oxygen deficiencies d of 0.5 and 0.33, ideal ordering causes the oxygen sites on every second or third chain to be vacant, resulting in the phases designated Ortho II and III. A complete description of the ordering in even non-equilibrated samples was given by Levine and Daumling (1992). In their model very small domains of the Ortho-II phase are combined such that the boundaries form a single Ortho-Ill unit. By adjusting the antiphase domain size all of the experimentally obtained diffraction data, on both slowcooled and quenched specimens, can be fitted to the model (see Sec. 15.4.4.1). Changes in the critical temperature provide additional evidence for oxygen ordering occurring even at very low temperatures. This is most dramatically seen in the work of Veal et al. (1990), on the annealing of quenched samples, and from studies of the depen-
dence of pinning on oxygen content, which is discussed in Sec. 15.4.7.4. 15.3.2 Bi-Sr-Ca-Cu-O Phase Equilibria As discussed in Sec. 15.2.4, it is now known that the 1-, 2- and 3-layer bismuth compounds do not have the nominal compositions denoted by the general formula for the homologous series, namely Bi 2 Sr2Ca n _ 1 Cu n O 4+ 2 n . Indeed, these nominal compositions do not form singlephase material (Golden etal., 1991a, b). Studies of both the B i - S r - C u - O and B i - S r - C a - C u - O systems indicate that a solid-solution range exists for the one- and two-layer superconducting phases (Saggio et al., 1989; Ikeda et al., 1989; Golden et al., 1991 a, b). There is some discrepancy as to the actual extent of the solid solution and also the temperatures of the phase formation, but this can probably be attributed to the use of both powders and bulk samples and the consequent difficulty in attaining phase equilibrium. To avoid some of these kinetic limitations, Golden and his colleagues used thin films and liquid precursors to ensure rapid equilibration. From their studies, it was found that the solidsolution ranges for the one- and two-layer compounds, in the projection onto the BiO-SrO-CaO section, were as shown in Figs. 15-10 and 15-11. Much-narrower ranges of solubility of CuO were found. In the case of the one-layer compound, the solid-solution range varied from 20.5 to 22 mol% of CuO. In the two-layer compound the range of solid solution extended from 29 to 31 mol% of CuO. In each case, the oxygen stoichiometry was assumed constant. In view of the uncertainty of the phase equilibria in the B i - S r - C a - C u - O systems, it is not surprising that there still remains some dispute as to the stability of
15.3 Phase Equilibria and Stability
773
CaO 21 mol Percent CuO
mol Percent SrO
5 One-layer Solid Solution Range
°-BiO1.5
SrO
Figure 15-10. A cut through the BiOx 5 -SrO-CaO-CuO quaternary system, at 21 mol% CuO, showing the extent of the solidsolution range of the one-layer superconducting bismuth phase at 800 °C (after Golden et al., 1991 b).
45 mol Percent BiO! .5
mol Percent SrO Two-layer Solid Solution Range
/ 45
40 mol Percent BiO-|
/ 50
BiO 1.5
Figure 15-11. A cut through the BiOx 5 -SrO-CaO-CuO quaternary system at 30 mol% CuO, showing the extent of the solidsolution range of the two-layer bismuth phase. The nominal composition, denoted as 2212, of the superconducting phase is well outside of the solid-solution range (after Golden et al., 1991 a).
5
the different superconducting bismuth phases and the temperatures at which they first form. There have been reports that at 750 °C only the one-layer phase is stable, while at 800 °C the one-layer and two-layer phases coexist, and that the three-layer phase is only stable at temperatures 830 °C. According to Golden et al. (1991 b), the formation of the two-layer bismuth
compound is mediated by the appearance of a liquid phase at 730 °C. Below this temperature, the two-layer phase does not form, even after a period of several hundred hours, whereas just above this temperature the phase forms in minutes. In more recent work, using Pb doping, it was also found that the three-layer phase only forms once melting begins (Golden et al.,
774
15 Oxide Superconductors
1992). The addition of lead appears not only to accelerate the formation of the three-layer phase but also to increase the size of the solid-solution phase field (Statt etal., 1988; Strobel and Fournier, 1990). 15.3.3 Crystal Growth
In the absence of any prior knowledge concerning the appropriate conditions for crystal growth of the oxide superconductors, the majority of single crystals have been formed from liquid phases produced by partial melting of the component oxides. Crystal growth of the oxide superconductors has recently been reviewed by Stupp and Ginsberg (1992), and so only the relationship to phase equilibria is briefly described here. The majority of single crystals of YBa2Cu3O7_<5 have been grown using the ternary eutectic liquid in the Y - B a - C u - O phase diagram (see Fig. 15-6) as a self-flux (Kaiser et al., 1987; Schneemeyer et al., 1987; Rice and Ginsberg, 1991). Only a small compositional region, around a Y: Ba: Cu ratio of 1:4:10 (Cu and Ba rich), has proved to be suitable. In this region, the flux melts incongruently, and crystal growth occurs between 930 and 980 °C. The flux is highly reactive with most crucible materials, even including noble metals such as gold and platinum, which leads to the crystals usually being contaminated by the crucible material, with a consequent deterioration in their superconducting properties. The flux also exhibits exceptional wetting properties, and in some cases can wick out of the crucible. More recently, with improvement in techniques and purer crucible materials, such as ZrO 2 and HfO 2 , more-conventional crystal-growth methods, such as the Czochralski growth technique, have been shown to be effective and will presumably be much used in the future.
Solidification processing, such as melt processing (Jin etal., 1988; Murakami etal., 1989), is a variation of crystal growth. In contrast to the method described above, the flux is produced by the decomposition of the specimen itself. Typically, a near-stoichiometric YBa 2 Cu 3 O 7 _ 6 specimen is made partially molten by heating above the peritectic decomposition temperature. Directional solidification can then be achieved by slowly cooling the specimen in a furnace, or pulling it through a temperature gradient. An attractive feature of melt processing is that it can result in specimens having large (millimeter-size) grains containing Y 2 BaCuO 5 as a second phase. The grains themselves are often not true single crystals, but contain many small-angle boundaries (Kimura et al., 1991). Recently it was shown that goodquality single crystals, possessing few subboundaries, can be grown in this way by using very-low growth velocities (Daumlingetal., 1992). All the crystal-growth methods that have been investigated produce crystals that are oxygen deficient. Thus, the asgrown crystals are rarely superconducting, except very close to the surface, and have to be subjected to a low-temperature oxygenation treatment. Due to the necessity of carrying out this treatment at low temperatures (400 to 450 °C), to assure full oxygenation, diffusion is very slow (and almost two dimensional) and long annealing times are required. These prolonged oxygenation times have limited the use of large single crystals. In contrast to the YBa 2 Cu 3 O 7 _^ phase most of the superconducting compounds in the B i - S r - C a - C u - O system melt congruently, and exist in equilibrium with a liquid phase. Thus, simply heating a mixture of the component oxides to the appropriate temperature, and maintaining it
775
15.3 Phase Equilibria and Stability
there, will result in the formation of single crystals of the superconducting phase, embedded in other phases. Single crystals have also been grown from inert, liquid fluxes, such as B 2 O 3 -doped KC1 flux (Yasuda and Takano, 1991). Due to the two-dimensional nature of the bismuth superconducting compounds the resulting crystals are typically very thin along the c axis (less than 30 jim), but may extend for several mm along the a and b axes. However, although they are relatively straightforward to grow, the resulting crystals are not of a constant stoichiometry because the single-phase regions exhibit extensive solid-solution features. The effects of such microscopic variations in stoichiometry have yet to be determined, but may be the reason for the variability in superconducting properties reported for the same single crystals when grown by different groups. Fortunately, as the superconducting properties of the one- and two-layer bismuth compounds do not depend strongly on their oxygen contents they do not need to be oxygenated, and so large crystals can be investigated.
rials. In untwinned, orthorhombic crystals at 300 °C, diffusion along the b direction (i.e., along the chains) was at least 100 times faster than diffusion along the a axis (perpendicular to the chains). This data, reproduced as part of Fig. 15-12, suggests that in-plane diffusion occurs by oxygen movement along the Cu-O chains. However, Rothman and his co-workers only measured the in-plane diffusion of oxygen. Differences between in and out-diffusion have been found by numerous workers. A strong dependence of the activation energy on the oxygen content was found (Tu et al., 1989; Tang and Lo, 1991), with diffusion being faster for more oxygen-deficient materials.
10-
9
1 :
Nfl
]
10-1
3,
BSCCO Single \ C r y s t a l ^ < 10-13 rBSCCO \ \ r O IO-1
8
^ O S ^
A
'-.
W
i !
*+ -
j
O+ O
\ \
: -.
^
r
15.3.4 Diffusion The diffusion coefficient, D, of oxygen in the YBa2Cu3O7_<5 phase has been measured using a variety of techniques, including tracer diffusion (Rothman et al., 1989; Faupel and Hehenkamp, 1990), electrical resistivity (Tu et al., 1988, 1989), neutron scattering (Als-Nielsen et al., 1989) and thermogravimetric analysis (Tang and Lo, 1991). Tracer diffusion of oxygen 18 O in YBa2Cu3O7_<5 (YBCO) single crystals was studied by Rothman et al. (1991). They found that at 400 °C the diffusion along the c axis was six orders of magnitude slower than the diffusion in polycrystalline mate-
Polycrystalline r " YBCO
\
IO-1 0.8
1.0
1.2
1.4 3
1.6
1.8
2.0
10 /7 Figure 15-12. Arrhenius plots for the rate of traceroxygen diffusion in single and polycrystalline samples of YBa 2 Cu 3 O 7 _ a and Bi2Sr2CaCuO2+(5. + diffusion in the a direction, A diffusion in the b direction, o diffusion in the c direction, and • diffusion in the a b plane, in a single crystal of YBa 2 Cu 3 O 7 -8 at a partial pressure of oxygen of 105 Pa. The rate of diffusion in the a b plane is approximately the same as for polycrystalline samples, whereas the rate of diffusion in the c-direction is orders of magnitude slower. The data also indicate that in YBa 2 Cu 3 O 7 _ 5 the rate of diffusion along the Cu-O chains dominates the diffusion in the a b plane, being much higher than in the a-direction (after Rothman et al., 1991, and Runde et al., 1992).
776
15 Oxide Superconductors
The thermodynamic factor, , as a function of both the oxygen stoichiometry and the temperature, was determined by Faupel and Hehenkamp (1990). They found that 0 was of the order of 100 for materials with stoichiometries 5 > 0.2, but increases manyfold for fully oxygenated YBa 2 Cu 3 O 7 _^, especially at low temperatures. Thus, the chemical diffusion coefficient may be as much as three orders of magnitude larger than the tracer diffusion coefficient, making fully oxygenated YBa 2 Cu 3 O 7 quite unstable. Very few measurements have been made of diffusion in the bismuth-based superconductors. Tracer diffusion coefficients for oxygen, summarized in Fig. 15-12, have been measured in Bi2Sr2CaCuO2+<5 (BSCCO) single crystals by Runde etal. (1992) leading to values for the diffusion coefficients, along the a, b and c axes, of Dab equal to 1.7 x 10" 5 exp(-0.93//c T) cm2/s, and Dc equal to 0.6xl0~ 5 exp (— 2.20/fc T) cm2/s, respectively. In contrast, cation diffusion is typically several orders of magnitude slower than oxygen diffusion in both the YBa 2 Cu 3 O 7 _ 3 and the 2212 materials (Routbort etal., 1991; Gorbik et al, 1992).
constants have been reviewed by Tholence etal. (1991), and by Ledbetter and Lei (1991) (see Table 15-2). There have been several reports of anomalies and structural transitions below room temperature, including some observed at Tc, but as yet no relationship has been established between the elastic constants and the mechanisms of superconductivity. Among the best data are measurements of the thermal expansion coefficient carried out at low temperatures by Meingast etal. (1991). The data are reproduced in Fig. 15-13 for all three crystallographic directions. At Tc there is a sudden increase in the thermal expansion coefficient (a), with a difference in the sign
• (a) ^
20
c axis
/ CO
***
b C
10
0 0
100
200
^ " ^ ^ 4
15.4 Single-Crystal Properties of Yttrium Barium Cuprate 15.4.1 Mechanical Properties Because of its crystal structure, YBa 2 Cu 3 O 7 _ a is expected to be a brittle oxide, with anisotropic mechanical properties and with the a b plane being the natural cleavage plane. The fracture toughness, measured by the indentation technique, is about 1.0MPam 1/2 (Cook etal., 1987), which is similar to that of other brittle solids, such as glass or silicon. The elastic
:
- (b)
300
a axis
^
^f
VI
CD
-1
b <
r
^
IV.. caxis 80
90
100
Figure 15-13. (a) Temperature dependence of the thermal expansion coefficients a along the principal crystallographic axes for a twin-free single crystal of YBa 2 Cu 3 O 7 _ 5 . In (b) the data in the immediate vicinity of the superconducting-transition temperature are compared to a mean-field behavior (shown as solid lines) (after Meingast et al., 1991).
15.4 Single-Crystal Properties of Yttrium Barium Cuprate
777
Table 15-2. Elastic constants (in GPa) of YBa 2 Cu 3 O 7 (from Ledbetter and Lei, 1991). Cn
C22
C 12
C 33
C44
C 55
C66
C 13
Reference
220 ±10 230 223
— 230 244
66 100 37
152±5 150 138
3O±5 50 61
— 50 47
80 85 97
— 100 89
Tholence et al. (1991) Reichardtetal(1988) a Ledbetter and Lei (1991)b
a
Data derived from inelastic-neutron-scattering phonon-dispersion curves; b these data represent an assessment of earlier data and an extrapolation using standard elastic theory to assure consistency with the measured bulk moduli and acoustic measurements.
for the a and b directions. The measurements are of particular significance because of their exceptional precision and also the fact that the crystals were untwinned, as the majority of earlier measurements had been carried out on twinned crystals. As a result of the molar-volume change accompanying the tetragonal-to-orthorhombic structural transition, changes in shape also occur. If constrained, the strains can be accommodated in two ways, i.e., by twinning and by fracture. Twinning can, in principle, relieve stresses in the ab plane, since the angle between the a and b axes is less than 90° (in fact, typically approximately 89°) and is also dependent on the oxygen content. Twinning in YBa2Cu3O7_<5 is ferroelastic in nature (Schmid et al., 1988) and so twin boundaries can be moved by the application of an applied stress. This is the basis for forming twin-free single crystals by oxidation under a uniaxial stress applied along one of the a, b crystallographic directions (Welp et al., 1989 a). Stresses in the c direction cannot be relieved by twinning and so can cause cracking. Cracking can occur as a result of either the molarvolume change on oxygenation, especially if there is a gradient in the oxygen content, as will be the case in oxygenating relatively thick pieces of material at low temperatures, or, in polycrystalline material, as a result of the anisotropy of the thermal-
expansion coefficient. These phenomena have been discussed in detail by Shaw et al. (1989) and by Clarke et al. (1989). As with stresses caused by anisotropic thermal-expansion coefficients in other ceramics, a critical grain size exists, below which microcracking is energetically unfavorable. This size, /c, is given by the relationship
where Kc is the fracture resistance, E is the elastic modulus, Aa AT represents the thermal expansion strain, and £ is a geometric constant. For YBa 2 Cu 3 O 7 _ 5 the critical grain size is calculated to be approximately 1 Jim; below this grain size, the strains have to be accommodated by twinning. An interesting consequence of the results obtained by Meingast et al. (1991), which show a change in the lattice parameter at Tc, is that they imply that going through the superconducting-transition point may itself cause internal stresses. 15.4.2 Optical Properties
One of the first features of the YBa 2 Cu 3 O 7 _ 5 materials to be noticed was that every specimen having the orthorhombic structure appeared to be twinned (see Fig. 15-14). This can be easily observed in the optical microscope, because YBa 2 Cu 3 O 7 _^ is optically active. Twins
778
15 Oxide Superconductors
Figure 15-14. Twinned structures in YBa 2 Cu 3 O 7 _ 5 , produced as a result of different oxygenation heat treatments (optical micrographs courtesy of T. M. Shaw).
can also be observed with smaller spacings in the scanning electron microscope, because of surface relief, and in the transmission electron microscope as a result of diffraction contrast. Detailed polarized-light analysis reveals that there are four possible domain orientations, consistent with the orthorhombic symmetry of YBa2Cu3O7_<5, with the twinning shear angle not being quite equal to 90° (the data of Schmid et al. (1988) suggest that the shear angle is approximately equal to 89°). This degeneracy can result in the formation of "puzzle" domains, that can be seen in the micrograph of Fig. 15-14b. The circular dichroism and birefringence observed in YBa 2 Cu 3 O 7 _ d has been subject to considerable, and as yet unresolved, debate. There are conflicting reports about variations in rotation angle and whether this can effect the superconducting properties; one group (Spielman et al., 1992 a) reported that there is no effect, another (Lyons et al., 1991) reported a small effect, and a third group (Weber et al., 1990) observed a large effect. More recently, Spielman et al. (1992 b) have searched for a detectable spontaneous polar Kerr effect in single crystals of YBa 2 Cu 3 O 7 _^ and Bi 2 Sr 2 CaCu 2 O 8 , but have found none. At
issue here, apart from obtaining a reliable value for the angle, is the belief that this latter provides direct and unambiguous evidence for whether superconductivity in YBa 2 Cu 3 O 7 _^ is caused by anyons or not. 15.4.3 Electromagnetic Properties in the Normal State
Studies of the normal-state electromagnetic properties of YBa2Cu3O7_<5 are proving to be an exceptionally rich field of research, with the material exhibiting properties as varied as antiferromagnetism (when 3 = 1), and semiconducting and insulating behavior. Describing these is quite beyond the scope of this chapter, and so we shall discuss only the electrical properties here. As expected from the known crystal structure, the electrical resistivity of YBa 2 Cu 3 O 7 _^ is anisotropic, with the resistivity having been found to be different for all three lattice directions; as successively purer single crystals have become available, the absolute values of the resistivities have decreased. The in-plane anisotropy has been measured recently on untwinned single crystals (Friedmann et al., 1990), and it has been found that the
15.4 Single-Crystal Properties of Yttrium Barium Cuprate
b direction, i.e., along the C u - O chains, has a resistivity that is about half of the resistivity along the a axis. Resistivities measured along the c axis are higher by about a factor of 200, than the in-plane resistivities. The data is shown in Fig. 15-15. As indicated in Fig. 15-15, the resistivities in the a b plane are very low, lower in fact than in some common metals. The nature of these resistivities is not understood, particularly since the electronic carrier densities seem very low, this latter being a common feature of all of the oxide superconductors. Even less-well understood is the temperature dependence of the resistivity; this is linear from Tc up to several hundred degrees, at which temperatures YBa 2 Cu 3 O 7 _ 5 begins to lose oxygen, and the resistivity consequentially increases at a faster-than-linear rate. Explanations have been proposed for the linear temperature dependence, by using Fermi-liquid theories (Levin et al., 1991), or by using particular features of the electronic structure, such as Van Hove singularities (Tsuei et al., 1990) but the origin of this behavior still remains to be resolved.
779
Evidence for the nature of the charge carrier in the normal state has come from measurements of the Hall coefficient (Tozer et al., 1987; Forro et al., 1988). Depending on the direction of the magnetic field with respect to the crystallographic axes, the Hall coefficient can be either positive or negative. In the a b plane the carriers are of hole-like character, and have a density of about 1 to 1.5 per unit cell. If the magnetic field is perpendicular to the c axis then the carriers have an opposite sign and behave like electrons. In polycrystalline materials, the Hall effect is dominated by transport in the a b planes, and so a positive Hall effect is always measured (Shafer et al., 1989). 15.4.4 Superconducting Properties
Basic superconducting properties are defined here as properties that are independent of the microstructure of the material. Typically, these are the upper critical field Hc2, the lower critical field Hcl, and the transition temperature Tc. Dependent quantities are the effective coherence length £, the magnetic penetration depth A, 200
o
100
125
150
175
200
222
Temperature (K)
250
275
Figure 15-15. Resistivities along the principal crystallographic axes for a twin-free single crystal of YBa 2 Cu 3 O 7 . o, •, n, resistivity along the a, b and c directions, respectively. Note the order-of-magnitude difference in scale for the resistivities in the c, and the a and b directions (after Friedmann et al., 1990).
780
15 Oxide Superconductors
and the Ginzburg-Landau parameter x. If conventional theories of superconductivity apply, then these quantities can be linked to normal-state parameters, such as the electronic mean free path, the resistivity, the carrier density, etc. These dependences have been reviewed by Orlando et al. (1979) and will not be repeated here. All of the superconducting properties are dependent on the composition, and in particular, the oxygen stoichiometry. To reach the fully oxygenated composition, i.e., S = 0 in YBa 2 Cu 3 O 7 _^, typically requires long annealing times of several weeks, leaving the oxygen content at a nominal value of 7. In single crystals, the diffusion distances are particularly long, and the oxygen content cannot be measured directly by non-destructive methods. It is likely, therefore, that many of the discrepancies existing between the results of different research groups that have been reported in the literature are attributable to incompletely or inhomogeneously oxygenated materials.
15.4.4.1 Transition Temperature
The critical transition temperature Tc, in YBa 2 Cu 3 O 7 -3 is quite sensitive to the oxygen content of the compound. A number of authors (Cava et al., 1987; Beyers et al., 1989; Veal et al., 1990) have reported that the plot of the transition temperature versus the oxygen content for this material shows two plateaux, one close to 90 K for 0 < d < ~ 0.1, and one in the region of 60 K for 0.25 <<5< 0.5 (see Fig. 15-16). More recently, Namgung et al. (1990) and Levine and Daumling (1992) have found a nearly linear decrease of Tc with increasing 8, and attribute this oxygen dependency to particular features of the oxygen ordering. A similar, linear dependence of the critical temperature on the oxygen content has also been noted in other yttrium barium cuprates, notably YBa 2 Cu 4 O 8 (Karpinski etal., 1990). A major difference between the two types of behavior mentioned above appears to be the ordering of the oxygen on
100
1 CD Q.
I
Figure 15-16. Variation of the superconducting-transition temperature with oxygen stoichiometry in YBa2Cu3O7_<5, o, (straight line) data for cystals that have been quenched, and • (curve with plateaux), data (from Beyers et al., 1989) for carefully equilibrated samples (after Levine and Daumling, 1992).
I
O
0.1
0.2
0.3
0.4
Oxygen Deficiency S
0.5
0.6
15.4 Single-Crystal Properties of Yttrium Barium Cuprate 0.6
Figure 15-17. Change in resistivity with annealing time, measured at room temperature after initial quenching at liquid nitrogen temperature, of a single crystal of composition YBa 2 Cu 3 O 6 4 1 . As shown, the material changes from being semiconducting immediately after quenching to being superconducting, with an accompanying increase in the transition temperature to an equilibrium value (after Veal et al., 1990).
As Quenched
o
0.4
a 0.2 DC
30
781
60
90
120
T(K) the Cu-O chain sites. Comparison of electron-diffraction patterns obtained from samples exhibiting the nearly linear Tc-versus-(5 dependence (Levine and Daumling, 1992) and those obtained from samples exhibiting the "plateau behavior" (Beyers et al., 1989) reveal significant differences in the superlattice reflections. Levine and Daumling (1992) show that the differences can be understood by using a model in which oxygen ordering occurs to form microdomains of type Ortho II and Ortho III symmetry, see Sec. 15.3.1.3, with the size of these anti-phase domains determining the appearance of the superlattice reflections. The difference in the dependence of Tc on the oxygen content thus becomes a function of the time needed to equilibrate the latter. These results are of considerable practical importance. For example, the studies by Veal and his colleagues (Veal et al., 1990) reveal that changes in the value of Tc can occur with time at room temperature, for samples that have been quenched first to liquid-nitrogen temperatures. This effect is particularly marked at oxygen stoichiometries close to the composition YBa 2 Cu 3 O 6 5 . Figure 15-17 shows an example of the temperature dependence of
the resistivity for a sample of composition YBa 2 Cu 3 O 6 4 1 . Immediately after quenching, the material is semiconducting but with increasing time at room temperature it becomes superconducting with a corresponding steady increase in the transition temperature, with the latter approaching a fixed equilibrium value. In the fully oxygenated material, YBa 2 Cu 3 O 7 , the critical temperature, as a function of various cation dopants, has been examined extensively. Details of the effect of these dopants has been reviewed by Beyers and Shaw (1989) and only a summary of the most important findings will be presented here. Briefly, the dopants can be classified according to their solubility and site preference in the structure of YBa2Cu3O7_<5. No truly inert dopants have been found, and even silver, which is used to form ohmic contacts (see Ekin et al., 1988) and also as a casing for wires, will react with YBa 2 Cu 3 O 7 _ 5 to a limited extent, thus lowering Tc. Some dopants, such as gold and platinum, substitute into the YBa 2 Cu 3 O 7 -d structure, but only have a relatively small effect on the value of Tc. In fact, gold seems to be the only element that actually causes an increase in Tc, when
782
15 Oxide Superconductors
substituting for copper on the chain site (Cieplak et al., 1990). The rare earth elements that are next to yttrium in the periodic table can all substitute for yttrium without significantly affecting the critical temperature, even if the element has a strong magnetic moment. For example, DyBa2Cu3O7_<5 actually has a higher Tc than YBa 2 Cu 3 O 7 _^, even though the Dy cation is strongly paramagnetic (Tarascon et al., 1987; Engler et al., 1987). Other dopants have a detrimental effect, causing a significant reduction of Tc at low concentrations and destroying the superconductivity at higher concentrations. Ions, such as Mg, and Zn, can substitute for Cu in the square-planar C u - O planes and decrease the value of Tc. These dopants have been used to systematically change the hole concentration in studies of the Tc-dependence on carrier concentration, and have led to the investigation of the so-called "holecone" that appears to be a general characteristic of oxide superconductors (Shafer et al., 1989) and also suggests that Tc goes through a maximum value as the number of carriers is varied by the doping process. Whether substitutional doping directly causes the change in carrier concentration and this alone is responsible for the change in transition temperature still remains to be established. Iron, nickel and cobalt dopants have also been used to modify the twinning structures in YBa 2 Cu 3 O 7 _^, since they reduce the anisotropy between the a and b lattice parameters. Such doping would, presumably, also alter the critical grain size for microcracking (see Sec. 15.4.1) but this effect has not yet been investigated in detail. 15.4.4.2 Critical Magnetic Fields The value of the upper critical field Hc2 is an important parameter since it provides
a limit to the magnetic field sustainable by a type-II superconductor. In low-temperature superconductors Hc2 can be measured resistively, or it can be extrapolated from the field and temperature dependence of the critical current density Jc. Below Hc2, the resistivity ideally drops to zero. This methodology works well in low-temperature superconductors because the influence of thermally activated flux flow (or other thermally induced effects) is limited to temperatures very close to Tc{Hc2\ so that for all practical purposes Hc2 is measured directly. In these cases, the resistivity, as a function of the temperature, exhibits an abrupt drop at Tc (H) that shifts to successively lower temperatures as higher magnetic fields are applied. In materials having higher transition temperatures, such as the oxide superconductors, more-complex behavior is observed at temperatures at which thermal activation effects can occur. Resistive transitions are broadened significantly, even in small applied magnetic fields, and even in single crystals. Thus, initial attempts to measure the upper critical field by using the same resistive measurement techniques as applied to low-temperature superconductors proved unsuccessful. Critical currents also become immeasurably small at magnetic fields that are substantially smaller than Hc2, namely the irreversibility field, Hirr (Malozemoff etal, 1988). Therefore, only equilibrium properties of the superconductor can be used to determine the actual Hc2. Typically, the equilibrium magnetization has been used, although specific-heat measurements in magnetic fields could also be used. The magnetization can be fitted to expressions provided by the Ginzburg-Landau equations (Tinkham, 1980). This method has been used by Hao etal. (1991) for a YBa 2 Cu 3 O 7 _^ single crystal in the H±c orientation; they found an upper critical
15.4 Single-Crystal Properties of Yttrium Barium Cuprate
field slope of 1.6 T/K, with a x value of 55, and a critical field HC(T = OK) of about 1 T. This value is slightly lower than the values obtained by Welp et al. (1989 b), also measured on single crystals. Both groups used single crystals that probably contained up to 10 at.% gold on the Cu chain sites. In contrast to these studies, significantly higher values of approximately 8 T/K, for both H\\c and HLc orientations, have been measured by using a thermomagnetic method that is independent of any flux-creep contributions (Palstra et al., 1990). The single crystals used by Palstra and his co-workers were grown by a technique that does not lead to gold incorporation. Magnetization measurements carried out on undoped, polycrystalline YBa 2 Cu 3 O 7 _ (5 specimens by Daumling (1991a, b) find even higher values for the upper critical field slope, about 12 T/K for H\ c, for a fully oxygenated specimen. The thermodynamic critical field HC(T = 0) is about 1.6 T, which is higher than the single-crystal values. However, the polycrystalline nature of the specimens leads to a greater uncertainty in the values that are obtained. Measurements have also been performed on samples that have been purposely doped with gold (Daumling et al., 1992), and these lead to values for both Hc and x that are similar to those found by Hao et al. (1991) on their single crystals. Thus, gold seems to have only a small influence on the critical temperature, but a large effect on the critical fields. No direct measurements for H±c exist and so estimates have had to be made using the anisotropy obtained from other measurements (for example, from the penetration depth). Using even the smallest values of the upper critical field slope (for H\\c), the value of Hc2(T = 0) is very large, at least 100 T, in comparison to the values of 28 T and 15 T (at 4 K), obtained for the com-
783
mercially used magnet materials Nb 3 Sn and NbTi, respectively. The coherence length is correspondingly small, with an upper limit of 1.5 nm, but possibly as small as 0.7 nm. This very small coherence length, together with its anisotropy, promises a rich variety of physical phenomena for YBa2Cu3O7_<5, but may also be responsible for the granular properties of polycrystalline samples (see Sec. 15-6), and for many of the difficulties encountered in developing these materials for current-carrying applications. The lower critical field Hcl is also an important parameter but has proved to be equally difficult to determine. By definition, Hcl is inversely proportional to the square of the magnetic penetration depth 2, and therefore, by measuring Hcl X can also be determined, and vice versa. The measurement ofHcl is difficult for two reasons. First, flux pinning, which resists flux penetration into a specimen, prevents the attainment of equilibrium, even if Hcl is exceeded. Secondly, most single crystals have a plate-like geometry that, for the H\\c orientation, causes large demagnetization fields. To overcome this latter problem early measurements involved a determination of the field at which the magnetization relaxes (Yeshurun and Malozemoff, 1988). Below Hcl no relaxation should take place. Values that were obtained later on similar crystals, using a method that extrapolates to the field of first flux penetration, resulted in smaller values, and a different anisotropy (KrusinElbaum et al., 1989). Recent values, obtained using a microwave method, seem to support the higher values (Wu et al., 1987; Sridhar et al., 1989). An anomalous upturn in the value of Hcl for both orientations has been observed (Wacenovsky et al., 1989), but it remains to be seen whether this anomalous temperature dependence
784
15 Oxide Superconductors
will be confirmed. The data obtained from various authors is replotted in Fig. 15-18. There is, as yet, very little consistency, and the iifcl values obtained for both orientations, as well as the anisotropy, vary by at least a factor of two. Direct measurements of the magnetic penetration depth have been carried out by a variety of techniques, including the muon spin-relaxation method (Uemura et al., 1988; Harshman et al., 1989). Recent measurements on single crystals yield values (Xah = 142 nm, Xc > 700 nm) that are in fair agreement with the lowest values obtained from Hcl measurements, considering the uncertainties involved in determination of the coherence length. 15.4.5 Critical Current Densities
For almost all conceivable applications, it is necessary that superconductors carry current without excessive dissipation. In electronic applications superconducting interconnect lines probably must carry critical current densities (Jc) in excess of
20
40
60
80
100
Temperature (K) Figure 15-18. The temperature dependence of JFfc l for YBa 2 Cu 3 O 7 _ d ; data reported in the literature, and obtained using different techniques (after Daumling, 1990).
105 A/cm2. In this type of application a magnetic field is not generally applied. However, for magnet applications the requirements are much more stringent, since approximately identical J c values are required, but now in the presence of high magnetic fields. Using liquid nitrogen as a cooling medium, applications such as superconducting motors or generators could become economically feasible. At low temperature (4.2 K) the oxide superconductors will have to compete with low-temperature superconductors, particularly the NbTi or Nb 3 Sn materials which are already commercially available. Even the rather exotic Chevrel-phase superconductors (Chevrel et al., 1971), used in the form of wires, have been shown to be capable of carrying substantial currents in magnetic fields larger than 20 T (Goldecker et al., 1989). In contrast to the critical magnetic fields and superconducting-transition temperature, the transport critical current density is not a fundamental property of a superconductor. In fact, the value of the critical current density that is attainable depends on extrinsic, microstructural parameters. The two most important of these for the oxide superconductors are the presence of regions of poor superconducting coupling in the material and the existence of inhomogeneous regions that can pin flux. Discussion of the former, which manifests itself as weak links that impede current flow over distances of the order of the grain size, will be discussed in Sec. 15-6 since it dominates the critical current densities of polycrystalline materials. Weak links within grains are also believed to exist (Daumling etal., 1988; Hibbs et al., 1988) under certain conditions, but these do not pose a major problem. In the absence of weaklink behavior, the attainable transport critical current is dependent on the magnitude of the flux pinning.
15.4 Single-Crystal Properties of Yttrium Barium Cuprate
One of the ironic consequences of the higher transition temperatures of the oxide superconductors is that thermally activated flux motion, which leads to non-zero resistances, becomes important in potential applications that might exploit the higher transition temperatures. This is in contrast to the low-temperature superconductors in which, because of their low operating temperatures, thermally activated flux motion can be assumed to be relatively unimportant. 15.4.6 Flux Creep and the Irreversibility Line
In all superconductors, a non-zero critical current density causes irreversibilities in the magnetization in the mixed regime. This is caused by flux-line pinning and has been the subject of many articles. An excellent review of this feature, and other related subjects, has been given by Malozemoff (1989). The magnetic-field distribution in the specimen is usually described by the critical-state model (Bean, 1962; Daumling and Larbalestier, 1989). In this model, the current is proportional to the gradient in
\
785
the flux-line density. In the steady state the elementary pinning force acting on each flux line is balanced by the Lorentz force, caused by the current. However, thermal activation changes this static picture and allows the flux lines to diffuse out of the potential in which they are pinned. This thermal creep leads to a decay of the critical state, which manifests itself as a dissipation of energy. As mentioned above, this phenomenon has been of little consequence in conventional superconductors because the low temperatures that are necessary to preserve the superconductivity make these thermal effects small, and hence these decay effects are also very small. In the oxide superconductors, particularly at high temperatures (> 30 K), these effects can, however, be large. They were first measured in polycrystalline samples by Miiller et al. (1987), and in single crystals by Yeshurun and Malozemoff (1988). The rate of flux creep is found to increase with the magnetic field, and at, and also above the irreversibility field, Hirr, all magnetic hysteresis disappears (Fig. 15-19). The irreversibility field is found (Malozemoff et al., 1988) to be proportional
C-axis aligned # powder 4 I H||C
Lai. 1.32 nm
6 \
TYBa 2 Cu 3 0 7
\
T
0.84 nm
Bi (2:2:2:3) i 1.23 nm
\ \ Bi (2:2:1:2) d = 1.23 nm 0.0
0.2
0.4
0.6
hAH) / r c ( 0 )
0.8
1.0
Figure 15-19. Irreversibility-line data for four superconducting oxides. The temperature is normalized to the transition temperature in zero field. The temperature dependence for Hc2 would, in each case, be considerably steeper and is therefore not shown (after Suenaga et al., 1992).
786
15 Oxide Superconductors
to (1 - T/Tc)2/3, where T is the measurement temperature. It should be noted that this field was initially mistaken to be the upper critical field but is now known to be quite different, and usually significantly lower. The irreversibility field can also be measured resistively (Palstra et al., 1988). The relation between flux-creep and resistive measurements, as a function of the field, was demonstrated by Tinkham (1988 a, b). Up to the time of writing, there is, however, still considerable debate as to whether the irreversibility line represents a true phase transition, i.e., from a liquid to a glassy state of the flux-line lattice (Fisher, 1989), or whether it should be simply regarded as a depinning line, as initially thought by Malozemoff et al. (1988). In favor of the depinning argument is the observation that the irreversibility line can be moved to higher fields if the strength of pinning is increased, for example by irradiation of the specimen (Sauerzopf et al., 1991; Civale etal., 1990). In addition, recent experiments regarding flux-line cutting (LeBlanc et al., 1991), have raised doubts about the existence of an extended "spaghetti-like" flux liquid, as have been envisaged in glassy models of the fluxline lattice. 15.4.7 Intra-Grain Current Densities and Flux-Pinning Mechanisms
One of the crucial, and as-yet, unresolved questions, is the cause of the very large transport critical current densities (Jc) that have been measured in good single crystals and thin films of YBa2Cu3O7_<5. The highest values obtained are of the order of the theoretical depairing current densities. In conventional, microstructurally optimized, practical low-temperature superconductors, the J c values typically measured at 4.2 K are about 1% of the depairing current density j c d . These, in turn, are orders-of-
magnitude larger than those measured in well-annealed single crystals of conventional superconductors. Similar, low values are found when well-homogenized polycrystalline alloys, such as NbTi, in which grain boundaries and dislocations are the only pinning centers, are measured (Moflfat, 1984). In fact, a perfect single crystal with no defects should have a J c value of zero (assuming that surface pinning is negligible). Thus, the extraordinary values for YBa 2 Cu 3 O 7 _ d and other oxide superconductors that are obtained from single crystals grown from the melt and with no deliberate attempts to introduce flux-pinning centers are remarkable. Many explanations have been suggested for the high Jc values measured for YBa 2 Cu 3 O 7 _^ and these are discussed in the following sub-sections. They include the possibilities that the twin planes, stacking faults, oxygen vacancies, and the structure itself can act as pinning centers. Artificial defects have also been introduced into single crystals, by irradiation with neutrons, protons, and ions, to further enhance pinning. 15.4.7.1 Excess Pinning at Finite Magnetic Fields
An effect often observed in the field dependence of the intragrain critical current density, measured from magnetic hysteresis loops, in single crystals and polycrystalline samples (but not in thin films) is a peak in the critical current density at a finite magnetic field, referred to by Daumling et al. (1990) as "excess" pinning or a "fishtail" effect (see Fig. 15-20). It consists of a nonmonotonic behavior in the critical current density at elevated temperatures (Xu et al., 1989; Senoussi et al., 1988; Daumling et al., 1990). In low magnetic fields, the Jc value decreases rapidly with increasing magnetic
15.4 Single-Crystal Properties of Yttrium Barium Cuprate
787
ical explanation still remains lacking. In polycrystalline samples, a similar effect, although not as strong in magnitude, has been observed in measurements of the transport-current density (Ekin et al., 1987; Seuntjens and Larbalestier, 1990). 15.4.7.2 Critical-Current Anisotropy
10 2
8
10
12
Magnetic Field (T) Figure 15-20. Critical current density results for YBa 2 Cu 3 O 7 _^, as a function of the magnetic field, measured at various temperatures, derived from magnetization loops when using the sample size as the scaling radius. low-temperature oxygenations for 300 h at 450 °C (LPP), and for 200 h at 450 °C (FG2); further oxygenations of 200 h, with slow cooling from 400 to 350 °C, for both LPP and FG2; and further oxygenation of the FG2 sample for 480 h at 375 °C (after Daumling, 1990).
field, then passes through a minimum, only to increase again, in some cases manyfold above this minimum. At very high magnetic fields the critical current density decreases again, reaching zero at the irreversibility field (this behavior is also seen in Fig. 15-33 below). The data may be plotted, alternatively, in terms of the pinning force density versus the reduced magnetic field, which also gives a peak at a finite field, similar to the "peak effect" of conventional superconductors (Kramer, 1992). The oxygen deficiency has a marked effect on the shape of the maximum, as described by Daumling et al. (1990). A number of causes have been suggested for this effect, among them granularity (Kupfer et al., 1989 a), and pinning by a second, superconducting phase (Xu et al., 1989; Daumling et al., 1990), but an analyt-
Assuming that the anisotropy in the ab plane can be neglected, several cases of varying orientation between an applied magnetic field and the current flow can be distinguished. In principle, all of the possibilities can be explored by using resistive measurements in which the direction of the applied current density can be varied independently of the applied magnetic field. (In magnetization measurements the current is perpendicular to the applied magnetic field only as long as the field is applied parallel to one of the principal axes of the superconductor.) However, the majority of the data found in the literature have been obtained for currents flowing in the a b plane, while varying the direction of the magnetic field. Values of current densities along the c axis are usually not measured, since the c axis in almost all samples only extends to a length which is typically less than 200 |im (as compared to several millimeters, or even centimeters, for the a b plane). A rather comprehensive set of measurements of the anisotropy of the transport critical current density, as a function of temperature and magnetic field, for a c axis film has been reported by Roas et al. (1990). Although their measurements were performed on thin films, for which there is a large geometric anisotropy that masks the true transport anisotropy, their results are nevertheless of interest for thin-film applications. In their study, the angle 0 between the magnetic field and the c axis was varied, with the current flowing in the ab
788
15 Oxide Superconductors
plane and perpendicular to the magneticfield vector. In this geometry, the direction of the Lorentz force could be varied from being parallel to the C u - O planes to being perpendicular to the C u - O planes. Some of their results are reproduced in Fig. 15-21. Extremely high values of J c are obtained when the field is parallel to the Cu-O planes, a geometry in which the flux lines are assumed to lie in the C u - O plane, with the Lorentz force pependicular to this plane. This is attributed to the existence of intrinsic pinning between the C u - O planes. Significantly lower values of Jc were observed when the Lorentz force acted in the C u - O plane, but a broad peak varying with angle, was observed at higher temperatures (60 and 77 K), attributable to the presence of twins and stacking defects.
A particular feature of these obeservations is that the angular dependence of the transport critical current density becomes more anisotropic with increasing field, but the corresponding currents decrease in magnitude. Magnetic measurements with HLc always produce an anisotropic critical state in the component of the current that has to flow along the c axis. Using "identical" single crystals of different thickness, Cronemeyer etal. (1990) deduced a critical-current anisotropy of about 30 for this particular case (at T = 5 K). Keller et al. (1990) on the other hand, reported much smaller values for the anisotropy in meltprocessed YBa 2 Cu 3 O 7 _ (5 , but it is possible that their material was not purely single crystalline. 15.4.7.3 Pinning by Twin Planes
7 • r=4.2K 6 . e = 0.5T
E
5
—"
4
o nsi
&
CI)
Q
T=40K 2.0 . B = 0.5 T T 1.5
A/\
J7\\
£
1.0
0.6 . T=60K e = 0.5Tt
o
•
A JV
riticalC
r
3
0.5
A7\
AA
0.4
T
\ J v r^^m. ft ^^ 0.3 0 flll.c
90° Sic
180°
270°
360°
B±c
Tilt Angle , 0 Figure 15-21. Variation in the critical current density, as a function of the angle 9 between the magnetic field and the c axis of a single-crystal thin film of YBa 2 Cu 3 O 7 _ 5 at a magnetic field of 0.5 T. Maximum pinning occurs when the flux lines are parallel, and the Lorentz force perpendicular, to the Cu-O plane (after RoasetaL, 1990).
As mentioned above, almost every single crystal of YBa 2 Cu 3 O 7 _ a is twinned. In view of the very short coherence lengths, there has been interest in ascertaining whether twin boundaries can act as pinning centers. A theoretical study of twinplane pinning was carried out by Kes and van den Berg (1990). Using a conventional model of S x pinning, introduced by Yetter et al. (1982), and adapted for twin boundaries, they predicted pinning of the magnitude required in order to explain the observed J c values. However, the field and temperature dependence does not match experimental data. The first systematic experimental work on the effect of twin boundaries was carried out by Wordenweber etal. (1989). They varied the twin spacing over more than one order of magnitude, from significantly larger to significantly smaller than the flux line spacing (at some fixed field), by the substitution of iron. (As mentioned
15.4 Single-Crystal Properties of Yttrium Barium Cuprate
789
Figure 15-22. Scanning electron micrograph of the flux lines emerging from a single crystal of YBa 2 Cu 3 O 7 _^, and decorated with evaporated ferromagnetic particles. The preference for pinning on the twin boundaries can be seen, as can the flux lattice in the regions away from the twins (micrograph courtesy of T. R. Dinger).
above, addition of iron decreases the difference in the a and b lattice parameters, thereby reducing the anisotropy strain.) No change in the pinning behavior (at 50 K) was noted, and therefore the authors concluded that twin boundaries did not significantly contribute to pinning in their samples. Indirect evidence for twin boundaries acting as pinning centers comes from photographs of flux-decorated single crystals (Dolan et al., 1989). An example of this is reproduced in Fig. 15-22. From pictures such as these, there does seem to be a correlation between the density of flux lines and the location of the twin boundaries. However, with the availability of singledomain crystals or twin-boundary-free crystals more direct experiments have since been carried out. Bauhofer et al. (1989) have shown that the flux-flow resistance has a sharp minimum value when the twin planes line up with the applied magnetic field. Similar experiments were also carried out by Welp et al. (1989 b). However, for the H || c orientation, crystals that were free of twin boundaries still showed large Jc values, especially at low temperatures, where Jc was hardly lower than for
twinned crystals. When the magnetic field was oriented parallel to the ab planes a large orientation effect was observed. In monodomain crystals, with only one twin habit direction, a strong increase in Jc was observed when the boundary planes were aligned with the direction of the magnetic field. 15.4.7.4 Pinning by Oxygen Defects Flux pinning by intrinsic oxygen defects, microscopically inhomogeneous oxygen concentrations, has been suggested by several authors as one reason for the high critical currents in apparently otherwise defect-free single crystals (Tinkham, 1988 b; Daumling et al., 1990). Although, nominally, the oxygen deficiency d in crystals of yttrium barium cuprate is assumed to be zero (mostly for convenience), this is generally not the case since the times for complete oxygenation can be quite long (from days to even weeks, depending on the temperature and sample size). Using typical oxygenation schedules reported in the literature the samples usually reach oxygen deficiencies 3 of between 0.05 and 0.1. This
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15 Oxide Superconductors
leads to a significant number of oxygen vacancies, which may be present in an ordered or a random arrangement, depending on the thermal history of the specimen. The first investigations of J c with varying oxygenation treatment were carried out by Daumling et al. (1990). In this study, both single-crystalline and melt-processed specimens were annealed at low temperatures (300 to 450 °C), in order to vary the oxygen content. The authors found that the "excess pinning" effect (see Sec. 15.4.7.1) decreased in magnitude as the annealing temperature was reduced (i.e., decreasing oxygen deficiency). The absolute value of the critical current density decreased as well, leading to the interpretation that single oxygen vacancies (on the chain sites) could constitute pinning centers. Further systematic studies in polycrystalline specimens seem to contradict this behavior since they all show a decrease of the critical current density with increasing oxygen deficiency (Theuss and Kronmuller, 1991; Daumling, 1991a, b). However, Daumling (1991a, b) has shown that the thermodynamic critical field Hc also decreases strongly with increasing oxygen deficiency, and so concluded that the density of pinning centers actually increases as the oxygen deficiency increases. One intriguing suggestion, made by Vargas and Larbalstier (1992) is that over a certain oxygen-concentration range, YBa 2 Cu 3 O 7 _^, decomposes into phases of fixed oxygen ordering, and that these regions are responsible for the flux pinning. 15.4.7.5 Irradiation Effects
Irradiation has long been known to increase flux pinning in conventional lowtemperature superconductors by the formation of point defects. Depending on the kind of radiation (neutron, proton, heavy
ions) and the dose, the damage is more or less extensive. Following in this tradition, irradiation studies have been performed on oxide superconductors. Neutron irradiation of YBa2Cu3O7_<5 ceramics was first carried out by Kupfer et al. (1989 b), who found that intragrain J c values increased markedly up to a limiting dose of 4 x 1018 cm" 2 . However, the intergrain Jc values were simultaneously reduced, and at a dose of 4 x 1018 cm" 2 the intergrain Jc had decreased by an order of magnitude. A similar reduction in magnitude for jci has also been measured in polycrystalline thin films (White et al., 1988), which has been attributed to the preferential amorphization of grain boundaries by the neutron irradiation (Clark et al., 1987). The effects of neutron irradiation on single crystals have also been studied and the results indicate that increases of almost two orders of magnitude are possible, depending on the temperature and fields used to make the transport measurements (van Dover et al., 1989; Sauerzopf et al., 1991). Neutron irradiation also alters the shape of the Jc-versus-field curves and the temperature behavior quite drastically (see Fig. 15-23). Proton irradiation appears to produce rather similar effects to those of neutron irradiation (Xiong et al., 1988; Civale et al., 1990). Irradiation with heavy ions produces markedly different effects to those obtained using irradiation with lighter particles. In propagating through the material, a heavy ion creates a cascade of defects along its path until it exits on the other side of the thin film or crystal. In addition to creating a cascade of damage, a characteristic of the damage cascade is that it is highly directional. As a result, an applied magnetic field can be aligned with the cascade direction in order to study the anisotropy of cascade pinning. Such an anisotropy has been reported by Civale et al. (1991), who
15.5 Thin Films
XT o
791
Figure 15-23. Magnetic field dependence of the intra-grain current density Jc in YBa 2 Cu 3 O 7 _^for the successively increasing neutron doses indicated. Measurements were carried out at 10 K (after Kupfer et al., 1989 b). 2
3
4
Magnetic Field (T)
found that heavy-ion irradiation can increase the J c values in crystal samples. 15.4.7.6 Precipitate Pinning
In low-temperature metal and alloy superconductors the most effective means of enhancing flux pinning has proved to be the introduction of non-superconducting precipitates. In NbTi superconductors the morphology and spacing of the a-Ti precipitates determines the attainable transport critical current density (Lee and Larbalestier, 1989). There have been a number of attempts to similarly exploit precipitate pinning to enhance the critical current density in the oxide superconductors, but they have yet to be applied in any systematic manner. Nevertheless, there are indications that the approach may prove feasible, despite the fact that strong pinning is only expected to pertain when the precipitate size is of the order of the coherence length, namely about 1 nm. In melt-processed YBa 2 Cu 3 O 7 _ a the solidification process itself leads to a two-phase sample, which can contain large volume fractions of the Y 2 BaCuO 5 phase. In general, the size of
these precipitates is rather large, about 10 jim, or even larger. Contradictory evidence has been presented on the influence of this phase on the critical current density. Murakami et al. (1989) reported increased Jc values in samples containing the Y 2 BaCuO 5 phase and attributed the increase to the presence of this phase. Increases have also been noted in sintered samples, but these have been attributed to the consequential reduction in the volume of secondary liquid phases during the solidification process. Another way of introducing precipitates into YBa 2 Cu 3 O 7 _^ has been demonstrated by Jin et al. (1990). In this process YBa 2 Cu 4 O 8 starting material was annealed, where it decomposed into YBa 2 Cu 3 O 7 _^, containing some inclusions of Cu-O. This process resulted in an increase in the transport critical current by a factor of ten.
15.5 Thin Films Considerable scientific and technological effort has been devoted to the fabrication of thin films of the different oxide su-
792
15 Oxide Superconductors
perconductors, both because of the potential for applications in superconducting electronics and, in the absence of large single crystals, the suitability of thin epitaxial films for measurement of the electromagnetic properties of the materials. Also, as a result of the widespread interest in oxide superconductors, a wide variety of thinfilm deposition techniques have been applied to the growth of films, in particular to yttrium barium cuprate, and vast literature has consequently developed. As with single crystals, one of the outstanding, and as yet unresolved, questions is why epitaxial films of YBa 2 Cu 3 O 7 _^, irrespective of how they are grown, can exhibit transport critical currents approaching the depairing current density.
Table 15-3. Substrate materials. Substrate
Crystal substrate
Lattice Dielectric constants constant a
N SrTiO 3 MgO 9% YSZ LaAlO 3 LaGaO 3
Cubic perovskite Cubic NaCl Cubic fluorite Hexagonal
a = 0.395 a = 0.4212 a = 0.516 a = 0.5464
>300 b 10 27 15
Orthorhombic perovskite
b = 0.5526 c = 0.77
25
NdGaO 3 Y2BaCuO5 MgAl 2 O 4 Cubic spinel BaZrO 3 Trigonal A12O3 Si Diamond cubic BaF 2 Cubic
22 a = 0.8059 a = 0.419 a = 0.514 a = 0.543
11 7.3
a
15.5.1 Epitaxial Growth
Dielectric constants are from Konaka et al. (1991) and are measured at GHz frequencies; b rising to > 1800 at 77 K.
It is now evident from a wealth of experience with all of the superconducting oxides that films having the highest currentcarrying capacity and the best chemical stability are aligned, epitaxial, though not necessarily single-crystal, films. As with the growth of semiconductor heterostructures and superlattices, the main criteria for epitaxial growth are close lattice matching and chemical compatibility between the film and the substrate. In the majority of cases, lattice matching to the basal plane of the superconductor has been preferred so as to produce films with the C u - O planes parallel to the film surface. The fact that the majority of the superconducting oxides are related to the perovskite or rock-salt structures has led to the selection of substrates having these crystal structures. This structural compatibility is illustrated in Table 15-3, which lists a number of the principal materials that have been used as substrates. Comparison with the lattice parameters of the superconducting oxides
shows that the lattice mismatches can be quite large, with the best match, to YBa 2 Cu 3 O 7 _^, for example, perhaps being LaGaO 3 or SrTiO 3 (see Fig. 15-24). However, in addition to their structural similarity, the choice of substrate has usually been dictated by other considerations, such as stability in the presence of an oxidizing growth atmosphere, chemical compatibility or favorable dielectric properties. Other substrate materials, such as sapphire, silicon and gallium arsenide, that promise potentially wider applications on account of their lower cost, availability in larger sizes, superior dielectric properties or their potential for hybrid semiconductor/superconductor devices are either poorly lattice matched or suffer serious chemical degradation during the film-deposition process. To avoid some of these problems, attention has recently been given to using intermediate, buffer layers
15.5 Thin Films
793
0.395
Figure 15-24. Lattice parameters of YBa 2 Cu 3 O 7 as a function of temperature between 900° and 0 °C. For comparison, the lattice parameters of the three substrate materials, SrTiO3 (o), LaAlO3 (o) and LaGaO 3 (•, o) are also shown (data for YBa 2 Cu 3 O 7 are from Nakahara et al., 1989). ao, b0 and at are the lattice parameters of the orthorhombic and tetragonal phases. 200
400
600
800
1000
n°o (see Sec. 15.5.3) to take advantage of the favorable properties of these substrates. Interestingly, few of the superconducting oxides are truly chemically compatible with the substrate materials that are chosen. Indeed, of all the substrates used for the growth of YBa2Cu3O7_<5, only Y 2 BaCuO 5 , and possibly BaZrO 3 , are known, from phase-equilibria studies, to be compatible. In all of the other combinations, some degree of reaction is expected but is kinetically limited by the short times and relatively low temperatures used for film growth. The extent of interdiffusion has been measured in a variety of ways, ranging from studies of the film-thickness dependence of the superconducting properties to high-resolution elemental microanalysis of film cross-sections by transmission electron microscopy (TEM) (Golden et al., 1990), and Z-contrast imaging in the scanning transmission electron microscope (STEM) (Pennycook et al., 1991). Whether interdiffusion simply reduces the conducting cross-section, or possibly acts as a source of flux-pinning centers, remains to be established. The crystallographic relationships between the films and the chosen substrate are, in the main, quite simple, usually being
cube-on-cube, but if represented in this way may be misleading. In almost every instance other than the most closely lattice-matched combinations, such as YBa 2 Cu 3 O 7 __£ on SrTiO 3 , the films have a mosaic microstructure about the exact crystallographic orientation relationships. The degree of misorientation, measured, for example, from in-plane and out-ofplane X-ray diffraction, often varies with deposition conditions and the combination of materials, but can typically be up to several degrees. As the films are often polycrystalline, containing distinct grain boundaries, the films are probably more accurately described as being highly aligned, rather than truly epitaxial. However, in the absence of quantitative models relating the transport properties of the polycrystalline films to their crystallographic misorientations, the distinction remains moot. Nevertheless, the epitaxy reported for many superconducting films is quantitatively different to that usually used in describing epitaxy in semiconductor structures, since the grain size of the superconducting films is small. The relationship between the degree of epitaxy of superconducting films and their superconducting transport properties has
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15 Oxide Superconductors
yet to be established in any detail, although general guidelines are known. For instance, single-crystal YBa 2 Cu 3 O 7 _^ films grown on SrTiO 3 substrates exhibit significantly higher Jc values than polycrystalline YBa 2 Cu 3 O 7 _^ films grown in an identical manner. Similarly, polycrystalline films of BaPb1_xBiJCO3 can carry significantly lower current densities than singlecrystal films. This result would suggest that single-crystal superconducting oxide films are a necessity for attaining large critical current densities. Yet, films of YBa2Cu3O7_<5 that have been grown on MgO substrates, can carry an equally large Jc in magnetic fields as that measured for the films grown on SrTiO 3 substrates, despite the fact that the former contain grain boundaries (Chan et al., 1989; Shin et al, 1990). On the basis of the bicrystal results of Dimos et al. (1990), this can be rationalized by assuming that if the grains have only a small mismatch across the boundaries, the critical current densities will be relatively unaffected. However, considerably more data need to be obtained before the effect of crystallographic misorientation at grain boundaries is fully understood (see Sec. 15.6.2). As the superconducting coherence length, £ab, in the ab plane of YBa2Cu3O7_<5 is significantly longer than that in the c direction (i.e., £c), there has been considerable interest in growing aaxis films so as to maximize the wavefunction overlap across the interfaces for possible device structures. Experimentally, it has been found that the growth of oaxis films is favored at high temperatures, whereas a-axis growth is favored at lower temperatures (Eom et al., 1990). The origin of this growth preference is unknown.
15.5.2 Growth Mechanisms
At the time of writing, little progress has been made towards understanding the mechanisms of growth of any of the superconducting oxide films or establishing whether there is any correlation with the attainable transport critical current density. TEM observations typically reveal the films to be highly defective, containing stacking faults, twins, and sub-boundaries, but few dislocations. They frequently also contain high densities of stacking defects or intergrowths of CuO or YBa 2 Cu 4 O 8 . Such compositional polytypism, consisting of intergrowths having different Cu-O layer sequences, has also been noted in many of the bismuth-based and thalliumbased cuprate films. Observations of the as-grown surfaces of YBa 2 Cu 3 O 7 _^ films, using the scanning tunneling microscope (STM) (Gerber et al., 1991; Hawley et al., 1991), present a simpler picture, indicating the presence of growth spirals associated with screw dislocations intersecting the surfaces (see Fig. 15-25). The implication of such observations is that the films have grown by the Burton-Cabrera-Frank mechanism (Burton et al., 1951). However, despite the fact that the pitch of the spirals corresponds to the c-axis repeat distance in YBa 2 Cu 3 O 7 _^, corresponding to a perfect screw dislocation, observations by TEM have failed to confirm the presence of such screw dislocations. Many other dislocations have been detected by TEM (see Nakahara et al., 1989) but none of these, primarily edge or mixed dislocations with b = <100)> have been reported in the STM observations. Nevertheless, the idea of island growth, mediated by screw dislocations, is supported by observations by Krebs et al. (1991), who made both in situ resistance measurements during film growth and resistivity measurements as a
15.5 Thin Films
Figure 15-25. Scanning tunneling micrograph of the surface of a YBa 2 Cu 3 O 7 _ a film grown on a [100]SrTiO3 substrate. The helical pattern which corresponds to an emergent screw dislocation can be seen. The step height is 1.2 nm, corresponding to a unit-cell-high step (micrograph courtesy of J. Mannhart).
function of temperature. They observed an abrupt drop in the resistance at a critical thickness of the growing film that corresponded to the thickness above which the resistivity fell to zero at the superconducting-transition temperature. On the basis of these observations, growth proceeds by the formation of isolated islands, each growing by the Burton-Cabrera-Frank mechanism, which impinge at the critical thickness. At this point the islands provide a percolative transport path in the film, which is indicated by both the drop in resistance and the onset of zero resistance as the material is cooled below Tc. There is evidence from reflection high-energy electron-diffraction observations of the growth of YBa2Cu3O7_<5 on [100]SrTiO3 that the initial stages of growth are layer-by-layer in type (Terashima et al., 1990). Subsequent STM observations of the same growth suggest that is an example of Stranski-Kras-
795
tanov growth, i.e., layer-by-layer growth up to a critical thickness (8-16 unit cells) followed by island growth (Zheng et al., 1992). This is consistent with the ion-channelling observations of YBa2Cu3O7_<5 films on SrTiO 3 , which suggest that films below a critical thickness are strained, whereas thicker ones are not (Xi et al., 1989). The presence of screw dislocations has important implications for understanding the large Jc that is attained in epitaxial YBa2Cu3O7_<5 films, since they are potentially strong vortex-pinning sites. Preliminary estimates by Gerber et al. (1991) and by Mannhart et al. (1992) indicate that the pinning derived from the density of screw dislocations observed by STM investigations should be sufficient to account for the measured critical current densities in low magnetic fields. This begs the question as to the role of all the other dislocations and growth defects seen by TEM, as well as the sub-grain boundaries formed by island impingement. However, these may become dominant at higher magnetic fields, where the vortex density becomes significantly greater than that of the screw dislocations. It is tempting to believe that the weak pinning that is exhibited by the bismuth-based and thallium-based cuprate films is the result of a weaker dislocation-vortex interaction in these materials, but screw dislocations have yet to be seen, or their densities measured. Also, as mentioned above, they can exhibit very high densities of intergrowths and stacking disorders, whose pinning effects still remain unknown. Some insight into the initial stages of the nucleation and growth of YBa 2 Cu 3 O 7 _ (5 films on MgO substrates comes from the TEM observations (Norton and Carter, 1991; Streiffer et al., 1991) of films with average thicknesses of only a few unit cells. In the work of Norton and Carter (1991), nu-
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15 Oxide Superconductors
cleation is clearly seen to occur at steps on the MgO substrate, with subsequent lateral growth of the islands. Such graphoepitaxial growth leads to the formation of an incoherent or semicoherent interface, with the films exhibiting rotational misalignment about the film normal. Similar work by Streiffer et al. (1991) also concludes that the films nucleate at steps but shows as well that the islands are only a few unit cells thick before coalescence occurs. They report that lateral growth occurs by the migration of unit-cell-high steps which suggests that growth occurs by the addition of complete unit cells rather than the individual perovskite sub-blocks which have a height of c/3. The resulting microstructure observed in these TEM studies may be best described as being a mosaic microstructure. Recent STM observations of the early stages of growth of YBa 2 Cu 3 O 7 _ 5 on MgO confirm that epitaxial growth is predominantly by the island mode of growth (Zheng etal., 1992). Growth of YBa 2 Cu 3 O 7 _ 5 on MgO is of particular interest for two reasons. The lattice mismatch is large and, despite the presence of grain boundaries, the YBa2Cu3O7_<5 films grown on MgO can exhibit values of Jc as large as those of single-crystal films on SrTiO 3 . One explanation for the growth of YBa2Cu3O7_<5 as a single crystal on [001]SrTiO3, but with a mosaic structure on [001] MgO, is in the possible growth variants on the two substrates. The small mismatch between the a, b and c/3 axes of the unit cell of YBa 2 Cu 3 O 7 _^, and the a-axis of SrTiO 3 , suggests that any of the three axes can grow parallel to [100] SrTiO 3 . As a result of this three-fold degeneracy in growth variants, only grain boundaries having a rotational misorientation of 0°, 90° and 45° will form when the different island variants impinge. Since 45° boundaries about [001] are
structurally equivalent to twin boundaries, only 0° and 90° boundaries will be apparent. Depending on the relative rates of nucleation and growth of the islands, the resulting film will be either an a-axis, a c-axis or a mixed a, c-axis film. In contrast, the lattice mismatch between the respective a axes of MgO and YBa 2 Cu 3 O 7 _^ is much greater, about 8.8%. Smaller mismatches can be achieved by rotation about [001] to align other directions in the a b plane of YBa 2 Cu 3 O 7 _ 5 with the [100] direction of MgO. For example, the lattice mismatch between the [110], [210], and [310] directions of YBa 2 Cu 3 O 7 _ 5 , and the [100] direction of MgO, are 2.8, 2.5, and 3.4%, respectively. Thus, the impingement of islands aligned according to various of these orientations, leads to a multiplicity of boundaries, i.e., 0°, 8.2°, 18.4°, 26.6°, 36.8°, 45°,..., 90° misorientations. In closing this sections, it should be remarked that the growth mechanism identified in the studies performed to date on the growth of YBa 2 Cu 3 O 7 _^ on MgO and SrTiO 3 substrates by sputtering or laser ablation may not necessarily be dominant under different growth conditions. For instance, by analogy with crystal growth in other materials, spiral growth is likely to be dominant only at low temperatures, over a range of supersaturations where homogeneous nucleation or ledge growth is not favored. At higher temperatures and supersaturations, film growth might be expected to occur by nucleation and growth. Furthermore, high-quality films can be grown by a wide variety of different techniques; they can be formed from the vapor, liquid and solid phases, and over a range of temperatures. For example, in addition to in situ crystallization and growth from the vapor, films can be formed by crystallization from amorphous precursor materials by heat-treatment, by chemical reaction or
15.5 Thin Films
by solidification. Examples of heat treatment of amorphous precusors include the growth of YBa 2 Cu 3 O 7 _^ by decomposition of trifluoroacetate precursors (Mclntyre et al., 1991) and the decomposition of nitrates (Gupta et al., 1988). It also includes the formation of 1-, 2- and 3-layer bismuth-based cuprate films by the decomposition and crystallization of metalorganic precursors, during which a transient liquid phase forms to facilitate the growth of the film (Golden et al., 1992). Examples of superconducting films grown by chemical reaction include the formation of YBa2Cu3O7_<5 by the oxidation of Y-Ba-Cu alloys, and the conversion of B a - C a - C u - O precursors to Tl 2 Ba 2 CaCu 2 O 8 by heating in the presence of a thallium-oxide vapor (Ladd et al., 1991). High-quality, epitaxial Bi 2 Sr 2 CaCu 2 + 3 films have also been grown by passing a molten front through Bi2Sr2CaCu2+<5 powders deposited on MgO substrates. 15.5.3 Buffer Layers
Although evidence for graphoepitaxial growth of YBa 2 Cu 3 O 7 _^ has been obtained, single crystal growth of YBa 2 Cu 3 O 7 _ a has usually relied on epitaxial growth upon a suitably matched substrate. Unfortunately, many of the most closely lattice-matched substrate materials have undesirable electrical properties, and/ or are very expensive, or are simply unobtainable in a reasonable size. For example, although SrTiO 3 has a perovskite crystal structure with a mismatch of only 1%, its dielectric constant and dielectric losses are too large for its use in microwave applications. Thus, in order to grow epitaxial oxide superconductor films on a variety of different substrates, the approach used has been to first grow a buffer layer, of intermediate lattice-spacing, on the desired sub-
797
strate material, and subsequently grow the superconductor film templated on the buffer layer. A selection of buffer layer/substrate combinations that have been used for YBa 2 Cu 3 O 7 _ a is given in Table 15-4. In many cases, the function of the buffer layer is also to act as a chemical barrier between the film and substrate, thus to preventing chemical reaction. Ideally, the buffer layer should, of course, be phase compatible with both the film and the substrate. However, in many combinations this is not the case, but reaction is kinetically limited since the processing temperatures are sufficiently low to preclude extensive reactivity. For many of the applications presently being considered, the substrate material plays a passive electrical role and interdiffusion into it does not affect its performance. However, in the area of potential semiconductor/superconductor hybrid devices and structures, interdiffusion of species can cause degradation of the electrical transport of the semiconductor, as well as adversely affect the superconducting transport properties. For this type of application, the buffer layer must act as an interTable 15-4. Buffer layer/substrate combinations for YBa2Cu3O7_(5. Buffer
Substrate
Reference
Si, GaAs Fork et al. (1991) c-ZrO2 c-ZrO2 Hwang et al. (1991) BaZrO 3 Si (100) Myoren et al. (1988) t-ZrO 2 A12O3 [1102] Fork et al. (1991) c-ZrO2/Si GaAs Shewchun et al. AlGaO 3 /Al 2 O 3 (1991) BaF 2 Si Lubig et al. (1990) CoSi2 Si Luo etal. (1991a) Si Jia and Anderson (1990) MgO GaAs Fork et al. (1991); Chang et al. (1992) Si Luo etal. (1991b) CeO,
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15 Oxide Superconductors
diffusion barrier, in addition to providing a template for epitaxial film growth. A very sensitive test of interdiffusional-induced degradation has been presented by Chang et al. (1991). They observed changes in the luminescence spectra from GaAs/AlAs quantum wells, located at different depths in a GaAs substrate, after the deposition of YBa 2 Cu 3 O 7 _d. By locating quantum wells of differing energies at different depths below the surface, they were able to monitor the depth of interdiffusion by examining the shift and broadening of the different peaks in the spectra. In subsequent work, buffer layers of Si 3 N 4 and MgO proved effective in preventing degradation of the semiconductor as well as the superconducting transition temperature (Tseng et al., 1992). A cross-section of the GaAs/MgO/ YBa2Cu3O7_<5 heterostructure is shown in Fig. 15-26. The exploratory work to find suitable buffer layers for the growth of high-quality oxide superconductors has had one unexpected benefit. Hitherto, the inability to grow single-crystal ferroelectric films on top of an electrically conducting thin film
has restricted efforts to grow high-quality, aging-resistant and electrically switchable ferroelectrics for integrated, thin-film applications. However, by growing epitaxial thin films of YBa 2 Cu 3 O 7 _ 5 and Bi 2 Sr 2 CaCu 2 O 8 as buffer layers on single crystal substrates, Ramesh et al. (1991) were able to grow ferroelectric films of B ^ T ^ O ! 2 that exhibited symmetric hysteresis loops and a remanent polarization that was comparable to the single-crystal values. Since the electrical properties of the YBa 2 Cu 3 O 7 _^ and Bi 2 Sr 2 CaCu 2 O 8 films in their normal state are adequate for use as electrode materials, simple latticematched epitaxial ferroelectric film/electrode structures have now become feasible. 15.5.4 Multilayer Films The demonstration of epitaxial superconducting film growth and the templated growth on epitaxial buffer layers has led to the development of techniques for growing multilayers of superconductors and insulators. In part this has been motivated by the desire to explore proximity
Figure 15-26. Transmission electron micrograph of a cross-section of a YBa 2 Cu 3 O 7 _^ film grown on an epitaxial, MgO-buffered, GaAs substrate. Low-angle grain boundaries in the cuprate film are arrowed (micrograph courtesy of M. De Graef).
15.5 Thin Films
coupling effects. For example, superlattices of the YBa 2 Cu 3 O 7 _ 5 /PrBa 2 Cu3O 7 _ <5 / YBa 2 Cu 3 O 7 _^ system show systematic variations in their transport properties with the thicknesses of the layers (Triscone et al., 1990). However, much of the work has also been directed towards the fabrication of device structures incorporating planar Josephson junctions. These applications require large-area, defect-free superconductor-dielectric-superconductor layers in which the thickness of the dielectric is approximately equal to the coherence length, so that an appreciable tunneling current through the insulating layer can be obtained. (It is interesting to note that the identification of a suitable dielectric, and the subsequent development of techniques for its reproducible growth, was a key hurdle that had to be overcome in the development of niobium- and lead-based Josephson-junction technology.) A number of
799
edge-junction formed at an artificial grain boundary produced by a local change in the epitaxy of a buffer layer (Fig. 15-27 a). In creating this novel structure, Char et al. (1991a, b) exploit the fact that MgO and SrTiO 3 adopt differing epitaxial relationships with R-plane sapphire, and so the subsequently deposited SrTiO 3 and YBa 2 Cu 3 O 7 _ (5 layers preserve that epitaxy. The sequence of fabrication steps that they use is to first deposit a seed layer of MgO onto a sapphire substrate, pattern the MgO and remove half of the MgO film by etching, deposit SrTiO 3 over the remaining MgO seed and the exposed sapphire, and then finally deposit a YBa 2 Cu 3 O 7 _^ film on top of the SrTiO 3 buffer layer. The SrTiO 3 film grows in two different orientations, separated by a 45° grain boundary, and acts as a template for the growth of the YBa 2 Cu 3 O 7 _ 5 film. The epitaxial relationships in the growth plane are found to be
[1120]Al2O3 || [110]SrTiO31| [001]YBa2Cu3O7__, and [1120]Al2O3 || [100]MgO || [100]SrTiO31| [001]YBa2Cu3O7_, studies have shown that trilayer films can be grown, for example the YBa 2 Cu 3 O 7 _^/ NdGaO 3 /YBa 2 Cu 3 O 7 _ 5 films reported by Boikov et al. (1991), but as yet the dielectric film that is produced has not been sufficiently thin or defect-free to form a true planar junction. Because of these difficulties, and the fact that edge or step Josephson-junction geometries are technically simpler to fabricate, these latter junctions have been at the heart of the majority of multilayer structures that have been made. As an example, multilayer superconducting quantum interference devices (SQUIDs) have been made, based on an
This process has been subsequently extended to form bicrystal junctions on a variety of substrates and to fabricate multilayer, fully integrated SQUIDs. An example is shown schematically in Fig. 15-27b for a SrTiO3-coated yttria-stabilized zirconia (YSZ) substrate, with YBa2Cu3O7_<5 films grown on a CeO 2 buffer formed on the MgO seed layer (Rosner et al., 1992). In this structure, the CeO 2 , PrBa 2 Cu 3 O 7 _^ (PBCO) and SrTiO 3 act as buffer layers, and the lower layers of YBa 2 Cu 3 O 7 _ a (YBCO) are electrical conductors. This example illustrates both the level of sophistication now achieved in producing multilayers, including the use of photolithographic techniques to define the location of
800
15 Oxide Superconductors ,45° grain boundary
[ooi] § H | [ooi]; 1 [no]
[100] =
YBCO i
YBCO j
SrTiCL | S r T i O
3
| R -plane sapphire]
(a)
1000ASrTiO« 1000Al_aAIO,
lOOOASrTiO, 100APBCO
100ACeO2
(b)
the junction and the vertical interconnects, and also the use within an integrated structure of oxides as dielectrics, conductors and superconductors. 15.5.5 Critical Thicknesses
Two apparently distinct phenomena presently prevent the growth of thick, single crystal films of oxide superconductors. One is the phenomenon of film microcracking, which is induced as a result of growth- and thermal expansion mismatch stresses. The other is the observation that above a certain thickness it is impossible to maintain the epitaxial growth of the growing film and grains with the differing crystallographic orientations that nucleate. This is in contrast to the growth of semiconductors, where nucleation of alternative growth variants may form but only rarely entirely new orientations. Although the observation of a critical epitaxial thickness is well documented (see, for example Carim et al., 1991), its causes are poorly understood. In some cases, it appears to be the result of new grains nucleating at the top surface. In other cases, it may be the result of an inability to control and maintain the local composition or the growth conditions, leading to re-nucleation. Microcracking of thin films, as a result of growth and mismatch stresses, has been
Figure 15-27. Schematic cross-sections of two different device structures based on the formation of a grain boundary by epitaxial growth on either side of a step edge, (a) A junction is induced in a YBa2Cu3O7_(5 (YBCO) layer at the step edge in the SrTiO3 layer which is grown epitaxially over the edge of a MgO layer on sapphire, (b) An integrated, multilayer SQUID, made by the successive epitaxial growth of several oxides to form a junction in the top layer of YBCO, over a series of dielectric layers, conductors and a ground plane (figure courtesy of Conductus, Inc.).
15.5 Thin Films
a perennial barrier to the fabrication of thin-film structures, often limiting the attainable thickness of the single-crystal films. In oxide superconductors, microcracking not only obstructs the current transport but can prevent the growth of films to thicknesses corresponding to the magnetic penetration depth, typically 0.15 jim for YBa 2 Cu 3 O 7 _ (5 . Microcracking has been reported to occur in the growth of YBa2Cu3O7_<5 films by laser ablation (Olsson et al., 1991), in bismuthate films (Enomoto et al., 1989), and during the molecular-beam epitaxy (MBE) growth of Ba1_JCKxBiO3 films (Hellman et al., 1991). A particularly striking example of thin film microcracking can be seen in Fig. 15-28, which shows a cross-section of an epitaxial film of YBa2Cu3O7_<5 grown on a [110]SrTiO3 substrate. An unusual feature of the growth of oxide superconductors is that the film stresses can arise as a result of both thermal expansion mismatch with the substrate and also by compositional changes, for instance during oxidation. In the case of [100]-oriented Ba 1 _ x K x BiO 3 films on [100] MgO the lattice mismatch is approximately 1.4%, less than the strains produced on cooling as the films oxidize. In YBa2Cu3O7_<5 there is a volumetric change of approximately 3% at the tetragonal-to-orthorhombic phase transition (see Fig. 15-24) (Nakahara et al., 1989). Despite this large strain, in the one comprehensive study, that has been made to date of microcracking in superconducting films
801
(Olsson et al., 1991), the growth stresses were found to be predominantly due to thermal expansion mismatch with the substrate, on cooling from the deposition temperature. According to the results of a linear elastic fracture mechanics analysis of the cracking of thin films under residualv tension, the microcrack spacing A, is related to both the film thickness t, and the film stress a, and is given by the equation
where Kf is the fracture resistance of the film. In the work of Olsson etal. (1991) the microcrack spacing in the <110> YBa2Cu3O7_<5 films grown on [110] SrTiO 3 substrates was found to obey this functional dependence over a range of film thicknesses, as shown in Fig. 15-29. Another prediction made from this fracturemechanics analysis is that there exists a critical thickness £crit, below which it is energetically unfavorable for microcracking to occur. This thickness (Olsson et al., 1991) is given by tcrit = 0.5(Kf/a)2 Experimental data, again drawn from the work of Olsson et al. (1991), indicate that films having a thickness less than the calculated tcrii (0.1 jim for films deposited at 600 °G do not contain any microcracks, whereas those with thicknesses above tcrit do. [As an aside, it is interesting to note that although considerable difficulty has
Figure 15-28. Transmission electron micrograph of a cross-section of an epitaxial film of YBa 2 Cu 3 O 7 _ a which has been grown on a [100] SrTiO3 substrate. The film thickness exceeds the critical thickness and microcracks (arrowed) form at approximately equidistant intervals (micrograph courtesy of E. Olsson).
802
15 Oxide Superconductors
2.0
il
A - 5.63A/F ACf/cr 1.5 -
1 1.0 £ O
750°C _
0.5
0.0 0.0
i
i
0.1
0.2
i
0.3
0.4
0.5
Film Thickness, t (jam) Figure 15-29. Comparison of the calculated and measured values of the microcrack spacing, as a function of film thickness, for epitaxial films of YBa 2 Cu 3 O 7 _ a grown on [110] SrTiO3 at two deposition temperatures. and represent the calculated values, and • and • the experimental values, for 625 °C and 750 °C, respectively (after Olsson et al, 1991).
been experienced over the years in clearly observing microcracks in ceramic materials, the microcracks in the YBa 2 Cu 3 O 7 _ (5 films were observable both by TEM and, after etching in bromine/ethanol, by scanning electron microscopy (SEM) techniques.]
the predictions of the Mattis-Bardeen (1958) theory at temperatures near Tc, but at lower temperatures the resistance becomes temperature-independent rather than varying exponentially with decreasing temperature (see Fig. 15-30). (Conventional metallic superconductors also exhibit a residual resistivity, related to their surface preparation, but it is generally of much lower value and is only apparent at much lower temperatures). Data comparing the results for different YBa 2 Cu 3 O 7 _^ samples, in different forms and measured in different laboratories, have been compiled by Piel and Muller (1991). From the data (Fig. 15-31), it is evident that untextured, polycrystalline materials exhibit substantially higher losses than oriented, epitaxial films. This suggests that losses are related, in some as-yet-undetermined way, to compositional heterogeneity and poor coupling across the grain boundaries. Although it has yet to be established in detail, 1U 1
87 GHz "^l^,
_
Polycrystalline
15.5.6 Surface Resistance Superconducting films offer potential advantages in passive microwave applications, since their resistance, at microwave frequencies, can be significantly lower than that of normal metal conductors. As a result the attainable quality factor can be substantially higher, and hence the frequency selectivity can be greater. Furthermore, because the superconducting gap of the oxide superconductors is larger than that of conventional superconductors, the cutoff frequency is correspondingly higher. Results obtained to date indicate that the surface resistivities of the best YBa 2 Cu 3 O 7 and thallium-based cuprate films approach
§
-
\go^^^
Ep'taxjal film
^
B m &
10-3
\
•
.
:
^tNv^^Nb3Sn CO 10 i
i
i
i
Tc/T Figure 15-30. Surface resistance at 87 GHz, as a function of temperature, for polycrystalline and (two) epitaxial films of YBa 2 Cu 3 O 7 _ 5 . For comparison, the corresponding data for superconducting niobium and Nb3Sn are also shown (after Piel and Miller, 1991).
15.6 Polycrystalline Materials
803
0 O
Figure 15-31. Surface resistance, as a function of frequency, / for polycrystalline and epitaxial thin films of YBa 2 Cu 3 O 7 _ a at 77 K, compared with corresponding data for niobium and copper. Results from different laboratories for polycrystalline samples fall within the shaded region, A data for epitaxial thin films: the continuous curving line represents the data obtained for the epitaxial material at 50 K (drawn after Piel and Miller, 1991 and Halbritter, 1990).
CD
10"° -
10
0.1
1
10
Frequency (GHz)
there appears to be a correlation between the RF properties and the DC properties, suggesting that the origin of poor RF and DC properties is related. For example, Young et al. (1991) have noted that high values of the RF quality factor Q correlate with high values of both the superconducting transition temperature and the critical current density. One possible explanation of this is that the RF losses are dominated by weak coupling across any grain boundaries and the additional impedance is inversely proportional to the Ic R product of the boundaries, and to the grain size (Hylton and Beasley, 1989).
15.6 Polycrystalline Materials Very soon after the discovery of the superconducting cuprates, it was found that the transport critical current densities of the polycrystalline forms were substan-
tially lower than those obtainable when using single crystals and epitaxial thin films. Furthermore, the presence of even relatively small magnetic fields caused the transport critical current density of the polycrystalline materials to be reduced even further. Such characteristics, which severely limit possible large-scale applications of the polycrystalline material, are now recognized to be a feature of all the cuprate superconductors. It is also reported to be a characteristic of polycrystalline samples of BaPb^^Bi^Og (Takagi et al., 1990). This behavior is in marked contrast to that experienced with metallic superconductors, where the introduction of interfaces, especially grain boundaries, by deformation processes increased fluxpinning, and hence the transport critical current density. Indeed, well-annealed, single crystals of many of the metallic superconductors exhibit very low transport critical-current densities until flux-pinning
804
15 Oxide Superconductors
centers are introduced (Campbell and Evetts, 1972). As a result, it is increasingly clear that many of the transport and magnetic properties of polycrystalline cuprate superconductors are closely related to that expected for "granular" superconductors, i.e., materials consisting of superconducting grains separated by internal boundaries that impede the flow of current. In such superconductors, the low-field behavior is dominated by inter-grain shielding currents, but at higher fields the grains become decoupled from each other and the magnetization is essentially entirely due to intra-granular currents (Clem, 1988). Hitherto, granular superconductivity had only been observed in two-phase materials, such as oxidized aluminum films or lead films containing lead oxide (Deutscher, 1984), rather than in phase-pure materials. It is worth noting here that, very recently, granular behavior has also been reported in bulk, polycrystalline samples of PbMoS. The authors (Cattani et al, 1991) claim that the granular behavior is a consequence of the very short coherence lengths in the material and the presence of oxygen contamination. The granular behavior of polycrystalline cuprate superconductors imposes severe restrictions on their use in large-scale applications, since the maximum attainable critical current depends on the strength of the superconducting coupling between the grains. Much remains to be established about the weak-link nature of the coupling between grains, but for a Josephson-type of coupling the coupling strength is expected to increase with decreasing temperature. This suggests that the granular behavior becomes less marked as the temperature is lowered. It may be for this reason that the weak-link behavior is less apparent in the 2- and 3-layer bismuth superconductors at 4.2 K and the material can sustain a high
critical current in the presence of large magnetic fields, after appropriate texturing (Tenbrink et al., 1990; Jin et al., 1990; Sato et al., 1991). A further consequence of granular superconductivity behavior is that a number of the superconducting properties appear to display a "glassy" type of behavior. (Time-dependent properties, such as flux creep, are not in themselves a defining characteristic of glassy behavior although they are sometimes indicative of it.) The first evidence for glassy behavior in cuprate superconductors came from susceptibility measurements on L a - B a - C u - O ceramics (Miiller etal., 1987), which indicated that the susceptibility decayed with time after zero-field cooling, but not after cooling in a field. Subsequent measurements have indicated that this time dependence is observed above, but not below, the irreversibility line. 15.6.1 Microstructural Effects
In polycrystalline materials there are many factors that limit the attainable critical current density (see the review by Clarke et al., 1989). Among these are microcracks, formed as a result of crystallographically anisotropic thermal expansion, the presence of secondary phases, particularly intergranular phases, grain boundaries, and twin boundaries (Fig. 15-32). Microcracks can be avoided by aligning the grains or by using a grain size less than the critical grain size for microcracking (Shaw etal., 1989). Similarly, by careful compositional control the formation of secondary phases can be avoided (Clarke et al., 1989). In the case of materials formed by sintering, potential residual undecomposed carbonate at the boundaries can also be avoided by proper control of the ceramic-processing steps (Shaw et al., 1990). However, even after stringent control of all
15.6 Poiycrystalline Materials
805
Figure 15-32. Optical micrograph of a poiycrystalline sample of YBa 2 Cu 3 O 7 _^ prepared by sintering. The micrograph illustrates the variety of microstructural features that can be present in poiycrystalline materials, including grain boundaries, twins, second phases, and microcracks (micrograph courtesy of T. M. Shaw).
the processing steps, there still remain grain boundaries with a distribution of crystallographic misorientations. Particular attention has been paid to these boundaries, since they are believed to be the major source of weak-link coupling between the grains. Given the anisotropic crystal structures of the oxide superconductors and the known anisotropy of their electromagnetic properties, one empirical approach to enhance the overall intergranular coupling has been to texture the material so as to align the a b planes from one grain to the next. The basis for this approach was subsequently affirmed by the results of measurements for individual grain boundaries, as a function of crystallographic misorientation (see below). A number of texturing techniques have been explored for thin films and bulk materials. For bulk materials, these include magnetic orientation (Tkaczyk and Lay, 1990; Seuntjens and Larbalestier, 1990), sinter forging (or uniaxial pressure), a combination of rolling and reannealing (Osamura et al., 1991), or
growth from the melt (Murakami et al., 1989; Jin et al., 1988; Salama et al., 1989) in a temperature gradient or under a magnetic field. As an example, in the magnetic orientational technique (Arendt et al., 1988) a sintered oriented ceramic is produced by allowing small powder particles to settle in a liquid under the influence of a magnetic field, using the magnetic field and the anisotropy of the normal-state susceptibility to orient the particles (Livingston et al., 1988). After the liquid has been evaporated the resulting cake is sintered, resulting in a textured ceramic that is highly anisotropic in its properties (Ekin et al., 1987; Tkaczyk and Lay, 1990). The current densities in textured ceramics have, so far, been rather disappointing from a practical point of view, being typically less than 2000 A/cm2 at 4.2 K in a field of 1 T, and still showing the rapid falloff of Jc with magnetic field typical of granularity. Ekin et al. (1989,1990) have shown that there exist two regimes in which a drop-off occurs. At very low magnetic fields the Jc is independent of the
806
15 Oxide Superconductors
field up to the value (< 1 mT) at which the coupling between the grains is broken, leading to a sharp decrease in the critical current. In an intermediate regime the critical current density is almost field-independent, only to fall again and approach zero as the upper critical field of the grains is reached (at very high fields). This behavior has been measured for samples of YBa 2 Cu 3 O 7 _ 5 , Tl 2 Ca 2 Ba2Cu 3 O 10 (nominal composition) and Bi0 7 Pb 0 ^SrCaCUi 8 O by Ekin et al. (1989), and some of their data are reproduced in Fig. 15-33. In the intermediate regime, the behavior of the material is strongly hysteretic, depending not only on the value of the magnetic field, but also on its previous history (McHenry et al., 1988). Taken together, these and other related results indicate that texturing has not yet been carried out to the extent necessary to remove the weak links, at least in the YBa 2 Cu 3 O 7 _^ materials. Greater success has been achieved with the two- and threelayer bismuth cuprates, both by severe deformation (in silver tubes) and by melt texturing, although above about 20 K the
current densities are small, due to thermally activated flux motion. The microstructural reason for this success is not known, but the weak links that are present in these materials are evidently less detrimental than those present in YBa 2 Cu 3 O 7 _,. At higher temperature there are indications that a true zero-resistance state does not exist in polycrystalline materials (Worthington et al., 1991). This conclusion is based on high-sensitivity current-voltage measurements, which show a change in the curvature of the V-I trace, indicating that a zero-resistance state could exist only below a line in the H-T diagram that the authors refer to as the "glass-transition" line. Similar results have also been obtained for epitaxial thin films (Koch et al., 1989), although these do result in a different glass-transition line. 15.6.2 Current Densities Across Single Grain Boundaries
As mentioned above, the major source of granularity in YBa 2 Cu 3 O 7 _ 5 has been
Figure 15-33. Critical current densities, measured at 76 K, for three polycrystalline oxide superconductors as a function of the magnetic field. All three show characteristic double-step behavior, seen as a ! sharp drop at low fields (due to the destruction of weak links), a plateau region, and then a further drop at high fields, with the latter attributed to flux-flow (after Ekin etal., 1989).
10" 10
Magnetic Field (T)
15.6 Polycrystalline Materials
identified as being grain boundaries (Dimos et al., 1990; Babcock et al., 1990). Similar, but less direct, evidence has been obtained for the boundaries being the cause of granularity in the other oxide superconductors, including the cubic BaK^^Bi^C^ compounds. The most-compelling experiments indicating the weak-link behavior of grain boundaries in YBa2Cu3O7_<5 are those reported by Dimos et al. (1990). By using lithographic techniques to define four terminal conductors on either side of, and across, single grain boundaries in templated thin-film bicrystals, they were able to make direct measurements of the coupling across the boundaries. They found that, for all but the smallest misorientations, the grain boundaries behaved as superconducting weak links, with a temperature dependence close to that predicted for superconductor - normal - superconductor (SNS) models in which the width of the weak link is comparable to the coherence length (Ambegaokar and Baratoff, 1963; Likharev, 1979) (Fig. 15-34). As further evidence for weak-link behavior, Dimos et al. (1990) showed that the grain-boundary
LO
0.2 -
807
critical current was extremely sensitive to small magnetic fields, and also displayed hysteresis when the field direction was reversed. Furthermore, these workers found that the misorientation angle across the boundary determines the ratio of the Jc value across the boundary to the Jc value inside of the grain. Their data for various crystallographic misorientations are reproduced in Fig. 15-35. The nature of the boundary (i.e., whether twist or tilt) seems to have very little influence on the criticalcurrent characteristics, and so they concluded that the misorientation angle is the major parameter determining the weaklink behavior. However, transport critical-current measurements on polycrystalline (but textured) thin films of YBa2Cu3O7_<5 on MgO substrates by Chan et al. (1989) and Shin et al. (1990) demonstrated that there also exist grain boundaries that do not impede current flow, but the particular boundaries in question were not identified. A similar finding was also made from critical-current-density measurements of flux-grown bulk bicrystals (Babcock et al., 1990).
Figure 15-34. Normalized critical current density, as a function of temperature, measured for different grain boundaries (GBs) in YBa 2 Cu 3 O 7 _ 5 . • Grain boundary with 5° crystallographic misorientation, • grain boundary with 10° crystallographic misorientation, and A grain boundary with 15° crystallographic misorientation. The curves labeled AB and SNS refer to the models of Ambegaokar and Baratoff (1963), and Likharev (1979), respectively (reproduced with permission from Dimos et al., 1990).
808
15 Oxide Superconductors 10°
Figure 15-35. The critical current density across individual grain boundaries as a function of their total crystallographic misorientation for YBa 2 Cu 3 O 7 _ 5 , measured at 5 K. The critical current density Jf3 is normalized by the critical current density of the grains on either side of the boundary, JCG. • Tilt about (001), • tilt about (100), and A twist about (100) (after Dimos et al., 1990).
2
10-
10
20
30
40
Misorientation angle (deg)
Again, apart from the occasional grain boundary, the general characteristics of the bulk bicrystal boundaries resemble closely the behavior of the thin film bicrystals of Dimos et al. (1990). Considerable information has now been obtained on the electrical and superconducting characteristics of individual grain boundaries. In addition to the findings of Dimos et al. (1990) Russek et al. (1990) and Char et al. (1991 a, b) have made systematic measurements of the current-voltage (I-V) characteristics of grain boundaries. They find that boundaries with a low critical current density have I-V characteristics similar to ideal resistively shunted junctions (RSJs), while those with higher current densities are more akin to that expected for one-dimensional flux creep and flux flow. For all of the boundaries, the critical current density is found to be proportional to the resistive voltage (i.e., the IcRn product) across the boundary. An example of this correlation is shown in Fig. 15-36, for the tilt boundaries found in films grown on MgO substrates (Moeckly
et al., 1993). This is in marked contrast to the properties of conventional Josephson junctions, for which the critical current density J c is independent of the Jc jRn product. In addition, the actual values of the / c jRn product, which range over about two orders of magnitude (10" 1 to 10 mV), are for the most part much less than that measured for a normal superconductor-insulator-superconductor junction, suggesting that the boundaries are composed of weaklink regions (microbridges) separated by large insulating regions whose thickness is greater than the coherence length (Russek etal., 1990; Halbritter, 1990). A model for certain grain boundaries acting as strong boundaries was presented by Eom et al. (1991), in which currents flow only in the C u - O planes. A twist boundary, where the grains are twisted about the <100> or <010> axes, would present a configuration on which every Cu-O plane on one grain has many contacts with other Cu-O planes in the other grain, thus always taking advantage of the longer coherence length along the a b direction. If no
15.6 Polycrystalline Materials
809
Figure 15-36. The relationship between the transport critical current densities across tilt boundaries in YBa 2 Cu 3 O 7 _ 5 epitaxial thin films, and their corresponding ICR products. • 45° tilt boundaries, and + 27° tilt boundaries (plus others). The solid line corresponds to a slope of 0.5, indicating that Ic R oc Jc1/2 (after Moeckly et al, 1993). Jc(A/cm2)
other boundaries were present in the sample then current also would not have to travel along the c-axis, the direction in which the coherence length is shortest. It has proved to be very difficult to find microstructural reasons for the weak-link behavior of grain boundaries. Except for the obvious presence of secondary phases at certain boundaries in ceramic samples, the grain boundaries appear to be similar to those in other crystalline materials. Examination of the crystallographic misorientation in flux-grown bicrystals reveals a preference for angular misorientations similar to those found for the coincidence site lattices of cubic materials (Smith et al., 1988). Grain-boundary dislocations have also been observed as expected (Chisholm and Smith, 1989). Two geometrical explanations have been proposed for the poor coupling across the grain boundaries. One is that the local strain field around grainboundary dislocations depresses the superconducting pair-potential in the immediate vicinity of the dislocation. A natural explanation for the angular dependence of the critical current density is that as the misorientation increases, the spacing between the dislocations decreases, as does the fraction of the area that remains superconduct-
ing. Although not inconsistent with the angular-dependence data shown in Fig. 15-35, the magnetic-field dependence indicates that the weak links are inhomogeneously distributed along the boundaries, in contrast to the regular and rather small (i.e., nanometer) spacings that would characterize a dislocation-based model. A second geometrical model has been presented by Zhu et al. (1991), which leads to a reduction in the oxygen concentration at the boundary. Since the lattice parameter of YBa2Cu3O7_<5 depends on the oxygen content, the coincidence-site lattice of a grain boundary must also change with oxygen content. This is must in turn lead to a strain at the boundary. Zhu et al. (1991) point out that there could be circumstances in which, in order to lower the boundary energy, the oxygen stoichiometry in the boundary will change. Such a change would, in turn, change the superconducting properties of the boundary. Quantitative microanalysis, carried out on a nanometer scale in polycrystalline materials by Babcock and Larbalestier (1989), shows that the boundaries are mostly "clean", but do show changes in the stoichiometry, not only across the boundary, but also along the length of it. How-
810
15 Oxide Superconductors
ever, there are difficulties associated with microanalysis in the TEM at spatial resolutions of the order of the superconducting coherence lengths (approximately 1 nm). A resolution of 1 nm is at the limit of existing microscopes, the power densities in a nanometer probe are enormous, and the threshold energy for displacement damage, particularly of oxygen atoms, is close to the energy of the electron beam. Nevertheless, recent microanalyses, such as that of Zhu etal. (1991), using electron energy-loss spectroscopy from regions as small as about 1 nm, indicated a deficiency in oxygen (in the grain boundaries examined) that is consistent with the known sensitivity of the superconducting properties to oxygen concentration. The important role of oxygen in determining the attainable critical current density has been further implicated in three other experiments. In the first, Kawasaki et al. (1991) annealed thin-film bicrystals in ozone and noted an increase in the grainboundary critical current density. With time, the critical current density decreased, presumably with loss of the additional oxygen introduced by the annealing treatment. Larbalestier et al. (1991) also find a strong dependence of the critical current density on oxygenation treatment. In the third experiment, the passage of high current densities in the normal state (at 300 K) across grain boundaries, was found to affect the transport critical current density in the superconducting state (Moeckly et al., 1993). An electromigration threshold is found, below which the critical current density across the boundary is increased, and above which it is decreased. The effect of the normal-state current is attributed to the electromigration of oxygen, which above the threshold level leads to disorder of the oxygen ions in the vicinity of the boundary.
15.6.3 Modeling As described above, many of the macroscopic properties of the oxide superconductors are consistent with their being granular superconductors. Furthermore, the fact that individual grain boundaries behave as superconducting weak links provides a justification for using models of granular superconductors in which the superconducting wave function is assumed constant in the crystalline grains, and each grain is weakly coupled to the next. Clem (1988) has introduced a simple continuum model to represent the granularity in the cuprates, incorporating crystallographic anisotropic properties in the grains, and used it to calculate several magnetic properties. Likewise, Halbritter (1990) has considered the high-frequency properties of a granular superconductor and used the same model to deduce the density of weak links, and their critical fields, from experimental data. In continuum approaches such as these, the coupling between grains is assumed to be constant from one grain to the next, as are the properties of each grain. In practice, for any of the oxide superconductors, especially those made by ceramic routes, considerable variability in the properties of the grain boundaries, grain morphology, crystalline orientation, texture and topology of interconnections can be expected. The effect of these variabilities is expected to have the greatest impact on percolative properties, such as the transport critical current density, and less on spatially averaging properties. Thus, in order to investigate how changes in materials parameters, such as microstructure and texture, affect the superconducting properties, more sophisticated models are required. One such model consists of a network of Josephson junctions, in which the coupling is varied
15.6 Polycrystalline Materials
from one junction to another in order to represent, for example, the variability in weak-link coupling between the grains. This approach is justified by the experimental findings that grain boundaries, in many cases, have I-V characteristics similar to those of an ideal resistively shunted Josephson junction (McCumber, 1968; Stewart, 1968). If each grain boundary is represented by a single Josephson junction, then the array of Josephson junctions represents the dual of the grain structure (Nichols and Clarke, 1991) thereby formalizing the relationship between the physical microstructure and the Josephson-junction array. Two groups have sought to incorporate a dependence of transport critical current density on grain boundary misorientation (Mannhart and Tsuei, 1989; Nichols and Clarke, 1991). Mannhart and Tsuei assumed a random network of Josephson junctions and estimated the upper and lower limits to the critical current of the network using topological constraints to the percolative current. Using this approach, they were able to predict the critical current density of polycrystalline fibers as a function of average grain size, on the basis of a random distribution of grains (Fig. 15-37). The approach adopted by Nichols and Clarke (1991) was to assume a regular lattice of Josephson junctions, but to orient the grains at random. They then used the experimental results of Dimos et al. (1990) to assign values for the Josephson coupling at each junction, according to the calculated misorientation between adjacent grains. The current flow through the array of junctions, each represented as a resistively shunted junction, was then computed to determine the critical current density. An important result of both approaches is that the critical current density of a polycrystalline material is not neces-
811
Average Grain Length (|iim) Figure 15-37. Calculated maximum and minimum values of the critical current densities of a polycrystalline fiber of an oxide superconductor, as a function of the average grain size (assuming that the grains are coupled by Josephson junctions). The fiber, consisting of "pie-shaped" grains, has a diameter of 2 um, and the maximum critical current density of any grain boundary is 106 A/cm2. The data points correspond to the computed values, while the curves are lines drawn through the points to help guide the eye (after Mannhart and Tsuei, 1989).
sarily the same as that of the grain boundaries, and that higher values than the average critical current density of the boundaries can be achieved by texturing. The physical basis of this conclusion is that the higher-current-carrying boundaries can shunt excess current around those with low critical current densities. This would also be the case if the boundaries acted as current-limiting switches, rather than as Josephson junctions, i.e., if the phase of the supercurrent across the junction were ignored. It can be expected that modeling the superconducting properties of polycrystalline materials so as to specifically incorporate their materials properties, will become increasingly important and begin to guide further development of these materials for critical-current applications. There exists, in addition to the continuum models, such
812
15 Oxide Superconductors
as Clem's model for granular superconductors (Clem, 1988), a rich literature of Josephson and superconducting-network models that have been explored in the last decade but remain to be applied to the design of materials. These models include ones treating the effects of disorder on the percolative and magnetic properties of networks (de Gennes, 1981; Alexander, 1983). Granular models also exist for the magnetic response of weakly coupled superconducting clusters that exhibit spin-glass behavior (Ebner and Stroud, 1985; Morgenstern et al, 1987).
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