Intermetallics Research Progress

INTERMETALLICS RESEARCH PROGRESS

INTERMETALLICS RESEARCH PROGRESS

YAKOV N. BERDOVSKY EDITOR

Nova Science Publishers, Inc. New York

Copyright © 2008 by Nova Science Publishers, Inc.

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Library of Congress Cataloging-in-Publication Data Intermetallics research progress / Yakov N. Berdovsky, editor. p. cm. ISBN-13: 978-1-60692--4 1. Intermetallic compounds. 2. Alloys. I. Berdovsky, Yakov N. TA483.I68 2007 620.1'6--dc22 2007034989 

Published by Nova Science Published by Nova Science Publishers, Publishers, Inc. ;Inc. New YorkNew York

CONTENTS Preface

vii

Chapter 1

High Temperature Corrosion of Intermetallics Zhengwei Li and Wei Gao

Chapter 2

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds Igor S. Golovin

Chapter 3

Nonstoichiometric Compounds V. P. Zlomanov and A. Ju. Zavrazhnov

Chapter 4

Semiconducting Intermetallic Compounds ---with Special Interest in Silicides and Related Compounds Yoji Imai

1

65 135

175

Chapter 5

Ductile, Stoichiometric B2 Intermetallics Alan M. Russell

213

Chapter 6

Ultra Slow Dynamics in Intermetallic Thin Films Marcus Rennhofer

237

Chapter 7

Crystallization Behavior and Magnetic Properties of Fe-Based Bulk Metallic Glasses Mihai Stoica, Stefan Roth, Jürgen Eckert and Gavin Vaughan

Index

261

279

PREFACE Intermetallics is concerned with all aspects of ordered chemical compounds between two or more metals and notably with their applications. This book covers new and important research on the crystal chemistry and bonding theory of intermetallics; determination and analysis of phase diagrams; the nature of superlattices, antiphase domains and order-disorder transitions; the geometry and dynamics of dislocations and related defects in intermetallics; theory and experiments relating to flow stress, work-hardening, fatigue and creep; reponse of deformed intermetallics to annealing; magnetic and electrical properties of intermetallics; structure and properties of grain and interphase boundaries; the effect of deviations from stoichiometry on physical and mechanical properties; crystallization of intermetallics from the melt or amorphous precursors. Chapter 1 - Intermetallic compounds can be simply defined as ordered alloy phases formed between two or more metallic elements. These materials have different crystal structures from those of the constituent metallic components and exhibit as long-range ordered superlattices. Their relatively low density, high melting point, high specific strength and due ductility make them the promising high temperature structural materials for aviation and aerospace applications. Among the big family of intermetallics, Fe-Al, Ni-Al and Ti-Al systems are attracting most of the attention. The objective of studies is to develop and utilize these intermetallic compounds as a type of important structural material whose overall properties is between nickel-based superalloys and advanced ceramics. However, a balance cannot always be achieved between mechanical and environmental properties. For example, iron aluminides have excellent resistance against oxidation and hot corrosion, however, their strength is relatively low. The higher specific strength and modulus than conventional Ni-based superalloys make Ti-Al intermetallic compounds of interest for aero-engine components, but the oxidation resistance of Ti-containing intermetallics is much lower than desirable; thus a key factor in increasing the maximum temperature in service is enhancing their oxidation and hot corrosion resistance while maintaining the excellent mechanical properties. This chapter is then intended to give an overview on the major efforts made over the last 20 years on high temperature oxidation and protection of intermetallic compounds including Fe-Al, Ni-Al and Ti-Al. In particular, the focus will be given to Ti-Al systems. After a general introduction on the structural and mechanical properties, the studies on the oxidation behaviors of these intermetallic compounds will be summarized based on the experimental observation reported in open literature. The emphasis will be put on the effects of alloying

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element, microstructure and coating/surface treatment. It should also be noted that only high temperature oxidation properties in air or oxygen will be addressed; no discussion on hot corrosion, carburization, nitridation and sulfidation. In the concluding remarks, the prospects of development and application for intermetallic compounds will be briefly discussed. Chapter 2 - A short introduction into anelastic behaviour of metallic materials is given, and a method of mechanical spectroscopy is introduced for better understanding of relaxation and hysteretic phenomena discussed in this chapter. Several examples of anelasticity due to different structural defects in disordered Fe-based alloys (Fe-Al, Fe-Ge, Fe-Si) are considered with special emphasis on the analyses of the carbon Snoek-type relaxation with respect to ‘carbon - substitute atom’ interaction in iron. The effect of ordering of substitute atoms on anelasticity in Fe-based alloys is analysed in terms of substitute atom content and type of order. Anelastic behaviour of iron-based D03 (e.g. Fe3Al) and D019 (e.g. Fe3Ge) intermetallic compounds is reported for a wide range of temperatures and vibrating frequencies to identify damping mechanism. Contribution from interstitial and substitute atoms, dislocations and vacancies in ternary iron-aluminium based alloys Fe-Al-Me (Me = metal: Co, Cr, Ge, Mn, Nb, Si, Ta, Ti, Zr) are analysed. Study of elastic and anelastic behaviour is supported by structural characterisation (XRD, TEM, DSC, magnetometry) of studied alloys, also considering sources for high damping capacity of some compositions. The following anelastic phenomena are found in studied alloys and discussed in this chapter: the Snoek-type (caused by interstitial atom jumps in Fe-Me ferrite) and the Zener (caused by reorientation of pairs of substitute atoms in iron) relaxation, the vacancy and dislocation related relaxations, amplitude dependent magneto-mechanical damping. A family of low-temperature internal friction peaks recorded due to self interstitial atoms in ultra fine grained intermetallics is used to characterise thermal stability of severely deformed (Fe,Me)3Al compounds. These effects are discussed using data available from literature and the author’s experimental data in the Hz and kHz ranges of vibrating frequencies for Fe-Al, Fe-Ge, Fe-Si binary and several ternary systems in disordered and ordered ranges of the phase diagrams including intermetallic compounds of Fe3Me type. Chapter 3 - A key issue in materials research is the preparation of semiconducting solid, intermetallic and other nonstoichiometric compounds with predetermined composition, structure, and, hence, properties. In connection with this, this paper scrutinizes the concepts of stoichiometry, nonstoichiometry, and deviation from stoichiometry and the use of phase diagrams in selecting conditions for the synthesis of nonstoichiometric compounds. Since nonstoichiometry and properties of compounds are associated with defects, attention is also paid to defect classification and formation. The behavior of defects in solid oxides, chalcogenides, carbides, and other compounds of transition metals ranges from the point defect regime, controlled by entropy, to the enthalpy-controlled regime. To develop an appropriate theory of nonstoichiometric compounds, it is then necessary to address crystalchemical and thermodynamic issues. This paper is also concerned with the defect structure of highly imperfect nonstoichiometric compounds with a broad homogeneity range: the concepts of defect and structural transition due to defect interactions and temperature effect. The thermodynamic aspect of the problem includes criteria for evaluating the stability of imperfect nonstoichiometric solids. It is considered the specifics of the concepts of existing, stable, and metastable phases, spinodal decomposition conditions, and issues associated with phase equilibria in homologous series of compounds with narrow homogeneity ranges. The

Preface

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paper also deals with synthesis methods and criteria for evaluating the homogeneity of nonstoichiometric solids. Chapter 4 - A growing number of B2 intermetallic compounds has been reported to exhibit high room temperature tensile ductility in the polycrystalline form when tested in normal room air at ambient temperature. These are noteworthy findings, since poor room temperature ductility and low fracture toughness are major impediments to wider engineering use of intermetallic compounds [1]. Most intermetallic compounds can achieve high tensile ductility at room temperature only by means of one or more “contrivances”, such as testing single crystals, testing in an ultra-dry atmosphere, testing specimens with a metastable disordered crystal structure, or testing compositions that are off-stoichiometry or to which third elements have been added. The first of these inherently ductile compounds, AgMg, was reported in the early 1960’s to have good room temperature tensile ductility without the need for any of these contrivances. A few years later, even greater room temperature ductility was reported for another B2 compound, AuZn. Within the past few years, similar reports have been made for B2 CoZr and a large family of rare earth B2 intermetallics (DyCu, YAg, YCu, and several others). Most of these compounds share several common characteristics: substantial differences in the atomic radii and electronegativities of the two constituent elements; existence in the binary equilibrium phase diagram as a Daltonide, line-compound with no perceptible deviation allowed from precise equimolar stoichiometry; the absence of stressinduced twinning or shape-memory-type phase transformations; and a positive temperature dependence of yield strength above room temperature. This chapter describes the experimental findings reported for these materials; the factors thought to contribute to their high ductility; the commonly observed yield strength maxima at elevated temperatures; the strain aging effects seen in some of these materials; the potential applications these materials may have; and the possibilities that “lessons learned” from their study may suggest ductilizing strategies that could be applied to other intermetallic compounds. Chapter 6 - Diffusion studies on the mesoscopic and macroscopic scale were done up to now via radiotracer technique for a wide range of diffusivities. Nevertheless, the resolution of diffusion depths is limited by the detector efficiencies and sputtering resolving power. On the other hand scattering methods with atomic resolution like quasielastic Mössbauer spectroscopy, nuclear resonant scaterring and quasielastic neutron scattering have very limited range of accessible diffusion coefficients, especially for slow diffusion at low temperatures. The authors advantageously applied grazing incidence nuclear resonant scattering (GINRS) of synchrotron radiation for the study of iron self-diffusion in technically most promising intermetallic thin films (L10-FePt, L10-FePd and B2-FeSi). The investigations are non-destructive and non-contaminating. It is possible to measure very low . The diffusion coefficients accessible rates of diffusion of about for investigation can be tuned in a certain range. The application of GINRS gives no direct access to jump frequencies and jump vectors of the diffusing atoms. Nevertheless, combining the method with results from "order-order" dynamics or Monte Carlo simulations allows the determination of the diffusion model. Chapter 7 - The expression “glass” in its original sense refers to an amorphous or noncrystalline solid formed by continuous cooling of a liquid, while a solid is defined somewhat arbitrarily as any body having a viscosity greater than 1014 Pa·s. A glass lacks three-

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dimensional atomic periodicity beyond a few atomic distances. It is characterized by a limited number of diffuse maxima in X-ray, electron and neutron diffraction and no sharp diffraction contrast in high-resolution electron microscopy. The glass-forming tendency varies widely. Some oxide mixtures form a glass at normal slow cooling rates of ~1 K/min, while monoatomic metals with possible incorporation of impurities require rates as high as ~1010 K/s. During the solidification no essential change in spatial atomic configuration occurs. A glass may be considered as a solid with frozen-in liquid structure. It is in general not in an internal equilibrium state and thus relaxes structurally to a more stable equilibrium state whenever atoms attain an appreciable mobility. Furthermore, a glass is metastable with respect to crystalline phase(s) and transforms to the latter upon heating through nucleation and growth. As a result of the requirement for rapid cooling, amorphous alloys have usually been prepared in form of thin sheets with a thickness below 0.1 mm. In the last 10-15 years it was found that a number of transition metal-based alloy systems may form bulk metallic glasses (BMGs). These alloys require much lower cooling rates for amorphization or bypassing crystallization upon cooling. Fe-, Co- or Ni- based metallic glasses are good candidates for application as soft magnetic materials because of the lack of crystal anisotropy. Fe-based alloys able to form magnetic BMGs are of the type transition metal – metalloid and often contain 5 or more elements. Usually, the metalloid content is around 20 at.%. In some cases, the magnetic properties of such BMGs can be enhanced by partial devitrification upon heating at a constant rate or by isothermal annealing. The change in magnetic properties is due to structural changes induced upon heating/annealing. Usually, the Fe-based BMGs form intermetallic metastable phases at elevated temperatures, which finally transform into crystalline stable phases if the heating goes further. Despite several studies published in the literature about Fe-based BMGs and their magnetic properties, just few of them deal with crystallization behavior and crystallization kinetics. The aim of this work is to present the crystallization behavior of some Fe-based BMGs and to link the structural changes with modification of the magnetic properties.

In: Intermetallics Research Progress Editor: Yakov N. Berdovsky, pp. 1-64

ISBN: 978-1-60021-982-5 © 2008 Nova Science Publishers, Inc.

Chapter 1

HIGH TEMPERATURE CORROSION OF INTERMETALLICS Zhengwei Li and Wei Gao Department of Chemical and Materials Engineering, The University of Auckland, Private Bag 92019, Auckland, New Zealand

ABSTRACT Intermetallic compounds can be simply defined as ordered alloy phases formed between two or more metallic elements. These materials have different crystal structures from those of the constituent metallic components and exhibit as long-range ordered superlattices. Their relatively low density, high melting point, high specific strength and due ductility make them the promising high temperature structural materials for aviation and aerospace applications. Among the big family of intermetallics, Fe-Al, Ni-Al and Ti-Al systems are attracting most of the attention. The objective of studies is to develop and utilize these intermetallic compounds as a type of important structural material whose overall properties is between nickel-based superalloys and advanced ceramics. However, a balance cannot always be achieved between mechanical and environmental properties. For example, iron aluminides have excellent resistance against oxidation and hot corrosion, however, their strength is relatively low. The higher specific strength and modulus than conventional Ni-based superalloys make Ti-Al intermetallic compounds of interest for aero-engine components, but the oxidation resistance of Ti-containing intermetallics is much lower than desirable; thus a key factor in increasing the maximum temperature in service is enhancing their oxidation and hot corrosion resistance while maintaining the excellent mechanical properties. This chapter is then intended to give an overview on the major efforts made over the last 20 years on high temperature oxidation and protection of intermetallic compounds including Fe-Al, Ni-Al and Ti-Al. In particular, the focus will be given to Ti-Al systems. After a general introduction on the structural and mechanical properties, the studies on the oxidation behaviors of these intermetallic compounds will be summarized based on the experimental observation reported in open literature. The emphasis will be put on the effects of alloying element, microstructure and coating/surface treatment. It should also

2

Zhengwei Li and Wei Gao be noted that only high temperature oxidation properties in air or oxygen will be addressed; no discussion on hot corrosion, carburization, nitridation and sulfidation. In the concluding remarks, the prospects of development and application for intermetallic compounds will be briefly discussed.

1. INTRODUCTION Intermetallic compounds can be simply defined as ordered alloy phases formed between two or more metallic elements. These materials have different crystal structures from those of the constituent metallic components and exhibit as long-range ordered superlattices. In comparison with conventional metallic materials, intermetallic compounds have the advantages of low density, high melting point, high specific strength and due ductility, which make them the promising high temperature structural materials for automobile, aviation, and aerospace applications. The ordered nature of intermetallic compounds also exhibits attractive high temperature properties due to the presence of long-range-ordered superlattices, which reduce dislocation mobility and diffusion processes at elevated temperatures [1]. Aluminide based intermetallics are distinctly different from conventional solid-solution alloys. For example, Ni3Al exhibits an increase in yield strength with increasing temperature, whereas conventional alloys exhibit a general decrease in strength with temperature [2-3]. Nickel and iron aluminides also possess sufficiently high concentration of aluminium, thus the formation of a continuous and adherent alumina scale on the external surface of the material could always be achieved. In contrast, most of the alloys and superalloys capable of operating above 700oC in oxygen-containing environments contain less than 2wt.% aluminium, and invariably contain high concentration of chromium for oxidation protection with chromia. Nickel and iron aluminides therefore could provide excellent oxidation resistance at temperatures ranging from 1100 to 1400oC owing to their high aluminium contents and high melting points [4]. Among the big family of intermetallic compounds, Fe-Al, Ni-Al and Ti-Al systems are attracting most of the attention; and the objective of studies is to develop and utilize these intermetallic compounds as a type of important structural materials whose overall properties will be between nickel-based superalloys and advanced ceramics. However, a balance cannot always be achieved between their mechanical and environmental properties. For example, iron aluminides have excellent resistance against oxidation and hot corrosion, however, their strength is relative low. The higher specific strength and modulus than conventional Ni-based superalloys make Ti-Al intermetallic compounds of interest for aero-engine components, but the oxidation resistance of Ti-containing intermetallics is much lower than desirable at elevated temperatures. Thus a key factor for Ti-Al based intermetallics in increasing the maximum temperature in service is to enhance their oxidation and hot corrosion resistance while maintaining the excellent mechanical properties.

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3

2. IRON ALUMINIDES 2.1. Introduction Due to their excellent oxidation resistance first noted in 1930s [5-6], iron alumindes have been subjected to extensive studies with respect to structural and functiuonal applications [7]. Iron aluminide with an Al content around 25at.% corresponds to Fe3Al, which exists in DO3 structure and is stable in the compositions ranging from 22 to 36at.% Al and from room temperature to about 550oC [8]. Above 550oC, the DO3 structure transforms to an imperfectly ordered B2 structure, which ultimately changes to a disordered solid solution. In addition to their superior environmental resistance (oxidation and sulfidation), iron aluminides also offer the advantages of low material cost, conservation of strategic elements, and a lower density in comparison with stainless steels. Therefore they have long been considered for applications in the petrochemical industries, conventional power plants, coal conversion plants, automobile and other industrial valve components, catalytic converter substrates and components for molten salt applications [9-10]. However, limited ductility at room temperatures, a sharp drop in strength above 600oC, and inadequate high temperature creep resistance render their acceptance for structural applications [11-12]. Elements such as Nb, Cu, Ta, Zr, B and C were considered for precipitation strengthening; while Cr, Ti, Mn, Si, Mo, V and Ni were added into iron aluminides for solid solution strengthening. In general, the addition of elements either for precipitation strengthening or solid solution strengthening to improve high temperature tensile strength and creep resistance resulted in low room temperature tensile elongations [13-25]. Chromium was found to be an effective addition to enhance the ductility of iron aluminides at higher aluminium contents, and a combination of alloying elements might lead to the optimization of overall mechanical properties. Iron aluminide with an Al content ranging from 36 to 50 at.% corresponds to FeAl with a B2 structure at room temperature. FeAl intermetallic alloys are lower in density by as much as 30 to 40%, compared with steels and other commercial Fe-based alloys. Due to their much higher Al contents, they all exhibit much better corrosion and high temperature oxidation resistance than Fe3Al and other conventional Fe-based alloys. However, associated with their intrinsic grain-boundary weakness and high environmental embrittlement sensitivity, they suffer from low room temperature ductility. Their mechanical properties, such as yield strength, fracture strength, creep strength, ductility and toughness could be improved by alloying (B, Zr, Hf etc), by heat terement and/or thermomechanical processing through microstructural control, and/or by composite development using fine oxide dispersions [2644]. High temperature oxidation resistance of metallic materials relies essentially on the formation of a slow-growing and mechanically-stable external Al2O3, Cr2O3 or SiO2 scale on their surface. Studies on the phase stabilities in the Fe-Al-O system demonstrate that Al2O3 will form on iron aluminides even at extremely low oxygen partial pressures. In practice, it has been found that approximately 15at.% Al is needed to suppress internal oxidation and overgrowth of the alumina scale by iron oxides at 800oC [45]. Obviously, the Al content in Fe3Al, FeAl and derived alloys are well in excess of this critical concentration; and as expected, alumina can form readily at temperatures above approximately 500oC upon exposure to oxidizing environments [46-48]. This alumina scale can provide superior

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corrosion resistance to iron aluminides not only in air or oxygen, but also under a variety of mixed gas and salt conditions. However, under real corrosion conditions, the protecvitity of this alumina scale will be dependent on its rate of formation and growth, its uniformity, and more importantly its adherence to the underlying alloys when undergoing thermal cycling. It is well known that alumina has many thermal stable and metastable phase structures. The predominant oxide formed on iron aluminides below 900oC is found to be γ- or θ-Al2O3, while α-Al2O3, the most thermaldynamically stable phase, forms after oxidation at temperatures higher than this level [46, 49-50]. The addition of Cr to Fe-Al based alloys can decrease the critical Al concentration for the formation of pure Al2O3 and reduce the oxidation rate of alloys containing less than 19.5at.% Al [51]. However, for iron aluminides (Fe3Al and FeAl) with quite high Al contents, air oxidation behaviour might not be dramatically affected by the addition of Cr [52].

2.2. Oxidation of Fe3Al and Its Alloys Alloying Fe3Al with additional elements can modify its mechnical properties as well as its oxidation behaviours. For example, it was found that an addition of Cr might decrease the oxidation and sulfidation resistance of Fe3Al based alloys [48, 53-54]. Similarly, the addition of Ti, V and/or Mo degrades their oxidation resistance in air. However, it has been found that additions of small amount of reactive elements, such as Zr and Y, could generally result in improved high temperature oxidation resistance of Fe3Al based alloys [52]. In the following sections, the influences of various alloying elements on the oxidation behaviours of Fe3Al and its alloys will be briefly summarized.

2.2.1. Effect of Cr The mechanical properties of Fe3Al can be improved most efficiently by adding 2-6at.% Cr, together with thermomechanical treatment [55-57]. Babu et al. studied the influences of Cr on the high temperature oxidation resistance of Fe3Al in oxygen [58]. They found that Cr addition increased the mass gain during the initial oxidation stage, which was supposed to be the result of the formation of chromia in this stage or the faster θ → α transformation favored by hexagonal chromia. Tortorelli and DeVan also observed that addition of Cr, even at concentrations as high as 10at.%, was detrimental to the oxidation resistance of Fe3Al between 800 and 900oC [48]. This was due to a faster oxygen uptake during initial stages, leading to overall higher parabolic constants. Velon et al. evaluated the role of Cr during the early stages of oxidation of Fe3Al containing 2 and 4 at.% Cr in dry air at 500oC [59], they concluded that the addition of 2 and 4% Cr increases the oxide growth rate of Fe3Al. At 500oC and low Cr content, the oxides, Cr2O3 and Al2O3, having the same corundum structure form a complete solid solution. It is therefore suggested that Cr2O3 forms a mixed oxide with Al2O3 by substitution of Al3+ by Cr3+. The oxidation resistance of Fe3Al at 500oC is then lost by the breakdown of the protecting properties of the continuous alumina layer because of the presence of Cr, leading to a faster diffusional transport of Fe ions through the mixed oxide (Al,Cr)2O3 layer compared to pure Al2O3 and growth of Fe oxides at the surface. Lee et al. also studied the oxidation Fe3Al containing 0, 2, 4 or 6at.% Cr at 1000oC in air [60]. The oxidation rate increased in the order of Fe28Al, Fe28Al6Cr, Fe28Al2Cr and Fe28Al4Cr. Cr

High Temperature Corrosion of Intermetallics

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therefore was not beneficial to oxidation resistance. The oxide scales that formed on Fe3Al-Cr alloys consisted primarily of α-Al2O3 containing a small percentage of Fe and less than 1% of Cr. The higher Fe concentration and the alloying with Cr are expected to give more foreign ion contamination in the alumina scale, leading to a higher growth rate. These scales were also non-adherent and fragile.

2.2.2. Effect of Ti An addition of Ti to Fe3Al could significantly affect the DO3-B2 transition temperature and change the phase fields as well as the thermal anti-phase boundary microstructure [6165]. Studies also indicated that Ti addition has prounced effects on the mechanical, trobological and aqueous corrosion properties of Fe3Al based alloys [66-72]. High temperature oxidation study showed that the parabolic rate constant of the Ti-bearing Fe3Al alloy was higher than that of unalloyed Fe3Al [58]. The presence of Ti influenced the initial oxidation stage and acted as a getter for oxygen since the free energy for the formation of Ti oxide is more negative than that of Fe. The oxide scale was adherent and composed of equiaxed grains and some nodules. The surface oxide predominantly contains Al with a small amount of Ti and traces of Fe, while the nodules contain a large amount of Ti, certain amount of Al and trace of Fe. The enhanced scale adherence by Ti alloying however was not clear. 2.2.3. Effect of carbon Iron aluminides produced recently by an electroslag-remelting process (ESR) were found to have improved strength when carbon was added as an alloying element [73-74]. This has been attributed to solid solution strengthening by the interstitial carbon atoms at low concentrations and precipitation hardening at high concentrations of carbon atoms. These alloys were further shown to exhibit a reduced susceptibility to environmental embrittlement. The authors have attributed the reduced susceptibility to the presence of carbides in the aluminides, although no study has been undertaken to examine the role of carbides. The effect of carbon on the oxidation behavior of Fe3Al alloys in the temperature range 700-1000oC in air has also been investigated by these authors [75-77]. In general, carbon is very detrimental to oxidation resistance of Fe-Al alloys, especially when the Al content is low. Fe3AlC0.69 carbide in Fe-Al-C alloys contains less Al than the Fe3Al matrix. About 30at.% Al of the carbide is replaced by C, probably making the carbide prone to oxidation attack [78-79], though no detailed studies had been found to correlate the Al content of carbide to its oxidation resistance. The difference in thermal stabilities of Fe3AlC and Fe3Al at the oxidizing temperatures might affect the overall oxidation behavior of the materials. However at higher temperatures, the carbide might decompose to Fe3Al, leading to a reduction in its volume fraction and offsetting the temperature effect in enhancing the oxidation tendency of the alloy. 2.2.4. Effect of RE Elements Yu et al. investigated the effects of cerium (Ce) addition on the oxidation resistance of Fe3Al-based alloys. The RE addition is aiming at the improvement of their oxidation resistance at the temperature above 1000oC [80]. In comparison with the Ce-free alloys, the most important features caused by a small amount of Ce addition are: (1) the oxidation rate decreases notably; (2) the alumina scale adherence is improved significantly; and (3) the

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ability of the oxide scale resisting to varied stress impact is improved. The authors believed that Ce addition has an effect on preventing outward diffusion of cations through the shortcircuit paths during oxidation and then the scale on the alloy may develop primarily by inward anion transport. This accounts for the elimination of cavities in the near oxide scale/alloy substrate interfacial area and the dramatic improvement in scale adhesion. Ce addition to the Fe3Al based alloys also results in significant refinement of oxide grains and reduction of Fe or Cr oxides in the alumina scale, which improves the strength of an alumina scale, due to the absence of cracks on the scales and a significant decrease of the oxidation rate. The effect of Y addition on the oxidation behavior of Fe3Al alloys was investigated in terms of oxidation rate and oxide adhesion in the temperature range of 800 to 1100oC by Kim et al [81-82]. The oxidation rates of these unalloyed and alloyed Fe3Al intermetallics are basically the same, however, the stabilities of the thermally grown oxide scales are quite different. Oxide layers formed on the Y-free Fe3Al alloys were severely convoluted and the alloy substrates were partially exposed due to scale spallation. The interface is wavy and the surface of the substrate is deformed due to the stresses generated during oxidation and cooling. Meanwhile, the oxide scales formed on the Y-containing Fe3Al alloys were flat, dense and adherent to the underlying alloy substrates. And the oxide scale/substrate interface seems to be straight with little deformation. Pegs at the oxide scale/substrate interface were also observed in Y-containing alloys. The pegs are enriched with O, Al and Y, and deficient in Fe, and are developed at the grain boundaries of the substrate near the oxide scale/substrate interface due to internal oxidation. The authors believed that the growth of oxide scales on Yfree alloys was governed by the countercurrent diffusion of Al and O. This growth mechanism indicated that new oxides would be formed in the oxide scales, and large stresses could be generated in the scales during oxidation, which may eventually lead to spallation of alumina scale. Y addition changed the growth process to predominant oxygen diffusion, leading to the formation of pegs and lower oxide growth stresses which then enhanced the adhesion of alumina scale to the alloy substrate. The influences of addition of mischmetal (a mixture of rare earth elements, 43wt.% Ce, 23 La, 18 Nd, 5 Pr, 3 Sm and 8 Fe) to Cr-alloyed iron aluminide (Fe-28Al-2Cr) on its high temperature oxidation behavior in oxygen were also studied [83]. The addition of mischmetal (Mm) to Cr-alloyed iron aluminides decreased the isothermal oxidation rate of the intermetallic compound in pure oxygen at 1057oC to the same level as that of the base intermetallic. The improvement in oxidation resistance due to Mm addition has been attributed to the lower rate of oxidation in the initial stages of oxidation.

2.2.5. Effect of RE Oxides Extensive studies with oxide dispersion strengthened Ni-based and FeCrAl-based high temperature alloys suggest that the creep resistance of materials could be dramatically improved by dispersion of fine stable oxide particles, such as Al2O3, Y2O3 and/or Y2O3-Al2O3 [84-88]. The use of reactive element oxide dispersions has also significantly improved the oxidation resistance of various Al2O3-forming alloys such as FeCrAl [89-91] and NiCrAl [9293]. Small additions of reactive elements such as Zr, Y or Ce to Fe3Al have been found to promote the oxide scale spallation resistance. The high temperature oxidation behavior of oxide dispersion-strengthened Fe3Al alloys has been characterized by Pint et al [94-96]. The results indicated that Al2O3 dispersion did not produce any typical RE effects though Al2O3

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dispersion flattened the thermally grown α-Al2O3 scale. The oxide scale formed at the same rate and had the same morphology and grain structure as a scale formed on an undoped Fe3Al alloy. The Al2O3-dispersed alloy also exhibited a shorter lifetime than that of the cast and undoped alloy. The lifetime was reduced as the Al2O3 content increased. This may be a result of particle coarsening. Large Al2O3 particles in the substrate may allow rapid transport of oxygen into the substrate when these particles come into contact with the scale. The addition of Y2O3 improved the alumina scale adhesion relative to a Zr alloy addition at 1200 and 1300°C. However, the Y2O3 dispersion was not as effective in improving scale adhesion in Fe3Al as it is in FeCrAl. This inferior performance is attributed to a larger amount of interfacial void formation on ODS Fe3Al. However, it appears that the large coefficient of thermal expansion (CTE) of ODS-Fe3Al alloy is the major reason for the great tendency for scale spallation. The stress generated by the CTE mismatch was apparently sufficient to lead to buckling and limited loss of scale at temperatures up to 1100oC, with an increasing amount of substrate deformation at 1200oC and above. This deformation led to increased scale spallation by producing an out-of-plane stress distribution, resulting in cracking or shearing of the oxide.

2.3. Oxidation of FeAl and Its Alloys 2.3.1. Effect of Ti Alloying with Ti could significantly improve the mechanical properties of FeAl alloys, for example, the high temperature creep resistance could be enhanced and superplasticity was observed by optimizing chemical composition and heat treatment processes [97-101]. The influence of Ti addition on the high temperature oxidation behavior of FeAl intermetallic alloys in air at 1000oC and 1100oC has also been investigated [102]. The parabolic rate constants show that the oxide scale formed on the surface of Fe-36.5Al-2Ti (at.%) alloy has a better protective effect than that of Fe-36.5Al alloy. There is only α-Al2O3 on Fe-36.5Al alloy while there are α-Al2O3 and TiO on Fe-36.5Al-2Ti alloy. In Fe-36.5Al alloy the Al2O3 grains are much finer than those in the Fe-36.5Al-2Ti alloy, which leads to the fast growth of Al2O3 scale. The authors therefore believed that Ti addition has a beneficial effect on improving the oxidation resistance of FeAl alloy and the positive influences of Ti can be summarized as the followings: (1) Ti addition can significantly improve the compactness of thermally grown oxide scales on the surface; (2) TiO has a better adherence to the substrate of FeAl alloy, leading to a better spallation resistance; (3) the coefficient of thermal expansion of TiO (10×10-6/K) is between α-Al2O3 (6×10-6/K) and FeAl (21×10-6/K). Therefore TiO in the oxide scale can reduce the thermal expansion difference between the oxide scale and the base alloy, resulting in reduced thermal stresses; and (4) Ti addition may improve the toughness of the oxide scales, therefore reducing the possibility of oxide scale fracture. 2.3.2. Effect of REs The effects of rare earth alloying elements, such as Hf, Y or Zr on the oxidation behavior of FeAl alloy have been studied by some researchers [103-105]. Smialek et al. studied the oxidation behaviors of Fe-40at.%A1 alloys doped with 1Hf, 1Hf + 0.4B and/or 0.1Zr + 0.4B at 900, 1000 and 1100oC. During isothermal oxidation, the Zr-doped alloy spalled extensively

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at all three temperatures, while the Hf- and B-doped alloy spalled only at 1100oC. During cyclic oxidation tests, formation of HfO2 particles within the scales associated with the oxidation of Hf-rich precipitates, A16Fe6Hf, in the alloy accelerated the scale spalling problem. Zr and/or B containing alloys were also lack of good cyclic oxidation performance and the large thermal-expansion mismatch between Al2O3 and FeA1 was the main concern for scale stability subjected to fast thermal cycling. In the tests with smaller amount of cylces, Xu’s results while indicated that addition of Y and/or Zr increased the scale spallation resistance of Fe-37at.%Al at temperatures ranging from 1000 to 1200oC significantly [104105]. FeAl alloys containing Zr did not show any spallation in this temperature range though the oxidation mass gain was slightly increased. The preferential oxidation of Y or Zr at the FeAl grain boundaries formed the teethlike oxides and played a role of ‘pinning’ centres and enhanced the adhesion of the oxide scales to the alloy substrate. Incorporation of Y or Zr in the scale/substrate interfacial area may change the nature and microstructure of the interface and prevent vacancy condensation. It was also supposed that doping of Y or Zr could improve the toughness of Al2O3 scales and reduce the tendency of scale fracture. Fine oxide dispersions (less then 50 nm) have been widely used to improve the creep strength of FeAl alloys at high temperatures [106-109]. Fe-40Al alloys with and without Y2O3 dispersion (0.5wt.%) were prepared by mechanical alloying and their isothermal and cyclic oxidation behaviors were characterized in the temperature range of 756 to 1118oC [110]. The ODS FeAl, in general, had a slightly higher oxidation rate than the FeAl alloy in the isothermal oxidation tests. Formation of cavities and voids was observed on the surfaces of both materials after oxidation and the addition of Y2O3 did not change the morphology and transport mechanism of the oxide scale. A higher content of Y2O3 dispersion in FeAl (1.0wt.%) however, may lead to enhanced oxidation properties at 1100oC as shown in Montealegre’s work [111]. In this study, the scale growth rate of the ODS FeAl is considerably lower than that of PM 2000, and this is the result of the development of a chemically purer alumina scale or one with a lower density of defects. The formation of dense scales on this ODS FeAl alloy is not accompanied by the void formation at the oxide scale/alloy interface, commonly observed in FeAl alloys after oxidation [112-114], so that a good adherence of the oxide scale to the alloy substrate can be inferred. However, the large differences in the thermal expansion coefficients of the oxide scale and the substrate still generate significantly large stresses during cooling and eventually lead to a strong tendency for spallation. This ODS FeAl alloy had been studied further between 750 and 1000oC in artificial atmospheres (20% oxygen + 80% nitrogen) [115]. The results confirmed that 1wt.% Y2O3 addition could decrease the isothermal oxidation rate of FeAl and increase the scale spallation resistance. Morphological observations suggested that the cation mobility might not be completely suppressed and could still have a contribution to the oxide scale formation. This result is further supported by Pedraza’s study [116]. The effects of Y2O3 content might be summarized as: (1) at lower temperatures, the increase of the Y2O3 content promotes the fast formation of α-Al2O3, leading to a more protective and thinner scale with a significant decrease of the oxidation rate; and (2) at higher temperatures, the increase of the Y2O3 content decreases the average grain size of the scale, hence yielding a relatively thicker scale due to enhanced reactant diffusion [117]. The most striking feature is the absence of scale spallation either during oxidation or during cooling of thin Fe-40Al foils [118-119], which contrasts with the spallation observed during the oxidation of massive specimens of similar aluminides at temperatures above

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900oC. The absence of scale spallation on the FeA1 foil was related to the fact that the alloy contains sufficient Zr [119] or to the changes in the dimensions of the specimens during oxidation [118], likely by a relaxation process of the residual thermal stresses by the creep of the substrate. However, partial scale spallation after relatively short exposures was still observed on Fe-40Al-1wt.%Y2O3 foil [120]. This has been attributed to the elevated residual compressive stresses induced by the difference in the thermal expansion coefficients of the alumina scale and the substrate. It was also believed that an ‘overdopping’ effect in the investigated alloy could not be discarded.

3. NICKEL ALUMINIDES 3.1. Oxidation of Ni3Al and Its Alloys 3.1.1. Introduction Ni3Al, which has an ordered fcc structure (L12), is one of the most attractive ordered intermetallics as high temperature structural materials due to its superior high temperature properties. The most attractive property of Ni3A1 is that its yield strength increases with increasing temperature from near ambient temperature, to approximately 600oC [121-123]. Single crystalline Ni3Al is highly ductile, whereas polycrystalline Ni3Al is brittle at ambient temperature and undergoes intergranular fracture. An extrinsic factor, i.e., environmental embrittlement, has been shown to be the major cause of low ductility and brittle intergranular fracture in binary Ni3Al. Alloying with B or Cr and/or grain refinement have been found to be the most effective way to improve the tensile ductility of Ni3Al when tested in air at room temperature [124-127]. Ni3Al can dissolve a substantial amount of alloying elements, and its mechanical and metallurgical properties can then be improved by controlling the solute concentration and second-phase formation [128-146]. The beneficial contribution of some typical alloying elements in Ni3Al alloys is described below [4]: (1) B: Reduces moisture-induced hydrogen embattlement and enhances the grain boundary cohesive strength; (2) Cr: Reduces oxygen embrittlement at elevated temperatures; (3) Hf: Provides high tmeprature strength through solid solution and prevents surface reaction of Zr with the ceramic shell material during investment casting by forming a protective oxide film; (4) Zr: Provides high temperature strength through solid solution, reduces solidification shrinkage and macroporosity through the formation of low melting point eutectic, and improves oxide spallation resistance during thermal cycling; and (5) Mo: Improves strength al low and high temperatures. In general, Ni3A1 has very high oxidation and corrosion resistance due to its high ability for the formation of α-Al2O3 scales which can ensure the isolatation of the alloy substrate from the aggressive enviroments. The phase composition of the alumina scales formed on Ni3Al however is relatively complex and is highly dependent on the oxidation conditions, in

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particular, temperature and time. At temperatures lower than 1000oC, the scales formed may consist mainly of an outer layer of NiO, an intermediate layer of NiAl2O4, and an inner layer of α-A12O3. Only α-Al2O3 will be formed on Ni3A1 at temperatures higher than 1200oC [147150]. During the initial stage of oxidation at low temperatures, NiO, NiAl2O4 and/or metastable transient (γ or θ) Al2O3 will form as commonly observed on Al2O3-forming FeCrAl alloys [151-159]. As the exposure time or the temperature increased, a phase transformation from these transient Al2O3 to the thermodynamically stable α-Al2O3 occurred. Thus the steady-state oxidation mechanism is governed by mass transportation through αAl2O3 grain boundaries, although the results may vary according to the real oxidizing conditions [160].

3.1.2. Effect of Alloy Production The production route of the alloys will exert some influences on the scaling behavior, therefore the uncertainties and discrepancies should be considered when collectively analyzing the oxide formation mechanism. Perez et al. studied the oxidation behavior of Ni3Al alloys prepared by power metallurgy [161-164]. Rapidly-solidified powders were produced by argon gas atomization. The powder was sieved and classified into different particle size. Particles were then canned and consolidated by hot isostatic pressing (HIPing) under 150 MPa pressure for 2 hrs at 1100oC. At low oxidation temperatures (<730oC), the oxide scale exhibited a three-layer structure: an outer NiO layer, an intermediate Ni layer, and an inner and thicker internal-oxidation-zone. The oxidation rate was controlled by diffusion through the outer NiO layer. At high temperatures, the oxide scale consisted of an outer NiO layer, an intermediate layer which depending on the temperature or exposure time may consist of a mixture of Ni and Al oxides or NiAl2O4, and an inner Al2O3 layer. At low temperatures, the exposure time and grain size can affect the oxide scale microstructure. For example, at 635oC, when the exposure was longer than 200 hrs, the scale would be composed of an outer NiO layer, an intermediate layer containing oxides of Ni and Al, and an inner healing Al2O3 layer. This healing layer could reduce the oxidation rate. As the particle size of the alloy decreased (<25 μm), the formation of the healing Al2O3 layer was enhanced due to the increased Al diffusion through grain boundary with a higher density. Thus the smaller the particle size, the smaller the oxidation rate. This mechanism is effective at low temperature range (<730oC). At higher temperatures (>830oC), there are no important variations between the mass gains of the materials with different particle sizes. However the cross sectional observations showed some differences, in general the thinnest scale corresponds to the smallest particle size alloy. At 930 and 1020oC, better oxidation behavior is evident for the coarser particle size materials. The number of scale intrusions in the substrate increased as the particle size decreased, leading to a more irregular oxide scale/alloy interface. These observations are opposite to that of Takeyama and Liu on fine- (17 μm) and large-grain (193 μm) specimens of Ni3Al oxidized at 1000oC for 15 min but consistent with those of Brill on the cyclic oxidation at 1000oC of cast and wrought Ni3Al [165-167]. 3.1.3. Effect of Alloying Elements Alloying Ni3Al with ternary, quaternary and quinary elements produces dramatic effects on oxidation resistance, scale adherence, ability to form an Al2O3 scale, and oxidation mechanisms.

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Addition of B is primarily to improve ductility of Ni3Al [125], and is often added in conjunction with other elements such as Cr, Hf, Ti or Zr, to improve strength [149, 168-169]. The addition of B to Ni3A1 was found not to improve the oxidation resistance and not to enhance the oxide scale adherence owing to the extensive formation of geometric voids on the substrate surface, although B addition improved the aqueous-corrosion resistance [170-172]. In conjunction with other elements, it seems to be beneficial [142, 173]. When added in relatively small levels, Cr slightly improves or does not degrade the overall oxidation behavior of Ni3Al, but becomes detrimental at or above 1300oC owing to blister formation as a result of transformation of Cr2O3 to volatile CrO3 [169, 174-175]. However with 8at.% Cr, oxidation rates may decrease at low temperatures, since Cr improves the ability to form a healing layer of Al2O3 [169, 176]. Cr implantation was also found to be beneficial to decrease the oxidation rate significantly by promoting the formation of a continuous alumina layer [177-179]. A classical hypothesis suggests that Cr could act as a secondary getter for oxygen, reducing its flux into the alloy when the primary getter (Al) is removed by oxidation [180]. The improvement in the ability to promote external Al2O3 formation might be a result of decreased oxygen solubility and transient oxidation or increased Al diffusion [181]. A more plausible explanation may be associated with the rapid formation of a protective (Cr,Al)2O3 layer, rather than a pure alumina layer [182]. Ti improves the scale adherence, especially when B is also added, but generally results in poorer oxidation behavior owing to high weight gains from the growth of Ti-containing oxides and disruption of the Al2O3 scale [172], while the addition of Ti alone (2.99wt.%) to Ni3Al tends to decrease the cyclic oxidation resistance [183]. Si addition is beneficial up to 3at.%, but are detrimental at a 10at.% level. Although a 3wt.% addition of Mo reduces overall oxide weight gain, the overall oxidation behavior is reduced owing to its limited solubility and thus, oxidation of the Mo-rich phases leads to the formation of volatile species. Lithium can also greatly improve the high temperature oxidation resistance of Ni3Al alloys. Substitution of Ni by Li can decrease the concentration of cation vacancy in p-type NiO, resulting in the decrease of the rate of oxidation according to the rule of Hauffe. Furthermore, additions of Li changed the morphology of oxide scales, made the oxide grains smaller and more homogeneous, densified the oxide scales and improved the mechanical strength of the oxide scales [184].

3.1.4. Effect of REs The reactive elements Hf, Y and Zr all improve the oxide scale adherence. The beneficial effects of a reactive element addition are maintained if Y is incorporated as an oxide dispersion. Hf and Zr, by themselves and when combined with B additions, tend to provide the best overall behavior [171-172, 185]. However, increased oxidation mass gains might be observed for the Zr- or Hf-containing Ni3Al alloys due to accelerated growth of Zr and Hf oxides when their contents are high. Even though the resultant scales are adherent, the increased oxidation leads to enhanced, probably unacceptable degradation rates. Y addition may also result in the formation of mixed Y2O3-Al2O3 scales, which tend to reduce the scale integrity. Kuenzly and Douglass studied the isothermal oxidation behavior of Ni3Al with and without Y addition (0.5wt.%) over a temperature range of 900-1200oC in air [186]. They concluded that the scaling behaviour in either alloy followed a strict parabolic law and the addition of Y did not alter the steady-state scaling rate of Ni3Al. The oxide scales on Ni3Al

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that were oxidized in air generally consisted of an outer layer of NiO, an intermediate layer of NiAl2O4, and an inner layer of Al2O3. Scale spallation was observed at all temperatures, especially on cooling the samples from the test temperature. The spallation of the scales on Ni3Al was attributes to the presence of numerous voids at the oxide scale/alloy interfaces. The presence of Y prevented the voids from forming. Based on a comparative analysis of the microstructures of the oxide scales developed on Ni3Al with and without Y, a vacancy sink mechanism was identified as the dominant mechanism for increased scale adherence to the Ycontaining alloys. Y-containing thin films were also applied onto Ni3Al alloys by an ion-plating method, and improvement on cyclic oxidation resistance was observed [187-188]. After deposition, the samples were treated at 1100oC in flowing hydrogen. During treatment, a scale with an outer (Y,Al)O layer and an inner columnar Al2O3 layer was formed. The presence of Ycontaining oxides reduced the diffusion of Al and O and also reduced the particle size of the oxide scale as well. The fine-grained (Y,Al)O-type oxide may enhance relaxation of growth stresses by permitting plastic deformation. They may also absorb the thermal-expansion stresses developed in the Al2O3 layer. Because the thermal-expansion coefficient of the (Y,Al)O-type oxide is smaller than that of Al2O3, a tensile stress is generated in the Al2O3 layer during cooling. This tensile stress may compensate the large compressive stress generated due to the difference in thermal-expansion coefficients between Ni3Al and Al2O3. In comparison with the positive roles of Y observed in the above studies, other studies with ion implantation showed that Y might be detrimental to the oxidation and scale spallation resistance [177-178]. The oxidation rates were slightly higher and the scales were prone to spallation. The negative effect of Y observed here could not be well explained. Tsipas studied the effect of Hf additions on the cyclic oxidation behavior of Ni3Al in an air environment and concluded that the stoichiometric and Al-rich Ni3Al suffered severe spallation, whereas the alloys with 2at.% Hf resisted scale spallation [185]. NiO was identified as the predominant oxide phase on both the retained and spalled scales in all the alloys studied. NiAl2O4, Al2O3 and HfO2 were reported to be present in the Hf-containing alloys. HfO2 protrusions from the scale into the alloy substrate of the Hf-containing alloys were attributed to enhanced adhesion of the oxide scale to the substrate. In addition, lack of spalling, buckling, ridging, or scale detachment, noted in the alloys to which Hf was added, was attributed to a reduction in the void formation at the alloy substrate, possibly due to elimination of vacancies from the alloy/scale interface to preferential sites such as HfO2. Taniguchi et al. examined the cyclic oxidation behaviour of Ni3Al alloyed with B, Ti, Zr and Hf [172]. The addition of Zr to Ni3Al and Ni3Al-0.1B increased the rate of alumina formation followed by a decrease in the rate during subsequent cycles because of the growth of ZrO2 particles that formed ahead of the alumina. Improved scale adherence in Zrcontaining Ni3Al was explained in terms of pegging of the alloy substrate by extensive penetration of Al2O3 and possible increase in oxide/alloy bond strength. Similar observations have been revealed by Chang et al [189]. The vacancy-sink mechanism was ruled out because significant number of voids was noted in both alloys after the oxidation process. The authors suggested enhanced plasticity of Al2O3 scales as the major reason for the improved scale spallation resistance.

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3.2. Oxidation of NiAl and Its Alloys 3.2.1. Introduction Nickel aluminide containing more than approximately 41at.% Al starts to form a single phase ordered B2 structure based on the body-centered cubic lattice. In terms of thermophysical properties, B2 NiAl offers more potential for high temperature applications than Ll2 Ni3Al. Even though NiAl has excellent oxidation resistance, higher thermal conductivity, higher melting point, and lower density, as compared with Ni3Al-based alloys, inadequate room temperature ductility has been a key limiting factor for its structural applications. There are at least three approaches possible for improving the ductility of NiAl, which include microalloying, macroalloying and microstructural control [190-205]. 3.2.2. General Scaling Behaviours NiAl is a material having great interest in high-temperature applications due to its high melting point and excellent oxidation resistance. It is also a base material for oxidation resistant coatings on high temperature alloys. The oxidation behaviour of NiAl and its alloys therefore has been studied extensively [206-208]. Oxidation of NiAl and its alloys at low temperatures normally leads to the formation of metastable transient Al2O3 phases such as γ-, δ-, and/or θ-Al2O3 [152, 209-214]. At higher temperatures, formation of metastable alumina phases might not be a problem [215]. Ni-containing oxides, such as NiAl2O4, have been observed during initial oxidation at temperatures lower than 1000oC [152, 216]. In general, the thermally grown α-Al2O3 scale has a poor adherence to the underlying metallic substrate due to the formation of voids at the oxide scale/alloy interface. When undergoing thermal cycling, scale spallation occurs, leading to rapid oxidation on the freshly exposed surfaces. Voids are formed by several mechanisms: (1) Kirkendall effect due to the different diffusivities between Ni and Al in NiAl [217-218]; (2) vacancy condensation during cooling; and (3) vacancy condensation due to a large change of the equilibrium vacancy concentration [219]. Sulfur, always presented in small quantities in the NiAl alloys, has a deleterious effect on the oxide scale adherence. Rivoaland et al. proposed a modified explanation of the sulfur effect [220-222]. During the growth of the transient alumina scale through outward diffusion, transient cavities are formed at the metal/oxide interface by vacancy injection. Sulfur segregation is favored at the Ni-rich metallic surface of these cavities and occurs as long as their surface remains free of oxide. Once segregated, sulfur remains at the interface as a vestige of the formation of the transient cavities that are expected to be filled by inwardanionic growth of the mature α-Al2O3. Segregated sulfur, trapped at the interface after the θ to α transformation of the scale, weakens the oxide adherence and favors the formation of interfacial voids and the decohesion of the oxide layer under growth and/or thermal stresses [223]. Appropriate additions of Hf, Y, Zr or Pt could, to some extent, counter the detrimental role of sulfur [224-229]. At reduced oxygen pressures NiAl is susceptible to fast internal or intergranular oxidation at low temperatures (500-1000oC) [230-231]. The transport of oxygen through the impuritiesdoped areas of the oxide scale formed in the initial oxidation stage led to the inward diffusion of oxygen into the Al-depleted zone. This process together with A1 diffusion from the interior resulted in discontinuous internal Al2O3 layer. The intergranular oxidation of NiA1 can be

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explained by inward penetration of oxygen into grain boundaries which are widened by outward diffusion of A1 and condensation of vacancies from the surrounding lattice.

3.2.3. Effect of REs Dramatic effects of alloying NiAl with one or more reactive elements or their oxide dispersions are commonly observed. The transport mechanisms are affected by alloying with reactive elements, resulting in a lesser contribution of outward Al diffusion. Reductions in αAl2O3 scale growth rates on reactive element containing NiAl have been observed, at least until the ridges have fully coarsened. However the metastable Al2O3 phase growth rates are increased [232]. The influence of Y implantation on the oxidation and spallation resistance of NiAl was investigated [233-235]. The presence of Y in the surface layer of the substrate improves the scale adherence and reduces the scale growth rate. Both these beneficial effects are resulted from the influence of Y on the growth mechanism of the oxide scale. Scales on pure NiAl grow as a result of simultaneous outward diffusion of aluminium and inward diffusion of oxygen. On Y-doped materials the oxide scale growth is only from the outward diffusion of aluminium as a result of which the main source of growth stresses in the scale is eliminated. However, Schumann found that Y implantation had limited effect on the improvement of scale adhesion on NiAl single crystals oxidized at 950oC since Y was concentrated in a small layer within the oxide scale, the newly formed oxide contains no Y and ion implanted Y cannot inhibit the formation of the interfacial voids [236]. Y-Al-garnet (YAG) particles were also observed and Y segregation to α-Al2O3 grain boundaries had been detected. In the study with NiAl-0.1wt.%Y, segregation of Y to both oxide grain boundaries and the oxide-alloy interface during oxidation at 1200oC was confirmed [237]. Zr addition seems to promote the formation of Al2O3 on the surface and/or improve the adhesion of the alumina scale [238-239]. Its segregation to oxide scale grain boundaries might influence aluminum transport [237, 240-241]. Scale adherence is improved in most cases when the concentration of reactive elements is not excessive enough to cause gross internal oxidation or reactions that form secondary intermetallic phases, and when the distribution of the reactive element phases is homogeneous. Doping concentration lower than 0.1% results in poor oxide scale adherence and excessive negative weight changes, whereas doping concentration higher 0.1% results in excessive positive specific weight changes, which are associated with gross internal oxidation of Zr. Nesbitt et al. modeled the oxidation of Zrcontaining NiAl alloys to correlate the stability of alumina scale and formation of spinel phase with Al depletion in the alloy, and thereby, established the maximum use temperature for the alloy as a function of specimen thickness and lifetime before spallation occurs [242]. Hf addition might decrease the oxidation mass gain of NiAl and lead to the formation of adherent alumina scales [243-247]. Fine oxide dispersions of Al2O3, Y2O3, ZrO2 or La2O3 had been added into NiAl to test their potential influences on the oxidation behaviours. Addition of 1vol.% fine Y2O3 dispersion showed excellent oxidation and scale spallation resistance in comparison with undoped NiAl [248-249]. However at much higher temperatures (1400 or 1500oC) the Y2O3 addition is less effective. ZrO2 seems to improve the scale adhesion [250]. However, the addition of HfO2 might not be able to improve the oxidation behaviour of NiAl [250]. Al2O3 additions increased the oxidation rate of NiAl but the scale adherence was good [251]. Larger ions such as Y, Zr, La and Hf appeared to slow the θ- to α-Al2O3 phase transformation,

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enhancing the formation of a ridge-type morphology [252]. However, other researchers argued that the presence of RE additions (Y and Ce) in NiAl suppressed θ-Al2O3 formation and enhanced α-Al2O3 nucleation [208]. Al2O3 might accelerate the transformation of alumina from metastable to stable pahse [251].

3.2.4. Effect of Other Elements When added in small amounts (>1-2at.%), most transition elements have little effect on the oxidation behaviour. Si, Ti and Cr tend to be detrimental [253], since additional phases that form due to the limited solubilities of the elements in NiAl may have poorer oxidation resistance than NiAl or may lead to disruption of the otherwise protective Al2O3 scale. Cr was observed to accelerate the θ-α-phase transformation and leads to higher Kp values for the final growth of α-Al2O3. The Cr effect on the oxidation kinetics was explained by Cr2O3 nuclei formation in the initial stage of oxidation which serves as nucleation site for α-Al2O3. A higher density of nuclei leads to a faster formation α-Al2O3 which is fine grained with more diffusion paths, causing faster oxide growth [209]. However, Si and especially Cr improve the hot-corrosion resistance of NiAl [254]. Refractory metals (W, Mo and V) are detrimental to oxidation resistance but may provide effective protection against sulfidation, particularly in reducing atmospheres when presented in the alloys with sufficiently high levels [255]. Pt, Pd, Ir, Re and Rh additions appear to be beneficial, especially when incorporated into nickel aluminide coatings used for hot corrosion and high temperature oxidation resistance [256-258].

4. TITANIUM ALUMINIDES 4.1. Oxidation of Titanium 4.1.1. Introduction Titanium, a transition metal, in the group ΙV B of periodic chart, has an atomic number of 22, and an atomic weight of 47.90. Normally, titanium exists in two allotropic modifications: α and β. α-Ti has an hcp structure under 882.5oC, the transition temperature. And its density is 4.51 g/cm3 at the temperature of 25oC. Between 882.5oC and the melting point, β-Ti forms, and has a bcc structure; its density is 4.32 g/cm3 at the temperature of 900oC. Titanium has been reputed as the ‘Third Element’. Its importance and application is the second only to iron and aluminum [259-261]. Commercially pure titanium (CP-Ti) has minimum titanium contents ranging from about 98.5 to 99.5%, and is used primarily for corrosion resistance. Unalloyed grades are also useful in applications requiring high ductility for fabrication but relatively low strength. Yield strengths of CP-Ti vary from 170 to 520 MPa simply as a result of variations in the interstitial and impurity levels. Oxygen and iron are the primary variants in these grades; strength increases with increasing oxygen and iron contents. The maximum service temperature of unalloyed grades of titanium for stress-free isothermal oxidation in air or oxygen is about 400oC. However, unalloyed titanium loses much of its strength at moderately low temperatures. Creep can occur at ambient and elevated temperatures.

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4.1.2. Oxidation of Titanium Titanium is a highly reactive metal capable of forming thermodynamically stable oxides, nitrides, carbides, and sulfides when exposed to oxygen, air, carbonaceous, and sulfurcontaining gases at low-intermediate temperature range. According to the Ti-O phase diagram, the stable oxides of Ti include Ti2O, TiO, Ti2O3, Ti3O5 and TiO2 [259]. The oxidation of pure Ti has been widely studied and all the results are in good agreement [262263]. Normally, after extended oxidation in air or high-pressure oxygen atmospheres at elevated temperatures, the oxide formed and detected is TiO2 only. However, trace of some other oxides in various valences might be formed, mixed, but not be detected. Oxidation of Ti follows different rate equations depending on temperature and testing time. In general, below about 400oC, the oxidation of Ti is logarithmic, whereas at 400-600oC a transition from logarithmic to parabolic or an approximately cubic oxidation is observed. Above 600-700oC, the oxidation rate of Ti in air and oxygen and other oxidizing media is typically parabolic, and after extended reaction it transforms into an approximately linear rate. The transition from parabolic to linear kinetics involves the formation of a continuous crack between the oxide scale and the alloy when the stresses in the oxide layer reach a critical value. Above 900-1000oC the linear oxidation is followed by a decreasing rate of oxidation with time. The decreasing rate has been ascribed to the formation of a compact diffusion barrier layer within the scale caused by the sintering and grains growth of the oxide. The oxidation of pure Ti is strongly affected by the presence of small amounts of water in the atmosphere. Motte et al. studied the influences of water on the oxidation of pure Ti at tempratures ranging from 650 to 950oC [264]. The water vapor pressure ranged from 0.5 to 18 Torr. At temperatures below 750oC, the oxidation kinetics can be divided into two stages. The first stage is observed over a limited time period and the oxidation follows an approximate parabolic time dependence. After extended oxidation, the rate accelerates, and a second stage is observed. During this second stage, the rate gradually decreases but the oxidation is not parabolic. At temperatures above 750oC, the first stage is not observed, and the oxidation does not conform to any usual rate equation. The scales on pure Ti are characterized by the presence of two layers, both layers being rutile. The outer layer is columnar and becomes less columnar with increasing temperature, while the inner one has a much finer and equiaxed grain structure. Galerie et al. also confirmed that incorporation of water vapor into atmospheres increased the oxidation rate of pure Ti due to rapid matter transport through hydroxide ion defects [265]. According to the work by Gobel et al. using oxygen tracers, the high kinetics in wet air might be related to the high reactivity of oxygen arising from water vapour [266]. Recently, the oxidation behavior of pure Ti was studied at 700 and 900oC in dry and moist synthetic air atmospheres upto 150 hrs exposure by Perez [267]. At 700oC, after an initial transient stage of 5 hrs, the mass gain in wet air is slightly higher than in dry air. The oxidation kinetics is governed by parabolic law over the entire oxidation process. Corrspondingly, the scale morphologies formed in these two atmospheres are very similar. At 900oC, the mass gain is initially higher in the water-containing atmosphere, but after 40 hrs of oxidation the mass gain in wet air is lower than that in dry air, resulting in a sharp decrease in the oxidation rate with progressing the oxidation under humidified conditions. A relatively dense homogeneous rutile layer is observed on the material oxidized in a humid environment. Perez believed that the much lower mass gain of Ti oxidized at 900oC under humid conditions was resulted from the formation of an innermost compact rutile layer, which can act as an

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effective solid-state diffusion barrier. The mechanism responsible for the formation of this compact layer is associated with the stresses acting in the scale and, consequently, with the creep rate of the rutile under the oxidation conditions. Water vapour induces deviations from the stoichiometry of rutile that affects the creep rate of the scale. The creep rate of less stoichiometry rutile should be higher than that corresponding to the more stoichiometric formed under dry conditions, so consolidation of the initially formed stratified layer takes place. A notable process accompanied with oxidation of Ti is the dissolution of large quantities of gaseous species, especially oxygen in the substrate during the oxidation process, this process is always accompanied by severe embrittlement of the substrate material. Below the α-β transition of titanium at 882.5oC, oxygen dissolves in the α- phase, up to about 30at.% and shows small variations with temperature. Above the transitional temperature, oxygen dissolves into the β phase, up to about 8at.% with temperature increases to 1700oC. Addition of oxygen stabilizes the α phase, i.e., the β phase may transform gradually to the α phase in turn. Oxygen diffusion in the β phase has a lower activation energy (about 115 kJ/mol) and is faster than in the α phase. Oxygen dissolved takes up a notable proportion of the total weight gain during the oxidation process. Calculation showed that 25-30% or more of the reacted oxygen dissolved in the metal at 700-750oC and more than 50% at 900-950oC [268].

4.1.3. Oxidation Protection of Titanium High temperature oxidation resistance of titanium can be achieved by a modification of the surface properties with coatings. TiAl3 coatings by hot-dipping and diffusion, silicide coatings by powder siliconizing and liquid phase alloying or laser surface alloying, have been applied onto pure Ti [269-272]. These coatings can provide certain protection to the underlying Ti substrate at temperatures ranging from 750 to 1000oC due to the formation of Al2O3 or SiO2/Al2O3 scales. However, the lifetime of the aluminide coatings on pure Ti at high temperatures is seriously influenced by the inward aluminium diffusion and by the outward titanium diffusion through the coating layers. The oxide scale is also showing an insufficient stability and integrity under thermal cycling conditions.

4.2. Oxidation of Titanium Based Alloys 4.2.1. Introduction Based on the phases present, titanium-base alloys can be classified as either α, near-α, αβ, or β alloys [259-261]. Alpha alloys that contain Al, Sn, and/or Zr are preferred for high temperature as well as cryogenic applications. Alpha alloys generally are resistant to creep at high temperatures. Alpha alloys that contain small additions of β stabilizer are classified as “near-α” alloys. Although they contain some retained β phase, these alloys consist primarily of α and behave like conventional α alloys. α-β alloys contain one or more α stabilizers or αsoluble elements plus one or more β stabilizers. These alloys retain more β phase after solution treatment than do near-α alloys; the specific amount depends on the quantity of β stabilizers present and on heat treatment. Beta alloys are richer in β stabilizers and leaner in α stabilizers than α-β alloys. They are characterized by high hardenability, with β phase

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completely retained. The effects of various alloying elements on phase and properties of Tibase alloys are summarized as the followings: (1) Aluminum: The addition of Al, an α stabilizer, increases tensile and creep strengths and moduli while reducing alloy density; (2) Tin: Sn is a less potent α stabilizer and a solid-solution strengthener that is often used in conjunction with Al to achieve higher strength without embrittlement; (3) Zirconium: Zr forms a continuous solid solution with Ti and is a weak β stabilizing element. It increases strength at low and intermediate temperatures. The use of Zr above 5 to 6% may reduce ductility and creep strength; (4) Oxygen: Oxygen content is usually kept fairly low, 0.10 to 0.15%, in this class of alloys. Although it strengthens Ti, the beneficial effects deteriorate at temperatures above 300oC. Increased oxygen content also tends to lower ductility, toughness, and long-term high temperature stability; (5) Molybdenum: Mo is the prime β stabilizer in near-α alloys. It promotes high strength in quenched and aged materials as well as increased hardenability. Alloys aimed at long-term creep strength have lower Mo content. Conversely, alloys aimed at shortterm high temperature strength or superior strength at lower temperature have greater Mo percentage; (6) Niobium: Nb is a β stabilizer, and is added primarily to improve surface stability during high temperature exposure; and (7) Silicon: Si is an important element in high temperature Ti alloys since it increases strength at all temperatures and has a marked beneficial effect on creep resistance. In aerospace industry, many Ti based alloys had been developed in consideration of the mechanical properties. Moreover, during the past half century, some types of Ti based alloys, as structural materials, have been spreading to applications in general industries, including energy, petrochemical, metallurgical, papermaking, medical and food engineering industry.

4.2.2. Oxidation of Titanium-Based Alloys The oxidation behaviour of titanium, dominated by scale formation and cracking, can be modified or improved by additions of appropriate alloying elements, such as Ta, Nb, Al, Zr, Hf, Si, Sn or Cr. Among these alloying elements, the effect of Al addition on the oxidation behaviour of Ti is relatively controversial among the obtained experimental results from various researchers. Menzies et al. [273] studied the oxidation behaviour of Ti-5Al in CO2 at 1000oC and indicated that this alloy oxidized more rapidly than pure Ti. However, Jenkins [274] showed that Ti-3Al alloy exposed to pure oxygen at temperatures between 750 and 900oC oxidized more slowly than did pure Ti, which was attributed to the formation of a protective scale of alumina due to the preferential oxidation of aluminium. An α-Al2O3 layer was found near the external interface and alumina was distributed in distinct sublayers of variable thickness. The number of alumina sublayers decreased with increasing temperature and above 950oC only an external alumina was identified. Other studies revealed that alumina existed near the external interface either in the alpha or gamma form. Some researchers also found that the amount of oxygen dissolution in Ti metal phase could be decreased since the rutile scale formed on Ti-Al alloys has a better barrier property; the beneficial role of Al can

High Temperature Corrosion of Intermetallics

19

be attributed to the decrease in the rate of diffusion of oxygen in the rutile, caused by the incorporation of Al ions in interstitial positions and by the dispersion of alumina in the layer [275]. The beneficial role of Si addition in the oxidation of Ti has also been widely studied and explained by several mechanisms [276-281]: (1) reduction of oxygen diffusion and solubility in the metallic matrix. Si can stabilise β phase, in which oxygen dissolution is relatively low; (2) decreasing inward diffusion of oxygen through the scale. For example, the passage of Si ions into interstitial position in the lattice of rutile will result in a slowing down of oxygen diffusion process; (3) slowing down the rate of rutile recrystallization and stratification by the presence of finely dispersed SiO2 particles, thus reducing the fraction of porosity in the scales; and (4) forming nitride-rich layer (TiN) at the interface between the scale and the metallic substrate is also related to the presence of Si in Ti. For Ti-Cr alloys, when the concentration of Cr3+ is larger than its solubility limit in TiO2, the precipitation of Cr oxides tend to form a physical barrier in oxide layer and progressively reduce the oxidation rate of the alloy [282]. The role of Ta in the increase of oxidation resistance of Ti is complex and not well understood. Chen and Rosa used the Wagner-Hauffe approach to explain the improved oxidation resistance of pure Ti at high temperatures [283]. According to this approach, addition of Ta5+ in TiO2 (Ti4+) should decrease the oxidation rate of the base metal, if it forms an n-type semiconducting oxide. The addition of Ta in Ti may also increase the compositional range of the oxygen-stabilized α-phase; reduce the solubility of oxygen in the metal and the mobility of Ti in the substrate and oxide [284]. Additions of certain quantities of Nb into Ti lower the scaling rate and the function of cation diffusion, change the oxidation mechanism and regularities, scale structure and composition, and increase the oxygen fraction in a diffusion layer and the depth of penetration. In general, the protective nature of these elements depends on the temperature, atmosphere and their concentration. Ti-6Al-4V (wt.%) is an important commercial Ti-base alloy, which has excellent resistance to general corrosion in aqueous solutions. It is also an important material for aeroengine production and one of the matrix materials for the fabrication of titanium-matrix composite materials (TMCs) [285-289]. Its oxidation behaviour in air between 650 and 850oC had been studied by Du et al [290]. It was found that the air oxidation of Ti-6Al-4V alloy followed a parabolic rate law at 650 and 700oC after a logarithmic period. Above 700oC this alloy oxidized according to linear-parabolic kinetics. At 850oC, oxidation of this alloy followed a parabolic rate law again after 50 hrs linear-parabolic oxidation. The oxide scale developed on this alloy consisted of alternating layers of Al2O3 and TiO2. The number of the Al2O3 and TiO2 layers increased with increasing exposure time and oxidation temperature. The external gas/oxide interface was always occupied by an Al2O3 layer and TiO2 was always identified at the oxide/substrate interface. Practical application of Ti-6Al-4V however is limited in the areas where hightemperature oxidation resistance is desired. When it is exposed at temperatures above 650oC, it becomes hard and brittle due to the dissolution of oxygen and nitrogen. Surface alloying with Al, Cr and Si is commonly used to improve its oxidation resistance by promoting the establishment of Al2O3 layer or SiO2 diffusion barrier [291-295]. Micro-plasma oxidation (MPO) in NaAlO2 solution was also used to prepare ceramic coating on Ti-6Al-4V with an attempt to increase its oxidation resistance [296]. The coating was composed of a large amount of Al2TiO5 and a little α-Al2O3 and rutile TiO2. During oxidation decomposition of

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Al2TiO5 increased the content of α-Al2O3 in the coating. This coating could decrease the oxidation mass gain; however, after extended exposure or at higher temperatures, the protectiveness of the coating was limited as accelerated oxidation could be observed. As titanium-base alloys generally have high strength-to-weight ratio, they are attractive alternative to nickel-base superalloys for certain turbine components. In the past 50 years, many special titanium-base alloys had been developed for the possible application in gas turbine engines, hot sections of airframes and other sections [297]. However the application limit typically occurs around 540-600oC for conventional Ti alloys due to oxidation in longterm exposures. Alloying elements, including V, Sn and Zr, were known to interfere with protective Ti oxide scale formation and then to accelerate oxidation rates of Ti. On the other hand, alloy additions of Mo, Cr (>10%), Nb, Ta, Al and Si all significantly enhance oxidation resistance to temperatures as high as 815oC. Optimization of these beneficial elements in Ti alloy has led to the development of various advanced titanium-base alloy systems with excellent strength and lightweight properties and environmental resistance, e.g., Beta-21S alloy (Ti-15Mo-3Al-3Nb-0.3Si, wt.%), IMI-834 (-829), Ti-1100, Ti-V-Cr(+C, Al or Si), etc [298-303]. The Beta-21S alloy is ~100 times more resistant than Ti-15V-3Al-3Sn-3Cr at 815oC. However, Beta-21S is still not as resistant as α2 or γ titanium aluminide materials and certainly not as good as the nickel-base alloys, such as René41 or IN718 [298]. The IMI series alloys can only tolerate prolonged exposure in air up to 500oC. Therefore, small addition of various elements for the protection of Ti or its alloy is not highly reliable for material protection, especially for those materials will be possibly used at elevated temperatures, although this type of titanium-base alloys will still be used for some components in aeroegine and automotive. Several coating systems are being examined for improving the oxidation resistance in the temperature range of 600-750oC [304-313]. In order to further improve the temperature limit, new alloy systems should be developed, and this has led to the development of titanium aluminides, titanium powder metallurgy alloys, and titanium matrix composites with more balanced properties [314-322].

4.3. Oxidation of Titanium Aluminides 4.3.1. Introduction At the beginning of 1970s, Ti-Al intermetallic compounds were developed as the first intensive and successful structural materials with fundamental deformation studies [323]. Actually, titanium aluminide based intermetallic compounds have been becoming attractive structural materials for application to aviation industry because of their low density, high melting point, high specific strength, and due ductility. The aim for development of titanium aluminides is to develop a sort of materials whose properties are between those of nickel-base superalloys and high temperature ceramics. According to the Ti-Al binary phase diagram [324], there are four intermetallic phases of interest for high temperature applications: Ti3Al (α2), TiAl (γ), TiAl2 and TiAl3. The development of Ti3Al and its alloys has been driven by the need to bridge the gap in temperature capability between conventional near-α Ti alloys and Ni-base superalloys such as INCO 718 or INCO 713. Ti3Al has a specific modulus and stress rupture resistance comparable to that of the superalloys however, the complete absence of room temperature

High Temperature Corrosion of Intermetallics

21

plasticity posed the primary challenge in using as a structural material. Additions of alloying elements and sutiable heat treatments can significantly improve its room temperature mechanical properties, and these become to be the key-points for the current development of Ti3Al-base alloys. γ-TiAl and its alloys are pursued mainly because of the desire to raise the thrust-to-weight ratio of high performance aircraft engines. γ-TiAl remains ordered to melting point at about 1440oC, this helps to retain strength and resist creep to high temperatures, and also results in high stiffness over a wide temperature range. Although the difficulty in plastic deformation also hinders its development, γ-TiAl and its alloys are still the most attractive candidate materials for components in aeroengines. TiAl3, having a tetragonal structure and the highest oxidation resistance, is of interest in the development of a new class of structural materials as well. As to their possible applications in elevated temperatures, it should always be remembered that long-term exposure at elevated temperatures needs a long-term protection provided by the oxide scale formed on the alloy surface. This protection is generally associated with a stable and adherent alumina, in which the diffusion of reactants is slow. However, of the titanium aluminide intermetallic phases, only TiAl2 and TiAl3 are capable of protective alumina scale formation over a wide range of temperatures. The critical concentration of Al required for the formation of exclusively external alumina scale is much higher than that in binary Ni-Al binary alloys. This kind of oxidation behaviour of titanium aluminide intermetallic compounds could generally be ascribed to the followings [325]: (1) The thermodynamic stabilities of the oxides of Ti and Al are quite similar, which can potentially make it difficult to establish an Al2O3 scale due to the competition from TiO or TiO2; (2) The activity of Al deviates from the ideal or regular solution obviously, and is much smaller than unity in Ti3Al and TiAl [326-327]. Combining the activities with standard free energy data for the oxides of TiO, TiO2 and Al2O3, it appears that TiO/TiO2 is more stable than Al2O3 for the alloys containing Al less than 50at.%; and (3) Ti and Ti-Al alloys are highly permeable to oxygen, and Al has a low diffusivity in lower-aluminium-containing alloys.

4.3.2. Oxidation of Ti3Al and Its Alloys 4.3.2.1. Introduction The structure of Ti3Al is DO19, and is the ordered structure of α-Ti, also names as α2phase. The compositional stability of α2-Ti3Al ranges from 22 to 39at.% Al. This compound is congruently disordered at 1180oC and an Al content of 32at.%. The stoichiometric composition, Ti-25at.%Al, is stable up to ~1090oC. The density of Ti3Al with stoichiometrical composition is 4.2 g/cm3, while its alloys have the density about 4.1-4.7 g/cm3. The Young’s modulus is in the range of 100-145 GPa, the shear elasticity is about 58 GPa, and the Poisson ration is 0.29 [328-330]. The mechanical properties (strength, ductility and creep) of Ti3Al alloys can be improved by alloying with Nb and/or processing control [331-341]. Ti3Al-base alloys under developed are basically based on Ti-(23-25at.%)Al-(1030at.%)Nb with additional alloying elements for further strengthening. It was believed that substitution of Ti by Nb could promote more slip systems in operation, then affecting the

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ductility. While, higher Nb concentration, results in the formation of further phases, i.e., β-Ti in the disordered state with an α2 structure or in the ordered state with a B2 structure and/or orthorhombic O-phase, which limit the slip length and have a significant and beneficial effect on the ductility. The O-phase exhibits better strength and toughness than Ti3Al. Single phase alloys of ordered orthorhombic have excellent creep resistance particularly after beta heat treatment. The creep resistance of the alloys could be improved with increasing volume fraction of the O-phase and decreasing volume fraction of the α2 phase. Based on the Nb concentration and phase structure, Ti3Al-base alloys can be divided into three groups: α2 or super-α2 alloys with 10-12at.%Nb, α2 + β (B2) alloys with 14-17at.%Nb, and O-phase alloys with 23-27at.%Nb. The mechanical properties of these alloys are highly dependent on the size, shape, distribution, composition, crystal structure and neighbourhood relationships of the various grains. The phase distribution can be varied appreciably by proper selection of the alloy composition and by heat treatment, e.g., thermomechanical treatments (TMT). The best combination of strength and ductility can be obtained through adjusting the size and amount of primary α2 phase, the proportion of α2 and β phases, and their distribution. In general, the development of Ti3Al-base alloys is focused on the O-phase alloys. Other alloying elements for improving the strength are Cr, Ta and Mo [342-347]. The latter is also advantageous for the creep resistance. Minor alloying additions of Fe, C and Si affect the creep behaviour significantly, with Fe having the most deleterious effect. V and Sn were also used for improving the properties [348]. Alloying with Zr increases both the strength and ductility, and microalloying with Y and B has been used to control the grain size and improve the ductility and workability. Very fine and stable grain sizes can be produced by rapid solidification of alloys with fine dispersions of rare earth oxides. In such alloys the small grain size improves the ductility, whereas the dispersoids enhance the strength at the expense of ductility. Similar effects can be produced by the precipitation of strengthening phases, such as the alloying of Ti3Al with Si to produce Ti5Si3 as a strengthening second phase.

4.3.2.2. Oxidation Behaviour and Resistance The protective oxidation behaviour, i.e., the formation of a continuous Al2O3 external scale, could not be expected due to the considerably low Al activity in Ti3Al and its alloys. Its oxidation kinetics between 600 and 950oC are generally reported to follow a parabolic rate law and the rate constants are slightly smaller than those of typical TiO2 formers. The oxide scales, normally layered and stratified, consist of an inner TiO2-rich region, an intermediate Al2O3-rich region, and an outer TiO2 region [349-350]. The oxidation of Ti3Al is generally more rapid in oxygen than in air [351]. It was believed that this is the result of a layer of TiN, which formed at the oxide scale/alloy interface during air exposures, and acted as a diffusion barrier for reactants. The detailed microstructure of the subsurface zone underneath the external oxide scale formed on Ti3Al alloys was studied by Dettenwanger and Schutze [352]. They found that the subsurface region has a complex microstructure and shows three distinct layers: an internal-oxidation zone with α-Ti(Al,O) and α-Al2O3; a ternary phase with composition Ti-21Al-15O; and α2-Ti3Al with dissolved oxygen. The oxidation resistance of Ti3Al can be improved through the addition of alloying elements, such as Nb, Si, Mo, Mn, V, W, Re and Ta. Nb, as a β-stabilizing element, can

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23

improve the poor room temperature ductility of Ti3Al, and also was proved to be a beneficial alloying element to the oxidation resistance. According to Reddy et al. [353], the oxidation kinetics of Ti3Al-Nb alloy was substantially reduced at temperatures ranging from 7501100oC in oxygen atmosphere in comparison with that of Ti3Al. Okafor and Reddy [325] found that the oxidation kinetics of Ti-30Al-2.7Nb follows a parabolic rate law in the temperature range of 750-1100oC. It was also shown that a denser oxide scale was formed on the Nb-containing alloy [354]. The oxidation products consisted mainly of rutile and alumina; no Nb oxides were identified. Wu et al. studied the individual/synergetic effects of Nb (0-20at.%) and Si (0-15at.%) on the oxidation behaviour of Ti3Al at 800 and 900oC in air [355-356]. For alloys with Nb addition, the alloy with about 10at.% Nb is found to yield the best oxidation resistance at both temperatures, consistent with other studies [357-361]. At 800oC, after 100 hrs exposure, no spallation of oxide scales on Nb-containing alloys can be found and the kinetics approximately obeys the parabolic rate law. While at 900oC, tiny spallation can be found. Based on the XRD and SEM results, the authors concluded that, the beneficial effects of Nb addition on the improvement of the oxidation resistance of the Ti3Al-base alloys are twofold. One is the doping effect both in the matrix and in the scale. First, the dissolved Nb in the matrix restrains the oxygen dissolution into the matrix ahead of scale formation. Second, the Nb doped oxide forms a compact scale with less porosity. Another positive effect of Nb addition is to promote the earlier formation of TiN at the scale/matrix interface of the Nbcontaining Ti3Al alloys [362-363]. The presence of TiN is a barrier to the inward diffusion of oxygen. The dissolved Si in the matrix can either reduce the oxygen dissolution at the beginning of oxidation or improve the scale morphology by doping. However, the effect of Si addition on the oxidation behaviour of Ti3Al-base alloys is essentially dependent on their microstructures and phase constitutions of the matrix. Their results also showed that when Si addition exceeded the solubility limit of Si in α2 phase, Ti5Si3 was introduced. At low temperature (< 800oC), the reported oxidation resistance of Ti5Si3 was really good. However, the Ti5Si3 formed was always in discontinuous distribution, so a continuous SiO2 layer seems to be impossible for Si-containing alloys, and actually was not revealed by experimental observations [364]. The combined addition of Nb and Si is more effective for improving the high temperature oxidation resistance of Ti3Al-base alloys than alloying alone. Oxidation behaviour of Ti-Al-Nb alloys with high Nb contents had also been studied. In the work of Mungole et al. [365], the parabolic rate constants of Ti-24Al-20/27Nb oxidized in oxygen in the temperature range of 850-1050oC were higher than that of alloys with lower Nb contents, such as Ti-24Al-11Nb and Ti-24Al-15Nb [363, 366]. They believed that the formation of Nb2O5 (the major constituent of the oxides formed was TiO2 while Al2O3 and Nb2O5 were the minor constituents) as a separate phase is possibly related to the lower oxidation resistance. The long-term oxidation behaviour of Ti-22Al-25Nb in air between 650 and 800oC for 500-4000 hrs was studied by Leyens and Gedanitz [359]. The alloy exhibited reasonable oxidation resistance (< 1 mg/cm2) in air at 650oC up to 4000 hrs and at 700oC up to 500 hrs, whereas at 800oC breakaway oxidation occurred after about 100 hrs. The isothermal oxidation behavior of Ti-25Al-18Ta had been investigated in pure oxygen at temperatures ranging from 850 to 1100°C by Reddy et al [367]. The oxidation kinetics followed a parabolic rate. The oxidation products were a mixture of TiO2, Al2O3 and small amounts of tantalum oxide. The addition of Ta to Ti3Al alloy decreased the oxidation rate of

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the alloy. However, the oxidation scale was not compact and exhibited significant spallation especially at high temperatures. At 1000oC, Ta was enriched at the interface between the oxide scale and the base alloy, resulting in the improved oxidation resistance. However, the addition of Ta appears to be less profitable than Nb addition. Ta addition to orthorhombic Ti2AlNb alloy (Ti-23Al-13Nb-5Ta-3Mo) also exhibits positive effect on the oxidation behaviour though this effect is not fully understood yet [368].

4.3.2.3. Oxidation Protection of Ti3Al and Its Alloys The most popular way for protection of Ti3Al based alloys is pack cementation [369374]. TiAl3 coatings could be produced on Ti3Al alloys through the simple pack aluminizing process. These coatings offered substantial improvement over the uncoated alloys in oxidation tests at elevated temperatures. The oxidation resistance of siliconized coatings is also superior [375]. However, cracks might be formed in the thick coatings (aluminide or silicide) due to their brittle nature, then have an adverse effect on the long-term oxidation process. Al film was sputtering deposited onto Ti3Al alloy and then subjected to interdiffusion treatment at 600oC for 24 hrs in high vacuum to form a TiAl3 layer on the surface [376]. This TiAl3 layer exhibits good adhesion with the substrate and plays a positive role in oxidation protection. Cyclic and isothermal oxidation tests at 800oC in air demonstrated that the Ti3Al alloy with an Al film of 3-5 μm thick could dramatically reduce its oxidation rate. The TiAl3 layer not only results in the formation of a continuous α-Al2O3 scale on the outer surface, but also inter-reacts with Ti3Al substrate to form a γ-TiAl layer during oxidation. The layered structure of α-Al2O3/γ-TiAl/α2-Ti3Al can maintain the integrity of the α-Al2O3 layer without microcracks and spallation. Li et al. used an electro-spark deposition technique to increase the Al content in the near surface region of a Ti3Al-Nb alloy. The results showed that a TiAl3 layer with a metallurgical bonding to the underlying alloy substrate was formed through this fast melting and solidification process. Significantly improved oxidation and scale spallation resistance could be observed at temperatures of 800 and 900oC up to 200 hrs exposure in air [377]. However, a potential problem associated with these Al-rich coatings is the interdiffusion between coating and substrate. These processes will result in the loss of Al from the coating and therefore long-term stability of alumina scale cannot be maintained. Sputtering deposited Ni-20Cr coating also provided certain protection to the Ti3Al-Nb alloy at high temperatures which is dependent on the formation of Cr and Ni protective oxides [378]. Plasma-sprayed MCrAlY and MCr type coatings deposited over a thin diffusion barrier of chromium or tungsten have been found effective in protecting alloys of Ti-24Al-12.5Nb1.5Mo and Ti-24Al-8Nb-2Mo-2Ta during 1000 hrs exposure in air at 815oC against oxidation and embrittlement [379]. A single sputtered-NiCrAlY coating and a complex coating with an inner ion-plated TiN layer and an outer sputtered-NiCrAlY layer have been established on a Ti3Al-Nb alloy with an attempt to improve the high temperature oxidation resistance [380]. Exposures at 850 to 950°C indicated that these coatings could, to some extent, improve the oxidation resistance. The main aspects of the oxidation of Ti3Al-Nb with and without coatings are as follows: oxide scales on uncoated Ti3Al-Nb at 850 to 950°C consisted of an external thin Al2O3-rich scale incorporating some TiO2 and an inner TiO2-rich scale doped with Nb. The NiCrAlY- and NiCrAlY-TiN-coated alloys were able to form an Al2O3 scale. Meanwhile, Ti oxides formed throughout the scales from the coating surface to the coating-alloy interface. The TiN layer had a beneficial effect on the corrosion resistance of the NiCrAlY coatings by

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25

inhibiting the diffusion of Ti, Ni, etc. The deterioration of the NiCrAlY-TiN coating is much slower. Nevertheless, coating-substrate interdiffusion and formation of Ti oxides in some regions still occur and partially destroy the protective ability of the coating system, which may be due to the defects existing in the coating. Al2O3, CeO2 and Y2O3 thin films were applied onto Ti3Al-Nb alloys by using sol-gel or electrochemical deposition techniques [381-382]. The results showed that oxidation and scale spallation resistance of the alloys could be improved by CeO2 and Y2O3 films. However, the effects of Al2O3 films on the oxidation resistance of Ti3Al alloys reported in these studies are controversial. Detrimental effects on oxidation and scale spallation ressitance were observed in Li’s study, while a benefical influence was reported in Zhu’s experiments. It is suggested that the different preparation methods and then different structural properties of the Al2O3 films might be responsible for these different observations. Anodic films were also prepared in solutions containing phosphoric acid and Na2SiO3 on Ti3Al alloys. The testing results indicate that the anodized Ti3Al can remarkably reduce the oxidation rate at 800oC and the improvement increases with the increasing anodizing voltage up to 350 V [383]. Enamel coating with a nominal composition of SiO2 (58.2wt.%), Al2O3 (6.3), ZrO2 (5.3), ZnO (9.0), CaO (4.1), and others (17.0) was applied onto Ti3Al alloys with different Nb contents [384]. Oxidation was conducted discontinuously at 750oC in air for 100 hrs. It was found that enamel coating could protect Ti3AlNb alloys from oxidation attack by acting as a diffusion barrier to oxygen and metallic components. However, the coating might degrade due to the rapid formation of Nb enriched sublayer and depletion layer at the interface of enamel/Ti3Al alloys with high Nb contents (23 and 27at.%). At the interface of enamel/Ti3Al17Nb, a dense mixture oxides layer formed at the side of enamel due to the outward diffusion and oxidation of Al and Ti. This thin interfacial interdiffusion layer probably improves the adhesion of the coating to the substrate. Nevertheless, a Nb enriched sublayer formed at the interface of enamel/Ti3Al-(23,27)Nb during oxidation. And a porous depletion layer was observed beneath this Nb enriched layer due to the outward diffusion of metallic components. As a result, oxygen could diffuse inwardly through the imperfect barrier layer and depletion layer to initialize internal oxidation.

4.3.3. Oxidation of TiAl and Its Alloys 4.3.3.1. Introduction Titanium aluminide, TiAl, normally named as γ-phase, has a L10 ordered face-centered tetragonal structure [385-387]. γ-TiAl can exist in a wide Al content ranging from 49 to 66at.%. This phase apparently remains ordered up to its melting point, approximately 1450oC. It has been found that single γ-phase TiAl alloy is brittle with practically no defromability at temperatures up to 700oC, and only above that temperature was plastic deformation observed. Correspondingly, it has a fracture strength of nearly 500 MPa up to about 700oC. Above that temperature, thermally activated softening occurs making plastic deformation possible, and the resultant yielding leads to yield strengths below the fracture strengths. Formation of Ti3Al as a second phase by reducing Al content can improve its ductility. It has been confirmed experimentally that the strength and ductility of two-phase α2 + γ TiAl alloy is higher than that of single γ-TiAl alloy. The mechanical properties of two-phase TiAl alloys can be optimized through suitable control of grain size and microstructure, i.e., appropriate heat

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treatments and thermomechanical processing microstructures for the two-phase TiAl alloys:

[388-409].

There

are

four

typical

(1) “Near-γ” microstructure (NG): consisting of equiaxed γ grains and some very fine α2 grains or precipitates; (2) Duplex microstructure (DP): consisting of γ grains and lamellae colonies, and a few small α2 precipitates in γ grains; (3) “Near-lamellar” microstructure (NL): consisting of γ/α2 lamellae and small amount of equiaxed γ grains in the form of full lamellar structure; and (4) “Fully-lamellar” microstructure (FL): consisting of fully γ/α2 lamellae. Different structures may result in significantly different mechanical properties. For example, TiAl alloys with FL microstructures have high temperature strength, fracture toughness and creep resistance, but low ductility at low temperatures. Alloys with a duplex structure may have good tensile ductility, but their fracture toughness, high temperature strength and creep resistance might be poor. In the following section, we will also see that TiAl alloys with different microstructures might exhibit different responses to oxidation attack. TiAl alloys with the best balance of mechanical properties will have a bright future for applications to turbine blades of aero-engines, nozzle components such as flaps, nacelle structures, acoustic honeycombs, car turbochargers and exhaust valves [410-417]. Besides carefully controlled heat treatments and thermomechanical processing (TMP), small additions of alloying elements are often used for optimization of the mechanical properties of the two-phase α2 + γ TiAl alloys [418-439]. V, Hf, Cr and Mn increase the ductility significantly and produce solid solution strengthening, with Cr being most effective and Mn being least effective. Nb, Ta and W also produce solid solution strengthening, but they decrease the ductility. Interstitial elements such as C and N affect the ductility, depending on the Al concentration and pre-treatments, and in particular they improve the creep resistance. However, it should be pointed out that the mechanisms on the influence of alloying elements on the mechanical behaviour of TiAl alloy are not fully understood yet, further studies are still needed. Huang summarised the effects of various alloying elements on the properties of TiAl alloys [440].

4.3.3.2. Oxidation Behaviour and Resistance The oxidation resistance of TiAl (and its alloys) is some higher than that of Ti3Al because of its higher Al concentration, but it is still orders of magnitude lower than that of typical alumina-forming alloys, e.g., NiAl. Oxidation of TiAl alloys with sufficient high Al concentration, i.e., single-phase alloys with at least 50at.% Al, leads to the formation of Al2O3 scales with correspondingly low oxidation rates only at temperatures below about 1000oC, whereas at higher temperatures complex scales develop with an outer rutile layer over a mixed layer of rutile and alumina, with markedly increased oxidation rates. According to Becker et al., the scale morphology formed in air can be divided into three types with the following layer system [441-442]: (1) metal⎪⎢fine grained TiO2 + Al2O3⎪⎢coarse grained TiO2 + Al2O3⎪⎢air; (2) metal⎪⎢fine grained TiO2 + Al2O3⎪⎢Al2O3⎪⎢TiO2⎪⎢air; and

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(3) metal⎪⎢Al2O3⎪⎢TiO2 + Al2O3⎪⎢air. The fine-grained inner (TiO2 + Al2O3) layer grows by inward diffusion of oxygen, while the coarse grained outer (TiO2 + Al2O3) layer as well as the outer TiO2 layer grow by outward cation transport. Along with heating or with increasing oxidation temperature, the composition, phase structure and microstructure of the oxide scale formed on TiAl alloy samples exposed to the oxidizing atmosphere are changing. Correspondingly, the oxidation kinetic curve could be divided into three stages [441, 443]. Stage I is the period for heating the sample to the oxidation temperature or during the initial/incubation period of oxidation at relatively low temperatures. In this stage, the scale is enriched with Al2O3 and the oxidation rate is low. The oxide scale formed has the structure of: TiAl ⎢⎢Al-depleted zone ⎢⎢Al2O3 ⎢⎢gas. During Stage II, the oxidation rate is high, the scale becomes to be a mixture of TiO2 and Al2O3, and the structure is: TiAl ⎢⎢Al-depleted zone ⎢⎢fine dispersive TiO2 + Al2O3 ⎢⎢Al2O3 ⎢⎢coarse dispersive TiO2 ⎢⎢gas. After a long enough exposure at a high temperature the breakaway oxidation might occur. This is explained in term of the formation of relatively large cracks in the scale. At very high temperatures, small cracks can be self healed by sintering of the outer TiO2 layer, resulting in repeated acceleration for short periods in the oxidation kinetics. The dissolution of Al2O3 grains adjacent to the outer TiO2 layer into it and their subsequent reprecipitation near the outer scale surface might also contribute to this breakaway. The scale structure in this stage is: TiAl ⎢⎢Al-depleted zone ⎢⎢fine dispersive TiO2 + Al2O3 ⎢⎢ coarse dispersive TiO2 + Al2O3 ⎢⎢gas. The phase composition and structure in the interfacial and subsurface regions were also subjected to detailed characterization. With Auger Electron Spectroscopy (AES) analysis, Beye and Gronsky found that when enough Al is withdrawn from the alloy matrix to maintain the formation and growth of the surface oxides, the interfacial region transforms into either Ti10Al6O or Ti10Al6O2, depending on the local oxygen concentration. Behind this transformation front, Ti10Al6O grains are transformed into Ti10Al6O2 with the introduction of oxygen from the outside [444]. Their further results with TEM and microanalysis revealed that the subscale consisted of two phases: one is hexagonal with a composition close to Ti6Al3O4, and the other is cubic with a composition of Ti3Al2O3. The hexagonal phase is actually a solid solution of O in Ti3Al and the cubic phase is new [445]. The phase structure of the subsurface depletion layer was also studied by other researchers with an attempt to clarify the crystal structure of the potential phases presented [446-455]. Zheng and Quadakkers believed that one phase is α2-Ti3Al with a high concentration of oxygen, and the other is a cubic phase with a composition close to Ti5Al3O2 (named as Z-phase, which is basically same as X-phase reported in other studies). The formation and maintenance of this phase during oxidation has significant influences on the formation and development of protective oxide scales on the TiAl surface. Protective alumina formation on TiAl alloys could be achieved if the composition of the sub-surface layer consists of Z-phase (Ti5Al3O2) rather than α2-Ti3Al. However the Z-phase was found to be metastable and eventually decomposed to α2(O) + Al2O3, on which the exclusive Al2O3 scale growth cannot be sustained. The “nitrogen effect” is also demonstrated on TiAl alloys. Contrary to that on Ti3Al alloys, the effect of nitrogen on the oxidation of TiAl appears to be detrimental due to the

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formation of intermixed TiN (or Ti2AlN) and Al2O3 at the metal/scale interface, even in the initial oxidation stage, retarding the formation of continuous Al2O3 scale with high protectiveness [453, 456-460]. Several mechanisms have been postulated [461]: (1) Nitrogen doping of an initial TiO2 scale results in more rapid oxygen transportation to the interface between oxide scale and Al-depleted zone; (2) The grain boundary diffusion of nitrogen through the oxide leads to the formation of AlN or possibly AlON at the interface between oxide scale and Al-depleted zone; and (3) Nitrogen grain boundary diffusion through the oxide scale to the interface between oxide scale and Al-depleted zone, consequently, stabilizes the Al-depleted zone with relatively low Al activity, thus, promotes the growth of TiO2 scale with a high growth rate and poor protectiveness. However, beneficial effects of nitrogen on the oxidation resistance of TiAl alloys could also be expected: (1) nitrogen might reduce the amount of oxygen dissolved in the alloy, so the oxygen embrittlement could be reduced [462]; and (2) nitrogen is beneficial as long as a near-continuous nitride layer, which is probably in equilibrium with the Z-phase, is stable beneath the oxide layer. In this way the formation of a wide α2-containing subsurface depletion layer, accompanied by internal oxidation, destruction of the outer alumina barrier layer and high oxide growth rates is prevented [463]. It is well known that many metals or alloys oxidize faster in water vapor containing atmospheres than in dry oxygen. For Fr-Cr, Fe-Si and/or Fe-Al alloys, the protective scale (Cr2O3, SiO2 or Al2O3), which develops in dry oxygen, fails to develop or cannot maintain after certain period of exposure in water vapour containing atmospheres [464-477]. It is normally observed that after an incubation period breakaway oxidation will take place and accompany by the fast formation and growth of nonprotective solvent metal oxides. However, the mechanisms involeved in these accelerataed diffusion and growth processes are not fully understood. Water in oxidizing atmospheres also has great influences on the scaling behaviour and the protectiveness of the oxide layer formed on TiAl alloys since H2O affects significantly TiO2 and leads to the anisotropic and enhanced growth of TiO2 due to enhanced diffusion. Kremer and Auer studied the effects of water vapour on the oxidation of Ti-50 at.%Al alloy at 900oC in O2 or O2-H2O-gas mixtures (p(H2O) = 3.8, 12.5, 15.4, 19.3 mbar; p(O2) = 0.2 bar) [478]. In the initial oxidation stage, the mass gain is less in water vapour containing oxygen atmospheres compared to dry conditions. After that rapid breakaway oxidation follows in wet oxygen. The oxidation is faster in wet oxygen than in dry oxygen and the oxidation rate increases with increasing p(H2O) and decreasing p(O2). The presence of water vapour in the oxidizing atmosphere also alteres the oxide scale microstructure. In dry oxygen the oxide scale establishes an intermediate, compact Al2O3 barrier layer, while in wet oxygen no such a compact barrier layer is formed, instead separate Al2O3 particles are formed and embedded in the outer TiO2 layer. Taniguchi et al. also found that the thin Al2O3-rich layer, which is usually formed during oxidation in dry oxygen or air, cannot be developed during exposure in wet oxygen or in wet argon atmospheres at 827 and 927oC [479]. The study by Zeller et al. focused on the oxidation behaviour of Ti47Al1CrSi in dry air and air containing 10 vol.% H2O at temperatures of 700 and 750oC [480]. Similarly, they found the presence of water accelerated the oxidation kinetics. However, after switching back to the dry

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air, the oxidation rate was immediately reduced. An oxygen-rich layer was observed on the samples exposed to water-containing air. This layer consisted of α-Ti and α-Al2O3 which were formed due to either internal oxidation or decomposition of the cubic Al-depletion phase. These authors also found that the presence of water would affect the high temperature fatigue lifetime due to the increased brittle subsurface zone [481]. The effects of alloying elements on the oxidation behaviour of TiAl have been studied extensively. The objectives of alloying are to decrease the growth rate of the intermixed TiO2/Al2O3 scale, to favour the formation of Al2O3, and to stabilize the Al2O3 scale. According to Taniguchi et al., the selection of alloying elements can be guided by the following proposed mechanisms [482-483]: (1) Valence-control rule: If the formation of TiO2 were suppressed or minimized, then the situation will become more favourable for the formation of an Al2O3-rich or an exclusive Al2O3 scale. For this purpose, the valence-control rule (VCR), or WagnerHauffe rule, is applicable. Diffusion of oxygen via oxygen vacancies will contribute to the growth of TiO2. Therefore, alloying elements that can decrease the oxygen vacancies in TiO2 will be very effective to decrease the overall oxide scale growth rate by inhibiting the fast growth of TiO2; (2) Wagner’s scaling model: The suppression of internal oxidation of Al to form discrete Al2O3 particles/platelets in the alloy substrate is also effective to produce a continuous Al2O3 scale on the specimen surface. The critical concentration of alloying element for its transition from internal to external oxidation was derived by Wagner and is shown as [484-485]:

N Al

⎛ πg ∗ S DOValloy ⎞ ⎟ NO ; ⎜⎜ D AlVoxide ⎟⎠ ⎝ 3

1

2

(3) It can be clearly seen that the transition can be enhanced through increasing the diffusion of Al, DAl, or decreasing the inward diffusion of oxygen, DO, or its surface S

concentration, N O ; Formation of a barrier layer: If the alloying elements can form discrete or near continuous aggregates with enough high stability in the oxide scale near the scale/substrate interface, the enrichment of Al2O3 might be resulted in near this interface, then the oxidation rate can be decreased. Also, if the enrichment of alloying element in the alloy substrate could take place, the oxygen solubility in alloy can be decreased, this will contribute to the decreased oxidation rate; and (4) Modification of the initially formed scale: If the nucleation, growth, nature or stability of Al2O3 formed in the initial oxidation stage can be modified or enhanced, the scale formed might be very rich in Al2O3. Experimentally, the effects of various ternary additions on the oxidation behaviour of TiAl alloy had been thoroughly studied. In the works of Shida and Anada, a variety of ternary elements were added into Ti-34.5wt.%Al [486-488]. The oxidation tests were conducted in

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air at 800 to 1000oC for 100 hrs. Based to the oxidation kinetics measured, these ternary elements were then classified into three groups according to their effects: (1) detrimental: V (0.5-5.0wt.%), Cr (0.5-5.0), Mn (1.5-5.0), Pd (2.0), Pt (2.0), and Cu (2.0); (2) neutral: Y (1.0wt.%), Zr (2.0), Hf (2.0), Ta (2.0), Fe (2.0), Co (2.0), Ni (1.5), Ag (2.0), Au (2.0), Sn (2.0), O; and (3) beneficial: Nb (2.0wt.%), Mo (1.5-6.0), W (2.0-6.0), Si (1.0), Al (37.5/63), C and B McKee and Huang studied the oxidation behaviour of a number of ternary and quaternary TiAl alloys in air under rapid thermal cycling conditions for periods of hundreds of hours in temperature range 850-1000oC [489]. It was found that, 4at.% additions of W or Nb increased oxidation resistance, whereas the presence of a similar concentration of Ta, Cr or V had an adverse effect. However, higher Cr (>8at.%) and Cr + Ta, Cr + Nb, Mn + Ta, Mn + Nb and Mn + W alloying combinations added to TiAl gave very oxidation resistant alloys [489-490]. It is commonly observed that the individual alloying with Nb is beneficial to the oxidation properties of TiAl as it did in Ti3Al alloys [491-500]. In general, enhancement of an external Al2O3 scale formation due to Nb addition could be possibly explained by the following mechanisms: (1) For β alloys, addition of Nb can stabilise the β phase in Ti-Al alloy. The diffusivity of Al in β phase is high, so according to Wagner’s criterion for the transition from internal to external oxidation, the critical concentration of Al for this transition can be formed with lower Al concentrations [501-502]. However, this approach appears to be impossible for TiAl alloy because of lower Al diffusivity in γ-phase than in βphase; (2) In TiAl alloys, the activities of Al and Ti deviate from the regular solution largely, the ratio between Al activity and Ti activity is so small that thermodynamically TiO or TiO2 is much more stable than Al2O3. The addition of Nb might increase the activity of Al at the interface of scale/alloy substrate, resulting in a decrease in Ti activity and increasing tendency to form protective Al2O3 [327, 499]. However, some researchers believed that the activity ratio (aTi/aAl) was not changed significantly by the addition of Nb either in α2-phase or in γ-phase [441, 503]. Further discussion on this point is difficult due to the lack of necessary data; (3) The major defect in rutile formed during oxidation in air at high temperatures is supposed to be the doubly charged oxygen vacancy. Some results indicated that Nb5+ substitutes for Ti4+ in rutile, i.e., the substitution of two foreign Nb cations with a valence of 5 will reduce one oxygen vacancy in the rutile lattice, then reduce the mobility of oxygen anion, and finally suppress the fast rutile growth [494, 504-507]. It is also possible that Nb5+ doping could decrease the solubility of Al in TiO2 therefore stimulate the formation an inner alumina barrier at the metal/subsurface region [508]; (4) Nb may stabilize the γ-phase. The consequence with regard to TiAl-Nb oxidation could be that the initially formed scale is in contact with the γ-phase over a longer period before Al depletion leads to α2 formation in the subsurface zone. According to

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the Al-Ti-O phase diagram, contact with the γ-phase should promote protective Al2O3 formation. This tendency is additionally supported by Nb enrichment in the subsurface zone during transient oxidation [441]; (5) Nb-rich oxides have been observed at the scale/alloy substrate interface, and can act as a barrier to diffusion under certain conditions [509]. It was also reported that the addition of Nb could accelerate the formation of Al2O3 and change the structure of the diffusion barrier against oxidation [492]. Additionally, it was suggested that the dissolution of oxygen into the matrix might be suppressed by Nb addition by which the weight gain could be decreased [494]; and (6) It is commonly observed that exposure of γ-TiAl alloys containing Nb at elevated temperatures in air will lead to the formation of such an interfacial structure: enrichment of Al beneath a Ti nitride layer [510-511]. This structure can, to a certain extent, provide resistance to oxidation, though above it an intermixed layer of TiO2 and Al2O3 was formed which is not as resistant as protective and thin α-Al2O3 layer. Effect of Cr addition on the oxidation behaviour of TiAl is also complex. Addition of up to 4at.% Cr to Ti and TiAl resulted in an increase in oxidation rate [282, 489-490, 493, 496, 512-513], however the presence of doped Cr might improve the adhesion of oxide scale with substrate alloy and benefit the thermal cyclic resistance [514]. The reason can be explained as the VCR, i.e., the incorporation of Cr3+ ions into the rutile can cause: (1) an increase in the number of anionic vacancies, and (2) migration of Ti4+ ions to interstitial positions. However, at higher concentrations (> 8at.%), Cr promotes the formation of continuous external layer of Al2O3. The possible mechanisms are summarized as the followings: (1) According to Luthra, the formation of Al2O3 protective scale on TiAl alloy is dominated by thermodynamic factors [327]. Substitution of Cr for Ti, therefore, can decrease Ti activity, while, Al activity is comparable or higher, i.e., the Al/Ti activity ratio increases, and results in the shift of thermodynamic stabilities of Al2O3 and TiO or TiO2. If Cr content is sufficient high, Al2O3 may become to be more stable than TiO or TiO2. However, some experimental phase studies of Ti-Al-O showed that there is no Ti-Al-O thermodynamic barrier to protective Al2O3 formation in the composition range of the Cr effect [515-517]; (2) The substitution of Cr for Ti, in sufficient quantities, leads to the formation of Ti(Cr,Al)2 Laves phase, which exhibits a low oxygen permeability and is capable of protective Al2O3 formation [518-523]. Therefore, alloys containing a significant volume fraction of Laves phase can form Al2O3 protective scale at lower Al concentrations. Furthermore, it is presumed that the “nitrogen effect” apparently does not operate in the presence of sufficient amount of Cr addition in the TiAl alloys. These two possible effects act together, promoting the formation and stabilization of alumina scale; and (3) Cr can act as ‘traps’ for oxygen then effectively reduce both the solubility and diffusivity of oxygen in titanium, therefore decrease the critical Al content for the external scale formation according to the criterion for the transition from internal to external oxidation proposed by Wagner [501].

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A surprising finding is the chlorine effect [524-533]. Kumagai et al. found that reactivesintered TiAl-Mn containing 200-1600 ppm chlorine exhibited excellent oxidation resistance in comparison with the cast TiAl [524]. As shown in the AES and XPS results, chlorine existed as Cl- ions in titanium oxide near the oxide/alloy interface. Also, according to the VCR, oxygen ion vacancies will decrease due to the replacement of oxygen ions with Clions, resulting in the smaller diffusion of oxygen in TiO2 lattice. Then the growth of TiO2 was inhibited. On the other hand, the formation of dense oxide scales containing chlorine in the initial oxidation stage, to a certain degree, can decrease the solubility and diffusion of oxygen into the alloy substrate, and then enhance the transition from internal to external oxidation of Al at lower concentration. Studies by Schutze et al. also indicated that other halogen elements, such as fluorine, iodine and bromine, have the same positive effect on oxidation resistance of TiAl alloys when they were doped into the alloys through ion implantation or wetting treatment [534-541]. The vaporization of Ti chloride was proposed as an effective mechanism according to Taniguchi, because this process might enrich Al in the surface layer [483]. Schutze et al. developed a metal chloride transportation model based on thermodynamic calculations of the stability diagram for the system of Ti-Al-O-Cl [525, 527, 530]. Basically, it is believed that this beneficial halogen effect is based on the selective transport of volatile Al halides and their subsequent oxidation on the surfaces of pores and microcracks within the inner region of the initially-formed scales. Taking chlorine as the example, it was assumed that there is a window in the chlorine concentration. In this window, the vapour pressure of volatile Al chlorides will be significantly higher than that of the Ti chlorides, resulting in considerable evaporation of Al phase. Consequently, Al could be preferentially transferred into the gas phase as AlCl and, oxidized to Al2O3. If the pressure of chlorine is so low that either the pressure of AlCl or the pressure of TiCl3 can reach the critical value, the transportation of metal can be negligible, no chlorine effect can be observed. Similarly, if the chlorine pressure is very high, both the transportation of Al and Ti are significant, negative chlorine effect will be observed. This mechanism is applicable to other halogen elements, since the vapour pressure of Al monobromide or monoiodide is orders of magnitude higher than those of the most volatile Ti halogenides. Other alloying elements, which can be possibly used to improve the oxidation resistance of TiAl alloy, are: (1) Mo, which may reduce oxygen solubility in the alloy or promote the formation and thickening of a protective continuous nitride layer [542-543]; (2) W, which may reduce oxygen solubility in the alloy or enhance the diffusivity of Al [512, 544]. Doping of W could also suppress the growth of TiO2 and then decrease the oxidation mass gain. The continuous nitride layer formed in W containing alloys seems to have an important role in stabilizing the protective Al2O3 scale [545]; (3) Si can form SiO2 which is acting as a barrier against oxidation together with the Al2O3 layer in the oxide scale [492-493]; (4) Ta, which might suppress the formation of α2 phase during exposure therefore increase the oxidation resistance [546]; (5) Sb, which possibly retards the dissolution of Al2O3 and stabilize the diffusion barrier [547];

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(6) Ag: Addition of approximately 2% Ag was found to improve the oxidation resistance of TiAl based alloys during oxidation at 800oC in air by promoting the formation of a continuous, external alumina based scale. Z-phase in the Al-depletion region could be stabilized by Ag addition and thus the formation of harmful α2-Ti3Al is suppressed [455, 548-553], hence the stability of the Al2O3 scale could be maintained. The mechanism concerning the Z-phase stablization by Ag is unclear and the effect is decreased as the oxidation temperature increases; (7) Ru: Precious metal alloying with 2at.% Ru leads to a 20% increase of the oxidation resistance of Ti-55Al under isothermal oxidation at 900oC in air. This influence is attributed to the formation of a protective layer of the ternary compound (G-phase) around the grains of the γ-phase. Initially, cyclic oxidation, Ru-alloyed TiAl alloy exhibited significant exfoliation of the oxide scale, however, this undesirable process stopped after oxidation for 220 hrs and was not observed during further thermal cycling exposure up to 450 hrs [554]; and (8) Rear earth elements and/or their oxides (Zr, La, Hf or Y): addition of RE (<1%) to TiAl has been reported to improve the oxidation resistance by forming very protective Al2O3 scales even under thermal-cycling conditions, however the beneficial effects become smaller at higher temperatures and with increases in the RE contents. RE addition, generally, results in a fine-grained oxide scale and tends to segregate in the grain boundary areas and at the interfaces of Al2O3, retarding effectively the inward diffusion of oxygen, thereby decreasing the oxidation mass gains. RE addition can also increase the oxide/metal interfacial stability, decrease the scale spallation tendency and maintain the long-term protectiveness of oxide scales on the alloy surface [482, 546, 555-567]. The influence of microstructure on the oxidation behaviour of TiAl had also been catching the attention. For the possible industrial application, TiAl alloys developed were basically two-phase alloys, i.e., α2 + γ, because the two-phase alloys have better strength and ductility than the single γ-phase alloys. According to the heat treatment, four typical microstructures can be formed. They are NG, DP, NL and FL as discussed previously. It can be clearly seen that striking differences exist among these microstructures. Since Al concentration, oxygen solubility, reactant diffusivity and density of grain boundary, are quite different in α2 and γ phase, the alloys with different structures, therefore might exhibit different scaling behaviours when they are exposed to oxidizing atmospheres at elevated temperatures. According to the results of Gil et al., upon high temperature exposures, γ-phase is an alumina former, while, α2-phase forms titania [568-569]. This difference is a direct result of the large difference between Ti and Al contents in these two phases. If in the alloy microstructure the α2-phase is finely distributed along with the γ-phase, alumina scale formation will dominate the overall oxidation behaviour. However, if the amount of α2-phase is high and γ-phase is oversaturated in Al due to the slower cooling from higher temperatures, an oxide scale, consisting mainly of titania will dominate the overall oxidation process. A similar result was also reported by Brady et al. for cast and heat-treated two-phase (γ + Laves) Ti-45Al-15Cr alloys [520].

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Perez et al. also reported the influence of microstructure of the two-phase Ti-46Al-1Cr0.2Si alloy on the oxidation behaviour in air between 600 and 900oC [570]. They concluded that the size and distribution of α2-phase could determine the oxidation rate and the type of scales formed. However, another experimental observation of the authors with Ti-46.8Al1Mo-0.2Si alloy showed that the oxidation behaviour in air at temperatures ranging from 600 to 900oC does not depend on the type of microstructures, i.e. lamellar or duplex [543]. Haanappel et al. studied the isothermal and cyclic oxidation behaviour of Ti-48Al-2Cr and Ti-48Al-2Cr-2Nb at 800oC in air with their emphasis on the microstructural effects [571572]. Their results showed that the growth rate, spallation behaviour, composition, structure and morphology of the oxide scales formed have no major relation to the microstructure of the base materials. Although the results obtained by these researchers are some different, it should always be remembered that, other factors, such as composition, concentration of minor element, surface finish, oxidizing atmosphere, testing procedure, and so on, might be different among different researchers. These factors might have some influences on the oxidation behaviour of alloys, but they have not been fully recognized yet. So it was believed that, if oxidation at various temperatures is considered, or the effect of alloying elements on oxidation is discussed, the influence of microstructure must be taken into account.

4.3.3.3. Oxidation Protection of TiAl and Its Alloys It had been observed that surface finishing might potentially affect the oxidation behaviour of TiAl alloys [453, 573]. The grinding processes induce certain deformation and also increase dislocation density in the near-surface region. Recrystallization may therefore result in additional grain boundaries, decreasing the grain size and increasing elemental diffusivities, then leading to the formation of an Al2O3 scale in the initial oxidation stage. Thus, besides the alloying approaches, various surface treatment techniques and coating systems have been applied to TiAl alloys to improve their high temperature oxidation resistance in aggressive environments. The major objective is to suppress the fast growth of TiO2 and promote the formation of protective α-Al2O3 scales on the outer alloy surfaces. 4.3.3.3.1. Diffusion Coatings If the content of Al in the alloy or in the near-surface region is high enough, the exclusive formation of an external Al2O3 scale could be expected on TiAl alloys. The simplest but most effective method to increase the Al content is aluminizing. Traditional aluminide coatings produced by pack cementation, electrodeposition or sputtering/inter-diffusion and/or electrospark depsotion processes have been widely applied onto TiAl alloys in order to form a layer of TiAl3 (and/or TiAl2) against oxidation [574-590]. Due to the higher oxidation resistance of TiAl3 and/or TiAl2, the isothermal and cyclic oxidation resistance of TiAl alloys can be improved significantly during relatively short testing time periods. The main problems associated with the conventional TiAl3 coating by conventional pack cementation are the relatively rapid diffusion of Al into the alloy substrate and crack formation in TiAl3 layer or even deeply penetrating into the substrate. The reason for cracking initialization is that TiAl3 with a low symmetry crystal structure is extremely brittle at ambient temperature. These processes will lead to the loss of Al and then the degradation of the coating systems, therefore, long-term protection could not be maintained. Cr, therefore was added into the TiAl3 layer to modify the chemical and mechanical properties of plain TiAl3 coatings.

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Alloying with Cr could form cubic L12 crystal structure which is highly symmetrical and may have a sufficient number of slip systems for homogeneous deformation [591-593]. Alloying TiAl with Cr, Nb, Si and REs can improve the oxidation resistance. Therefore, Nb-Al, silicide and/or composite coatings with Al + Cr, Al + Si, produced through chromizing and siliconizing processes have also been actively developed through pack cementation, liquid-phase processes and PVD + vacuum diffusion treatment [594-613]. These processes could improve the oxidation resistance of TiAl; however, the long-term stability is still a concern though the inward diffusion of Al could be partially inhibited by modification of coating structures by incorporating other elements.

4.3.3.3.2. Metallic Coatings Plasma sprayed coatings of NiCrAlY of 100 and 200 μm thickness or CoNiCrAlY of 50 to 60 μm thickness on TiAl decreased the oxidation rate to a certain degree [614-615]. The application of a fine-grained Co-30Cr-4Al coating about 30 μm to TiAl by magnetron sputtering resulted in alumina scale formation [616-617]. However, at higher temperatures, accelerated oxidation took place after a short protective stage. This is related with the formation of micropores at the oxide scale/coating and coating/substrate interfaces as oxidation proceeded. Recrystallization of coatings during oxidation and a Kirkendall effect due to preferential diffusion of Co into the substrate are responsible for this pore generation. Furthermore enhanced outward diffusion of Ti and appearance of fast growing rutile mounds on the scale will contribute to the accelerated oxidation. CoCrAlY, NiCrAlY and FeCrAlY overlay coatings had also been deposited onto TiAl by sputtering. Oxidation tests at 9001000oC showed that these coatings could improve the oxidation resistance due to the formation of α-Al2O3. However these coatings also suffered severe interfacial interdiffusion and pore generation which eventually caused the failure of the coatings [618-620]. A nickel aluminide coating was developed on TiAl alloy by electroplating a Ni film followed by a high Al activity pack cementation [621-622]. The coating has a duplex layer structure, an outer Ni2Al3 layer and an inner TiAl3/TiAl2/TiNiAl2 layer. This coating could ensure the formation and maintenance of a protective Al2O3 scale during oxidative exposure at 900oC. Heating at high temperatures also leads to the structural change of the coating, which has an outer β-NiAl and inner TiAl2 and TiNiAl2 layers after 1000 hrs, and finally TiNiAl2 with TiAl2 + τ3 phase (Ti-Al-Ni) after 10,000 hrs. The phase transformation also results in the formation of voids within the outer layer. Composite coating containing Ti5Si and TiSi had been applied onto Ti-48Al-2Cr-2Nb using laser cladding of mixed NiCr-Si precursor powders [623]. The relatively continuous and dense hybrid oxide scales consisting of Al2O3 and SiO2 provide a better oxidation resistance to the substrate in comparison with of the brittle and porous TiO2-enriched oxide scale formed on uncoated alloys. Currently, some researchers suggested that TiAlCr based coating systems may have a better compatibility with the TiAl alloy substrates due to their similar compositions and structures. Two-phase TiAlCr alloys (L12 + Cr2Al and/or γ + Laves phase) have been accepted as the most appropriate coating materials to improve the high-temperature oxidation resistance of TiAl alloys [523, 553, 624-633]. The oxide scale formed at 800-1000oC normally consisted of a continuous alumina layer providing excellent protection to the underlying alloy substrate. Doping with Hf or Y can further refine the grain size in the surface

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oxide layer and result in a smooth morphology of the oxide layer with an improved adherence to the substrate. However, for the long-term protection of TiAl alloys with applied TiAlCr coatings, the interfacial diffusion processes (formation of brittle phases) at elevated temperatures (>900oC) and mechanical mismatch (CTEs and thermal stresses) between the coating and the substrate must be carefully considered.

4.3.3.3.3. Ceramic Coatings Alumina coating produced by chemical vapour depsotion (CVD), micro-arc oxidation (MAO) or reactive sputtering process can provide limited protection for TiAl alloys [634637]. While it was also reported that enamel coating can provide very good protectiveness for TiAl under isothermal and cyclic oxidation [637-638]. SiO2 coating was also applied onto TiAl alloys by magnetron sputtering [639]. Oxidation tests at 850oC in air showed that the cyclic oxidation properties of TiAl alloys could be improved since this coating could serve as a barrier layer to the inward diffusion of oxygen and outward diffusion of metallic ions. An anodic alumina layer has also been applied onto TiAl alloy substrate by sputter-depositing aluminum and subsequent anodizing of the Al layer [640]. This thin alumina layer, less than 500 nm thick, can suppress effectively the interdiffusion between the oxidation-resistant alloy coating (Al-21at.%Nb-10at.%Cr alloy) and the TiAl substrate, particularly when a thin Al layer is remained beneath the anodic alumina. Silicon nitride (Si3N4) films of different thicknesses (0.5, 1 and 2 μm) had been deposited onto TiAl by ion-beam-enhanced deposition (IBAD) [641-643]. Cyclic oxidation tests carried out at 1027oC for at least 30 cycles (600 hrs) showed that the nitride film of 0.5 μm thickness has an excellent oxidation resistance. However, this effect decreases as the thickness of the coating increases. The excellent oxidation resistance comes from the formation of a thin layer rich in Al2O3 beneath the outer TiO2 layer. The less effectiveness for oxidation resistance of the thicker film is related to the local fracture of the coating and the spalling off of the oxide scale. Thermal barrier coatings (TBCs) have also been applied onto TiAl alloys to to reduce the service temperatures on the component surfaces and then to prolong the service life of these alloys [644-646]. Before the application of the TBCs (zirconia or partially yttria stabilized zirconia coatings), the surfaces of the TiAl alloys were subjected to suitable treatments, such as preoxidation or deposited with TiAl3 or TiAl2 diffusion coatings, or Ti-Al-Cr, TiAlCrYN coatings. Oxidation tests showed that the oxidation resistance of the material system is highly dependent on the surface treatment of the TiAl alloy. TiAl3 aluminide coating provided an excellent oxidation protection associated with the formation of a continuous alumina scale. The TBCs did influence the oxidation behaviour: (1) interdiffusion and/or reaction processes between TBCs and thermally grown oxides were observed; and (2) fast growth and cracking of titania scales on sample surface without enough oxidation protection finally led to the failure of the thermal barrier coating systems. 4.3.3.3.4. Ion Implantation Ion implantation can add an element into the surface layer of an alloy in a well-controlled and reproducible manner (depth and dose) [647]. This processing can dramatically change the composition and microstructure of the surface or near surface region, while the properties of the bulk material will be remained. It can thus serve as a powerful tool to study the influence

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of various elements on the oxidation behavior of TiAl. Similar with alloying approach, it has been found that ion implantation of Nb [648-659], Si [660-661], Cr [662], Zn [663], Ta [664], Mo [665-666], W [667-668], C [669], Al [670] and/or combined ion implantation [671-672] showed a large beneficial effect on the oxidation behaviour. The improved oxidation resistance is mainly attributable to the formation of Al2O3 layers or Al2O3 rich layers in the oxide scale during the initial stages of oxidation or to the decreased anion and cation transport in the scale (due to decreased defect concentration or formation of other diffusion barriers). C implantation leads to the formation of a C rich layer which acts as a barrier to the inward diffusion of O in the early stage of the oxidation, but this effect will disappear soon due to the fast consumption of C. Combined implantation of C and Nb could get a better effect on oxidation resistance enhancement. On the other hand, implantation with smaller doses might be ineffective for improving oxidation resistance, neutral or even detrimental effects on the oxidation resistance of TiAl alloys therefore had also been found. The main problems associated with ion implantation are: (1) difficult to perform implantation over parts with complex shapes or on large areas with high uniformity; (2) expensive for operation; and (3) holding the beneficial effects for longer exposures.

4.3.3.3.5. Preoxidation at Low Oxygen Partial Pressures The preoxidation treatment of TiAl alloys in SiO2, TiO2 or Cr2O3 powder packs resulted in very thin scales, virtually Al2O3 scales after further oxidation at higher oxygen atmospheres (pure oxygen or air) [556, 673-675]. It was also found that the scale thickness decreased as the dissociation pressure of the powder decreased. The superior oxidation resistance was attributable to the formation of a scale very rich in alumina by the preoxidation. Similar results had been observed on TiAl-Mn alloy preoxidized in CO-CO2 gas mixture with a very low equilibrium partial pressure of oxygen then oxidized at 1000oC up to 600 hrs [676]. Gray et al. observed that the heat treatment of TiAl alloy in a silica capsule under low oxygen partial pressures at 1010oC for 50 hrs produces a thin (1-2μm) Ti5Si3 external film on the sample surface [677]. The Ti5Si3 layer is formed by dissociation of the silica capsule to form SiO, which reacts with Ti in TiAl at very low oxygen partial pressures. The Ti5Si3 layer confers significant improvements in oxidation resistance for at least 500 hrs in air at 900oC. TiAl alloys were oxidized in argon atmospheres with low oxygen partial pressures (Po2 ≈ -17 10 and 10-20 atm) at 800oC to investigate the potenetial of Al selective oxidation [678]. The low Po2 atmospheres were created by using a solid-state oxygen pump system [679-680]. GAXRD and FE-SEM characterizations did not support the preferential formation of aluminium oxides in the initial oxidation stage, instead, titanium oxides, such as Ti2O or TiO were detected. Similarly, Legzdina et al. found that annealing of single phase Ti-52.1Al-2Ta (at.%) in the temperature range 550-900oC in low partial pressures of oxygen (10-5 or 10-9 atm) resulted in the formation of a multi-layered surface oxide structure with the outer layer being Al2O3 followed by a layer of TiO2 [681]. These results are quite different from those observed in oxide packs. It is suggested that this might be related to the relatively high oxygen patial pressures in comparion with the equilibrium dissociation pressures of Al and Ti oxides at these temperatures, or related to the presence of trace amount of water, nitrogen or other impurities in the annealing atmospheres [682]. The oxidation resistance can also be improved through preoxidation in air followed by polishing [683]. This characteristic is attributed to the compressive stress relief associated

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with the removal of the outer TiO2 layer, the stress relief will alleviate cracking or rupture of the scale simultaneously reduce the stress-assisted diffusion in the scale. Also, removal of TiO2 can reduce the catalytic effect, which favours the dissociation of molecular oxygen into oxygen atoms.

4.3.3.3.6. Presulfidation in S-Containing Atmospheres In S-containing atmospheres, Ti can react with S preferentially to form titanium sulfides. As the sulfides grow by the outward diffusion of Ti, Al will be enriched on the substrate surface, resulting in the formation of Al-rich titanium aluminide layers, such as TiAl3 and/or TiAl2, which has a better oxidation resistance than TiAl substrate [684-687]. In comparison with conventional pack cementation, lower stresses present in the coatings. Addition of Cr to the TiAl can also improve the oxidation resistance of TiAl alloys after sulfidation treatment. It was found that sulfidation processed TiAl-10Cr alloy showed very good oxidation resistance at 900oC up to 750 hrs, due to the formation of a continuous Ti(CrAl)2 Laves layer, which was formed by a reaction between TiAl2 and the (Cr,Ti)Al2 formed by sulfidation. A protective Al-rich oxide scale was developed on the continuous Ti(CrAl)2 Laves layer. Other elements, including Ag, Co, Cu, Fe, Ge, La, Mn, Mo, Nb, Ni, Si, Ta, V, W, V, Zr and Y (2at.%), have been added into the alloy substrate to investigate their potential infleunces on the oxidation behaviour of sulfidation processed TiAl alloys. TiAl alloys containing Cr, Fe, Ge, La, Mo, Nb, Ni, Ta, W and Y oxidized slower than unalloyed TiAl, while, alloys containing Ag, Co, Cu, Mn, Si, V and Zr may oxidize slightly faster than the binary TiAl. The enhanced oxidation property is mainly due to the formation of a continuous layer of Laves phase Ti(Al,X)2, formed from X-Al and TiAl3 layers. 4.3.3.3.7. Nitridation Treatment The effects of nitridation on the oxidation behaviour of TiAl were investigated by Perez and Adeva [688]. The Ti-48Al-2Cr alloy samples were subjected to nitridation treatment at 800oC for 10 hrs and then oxidized at 800oC in air. It was found that nitridation resulted in the formation of a thin and continuous nitride layer consisting of a mixture of TiN, AlN and Ti2AlN which can act beneficially as a diffusion barrier during the initial transient stage, preventing oxygen dissolution in the α2-Ti3Al phase of the alloy and decreasing the total oxidation mass gain. The oxidation mechanism of the alloys was not changed due to the nitridation, however, the formation over the mixed alumina-rutile layer of an alumina-rich layer could reduce the oxidation rate. 4.3.3.3.8. Phosphoric Acid Surface Treatment Ti-48Al-2Cr-2Nb alloy, treated by surface painting with phosphoric acid (85% in water) and calcination, oxidized at 800oC in air up to 500 hrs with a significantly lower rate than untreated materials [689]. It was found that the reduced oxidation rate was associated with a continuous or near continuous inner alumina layer, as compared to an intermixed alumina/titania scale on the untreated specimen. However, the mechanisms invoved in the enhanced formation of alumina layer was not clear. Polished Ti-50Al alloys were also treated by anodization in the electrolytic solution of 4 wt% phosphoric acid at 18oC for 45 min. The anodic films, which are amorphous and contain substantial amount of phosphorus, can slow down the formation of rutile and α-Al2O3 during

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cyclic oxidation in air at 800oC. The doping effect of phosphorus ions in Ti oxide can account for the improvement of high temperature oxidation of Ti-50Al alloy [690]. Brou et al. dipped Ti-54Al alloy specimens into a low concentration orthophosphoric acid solution (0.3M) at room temperature for 1 min, and then dried in air for 24 hrs [691]. They found that this chemical treatment can significantly decrease the oxidation mass gain of the TiAl alloy during an exposure at 800oC in air up to 500 hrs. They believed that this treatment gives rise to a homogeneous deposit containing orthophosphates groups and the subsequent oxidation mainly induces the formation of pyrophosphate, TiP2O7, instead of the usual TiO2/Al2O3 mixed phase. The pyrophosphate layer is responsible for the drastically reduced oxidation kinetic.

4.3.3.3.9. Fluidized Bed Treatment A surface treatment using a fluidized bed with WO3 powders had been developed to improve the high temperature oxidation resistance of TiAl alloys [692]. The reagent used was a mixture of 40wt%WO3 powder with 60%Al2O3 powder. The bed was fluidized by an argon gas flow. Specimens were treated in the bed at 1000oC for 2 hrs. The oxidation tests were carried out at 900 and 950oC for 200 hrs in air and in a typical exhaust gas atmosphere. The cyclic oxidation resistance of TiAl-base alloys was significantly improved. The excellent oxidation resistance obtained is attributable to a continuous and sound Al2O3 surface layer formed during the treatment. This protective layer acts as a barrier against the formation of a complex oxide scale consisting of a TiO2 layer and a porous inner layer of TiO2 and Al2O3. 4.3.3.3.10. Micro- and Nano-Crystallization Micro- and/or nano-crystallization are very effective in promoting the formation of protective alumina scale on the alumina forming alloys [693-699]. Sputtering is then used to build up a fine-grained TiAl coating on the alloy substrtae with similar compositions. The cast TiA1 alloy normally forms a TiO2-Al2O3 mixed scale, and this scale type cannot be changed by microcrystallization as revealed in Wang’s experiements [700]. The authors believed that microcrystallization may also increase the solubility and diffusivity of oxygen or enhance the diffusion of Ti, therefore, preferential oxidation of Al could not be promoted. However, the scale adhesion was significantly improved by microcrystallization since (1) the bonding between the oxide scale and the metallic substrate is enhanced by many pegs formed along the columnar structure, which anchor the scale to the metal; and (2) stress relaxation in the oxide scale could be enhanced due to plastic deformation of the fine grained metallic substrate. Wendler et al. found that nano-crystalline coatings alloyed with ternary or quaternary elements (Ag, Cr, Mo, Nb, Si, Ta or W) could improve the oxidation resistance of Ti40at.%Al alloy [544, 701]. The oxidation parabolic rate constants of some coatings are five orders of magnitude less than that of the bare TiAl substrate. The higher oxidation resistance of the coatings is a result of the thin α-Al2O3 layer formation on the surface of the substrate during oxidation, and this dense, adherent and uniform α-Al2O3 layer composed of fine oxide grains is due to a fine-crystalline structure of the magnetron deposited coating as well as the effect of the alloying element.

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4.3.4. Oxidation of TiAl2 and Its Alloys 4.3.4.1. Introduction TiAl2 is one of the four intermetallic phases in the Ti-Al binary system, which has been largely overlooked, probably due to the fact that this phase did not appear in early compilations of Ti-Al phase diagrams. TiAl2 was first determined to have the HfGa2-type, tetragonal, space group I41/amd [702]. Mabuchi et al. used the pack cementation technique to produce TiAl3 coatings on TiAl, and found that the intermediate layers crystallize in the HfGa2 structure type [574]. TiAl2 is a re-entrant phase: at low and high temperature TiAl2 has the ZrGa2 type of structure, orthorhombic, space group Cmmm, labeled as h-TiAl2, and in the intermediate temperature the crystal structure is of HfGa2 type [703-705]. With its higher aluminium content, TiAl2 would be expected to have a lower density and better oxidation resistance than Ti3Al and TiAl, potentially making it an attractive elevated temperature alloy. However, the studies now available are mainly focused on its phase stability and crystal structure. The very limited works on its mechanical and oxidation properties were finished by Benci et al. [706-707]. Actually, their research group has been characterizing the structural and mechanical properties of TiAl2 as a function of the processing method. TiAl2, which has been rapidly solidified by melt spinning, has the L10 crystal structure. As-cast, cast and annealed, cast and HIPed, and melt-spun and annealed TiAl2 all have the HfGa2 crystal structure. Furthermore, they evaluated the possibility of using TiAl2 as high temperature structure materials. The TiAl2 specimens were prepared in three conditions: as-cast, cast and hot isostatically pressed, and hot isostatically pressed powders. The mechanical properties were determined with measurement of the compressive yield strength at various temperatures. The compressive yield strength of as-cast and cast and HIPed TiAl2, which is about 700 MPa at room temperature and decreases with increasing temperature to about 400MPa at 800oC, is about four times greater than the yield strength of cast TiAl3. The compressive yield strength of powder-processing TiAl2 is approximately 1350 MPa at room temperature, much higher than that of as-cast, cast and HIPed, cast TiAl3, and powder-processing TiAl. However, the yield strength decreases rapidly with increasing temperature. At 850oC, it is about 350 MPa. But at 700oC, the yield strength of powderprocessing TiAl2 is still about 50% greater than that of PP TiAl. The plastic engineering strain-to-failure for as-cast TiAl2 is low at room temperature, about 0.3%, and increases gradually with increasing temperature, to about 4% at 850oC. This extent of plastic deformation is still larger than that of TiAl3. The plastic strain-to-failure for powderprocessing TiAl2 is the highest among these three materials. At room temperature the plastic strain-to-failure was measured to be 5%, increasing to 17% at 500oC and over 60% at temperature above 775oC. 4.3.4.2. Oxidation Behaviour and Resistance The oxidation tests were carried out at 815 and 982oC in air for a time period of 100 hrs [706]. The comparisons with other kind of Ti-Al materials clearly indicate that the oxidation resistance of TiAl2, especially powder-processing TiAl2, is much better than that of other TiAl intermetallics with lower Al contents and is comparable with that of TiAl3 under this oxidation condition. The morphology observed on PP-TiAl2 showed a multi-layer structure,

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some parts are rich in the oxide of Al, however on other parts, oxide of Ti is formed. Oxidation data showed that Al2O3 might be formed at temperatures higher than 800oC. However, no long-term study of TiAl2 oxidation is available in open literature. So, the oxidative lifetime of TiAl2 is still complicated due to the potential formation of a subscale layer of the TiAl phase resulted from the limited solubility range of Al in TiAl2 and consumption of Al from TiAl2 to form Al2O3. It was believed that the formation of underlying subscale layer of the TiAl phase could degrade the ability to maintain Al2O3 formation in air. TiAl2 coating about about 20 μm thick was also applied onto TiAl alloy using magnetron sputtering deposition [708]. It was found that an external Al2O3 layers with a θ-phase structure was formed on the TiAl2 coatings at 800 and 900oC, and the θ-Al2O3 scales showed a high protective ability with low mass-gains and good scale adherence. Fine-grained coating microstructure of the TiAl2 coating was believed to have played a role in promoting the formation of Al2O3. After oxidation, an inter-diffusion region of about 5 μm was observed between the TiAl2 coating and the γ-TiAl substrate, which could act as a metallurgical bonding between the coating and the substrate.

4.3.5. Oxidation of TiAl3 and Its Alloys 4.3.5.1. Introduction TiAl3 is one of the intermetallic compounds named as trialuminide [709]. It crystallizes with the tetragonal D022 structure. The Young’s modulus of polycrystalline TiAl3 at room temperature reaches the level of 216 GPa, and is of the order of that of the Ni-base superalloys. The strength of TiAl3 at room temperature is low compared with other titanium aluminides. At the same time, TiAl3 is extremely brittle at temperatures below 600oC because of its low symmetry D022 structure with few slip systems. It is believed that the microstructure can be changed from D022 to L12 through alloying process. The cubic L12 structure is more symmetric than the tetragonal D022 structure and has a sufficient number of slip systems; thus it should be more deformable. Ternary L12 phases have been obtained by alloying TiAl3 with Cr, Mn, Fe, Co, Ni, Rh, Pt, Pd, Cu, Ag, Au and Zn. It has been reported that these modified TiAl3-base alloys showed compressive ductility to some extent at room temperature and a small tensile ductility [710-720]. Elastic moduli have been measured and the Young’s moduli have been found to be 200 GPa for Ti-67Al-8Ni and 192 GPa for Ti67Al-8Fe. The compressive yield strength of Ti-66Al-9M with M = Fe, Cr, Mn or mixtures of these transition metals is of the order of 300 MPa between room temperature and about 800oC, i.e., there is a strength plateau or a slight positive temperature dependence. Much better mechanical properties can be obtained by variations in the composition and the microstructure, and in particular by the development of multiphase composites [721-722]. 4.3.5.2. Oxidation Behaviour and Resistance Because of its extremely high Al content, TiAl3 and its alloys should be able to form a protective external Al2O3 scale on the surface and maintain the stability. Therefore TiAl3 is an attractive material for high temperature applications. The comparison between the oxidation resistance of TiAl and TiAl3 had been conducted by Umakoshi et al [723]. Their result showed that the oxidation kinetics of TiAl3 in pure oxygen at temperatures between 800 and 1000oC followed the parabolic rate law, and its oxidation resistance is much better than that

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of TiAl under the same oxidation conditions, and the tendency became more remarkable with increasing oxidation temperatures. Oxidation kinetics of cast TiAl3 had also been studied by Smialek et al [724]. It was shown that the isothermal exposure of drop cast TiAl3 above 1000oC exhibited parabolic oxidation behaviour controlled by protective α-Al2O3 scale formation. Below 1000oC, high anomalous rates at short times can be observed, this phenomenon was explained as the inhomogeneous microstructure of the TiAl3 casting, and the internal oxidation resulted from the existence of second phase. Actually, it was noted that the processing of TiAl3-X alloys is crucial since the cast alloys usually contain residual pores and second phase particles. The elimination of these defects by post-solidification treatments, i.e., heat treatment, hot working, hot extrusion, or forging, is difficult. From this result, it can also be found that the microstructure must be taken into account when oxidation resistance was compared in wide temperature range or between different researchers. Oxidation behaviours of TiAl3 alloyed with Ag, Cr, Cu, Fe, Mn and Ni had also been studied [372, 725-729]. The results obtained showed that both Ti-67Al-8Ni and Ti-66Al-9Fe exhibited excellent oxidation resistance in air at temperatures up to 1100oC following approximately parabolic rate law. Microstructural analysis of these two TiAl3-base alloys showed continuously protective Al2O3 oxide scale on the oxidized specimens in the entire testing temperature range. Neither internal oxidation nor the oxides containing Ni or Fe was found. The scales adhere well to the substrate material so that no spalling occurred. In contrast with Ni and Fe modified alloys, mass gains of TiAl3-Mn over 1000oC increased quickly, pits consisting of Al2O3 mixed with TiO2 particles started to develop locally through the Al2O3 scale and the growth of tiny TiO2 crystals at these places on outer surface. At 1200oC, Ti-67Al-8Cr alloy exhibited excellent cyclic oxidation resistance; the oxide formed was primarily α-Al2O3. At lower oxidation temperature, such as 800 and 1000oC, thin and continuous Al2O3 scale formed on Ti-67Al-8Cr and Ti-66Al-9Mn, and showed low oxidation rate. Addition of 10at.% Cu into TiAl3 did not improve the oxidation property since the oxide scale was composed of TiO2 and CuO in addition to Al2O3. Dense and protective α-Al2O3 scale was developed on Ag alloyed TiAl3 oxidized at 1000oC in air for a long exposure of 30 days. These results make some researchers believe that modified TiAl3 alloys with L12 structure might become to be the potential high temperature structural materials because of their good oxidation resistance and applicable ductility. Actually, TiAl3 and its alloys have widely used as protective coatings for Ti, Ti3Al, TiAl and also steel substrates used in high temperature corrosion and erosion environments [730-737].

5. CONCLUDING REMARKS Resistance to environmental degradation is one of the key requirements for the practical application of a special material due to the consideration of economy and safety. Oxidation at elevated temperatures in oxygen-containing atmospheres is one of the most common degradation forms induced by the interactions between a material and the environment. Aluminides based intermetallic compounds, such as Fe-Al, Ni-Al and Ti-Al, rely on the formation of a highly protective alumina scale on their external surface to effectively isolate the underlying alloy substrate from the aggressive atmosphere. These aluminides have much higher aluminium contents in their bulks in comparison with conventional iron- or nickel-

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based alumina forming alloys (FeCrAl or NiCrAl). However, the formation, growth and maintenance of the alumina scale may vary considerably amongst these intermetallic compounds. The study on the high temperature scaling behaviour of these intermetallic compounds and their derived alloys therefore has been a topic for the materials research community; and the majority of the works focuses on the potential influences of alloy composition and microstructure on the formation ability and characteristics of the protective alumina scale. The extensive lab tests do provide new knowledge for a better understanding of the mechanisms involved in the growth and failure processes of the alumina scale, and for the successful design and development of new materials. However, fundamental studies on thermodynamic equilibrium phase diagrams, defects, diffusion processes, phase transformations, crystal structures and electronic structures are lack. Compuational modelling together with sound experimental supports will be a powerful tool to develop strategy for material design, and should be strengthened in future studies. Practical applications, i.e., the commercial utilization of parts fabricated with these materials, however, will require more information concerning the properties of these materials since the enviroments in which the parts will be exposed are much more complex than the conditions set in lab tests. Corrspondingly, the response of the materials might be some different to that observed in lab. At present, the tests of these intermetallic compounds and their derived alloys in simulated or real environments are very limited. Furthermore, lab tests are normally carried out for a limited exposure time although at temperatures slightly higher than the practical ones. Long-term tests are necessary to evaluate the lifetime of the working pieces, and should be emphasized. Coating is an effective way to protect the underlying alloy substrate from attack. However, a satisfactory coating system requires at least the following characteristics: (1) excellent adhesion to the underlying alloy substrate; (2) superior oxidation resistance by forming highly protective and mechanically strong oxide scales within long exposures; and (3) limited interdiffusion between the coating and the substrate that does not result in the formation of depletion zones and/or brittle phases. Unfortunately, for some intermetallic compounds, the coating systems under investigation could not meet these requirements. The solutions therefore may largely rely on the development of materials with more rational alloying and strengthening strategy and on the realization of innovative coating design.

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[712] H. Mabuchi, K. Hirukawa, H. Tsuda and Y. Nakayama, Scripta Metall. Mater., 24 (1990) 505. [713] H. Mabuchi, K. Hirukawa, K. Katayama, H. Tsuda and Y. Nakayama, Scripta Metall. Mater., 24 (1990) 1553. [714] W.O. Powers and J.A. Wert, Metall. Trans. A, 21 (1990) 145. [715] Y. Nakayama and H. Mabuchi, Intermetallics, 1 (1993) 41. [716] R.A. Varin, L. Zbroniec and Z.G. Wang, Mat. Res. Soc. Symp. Proc., 646 (2001) N3.11.1. [717] S. Miura, J. Fujinaka, R. Nino and T. Mohri, Mat. Res. Soc. Symp. Proc., 646 (2001) N5.15.1. [718] Yu.V. Milmana, D.B. Miracle, S.I. Chugunova, I.V. Voskoboinik, N.P. Korzhova, T.N. Legkaya and Yu.N. Podrezov, Intermetallics, 9 (2001) 839. [719] C. Colinet and A. Pasturel, Intermetallics, 10 (2002) 751. [720] C. Colinet and A. Pasturel, J. Phys. Condens. Matter, 14 (2002) 6713. [721] M. Heilmaier, H. Saage and J. Eckert, Mater. Sci. Eng. A, 239-240 (1997) 652. [722] Y.Y. Fu, R. Shi, J.X. Zhang, J. Sun and G.X. Hu, Intermetallics, 8 (2000) 1251. [723] Y. Umakoshi, M. Yamaguchi, T. Sakagami and T. Yamane, J. Mater. Sci., 24 (1989) 1599. [724] J.L. Smialek and D.L. Humphrey, Scripta Metall. Mater., 26 (1992) 1763. [725] K. Hirukawa, H. Mabuchi and Y. Nakayama, Scripta Metall. Mater., 25 (1991) 1211. [726] L.J. Parfitt, J.L. Smialek, J.P. Nic and D.E. Mikkola, Scripta Metall. Mater., 25 (1991) 727. [727] S.P. Chen, W. Zhang, Y.H. Zhang and G.X. Hu, Scripta Metall. Mater., 27 (1992) 455. [728] D.B. Lee, S.H. Kim, K. Niinobe, C.W. Yang and M. Nakamura, Mater. Sci. Eng. A, 290 (2000) 1. [729] N. Yamaguchi, T. Kakeyama, T. Yoshioka and O. Ohashi, Mater. Trans. JIM, 43 (2002) 3211. [730] B.G. McMordie, Surf. Coat. Technol., 49 (1991) 18. [731] A. Hirose, T. Ueda and K.F. Kobayashi, Mater. Sci. Eng. A, 160 (1993) 143. [732] C. Leyens, M. Peters and W.A. Kaysser, Surf. Coat. Technol., 94-95 (1997) 34. [733] H.G. Jung, D.J. Jung and K.Y. Kim, Surf. Coat. Technol., 154 (2002) 75. [734] H.G. Jung and K.Y. Kim, Oxid. Met., 58 (2002) 197. [735] D.Q. Wang, Z.Y. Shi and Y.L. Teng, Appl. Surf. Sci., 250 (2005) 238. [736] T. Wierzchon, H. Garbacz and M. Ossowski, Mater. Sci. Forum, 475-479 (2005) 3883. [737] S.G. Liu, J.M. Wu, S.C. Zhang, S.J. Rong and Z.Z. Li, Wear, 262 (2007) 555.

In: Intermetallics Research Progress Editor: Yakov N. Berdovsky, pp. 65-133

ISBN: 978-1-60021-982-5 © 2008 Nova Science Publishers, Inc.

Chapter 2

ANELASTICITY OF IRON-BASED ORDERED ALLOYS AND INTERMETALLIC COMPOUNDS Igor S. Golovin* Physics of Metals and Materials Science Department Tula State University, Lenin ave. 92, Tula 300600 Russia

ABSTRACT A short introduction into anelastic behaviour of metallic materials is given, and a method of mechanical spectroscopy is introduced for better understanding of relaxation and hysteretic phenomena discussed in this chapter. Several examples of anelasticity due to different structural defects in disordered Fe-based alloys (Fe-Al, Fe-Ge, Fe-Si) are considered with special emphasis on the analyses of the carbon Snoek-type relaxation with respect to ‘carbon substitute atom’ interaction in iron. The effect of ordering of substitute atoms on anelasticity in Fe-based alloys is analysed in terms of substitute atom content and type of order. Anelastic behaviour of iron-based D03 (e.g. Fe3Al) and D019 (e.g. Fe3Ge) intermetallic compounds is reported for a wide range of temperatures and vibrating frequencies to identify damping mechanism. Contribution from interstitial and substitute atoms, dislocations and vacancies in ternary iron-aluminium based alloys Fe-Al-Me (Me = metal: Co, Cr, Ge, Mn, Nb, Si, Ta, Ti, Zr) are analysed. Study of elastic and anelastic behaviour is supported by structural characterisation (XRD, TEM, DSC, magnetometry) of studied alloys, also considering sources for high damping capacity of some compositions. The following anelastic phenomena are found in studied alloys and discussed in this chapter: the Snoek-type (caused by interstitial atom jumps in Fe-Me ferrite) and the Zener (caused by reorientation of pairs of substitute atoms in iron) relaxation, the vacancy and dislocation related relaxations, amplitude dependent magneto-mechanical damping. A family of low-temperature internal friction peaks recorded due to self interstitial atoms in ultra fine grained intermetallics is used to characterise thermal stability of severely deformed (Fe,Me)3Al compounds. These effects are discussed using data available from literature and the author’s experimental data in the Hz and kHz ranges of vibrating frequencies for Fe-Al, *

Now with the Department of Physical Material Science, The Faculty of Physics and Chemistry, State Technological University, Moscow Institute of Steel and Alloys, 4 Leninsky prospekt, 119049 Moscow, Russia, [email protected]

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Igor S. Golovin Fe-Ge, Fe-Si binary and several ternary systems in disordered and ordered ranges of the phase diagrams including intermetallic compounds of Fe3Me type.

Key words: anelastic relaxation, mechanical spectroscopy, internal friction, Fe-based alloys and intermetallic compounds, ordering.

INTRODUCTION a) Internal Friction Mechanical spectroscopy (MS), referred to as the internal friction (IF) method in earlier literature, offers special opportunities to study elastic and anelastic phenomena in metals and alloys at the atomic level, providing response, e.g., from interstitial atoms, vacancies, substitutional atoms, dislocations, grain and magnetic domains boundaries, phase transformations, etc. Fundamentals of this method are given in several textbooks and monographs: Zener 1948 [1], Mason 1958 [2], Krishtal et al. 1964 [3], Nowick and Berry 1972 [4], De Batist 1972 [5], Postnikov [6], Lakes (1999) [7], Schaller et al. 2001 [8], Blanter et al. (2007) [9], and for this reason are considered in this chapter very shortly with respect to studied alloys only. A mechanical loss peak (Q-1) in case of a relaxation effect with a single relaxation time no matter which relaxation mechanism is involved - is well-known as described by a Debye equation with respect to IF:

Q −1 (ω ) = Δ ⋅

ωτ 1 + (ωτ ) 2

(1a)

and elastic modulus:

E (ω) = ER (1 + Δ

ω2τ 2 Δ ) = EU (1 − ), 1 + ω2τ 2 1 + ω2τ 2

where τ is the relaxation time, Δ is the relaxation strength,

(1b)

ω = 2π f with f being the

frequency of the mechanical vibrations, ER and EU are relaxed and unrelaxed modulus. Two values: τ and f can be varied in eq. (1) in experiments. Consequently two types of amplitude independent tests can be carried out: (i) In frequency dependent IF tests (FDIF) at a fixed temperature (τ is a constant in eq. (1a) for a given temperature), the frequency f is varied over a few orders of magnitude. This method allows direct measurements of Q-1 and E spectra vs. ω⋅τ as introduced by eq. (1) or vs. f, and leads to the result shown in Figure 1.a.

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67

(ii) Most of the existing mechanical spectroscopy set-ups (e.g., vibrating reeds, torsion pendula) allows measurements of Q-1 as a function of temperature (T) but not frequency, i.e. to measure temperature-dependent internal friction (TDIF) (Figure 1.b). The temperature dependence (e.g., for jumps of atoms) is typically described by the Arrhenius equation:

τ = τ 0 exp( H / kT ) ,

(2)

where H is the activation energy (or enthalphy) of the physical phenomenon which controls the relaxation process. For a fixed frequency and a single relaxation time, the temperature dependence of Q-1 is described by the equation:

⎧ H ⎛ 1 1 ⎞⎫ Q −1 (T ) = Qm−1 cosh −1 ⎨ ⎜⎜ − ⎟⎟⎬ . ⎩ R ⎝ T Tm ⎠⎭

(3)

Thus, relaxation phenomena can be described in terms of either frequency or temperature. Analytical solutions for more complex cases, e.g. for distribution of relaxation times, can be found in literature (e.g.[8]). Collection of such data for different metallic materials can be found in [9-11].

(a)

E(ω)

EU ER

(b) E (T)

ER(T)

Δ/2

EU(T)

-1

Q (ω)

-1

Q (T)

1.144

-2

-1

0

log ωτ

1

2

Tm

T

Figure 1. Dynamic modulus E and internal friction Q−1 of the standard anelastic solid [9]: (a) as a function of frequency on a log ωτ scale; (b) as a function of temperature at constant frequency. In the latter case, the relaxation-induced step in E(T) is superimposed on the intrinsic temperature dependence of EU(T) and ER(T) [9].

Amplitude dependent IF (ADIF) tests allow us to study damping capacity of metals and alloys, to distinguish and analyse magnetic and non-magnetic, most often dislocation, damping as a function of amplitude of vibrations. A specific damping index (SDI) is the quantitative specific damping capacity Ψ (Ψ = ΔW/W, where ΔW is the energy absorption during one cycle, and W is the maximum elastic stored energy during the cycle; Q − 1 = ΔW/2 π W = Ψ /2 π ) measured by means of a torsion pendulum, when the maximum surface shear stress amplitude is one-tenth of the 0.2 tensile yield strength. This measure is denoted as

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Igor S. Golovin

Ψ0.1σ YS

or more shortly as Ψ0.1, and compared for various materials [12]: Those with Ψ0.1 < 1% are called low damping materials, those with 1 < Ψ0.1 < 10% medium damping, and those with Ψ0.1 > 10% high damping materials. Five structural mechanisms responsible for high damping are recently distinguished [13].

b) Materials Discussed in this Chapter Several groups of iron-based materials are discussed in this paper. Some of them are “true” intermetallic compounds (I) while the rest of them are either alloys on the basis of these compounds (II) or alloys with the compositions in which amount of alloying elements is not sufficient for forming an intermetallic compound (III) in iron but is helpful for better understanding of physical origin of acting anelastic mechanisms: I)

Fe3Al, Fe3Si, Fe3Ge;

II) Fe3(Al,Me) or (Fe,Me)3Al alloys, where Me stays for Cr, Si, Ge, Mn, Co etc.; III) Fe-Al, Fe-Si, Fe-Ge, Fe-Ga, Fe-Al-Si, Fe-Al-Cr ordered and disordered alloys. The second (II) group is built by using the following ternary Fe-Al alloys: 1) strongly carbide forming elements like Ti, Nb, Zr, Ta were added to trap carbon, some of these elements enhance the yield strength by Laves phases; 2) elements providing increased ductility and strength like Cr, which is also a carbide forming element; 3) elements which enhance the tendency to ordering (Si), and are not strongly form carbides; 4) elements (Mn, Ge, Co) which do not strongly affect the interstitial carbon concentration and may affect ordering in different ways. In the Fe-rich corner of the Fe−Al phase diagram there are three phases, namely disordered A2, ordered D03 and differently ordered B2 phases. In the D03 ordered (Fe3Al) structure there are three types of sublattices with sites denoted as 4a, 4b, and 8c in Wyckoff’s notation. In the binary D03 structure the 4a positions are occupied by Al atoms, while 4b and 8c positions are occupied by Fe atoms; in B2 Al atoms are randomly distributed on 4a and 4b sites. In ternary alloys each or all of these sublattices can be occupied by Me atoms. In case of the D03 structure the 4b sublattice, i.e. Fe antisite positions, are preferably occupied by Me atoms; this structure type is called L21. At higher temperatures or higher Al concentration the D03-to-B2 transformation takes place. The Curie temperature TC for a given alloy is different in the A2, B2, and D03 phases. Alloying Fe-Al by a “third” element (Me) changes the parameters of order and the temperatures of phase transformation: Si improves the D03 order and thus increases the transition temperature TO from D03 to B2; Nb and Zr have the same effect on TO, and in addition they produce Laves phases; Co stabilises the B2 phase; Cr and Mn change TO only

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69

slightly up to certain concentrations; Ge being added in significant amount produces L21 order and at lower concentrations increases TO. Interstitial atoms, which in the case of Fe−Al-based alloys are mainly carbon atoms, occupy octahedral interstice positions in bcc iron and also in derivatives from the bcc lattice, i.e. in D03, B2 or L21 lattices. The interaction between Me1Me2 and C-Me atoms and its influence on the parameters of anelasticity (e.g., the Snoek-type and Zener relaxation) is one of the main subjects of this paper. The third (III) group of studied alloys with amount of alloying elements from 3 to 13 at.% was used to clarify these effects in disordered alloys. Different types of order take place in Fe-Ge alloys with Ge < 40 at.%: namely there are the B2 (α1), D03 (α2), and L12 (ε′) cubic phases, and the D019 (ε) and B81 (β) hexagonal phases. Several Fe-Ga alloys are also studied. The B2 and D03 order takes place in Fe-Si binary alloys. Tendency to ordering increases in these systems from left to right: Fe-Al, FeGe, Fe-Si [14]. Most of the Fe-(3÷50)Al, Fe-Al-(Si, Ge, Cr, Co, Mn), Fe-Si, Fe-Ge alloys (∗) were produced at the Institute for Physics of Condensed Matter at the Technical University of Braunschweig by induction melting of 99.98% Fe, 99.999% Al and additions of the third elements under argon atmosphere in a vacuum induction furnace (Mrs. U. Brust). A small amount of carbon (typically from 0.005 to 0.04 %) was added in order to attain a sufficiently developed Snoek peak to study carbon related effects. That is why it would be more correct to speak about multi-component Fe−Al−(Me)−C alloys, however, for simplicity the indication of carbon is omitted everywhere below. Several Fe-(10-12)%Al alloys were produced at the Moscow Central Research Institute of Iron and Steel Industry (Dr. I.B. Chudakov). The FeAl-Me (Me = Ti, Nb, Zr, Ta) and several Fe-Al-Si alloys were produced at the Max-PlanckInstitut für Eisenforschung GmbH, Düsseldorf (Dr. F. Stein): details of the compositions, structures and production procedure are given in the cited papers. The nominal compositions of all alloys used in this research and the compositions were determined by inductively coupled plasma optical emission spectroscopy (ICPOES analysis) and for carbon by combustion to CO2. The amount of nitrogen in our alloys was at least two orders of magnitude lower than that of carbon, and therefore neglected in further consideration.

c) Mechanical Spectroscopy Equipment Damping Q-1 and modulus change (shear modulus G or Young’s modulus E, both are ∼ f , where f is the resonance frequency of torsional or flexural vibrations, respectively) were measured in several set-ups: 2

1) in two inverted torsion pendula using free decay vibrations in the frequency range from 0.5 to 3 Hz at Tula State University (Russia) Figure 2 carried out in saturated magnetic field 2400 A/m in the temperature range below 930K and at the Rosario National University (Argentina) in the temperature range from RT to 1300K; 2) in vibrating-reed set-ups (from 0.2 to 3 kHz) at the Technical University of Braunschweig (Germany), two of them with optical detection of the vibrations Figure ∗

All compositions in this paper are given in atomic per cents if not specified differently

70

Igor S. Golovin 3, the third one with electrostatic registration: all in the temperature range from 80 to 900 K;

Figure 2. Inverted torsion pendulum PKM-TPI (Tula State University): 1 - lower cover, 2,8 –let and outlet, 3 – window from quartz glass, 4, 14 – damper, 5 – mirror, 6, 16 upper cover “bell”, 7 – insulator, 9 – bottom of bell, 10 – thermocouple, 11 – internal pipe, 12 – torsion mandrel, 13 – stand, 15 – magnetos, 17 – to vacuum system, 18 - specimen, 19 – jaw. 1

Vacuum chamber (a): 1 2 3 4 5 6 7 8 9 10

2 3 4 5 6

Entry for liquid nitrogen Entry for furnace (upper part) Entry for furnace (lower part) Entry for three thermocouples Current feedthrough for electrode Flange for sample holder Helmholtz-coils Furnace with specimen holder and specimen Laser with adjusting holder Double thermo isolation

Stereomicroscope (b): 11 Outlet for photodiode 12 Power supply for photodiods 13 Motor microscope adjusting

7 8

9 11 12 13 10 7

Vacuum chamber (a)

Stereomicroscope (b)

Figure 3. Vibrating reed (Technical University of Braunschweig)

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

71

3) in two inverted torsion pendula using forced vibrations in the frequency range from 10-4 to 10 Hz (FDIF) in the temperature range from RT to 900 K at the ENSMA Futurscope (France), and TDIF (f from 0.1 to 1 Hz) at Ecole polytechnique fédérale de Lausanne (Switzerland). This complex of different mechanical spectroscopy techniques allowed us to study main features of most of the phenomena listed in the introduction with respect to temperature, frequency and amplitude of vibrations. The measurements were mainly carried out at vibrating reeds of TU-Braunschweig (in cooperation with Profs. H.-R. Sinning and H. Neuhäuser) [15, 16] and at torsion pendula Tula State University [17]. Several IF tests were carried out in cooperation with colleagues in different places: isothermal studies of the Zener relaxation using frequency dependencies of IF (FDIF) at ENSMA Futurscope (Prof. A. Rivière), high-temperature low-frequency tests at Rosario National University (Prof. O. Lambri), and low-temperature low-frequency tests at Ecole polytechnique fédérale de Lausanne (Prof. R. Schaller). For specimen characterisation TEM (transmission electron microscopy), SEM (scanning electron microscopy), LOM (light optical microscopy), XRD (X-ray diffraction), DSC (differential scanning calorimetry), positron annihilation and vibrating sample magnetometry methods were applied. There structural results are only shortly mentioned in this paper due to the problem of length of the chapter, and similar studies in other chapters in this book. Nevertheless these studies were taken into account in the interpretation of IF effects and reported in the cited papers.

ANELASTIC RELAXATION MECHANISMS I. Dilute Iron Based Alloys: The Snoek and the Snoek-Type Relaxation I.1. Definition and General Theory The effect of anelastic relaxation in a steel tuning fork with a bcc lattice, which later became classical, was for the first time experimentally described more than a century ago [18]. Its nature was related to the presence of interstitial atoms (carbon and nitrogen) in iron in 1939 [19]. Its full physical interpretation as an effect of directional diffusion of interstitial atoms under stress was given by Dr. Jacobus Louis Snoek in 1941 [20]. Later, a similar effect was revealed in a whole number of bcc metals of group VB (V, Nb, Ta) and VIB (Cr, Mo, W) of the periodic table and was called the Snoek effect [4]. Most recently this phenomenon has been reviewed with respect to pure metals by Weller in [21]. The activation energy of the Snoek relaxation process is equal to the activation energy H of the interstitial atoms diffusion: both processes have the same origin. The Snoek peak temperature Tm is determined by the diffusion characteristics of dissolved atoms as: Tm=H/{Rln[π a02 f/(18D0)]},

(4)

where f is the imposed frequency of mechanical vibrations, a0 is the lattice parameter, D0 is the pre-exponential factor in diffusion equation: τ0 = a02/(36D0), see eq. (2).

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Igor S. Golovin

The peak maximum Qm-1 depends on 1) the atomic fraction of interstitial atoms in the solution (C0), 2) the value of “elastic dipole strength” (| λ2 - λ1 |) produced by interstitial atoms (IA) located in octahedral interstices of the bcc lattice of metals, and on the direction of the stress applied to the crystal lattice (Г): for polycrystalline samples, averaging for all grain orientations which gives Г ≈ 0.2: Qm-1 ~ C0⋅(λ1 - λ2)2⋅F(Г)/(RTm) .

(5)

In α-Fe carbon content up to 1 ppm can be detected in commercial steels [22]. Substitution atoms (SA) in a host lattice must influence the parameters of the original Snoek relaxation by SA-IA interaction, i.e. by a change in the activation energy of the relaxation, and by a change of the value (λ1−λ2), i.e. the relaxation strength. Already at the early 1950s, first attempts were done to investigate the parameters of the Snoek peak by temperature dependence of internal friction not only in pure metals but also in bcc alloys, first of all in iron-based alloys (Wert [23-25], Dijkstra and Sladek [26]). Finally, the Snoek relaxation can also be observed in many bcc dilute alloys [9]. The theory of the influence of SA–IA interaction on the Snoek relaxation was given by Koiwa [27,28] and has been proved in many experimental papers mainly for iron-based alloys. The important question is if the Snoek-type relaxation can also be observed in bcc alloys with significant concentration of substitutional atoms. The substitute atoms create energetically non-equivalent positions for interstitial atoms in the host bcc lattice: the interaction between interstitial (i) and substitutional (s) atoms must influence the relaxation parameters. For this reason the Snoek-type relaxation in alloys is sometimes denoted in literature as the “i-s” peak. Nevertheless, this “i-s” relaxation in alloys can be explained in terms of the Snoek theory supplied with additional parameter of the SA–IA interatomic interaction in the crystal lattice (which leads to a change in the activation energy of diffusion of dissolved IA near the relatively immobile SA), one can define this anelastic phenomena as the Snoek-type relaxation, i.e. the relaxation with the same mechanism originally proposed by Snoek.

I.2. Review of Experimental Results Those trends which are known from the behaviour of heavy interstitial atoms (C, N)1 in low alloyed iron are inherited by Fe-based alloys and intermetallic compounds born from bcc structure (e.g. the B2, D03 and L21 structures), and thus these trends are interesting for our consideration. Substitutional atoms in a host lattice must influence the parameters of the original Snoek relaxation via IA-SA (or “i-s”) interaction, i.e., by a change in the activation energy of the relaxation, and by a change of the value (λ1 − λ2), i.e., the relaxation strength. In spite of more than 50 years of study since the pioneering works of Wert on alloyed iron, the experimental situation about the influence of SA on the Snoek relaxation has remained not well systemised. Some SA may not affect the position and height of the Snoek peak, others may reduce the

1

Oxygen (O) does not contribute to the Snoek relaxation in iron.

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

73

peak height, lead to the appearance of additional peaks at higher temperature besides the height reduction, or suppress the Snoek peak and produce new peaks at higher temperatures. In the case of carbon Snoek relaxation in iron a clear effect of substitute atoms in Fe-Al and Fe-Si systems has been noticed in literature [25, 29-36] in contrast with no-effect or very little influence in Fe-Ni, Fe-Ge. One can also find contradicting results in the literature for example with respect to Co and Cr in α-Fe. In some cases existing controversies can be explained by the fact that the authors studied alloys with different amounts of alloying elements. The nitrogen Snoek peak in iron is influenced by the presence of Cr [37], Mn [38,39], Mo and V. All these elements do not produce ordering in corresponding binary ironbased phase diagrams. The nitrogen Snoek peak plays a much less important role in Fe-Albased alloys and intermetallics due to trapping of N into AlN, and is not considered in corresponding subchapters as well as the hydrogen Snoek peak. A review on these peaks can be found in [9,40]. We do not consider in this paper the effect of interstitial atom complexes on the Snoek relaxation which results most generally in the peak broadening. Examples of the carbon Snoek peak in Fe-Al, Fe-Co, Fe-Ge, Fe-Si with ~3% of substitute atoms are given in Figure 4. Similar examples for Fe-Al-Si alloys are given in §III. Fitted Debay peaks are added in insets to Figs. 4. The following fitting method was applied in this paper: Computer analysis of TDIF and FDIF spectra. The program employed (∗) for the analysis of relaxation spectra is based on the eq.(1a) that describes the relaxation “Debye” maximum of IF as a function of temperature at a constant imposed vibration frequency (ω = 2πf) assuming an Arrhenius law for the frequency (1/τ) of atomic jumps (eq.(2)). In the case of a normal (Gaussian) distribution of the relaxation times τ, the shape of the IF curve is determined by the broadening parameter β (distribution of relaxation times): −1 Q −1 (T ) = Qmax

−1 max

Q

⋅ ω ⋅τ 0

∞

exp(− z 2 ) ⋅ ω ⋅ τ ⋅ exp( β z )dz ∫ 1 + [ω ⋅τ ⋅ exp(βz )]2 = −∞

∞

exp(− z ) 2 dz ∫ exp(−( H / RT + βz)) + (exp(H / RT + βz)) −∞ ,

(6)

where z = lnτ, H is the effective enthalpy of activation of the relaxation process, and R is the universal gas constant. The program permits one to use two fitting parameters: the number of peaks that are introduced and the parameters of broadening of each peak. The enthalpy of the relaxation process can be taken from an independent source rather than be used as an adjustable parameter in the analysis of experimental data. The fitting technique used for the analysis of frequency dependent IF spectra is similar: The program based on the eq.(1a) that describes the relaxation “Debye” maximum of IF as a function of frequency at a constant temperature. The relaxation time τ0, the activation energy H, and the distribution of relaxation times β can be fitted in the program. In case none of these parameters is known from the Arrhenius plot, they can be estimated from this fit for a given temperature of measurements, in case some of them are known from the Arrhenius plot they can be fixed in the program: ∗

Semin, V.A.; Golovin, S.A.; Golovin, I.S. Program for analyses of temperature (i) and frequency (ii) dependent internal friction data (Russian registration number № 2005611581 (i) and № 2006610674 (ii)).

74

Igor S. Golovin

f ( x, β ) =

( )

2 1 ∞ ωτ ⋅ exp ( βξ ) exp −ξ ⋅ d ξ = ∫ 2 π −∞ 1 + ( ωτ ) exp ( 2βξ )

Q −1 −1 2Qmax

,

(7)

where z = ln(τ/τ0) and x = ln(ωτ0). (a) -1

Q

Fe-3Ge

(b) -1

Q

490

T1=388 K

experim. Fe-C-Fe

0.008

0.009

-1

T1=389 K

experim. Fe-C-Fe

Q

Fe-3Co

H1=0.86 eV

H1=0.9 eV

0.006

β1=0.71

Q

0.006

β1=0,5

485

-1 0.004

0.009 0.004

0.002 -1

0.002

0.0020

0.006

0.0024

0.0028

1/T [K ]

0.006

-1

1/T [K ]

f [Hz]

0.0020

480

0.0024

0.0028

0.0032

480

0.0032

f [Hz]

475 0.003

0.003 470

470

300

350

400

450

500

300

T [K]

350

(c) Fe-3Al

Q

0.006 -1

450

500

T [K]

(d) experim. Fe-C-Fe Fe-C-Me sum.

-1

0.004

Q

400

-1

T1=388, Q =0.0048 H1=0.84, β1=0.68

Q

-1

T2=429, Q =0.0033

3%

-1

Fe-3Si Fe-2Si

H2=1.1, β2=1.35

530

0.002

470

460

0.006

-1

1/T [K ]

0.004

0.0020

0.0024

0.0028

0.0032

450

520

0.004

f [Hz]

2%

f [Hz]

0.002

400

0.002

510 390

300

350

400

450

500

550

T [K]

300

350

400

450

500

T [K]

Figure 4. Influence of Ge, Co, Si and Al (all elements ~3 at.%) on the carbon Snoek peak. Insets: fit of experimental data by Debye peaks.

Results of the Snoek-type mechanism studies can be summarised with respect to alloying elements in bcc iron in the following way: Every substitute (Al, B, Co, Cr, Cu, P, Si) reduces Snoek peak height even if the amount of solute C is the same, and this causes an increase in the proportionality constant between the Snoek peak height and carbon content. In the range where substitutes content is dilute, Co, Mn, Cr, Si, P and Al lead to decreases in Snoek peak height in this ascending order. Cu leads to additional damping component which is explained by C-Cu interaction. The solute carbon presence in the region where the lattice distortion around the substitute atoms is greater than the threshold value (the order of 10-3) cannot contribute to the Snoek peak and the volume of influence region increases as the difference in atomic size increases. The strain field generated by a substitutional atom due to the difference in atomic size is the reason for the reduction in Snoek peak height [35]. The Snoek peak in Fe-C-Ge and Fe-C-Co alloys is unimodal (Figure 4 a,b) at least up to a certain concentration of SA; its parameters are relatively close to those of the carbon Snoek peak in iron. Cobalt (≤4% [36]) increases the activation energy of the peak slightly, at higher

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

75

concentration of Co in Fe the Fe-C-Co component of the Snoek peak can be observed [32]. The Snoek peak in Fe-C-Al alloys is formed by two components (Figure 4c): a peak in which parameters correspond to those of the Snoek peak in pure iron (Fe-C-Fe) and a second peak whose parameters are determined by an additional interaction between C and Al atoms (Fe-CAl). The Snoek peak in Fe–C–Si (Figure 4d) is at least broadened (as shown for Fe-3Si by dotted line); in some tests the Fe-C-Si relaxation component is clearly observed (Figure 4d) [30, 36, 41]. The shape of the Snoek-type peak in Fe-Si alloys is sensitive not only to the heat treatment regime but also to inhomogeneous distribution of Si in Fe and can be slightly different from sample to sample: for that reason it is difficult to conclude if the peak at ~450K (Figure 4.d) is a part of the Snoek peak or has another reason (see also §III.3). The activation energy of the Fe-C-Al peak is higher than the basic peak by ~0.2 eV due to an additional (elastic) C-Al interaction in the solid solution. The Fe-C-Al peak is twofold as wide as the basic (Fe-C-Fe) peak, which reflects the existence of a set of different (in their energy state) positions for C atoms depending on their distance from an atom or atoms of Al. Based on the magnitude of the critical concentration at which the basic (Fe-C-Fe) peak vanishes and only the Fe-C-Al remains (~12%Al), i.e., at which the C atom always feels the Al atoms, the range of the C-Al interaction was estimated as equal to at least three coordination shells [36]. At a comparable concentration of Al and Si in the Fe-Al-Si alloys, Al exerts a greater effect on the profile of the temperature dependence of IF in the range of the Snoek relaxation, which is explained by its more efficient contribution to the long range elastic interaction with C atoms [36, 56]. In both binary (Fe-Al, Fe-Si) and ternary (Fe-Al-Si: see §III.3) alloys, an increase in the temperature of heating for quenching leads to an increase in the Fe-C-Fe component at the decrease in the Fe-C-Me component of the Snoek peak. Low temperature (<675K) ageing of quenched in specimens leads to a decrease in both Fe-C-Fe and Fe-C-Me peaks, while ageing at higher temperatures changes TDIF and ADIF in several Fe-(1.5-4)Al-(2-4)Si alloys due to new carbon redistribution between solid solution and dislocations: the Snoek-type peak increases (C atoms go to solid solution), dislocation mobility and ADIF slope increases, and a new peak at ~600K (450 Hz) due to motion of dislocations decorated with weak pinning points appears at higher temperatures as compared with the Snoek peak [36, 42]. Carbon forming elements (Cr, Mo, V, W) lead to a decrease in the Snoek-type peak height due to trapping of carbon to carbides, in a few papers the second Fe-C-Me peak was reported in these systems mainly for “weak” carbide forming elements (Mn, sometimes Cr (43-46). Effect of other studied elements (e.g., As, Ni, Sn) is not well systemised. Two additional components to the main nitrogen Snoek peak were noticed in the Fe-MnN system [38]: one (Mn-N-Mn component) below and one above (Fe-N-Mn) the Fe-N-Fe peak. Study of Fe–Cr–N alloys demonstrated clear appearance of the second component of the Snoek peak which can be called Fe-N-Cr for simplicity reasons. Within the framework of the simplified theory [27] where the influence of a substitutional atom is assumed to extend to the second neighbour shell, the observed relaxation spectra for Cr levels ranging from 0.05 to 0.2 at.% can be satisfactorily reproduced, and the binding energy of a Cr–N pair has been determined to be in the range between 0.16–0.18 eV [47]. Rare earth elements (As, Ce, La, Y) decrease and broaden the nitrogen Snoek peak, and a tendency to separate the peak into two peaks takes place [48]. According to the IF data, rare earth elements have a tendency to segregate. This short analysis of substitution atoms’ influence on the Snoek relaxation in iron

76

Igor S. Golovin

gives a key for interpretation of the contribution of interstitial atoms in Fe-based ordered alloys and even intermetallic compounds.

II. FE-AL ALLOYS INCLUDING FE3AL COMPOUNDS: THE SNOEK TYPE PHENOMENA AND OTHER TYPES OF ANELASTIC RELAXATION II.1. The Snoek-Type Relaxation in Fe-Al Ordered Alloys The Snoek-type relaxation in Fe-Al alloys was first discovered by Fishbach in 1962 [49], and reported later in many research papers [50-60]. Influence of Al concentration. The first systematical studies of the influence of Al content in iron on the Snoek-type relaxation were done by Jänicke et al. [51] and Tanaka [52]. Selected data from [52] are presented in the Figure 5.a in normalised ((Q-1-Qb-1)/(Qm-1- Qb-1) = 1) form: original data are shown in the inset. The main result of C-Al interaction on the Snoek peak is that the peak shifts to a higher temperature, the activation energy of the peak and the peak width increase: the carbon atoms obtain new distribution in activation energies for diffusion jump ‘under stress’ [55]. The peak height decreases in accordance to the peak width: not the peak height but the area under the peak becomes proportional to the carbon content in Fe(Al). Two components of the Snoek peak are distinguished and computed [56,57] (Figure 5.b, data are normalised for better visualisation): the first peak corresponds to Fe-C-Fe positions, the second peak corresponds to Fe-C-Al positions for carbon atoms. The Fe-C-Fe peak decreases while the Fe-C-Al peak increases with each increase in Al concentration in iron. Influence of Al atom ordering. For Fe-Al alloys with the Al concentration of more than 12%, the Fe-C-Fe peak is not distinguishable in the TDIF spectrum [36, 56]. On the other hand, the Al atoms ordering becomes possible if Al > 10-12%. The pronounced effect of ordering (annealing below 675K) and disordering (quenching from 1075-1275K) was recorded for Fe-22Al alloy [58]. Disordering results in the peak broadening due to an increase in different types of positions for C atoms in bcc Fe(Al) solution, while the peak height decreases correspondingly. If ordering takes place, the number of positions for C atoms in Fe(Al) ordered solution decreases and the peak becomes more narrow but correspondingly higher. The effect of ordering depends on time and temperature of annealing [58]. The effect of ordering in as quenched and annealed alloys with a different Al content is shown in Figure 6 [59]. The peak width in as quenched from disordered A2 range specimens increases significantly with increase in Al% in iron from ~10 to ~ 22%Al (βmax > 3), then decreases to β = 1.5-2.0 in the D03 and B2 ordered ranges. Similar effect in quenched and aged specimens is smaller because of short and long range ordering even for alloys with less than 22%Al, and β ≤ 1.5 for alloys with Al > 22%.

-1

(Q (T)-Qb )/(Q (Tmax)-Qb )

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

Fe-C-Al

-1

-1 -1

-1

0.8

-1

0.6

Fe 0.68Al 1.51Al 2.30Al 5.86Al 8.79Al 11.1Al

8.79 0.68 2.3 5.86 1.51

0.4

11.1

0.2 ~1.2 Hz 0.0 300

350

(a)

400

450

T [K]

500

-1

Q -Qb /Qmax -Qb

-1

Fe-C-Fe

1.0

Fe 2.9Al 7.1Al 8.5Al 10.6Al

1.0

0.8

Fe-C-Fe

77

Fe-C-Al

0.6

8.5 0Al

2.9

7.1 10.6

0.4

0.2 ~ 500 Hz 0.0 300

350

400

450

T [K]

500

(b)

Figure 5. Influence of Al content (in the range between 0 and 12 at%) on “normalized” TDIF in bcc FeAl alloys: a) as measured at torsion at ~1.2 Hz by Tanaka [52], original data are presented in inset, and b) as measured at bending at ~500 Hz by Strahl et al. [56]. For better visualisation the peaks height is normalised to one: two components of the peak can be seen in both cases.

Influence of C content. The effect of carbon on the peak height was reported by several authors in 1970-1980 (e.g. in [50-53]) but questioned more recently in [63,64], and reviewed in [60]. The increase in the peak height with increase in C content in Fe-25/31Al alloys can be seen in Figure 7 [61]. The dependence of the area under the peak on carbon content is practically linear. The usage of single crystals of Fe-26Al confirms the typical for the Snoek relaxation orientation dependence of the Qm-1 on Г [62]. Influence of other Me atoms. The additions of carbide and non-carbide forming elements to Fe-(20-25)Al alloys acts differently on damping spectra. While non-carbide forming elements (Si, Ge, Co, Mn) produce like in α-Fe little influence on the Snoek-type peak height, shape and temperature in Fe-Al, strong carbide formers (Nb, Ta, Ti, Zr) completely eliminate the Snoek-type peak confirming the carbon Snoek-type origin of this effect. Cr, being a less strong carbide-forming element, decreases peak, modifies peak shape and shifts it to a higher temperature. See §III for further details. Contribution of vacancies. The diffusivity of thermal vacancies in Fe-39Al (B2 phase of Fe-Al phase diagram) studied by positron lifetime spectroscopy [63,64] are characterized by the effective enthalpies HF = 0.98 eV for vacancy formation and HM = 1.7 eV for vacancy migration. These values are close to the activation energy of the Snoek type and X relaxation (see §II.2). In case of quenching from high temperature these two types of relaxation (due to carbon and due to vacancies) can overlap in the same temperature range in Fe-Al alloys [59, 65]: increase in Al% and annealing temperature above 1275K before quenching increases contribution of vacancies. Nevertheless the peak drastically decreases in the presence of carbide forming elements proving the dominating role of carbon.

78

Igor S. Golovin

β for the Snoek peak

4

quenched from B2

quenched from A2

in quenched state quenched and aged

3

2

1 short-range order

long-range order

0 0 10

15

20

25

30

35

40

at. % Al in Fe Figure 6. Influence of Al concentration and regime of heat treatment (quenched = partly disordered state, aged = ordered state) on the width β of the Snoek-type peak. Arrows indicate influence of ordering [59].

(a) Fe-31%Al

100

31.0Al-0.006C ~270 Hz

-1

~ 500 Hz Fe-26% Al + 0.3% Nb + 2% Ti

80 60

with Ti or Nb

~2 Hz

-1

30

~ 2 Hz Fe-26% Al + 0.3% Nb + 2% Ti

without Ti and Nb

-4

30.7Al-0.003C ~400 Hz

S

120

31.2Al-0.009C ~520 Hz

Q , 10

-4

40

Q -Qb , 10

50

-1

60

(b)

20 10

heating

X

~500 Hz

40 20

cooling

0 400

0

500

600

T [K]

400

500

600

T [K]

700

Figure 7. a) Influence of carbon content in alloys of Fe-31%Al (quenching from 1220 K) on the Snoektype peak height at heating. No peaks occur during subsequent cooling. b) Influence of carbide forming elements (Nb and Ti) and measuring frequency (~2 and ~500 Hz) on the temperature dependent IF for Fe-26%Al alloy after water quenching from 1270 K [61].

Modelling. Results presented in Figure 5 were used in the simulations as a Snoek-type effect. They show that the Fe-C-Fe, i.e. “pure iron” component is not seen more in the Snoektype peak if the Al concentration in iron is more than 10-12%. It means that if there are 1012%Al in iron the Al atoms always affect C atom jumps in the Fe(Al) solid solution. From this the effective distance of the C-Al interatomic interaction can be estimated from

5 ⋅a /2

(a is lattice parameter) or as three coordination spheres as a minimum and 9 ⋅ a / 2 (six coordination spheres) as a maximum [56]. Monte Carlo simulations based on KhachaturianBlanter approach (see Appendix) using energies of the long-range strain-induced (‘elastic’) pair interatomic C-Al interaction supplemented by ‘chemical’ repulsion demonstrate [55] the

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

79

strong influence of ordering reaction on carbon redistribution around Al atoms and correspondingly on parameters of the Snoek-type peak (Figure 6): this effect is stronger in FeAl alloys with Al < 25% with the A2-to-D03 transition [55] than in alloys with Al > 25at.% with the B2-to-D03 transition [59]. The main factor which determines the effect of Al on the carbon Snoek-type peak is the long-range (up to five coordination shells [55]) ‘elastic’ interaction. The ‘elastic’ C-Al attraction significantly increases the peak temperature and the ‘chemical’ C-Al repulsion according to Lennard-Jones potential compensates this increase but not completely: the carbon Snoek peak temperature in Fe-Al is higher than in α-Fe. Concluding remarks to §II.1. The mechanism of the Snoek relaxation in metals may be extended to the Snoek-type mechanism in bcc alloys, in particular in Fe-Al alloys. The Snoek-type mechanism means that the origin of this phenomena in alloys is the same with the Snoek relaxation in metals: an interstitial (in our case carbon) atom jumps under the stress in alloyed iron with bcc stucture, and parameters of these jumps, i.e. parameters of the relaxation process are influenced by interstitial (C) – substitutional (Al) atoms interaction in solid solution. Foreign Me atoms and vacancies can modify parameters of the Snoek-type peak or contribute in the same range of temperatures independently.

II.2. The Vacancy and Vacancy-and-Carbon Complexes Related Phenomena (The X Peak). This relaxation effect with average activation energy about 1.7 eV has been repeatedly observed in Fe-Al alloys since 1996 by different authors [63-67]. The term “X peak” was introduced in our papers [59, 60] to call somehow this relaxation effect. The temperature location and the peak height at TDIF for the X relaxation curve (for f ~1 and 0.1 Hz) can be seen in Figure 8, and for f ~ 500 Hz in Figure 7. The X relaxation is practically not observed for alloys with Al < 25%, which is nevertheless possible is case of very quick quenching from high temperatures and using low frequency measurements even in Fe-12Al alloys. Proposed mechanisms. An elegant interpretation of the X peak (e.g. in Fe-37.5Al alloy the peak parameters are: activation enthalpy H = 1.7 eV, τ0 = 10-13 s and Qm-1 = 0.0012) was suggested in terms of vacancy reorientation: as reorientation related effect of “pure” vacancies [64] or iron-cite-vacancy VFe-and-Fe atom complexes [63]. A strong argument favouring this approach is that the activation energy for vacancy migration and the activation energy deduced from X-peak are rather similar. A similar explanation but in terms of movement of Al atom by means of thermal vacancies was given more recently for the IF peak in Fe-29Al alloy with parameters: H = 1.64 eV, τ0 = 1.2×10-15 s and Qm-1 ~ 0.001 in [68]. Contrary to the above vacancy-and-metal atom-related explanations it was noticed that a similar peak (H = 1.6 eV, τ0 = 1.7×10-14 s) in Fe-32Al depends on the carbon content and the peak was explained as the “second” Snoek-type peak (i.e. jumps of carbon atoms) in the presence of an additional phase, other than equilibrium D03 [66, 67,69]. At the same time the “ordinary” Snoek-type peak in the D03 structure was reported at lower temperatures. The hypothesis of C-vacancy complex formation in Fe-Al-C-vac system is discussed in [70].

Igor S. Golovin

-1

Q , 10

-4

80

< 25 % Al

50

α -F e

40

1 1 .7 % A l 2 2 .5 % A l

30

S

20 10 0 80

300

500

-4

60

T [K ]

700

X

> 25 % Al 3 1 .5 % A l 35% Al 40% Al

-1

Q , 10

Z

40 20 0

400

600

T [K ]

800

(a) 0.012

2.3

-1

2.2 0.008 2.1

G, arb

tanφ (Q )

Fe-25%Al, f=0.1 Hz

0.004 2.0 Snoek peak

X peak

0.000

1.9 300

400

500

600

T [K]

(b) Figure 8. Examples of the X peak: a) overview of the Snoek-type, X and Zener peaks in Fe-Al alloys (~1 Hz) and b) TDIF in Fe-25Al (0.1 Hz: forced vibrations), changes in relative shear modulus (right scale) are discussed in §II.6.)

Experimental results. Several tests have been carried out to study the mechanism of the X relaxation peak in Fe-Al alloys (the X peak was also recorded in Fe3Al intermetallic compound after quenching [58, 71]). The summary of these experiments shows that: a) The peak increases with increase in Al content at least between 25 and 40% (Figure 8a) [58,71]. In the range above 40%, the situation is more complicated; increase in

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

81

annealing temperature before quenching (i.e. increase in concentration of thermal vacancies) increases the peak height. The difference of activation energies between the Snoek-type peak and the X peak remains about 0.5 eV in almost all tests [74], b) The peak height is very sensitive to heating rate during TDIF measurements: the annealing of alloys decreases it drastically; moreover, the peak decreases at the same time with the measurements of the Q-1 as a function of temperature. For this reason a decrease in resonance frequency, i.e. temperature of the peak, helps always to have a higher peak (Fig 8b): e.g. increase in the frequency from 0.1 to 500 Hz decreases the peak by nearly one order of magnitude (see Figure 7b and 8b). This effect of heating rate on the peak height was recently studied by Han [65,75]. c) The peak dependence of the C content in as quenched Fe-25Al and Fe-31Al alloys was demonstrated mainly on a qualitative level [61] because of the peak instability with respect to heating during TDIF tests. In ternary Fe-Al-Me (Me = Cr, Ge, Mn, Nb, Si, Ta, Ti, Zr) alloys (see in §III) the peak was never recorded in the presence of strong carbide forming elements Ti, Nb and Zr, Ta; the same concerns also the Snoek-type peak. The peak parameters are modified if Cr added in Fe-Al: peak shifts to higher temperature, i.e. higher activation enthalpy and the peak height decreases. At cooling the X peak decreases more than the Snoek peak. The peak is only little changed if Si, Ge or Mn are added, some weak tendency to decrease in the peak temperature can be seen in the presence of Si and Ge in Fe-Al. d) The peak splits into two peaks if Al concentration in Fe-Al is above 30% (see e.g. Figure 8a, curve for Fe-35Al or in [59]), the height of each partial peak depends on quenching temperature and exhibits more complicated behaviour in alloys with more than 40%Al presenting probably both carbon-and-vacancy and triple vacancy complexes contribution. This later viewpoint was recently studied for alloys with >40%Al in [65,75]. Simulations. Computer simulations of the X relaxation in Fe3Al were carried out using a model of carbon atom diffusion under the applied cyclic stress in an Fe3Al-vacancy-C solid solution (see Appendix); the results of these simulations were compared with experimental data. The following factors were taken into account in the modeling: concentration of C atoms, vacancies and degree of Al atom ordering (Figure 9). The simulations show that carbon atom jumps near vacancies in the Fe3Al intermetallic compound can lead to an anelastic relaxation with activation energy higher than that of the carbon Snoek-type relaxation. In terms of internal friction this type of anelasticity leads to the appearance of the X peak. Thus, the X peak is a complex effect in which both interstitial atoms and vacancies are involved [72, 73, 75]. From these experimental results and calculations it can be concluded that the peak is strongly affected by the presence of both carbon and vacancies in Fe(Al) solid solution. It can be suggested that complexes carbon-and-vacancy and vacancy-and-vacancy are responsible for the X relaxation [74]. These two peak components are recently distinguished in [65, 75]: the 1st – smaller but more stable with respect to annealing - due to carbon-and-vacancy, the 2nd – due to vacancies complexes in Fe-Al-C-vac system. This second vacancy-related peak is very sensitive to heating, that is why it can be recorded only if a high heating rate (> 5 K/min) is used. At slower heating this peak decreases due to vacancy decrease during the measurements.

-1

0.6 0.5

QX /Qo

-1

QX /Qo

0.8

-1

Igor S. Golovin

-1

82

degree of order

0.4 0.3

0.6

carbon

0.2 0.1

0.7

0.8 η

0.9

1.0

0.4

vacancies 0.2

0.0 0.00

0.02

0.04

0.06

0.08

0.10

at. %

Figure 9. Dependence of the X peak height (arb. units) on carbon concentration (1) at vacancy concentration 0.094% and on vacancy concentration (2) at carbon concentration 0.047 %. Inset: Dependence of additional peak high on a long-range order parameter (C = 0.047 %, vac = 0.094 %).

II.3. The Zener Relaxation The existence of solute next neighbour atom pairs in crystalline lattice results in a relaxation maximum, well known as the Zener peak [76] in a temperature range where the solute atoms are mobile and enable reorientation of the solute atom pair in the lattice under the action of the applied stress. The Zener relaxation in Fe-Al was first reported in 1960 by Shyne and Sinnot [77] and then by several authors. The origin of this phenomenon is stressinduced ordering of Al atom pairs in iron by short-range diffusion jumps. The theory of the Zener relaxation proposes the relaxation magnitude (δJ) is [4]:

δJ = [ f ( χ o , C Al ) × (C Al2 (1 − C Al ) 2 ) / k BT ] × β a 2 ( dU p / da p ) 2

(8)

where T is temperature, kB is Boltzmann’s constant, the term CAl2(1-CAl2) exhibits the concentration dependence of δJ: CAl is the atomic concentration of Al in iron; the function f(χo,CAl) reflects the effect of order of Al atoms on δJ: χo is a parameter of short range order in the absence of external stress, f(χo,CAl)=1 for the disordered state and f(χo,CAl)=0 for the complete ordered state (the Zener relaxation is impossible in 100% ordered alloy); β is a dimensionless geometrical parameter, a is the interatomic spacing, ap – the same in the direction “p”, Up is the ordering energy in the direction “p”, p is a direction of applied stress. Activation energy of the Zener relaxation should be close to the activation energy of Al atoms diffusion in iron [78, 79]. Effect of Al atoms Concentration and Ordering a) Temperature dependent internal friction (TDIF). The Zener peak temperature in Fe-Al alloys as measured at frequency ~1 Hz is close to 790-805K, and moves to a higher temperature if the frequency of measurements is higher [49, 50, 80]. These temperatures

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

83

correspond to the A2 disordered range of the Fe-Al phase diagram for alloys with Al <2022%. This means that the relaxation strength of the peak depends on Al concentration only because term f(χo,CAl) ≈ 1 in eq. (7) in this range. Indeed, in this range Al < 20% the dependence ΔZ ~ CAl2 was observed in several papers [49, 50, 59, 68, 77, 80] as shown in Figure 10. Increase in Al concentration to 20% and higher leads to ordering (f(χo,CAl) < 1, in completely ordered state f(χo,CAl) = 0), and the peak decrease is clearly noticed in Figure 10 for Al > 20%. The temperature for the D03-to-B2 order transition in binary Fe-Al alloys with Al concentration close to 25% is about 820K, i.e. close to the Zener peak position if measured at ~10 Hz. The disadvantage of the TDIF tests in the temperature range close to the orderdisorder or order-order phase transformations is that the structural state of alloys changes during TDIF tests, which restricts applicability of the Arrhenius plot to determine activation diffusion of Al in iron.

100 -4 -1

75

T, K

Qm , 10

frequency in kHz: 850 1 [50] 0.3 [104] 0.2 [56] 0.05 [66]

frequency in Hz: 1.3 [80,122] 3 [63,64] 1.4 [49] 1.8 [58]

B2'

Lines of the Fe-Al diagram

50

800

B2L

750 25

D03

A2 0

0

10

20

30

B2 40

700

at. % Al in Fe Figure 10. Zener peak height (QZ-1) vs. Al %.

The TDIF tests demonstrate the Zener peak broadening in Fe-Al-Me (Me = Cr, Si) alloys mainly from high-temperature side. This effect comes from a contribution of Me atoms to the Zener effect [81, 82], i.e. to the short-range diffusion jumps. The Zener relaxation in Fe-Al-Si ternary alloys, as studied by TDIF, demonstrates a double-headed Zener peak caused by AlAl and Si-Si pairs reorientation under stress Fe-Al-Si alloys [82]. The broadening of the Zener peak from high temperature side in Fe-Al-Cr alloys was observed by TDIF [81] and FDIF [86] tests (see §II.4). b) Frequency dependent internal friction (FDIF). The isothermal FDIF spectroscopy allows one to measure a peak at a fixed temperature [83], i.e. practically at equilibrium conditions in different ranges of the phase diagram (Figure 11a, inset). Such tests demonstrate a difference in the Zener peak parameters in different phases, i.e. the difference in the relaxation strength (Figure 11a) and activation energy (Figure 11b) of the Zener relaxation in the D03 or B2 ordered and the A2 disordered states of the Fe-Al alloys [84, 85] and gives values of the activation energy in these phases very close to the diffusion experiments [78,79].

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Igor S. Golovin

The activation energies of the Zener relaxation in A2, B2 and D03 phases are in the same sequence as the activation energies of diffusion in these phases, i.e. HA2 < HB2 < HD03 (Table 1). 40

T=738 K 1.165

Modulus arb. units

4

Q (10 )

100

-1

30

80

882 856 833

4

1.160

20

2

809

step-by-step: heating cooling

60

ln (freq./Hz)

10

4 -1

Q x10

Fe-25.8Al

1.155 0 -3

-2

-1

0

1

2

log10(freq./Hz)

738 692 723 40 668 708

783

768

753

0 -2 -4 -6

20

D03

-8

-3

-2

-1

0

1

B2

-10

2

1.6

1.5

1.4

1.3

log10 (freq./Hz)

1000/T (K)

(a)

(b)

1.2

1.1

Figure 11. Zener relaxation in the Fe-25.8Al alloy: (a) overview of Zener peaks measured at different temperatures between 668 and 882 K; inset in left-upper corner: isothermal tests at 738 K: IF and relative modulus supplied with exponential background, and IF peak after background subtraction; (b) Arrhenius plot [84].

Table 1. Parameters of the Zener relaxation in Fe-21.7Al, Fe-25.9Al and Fe-28Al-3Cr [84,85] alloys and diffusion data for Fe-25.5Al [78,79]. Alloy, at.%

Zener relaxation f [Hz]

Fe-21.7Al

Fe-25.9Al

T [K]

10-4-102

10-4-102

H [kJ/mol]

Activation energy of diffusion (Fe-25.5Al), kJ/mol

τ0

[sec]

Interdiffusion [79]

2

Fe-28Al-3Cr 10 -10

Al tracer Fe tracer diffusion diffusion [79] [78]

< 730

271±6

9.1×10-18

D03+A2

730-773

238±6

4.3×10-17

A2

< 820

286±8

4.8×10-19

> 820

235±2

8.0×10-17

269±17 231±5

-4

Structure

< 835

276±5

2.8×10-19

236±3

278±5

D03

232±2

B2

217±8

A2 D03 / B2

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

85

The increase in the activation energy of the self-diffusion with increase in order parameter (η) is in agreement with the Girifalco’s theory: H(η) = Hη=0×(1+ αη2), where α is a parameter. The activation energies of the Zener relaxation are lower than the activation energies of interdiffusion in B2 and are practically the same as the activation energy of the Al tracer diffusion in B2 [79], i.e. the Al self diffusion in Fe-26Al. Practically exact fit in the B2 range can be incidental: the Zener reorientation mechanism involves vacancy and host atom jumps but not only single Al atoms diffusion, and should be slightly below the activation energies for solvent and solute self diffusion. It is notable that the FDIF provides an opportunity to study diffusion at relatively low, untypical for diffusion experiments, temperatures, i.e. in low-temperature phases like the D03 phase in Fe-Al. The f(χo,CAl) function in eq. (8) can be analytically determined in case the degree of order can be quantified in the same temperature range with FDIF tests. As yet we have not succeeded in the corresponding X-ray experiments in situ due to oxidation of the specimen surface which might be interesting in the future. The mechanism of the Zener relaxation in ternary Fe-AlMe alloys should be studied carefully to find out contribution of Al-Al, Me-Me and Al-Me pairs.

II.4. High temperature relaxation: grain boundary / dislocations Grain boundary (GB) relaxation is one of the earliest examples of damping in polycrystals. Zener found for polycrystals (grain size d) with random GB (width δ) a relaxation time τσ [87]:

τσ =

ηd σd = , GU δ GU v(0)

(9)

where η is an appropriate viscosity for grain boundary sliding (correlated with atomic self diffusion: η = kT/Da, D = ½νja2 is the diffusion constant, νj is the jump frequency, a is the atomic distance), GU is unrelaxed shear modulus, σ is acting stress, v(0) = σb/η is initial shear velocity. Later studies have shown that the GB relaxation in alloys is more complex, and should be associated with dislocations rather than with grain boundary sliding [88]. The GB-related peak in Fe-Al is mentioned in several papers [50, 81, 83]. According to Hren [50] the GB peak in Fe-24.8Al (at ~970 K, 950 Hz) is recorded only at ~50K higher temperature than the Zener relaxation for the same alloy. Wert [89] reported the GB peak in Fe-28.3%Al at higher temperature 1023K (torsion frequency is not indicated in this paper but from the specimen size one can estimate it to be ~1 Hz). In both cases the increase in the grain size leads to a decrease in the IF peak height, and from this the GB origin of the peak was concluded. The IF peak at ~750 K (~4 Hz) with H ≈ 1.8 eV and τ0 = 10-14 s in Fe-50%Al nanocrystalline alloy was also attributed by the authors to the GB peak [90]. Pavlova et al. [82] explained a decrease in the IF of Fe-Al-Si alloys in the temperature range from 870 to 980K with increase in annealing temperature of the specimens and corresponding growth of grain size by the GB relaxation. Lambri et al. [91] has repeated the measurements of the same Fe-Al-Si alloys and

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found that the IF peak at (~1000°C) depends very much on the temperature of the D03-to-B2 transition (Figure 12): contrary to a symmetrical peak in B2 phase, the high temperature peak is very much suppressed in the D03 phase which can be explained by lower dislocation mobility in the D03 structure (see §III.3).

120

3

Q [10 ]

100

-1

80

Fe-6Al-10Si Fe-8Al-7Si Fe-5Al-20Si Fe-12Al-12Si Fe-26Al

60 40 20 0 600

700

800

900

1000

1100

1200

1300

T [K] Figure 12. Q-1(T) curves in the range of elevated temperatures (f ~ 1 Hz) for Fe-5Al-10Si, Fe-8Al-7Si, Fe-25Al, Fe-12Al-13Si, and Fe-5Al-20Si specimens after background subtraction.

High temperature IF peaks in Fe-38Al alloy were studied by San Juan et al. [92] using a forced torsion pendulum (10−3 to 10 Hz). Two peaks have been observed at about 780 and 1100K (1 Hz), which are largely superposed in the intermediate temperature range. Both peaks were attributed to relaxation mechanisms. The low temperature peak was identified as the Zener relaxation of Al atoms. The activation energy of the high-temperature peak has been determined to be Hact = 2.87 (±0.05) eV, a pre-exponential factor τ0 =10−15 s, and a broadening of the peak of the Gaussian distribution with β ≈ 4. The opportunity for the GB relaxation in this alloy was according to authors completely blocked by the presence of the Y2O3 particles, and other very small particles (less than 50 nm) of Y and Al oxides. The peak was attributed to the kink pair formation (KPF) mechanism of the 〈100〉 dislocations on their {100} glide planes. The measured τ0 ( = 10−15 s), corresponds well to a dislocation motion controlled by the KPF mechanism: in bcc metals the value of τ0 for the so-called γ peak due to KPF on screw dislocations is between 10−13 and 5×10−17 s [93], and in particular it is in between 4×10−13 and 1.2×10−15 s for pure iron [94]: (the activation energy of the γ peak in iron is lower). Thus this peak is associated with the intrinsic motion of such 〈100〉 dislocations in the B2 ordered phase which is in agreement with Lambri’s conclusion about dislocation-related origin of this peak [91] (see also in III.3). Similar high temperature peaks were observed using FDIF technique in Fe-25Al-(3, 9, 15)Cr alloys by Rivière in [86] Figure 13: the high temperature background was lower in these experiments as compared with [92] which makes a question about the Y2O3 particles contribution due to a difference in the thermal expansion coefficient of the matrix and

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

87

particles. The activation parameters (τ0, H, and β) for the P1 (Zener) peak and the P2 (GB) peak at higher temperature for Fe-25Al-9Cr were estimated by fitting by the program discussed in §I.1 and are given in Figure 13. (see also in III.2).

200

T=838 K

P2

150

927 K

867

300 -4

838

898

Q , 10

100

-1

823

150

0

-4

-2

0

2

lo g 1 0 (fre q ./H z )

-1

estim ated background

Q , 10

200

experim ental curve

Fe-25Al-9Cr T=838 K

experiment

P1 P2 sum

-4

50

β2=1.9 -17

P2

P1 (Zener)

P1

-4

-3

-2

-1

0

1

log 10 (freq./H z)

(a)

2

3

-18

τ01=5x10

P2 H2=2.95

P2 50

difference

β1=0.95

100

100

0

P1 Zener H1=2.54

0 -4

-3

-2

-1

0

1

τ02=1x10

2

3

log10 (freq./Hz)

(b)

Figure 13. Q-1(f) curves at elevated temperatures for specimens of Fe-25Al-9Cr alloys: a) experimental data at 838K with and without background. Inset: peaks at different temperatures, b) results of the peak deconvolution (Golovin and Rivière).

II.5. Low temperature relaxation: effect of deformation A broad, sometimes plateau-like, IF peak has been recorded in several Fe-(20-30)Al alloys at low temperatures (Figure 14a) [61]. It was suggested to be caused by dislocations and point defects (vacancies, self interstitial atoms) and enhanced by deformation (D-peak), in the temperature range of 200 to 300 K (activation enthalpy is roughly about 0.43 to 0.65 eV). The D peak is observed in a temperature range where from plastic deformation studies it is known that the strain rate is controlled by single (partial) screw dislocations moving in the ordered lattice by nucleation and rapid sidewise motion of double kinks [95] with an activation enthalpy for double kink formation of 2Hk = 1.08 eV, i.e. roughly twice the D activation enthalpy. During vibration with low amplitude, on dislocations which are in general inclined to the Peierls valleys, single kinks (generated at the anchoring points of dislocations) move in the microyield region according to the picture in [96], interacting with point defects. The large width of the D “peak” may be due to different kinds and configurations of obstacles for this sidewise kink motion and may be supposed to be composed of γ peak [97] and Hasiguti peaks [98], consisting of reversible and irreversible components [99]. The inverse modulus (E(T)) effect accompanied the D peak in some tests [61] may also result from dragging of points defects according to [100], where “dragging” means in fact short-range diffusion in the dislocation core region.

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30

F e -2 5 % A l: 1 0 0 0 °C , a ir c o o lin g

-1

Q , 10

-4

A larger peak is observed after quenching than after slow cooling [61], quenching produces a high vacancy concentration (vacancies can help in dislocation kink formation and migration), and additional dislocations may have been also produced due to thermal stresses. The D peak divides IF background into two parts: below peak temperature of the lowtemperature background is higher, and above the peak – background is lower. This amplitude dependent effect is bigger if higher amplitude of deformation is used (Figure 14a). The decrease of the D peak itself with increase in Al concentration (in quenched alloys with 22 to 31%Al) indicates a contribution of vacancies whose concentration is known to increase [101]. For high Al concentrations (> 30 at.% Al) the D peak seems to be suppressed. While the Snoek and X peak height clearly correlates with the C content, the D peak shows a complex behaviour, possibly because the dislocation kink mobility is affected by carbon, vacancies and self interstitial atoms. The D peak is also observed in several ternary, e.g. in Fe-Al-Cr, alloys [102].

D

5 20

4 3 2

10

1

1)

ε o ~ 0.7 1 0

2)

5 εo

200

-5

3)

10 εo

4)

20 εo

5)

23 εo

T [K ]

300

Fe-27Al

-1

Q , 10

-4

6 5 4

300

200

3

Q m ax

2

Q m in

-1

-1

100

S

1 0

1

ε, %

(bending)

2

Area under the D peak [arb. units]

specimen is broken

(a)

(b) Figure 14. The D peak in Fe-25Al alloys: a) Influence of amplitude of measurements (curves 1 to 5) on TDIF in Fe-25Al alloy after air cooling from 1270 K; b) Influence of cold-work deformation by bending on the D peak height (left scale) and area under the peak (right scale) for Fe-27Al. Before and between cold working the specimen was annealed at 775K, 1 h.

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

89

Fig 14b shows an example of the D peaks in Fe-26.6at%Al after annealing at 500 oC and step by step bending deformation. The increase of QDmax-1 up to a strain of ε ≈ 1 % reflects the increase of dislocation density in microyield, where long straight screw dislocations are produced by sidewise movement of the easily mobile edge components [96]. The observed dependence supports the idea that at least a part of the damping effect is due to kink nucleation and motion in dislocations.

Figure 15. Structure of Fe-25Al (dark field): a) antiphase D03 domains in annealed at 573 K state ([110](111)) prior to deformation, b) size of grains after HPT deformation, and c) HTP specimen after heating to 923 K: antiphase D03 domains. All images are taken in ~3 mm from the specimen center. Deconvolution of the D peak into several partial peaks for Fe-25Al (d) and Fe-25Al-9Cr (e): Insets dependence of partial peaks from annealing temperature for Fe-25Al and Fe-25Al-9Cr alloys [96, 98].

As low ductility of Fe3Al prevented a closer study of the influence of bending deformation, samples of the intermetallic compound Fe3Al were subjected to high pressure torsion (HPT) deformation. Typically, the average grain size ( d ) in as cast Fe3Al is ~0.1 mm. Well-annealed (72 h at 573 K) Fe3Al is characterised by D03 atomic order with clearly visible domains and antiphase boundaries (Figure 15a). After the HPT deformation (P = 3 GPa, γ = 160) [103], d is comparable to the average size of the D03 domains: ultra fine

90

Igor S. Golovin

grains with a mean size of ~100 nm (at 3 mm distance from the centre, Figure 15b) are dominating in the outer parts of the HPT specimen. Further heating to 920 K during the TDIF tests not only removes the IF peaks but also leads to recrystallisation, grain growth, and atomic ordering (Figure 15c). The D-peak in Fe-25Al is shaped by HPT into a family of five IF peaks: 1, 21, 22, 23, 3 (Figure 15d) which were separated by a numerical decomposition procedure (dashed lines). The D peaks family was also recorded in different Fe-Al-Me alloys (Me = Cr, Ge, Mn, Si etc.) [104]. Comparison between the D peaks in Fe-26Al and Fe-26Al-5Cr [102] shows a difference in the magnitude of the partial peaks from the D-family (Figure 15e). These single peaks are similar to the Hasiguti peaks [98] in cold worked / irradiated metals, i.e. they are caused by coupling of dislocations and different point defects [97]. A distinct group is formed by the “2n“ peaks, which are reduced by annealing more effectively than the other peaks (Figure 15 c,d). These 2n peaks are apparently caused by relatively unstable configurations or associations of point defects. After heating to 500 K with 1 K/min, neither a modulus defect nor the group of the 2n peaks are detected any more. Generally these peaks can be classified as Hasiguti peaks, which typically consist of a several Debye peaks caused by coupling of dislocations and point defects and their segregations. The interaction of the strain field of a dislocation with the strain field of point defects leads to relaxation effects if either the dislocation or the point defect move, or if the dislocation breaks away from the point defect with a characteristic thermally activated relaxation time. Better understanding of atomistic mechanism of the single peaks in Fe3Al should contribute to better understanding of both dislocation behaviour at low amplitudes of vibration in Fe-Al and instability at early stages of annealing of severely deformed alloys [102].

II.6. Elasticity Temperature dependence of elastic modulus of Fe-(24-28)Al alloys in the range from room temperature to 600 °C depends mainly on two factors: the order-disorder (mainly the D03-to-B2) transition, and ferro-paramagnetic (D03(f) to D03(p)) transition [105, 106]. We would only emphasise the contribution of the third factor: the contribution of anelastic relaxation phenomena such as the Snoek-type or X relaxation to the E(T) dependence. Modulus of elasticity, E, is proportional to the resonance frequency: E ~ f2. In this paper we did not calculate exact values of modulus, instead the results are given in terms of resonance frequency (f). Quenching leads to formation of the Snoek and X peaks: TDIF curves for the same alloy with 25.5%Al in well annealed (curve 1) and as quenched (curve 2) states is shown in Figure 16. The relaxation peaks are supplied with decrease in modulus (resonance frequency) and denoted as the ΔS and ΔX effects, correspondingly, in agreement with the scheme given in Figure 1. Relation between dissipated energy and modulus is known as Kronig-Kramers relation (eqs. (1a) and (1b)). Increase in quenching temperature increases ΔS and ΔX effects by increase in C and vacancy concentration in solid solution. In contrast with quenched-in state this effect does not take place in well annealed state (curve 1). Concentration dependence of Curie temperature (TC) is much stronger than temperature of the D03-to-B2 (TO) transition [114]. If phase and magnetic transitions in Fe-25Al alloy are

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

91

close to each other, an increase in Al concentration up to ~28% practically does not influence temperature of phase transition, while Curie point decreases significantly. Experimental curves for Fe-(23-26)Al can be found in [107, 108]. Alloying of Fe-25Al alloys by most of the studied elements (Cr, Ge, Mn, Si, Ta, Ti) decreases Curie point while influence of these elements on the temperature of the D03-to-B2 transition is different: Cr and Mn do not influence this temperature at least up to 5% solute element, Ge, Si and Ti increases this temperature and thus influence the temperature dependence of modulus [104].

Fe-25.5Al S

D03 D03(f)

460

B2

f [Hz]

D03(p)

100

220

450

Z -4

Q , 10

215

X

1 2

-1

440

ΔS

210

ΔX

2

10

430

205

1

400

500

600

700

800

900

T [K]

Figure 16. Temperature dependent internal friction and resonance frequency curves in Fe-25.5%Al alloy: (1) in well annealed (f ~ 200 Hz) and (2) in as quenched states (f ~ 400 Hz)

Pseudoelastic behaviour of D03 ordered Fe3Al single crystals (Al = 22–25%) with high recovery ratio both in tension and compression was reported [155, 156]. The recovery ratio in D03 ordered state shows a maximum near Al = 23%. In contrast, the recovery ratio of the crystals annealed in the α, B2, (α+B2) and (α+D03) phase regions was small. When large pseudoelasticity takes place, superpartials with b = 1/4[111] moved independently leaving the nearest-neighbour antiphase boundaries. During unloading, the nearest-neighbour antiphase boundaries pulled back the superpartials resulting in the pseudoelasticity. The pseudoelastic behaviour of the D03-ordered Fe3Al single crystals depends strongly on the ordered domain structure. The fine domain structure accelerated the individual motion of 1/4[111] superpartials and suppressed the activation of the secondary slips resulting in the superior pseudoelasticity near Al = 23%.

II.7. Histeretic Effects Dislocations and magnetic domain walls (DW) give contributions to amplitude dependent internal friction (ADIF). These contributions in Fe-Al can be separated using external saturated magnetic field in which magnetic contribution is completely suppressed: see Figure

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Igor S. Golovin

17a for ADIF for Fe-10.4Al alloy at torsion. Both dislocations and magnetic domain walls contributions to amplitude dependent internal friction are also temperature dependent and practically frequency independent in Hz and kHz ranges. High damping capacity due to magnetomechanical hysteresis is determined by irreversible movement of domain walls (90°type for Fe-Al alloys) – see TEM picture of magnetic domains inserted into the Figure 17a. The dissipated energy accompanying DW motion depends on the DW mobility. The mobility of DW is controlled by three factors: a. Structure and size of magnetic domains and DW, i.e. magnetic parameters of alloys; b. Structure of the crystalline lattice in which the DW moves; c. Interaction between the DW and imperfections of the crystalline lattice. There is only a limited number of papers considering all these three points together. Phenomenologically the energy loss ΔW due to magnetic domains for a vibration stress (σ) below some critical stress (σc) is given by the Rayleigh law:

ΔW = Dσ3 ( σ < σc ; D is constant).

(10.a)

For large stresses ΔW saturates and is given by:

ΔW = kλSσc ( σ > σc ),

(10.b)

and the specific damping capacity Ψ is defined as Ψ = ΔW/W. The magnetomechanical damping in ferromagnetic materials has its source in the stressdriven irreversible movement of the magnetic DW. The maximum damping at ADIF is proportional to λSE/σi (λS is the saturation magnetostriction, and σi is the average internal stress opposing domain boundary motion, k = 1 is a constant characteristic of the shape of the hysteresis loop) [109]. For a Maxwell distribution of internal stresses the value of hysteretic IF (Qh-1) was described by Smith and Birchak as: Qh-1 = 0.34kλSE / πσi (at σ ≈ σmax),

(11.a)

Qh-1 = 4 kλSE / 3πσi2 (at σ < σmax).

(11.b)

The dependence of Qh-1 on σi for constant amplitude of external stresses σ : Qh-1 ~ 1/σim, where m = 2 ( for σ « σi ) and m = 1 (for σ = σmax), which corresponds to the data in Figure 17a. The magneto-mechanical amplitude-dependent contribution to IF in Fe−Al alloys was studied in several research papers [60, 89, 110-112, 161, 162]: it was shown that this contribution occurs at room and elevated temperatures, and that it is high enough to consider Fe-(10−12)%Al alloys as high damping materials with Ψ up to 60% (Figure 17b). The temperature dependence of the magneto-mechanical contribution to damping for Fe-25Al (Figure 17c) is in reasonable agreement with the magnetisation curve (Figure 17d), its contribution to the elastic modulus below the Curie point can be seen directly in the f(T) curve in Figure 16. The magnetisation curve is affected by the D03-to-B2 transition. This results in

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

93

two “Curie points” as known since 1935 [113]. The data extrapolation from the D03 range gives the Curie temperature in the vicinity of 800 K (TC(D03)), while the Curie point at higher temperatures represents some contribution of the disordered phase, in agreement with the Fe−Al phase diagram [114, 115].

Figure 17. Amplitude dependent internal friction in Fe-Al alloys: a)

Typical ADIF curve (Fe-10%Al) with the peak due to magnetomechanical losses, torsion. Inset: magnetic domains – source of high damping. The Lorentz image of magnetic structures after saturating with an external field of 2T (tilted at +30).

b)

Influence of Al content and heat treatment (cooling in air, in furnace, stepwise regulated cooling) on maximal damping (δmax) [106,107],

c)

Influence of measuring temperature on ADIF in Fe-25%Al at torsion [60],

d)

Influence of measuring temperature on magnetization in Fe-26%Al alloy.

Concluding Remarks to §II. Several conclusions about mechanisms of different effects in binary Fe-Al based alloys were done in corresponding paragraphs. The following anelastic phenomena (relaxation peaks) are recognised in Fe-Al alloys and contribute to temperature dependent properties of Fe-Al alloys:

94

Igor S. Golovin 1. the Snoek-type relaxation (carbon atom jumps in Fe-Al solid solution: H = 0.9-1.25 eV), 2. the Zener relaxation (substitution atom (Al) pairs reorientation: 2.3-2.9 eV), 3. the vacancy-and-carbon related relaxation (the “X” peak: 1.5-1.8 eV), 4. the vacancy complexes reorientation phenomena (1.6-1.8 eV), 5. the grain boundary peak, also interpreted as dislocation-related peak (~ 3 eV), 6. the deformation-related (“D”) relaxation at subzero temperatures (0.43-0.65 eV), 7. powerful amplitude dependent magnetomechanical damping in Fe-(10-12)Al alloys.

At present the anelastic effects related to the point defects (the Snoek-type and Zener peaks) diffusional reorientation are studied both on qualitative and quantitative levels. The “map” of activation energies for three peaks: the Snoek-type (S), Zener (Z), and the X peak (relaxation effects numbered above as n.3 and n.4 are considered in this “map” as one X peak) against Al% is given in Figure 18 as a function of Al content in iron. More complicated anelastic effects due to complexes of point defects (the Hasiguti and X peaks) are studied mainly on a qualitative level, and their better understanding is needed prior to their possible applications for structural studies. Nevertheless they can give some information about vacancy contribution to anelastic properties (the “X” peaks n.3 and n.4) or about the beginning of recovery processes of severely deformed alloys (the “D” peak family) at least on the qualitative level. Very little as yet known from mechanical spectroscopy about high temperature (grain boundary?) dislocation behaviour in differently ordered and disordered phases of iron aluminides which is probably the most actual direction for future study. There is a reasonable understanding of magnetic contribution to mechanical damping in Fe-Al alloys which allows one to use some of them for high damping applications. Pseudoelastic behaviour of Fe3Al-based alloys should be considered for different applications.

III. TERNARY FE-AL BASED ALLOYS Fe−Al based alloys have gained considerable interest owing to their attractive mechanical properties which can be improved by addition of appropriate third elements (e.g. see proceedings of Discussion Meetings on the Development of Innovative Iron Aluminium Alloys (Düsseldorf 2004; Toulouse 2005; Mettmann 2006; Interlaken 2007)). Fe−Al alloys with strengthening intermetallic phases are promising candidates for structural applications. In this chapter we provide further evidence and arguments in favour of the mechanisms proposed in Sect. II, by checking the changes of the peak parameters with additions of third elements, e.g. those which trap carbon interstitials into strongly bound carbides. They are grouped in the Sections III.1. Fe−Al−(Nb, Ta, Ti, Zr); III.2. Fe−Al−Cr; IV.3. Fe−Al−Si; III.4. Fe−Al−(Co, Ge, Mn), and the results are discussed with respect to their anelastic mechanisms identified in binary Fe−Al alloys.

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

95

III.1. Ternary Fe−Al−Me Alloys, Me = Nb, Ta, Ti, Zr These four systems have some similarities and can be discussed together: the Ti, Nb, Zr and Ta having different solubility in Fe−Al are strong carbide forming elements in iron-based alloys: they produce MeC carbides, e.g. TiC, TaC, and NbC in Fe-(15−26)Al alloys [116]. The Nb, Ti and Ta increase the temperatures of the D03-to-B2 and the B2-to-A2 transformations in Fe−Al [117], which agrees with our own DSC data (0.3 at.% Nb: TO = 823 K, 2 at.% Ti: TO = 945 K, 4 at.% Ti: TO = 1048 K), and Ti and Ta in alloys with higher concentration lead to the L21 order, in which not only Fe and Al atoms are D03-ordered but also Ti and Ta atoms occupy positions of the (4b) sublattice. Nb and Zr have low solubility in Fe-Al and in particular in the D03 phase.

Figure 19. Structure of Fe-23Al-15Zr (a) and Fe-25Al-6Ta (b) alloys.

In all these alloys neither the Snoek-type nor the X peaks were recorded (Figure 7): Ti, Nb, Zr, Ta trap free C interstitials into MeC carbides, thus suppressing the Snoek and X peaks. This effect takes place even in Fe−Al alloys containing 0.1 at.% Zr or 0.3 at.% Nb: already such small amounts of Zr or Nb erase the S and X peaks. Very little influence of carbide forming elements on the vacancy concentration in these alloys after different regimes of quenching was found [54]. The fact that both the Snoek and the X peaks are suppressed in all alloys containing a strong carbide former supports the conclusion about C in solid solution as the decisive ingredient for these relaxations, similar to those discussed for the binary alloys (§II.1 and §II.2).

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If a certain concentration of Ti, Ta or Zr in Fe−Al is exceeded, these elements produce different second phases (Figure 19), e.g. Laves phases: Zr2(Fe,Al) hexagonal C14 (λ1) and cubic C15 (λ2), ThZr12-type τ1 phase in Fe−Al−Zr alloys, and hexagonal C14 Laves phases (Fe,Al)2Ti, (Fe,Al)2Nb or (Fe,Al)2(Ti,Nb) in Fe-Al-Ti,Nb alloys, or (Fe,Al)2Ta precipitates [116-119]. In the examples of Figure 18 the phases could be distinguished by Vickers hardness measurements (HV) as follows: For Fe-23Al-5Zr (Figure 19a) the dark phase (HV = 712) represents a eutectic, the bright one (HV = 1085) the Laves phase; for Fe-25Al-6Ta (Figure 19b) the dark phase (HV = 1145) is the eutectic, and the bright phase (HV = 430) mainly Fe−Al solid solution. Two temperature ranges can be distinguished in such “peak-free” Q-1(T) curves for Fe20Al-0.1Zr in Figure 20 between 100 and 800 K, (I) below 400 K, and (II) above 450 K. Taking into account the related increase in f(T) and the start of decrease in the heat flow (DSC signal), this effect can be explained by the higher dislocation mobility in quasi-quenched disordered specimens in range “I”, while the decrease of mobility and consequently of the damping background between 400 and 450 K is supposed to be the result of ordering. Indeed the effect is smaller in the second heating run of the same specimen, which has been cooled down in the vibrating-reed furnace instead of quenching: in the second run the specimen is better ordered as compared to the quenched one. The increase in Zr content to 4% (in Fe40Al) and to 12.5% (in Fe-20Al) leads to a well pronounced decrease of this effect. This may be due to the Laves phase in the 12.5Zr containing alloy which restricts the dislocation motion in the Fe−Al phase. Similar effect in Zr-free Fe-25Al alloy was observed at lower temperature (Figure 14a).

4 -1

D03 + A2

(A2) as quenched

A2 (ferro)

50 Fe-20Al-0.1Zr (wq 1273 K) test-1 40 test-2 f 30 DSC 20 Fe-20Al-12.5Zr

560

TC 0.09

DSC, mW/mg

10

0.14

f [Hz]

Q [10 ]

60

540

0.04

(I)

(II)

520

0 200

400

600

800

T [K]

Figure 20. Fe-20Al-0.1Zr (quenched from 1273K): Damping Q-1 (T), frequency f(T), and DSC curves. Q-1(T) for Fe-20Al-12.5 Zr is added for comparison.

Ti (2 and 4 at.%) decreases the Zener peak in Fe-26Al while no clear effect of the low content of Nb (0.3 at.%) was recorded in Fe-26Al [61], neither 0.1 nor 12.5 % Zr in Fe-20Al change substantially the range of Zener relaxation (Figure 20) due to the low solubility in FeAl. The Zener peak decreases if the transformation temperature TO increases by alloying and

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

97

if the added metals have reasonable solubility (e.g., Ti); no effect on the Zener peak occurs in case of low solubility (e.g., Zr, Ta, Nb). Alloying by Zr – contrary to the effect of Ti, Ta or Nb – leads to a prominent effect between 370 and 470 K: the level of IF decreases with increasing temperature in this range, although the increase in temperature does significantly influence neither the volume fraction nor the composition of phases in Fe−Al−Zr alloys [118]: The Zr content of the Laves phase in the Fe-23Al-15Zr alloy is 24.0 (after quenching from Tq = 1070K), 23.6 (Tq = 1270K), and 23.3 at.% (Tq = 1420K). At the same time after these treatments the IF differs in the low-temperature range (see also Figure 14).

III.2. Ternary Fe−Al−Cr Alloys An important feature of this system is the high solubility of both Al and Cr in bcc iron. Fe-25Al alloys are often additionally alloyed by Cr, in order to increase not only their yield stress but also their ductility and workability. The Cr atoms occupy the 4b or 8c positions, with some preference of next nearest neighbour Al positions [120]. The lower dissociation energy W(Cr −Al) = 0.6960 eV for Cr-Al pairs than for Fe−Al pairs (W(Fe−Al) = 0.7457 eV) is responsible for the mentioned decrease of the APB energy. The ordering transition temperature is not changed significantly [121] by Cr addition of <15% (Table 2). The density of vacancies in Fe-25Al-(15-25)Cr alloys quenched from 1273K was detec-ted to be about cV ≈ 3× 10-5 at-1 which is three times lower than that in Fe-25Al (cV ≈ 10-4at-1 [56]).

D 0 3 ordering

-1

15Al-15Cr

31A l 26A l-5C r TO TO 4

0.004

31Al 26Al-5Cr 15Al-15Cr

2

31Al

Q (heat flow)

Q -Qb

26Al-5Cr

-1

0.006

0

0.002

TO

-2

26A l-5C r 0.000 300

400

500

600

700

800

900

T [K]

Figure 21. Damping curves (with subtracted background Qb-1) and heat flow curves (right hand scale) comparing the binary alloy Fe-31%Al with two Fe-31(Al+Cr) alloys: U Fe-26Al-5Cr and V Fe-15Al15Cr. (Frequency f ∼ 2 Hz)

Chromium is a carbide forming element in iron and in Fe-26Al [56a], although not as strong as Ti, Nb, Ta or Zr: chromium carbides can be dissolved at quenching, so some interstitial carbon remains in solid solution after water quenching. Calculations [122] have

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demonstrated that the C−Cr ‘chemical’ plus ‘elastic’ interaction in iron takes place up to the fourth or fifth coordination shell. This explains the observation that the Snoek-type and X peaks (Figure 21) for alloys Fe-30%(Al+Cr) if the Al content exceeds the Cr content, and the shift to higher temperatures with respect to those of Fe-31at.%Al due to the additional C−Cr interaction [80]. Substituting Al atoms by Cr in Fe-30(Al+Cr) alloys leads to a decrease in hardness. For Fe-15Al-15Cr long-range order is not detected by TEM but superdislocations which are typical for D03 order can be seen while XRD only indicates some order. The Zener peak smears to the direction of higher temperatures since the activation energy of Cr diffusion in Fe3Al is higher than that of Al (Figure 21). The activation energy of Cr diffusion in iron and also in Fe-27Al (232 ± 5 in A2 and 239 ± 3 kJ/mol in B2 phases) is higher than the activation energies of Al diffusion in iron [123]. Table 2. Hardness of (Fe,Cr)3Al alloys after annealing for 48 h at 750 K, D03-to-B2 transition temperature and Curie temperature as a function of Cr% (alloys with ≤ 15Cr are D03 ordered, the alloy with 25Cr is B2). Fe-25Al-2.5Cr Fe-26Al-5Cr Fe-25Al-8Cr Fe-25Al-15Cr Fe-25Al-25Cr 321 297 280 284 361 823 825 825 793 ~740 ~750 ~560 ~425 ~410

Q

-1

700

800

T900 [K]

Fe-26Al

25Al-5Cr ~540Hz

0.008

-1

25Al-15Cr ~220 Hz

Fe-26Al 0.010 ~220 Hz

-1

Fe-25Al 308 819 ~780

Q -Qb

Alloy HV TO (K) TC (K)

0.004 25Al-15Cr

0.006

0.004

0.002 25Al-9Cr

0.002 ~2 Hz tests (Zener peak)

400

500

600

700

800

0.000

T [K]

Figure 22. Q-1(T) in Fe-25Al-(5÷15)Cr for 390-540 Hz, right-hand part of the figure with scale at the top for ~2 Hz (Zener peak).

For the case of a fixed Al content (∼25 at. %) and Cr substituting Fe, all above mentioned tendencies can also be seen but the relative changes are different (Figure 22). First, D03 order is observed by TEM in Fe-26Al-5Cr, Fe-25Al-8Cr, Fe-25Al-15Cr and Fe-25Al-25Cr composition after annealing at 748 K and quenching. Some selected TEM structures of Fe−25Al−Cr alloys with different Cr content are presented in Figure 23 showing fine and

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

99

coarse D03 domains in all studied alloys after short and long annealing, respectively. B2 order is found in Fe-25Al-15Cr and in Fe-25Al-25Cr after quenching. The fine D03 domains form after 48 h annealing at 750 K in Fe-25Al-25Cr which is rather close to the D03-to-B2 transition. The temperatures of the A2-to-D03 and D03-to-B2 as well as of the ferro- to paramagnetic transformation for Fe-25Al-Cr alloys are shown in Table 2. The decrease in the Snoek-type and X peak heights is due to trapping of carbon atoms in chromium carbides, while some shift of the Snoek peak to higher temperature is the result of the C−Cr interaction in solid solution [122]. The Snoek and X peaks can hardly be distinguished in some cases: only by adding Cr stepwise into Fe−Al, is it possible to see the retaining contribution of these peaks in Fe-Al-Cr alloys with high Cr content, e.g. in Fe-25Al15 and -25%Cr.

Figure 23. TEM micrographs showing the D03 structure in Fe-26Al-5Cr (dark field, [110](111)): quenched from 1120K and annealed 3h at 570K (fine domains) (a) and quenched from 1170K and annealed 48 h at 750K (coarse domains) (b) Fe-25Al-8Cr quenched from 1120K and annealed 3 h at 570K (c) and 48h at 750K (d), Fe-25Al-15Cr, quenched from 1170K and annealed 100 h at 750K (e), and Fe-25Al-25Cr quenched from 1170K and annealed 48 hrs at 750K (fine domains) (f).

The Zener relaxation is slightly broadened and shifted to higher temperatures: this effect is better seen in the low-frequency tests (Figure 22: right scale). In case of high frequency

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tests the Zener peak position is beyond the range of our TDIF measurements. The Zener peak parameters in Fe-25Cr-5Al as reported in [124, 125] are: H = 245 kJ/mol (τ0 = 2.6×10-17 s), which is surprisingly more close to Fe-25Al than to the Fe-25Cr alloy if compared with [80, 126]. The peak shape was also recorded to be close to the Debye peak with a single relaxation time. 200

100

P1

P2

867K 853K

1st run

927K

1st run 898K 150

838K

883K

-1

-1

Q x10

Q x10

4

4

75

808K

100

50

853K

763K 748K 673K 718K 25

823K

50

793K 0

0 -4

-3

-2

-1

0

1

log10 (freq./Hz)

(a)

2

3

-4

-3

-2

-1

0

1

2

3

log10 (freq./Hz)

(b)

Figure 24. The Fe-26Al-8Cr alloy: P1 (a) and P2 (b) peaks measured at different temperatures.

Effect of Cr on low temperature IF in severely deformed Fe-25Al alloy, and the effect of Cr in high temperature range were already discussed in §II.5 and §II.4, consequently. The isothermal mechanical spectroscopy technique was applied [86] to study the high temperature relaxation in several Fe-Al-Cr ternary alloys. As the example we can consider Fe-26Al-8Cr alloy (Figure 24). The TO transition (825K) in this alloy takes place according to DSC tests at practically the same temperature as in Fe-26Al, while the Curie point is about 250 K lower. Two peaks the P1 (Zener) and P2 peaks are overviewed [86]. The P1 peak - in both the D03 (paramagnetic) and B2 ranges, the P2 peak - above D03-to-B2 transition. Similar to the Fe-26Al alloy, the P1 (Zener) peak height increases in Fe-26Al-8Cr with increase in temperature if the temperature of isothermal test is more than 720K. The same is also true for the P2 peak (Figure 24). The P1 peak height below 720K does not change pronouncedly. Activation parameters for the peaks were found as following: the P1 peak: H = 290 kJ/m, τ0 = 5×10-20 s., and the P2 peak (experimental data at step by step cooling from 928K are used): H = 282 kJ/m, τ0 = 10-17 s.

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

101

Table 3. The P1 peak parameters for several selected temperatures ♣. n. Alloy 1 Fe-26Al

T, K Qm-1

β 2

Fe-28Al-3Cr

T, K Qm-1

β 3

Fe-26Al-8Cr

T, K Qm-1

β 4

Fe-25Al-15Cr

5

Fe-25Al-25Cr

T, K Qm-1

β T, K Qm-1

β

The Peak1 parameters at different temperatures 692 708 723 738 753 768 783 809 20 20 29 32 37 44 49 66 1.4 1.4 1.22 1.25 1.39 1.39 1.42 1.42 688 707 746 766 785 804 824 12 14 21 33 41 50 57 1.2 1.2 1.4 1.33 1.5 1.5 688 718 733 748 763 793 838 853 24 24 28 31 38 41 77 87 1.2 1.38 1.39 1.34 1.39 1.35 1.38 1.36 703 718 733 748 763 808 823 839 35 38 42 45 53 67 82 86 1.5 1.55 1.4 1.4 1.41 1.37 1.6 1.7 763 778 793 808 823 838 73 68 51 67 78 68 2.1 2.3 1.7 1.7 1.9 1.6

833 78 1.42

867 94 1.45 853 92 1.9 853 66 1.7

The P1 peak width and height at different temperatures are collected in Table 3. In all ternary alloys except Fe-25Al-25Cr composition the increase in the P1 peak height with temperature of measurements is observed (Figure 25). Increase in the peak height with temperature might be a result of several reasons and one of them is decrease in order in the alloy. The influence of temperature on β is not well pronounced in contrast to the influence of Cr content: increase in Cr content in Fe-25Al-Cr alloys increases value of β. This means that Cr increases the relaxation time distribution. Nevertheless, we did not observe double headed Zener peak as it might be expected in case two types of pairs: Al-Al and Al-Cr contribute independently to the Zener effect. As it concerns the P2 peak it is possible to give the following information: despite its higher temperature (or lower frequency) location of its activation energy is lower than that for the P1 peak in the same alloy, values of β are higher, and it was not observed either in Fe26Al or in Fe-25Al-25Cr composition. The grain boundary peak in Fe-25Cr-5Al with the activation parameters H = 4.07 eV and τ0 = 6×10-24 s was found in [124] and more recently confirmed in [159]. The activation parameters of this grain boundary peak in Fe-25Cr-5Al are very different those which are found for the P1 and P2 peaks in Fe-25Al-(3-25)Cr in [86] and partly presented in figures 24 and 25.

♣

Peaks measured in the D03 range of are typed by normal font on the grey background, peaks measured in the B2 range are typed in italic.

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Igor S. Golovin

-1

4

Qm x 10

-1

β

Qm

100

β 2.5

25Al-25Cr

2.0

50

1.5 0 100

700

750

800

850

25Al-15Cr

2.5 2.0

50

1.5 0 100 50

700

750

800

850

26Al-8Cr

2.5 2.0 1.5

0 100 50

700

750

800

850

28Al-3Cr

2.5 2.0 1.5

0 100

700

750

800

850

26Al

2.5 2.0

50

1.5 0 700

750

800

850

T, K Figure 25. Overview of the P1 peak height (Qm-1, left scale) and width (β, right scale) as a function of temperature of isothermal measurements for all alloys studied.

III.3. Ternary Fe−Al−Si Alloys Contrary to the two previous groups, the addition of Si in Fe-Al neither produces new phases nor is C strongly trapped in carbides. Si improves the D03 order, increasing the transition temperatures of the D03-to-B2, and B2-to-A2 transitions in agreement with [14]. After annealing at 748 K for 100 h, XRD analyses confirm the D03 order in all these alloys. The increase of hardness (HV) with substitution of Al by Si atoms in Fe3(Al+Si), and the corresponding decrease of the D03 lattice parameter (a) is presented in Table 4, where also the ordering temperature TO and the Curie temperature TC are given as determined by DSC and magnetisation measurements, respectively. If quenched from 1273 K the density of vacancies in Fe-25(Si+Al) alloys was detected to be 3−10 times lower than that in Fe-25Al. The temperature range in which the damping peaks are developed for these alloys is close to the Curie point and order−disorder transition (Table 4). The D03 order was detected not only in Fe-25(Al+Si) but also in Fe-15(Al+Si) alloys (Figure 26), with a similar effect of Si substitution on hardness and lattice parameter.

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

103

Table 4. Hardness in Fe3(Al+Si) alloy after annealing for 100 h at 750 K, D03-to-B2 transition temperature, Curie temperature and lattice parameter as a function Al and Si content. Alloy HV TO (K) TC (K) a (nm)

Fe-25Al 308 819 ~780 (in D03) 0.57932 [113]

Fe-20Al-5Si 426 1021 737 0.57582(42)

Fe-12Al-12Si 459 1195 742 0.57126(16)

Fe-5Al-20Si 536 1389 789 0.56645(15)

Fe-25Si 537 790 0.56622(13)

Figure 26. TEM micrographs of the Fe-20Al-5Si alloy: after quenching from 1170K (a), after 100 h annealing at 750K (b), after 100 h annealing at 900K (c) and the Fe-5Al-10Si alloy after 100 h. annealing at 750K (d) (dark field, [110](111)).

The development of the Snoek peak in binary Fe-3Si and Fe-3Al alloys was already discussed in the §I. The peak in Fe-Al-Si alloys with Al/Si content (in at.%): 0/2, 0/5, 1.6/3, 3/3, 4/2 clearly consists of two components (Figure 27): a left-side shoulder (P1) corresponds to the “ordinary” Fe-C-Fe Snoek peak in α-Fe, i.e., this effect is produced by C atom jumps in the solid solution with local Fe atom surrounding. The second peak (P2) is the result of Snoek-type C atom jumps near Fe-C-Me positions. Temperature positions of both peaks are frequency dependent. Al atoms produce a bigger effect as compared with Si on the P2 component of the Snoek-type peak: nevertheless even in Fe-(5-6)%Si alloys local B2 order and distortion of bcc units in the presence of Si atom were detected [158]. If the amount of

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Igor S. Golovin

Al/Si in iron increases to 7/2, 6/5, 9/4, 5/10, 8/7 the peak further shifts to higher temperatures due to a new high-temperature contribution, and a very small contribution of the “ordinary” Fe-C-Fe (P1) peak can still be seen. The P2 peak becomes dominating, the third peak from the right side appears (a weak peak can be distinguished even in 4/2 composition, see Figure 27). This third peak can be another component of the Snoek-type peak or it can be caused by vacancies.

Q

P1

-1

Fe-1.5Al-3Si wq1000K

0.006

P2

840 510

0.002

500

400

450

Q

Fe-4Al-2Si wq1000K

-1

220

f [Hz]

P2

0.004

P1

215 ?

0.002 210

f~500 f~800 350

0.006

f [Hz] 860

0.004

300

880

490 500

550 T [K]

300

350

400

450

500

550 T [K]

Figure 27. TDIF curves for Fe-1.5Al-3Si (upper) and Fe-4Al-2Si (lower) both water quenched from 1000 K. Different frequencies are used (right scale). The P1 peak corresponds to Fe-C-Fe, and the P2 peak corresponds to Fe-C-Me (Me = Al, Si) components of the Snoek-type peaks.

This effect was also reported in [127] for the Fe-6wt.%Si (∼11.3at.%Si) alloy at 570 K. At this stage we can conclude that at least the main contribution to this anelastic phenomena in ternary Fe-(0-4)Al-(0-5)Si disordered alloys is due to the Snoek-type relaxation, while in Fe-(5-9)Al-(2-10)Si ordered alloys the third component is added to the relaxation process. This third component of the peak decreases with ageing faster than the P1 and P2 peaks supporting the idea of another mechanism of this peak. Computer analyses of the Snoek-type peak are given in Figure 28: increase in % or alloying elements increases the Fe-C-Me component of the peak (Figure 28, a and b) while increase in quenching temperature increase the Fe-C-Fe component of the peak (Figure 28, b and c) due to more random distribution of C atoms. Apart from the Snoek-type peak, the X, Zener and the GB peaks are recorded in Fe-Al-Si alloys. An increase in the Si content in Fe3(Al,Si) from Fe-20Al-5Si to Fe-12.5Al-12.5Si and Fe-5Al-20Si decreases the Snoek peak. The X peak is not well distinguishable in two later compositions, the Zener peak decreases in height and seems to shift slightly to higher temperatures. The Zener peak shape and position appears to be a compromise between those of the binary Fe−Al and Fe−Si alloys. It can be shown [83] that the Zener peak in ternary Fe−Al−Si alloys with both 20Al-5Si and 5Al-10Si can be well fitted by two peaks (Figure 29) due to reorientation of Al-Al (H ≈ 2.45 eV, Tm ≈ 808K) and Si-Si (H ≈ 2.97 eV, Tm ≈ 837K) atom pairs.

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

0.006 -1

Q

-1

T1=379, Q =0.0064

-1

T2=433, Q =0.0019

0.004

-1

Fe-1.6Al-3Si wq1000K 500Hz experim. Fe-C-Fe Fe-C-Me sum.sim.

H1=0.84, β1=0.83

H2=1.12, β2=1.25

P2

Q

T1=388, Q =0.0034

-1

H1=0.84, β 1=0.9

0.004

-1

T2=443, Q =0.0054 H2=1.05, β 2=1.54

P1

0.002

0.002

P2

0.000 0.0020

0.0023

0.0026

P1

0.000

0.0029 1/T [K-1]

0.0020

(a)

0.0023

0.0026

Fe-3Al-3Si wq1000K 500Hz experim. Fe-C-Fe Fe-C-Me sum.sim.

0.0029 1/T [K-1]

(b)

0.006

Q

105

-1

Fe-3Al-3Si wq1175K 500Hz experim . Fe-C-Fe Fe-C-Me sum .sim .

T 1 =375, Q =0.0059 H 1 =0.84, β 1 =1.0

-1

-1

T 2 =425, Q =0.0034

0.004

H 2 =1.07, β 2 =1.95

P1 0.002

P2

0.000 0.0020

0.0023

0.0026

0.0029 1/T [K -1 ]

(c) Figure 28. Computer fit for the P1 and P2 components of the Snoek-type peaks: a) Fe-1.5Si-3Al water quenched from 1000K, b) Fe-3Si-3Al water quenched from 1000 K, c) Fe-1.5Si-3Al water quenched from 1175 K. single peaks sum experiment (~ 1 Hz)

0.0015 -1

-1

Q -Qb

Al-Al peak

0.0010 Si-Si peak 0.0005

0.0000 1.1

1.2

-1

1.3 1000/T [K ]

Figure 29. Computer splitting of the Zener peak in the Fe-20Al-5Si alloy into two peaks attributed to reorientation of Al-Al and Si-Si atomic pairs.

106

Igor S. Golovin

The relaxation strength of the Zener relaxation Δ = 2Qmax-1 in disordered alloys is proportional to both the amount of substitute atoms and the relaxation strength per atom pair. As Al atoms are bigger and Si atoms smaller than Fe atoms, both Al-Al as well as Si-Si pairs give rise to an increase of the Zener peak height due to changes of the local lattice parameter. Selected data from literature (results of Tanaka [126] – open triangles and our results [160] – closed triangles) are shown in Figure 30 demonstrating the increase in the peak height with both Si and Al content until ordering takes place at ~11 at.%Si or >20 at.%Al in binary alloys.

150

Δ

Ternary: Si+Al (Si/Al)

Binary: Si [126] Si [160] Al [126] Al [160]

100

4/9 6/8

12/13 and 20/5

10/5

5/6 50

2/6

150

Δ 100

50

5/20

Ternary: Si+Al (Si)

Binary: Si [126] Si [160] Al [126] Al [160]

5 2 20

10

5

6

2/18

4 12

2

0

0 5

10

15

20

at. %

(a)

25

30

5

10

15

20

at. %

25

30

(b)

Figure 30. The relaxation strength of the Zener peak (Δ in binary Fe–Si and Fe–Al and in ternary Fe– Si–Al alloys. Some data for binary alloys were added from [126] (open triangles: up – for Si, down – for Al). Data for ternary alloys [160] are shown by circles. In the left figure, Δ is given as a function of the total amount of Si+Al in at.% and the respective Si and Al contents are indicated at the experimental point as Si/Al. In the right figure, Δ is given as a function of the Al content and the amount of Si in at.% is indicated at the experimental points.

In ternary alloys, the occurrence of Si-Al pairs may reduce the contribution to the Zener relaxation compared to the binary alloys. Indeed the Zener relaxation in all ternary alloys is significantly lower than in binary alloys. This can be seen in the plot of the peak height as a function of the total amount of substitute atoms (Figure 30a). There are at least two reasons for that. Firstly, ordering, which leads to a decrease in the Zener peak height, starts at lower alloying element concentrations in Fe–Si–Al alloys than in Fe–Al alloys. The second reason is that Al and Si atoms in iron at least partly compensate for the elastic distortions produced by each species. This effect can be seen in Figure 30b: For a constant Al content, the addition of Si strongly reduces the Zener peak height (the alloy Fe–9.6Si–5.4Al seems to be an exception; the reason for that is not clear at the moment). Figure 31 shows the lattice parameter in dependence on the Si/Al ratio. As expected, Si decreases and Al increases the lattice parameter of α-Fe. In the ternary alloys it is lower than in α-Fe if Si/Al > 1 and vice versa. Al results in an additional increase of the hardness of the Fe–Si alloys (Figure 31b). However, the effect of Al on the hardness increase in Fe–Si–Al alloys is weaker than that of Si. The height of the high temperature peak (Figure 12) depends on the order degree of the Fe-Al-Si alloys as it can be judged by in situ neutron diffraction studies (wavelength was λ =

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

107

1.28 Å) performed at the D1B powder diffractometer in the Institut Laue Langevin, Grenoble, France (Figure 32) [91]. The diffraction pattern measured at room temperature for the Fe12Al-13Si specimen (empty circles), the Rietveld refinement (full line) [163] and the difference between measured and calculated profiles are shown in Figure 31,a. The sample exhibits a D03 order. The small differences between the fitted pattern (full lines) and the experimental points are due to preferential orientation (texture effects) of the grains. Figure 31,b shows the evolution of the relative integrated intensity of the (111)/(220) and (200)/(220) reflections as a function of temperature. During cooling the order degree is restored. The (200)/(220) intensity ratio shows an increase below ~800 K that can be attributed to an initial increase of the B2 nearest neighbours order. The as quenched sample recovers the B2 order degree since the B2 - A2 transition is well above the measured temperature range. On the other side, the D03 order evolves mainly near the equilibrium value of the D03 order parameter since the D03 - B2 transition is at a lower temperature. HV

2,90

1.8/17.7

a, A

0/25

5.5/6.8 300

2/4

2,88

Fe

1.8/17.7 0/25

1.9/6.9

7/8 250

12.9/12.4

6/3

2,86

4.7/5.9

9/6 200

2,84

1.9/6.9

25/0 14/0 0

[a]

5

10

15

20

Si+Al (at.%) in Fe

5

25

[b]

Si/Al, at.%

2/4

150

2,82

10

15

20

25

Si + Al (at.%) in Fe

Figure 31. Lattice parameter (a) and hardness (b) of studied alloys in dependence on Si+Al content in Fe (numbers near experimental points indicate Si/Al contents in at.%.

The dislocation structure and solute atoms interacting with grain boundaries control the damping spectrum (Figure 12). The absence of the peak at ~1000K during heating in Fe25(Al+Si) and some Fe-15(Al+Si) alloys is due to a reduced dislocation and grain boundary mobility in the D03 state: dislocations can move in the D03 state in pairs only which leads to a decrease in their mobility. The appearance of the damping peak during cooling in Fe15(Al+Si) can be associated with a higher mobility of the recovered grain boundaries [91]. In conclusion to section III.3: the substitution of Al by Si, forming no carbides and improving the D03 order (increasing the transition temperature to B2) preserves the Snoektype and X peaks, although they are smaller than in Fe−Al and shifted to lower temperatures, indicating the difference in C-Si and C-Al interaction in solid solution, however, keeping C interstitial jumps as essential reasons for these peaks. Si also tends to lower the concentration of vacancies, in agreement with the reduction of the X peak. The Zener peak is again a mixture of the corresponding Fe-Al and Fe-Si peaks, significant decrease in the Zener peak relaxation strength can be a result of formation A-Si pairs. The anelastic phenomenon at

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about 1000K (~1 Hz) can be most probably attributed to interaction of dislocations and grain boundaries in ordered and disordered phases.

Figure 32. a) Rietveld refinement of the Fe-12Al-12Si specimen at room temperature. The fitting is performed according to the D03 structure; b) Evolution of the relative integrated intensity of the (111)/(220) and (200)/(220) reflection as a function of temperature.

III.4. Ternary Fe-Al-(Co, Ge, Mn) Alloys In spite of many differences in these alloys (e.g., Ge improves the D03 order, Co improves the B2 order, and Mn (<5%) has no pronounced influence on order in Fe3Al), the main features of the relaxation spectra remain similar to those in the binary Fe−Al alloys [81,104]. Fe−Al−Co. The Snoek-type and Zener peaks are recorded in all Fe−Al−Co alloys. The X peak appears in a few measurements but was not well reproducible. The activation energies of Co diffusion in Fe-27Al are 291 ± 4 in A2 and 283 ± 11 kJ/mol in B2 phases [123]. Correspondingly, the Zener peak in Fe-20Al-5Co shifts slightly to higher temperatures, while the Snoek peak very slightly shifts to lower temperature as compared with Fe-25Al because of the lower Al content. XRD shows the B2 order in the specimen both after quenching from 1270K (lattice parameter a = 0.28874(10) nm) and after additional 100 h annealing at 650K (a = 0.28896(9) nm). The B2 domain structure was detected by TEM, too. Fe−Al−Mn. If Mn is added to Fe-25Al the TO temperature of the D03-to-B2 transition is slightly increased: ~833K (Fe-25Al-2Mn) and ~848K (Fe-25Al-5Mn). Mn is a weak carbide forming element; the activation energy for Mn diffusion in Fe-27Al is 231 ± 5 kJ/mol in the A2 and 234 ± 3 kJ/mol in the B2 phases [120] is close to the activation energy of Al self diffusion in Fe-25Al (236 ± 3 kJ/mol) [79]. Very little influence of ≤ 5% Mn on hardness is detected (HV from 304 to 316). All this is consistent with the small effect of adding 2 or 5% Mn in Fe-25Al on the IF curves. The Snoek, X, and Zener peaks again can be seen in the damping curve. Fe−Al−Ge. The repulsive interaction between Al and Ge atoms in iron [128] improves the D03 order in Fe-Al-Ge alloys, and increases the D03-to-B2 transition temperature [14, 129]. TO in Fe-25Al-5Ge is about 925 K, in Fe-12Al-13Ge about 1190K; from this we

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conclude that our IF tests were carried out in the range of the D03 phase. TC in Fe-12Al-13Ge is ≈ 760K (all DSC), and in Fe-20Al-5Ge TC ≈ 800K (magnetometry). Adding of Ge in Fe-Al as well as substitution of Al by Ge leads to a pronounced increase of hardness, e.g. for Fe12Al-13Ge HV = 413. The damping curves Q-1(T) for these Fe-Al-Ge alloys are similar to their Fe-Al prototypes: the same Snoek-type and Zener peaks are recorded in all alloys, some indication of the X peak is recorded in the 25% Al and 20% Al containing alloys. Substitution of Al by Ge decreases the X peak which is not observed in the Fe-12Al-13Ge alloy. The Fe-Ge-Al alloys are discussed in the next sub-chapter. In conclusion, these additional elements exert only little influence on carbide formation, but in case of Ge and Co they affect significantly the ordering temperatures in the opposite directions (Ge increases TO, while Co decreases it). All these alloys can be considered as FeAl-based alloys. Thus only small changes in the IF curves are observed in the case of Fe-AlMn alloys, while in the case where the 13%Ge or 5%Co are added in the Fe3(Al,Me) compound only the Snoek and Zener peaks can be seen, in agreement with the proposed relaxation mechanisms. In all three systems the Snoek-type and X peaks anneal out after heating to high temperature, contrary to the stable Zener peak confirming the mechanisms proposed for these phenomena.

IV. FE-GE AND FE-GA ALLOYS Contrary to the Fe-Al and Fe-Si phase diagrams which are also known by their strong tendency to ordering of substitutional atoms, the Fe-Ge and Fe-Ga diagrams are still under investigation; uncertainties exist especially in the low temperature range. Structure of alloys and intermetallic compounds of these systems is also less studied. For example, there are ranges of magnetic transformations which are either not indicated in the phase diagram [130] or are given for selected areas only [114, 131]. Contrary to Fe-Al and Fe-Si systems, very few results on anelasticity in Fe-Ge and Fe-Ga alloys can be found in the literature [36, 132-134, 157]. For that reason we provide the reader with some information on these alloys not only with respect to their elastic and anelastic properties but also with some structural studies. There is considerable interest in the Fe-Ge alloy system as a model system [135] involving several phase transformations including structural ordering [136] and variation of ferromagnetic properties [137, 138], as shown, e.g. by X-ray and neutron diffraction studies [139] and by investigations applying the Mössbauer effect [135, 137, 139-142]. Recently, starting from rapidly solidified alloys [131] or from mechanically alloyed material [140], valuable information on the phase selection during heat treatments has been provided for the various, sometimes metastable phases.

IV.1 The bcc Fe-3%Ge and Fe-3Ga alloys. The Fe-3Ge specimen was characterised by DSC (Figure 33a) and magnetometry, which yield a Curie point TC ~ 762 oC / 1035 K, the α - γ transition temperatures 1075 oC / 1348 K (heating), 1035 oC / 1308 K (cooling), and γ - α transition at 1301 oC / 1574 K (heating), 1279

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o

C / 1552 K (cooling). These points are in reasonable agreement with literature data. XRD after water quenching from 1000K (5 hrs) shows the bcc lattice with the lattice parameter 2.87579±0.00044 Å. Similar behaviour with α - γ transition is observed in Fe-3Ga specimen (Figure 33.b)

TC~760C

0.4

DSC, mW/mg

DSC, mW/mg

TC~757C

0.2

1280 -1300

1060

1030 - 1070

0.3 0.2 0.1

Fe-3Ge 0.0 -0.1

1206 1137 1264

0.1

Fe-3Ga 0.0

-0.2

400

α −− γ

2run

-0.3 600

800

1000

1200

γ −− α

1400

1600

α

-0.1 400

600

800

1000

1200

γ 1400

α 1600

T [K]

T [K]

Figure 33. Heat flow in the Fe-3Ge (a) and Fe-3Ga (b) specimens.

An IF (P1) peak practically at the same temperature as the carbon Snoek peak in “pure” α-Fe occurs in Fe-3.6Ge-0.03C (denoted below as “Fe-3Ge”) (Figure 4a). The carbon Snoek peak in Fe-3Ga has also no pronounced difference with the Snoek peak in α-Fe [86]. The peak position depends on measurement frequency corresponding to activation parameters of the peak in Fe-3Ge using an Arrhenius plot as: H = 0.86 eV and τ0 = 2×10–15 s [86]. Based on these values of the activation energy and relaxation time, we can classify this peak in both Fe3Ga and Fe-3Ge as the carbon Snoek-type peak. The peak is slightly wider than a Debye peak with a relaxation time distribution of 0.4 <β < 1.4. The peak height depends on annealing temperature before quenching and the cooling rate. If Fe-3Ge and Fe-3Ga specimens are quenched from the α + γ range (>1050 K) the Snoek peak is obviously smaller. A decrease in the cooling rate lowers the peak height and induces some tendency to form a second (P2) peak at higher temperatures (not shown in Figure 4a). This effect of double headed peak is much better pronounced in the Fe-Al or Fe-Si systems (Figure 4, c,d). The two Snoek-type peaks result from carbon jumps within the Fe-CFe and Fe-C-substitute atom (Al, Si) surroundings. In the case of the Fe-C-Ge and Fe-C-Ga systems, this tendency is very weak and is near the resolution limit of our experiments. The experimental data obtained for the main (P1) Snoek peak in Fe-3Ge do not reveal distinct regularities in the variation of the parameter β depending on the measurement temperature (i.e., on the resonance frequency) which could clarify the origin of the peak broadening. It is known [26] that the absence of a temperature dependence of β indicates a Gaussian distribution of the preexponential relaxation times (ln τ0); a dependence for β of the T-1 type indicates a Gaussian distribution of the activation energies. The values of β do not correspond to either of these dependences, as is seen from the data presented in the table below. T [K]

β Fe–3Ge

334 0.4

369 0.7

386 0.7

388 0.7

393 1.4

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The height of the Snoek peak measured after rapid quenching is proportional to the carbon content in the alloy: Q–1 = k · C [at. %]. The coefficient of proportionality k for the Fe3Ge alloy water quenched from 1000 K (f ~500 Hz, heating rate 1 K/min) differs only slightly from that in “pure” iron: in α-Fe–C, we have obtained in the same tests k = 0.35 [4], and in Fe–3Ge, kGe = 0.32. These values are within the accuracy of the determination of carbon content in these alloys.

IV.2 The bcc-originated Fe-12%Ge and Fe-13Ga alloys. The Fe-12Ge specimen was characterised by DSC and magnetometry [164], which yield for the Curie point TC ~1000 K and the solidus temperature TS = 1620 K. A phase transition interval (1300–1350 K) was detected in this alloy (Figure 34). These points are in reasonable agreement with phase diagrams [114, 115]. After 24 h of homogenizing treatment at 1273 K followed by air cooling inside the quartz ampoule in a vacuum, weak ordering in the bcc solution (both D03 and B2) is detected.

0.3

Sol ~1350 DSC, mW/mg

0.2

TC~728C

0.1

150

B2

A2 100

heating 0.0 -0.1

cooling

50

-0.2 -0.3 400

1030 - 1080C 600

800

1000

1200

1400

magnetization (emu/g)

Fe-12Ge

0

1600

T [K]

Figure 34. Heat flow (left scale) and magnetometry (right scale) of the Fe-12Ge sample.

In the “as quenched” state two IF peaks (the P1 and P3 peaks) were recorded at lower temperatures (Figure 35). The P1 (Snoek) peaks in Fe-3Ge and in Fe-12Ge have the same origin, i.e. C atom jumps in the bcc solid solution. The P1 peak in the Fe-12Ge alloy is lower because of a lower carbon content than in the Fe-3Ge alloy. At the same time the P1 peak in Fe-12Ge is broader (Figure 35, inset: β ~ 3) and can be a sum of the P1 and P2 peaks. A similar effect of alloying on the carbon Snoek peak was reported in Fe-Al-C alloys, and is related to the C-Al long-range elastic interaction in iron.

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1E-3

Fe-12Ge-0.01C V=1K/min

250

wq1273K exper. P1 P3 sum.

0.002

Q

-1

f [Hz]

0.001

-1

1/T [K ]

Q

0.0020

P3

-1

0.0025

240

0.0030

P1 230

wq1173K wq1273K

1E-4

220 300

400

500

600

700

800

T [K]

Figure 35. Temperature dependent IF and resonance frequency curves for Fe-12Ge alloy after quenching from 1173 and 1273K. The P1 and P3 peaks are denoted. Inset: example of deconvolution of an experimental curve into two Debye peaks with different width.

30

Q , 10

-4

Fe-12Ge wq 1000K, 3 h., V = 2K/min

-1

P1

P3

2300

f, Hz 2200

~430 Hz 20

440 10 430

~2250 Hz 0 300

400

420 500

600

T [K]

Figure 36. TDIF curves for Fe-12Ge-0.01C at heating to ~700 K and cooling (free cooling): at ~430 Hz (in black) and at ~2250 Hz (in grey). Frequencies are shown at the right scale.

The P3 peak is accompanied by an increase of the resonance frequency. This effect cannot be linked with the ferro- to paramagnetic transition similarly to the Fe-Al alloys, as the Curie point in this alloy was extrapolated from the heat flow data to be ~1000 K. The P3 peak is more pronounced in specimens quenched from higher temperatures. A possible explanation of this peak can be either an effect of thermal vacancies or an effect of ordering. In both cases the P3 peak stability with respect to annealing should be different to the P1 peak caused by carbon atoms in the solution. Indeed, after heating to ~700 K (Figure 36), the P3 peak completely disappears at cooling in contrast to the P1 peak. On cooling from 870 K neither

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the P1 nor the P3 peak is recorded. The effect of ordering in Fe-12Ge was not obvious from the existing X-ray data: A small peak corresponding to the B2 phase is observed after air cooling of Fe-12Ge alloy from 1273 K, low temperature annealing. The lattice parameter for the bcc structure was a = 2.88712 ± 0,00166 Å in the as cast state, a = 2,88470 ± 0,00014 Å after 24 h homogenizing at 1273 K, and a = 2,88460 ± 0,00008 Å after additional low temperature (648 K, 200 h) annealing. The shift of the IF peak temperature with measuring frequency is more pronounced for the P1 peak than for the P3 peak, which suggests that the P3 peak can be linked with phase ordering over a certain temperature range. An IF peak at 773 K (f ~1 Hz) with parameters Н = 2.05 eV, β < 0, Δ = 0.01, and τ0 = 1013.5 s was found earlier [132] in the Fe-15wt.%Ge (~12at. % Ge) alloy which in equilibrium state belongs to the α1 (B2) structure, and was classified as a Zener peak overlapping with the grain boundary peak at the high temperature side for a certain structural state. However, these parameters are not typical for a Zener relaxation: e.g. the negative value of β, and the value of the relaxation strength Δ = 0.01, which seems to be too high for a Zener relaxation in an alloy with relatively low (12 at.%) content of Ge. In our low frequency (~2.1 Hz) TDIF tests of the Fe-12Ge specimen (Figure 37) we also observed an IF peak (P4) at Tm ≈ 775 K with parameters relatively close to those reported in [132]: in the as cast state, Δ = 0.006, β ≈ 1, in water quenched state after 5 h annealing from 1000K Δ = 0.012, and in water quenched state after 24 h annealing at 1273K Δ = 0.01. At this stage it is not clear if another IF peak (P5) proposed in [132] to be a grain boundary peak can be distinguished in the TDIF curves (Figure 37) or not. For reason of better comparison between our data and results given in [132], we added to the Figure 37 temperature scales in Kelvin and Centigrades as well as in (Q-1-Q300-1) and (δ - δ300) , where index “300” means that the background at 300°C was subtracted from the experimental curves. The average grain size in Fe-12Ge is 0.4 mm. As can be seen from Figure 37, the high temperature background depends strongly on the state of specimens: the lowest level is observed after 5 h annealing at 1000K followed by water cooling. Computer fitting to curve 2 using the activation energy 2.05 eV proposed in [132] (we do not have our own data for Arrhenius plot) gives a peak at 760K (for 1.5 Hz) and β = 0.68. To compensate peak asymmetry, a second small peak (695K, 1.95 eV, β=1.65) was proposed by fitting procedure. To summarise: the Snoek-type peak P1, the P3 peak (most probably the effect of ordering at annealing) and a Zener peak are observed in Fe-12Ge-0.01C alloy. Similar P1 and P2 peaks are recorded in quenched Fe-13Ge alloy (Figure 38). The P1 peak in Fe-3Ge and Fe-12Ge, and in Fe-3Ga and Fe-13Ga has the same origin: C atom jumps in bcc solid solution (the Snoek peak). The P2 peak is not well seen in Fe-12Ge but is clearly seen in Fe-13Ga (C atom jumps in positions Fe-C-Ga). The P3 peak (at 460-470K dependently on frequency) increases if quenching temperature increases. At cooling the only P3 practically disappears while the P1 and P2 peaks can be still well distinguished. Most probably the P3 peak has a different origin than P1 and P2 peaks: the P3 peak can be caused by thermal vacancies. No peaks were observed at higher temperature using tests at ~200 Hz, while at ~3 Hz tests two more (P4 and P3) peaks were resolved and can be attributed to the Zener and grain boundary relaxation (Figure 38, inset) similarly to the situation in Fe-12Ge (Figure 37).

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-1

-1

Q -Q 300 0.04

650

Fe-12Ge K 800 700 T, 750

δ−δ 300 850 0.12

0.03

0.09

P5

0.02

1 2 3

0.01

350

400

0.06

P4

450

500 o

0.03

550

600

T, C Figure 37. TDIF curves (f ~2 Hz) for Fe-12Ge alloy in as cast state (1), quenched from 1000 K (2), quenched from 1273 K (3). Inset: results for Fe-12 at.% Ge alloy according to [132].

Fe-13Ga 100

0.015 f ~ 2,7 Hz

Q

wq 1000K (3h)

0.010

-4 -1

Q , 10

f, Hz 230

P4

P3 80

P5

wq 1000K + annealing 500K

-1

225

0.005

220 400

60

P1

600

T [K]

800

215

P2

40

210 205

20

0 300

Heating Cooling 400

500

600

700

800

200

T [K]

Figure 38. TDIF curves at heating and cooling for Fe-13Ga alloy. Inset: high temperature part of internal friction as measured by torsion ~2 Hz.

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

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The broad maximum observed at about 370K (~1 Hz) in the 17Ga specimen was attributed to the Snoek relaxation of carbon in solution [157]. If frequency is taken into account this peak corresponds to our P1-P3 peaks in Fe-13Ga which looks at low frequency tests as one broad peak (Figure 38, inset). The damping capacity of Fe–Ga solid-solution alloys, of 6, 12 and 17 Ga has been investigated over wide ranges of temperature and frequency [157]: high damping (Q-1 ~10−2) which is almost independent of temperature and frequency was observed and is attributed to magnetoelastic hysteresis. As expected from the large magnetostriction, the damping capacity of the alloys, particularly of 12 and 17% Ga, is promising for applications to high-damping materials.

IV.3. The bcc/hexagonal Fe-19Ge and Fe-21Ge alloys. On heating, both of these alloys cross the solvus line twice: according to both Kubashewski’s [114] and Massalsky’s [115] phase diagrams they have bcc structure below and above the solvus lines. According to our DSC data (heating 10 K/min), the Fe-21Ge alloy shows the ε - α transition at ~1358 K, the Fe-19Ge at ~1142 K. The Curie point for 19 and 21Ge is 887 and 878 K, respectively. The DSC data provide the transition temperatures for Fe-19Ge at 1446 K (solidus) and 1567 K (liquidus); for the Fe-21Ge alloy solidus is at 1432 K and liquidus at 1532 K, all in good agreement with the existing phase diagrams.

intensity /counts

300

1275K, 24h + 1220K, 24h, water quenched + 650K, 200 h ε − phase α - phase

250 200

(201)

150

(200) (002)

100 50 0 40

42

2 Θ44 [ ° ]

46

Figure 39 X-ray diffraction patterns of homogenized at 1273K (24 h) Fe-21Ge alloy additionally quenched from 1220, and finally annealed 200 h at 648 K.

In the medium temperature range the structure of these alloys (especially for Fe-21Ge) is a mixture of the ordered bcc phases (B2 above ~950C or D03 below ~850C according to Massalski’s phase diagram) and the ε phase. The Fe-21Ge alloy was first homogenised at 1275K for 24h, subsequently annealed at 1220K for 24h to produce a mixture of ε and α phases, and water quenched. XRD shows (Figure 8) the presence of the hexagonal phase (marked by full down triangles) and a peak at 44.35o arising from (110) reflection of α phase. After additional annealing at 650K for 200h, only the α phase was detected in the structure

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(marked with an open triangle in Fig 8) with the lattice parameter a = 2,88542 ± 0,00029 Å. A very weak B2 ordering of the α phase can be detected by arising of diffraction peaks at 31° and 55°, reflection (100) and (111), respectively [164].

Fe-19Ge

P3 P1

510

15,0

500

12,5

10,0 300

f, Hz

wq 1000K, 5h V = 2K/min

-1

Q , 10

-4

Figure 40. Light microscopy structure of alloys with 19 (left) and 21Ge (right) after quenching from 1223K

490 400

500

T, K

600

Figure 41. TDIF curves for Fe-19Ge-0.01C at heating to ~700K and cooling.

TDIF curve in case of Fe-19Ge (Figure 41) is similar to that in Fe-12Ge: two peaks P1 and P3 are observed, the stability of the P1 peak with respect to heating is higher than that one for the P3 peak. Similar peaks were absent in Fe-21Ge alloy as no carbon was added to this composition in contrast with other alloys.

IV.4. Fe3Ge alloy with hexagonal phases IV.4.1. Structure Heat flow (DSC). The phase transformation in the Fe-27at.%Ge alloy has been studied by means of DSC at a heating rate of 10 K/min. First DSC runs up to 1273K were performed with homogenised specimens, which exhibit a discontinuity of heat flow rate dependence at 638K in the heating curve (Figure 42a) and which appears also in the cooling periods [134]. Later, the sample of the Fe-27Ge alloy has been exposed to two cycles from room

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temperature (293K) to 1573K followed by cooling to 373K. The peaks have been analysed from the second run only, as the first run was used to homogenise the material and to produce a ball shaped specimen after the first melting and crystallisation. In the high temperature region above 1323K three different peaks are observed (Figure 42b). The first reaction (peak I in Figure 43b) starts at 1370K, the maximum of the related peak is measured to 1377K, the reaction ends at 1382K. A second peak (peak II), which is much more pronounced, starts at 1381K; the maximum is found at 1398 K and the reaction finishes at 1403K. From the shape of the second peak, it can be concluded, that a third reaction (peak III) is occurring at about 1400K, which is clearly visible during the cooling cycle. (The temperature differences of the three observed peaks for the heating and cooling periods is due to the limited heat conduction at the rather high heating/cooling rate (10 K/min), as well as due to some hysteresis owing to nucleation.) Comparing the DSC measurement with the known binary phase diagram Fe-Ge [131], the low temperature peak (638K in Figure 42, inset) cannot be related to any first order phase transformation. It is possible and the shape of the heat flow curve suggests that there is a second order transformation like a change from ferro- to paramagnetic material behaviour. The material behaviour in this temperature region has further been studied by other methods and is discussed below.

DSC, mW/mg

1.0

0.5

DSC, mW/mg

1.5

0.09

P2h 0.08

P1h

0.07 625

650 T [K]

0.0

P3c

-0.5

P1c

-1.0 103.100mg 10 K/min

P2c -1.5 1320

1340

1360

1380

1400

1420

T [K]

Figure 42. DSC-measurement temperature regions. At cooling three clear peaks are recorded. Exothermal reactions lead to negative energy values. Inset: low temperature range, heating [164].

The first high temperature peak (peak I) is most likely related to the eutectic reaction (ε + β → ε + L) at 1378K. The second peak (peak II) can then be related to the transformation ε → α + L. The α-phase is melting at about 1400K. As these two temperatures are close to each other, the two reactions in the DSC superimpose because of the low heat conductivity of the alumina crucible used in the experiments. Therefore, the phase transformation temperature related to the third peak (III) can be estimated only roughly. A simulation of the correct peak shapes is difficult so that different approaches have been made to ensure good statistics. The transformation energies roughly estimated are for peak I: ~15 J/g, peak II: ~ 91 J/g, and peak

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III: ~ 8 J/g. The structure of the studied alloy after solidification is found to lie in the region of ε phase and ε + β eutectic. Light optical metallography and EDX analysis. Two-phase structure is recorded in the studied alloy directly after casting (Figure 43a): ε phase dendrides develop from the melt (L) and B2-type ordered (α2) phases by a peretectic reaction L + α2 → ε (ε is the hexagonal D019 type ordered phase which exists in the range of 23.8-25.7 at.% Ge) and the eutectic ε + β (β is the hexagonal B81 type ordered phase). As judged by optical metallography, the annealing at 1273К (24 h) results in homogenisation of the alloy: the dendridic structure is not observed any more.

a

b

Figure 43. Structures of the Fe-27Ge alloy as observed by light optical microscopy (a) in as cast state, (b) after homogenising for 24 h at 1273 K and additional low temperature annealing for 100 h at 648 K.

Low-temperature annealing for 100 h at 648 К of specimens homogenised at 1273K for 24 h, i.e. in the two-phase range of the Fe-Ge phase diagram, leads to formation of a two type grain structure (Figure 43b). According to the phase diagram these phases should be α1 (D03 type ordered phase) and β phases, but this conclusion is wrong if the results below of X-ray, vibrating sample magnetometry and EDX data are taken into account. EDX analysis of the structure presented in Figure 43b shows that the brighter phase has about 27Ge referring to the epsilon phase (ε), while the darker grey phase with ~38Ge refers to the beta phase (β). The average value for an area scan by EDX was 28.7 at.%Ge. X-ray diffraction. X-ray diagrams were measured after annealing at 1273K for 24 h and after a second heat treatment at 648K for 100 h. The significance of the XRD-results is limited to some extent because of the large grain size and some texture effects in the tested specimen leading to measured intensities deviating from values given in literature. The diffraction patterns of the 1273K / 24 h sample (Figure 44, inset) [134] show mainly lines which refer to the ε-phase. All peaks with a relative intensity of more than 5% are indexed by means of the primary ICDD pdf reference data for the ε-phase (25% Ge) [143]. The parameters of the hexagonal lattice (P63/mmc) are a = 5.177(2) Å and c = 4.233(2) Å which indicate an only marginal deviation from the typical c/a value given in the literature. This difference might be caused either by the slightly higher Ge-content of the tested sample than that used by Cabrera et al. [140], or by interstitially dissolved carbon atoms. Next to the hexagonal ε-phase no peaks of the α-phase are detected. The results of the chemical analysis

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by EDX and also DSC in combination with the phase diagram suggest the presence of at least a small fraction of the β-phase but this is not confirmed by XRD where this phase cannot be clearly detected. The presence of the ε′-phase in the sample cannot be excluded since most of the main ε′-peaks show 2θ-values which lie next to lines of the ε-phase. Small shoulders at some of the corresponding ε-peaks and a small peak at 2θ = 49.64°, which might refer to the ε′-[2 0 0]-line, indicate the existence of a small amount of the ε′-phase but this cannot be proved by the XRD-experiments performed so far. However, there are several peaks which could not be assigned to known FeGe-phases, thus making further investigations necessary.

1200

200

ε β

intensity /counts

1000 800

150

600 400

100

200 0 20

50

40

60

80

100

120

140

0 20

40

60

80

100

120

140

2Θ [°]

Figure 44. X-ray diffraction patterns of homogenized at 1273K (24 h) Fe-27Ge alloy after additional annealing for 100 h at 648 K. Insert: X-ray diffraction patterns of homogenized Fe-27Ge alloy after 24 h annealing at 1273K.

After the additional low temperature annealing at 648 K for 100 h two major phases are detected (Figure 44). The ε-phase is still present with almost identical lattice parameters (a = 5.177(1) Å and c = 4.226(1) Å). In addition the hexagonal β-phase (B81) can be observed. The lattice parameters (P63/mmc) are a = 4.018(2) Å and c = 5.000(6) Å indicating a smaller c/a value in comparison to that in literature, probably caused by the lower Ge-content in the tested sample than that used in the work of [144]. No evidence for the presence of the αphase was found. Also, in accordance with the sample discussed before, there are the same weak signs for a small amount of the ε′-phase. Furthermore, the unidentified peaks from the 1273K / 24 h sample are conserved. In agreement with optical microscopy and EDX analyses, the homogenised sample contains clearly only ε phase, while β is not detectable by X-rays (either because of a very small amount or distribution in very small particles) and ε′ may be present in a small amount only. After additional annealing for 100 h at 648K, however, clear β phase appears besides ε and the possible small amount of ε′ remains.

IV.4.2. Properties Magnetic properties. Several different ranges can be distinguished in the thermomagnetic curves for both as cast specimens and those homogenised at 1273K (24 h) (Figure

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Igor S. Golovin

45). Below ~370 K magnetisation increases with rising temperature, while it decreases above 370 K for an external field of H = 160 kA/m; the maximum shifts to lower temperatures if the external field increases, e.g. to 170K for 800 kA/m (data not included in Figure 45, see in [134]). The decrease of the magnetization with decreasing temperature below the maximum at point “a” (370K) may be caused by a canting of the electron spins. A canting in the hexagonal phase (B82 structure) was observed by Adelson et al. [139] in different FexGe alloys for x = 33 up to x = 40 but this observation is not supported by data from Yamamoto [137]. More likely a spin flip transition takes place as already observed by Drijver et al. [138], i.e. a spin reorientation (2nd order transition) in the hexagonal ε (D019) phase at 380K, where the spin orientation changes from parallel to perpendicular to the c-axis. For both models (canting and flipping), a suppression of the decrease in magnetization in higher fields is to be expected which is observed in our experiments [134]. The following critical points are observed at elevated temperatures: a) at 525 K a clear “shoulder” in the decreasing magnetisation can be seen, b) at 640 - 660 K the magnetisation drops down drastically, c) at 780 K the remaining low magnetisation disappears.

-96

~530K

100

-64

-32

0

32

64 H [kA/m]

100.0 Hmax=915 kA/m

a)

80 kA/m/min

magnetization (emu/g)

50.0 0.0

80

T = 300 K T = 450 K T = 560 K T = 830 K T = 950 K

-50.0

60

-100.0 -12

40

-8

b) ~670K

-4

0

4

8 H [kOe]

c) ~780K

20

Fe-27Ge 0 400

600

T [K]

800

1000

Figure 45. Temperature dependence of the magnetization for Fe-27at %Ge (1273 K, 24 h, in air) at external field of 800 kA/m. Inset: field dependence of the magnetization at different temperatures.

Point “a”. The Curie temperature extrapolated to TC ≈ 530 K most probably corresponds to the β phase, which is present in the structure, although this is not resolved by XRD, however, is indicated by the DSC data. The β phase is thermodynamically stable in a wide range of temperatures. The Curie temperatures for the β phase given in literature vary from TC = 430K in Fe-50Ge [145] over TC = 485K in Fe-37Ge [146] to TC = 500K in Fe-35Ge [147].

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

121

Our own test of Fe-37Ge gives a value of TC = 505K. A decrease of TC with increasing Ge content in Fe-Ge β alloys was also shown by Kanematsu [147] (from 500K for Fe-35Ge to 150K for Fe-43Ge) and by Konygin et al. [142] (from 480K for Fe-35Ge to 400K for Fe40Ge). The observed change at ~530K is not accompanied by a pronounced change, neither in heat flow nor in elastic modulus, indicating an only small volume fraction of β phase in accordance with the XRD result. Point “b”. The steplike decrease of magnetisation around 640-660K is associated with the Curie temperature of the hexagonal ε phase, which is dominating in the structure of the studied alloy. Also notable is that point “c” correlates with the discontinuity (at 638K) in the DSC curves and with a critical point in the temperature dependence of the elastic modulus (see below). Yamamoto [137] suggests the Curie temperature for the ε phase to be TC = 655K, and Drijver [138] TC = 640K (both for Fe-25Ge, D019 structure), which reasonably complies with that from Figure 29. Point “c”. The temperature 780 K corresponds to the Curie temperature of the cubic ε′ L12 ordered phase as shown by Yamamoto (TC = 755 K) [137] and Drijver (TC = 740 K) [138]. Tracks of this phase were found in our X-ray study at room temperature; the volume fraction of the ε′ phase at elevated temperatures might increase according to the phase diagram, i.e. during the measurement in Figure 45. For temperatures above 780K a very small collective magnetism is still observed as can be seen in the inset of Figure 45, inset. Possibly it arises from a very low volume fraction of α phase (TC for the α phase is about 870K) which is not detectable by XRD. Above 860 K the specimen shows pure paramagnetic behaviour. The average magnetic moment of the iron atoms was calculated from the saturation magnetization of the hysteresis loops measured at different temperatures (Figure 31 inset). The average magnetic moment decreases with increasing temperature and nearly vanishes for temperatures exceeding 780 K. The saturation value of the magnetic moment of iron at T → 0 K is about 1.7 μB which is in good agreement with the results of Konygin et al. [142]. The corresponding values obtained by Mössbauer spectroscopy are in the range of 1.1 μB [139] to 2.0 μB [138]. Elastic and anelastic properties. The elastic properties of the alloy were studied in several structural states in terms of the resonance frequency (E ~ f2) of flexural vibrations with the specimen clamped at one end. One specimen was tested after the homogenising treatment at 1273K (24 h) and slow cooling (curve 1), the second specimen (curve 2) after additional low temperature annealing (100 hrs at 648K) was tested (Figure 46). Curves n.1 and n.2 are rather similar: the difference in the absolute values of the f does not have any physical meaning, but is the result of different lengths of the specimens. Both curves n.1 and n.2 have two “critical points” appear at ~373K (n.I) and at ~633K (n.II). Both of these effects are enlarged in the two corresponding insets. Point n.II correlates with critical points in the heat flow and magnetometrical curves. Point n.I is also in some correlation with the effect in the thermo-magnetic curves if they are measured in a low magnetic field (the resonance frequency in Figure 33 was measured in the absence of any external magnetic field). In terms of magnetic structures both of these effects (n.I and n.II) can be considered as order-disorder transitions, which are reflected in the changes of the course f(T) of the specimen. The latter transition manifests itself in a smaller negative slope of f(T) in the paramagnetic state (T > 630K) than in the ferromagnetic state at lower temperatures.

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Igor S. Golovin

f [Hz]

1)

1273K, 24 h., air

620

600

n.I n.II 1

580

2

2) 560 300

plus 650K,100 h.,air 400

500

600

700

800

T [K] Figure 46. Temperature dependencies for resonance frequency (E ~ f2) for different specimen states: 1) homogenized at 1273K (24h) and slowly cooled down in air – heating and cooling curves, and 2) additionally aged at 650K (100 h) after homogenising at 1273 K, 24 h.

-1

Q , 10

-4

40

[1] 1273K, 24 h., air [1a] heating, [1b] cooling plus 650K, 100 h. [2]

20 [1а] [1b] [2]

0 400

500

600

700

800 T

[K]

Figure 47. Temperature dependencies of internal friction (resonance frequency see in Figure 46) for different specimen states: (1) homogenised at 1273 (24 h) and slowly cooled down in air – heating and cooling curves, and (2) additionally aged at 650K (100 h) after homogenising at 1273K (24 h).

A well defined IF peak can be seen around 670K as measured for bending vibrations (roughly at 500 Hz) – Figure 47. This peak is a relaxation peak and a change in the resonance

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

123

frequency shifts the peak temperature. For example the peak position is about 570K if it is measured at ~2 Hz. As can be seen from Figure 47, neither the peak height, nor the peak position appreciably change if measured during heating or cooling and for specimens after different heat treatments. Such a lacking variation of the peak position is normally attributed to a phase transformation which needs overheating or undercooling to initiate the reaction. A variation in the peak height might be reasonably expected if heating changes the concentration of defects responsible for the peak formation (e.g., the carbon Snoek-type peak in Fe-3Ge or 12Ge alloys). The carbon Snoek-type peak is not observed for the Fe-27Ge composition: contrary to Fe-3Ge and Fe-12Ge alloys with bcc structure, this peak is crystallographically forbidden [1] in the hexagonal phases dominating the structure of Fe-27Ge. The activation enthalpy and the pre-exponential frequency factor were estimated for the peak using an Arrhenius plot and result in H = 1.78 eV and τ0 = 2⋅10-17 s, respectively. The activation enthalpy obtained is lower than that determined for the ε′ phase formation (~2.6 eV according to [148]). The values of H and τ0, as well as the stability of the peak height and position with respect to heating - cooling experiments rather suggest that this peak can be classified as a Zener peak, i.e. the peak is caused by reorientation of pairs of substitutional atoms (Ge in Fe) under the applied stress. 0.0020

Fe-27Ge 1000°С, 24hrs, air

-1

Q

0.0020

Fe-27Ge 1000°С, 24hrs + 375°С, 100hrs experiment peak 1 peak 2 simulations

-1

Q experiment peak 1 peak 2 simulations

0.0015

0.0015

-1

T1=660, Q =0.0016

0.0010

-1

T1=654, Q =0.0017

0.0010

H1=1.78, β1=1.20

H1=1.78, β1=1.20

-1

-1

T2=599, Q =0.0007 H2=1.26, β 2=0.92

0.0005

0.0000

T2=591, Q =0.0006 H2=1.02, β2=0.98

0.0005

0.0000

0.0014

0.0016

1/T, K

0.0018 -1

0.0020

0.0014

0.0016

0.0018

0.0020

0.0022

-1

1/T, K

Figure 48. Simulations of temperature dependencies of internal friction data for two states: 1273 (24 h), and 1273 (24 h) plus additionally aged at 648 K (100 h): Temperatures, height, activation energies (eV) and relaxation time distribution for two simulated peaks are shown at each figure.

It should also be noticed that the relaxation strength of the IF peak (Δ = 2Qmax-1) in all cases was Δ ≈ 0.0036 except for the case of quenching from 1273K. The reason for an increase of the peak height after quenching is not finally clear and, taking into account the observed inverse dependence of f(T), cannot be completely assigned to a relaxation process. Two hypotheses can be considered: first, quenching increases the vacancy concentration and decreases the degree of order in the studied alloy, both factors should increase the Zener peak height. The order-disorder transition may lead to the “anomalous” increase in elastic modulus. Second, the relaxation (Zener) peak can overlap around 673K with a phase transition peak (from undercooled ε to ε′ phase), which is not studied in this paper. This latter idea is partly supported by low frequency tests [133], where in addition to the main peak at ~573K another peak at ~673K was recorded. In any case distinguishing between different contributions to the

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Igor S. Golovin

IF peak at around 673K is not possible if measured at 400 - 600 Hz, and further analysis of the IF peak at around 673K should be performed using states of the alloy closer to equilibrium. Computer analysis of TDIF spectra were carried out according to eq. (6). The information on the enthalpy of activation of the relaxation process is taken from an Arrhenius plot of the reciprocal peak temperature on the logarithm of the frequency of vibrations (Н = 1.78 eV, τ0 = 2⋅10-17 s). The approximation of experimental data (practically independent of heat treatment) by one Debye peak shows values β ≥ 2 and does not fit well to the experimental data due to an asymmetry of the peak. This peak asymmetry and values β ≥ 2 are not typical for a Zener relaxation. Taking into account the coexistence of at least two phases in the specimen structure (ε and β), two Debye peaks were introduced into the fit procedure: peak n.1 with the mean value of activation energy deduced from the Arrhenius plot, and peak n.2 with all parameters free. The results of computer simulations with two introduced peaks fit the experimental results more reasonably (Figure 48) with a least square deviation of < 10-5. It should be noticed that a very small difference in the deconvolution of experimental data into partial simulated peak is achieved in all cases except for water quenching from 1273K with strongly non-equilibrium structure. The mechanism of the second peak found by this procedure at lower temperature (1/T > 0.0017) is probably a Zener relaxation in the phase with lower volume fraction (β phase).

Summary to section IV. The structures and magnetic states of several Fe-Ge alloys studied by DSC, XRD, and magnetometry agree (with few exceptions) reasonably with those in published phase diagrams, better with the phase diagram given by Massalski. In the following, we summarize the new results on IF (mechanical spectroscopy) achieved in this investigation for alloys of Fe with 3…27 at.%Ge. A Snoek-type peak is recorded in Fe-3Ge and Fe-3Ga with parameters close to those for pure Fe. The peak has a slightly larger width (parameter β = 0.4….1.4). A similar Snoek-type peak overlapping with another relaxation process (P3) with slightly higher activation energy is found in Fe-12Ge and Fe-19Ge, corresponding most probably to carbon atom jumps in FeC-Fe, Fe-C-Ge, and Fe-C-Ga surroundings. This indicates some long-range (mainly elastic) interaction between C and solute atoms. The P3 relaxation is attributed to contribution of vacancies. A Zener peak was recorded in the Fe-12Ge and Fe-13Ga alloys. Zener peak in Fe19 and -21Ge alloys is weaker due to ordering effect. High damping capacity was recorded in Fe-12 and 17Ga specimens. While the previous alloys are all based on the bcc structure mainly (in as quenched state Fe-19 and -21Ge alloys have two phase (α + ε) structure), the Fe-27Ge alloy is basically hexagonal, and a high stability of the high temperature hexagonal ε (D019) phase at room temperature is confirmed, much below the range in the common phase diagrams. The second phase at room temperature is the hexagonal β (B81) phase, and a little amount of the cubic ε′ phase is also present in the alloy. The variations of the elastic modulus are consistent with the phase changes mentioned before. A broad asymmetric relaxation internal friction peak is found around 670 K. Its relaxation strength Δ ≈ 0.0036 being independent of the heat

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

125

treatment regime, a relaxation time distribution corresponding to a broadening parameter of β ≈ 2, a mean value of the activation enthalpy H of about 1.8 eV, and the pre-exponential relaxation time τ0 = 2⋅10-17 s suggest that this peak arises from Zener relaxations in the mixture of the ε and β phases in the Fe-27Ge alloy. An increase in the Ge content in Fe decreases the ferromagnetic properties of the alloys and consequently decreases their damping capacity.

ACKNOWLEDGEMENTS The author is grateful to H. Neuhäuser, H.-R. Sinning, F. Stein (Germany), A. Rivière (France), O. Lambri (Argentina), M.S. Blanter (Russia) and S.A.T. Redfern (UK) for longrunning cooperation, to U. Brust and D.W. Zachmann for the help in producing and chemical analyses of the alloys, to S.B. Golovina, Ch. Grusewski, S. Jäger, T. Abraham, C. Mennerich, C. Siemers, J. Čížek, M. Maikranz-Valentin for valuable help in experiments, to former and recent students A. Strahl, T. Pavlova, T. Sazonova, T. Ivleva, and O. Sokolova for their enthusiasm. Financial support by DFG, the Royal Society and RFFI is gratefully acknowledged.

APPENDIX Method of computer simulation. The internal friction Q−1 is calculated as a sum of Debye contributions of different interstitials, in this case carbon atoms [149, 150]: N

Q −1 = ∑ [δ ⋅ (ω ⋅τ p ) /(1 + (ω ⋅τ p ) 2 )]

(A1)

p =1

where: N is the number of C atoms in the model crystal; ω and f (=1Hz) are the angular frequency and the frequency of oscillation, respectively; δ is the relaxation strength per carbon atom; T is the temperature; τp is the relaxation time for the p-th interstitial atom: τp = τ0exp(Hp/kBT),

(A2)

where Hp is the diffusion barrier for the p-th atom, kB is the Boltzmann constant, τo is the preexponential factor of the relaxation time. HP = H - EP, where H - the diffusion barrier (activation energy of the Snoek relaxation) in Fe-C dilute solid solution, and Ep is the energy of p-th carbon atom interaction with other C atoms, Al atoms, and vacancies:

E p = ∑W j

( C −C )

(r p − r j )C (r j ) + ∑ W (C − Al ) (r p − rm )C (rm ) + ∑ W (C −vac) (r p − rk )C (rk ) m

k

(A3)

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Igor S. Golovin

where the vectors rp and r j describe the positions of the octahedral interstices, rm and rk those

of

the

crystalline

lattice

points;

W ( C −C ) ( rp − rj ) , W ( C − Al ) ( rp − rm )

and

W ( C −vac ) ( rp − rk ) are the energies of C-C, C-Al, and C-vacancy pair interactions, respectively, and C( r ) are the corresponding occupation numbers on the octahedral interstices and lattice points. C( r )=1, if the interstitial or lattice point is occupied by a solute atom or a vacancy; C( r )=0, otherwise. Taking the solute interaction into account, the following assumptions were made: (i)

The long-range C-C and C-Al pair interactions as well as the short-range Cvacancy interaction affect the energy of C atoms in the octahedral interstices EP. This changes both the C distribution (short-range order of C atoms) and the diffusion barriers Hp of the individual C atoms.

(ii)

The pre-exponential factor τ0 of the relaxation time τ is independent of the solute interaction.

(iii)

Each C atom has the same relaxation strength δ, which is inverse proportional to temperature according.

Monte Carlo simulations were carried out to calculate the short-range order configuration, energy changes, energy distribution and individual diffusion barriers of the carbon atoms. The internal friction was calculated at each temperature by averaging Q-1 over the atomic configurations obtained from the Monte Carlo simulation. Easily-moved carbon ♣ atoms (0.0235-0.094 at. %) are distributed randomly at the octahedral interstices of a crystalline lattice in a model crystal of size 22×22×22 a3 (a is the lattice parameter of the bcc host lattice) with periodic boundary conditions. Immobile Al atoms (25 at. %) and vacancies (0.0235-0.094%) were distributed in the crystalline lattice by different methods. The Al atoms were placed in the D03 lattice with different degrees of order (η): η = (P - СAl) / (1-q) , where q = 0.25 is the fraction of Al sites in the D03 structure of the perfect Fe3Al intermetallic compound, CAl = 0.25 is the Al concentration in the alloy, and P is the part of the Al sublattice in the D03 structure that is actually occupied by Al atoms. The other Al atoms were randomly distributed on the Fe sublattice. We have varied the degree of order in our simulations between η = 1 (completely ordered alloy: Fe3Al) and η = 0.67. This allows to find out regularities of the influence of ordering on the parameters of the relaxation (or internal friction) spectrum. Vacancies were distributed either randomly through all possible positions or only through the Al sublattice in the D03 ordered structure. The Hamiltonian χ of the system is equal to the sum of all pair interaction energies [150]:

∑

∑

⎧ W ( C − C) (rp − r j )C(rp )C(r j ) + W ( C− Al) (rp − rm )C(rp )C(rm )⎫ ⎪⎪ p, m 1 ⎪⎪ p, j χ= ⎨ ⎬ 2 ⎪+ W ( C − vac) (rp − rk )C(rp )C(rk ) ⎪ ⎪⎩ p, k ⎪⎭

∑

♣

this carbon concentration corresponds to carbon content in the experiments

(A4)

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

127

These Hamiltonian was minimised by Monte Carlo method, the equilibrium state was chosen to correspond to it’s minimum.

Energies of interatomic interactions. The configuration term of the internal energy is usually considered in similar problems [151]. That is why the energies of the atomic pair interactions which do not contribute to the configuration term are not taken into account by eq. (A3). For this reason, Al-Al, Al-vacancy and vacancy-vacancy interactions are missing in eq. (A3): for the temperature range chosen in this simulations only carbon atoms are considered to be mobile. Also, the interactions with the host metal atoms (Fe) are not considered, because such interactions do not give rise to the configuration energy. The interaction of solute atoms with the host atoms was taken into account indirectly during the calculations of the C-C, C-Al and C-vacancy interaction energies. There are still no reliable first-principles calculations of C-C and C-substitutional atom interaction energies. This implies that we used the energies of the long-range strain-induced (elastic) C-C pair interactions in α-Fe from [149] and C-Al from [152] supplemented by Coulomb repulsion between interstitials and “chemical” interstitial-substitutional interaction in two nearest coordination shells. These values of the C-Al energies are displayed in Table 2 of Ref. [55]. The Coulomb C-C repulsion is taken into account according to [153]. The energy of “chemical” C-Al interaction was equal to +0.4 eV in the first coordination shell (negative values mean attraction, positive ones repulsion). The energy of C-vacancy interaction was taken into account in the first coordination shell only. This value was calculated by the first-principles calculation in [154] and is equal to – 0.24 eV. The following parameters of the carbon Snoek relaxation in pure α-Fe are used in our calculations: H = 0.87 eV and τ0 = 2 × 10-15 s.

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Postnikov, V. S. Internal Friction in Metals; Metallurgiya: Moscow, 1974. Lakes, R. S. Viscoelastic solids; CRC Press: Boca Raton, 1999. Schaller, R.; Fantozzi, G.; Gremaud, G. (Eds.) Mechanical spectroscopy Q–1 2001 with

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[134] Golovin, I. S.; Jäger, S.; Mennerich, Chr.; Siemers, C.; Neuhäuser, H. Structure and anelasticity of Fe3Ge alloy; Intermetallics, 2007, Vol 15/12, pp 1548-1557. [135] Jartych, E.; Oleszak, D.; Kubalova, L.; Vasilyeva, O. Ya.; Zurawicz, J. K.; Pikule, T.; Federov, S. A. J Alloys Comp 2007, 430, 12-17. [136] Chen, Q. Z.; Ngan, A. H. W.; Duggan, B. J. J Mater Sci 1998, 33, 5404-5414. [137] Yamamoto, H. J Phys Soc Japan 1965, 20, 2166-2169. [138] Drijver, J. W.; Sinnema, S. G.; van der Wonde, F. J Phys F: Metal Phys 1976, 6, 21652177. [139] Adelson, E.; Austin, A. E. J Phys Chem Solids 1965, 26, 1795-1804. [140] Cabrera, A. F.; Sánchez, F. H. Phys Rev B 2002, 65, 094202-1-9 [131] Elyatin, O. P.; Khachatryan, M. Kh. Metallovedeie Termicheskaya Obrabotka Met 1972, 11, 15-18. [142] Konygin, G. N.; Yelsukov, E. P.; Porsev, V. E. J Magn Magn Mat 2005, 288, 27-36. [143] Turbil, J. P.; Billiet, Y.; Michel, A. C R Seances Acad Sci C 1969, 269, 309. [144] Kanematsu, K.; Yasukochi, K.; Ohoyama, T. J Phys Soc Jpn 1963, 18, 1429-1436. [145] Oleszak, D.; Jartych, E.; Antolak, A.; Pekala, M.; Szymanska, M.; Budzynski, M. J All Comp 2005, 400, 23-28. [146] Yasukochi, K.; Kanematsu, K.; Ohoyama, T. J Phys Soc Jpn 1961, 16, 429-433. [147] Kanematsu, K. J Phys Soc Jpn 1965, 20, 36-43. [148] Predel, B.; Frebel, M. Z Metallkde 1972, 63, 393-397. [149] Blanter, M. S.; Khachaturyan, A. G. Metall Trans A 1978, 9, 753. [150] Blanter M. S. Phys Rev B 1994, 50, 3603. [151] Khachaturyan, A. G. Theory of Structural Transformations in Solids; Wiley: New York, 1983. [152] Blanter, M. S. Phys Met Metallography 1981, 51, 136 (in Russian). [153] Blanter, M. S.; Fradkov, M. Ya. Acta Metall Mater 1992, 40, 2201. [154] Slane, J. A.; Wolverton, C.; Gibala, R. Mat Sci Eng A 2004, 370, 67-72. [155]. Yasuda, H.Y; Nakajima, T.; Nakano, K.; Yamaoka, K.; Ueda M.; Umakoshi Y. Acta Materialia 53 (2005) 5343–5351 [156] Yasuda, H.Y; Nakajima, T.; Murakami, S.; Ueda M.; Umakoshi Y. Intermetallics. Intermetallics 14 (2006) 1221-1225 [157] Ishimoto, M.; Numakura, H.; Wuttig, M. Mat Sci Eng A 442 (2006) 195–198 [158] Ershov, N.V; Arzhnikov, A.K; Dobysheva, L.V; et al. Physics of Solid State, 2007, Vol. 49, No. 1, p. 67-74. [159] Zheng-Cun Zhou, Materials Science and Engineering A, in press [160] Golovin, I.S.; Serzhantova, G.V.; Sokolova, O.A.; Semin, V.A.; Jäger, S.; Sinning, H.R.; Stein, F.; Golovin, S.A. Abstract book IIAPS XI, Tula, Russia, 24-28.09.2007, p. 55: to be published in Solid State Phenomena [161] Mielczarek, A.; Riehemann, W.; Sokolova, O.A.; Golovin, I.S. Abstract book IIAPS XI, Tula, Russia, 24-28.09.2007, p. 97: to be published in Solid State Phenomena. [162] Chudakov, I.B.; Polyakova, N.A.; Mackushev, S.Yu.; Udovenko, V.A. Abstract book IIAPS XI, Tula, Russia, 24-28.09.2007, p. 93: to be published in Solid State Phenomena. [163] The Rietveld Method, Edited by R. A. Young, International Union of Crystallography, Oxford University Press, Great Britain,1993.

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[164] Golovin, I.S.; Ivleva, T.V.; Jäger, S.; Neuhäuser, H.; Redfern, S.A.T.; Siemers, C. Abstract book IIAPS XI, Tula, Russia, 24-28.09.2007, p.53: to be published in Solid State Phenomena.

In: Intermetallics Research Progress Editor: Yakov N. Berdovsky, pp. 135-173

ISBN: 978-1-60021-982-5 © 2008 Nova Science Publishers, Inc.

Chapter 3

NONSTOICHIOMETRIC COMPOUNDS V. P. Zlomanov∗1 and A. Ju. Zavrazhnov2 1

Department of Chemistry, Moscow State University, Vorob’evy gory 1, Moscow, 119899 Russia 2 Department of Chemistry, Voronezh State University, Universitetskaya pl. 1, Voronezh, 394-006 Russia

ABSTRACT A key issue in materials research is the preparation of semiconducting solid, intermetallic and other nonstoichiometric compounds with predetermined composition, structure, and, hence, properties. In connection with this, this paper scrutinizes the concepts of stoichiometry, nonstoichiometry, and deviation from stoichiometry and the use of phase diagrams in selecting conditions for the synthesis of nonstoichiometric compounds. Since nonstoichiometry and properties of compounds are associated with defects, attention is also paid to defect classification and formation. The behavior of defects in solid oxides, chalcogenides, carbides, and other compounds of transition metals ranges from the point defect regime, controlled by entropy, to the enthalpy-controlled regime. To develop an appropriate theory of nonstoichiometric compounds, it is then necessary to address crystal-chemical and thermodynamic issues. This paper is also concerned with the defect structure of highly imperfect nonstoichiometric compounds with a broad homogeneity range: the concepts of defect and structural transition due to defect interactions and temperature effect. The thermodynamic aspect of the problem includes criteria for evaluating the stability of imperfect nonstoichiometric solids. It is considered the specifics of the concepts of existing, stable, and metastable phases, spinodal decomposition conditions, and issues associated with phase equilibria in homologous series of compounds with narrow homogeneity ranges. The paper also deals with synthesis methods and criteria for evaluating the homogeneity of nonstoichiometric solids.

∗

E-mail: [email protected]

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1. STOICHIOMETRY, NONSTOICHIOMETRY AND DEVIATION FROM STOICHIOMETRY In chemistry and materials research, relationships between interacting substances are governed by the laws of stoichiometry (by stoichiometry). These characterize the composition of chemical substances and have been derived by systematizing experimental data. Among the most important laws of stoichiometry are the law of constant composition and the law of multiple proportions. The law of constant composition states that the chemical composition of a substance is independent of the method by which the substance was prepared. It turns out, however, that preparation conditions may have a significant effect on the composition of substances. According to the law of multiple proportions, the weight fractions of the elements forming a chemical compound are in the ratio of small whole numbers. Both laws stem from the atomistic theory and indicate that, when molecules are formed from atoms, the resulting chemical bonds must be saturated. Indeed, any change in the number of atoms, their nature, or their mutual arrangement corresponds to the formation of a new molecule with new properties. Are the laws of constant composition and multiple proportions always obeyed? It was long thought that only those chemical compounds exist whose composition meets the law of multiple proportions. Such compounds are stoichiometric and were named daltonides in honor of Dalton. However, with advances in analytical techniques, the properties of most inorganic solids—vapor pressure, electrical conductivity, diffusion,and others—were found to depend on their composition.The structure of such compounds, i.e., the spatial arrangement of their components, remains unchanged, while their concentrations vary continuously in a certain range, which is called the homogeneity range. Such compounds are called nonstoichiometric or compounds of variable composition.Earlier, they were called berthollides, in honor of Claude Louis Berthollet, a compatriot of Prouste. Nonstoichiometric compounds can be thought of as solid solutions of their components, e.g., of cadmium and tellurium in CdTe. The width of the homogeneity range is characterized by deviations from stoichiometry. The stoichiometric composition of a solid chemical compound, e.g. AnBm, where n and m and prime integers, is the composition which meets the law of multiple proportions. A deviation from stoichiometry, Δ, or nonstoichiometry, is the difference in the ratio of the number of nonmetallic atoms B per formula unit to that of metallic atoms A between nonstoichiometric, AnBm+δ (δ ≠ 0) and stoichiometric AnBm (δ = 0) solid

Δ=

m +δ m δ − = n n n

(1)

In an A–B–C ternary, it is convenient to express the composition of a solid phase, (A1– through the mole fraction x of the binary compound and nonstoichiometry? Nonstoichiometry can then be quantified by the difference in the ratio of equivalent numbers of nonmetallic and metallic atoms between nonstoichiometric and stoichiometric solids. For example, for (Pb1–xGex)1–yTey structure) we have

xBx)1–yCy,

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137

Δ = y /(1 − y ) − 1 / 1 = (2 y − 1) /(1 − y )

(2)

The mole fraction of a binary compound (molarity) determines fundamental properties of nonstoichiometric crystals, such as their band gap and heat capacity. Nonstoichiometry influences the carrier (electron or hole) concentration and, therefore, the galvanomagnetic and optical properties of nonstoichiometric crystals.

2. NONSTOICHIOMETRY AND DEFECTS Solid chemical compounds (SAB) can be grown from vapor, melts (solutions), or other solid phases, which are called nutrient (N). The synthesis process can be thought of as transfer of atoms of components A and B from the nutrient to normal lattice sites and in the structure of compound AB, (3)

x + V x + ΔG А N =АА B 1 K1 =

(3.1)

[A Ax ][VBx ] = exp(−ΔG1 /( kT )) aA

(4)

x + V x + ΔG B N = BB A 2 K2 =

[ BBx ][VAx ] = exp(− ΔG2 /(kT )) aB

(4.1)

х

х

where aA and aB are the activities of the components. The formation of VB and VА

vacancies in reactions (3) and (4) is necessary for maintaining the ratio of A and B sites unchanged. Since the A and B atoms differ in size, and the Gibbs energy ΔG1 differs from ΔG2, reactions (3) and (4) differ in equilibrium constant, K1 ≠ K2, and, hence, the crystal contains х

different amounts of A and B atoms, [ А Ах ] ≠ [ В В ]. This means a deviation from stoichiometry, i.e., the B: A atomic ratio in the crystal differs from that in a stoichiometric crystal. х

Note that the properties of crystals are influenced not by nonstoichiometric А Ах and В В atoms, which occupy normal lattice sites, but by the resulting defects (structural х

х

х

х

imperfections). Such defects include VА and VB vacancies А i and B i interstitials:

A n = A ix + ΔG3

(5)

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B n = B ix + ΔG 4

(6) х

х

This is associated with the fact that the А А and В В species are incorporated into the х

х

crystal without altering its energy structure. At the same time, near defects ( VАх , VB , А i х

and B i ) the energy field and, hence, the electrical, chemical, mechanical, and other properties of the crystal are altered (Figure 1). Thus, defects play an important role in determining the structure and properties of crystals.

Figure 1. Schematics of the energy spectra of (a) an ideal crystal and (b) imperfect crystal containing VA vacancies.

3. CLASSIFICATION AND FORMATION OF DEFECTS In an ideal (perfect) crystal, all of the structural elements (atoms, ions, molecules, and others) reside in normal lattice sites, characteristic of its structure. Heating, irradiation with

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high-energy particles, or mechanical influences break down the ordering of atoms on normal lattice sites, causing some of them to leave their positions. Imperfections in the arrangement of atoms on lattice sites are called defects. According to defect geometry and size, one distinguishes extended and point defects (Figure 2) [1]. The size of point (0D) defects is comparable to interatomicdistances. 0D defects include electronic defects (holes, electrons, and excitons), energy defects (phonons and polarons), and atomic point defects (APDs). The APDs in crystals of a nonstoichiometric х

х

compound AB are VАх and VB vacancies (vacant lattice sites); А iх , B i and Fiх interstitials; and impurity atoms F (symbol x signifies that the defect is neutral relative to its environment). Since the formation of APDs is an endothermic process, with a small energy consumption, Ef = 0.5–3 eV, APDs are in equilibrium, and their density depends on synthesis conditions: temperature and partial vapor pressures of the components. The size of APDs is not very large, 0.1− 0.5 nm, but they give rise to polarization of their local environment, resulting in small displacements of the neighboring ions, and have a significant effect on the physical and chemical properties (diffusion,electrical, solubility, and others) of nonstoichiometric solids. Vacancies, interstitials, and antisite ( А Вх , В Ах , FAх , FBх ) defects are native defects of crystals. The density of such defects is in thermodynamic equilibrium at any temperature T > 0 and is given by Cj = exp(–Wj /(kT), where Wj is the formation energy, 0 < Wj < 3 eV. With increasing temperature, the APD density increases. During cooling of a crystal to room temperature, some of the APDs may annihilate by different mechanisms.

Figure 2. Classification of defects.

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Nevertheless, even after extremely slow cooling the crystal contains a large amount of APDs. Excess APDs may originate not only from heating or stoichiometry changes due to reactions (3, 4, 5−6) but also from fast-electron (>1 MeV) irradiation at very low temperatures. Vacancies and interstitials result then from Rutherford collisions of electrons with atoms of the crystal and are frozen in the lattice, where they can be investigated. To determine the symmetry and structure of defects, special methods are needed, capable of probing the defect structure on an atomic scale. Such methods include electron paramagnetic resonance (EPR), electron–nuclear double resonance (ENDOR), optically detected EPR and ENDOR, local vibrational mode spectroscopy [2,], scanning tunneling microscopy (STM), atomic probe field ion microscopy, and electron energy loss spectroscopy [3]. Oppositely charged APDs may attract one another, forming new APDs − electrically

(

neutral defect complexes, e.g. ( VA− ⋅ VB+

)

x

(

and VA− FB+

)

x

. Dipole − dipole interaction leads

to the formation of ATD accumulations or clusters, which may serve as nuclei for phases with other compositions in nonstoichiometric crystals (see Section 4.2). Extended defects include linear (1D), 2D, and 3D defects [4−7] (Figure 2). Consider some of their characteristic features. Linear defects, or dislocations, are similar to point defects in two dimensions, where their size is comparable to the lattice parameter. In the third dimension, dislocations have a significant, or even infinite, length. The simplest type of dislocation is an edge dislocation − an edge of an extra half-plane inserted in a solid crystal. The atoms along an edge dislocation are not fully coordinated, and the two parts of the crystal along them are displaced relative to one another by one interatomic distance. In the case of an edge dislocation, the force responsible for the displacement of the two parts of the solid is normal to the dislocation line. Another important type of linear defect is a screw dislocation. In this case, the displacement vector is parallel to the dislocation line. Screw dislocations convert subsequent atomic planes to spiral surfaces. One possible mechanism of dislocation generation is through the formation of planar vacancy clusters. The atoms along a dislocation have unsaturated (“dangling”) chemical bonds. The excess energy of such atoms reduces kinetic barriers and influences the rates of mass transfer, crystal growth, and chemical reactions. The ease of dislocation nucleation and propagation leads to plasticity and a strong reduction in the mechanical strength of many materials, primarily, metals. At the same time, dislocations may raise strength and hardness. The reason for the hardening is that impurity atoms and grain boundaries impede dislocation movement. Dislocations are electrically active defects: they may act as donors, acceptors, recombination centers (reducing the lifetime of minority carriers), and scattering centers. Dislocations originate from mechanical influences on the solid. Their propagation is closely related to APDs. For example, vacancies play an important role in dislocation climb. The atoms sitting on the edge of the extra half-plane forming a dislocation may move if there is a nearby vacancy. Planar (2D) defects (Figure 2) include solid (crystal) surfaces, block (domain) boundaries, stacking faults, and crystallographic shears. 2D defects range in area from 4 to 105 nm2 (grain boundaries, crystallographic shears). The difference in local environment between surface and bulk atoms and ions leads to a reduction in coordination number or distortion of coordination polyhedra in the surface layer. The Gibbs energy of surface atoms

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is higher than that of bulk atoms. The surface energy of crystals of nonstoichiometric compounds is 0.5–2.0 J/m2. Crystals typically have a mosaic or domain structure, with a domain or block size of up to ~10000 Å. Mosaic blocks have a relatively perfect structure, but neighboring blocks differ in orientation. The misorientation angle may be very small, from a fraction of a second of arc to 1o. Regions between domains (blocks) are called block boundaries. They may be planar or curved, or may have the form of a crystal face. If the normal to a block boundary is perpendicular to the rotation axis relating the block orientations, the blocks are said to be separated by a tilt boundary. If the normal is parallel to the rotation axis, the blocks are separated by a twist boundary. A crystal consisting of several phases always contains interfaces with significant energies. An interface between two phases may be coherent, incoherent, or semicoherent. An interface is coherent if there is a perfect lattice match between the planes in contact. Such interfaces have a low energy (≤ 0.015 J/m2). One example of a coherent interface is the boundary of the MgFe2O4 spinel precipitated in magnesium oxide, MgO. The reason for this is that the oxygen atoms in both MgO and MgFe2O4 are close-packed, which allows the precipitate to maintain coherency with the parent phase. Semicoherent interfaces result from a sufficiently large lattice mismatch between phases in contact. They include so-called low-angle boundaries and have the form of a network of periodically arranged edge dislocations. Their energy depends on the relative orientation of the two grains. At large misorientation angles (>5o), the parts of a nonstoichiometric crystal under consideration are called crystallites or grains. A solid phase containing high-angle boundaries is called a polycrystal. A special case of a high-angle boundary is a twin. A twin boundary separates two regions of the crystal that are related by reflection. Twinning takes place in many minerals and is responsible for coprecipitation of, e.g., calcite and feldspars. Stacking faults are variations from a regular, e.g., cubic or hexagonal, stacking sequence of atomic layers in a crystal structure. A stacking fault is a thin, diatomic layer with identical structures on both sides. Such defects form during crystal growth. 2D defects also include intergrowths and crystallographic shears. Epitaxy and polytypism are examples of intergrowths along solid–solid interfaces. Epitaxy is of great technological interest because it offers the possibility of producing thin single-crystal semiconductor films on appropriate substrates. Such structures are used in integrated circuits, optoelectronic converters (lasers, photodetectors, and solar cells), electronic amplifiers, and other devices. Intergrowths of crystals may, in principle, be thought of as modulated structures in which the intergrowth boundary is a periodic disturbance. To form an intergrowth, two structures must be identical in atomic configuration along some crystallographic plane. One example of a periodic intergrowth structure is the family of AxWO3 (A = alkali metal, alkaline-earth metal, Bi) tungsten bronzes, in which WO3 slabs are intergrown with hexagonal bronze layers. The formation of intergrown bronzes seems to be related to particular growth conditions. Intergrowths may have periodic (ordered) or aperiodic (disordered) boundaries. Among the most important 2D defects are crystallographic shears—planes at which the coordination polyhedra of two ideal structures in contact are rearranged.

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Several key features of 2D defects warrant attention. First, they have a high formation energy (>3 eV) and are kinetically stabilized nonequilibrium defects. The frozen-in state of 2D defects is responsible for their “memory” of the preparation history. Second, they produce no stoichiometry changes. Third, planar defects result from interactions between APDs and have a significant effect on the reactivity and physical properties of nonstoichiometric crystals. Bulk (3D) defects (Figure 2) extend over regions that are larger than the lattice parameter in the three dimensions. In fact, these are macroscopic structural imperfections forming during growth and subsequent processing. Bulk defects include individual blocks; mosaics (a set of many low- and high-angle boundaries); inclusions (microprecipitates), which result from phase transformations, e.g., decomposition of solid solutions; magnetic domains (regions of aligned spins or electric dipoles), Guinier–Preston zones (variously spaced, aligned platelets several unit cells in thickness, having the same composition as the crystal), pores, and cracks. Bulk defects can be thought of as resulting from defect association and ordering processes, e.g., vacancy association in the case of pores. In addition, bulk defects include tensile and compressive elastic stresses. There are also other types of defects: orientation disorderingand motion disordering. The former type appears in ferromagnets. At low temperatures, all of the magnetic moments in a magnetic material are parallel or antiparallel. With increasing temperature, the magnetic moments deviate from the preferred orientation. The deviations can be regarded as defects. Motion disordering (defects) is observed at T > 0, e.g., in ammonium halide crystals, where some polyhedra rotate out of phase with others.

4. DEFECTS IN SOLID NONSTOICHIOMETRIC COMPOUNDS WITH NARROW AND BROAD HOMOGENEITY RANGES To characterize a nonstoichiometric region, it is necessary to determine its width, the nature of the defects responsible for deviations from stoichiometry, and the defect structure of the crystal. The deviation from stoichiometry, i.e., the width of the homogeneity range, varies widely from system to system. It may be small, so that it can be only assessed by indirect physical methods (galvanomagnetic, optical, and others) and not by chemical means. At the same time, deviations from stoichiometry may be so large that defect interactions become significant, leading to defect ordering, clustering, superstructure formation, longrange ordering, and the formation of new nonstoichiometric phases differing in symmetry, energetics, and other aspects from the parent phase. In such systems, defects are intrinsic components of the crystal structure rather than being chance imperfections. Consider in detail the defect structure of crystals of nonstoichiometric compounds with narrow and broad homogeneity ranges.

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4.1. Defects in Solid Nonstoichiometric Compounds aith a Narrow Homogeneity Range The homogeneity range of such compounds is less than 0.1 at % in width, and nonstoichiometry is due to APDs, which can be thought of as quasi-components. In solidstate chemistry, this approach was developed by Wagner and Schottky [8], Frenkel [9] and Kröger [10]. In the dilute solution approximation, in which activities are replaced by concentrations, the formation of point defects in nonstoichiometric AB1+δ crystals with a narrow homogeneity range can be described by a set of quasi-chemical reactions with appropriate equilibrium constants K:

" O" = VAx + VBx + H Sh

(7)

⎛Δ H ⎞ K Sh = [VAx ][VBx ] = exp(Δ r S/k)exp⎜ r Sh ⎟ ⎝ kT ⎠

(7.1)

VAx = VA' + h + + E a Ka =

[VA' ]p [VAx ]

(8)

⎛E ⎞ = exp(Δ r S/k)exp⎜ a ⎟ ⎝ kT ⎠

(8.1)

x =V' +e _ +E VB B b Kb =

(9)

⎛E ⎞ = exp(Δ r S/k)exp⎜ b ⎟ ] ⎝ kT ⎠

[VB' ]n [VBx

(9.1)

"O"= e _ + h + + E r

(10)

⎛E ⎞ K i = np = exp(Δ r S/k)exp⎜ i ⎟ ⎝ kT ⎠

(10.1)

1/2X 2 (g) = X Xx + VAx + H BV

(11)

2

K BV = 2

[1 − [VAx ]][VAx ] p1/2 B2

n + [ VA' ] = p + [VB⋅ ]

=

VAx p1/2 X2

⎛ H BV2 = exp(Δ r S/k)exp⎜ − ⎜ kT ⎝

⎞ ⎟ ⎟ ⎠

(11.1)

(12)

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Here, “0” is the initial state of an ideal crystal; symbols x, ' and + refer to neutral, negatively charged, and positively charged vacancies, respectively; e − is an electron; h+ is a hole; X Xx is a neutral X atom on its own site; n and p are the electron and hole concentrations, respectively; square brackets represent the concentration of the species enclosed (fraction of the sites); {1–[ VAx ]} < 1 since [ VAx ]< 1; ΔH and E are energies; and ΔrS is the entropy of reaction. Reaction (7) describes the formation of neutral atomic defects through thermal disordering, and reaction (11) represents the formation of neutral defects owing to nonstoichiometry Reactions (8) and (9) represent the appearance of electrons and holes h+ via the ionization of atomic defects, and reaction (10) describes the generation of electrons and holes owing to intrinsic conduction, when electrons are excited to the conduction band, leaving holes in the valence band. The electroneutrality condition (12) corresponds to the minimum energy of the nonstoichiometric crystal. In deriving the system of Eqs. (7)–(12), we assume that the predominant defect species, ionization energies Ea and Eb, band gap Ei, degree of APD ionization, and partial vapor pressures of components ( p A(V) , p B2 (V) , p AB(V) ) over the nonstoichiometric crystal are known. According to the phase rule, a two-phase state (vapor + solid) of a binary system at T = const is described by one independent parameter, the partial pressure p B 2 , which determines the deviation from stoichiometry.

Figure 3. Defect diagram of an AB 1 + δnonstoichiometric crystal heat-treated in B vapor ( Ki > K S ): (I, V) SAB + V + L heterogeneous equilibria; (II–IV) SAB + V equilibrium. The diagram specifies the defect densities at points A–C.

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145

Solving the system of six equations in six unknowns ([ VAx ],[ VBx ], [VA' ] , [VB⋅ ] , n, and p), one can readily find [10] defect densities [ ] as functions of p B2 and the product of equilibrium constants: [ ] = f( p B2 , ∏j Kj (T). Such plots are presented in Figure 3. Regions II, III, and IV correspond to electronic (n-type), intrinsic, and hole (p-type) conduction, respectively. In region III, the carrier concentration is only determined by the band gap Ei: n = p = exp(–Ei /kT), and is independent of the partial pressure and, accordingly, of nonstoichiometry δ. These relations can be verified in experiment by measuring the Hall coefficient and the concentration of majority carriers (n and p) in AB1+ δ crystals annealed at constant temperature and different partial pressures. If the experimentally determined slopes of lines in regions II and IV (Figure 3) coincide with those obtained using model solutions, the model under consideration [Eqs. (7)–(12)] is sufficiently accurate, and one can evaluate unknown constants. Measuring n and p as functions of and K at different temperatures, one can find temperature – dependent equilibrium constants,

⎛Δ Н⎞ K = exp(Δ r S/k)exp⎜ r ⎟ , ⎝ kT ⎠ and the corresponding thermodynamic parameters: entropy ΔrS and enthalpy ΔrH of quasichemical reactions involved in defect formation. If experimental data and calculation results disagree, the model can be corrected by taking into account additional defect species (interstitials, APD complexes, and others) and varying the degree of their ionization. On the other hand, a model of an imperfect nonstoichiometric phase can be refined by independent methods: by measuring the selfdiffusion coefficient [11] and galvanomagnetic and optical parameters as functions of composition and temperature or by comparing x-ray (calculated) and pycnometric (measured) densities [5, 12, 13]. As an example, Table 1 lists the enthalpies ΔrH and entropies ΔrS of formation for quasichemical defects in nonstoichiometric III–V compounds [3, 12, 13]. The dominant defect species in these compounds are metal vacancies and interstitials and nonmetal interstitials and vacancies . The defects were identified by measuring density, lattice constants, and galvanomagnetic and optical parameters, and also selfdiffusion coefficients as functions of temperature and partial pressures [5 – 13]. The results can be used to locate the homogeneity range of the compounds studied. As an example, Figure 4 presents data for GaAs. Knowledge of the properties of nonstoichiometric defects is critical for understanding and controlling the nonradiative recombination and degradation times in lasers and lightemitting diodes based on nonstoichiometric III–V compounds and the effect of heat treatment on carrier concentration. The dominant defect species and the thermodynamic functions of defect formation were also reported for other compounds: GaN [14], II–VI [15−17] and IV–VI [18−20]. Such data are needed for understanding the chemical properties of nonstoichiometric compounds, their oxidation and sintering behavior, phase transformations, etc. [10].

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Point-defect equilibria can be described using not only the quasi-chemical approach but also statistical thermodynamics. In the latter approach, one makes up a total energy distribution function for a model of the defect structure. This function is used to derive an expression for the free energy of the system, which is then minimized to give equilibrium conditions [21]. The final result is the same as in the quasi-chemical approach: the density of nonstoichiometric defects as a function of partial nonmetal pressure and temperature. For example, the composition of the metal-deficient transition-metal monoxides M1– xO (M = Mn, Fe, Co, Ni) is a power-law function of oxygen partial pressure: x ∝ p О 2 metal vacancies ( VМx = VМ2- + 2h+) and x ∝ p О2

1/ 4

1/6

for doubly charged

for singly charged vacancies ( VМx = VМ- +

2h+). Table 1. Enthalpy ∆rH and entropy ∆rS of defect formation in III–V compounds

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147

The thermodynamics of nonstoichiometry can also be analyzed using the relative partial Gibbs energy,

ΔG(O 2 ) = μ O 2 − μ oO = RTlnp O 2

(13)

2

where μ O 2 is the chemical potential of oxygen in solid M1– xO, μ 0O 2 is the standard chemical potential of oxygen, and p O 2 is the oxygen partial pressure in the system M1– xO(s) + vapor. Since

ΔG(O 2 ) = nRTlnx

(14)

ΔG (O 2 ) must be a linear function of lnx, with a slope n that characterizes the dominant defect species: n = 6 for doubly VМ2- charged vacancies, n = 4 for singly VМ- charged vacancies, etc. Plots of ΔG(O2) against lnx can be constructed using thermogravimetric or coulometric data.

Figure 4. Temperature dependences of APD densities for As-enriched (solid lines) and Ga-enriched (dashed lines) gallium arsenide.

Such plots for the system Fe1 – xO(s) + vapor (O 2 ) [22] are presented in Figure 5 which indicates n values for different defect models. As seen, n = 6 for x ≥ 0.09, which corresponds 2to VFe doubly charged vacancies. The value n = 5 corresponds to (VFeVFe)4− associates. The 22values n = 3 and 4 observed for x < 0.09 are attributabl to the [4 VFe −Fe 3i+ ]5− and [16 VFe –

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5Fe 3i+ ]17− defect complexes, respectively. The formation of such defect complexes was confirmed by x-ray diffraction. These results highlight the importance of combined thermodynamic and structural characterization of nonstoichiometric compounds.

Figure 5. Composition dependences of the relative partial molar Gibbs energy Δ⎯G (O2 ) for Fe 1 – x O [22].

4.2. Problems in the Theory of Solid Nonstoichiometric Compounds with a Broad Homogeneity Range The approximation of randomly distributed, noninteracting APDs is of limited utility and is only applicable to nonstoichiometric compounds with a homogeneity range no broader than 0.1 at %, that is, to many oxides, chalcogenides, halides, and p-block pnictides. There are, however, many compounds, in particular transition-metal oxides, which have substantially broader homogeneity ranges. Characterization of such compounds by neutron diffraction, high-resolution electron microscopy (HREM), Mössbauer spectroscopy, coulometric titration, and other techniques demonstrates that their properties cannot be understood in terms of classical APDs. The behavior of structural defects in such compounds ranges from the point-defect regime, controlled by entropy, to enthalpy control, as in the case of the decomposition of crystals with a broad homogeneity range into discrete phases with narrow homogeneity ranges, or vacancy ordering accompanied by crystallographic shears. To develop an appropriate theory of nonstoichiometric compounds with a broad homogeneity range, it is

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necessary to address both the crystal-chemical and thermodynamic aspects of such compounds. The crystal-chemical aspect of nonstoichiometric compounds is related to the structure of imperfect crystals with a broad homogeneity range. The thermodynamic aspect involves evaluation of criteria for the stability of imperfect crystals with a broad homogeneity range. In light of this, we will scrutinize the concepts of existing stable and metastable phases, consider conditions leading to phase separation by virtue of the instability of a nonstoichiometric compound with a broad homogeneity range, and analyze the concepts of phase and two-phase region with application to homologous series of compounds with narrow homogeneity ranges.

4.3. Crystal-Chemical Aspects of Nonstoichiometric Compounds with a Broad Homogeneity Range In solid nonstoichiometric compounds with a broad homogeneity range, structural defects interact and undergo ordering (self-organization), forming superstructures. The behavior of defects ranges from the point-defect regime, controlled by entropy, to enthalpy control, as in the case of crystallographic shears. Large deviations from stoichiometry lead to the formation of new defect species (associates and clusters), influence their distribution over lattice sites, and may alter the lattice symmetry. A high degree of local ordering extends beyond the nearest neighbor environment, which implies that the “former” defects become structural elements and that the observed crystallographic and thermodynamic properties of nonstoichiometric phases are due to the loss of long-range order in the soloid. In connection with this, consider the key crystalochemical aspects of highly imperfect, nonstoichiometric compounds with a broad homogeneity range: (1) the concept of structural defect in such nonstoichiometric compounds; (2) structural rearrangement in response to changes in composition (nonstoichiometry) and temperature. If a crystal contains a high density (>10 at %) of randomly distributed APDs, it is difficult to ascertain on purely crystal-chemical grounds which atom sits on a normal lattice site and which occupies an interstice. As a result, the symmetry of a nonstoichiometric crystal may be difficult to identify. As an example, Figure 6 shows a schematic of a 2D lattice which may be thought of both as a primitive lattice containing 25% of vacant sites and as a cubic lattice with 25% of the interstices occupied. Such problems are encountered in crystal-chemical analysis of nonstoichiometric compounds in which the average number of atoms per unit cell differs from the number of available sites, and the cation or anion sublattice is deficient or enriched in atoms. Among such compounds are Ga2S3 and similar III2–VI3 chalcogenides, binary (AgI) and ternary (Ag2HgI4) iodides, solid phases in the Ni–Te system between NiTe (NiAs structure, B8) and NiTe2 (CdI2 layered structure), and many other transition-metal compounds. Atomic defects (vacancies) in such systems are structural elements to the same degree as occupied sites. The

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difference between basic vacancies (structural elements) and faulty vacancies (resulting from structural disordering) accounts, e.g., for the fact that the Ga2S3 structure contains many vacancies but dissolves only small amounts of excess gallium [10].

Figure 6. Schematic of (a) a 2D lattice containing 25% of vacant sites and (b) a diamond-type primitive lattice with 25% of the interstices occupied.

For crystals built from various structural units, it is reasonable to define the concept of ideal crystal and to analyze disordering relative to such a crystal. In an ideal crystal, all identical or different structural elements (atoms, vacancies, and others) are ordered on equivalent sites and are related by symmetry elements. In the simplest structures of binary compounds with the AB or AB2 stoichiometry, the A and B atoms occupy positions displaced relative to one another, and the crystal symmetry is determined by the long-range order. Such crystals are built up of simple components identical in structure, corresponding to one of the fourteen Bravait lattices, e.g., cubic (NaCl type) or hexagonal (NiAs type). At the same time, the structures of many compounds in multicomponent systems, including those of YBa2Cu3O7–δ and many other mixed oxides, consist of coherent intergrowths of different blocks, e.g., rock-salt (NaCl), fluorite (CaF2), and perovskite (CaTiO3) blocks, stacked in the direction of the largest unit-cell parameter. Necessary conditions for the formation of intergrowth structures consisting of alternating simple blocks are, first, that blocks differing in structure be lattice - matched in a certain plane, second, that the different metals involved be chemically compatible (electronic configuration and oxidation state) and similar in chemical bonding (overlapping of atomic orbitals) between the metal and oxygen atoms, and, finally, that the unit cell be electrically neutral [23]. If coherent boundaries in intergrowth structures become elements of the supercell, they should not be regarded as structural defects. Thus, from the crystal-chemical viewpoint, defect ordering in nonstoichiometric compounds with a broad homogeneity range alters the concepts of ideal crystal and defect. The resulting ordered groups or defect clusters should be thought of not as distortions of the ideal structure but as native structural elements of a new ideal crystal. Its state can be taken as a standard state, relative to which any deviation from the ordered arrangement of structural elements will be regarded as a defect.

Nonstoichiometric Compounds

151

This situation is analogous to that in crystals of chemical compounds (binary, ternary, and more complex) built from coherent intergrowths of different blocks. The decomposition of high-temperature nonstoichiometric phases to a number of ordered phases with narrow homogeneity ranges may be caused by changes not only in composition (nonstoichiometry) but also in temperature. Consider a schematic of structural changes in an initially disordered system (Figure 7), illustrating the effect of nonstoichiometry on the nature of structural elements and their distribution. The topmost box in Figure 7 represents nonstoichiometric phases with narrow (<0.1 at %) homogeneity ranges and randomly distributed APDs. As the homogeneity range becomes broader, the interaction between APDs leads to their partial or complete ordering, the development of short- or long-range order, and the formation of homologous series of new phases with narrow homogeneity ranges (Figure 7 bottom box). The ordering of APDs in response to compositional changes or a decrease in temperature may follow two mechanisms: APD assimilation into the structure of the crystal and APD elimination through local rearrangement of coordination polyhedra. In both cases, the formation of a new, intermediate compound requires that the new structure be perfectly periodic in the three dimensions.

Figure 7. Schematic diagram of structural changes caused by point-defect interactions and ordering.

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Wüstite, Fe1–xO (0 < x < 1), provides an example of a nonstoichiometric compound in which the ordering APDs proceeds through their assimilation into the structure. Stoichiometric wüstite, FeO, crystallizes in the NaCl structure, with the Fe2 + ions sitting in octahedral sites. Chemical analysis data, comparison of measured and X-ray densities, and neutron diffraction results indicate that the structure of Fe1–xO is deficient in Fe atoms rather than being enriched in oxygen relative to the stoichiometric composition FeO. The presence of Fe vacancies leads to structural relaxation in their nearest neighbor environment. By virtue 2and and Fe3+ attract one another and tend to occupy of electrostatic interaction, VFe

neighboring sites with octahedral oxygen coordination (Figure 8). At the same time, an energetically more favorable configuration is an Fe3+ ion occupying a tetrahedral interstice. This leads to the formation of another vacancy in an octahedral site such that the Fe3+ ion is located symmetrically with respect to the two vacancies. The resultant cluster (Koch cluster) comprises four oxygen ions (in the corners of a tetrahedron), two Fe2+ ions, two vacancies (in octahedral sites), and one Fe3+ ion (in the center position of the tetrahedron). At high temperatures, such clusters are distributed at random and interact with one another only weakly. With decreasing temperature, however, they attract one another, forming larger clusters. At a sufficiently high concentration, such multiclusters form a superstructure which can be detected by X-ray diffraction. The above model for the nonstoichiometry of wüstite, Fe1– xO, is equivalent to dissolution of magnetite, Fe3O4, in wüstite and accounts for the broad homogeneity range of the forming nonstoichiometric phases. Another example of a nonstoichiometric compound in which the ordering of APDs proceeds through their incorporation (assimilation) into the new structure is uranium dioxide, UO2+ x, containing oxygen in excess of its stoichiometric content: 0 < x ≤ 0.25. In the structure of stoichiometric UO2 (fluorite type), the oxygen atoms sit in the cube corners, and the uranium atoms sit in the interstitial sites in the center of each of the eight octants. In the assumed structure of clusters in UO2 (Figure 9), an extra oxygen atom in such an interstice is displaced from the center position along [110], i.e., toward one of the cube faces. By virtue of electrostatic interaction, the two neighboring oxygens are displaced from their normal sites along [111] and occupy neighboring empty interstices. Thus, instead of one interstitial atom, a cluster is formed which comprises three interstitial oxygens and two vacancies.

Figure 8. Koch clusters in Fe 1- x O.

Nonstoichiometric Compounds

153

Figure 9. Schematic of a cluster made up of three interstitial oxygens and two vacancies in UO 2 + x: (1) oxygen ions, (2) ideal oxygen interstitial, (3) interstitial oxygen atoms, (4) oxygen vacancies.

Note that X-ray, neutron, and electron diffraction techniques probe only an average crystal structure and, sometimes, give a wrong idea of the local structure of nonstoichiometric crystals. It is, therefore, important to take advantage of techniques capable of probing the local structure, including near neighbors 10–20 Å from a defect. Among such precision methods are high-resolution transmission electron microscopy, STM, atomic force microscopy, and magnetic force microscopy [3, 24−26]. The ordering of APDs in response to compositional changes and a decrease in temperature may occur not only through their assimilation into the structure of the crystal but also through their elimination upon local rearrangement of coordination polyhedra. This mechanism of APD elimination [6, 7, 21, 27, 28 ] can be illustrated by the examples of MoO3 and WO3 (ReO3 structure). Figure 10 shows the structure of MoO3 projected along one of the crystallographic axes. This structure is made up of MoO6 octahedra which share corners so as to form a 3D framework. Partial reduction of MoO3 leads to significant oxygen loss, resulting in a high concentration of oxygen vacancies (squares in Figure 10). The interaction between oxygen vacancies reduces the separation between them, giving rise to local elastic stresses (the arrow in Figure 10), which, in turn, cause local rearrangement of octahedra, so that some of them become displaced relative to others along so-called crystallographic shear planes (solid lines in Figure 10). This is accompanied by elimination of oxygen vacancies , which are replaced by oxygens of the displaced octahedra. As a result, the structure becomes denser, and the MoO6 octahedra become edge-shared 1. Crystallographic shear planes have the form of thin, platelike regions between 2D blocks having the

1

In TinO2n–1 and TinO2n–1, the octahedra share edges so as to form ribbons before crystallographic shear and share faces after it.

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undistorted parent structure. Owing to the structure densification, the amount of anion sites is smaller than that in the parent structure, while the Re : O ratio in the shear planes is larger.

Figure 10. Schematic illustrating the development of a crystallographic shear in crystals with the ReO3 structure; the\ arrow shows the shear direction, and the solid line represents the crystallographic shear plane.

An increase in the number of crystallographic shear planes and the elastic energy arising from the coherent match between two types of planes lead to their ordering. Neighboring crystallographic shears are separated by slabs of the parent phase. Periodic repetition of such slabs and shears results in a new phase with a perfectly stoichiometric composition. The composition is controlled by two factors: the number of eliminated anion sites (the change in the anion-to-cation site ratio) and the thickness of the slab of the parent phase sandwiched between neighboring crystallographic shear planes. The latter depends on crystallographic direction. Thus, the above process leads to the formation of intermediate phases, such as TinO2n–1 and MonO3n–1, which differ slightly in composition. Since such intermediate phases are formally similar to saturated (CnH2n+2) and unsaturated (CnH2n+1) hydrocarbons, they are called homologous series of intermediate phases. Further reduction, that is a decrease in n in the general formula of the series, is accompanied by a decrease in the separation between neighboring shear planes. Ingoing from one member of a homologous series to another, the separation between neighboring shear planes changes jumpwise. Each member of a homologous series can be regarded as a distinct phase, having a very narrow homogeneity range. Two neighboring phases in a homologous series are separated by a two-phase region. At high temperatures, the homogeneity ranges of such phases may broaden. In some cases, e.g., in CeO2–x, the difference between homologues may vanish, leading to the formation of a broad solid-solution range above a critical temperature. In this process, the shear planes seem to persist, but their repetition loses periodicity. Randomly distributed crystallographic shears are called Wadsley defects. In the MonO3n–1, WnO3n–1, TinO2n–1 and VnO2n–1 homologous series, crystals contain one set of equally spaced, parallel crystallographic shear planes, and the slabs of the parent phase

Nonstoichiometric Compounds

155

are sandwiched between neighboring shear planes. At the same time, in partially reduced Nb2O5 and mixed oxides in the Nb–Ti–O and Nb–W–O systems, crystallographic shear structures are formed by two, mutually perpendicular sets of shear planes. As a result, the regions of the parent, unreduced phase have the form of blocks or infinite columns, rather than infinite layers. They may be connected in different ways, and the resultant configuration retains the ReO3 structure, with only slight changes in M : O ratio. Note that, in block structures, nonstoichiometry may be due to APDs and 2D defects − disordered shear planes (Wadsley structures). Such defects, responsible for nonstoichiometry, were observed in binary (NbO2.48–NbO2.50) and ternary (GeO2 · 9Nb2O5) oxides [7]. Within the blocks, the oxygen sites and octahedral cation sites are occupied. The excess cations reside in the channels formed by the corners of the columns. The relative amounts of cations on the tetrahedral and octahedral sites determine nonstoichiometry. Since there is no evidence of superlattice ordering in the germanium niobium oxide, it seems likely that there is a random distribution of structural elements, as supported by Raman scattering data. Crystallographic shear structures are commonly investigated by x-ray diffraction and

−

HREM. Figure 11 shows an HREM pattern of a ( 120 ) crystallographic shear in a WO3– x crystal. Crystallographic shears provide a means of accommodating anion deficiency without additional point defects or cation displacements but, as pointed out above, they alter the anion coordination in the shear planes.

Figure 11. HREM pattern of a (⎯ 1 2 0 ) crystallographic shear in a nonstoichiometric WO 3-x crystal.

To conclude the analysis of the crystal-chemical aspects of the chemistry of nonstoichiometric compounds with a broad homogeneity range, note the following: (1) With increasing defect density and decreasing temperature, defect interactions become stronger, leading to the development of short- and long-range order. As a

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V. P. Zlomanov and A. Ju. Zavrazhnov result, the initially broad homogeneity range of high-temperature nonstoichiometric phases breaks down into a number of discrete, ordered phases (Figure 7). (2) As a result of the structural changes in question, the initially randomly distributed defects become structural elements of the new phases. This changes the meaning of the concept of ideal crystal as a standard state with reference to which defect formation processes are analyzed. The resultant structures are made up of coherent intergrowths of blocks differing in composition and structure. At this new level of structural organization, further disordering and point-defect formation processes are possible.

The types of ordering and the possible resultant structures were analyzed in detail in [5, 6, 28−30].

4.4. Thermodynamic Aspects of Solid Nonstoichiometric Compounds with a Broad Homogeneity Range The width of the homogeneity range of a nonstoichiometric compound depends on the properties of both the phase in question and the other coexisting phases. Beyond its homogeneity range, a nonstoichiometric solid is unstable and may decompose into coexisting phases. In light of this, let us scrutinize the concepts of existing, stable, and metastable phases. Solid nonstoichiometric compounds are commonly synthesized under fixed basic process parameters (temperature (T), pressure (p), and nutrient (N) composition), which govern the Gibbs energy of the solid GS(p, T, x), and that of the nutrient, GN (p, T, x). Nonstoichiometric compounds with a broad homogeneity range exist most frequently at high temperatures. At low temperatures, the configurational entropy decreases, and the homogeneity range of the high-temperature nonstoichiometric phase breaks down into a number of ordered phases with narrow homogeneity ranges. In crystals of nonstoichiometric compounds with a broad homogeneity range, decomposition is also possible at T = const. Increasing the density of nonstoichiometric defects gives rise to defect interactions, leading to the formation of associates, clusters, and polyatomic groups, i.e., to changes in the composition and hence energy, GS (x, T), of the nonstoichiometric crystal. As a result, the nonstoichiometric compound becomes unstable toward decomposition into neighboring phases. At the same time, the parent compound is not completely unstable. If there are no second-phase crystals, and spontaneous nucleation is kinetically hindered, the parent phase may exist indefinitely, even though its composition lies beyond its homogeneity range. This phase is metastable, but the phase transition only begins after at least one viable nucleus appears. One example of a metastable nonstoichiometric compound is the high-Tc superconductor YBa2Cu3O7–δ . This compound exists because its equilibrium decomposition products have no time to form during synthesis [31]. The question of existence is of importance in selecting conditions for the preparation of a solid nonstoichiometric compounds, and the question of stability is crucial for the application of such compounds.

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What are the meanings of these concepts, and is there any difference between them? To answer these questions, one can use the fundamental relation Ar(d ξr/dt) ≥ 0, where Ar and ξr are the affinity and coordinate of the r-th chemical transformation, and t is time [32]. At a constant temperature, pressure, and composition of the reactants, chemical affinity Ar can be related to the Gibbs energy change: Ar = –ΔrG. Thus, a necessary condition for the existence of a compound is a negative value of ΔrG for its formation. The reaction rate is then dξ r /dt ≥ 0, and the compound can be synthesized. In practice, however, synthesis can be accomplished if the compound exists at least for a time sufficient for its identification by chemical and structural means. The concept of phase stability differs from the concept of existence and is only meaningful if the processes which can disturb it, e.g., phase transformations, are specified. For a two-component compound A1– xBx, one A1– x''Bx'' such process is its formation from two coexisting nonstoichiometric compounds A1– x''Bx'' and A1– x'Bx', (1 − η)A1– x'Bx' + η A1– x''Bx'' = A1– xBx ,

(15)

where η = (x – x')/(x '' – x') and x'' ≥ x ≥ x'. The Gibbs energy of this process is given by ΔrG(x) = G(x) – (1 – η)G(x') − ηG(x'' ),

(16)

where G is the Gibbs energy of the coexisting phases. At a given pressure and temperature, a necessary and sufficient condition for the stability of the A1– xBx phase with respect to the A1– x''Bx'' and A1– x'Bx' phases is a negative value of ΔrG(x) [32]. If this condition is not fulfilled, the phase is metastable. Since 0 ≤ η ≤ 1, the condition ΔrG < 0 is equivalent to the strict convexity of G ≠ G(x) in the composition range x' ≤ x ≤ x''. As an example, Figure 12 shows the composition dependence G(x)p, T for system A–B, which contains two thermodynamically stable phases (1, 2) and two existing, but unstable phases (3, 4). These latter may exist as metastable phases if a new phase does not nucleate. In such a case, the system will contain phases 2–4, represented by the convex broken line G2 = G2 (x)p, T. At x' = 0 and x'' = 1, reaction (15) corresponds to the standard Gibbs energy ΔfG0 of formation of the nonstoichiometric compound A1– xBx from its components A and B: ΔrG = = ΔfG0. Therefore, a condition for its stability is ΔfG0 < 0. Thus, stable phases lie on the convex broken line G(x), with breaks corresponding to stable phases and linear portions corresponding to the Gibbs energy of two-phase mixtures. Stable nonstoichiometric compounds remain unchanged after the action of a disturbing influence (fluctuations in temperature, pressure, or component concentrations (nonstoichiometry) has been ceased. The loss of stability means a change in phase composition, that is, decomposition or the formation of new phases. The question that now arises is whether the phase separation caused by the complete instability of a nonstoichiometric compound may occur more rapidly than that resulting from the change in chemical potential due to a second phase. It seems likely that the stability of a crystalline structure toward stoichiometry changes is limited. Spontaneous immiscibility at low temperatures and a broad homogeneity range at high temperatures result in a critical temperature Tc of the existence of a nonstoichiometric phase with a broad homogeneity range

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and lead to the formation of two-phase regions below Tc. Phase separation conditions can be described in terms of the thermodynamics of spinodal states [33, 34]. Spinodal states are boundaries of states in which a phase remains homogeneous in spite of changes in its state. Reaching such a boundary, the phase becomes unstable and converts to another phase which differs in properties and structure from the parent phase. The stability limits are called spinodals. The necessary conditions for spinodal phase separation are illustrated in Figure13. Above Tc, the G(x)T curve has a usual concave shape over the entire homogeneity range (Figure 13), with dG/dxB > 0 and d2G/dxB2 > 0. At a lower temperature, T2 < Tc, the curve has two inflections (spinodal points), where d2G/dx2B = 0. Between these points, d2G/dx2B < 0. Any composition between the spinodal points is completely unstable since, in this range, any composition fluctuation reduces the Gibbs energy and is, therefore, irreversible and spontaneously propagating [6, 33−35]. The compositions of the disproportionation products (Figure, 13, points a, b) are defined by the tangency points of the tangent common to the two segments of the curve. Note that phase separation in a spinodal point covers large volumes, is initiated by small order and composition fluctuations, and is a continuous transformation, whereas nucleation of a new phase occurs at large composition and order fluctuations in a small volume and is, therefore, not a continuous but a jumplike process. Consequently, coexisting low-temperature phases and the phase stable above Tc must have topologically related structures. Nonstoichiometric phases with a critical temperature and structurally related (e.g., different ordering configurations) intermediate phases would be expected to be unstable to spinodal decomposition. An example is provided by the iron–oxygen system, whose G–xO diagram is shown schematically in Figure 14. Above 570 0C, wüstite, Fe1–xO, coexists with Fe and magnetite, Fe3O4. Below 5700C, the metastable, quenched wüstite decomposes into Fe-enriched and oxygen-enriched FeO phases. The decomposition occurs spinodally and involves no nucleation processes. One possible Fe-based spinodal decomposition product is stoichiometric FeO, which is also metastable with respect to the end products. The oxygenenriched decomposition product differs from the Fe3O4 spinel − whose formation requires nuclei − and seems to consist of ordered defect clusters, each comprising an Fe3+ interstitial and two VFe2− vacancies bound to it: (VFeFeiVFe)– (Figure 8). This configuration is more stable than an isolated vacancy and is a structural element of the Fe3O4 resulting from wüstite conversion above the critical Fe content. The discovery of crystallographic shear and block structures, and also of infinitely adapted structures [5−7] in TinO2n–1 with 4 ≤ n ≤ 10, in which the crystallographic shear plane rotates in its own zone from one stable direction to another, presents some difficulties as to the use of the phase rule and, particularly, the concept of chemical composition. To quantify chemical composition, one should specify, first, the structural constituents involved and, second, the unit of measure. As structural constituents, one can use not only atoms, APDs, etc., but also extended defects (clusters, shear planes, and others) that result from ordering processes and become constituent elements of the crystal. The somewhat arbitrary choice of structural constituents will not cause negative consequences if their amounts are consistent with chemical analysis data, do not disturb the electroneutrality of the system, and fit with the measured composition dependences of properties. Constituents are called independent, or

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components of the system if they meet the above requirements (are fully consistent with measured properties) and cannot form from one another (independence condition) [36]. Another unanswered question in this context is whether Wadsley defects (disordered crystallographic shear planes) and the homologous series TinO2n–1 (4 ≤ n ≤ 10) can be regarded as distinct phases [5]. The third question is whether the phases in the above homologous series are separated by two-phase regions. The answers to the last two questions are probably “yes”, since all of the above compounds meet Gibbs’ definition of a phase where x is the mole concentration of independent structural constituents, or components of the system. At the same time, such “weak” phases are characterized by small magnitudes of the Gibbs energy of formation ΔfG from neighboring coexisting phases. Characteristically, they have narrow G(x) curves lying on a convex broken G(x) line. The breaks in the broken line correspond to the Gibbs energies of such phases, and the linear portions correspond to the Gibbs energies of two-phase systems (Figure 12). Thermodynamic analysis of the existence and properties of such low-stability phases was carried out by Voronin [32]. The reason for the existence of two-phase regions is that there are complete instability boundaries of a homogeneous state, at which the parent phase decomposes into two new phases. As pointed out above such boundaries are formed by spinodals (Figure 13) of the parent and forming phases. For first order phase transitions, the spinodals of the two phases issue from the critical point and run downward in different directions, encompassing the phase-transition region from the two sides. Thus, the spinodals make up an inner boundary of the first-order phase-transition region, where only a two-phase state is stable.

Figure 12. Schematic composition dependences of Gibbs energy for (1, 2) stable and (3, 4) metastable phases in system A–B.

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Figure 13. Schematic composition dependence of Gibbs energy illustrating spinodal phase separation: (ac, db) metastable states, (cd) labile state; (a, b) compositions of stable phases.

Figure 14. Schematic composition dependence of Gibbs energy for the Fe–O system in the range 200– 350°C, illustrating spinodal decomposition and the formation of Koch clusters.

5. PHASE DIAGRAM AS A KEY TO SELECTING CONDITIONS FOR THE SYNTHESIS OF NONSTOICHIOMETRIC COMPOUND A major problem in materials research is the preparation of NONSTOICHIOMETRIC COMPOUNDS with predetermined composition and properties. Targeted synthesis of such compounds involves control over phase transformations. For this reason, to optimize synthesis parameters data on phase equilibria are needed. Geometrically phase equilibria in a two – component system with volatile component can be represented using a threedimensional pressure (P)- temperature (T)- composition (x) diagram or its two-dimensional

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T−x, P−T and P−x projections [10, 36 - 38]. Consider first the key features of a T–x (Figure 15) phase diagrams: the solidus, liquidus and vapor lines, difference in composition of solid nonstoichiometric compound SAB, liquid (L) and vapor (V) at the maximum melting max temperature Tm, AB , the invariant points of congruent melting, sublimation. The maximum max melting temperature Tm, AB is a temperature when a nonstoihiometric solid SAB appears to be

melted and above which can not exist . The solidus (S'S''), liquidus (L'L'') and vapor (V'Vmax V’') lines on Figure 15 represent the temperature dependence of the composition of solid, liquid and vapor phases which are in equilibrium . The homogeneity range of a solid SAB is limited by the solidus line. The homogeneity range may include the stoichiometric composition or not. At the maximum melting temperature coexisting phases have different compositions; xS ≠ xL ≠ xV [37]. The temperature where the compositions of the solid and liquid phases are identical (xS congr == xL) is called the congruent melting temperature Tm, AB of phase SAB. The temperature

where the compositions of the solid and vapor are identical t (xS = xV) is called the congruent congr max sublimation temperature Tsublcong . The compositions corresponding to Tm, AB , Tm, AB and

Tsublcong differ from the stoichiometric composition δ = 0 of the solid phase A1/2– δB1/2+δ (x = 1/2 + δ), where δ is the deviation from the stoichiometric composition AB). P–T projection of the P–T–x diagram is shown in Figure 15b. The line Q1 Tmс Q2 represents the equilibrium SAB + L + V and is of interest for the growing of nonstoichiometric solid AB (SAB) from the melt. The three-phase equilibrium is seen to be possible over a wide range of temperatures and pressures; but once P is given, T is fixed. The composition of solid AB liquid (L) and vapor (V) coexisting under various conditions of P and T varies, as shown by the solidus, liquidus and vapor lines in Figure 15a. The general the compositions of the various phasea are different. In the situation as given in Figure 15, two special points Tmс and

TSс occur, where the composition of two of the phases are identical: (1) at point Tmс the composition of the liquid is identical within that of the solid (xL =

x SAB ); (2) at a pont TSk the composition of the solid nonstoichiometric AB is equal to that of the vapor ( x SAB = xV). Whenever possible, the synthesis of solid AB will be carried out at or near congruent points

Tmс

or

TSс .

The concept of congruence is of importance in the synthesis of nonstoichiometric compounds because a difference in composition between the nutrient (N) (vapor or melt) and solid gives rise to flows of rejected material and the associated kinetic instability of the growth interface.

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Figure15. (a) T–x and (b) p–T projections of the p–T–x phase diagram of a binary system containing a chemical compound S AB.

It may well be, however, that the congruent points occur at a pressure or temperature too high to be reached ubder normal conditions. In this one can work at other parts of the threephase line where the solid is in equilibrium with liquid at lower temperatures and pressures. This has been applied, for instance, for the synthesis of nonstoichiometric InP: whereas the pressure near the maximum temperature is 60 atm, indium-rich melts have much lower vapor pressure [10] and therefore solid synthesis from such melts is much more convinient. At a fixed vapor pressure of the more volatile component, supersaturation is created by cooling or heating a three-phase system. The latter corresponds to the temperature range T < T2 in Figure 15. For example, cadmium telluride crystals can be prepared by heating cadmium- enriched melts [10]. Note that the composition of crystals grown by the vapor–

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liquid solid process always corresponds to the solidus line, that is, to the limit of the homogeneity range.

6. APPROACHES FOR CONTROLLING THE NONSTOICHIOMETRYOF SOLIDS The nonstoichiometry of inorganic compounds can be controlled using the following approaches: (1) (2) (3) (4) (5)

annealing of grown crystals at fixed partial pressures of their components; varying the partial pressures of vapor species during vapor or melt growth; chemical vapor transport; coulometric titration; deposition of films of nonstoichiometric compounds from solutions containing coordination compounds.

6.1. Control Over the Vapor Composition and the Nonstoichiometry of Solids Equilibria involving the vapor phase play an important role in crystal growth and nonstoichiometry control. The compositions that can be obtained by annealing solids in an vapor of constant composition (xV) fall within the stability regions in the T–x and p–T projections (Figure 15), where each point represents one composition x (nonstoichiometry δ) if the temperature and partial pressures pi of vapor species are maintained constant: x(δ) = f(T, pi). The resultant composition may lie within or on the boundary of the homogeneity range, which depends, according to the phase rule [37 ] , c = k + 2 − r − α where k is the number of components, 2 is due to the presence of two external fields (baric and thermal), r is the number of phases, and α is the number of independent constraints on the intensive parameters c . For example, in a binary (k = 2) system A–B, one can obtain any composition within the homogeneity range using the vapor–solid equilibrium (r = 2) and maintaining the annealing temperature and partial pressure (pA or pB ) constant. The choice of the component determining the compositions of the vapor phase and nonstoichiometric crystal is dictated by the condition: the applied pressure (pi)appl must exceed the pressure of that component corresponding to the congruent sublimation ( pI )congr of the compound: (pi)appl > (pi)congr. Otherwise, (pi)appl will be determined not by the “cold” point temperature but by the temperature of the solid being annealed, and the system will prove uncontrollable [10]. In the first and second approaches above, the vapor pressure of the major component can be controlled in both open and closed systems. 1. If the amount of a volatile component in a closed isothermal system is such that, at the experimental temperature, it vaporizes entirely, the pressure is proportional to temperature (Gay-Lussac law). This approach was used to grow nonstoichiometric gallium arsenide crystals [10].

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V. P. Zlomanov and A. Ju. Zavrazhnov 2. If the amount of a component in a closed isothermal system is such that, at the experimental temperature, it vaporizes only partially, the vapor pressure pi is related to temperature by pi = Aexp(–HV)/(RT). This approach was used to synthesize zinc oxide crystals with different deviations from stoichiometry [39]. 3. Most frequently, use is made of closed two-zone systems, as exemplified in Figure 16. Solid AB, whose stoichiometry is to be changed, is maintained at temperature TAB, and a pure volatile component B is maintained at a lower temperature TB: TAB > TB. Such systems were used to vary the nonstoichiometry of II–VI [16, 40], III–V [41, 42 ], IV–VI [43], and many other compounds. Instead of a pure component, one can use A + AB or AB + B solid mixtures. The vapor pressure pB is then only determined by temperature TB, but the composition of the end product corresponds to the boundary of the homogeneity range. This method was used to vary the nonstoichiometry of PbTe [44] and Nb2O5 [45].

Figure 16. Schematic of a two-zone system for varying the nonstoichiometry of AB 1+δ solid.

Figure 17. Procedures for controlling the S2 vapor pressure over (a) ZnS and (b) CdS at 1250 K in an H2S + O2 atmosphere [10].

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The partial pressure of a component can be controlled using one of its gaseous compounds that dissociate on heating. For example, an H2 + H2S mixture was used in open flow systems to produce an appropriate sulfur pressure, and H2 + H2O and CO + CO2 mixtures were used to maintain the required oxygen pressure. The procedures for controlling the vapor pressure p S2 over ZnS and CdS are illustrated in Figure 17 [10, 46, 47].

6.2. Nonstoichiometry Control during Solid Synthesis To control the nonstoichiometry of binary compounds during synthesis, one can use the system shown schematically in Figure 18. AB vapor is transported along the ampule owing to a temperature gradient, and component B is maintained at a lower temperature TB (“cold” end), which ensures the required partial pressure pB. The solid stoichiometry is controlled by varying the growth temperature TAB and accurately maintaining temperature TB. Such a procedure was used in the vapor growth of PbS and PbSe crystals with low (down to 1016 cm−3) carrier concentrations [48] and perfect CdTe and CdZnTe crystals [49]. In melt growth of nonstoichiometric compounds, use is commonly made of the Bridgman process and Czochralski pulling.

Figure 18. Schematic illustrating nonstoichiometry control during vapor growth of AB 1 +δcrystals.

In the former process, the boat shape is such as to select a single nucleus, and the vapor composition is determined by temperature TB. A more effective method for the crystal growth of gallium arsenide is the liquid-encapsulated Czochralski (LEC) process at a controlled pressure of the volatile component [50]. A crystal puller schematic is shown in Figure 19. The growth zone is made air-tight using a liquid B2O3 or Ga layer. The arsenic vapor source is maintained at 617°C, which ensures the optimum arsenic vapor pressure for the growth of dislocation-free GaAs crystals. The temperature gradient can then be substantially reduced, with no risk of surface decomposition of the growing crystal. This procedure enables the growth of GaAs single crystals 10 and 15 cm in diameter, with dislocation densities below 5 ⋅ 103 cm−2.

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Figure 19. Schematic of a liquid (B2O3) encapsulated CZ system for the crystal growth of GaAs at a controlled arsenic pressure: (1) B2O3 (or Ga) encapsulation layer, (2) heaters, (3) GaAs seed, (4) GaAs crystal (5) As vapor source at 617 C, (6) B2O3 flux, (7) GaAs melt.

Figure 20. Schematic of a three-zone system for varying the nonstoichiometry of crystals of an (A 1 – x B x) 1 – δ C 1 + δ ternary compound.

In ternary systems, nonstoichiometry can be controlled using three-zone annealing (Figure 20). The reservoirs containing B and C source materials are connected to the tube containing (A1–xBx)1–δC1+δ by capillaries, which prevents rapid transport of components B and C. Similar configurations can be used for melt or vapor growth of nonstoichiometric ternary compounds. At the same time, one can use two-component, two-phase mixtures, which ensure appropriate vapor pressures of both components at a constant temperature [19, 49].

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6.3. Nonstoichiometry Control Using Chemical Vapor Transport [51, 52] The nonstoichiometry of compounds containing a nonvolatile component can be varied using chemical vapor transport. The basic principle of the method is to introduce or remove such a component through selective chemical vapor transport (Figure 21). The sample, e.g., GaSe, is located at one end of an ampule and is maintained at temperature T2, and the Ga source (or getter) material is located at the other end, at temperature TB. The transporting agent is gallium triiodide, GaI3. Gallium transport from the sample to the Ga charge or in the opposite direction is due to the reversible reaction 2Ga(GaSe sample or charge) + GaI3(V) = 3GaI(V). The Ga transport direction and, hence, the nonstoichiometry of the GaSe single crystal depend on the Ga source (getter) temperature T1, GaSe sample temperature T2, and source (getter) composition x1. If metallic gallium is used as the charge, the sample composition x2 and nonstoichiometry depend on two operational parameters of annealing: T2 and T1. It is convenient to represent these conditions in a T2–T1 – x2 3D phase diagram or its T2 –T1 projection (Figure 22) showing the stability regions of the phases involved.

Figure 21. Schematic illustrating a vapor transport procedure for varying the nonstoichiometry of four GaSe samples; T2΄ is the GaSe temperature and T1 ΄, T1΄΄ T1΄΄΄ and T1 ΄΄΄΄ are the Ga source (getter) temperatures.

Figure 21 illustrates the procedure for varying the nonstoichiometry of GaSe1+δ. The composition of the resultant materials was evaluated by x-ray diffraction and cathodoluminescence spectroscopy. The results were used to construct a partial T–x projection of the p–T–x phase diagram of the Ga–Se system, which takes into account GaSe

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polytypism (Figure 23). To successfully control the nonstoichiometry of an inorganic compound using chemical vapor transport, the transporting agent should not dissolve in its crystals and should not form binary or ternary compounds with the second component (Se). Chemical vapor transport was used to vary the nonstoichiometry of gallium selenides and indium sulfides [51, 52 ].

Figure 22. T1–T2 phase diagram representing conditions for controlling the nonstoichiometry of GaSe and Ga 2 Se 3 using chemical vapor transport.

Figure 23. (a ) T - x phase diagram of the GaSe system; (b ) Homogeneity ranges of the two polytypes ε - GaSe and γ – GaSe.

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6.4. Nonstoichiometry Control Using Coulometric Titration Coulometric titration is an electrochemical analytical technique. Its basic principle is to evaluate the weight change of the sample from the quantity of electricity consumed. In coulometric titration, electrolysis is commonly carried out at a constant current since the concentration of the substance to be converted to the reagent can be sufficiently high to remain constant throughout “titration.” The quantity of electricity is then evaluated from the current and electrolysis time. The current can be determined potentiometrically from the voltage drop across a standard series-connected resistor. As an example, consider the cell

An applied voltage causes Ag+ ions and electrons to migrate to the right of boundary I and to the left of boundary II, respectively. Since AgI possesses no electronic conductivity, the electrons must remain in Ag2S. As follows from the electroneutrality condition, an equivalent amount of Ag+ also remains in Ag2S, resulting in transport of silver atoms to Ag2S. Their concentration can be determined from the quantity of electricity passed through the cell. Thus, the process offers the possibility of controlling the Ag2S nonstoichiometry. At the opposite current direction, silver atoms leave Ag2S owing to Ag++ transport through AgI and electron transport to the platinum electrode. Coulometric titration is conceptually similar to nonstoichiometry control via annealing of crystals in vapors of their components (pi). In both procedures, new phases − pure components or neighboring solid compounds − form when the potential E (µ = nFE) and partial pressure pi (µi = µio + RTlnpi) reach the boundary of the homogeneity range. At the same time, electrochemical titration has the advantages of high accuracy, simple equipment, and high sensitivity. The cell must offer 100% current efficiency for the substance to be processed, and the electrodes must possess only ionic conductivity. Coulometric titration was used to vary the nonstoichiometry of silver, copper, and lead chalcogenides [53−56]; Cd1+xCr2Se4 and Cu1+xCr2Se4 spinels [57] TiO2, NbO2 [ 58], MgFe2O4, NiFe2O4 [59 ] and other compounds.

6.5. Synthesis of Nonstoichiometric Compounds with a Broad Homogeneity Range Solid nonstoichiometric compounds with a broad homogeneity range are commonly synthesized at high temperatures by directional solidification, vapor phase processes, or solidstate recrystallization [60]. The composition of the growing solid depends on the synthesis temperature and nutrient composition. Given the broad homogeneity range (>1 at %) of the compounds in question, the appropriate charge is prepared by weighing the starting reagents. Since there are several coexisting phases during growth (S + L + V, S1 + S2, etc.), the

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composition of the grown crystals lies at one of the boundaries of the homogeneity range (the largest deviation from stoichiometry). Solid compositions falling within the homogeneity range can be obtained by vapor growth at appropriate constant partial pressures of the components [10, 43]. The preparation of solids with controlled nonstoichiometry is impeded by the facts that a high-temperature phase with a broad homogeneity range may decompose during cooling into a number of phases with narrow homogeneity ranges and that retrograde solubility may lead to precipitation of solid components and other phases. Nonstoichiometric compounds can be synthesized and characterized in different temperature ranges. At low temperatures, kinetic hindrances may prevent the system from reaching true equilibrium. Indeed, compositional homogeneity of such a phase can only be reached through diffusion, but diffusion coefficients drop with decreasing temperature and increase with increasing nonstoichiometry, as, e.g., in the iron sulfide Fe1–xS [61]. In other words, a sulfide containing ordered vacancies has a low self-diffusion rate. This seems to be responsible for the high stability of iron alloys toward corrosion in H2S atmosphere, which produces a continuous film of the ordered phase Fe9S8 or Fe7S8 [6, 62].

7. CRITERIA FOR EVALUATING THE HOMOGENEITY OF NONSTOICHIOMETRIC SOLIDS The Gibbs energy G of a solid is a statistical quantity related to a distribution function. The average G determines the most likely distribution of 0D, 1D, 2D, and 3D defects. Since there may be fluctuations about the average value, in a closed system (a solid of constant bulk composition at constant temperature) configuration fluctuations may have the form of compositional changes within a small region as a result of random motions of particles into or from a volume element. The question that arises in this context is what solid can be considered homogeneous? The inhomogeneity of a solid phase is characterized by a random distribution of constituent structural elements. Among such structural elements are constituent atoms sitting in normal lattice sites and various 0D, 1D, 2D, and 3D defects (Figure 2). Inhomogeneity can be quantified using three types of distributions: (1) distribution of structural elements (building blocks) within some measurable volume, (2) distribution of such volumes over the solid, and (3) distribution of characterization results and properties of the solid phase. A solid can be considered homogeneous if

C i − 1/N

N

∑C

i

≤σ

i =1

where σ is the confidence interval, and Ci is the concentration of structural elements in the ith microvolume. If this inequality is not fulfilled for at least one value of i, the solid should be considered inhomogeneous. For practical application of a material, those deviations of a property in a given volume from the weighted-average value for the entire system which fall

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beyond the confidence interval are of consequence. In this regard, an inhomogeneity can be thought of as a set of values of the property being measured which fall beyond the limits in question and are taken over all the microvolumes. Analysis of generalized homogeneity criteria with the use of an autocorrelation function was performed by Nikitina et al. [63 ]. Thermodynamic analysis of defect ordering and interpretation of the composition dependences of physical properties with allowance made for short- and long-range order in terms of the structural elements (cluster components) considered above were reported by Men’ et al. [64].

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[8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

Van Bueren, H.G., Imperfections in Crystals, New York: Interscience, 1961. Stavola, M., Semicond. Semimet., 1998, vol. 51A, p. 47. Handbook of Semiconductor Technology, Jackson, K.A. and Schröter, W., Eds., Weinheim: Wiley-VCH, 2000. Fistul’, V.I., Fizika i khimiya tverdogo sostoyaniya (Physics and Chemistry of Solids), Moscow: Metallurgiya, 1995. (in Russian). West, A.R., Solid State Chemistry and Its Applications, Chichester: Wiley, 1985. Rabenau, A., Problems of Nonstoichiometry, New York: North Holland, 1970. Rao, C.N.R. and Gopalakrishnan, J., New Directions in Solid State Chemistry: Structure, Synthesis, Properties, Reactivity, and Materials Design, Cambridge: Cambridge Univ. Press, 1986. Wagner, C. and Schottky, W., Z. Phys. Chem., 1930, vol. 11, p. 163. Frenkel, J., Z. Phys., 1926,j vol. 35, p. 652. Kröger, F.A., The Chemistry of Imperfect Crystals,2nd ed. Amsterdam: North-Holland, 1973. Atomic Diffusion in Semiconductors, Shaw, D., Ed., London: Plenum, 1973. Bublik, V.T. and Mil’vidskii, M.G., Materialovedenie, 1997, no. 2, p. 21.(in Russian). Bublik, V.T. and Mil’vidskii, M.G., Materialovedenie, 1998, no. 5, p. 16. ( in Russian). Li Jing-Bo and Tedenac, J.C., J. Electron. Mater., 2002, vol. 31, no. 4, p. 321. Fochuk, P., Korovyanenko, O., and Panchuk, O., J. Cryst. Growth, 1999, vol. 97, no. 3, p. 603. Kukk, P.L. and Altosaar, M., J. Solid State Chem., 1983, vol. 98, no. 1, p. 1. Berding, M.A., van Schiefgoarde, M., and Paxton, A.T., J. Vac. Sci. Technol., 1999, vol. 8, p. 1103. Novoselova, A.V. and Zlomanov, V.P., Curr. Top. Mater. Sci., 1981, vol. 7, p. 643. Zlomanov, V.P., Demin, V.N., and Gas’kov, A.M., J. Mater. Chem., 1992, vol. 2, no. 1, p. 31. Kuznetsov, V.L. and Zlomanov, V.P., Neorg. Mater., 1999, vol. 35, no. 4, p. 263 [Inorg. Mater. (Engl. Transl.), vol. 35, no. 4, p. 197]. Chebotin, V.N., Fizicheskaya khimiya tverdogo tela (Physical Chemistry of Solids), Moscow: Khimiya, 1982. (in Russian). Sörensen, O.T., Nonstoichiometric Oxides, New York: Academic, 1981, p. 271.

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[23] Abakumov, A.M., Antipov, E.V., Kovba, L.M., et al., Usp. Khim., 1995, vol. 64, no. 8, p. 769.( in Russian). [24] Buseck, P.R., Cocoley, J.V., and Eyring, L., High-Resolution Transmission Electron Microscopy and Associated Techniques, Oxford: Oxford Univ. Press, 1988, p . 371. [25] Eyring, L. and O’Keefe, M., The Chemistry of Extended Defects in Non-metal Solids, Amsterdam: North Holland, 1970, p. 380. [26] Wiesendanger, R. and Guntherodt, H.J., Scanning Tunneling Microscopy II, Springer Ser. Surf. Sci., 1992, vol. 28, p. 42. [27] Trushin, Yu.V., Fizicheskoe materialovedenie (Physical Principles of Materials Research), St. Petersburg: Nauka, 2000, p. 235. (in Russian). [28] Van de Valle, C.G. and Neugebauer, J., Phys. Rev. Lett., 2002, vol. 88, p.103. [29] Gudilin, E.A., Targeted Synthesis of Inorganic Superconductors Based on Rare-Earth Barium Cuprates, Doctoral (Chem.) Dissertation, Moscow: Moscow State Univ., 2003.(in Russian). [30] Kienle, L. and Simon, A., J. Solid State Chem., 2001, vol. 161, p. 385. [31] Voronin, G.F., Zh. Neorg. Khim., 1999, vol. 39, no. 11, p. 1763.( in Russian). [32] Voronin, G.F., Neorg. Mater., 2000, vol. 30, no. 3, p. 342 Inorg. Mater. (Engl. Transl.), vol. 30, no. 3, p. 271]. [33] Novikov, I.I., Termodinamika spinodalei i fazovykh perekhodov (Thermodynamics of Spinodals and Phase Transitions), Moscow: Nauka, 2000. (in Russian). [34] Gerasimov, Ya.I., Dreving, V.P., Eremin, E.N., et al., Kurs fizicheskoi khimii (A Course on Physical Chemistry), Moscow: Gostekhizdat, 1963, vol. 1, p. 367. (in Russian). [35] Cahn, J.W., Acta Metall., 1961, no. 41, p. 795. [36] Voronin, G.F., Osnovy termodinamiki (Principles of Thermodynamics), Moscow: Mosk. Gos. Univ., 1987. (in Russian) [37] Zlomanov, V.P. and Novoselova, A.V., P–T–x-Diagrammy sostoyaniya sistem metal– khal’kogen (P–T–x Phase Diagrams of Metal–Chalcogen Systems), Moscow: Nauka, 1987.(in Russian). [38] Storonkin, A.V., Termodinamika geterogennykh system (Thermodynamics of Heterogeneous Systems), Leningrad: Leningr. Gos. Univ., 1967, part 1.( in Russian). [39] Scharowsky, E., Z. Phys., 1953, vol. 135, p. 318. [40] Nishizava, Ex. J. and Oyama, Y., Mater. Sci. Eng., 1994, vol. 12, nos. 6–8, pp. 273– 426. [41] Nishizava Jun-ichi, I Int. Symp. on Point Defects and Nonstoichiometry, Sendai, 2003, p. 1. [42] Neubert, M. and Rudolph, P., Progr. Cryst. Growth Charact. Mater., 2001, vol. 43, p. 119. [43] Zlomanov, V.P. and Yashina, L.V., in Lead Chalcogenides: Physics and Applications, New York: Taylor and Francis, 2002, p. 37. [44] Brebrick, R.F. and Gubner, E., J. Chem. Phys., 1962, no. 36, p. 170. [45] Van Lierder, W. and de Jonghe, L., Solid State Commun., 1964, vol. 2, p. 129. [46] Van Gool, W., Principles of Defects Chemistry of Crystalline Solids, New York: Academic, 1966, p. 327. [47] Van Gool, W., Philips Res. Rep., Suppl., 1961, no. 3, p. 361. [48] Prior, A.C., J. Electrochem. Soc., 1961, vol. 108, p. 82.

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[49] Goldgirsh, A., Shusterman, S., Zilber, R., and Azouloy, M., Programme and Abstracts of Symposium Solid Solutions of the II–VI Compounds, Zakopane, 2002, p. 20. [50] Osvenskii, V.B., in Fundamental’nye problemy rossiiskoi metallurgii na poroge XXI veka (Critical Issues in Russian Metallurgy on the Threshold of the 21st Century), Moscow: Ross. Akad. Estestv. Nauk, 1998, vol. 4, p. 85. (in Russian). [51] Zavrazhnov, A.Yu., Turchen, D.N., Naumov, A.V., and Zlomanov, V.P., J. Phase Equilib., 2003, vol. 24, no. 4, p. 330. [52] Zavrazhnov, A.Yu., Zarzyn, I.D., Turchen, D.N., et al., Inorg. Mater., 2004, vol. 40, suppl. 2, p. 101. [53] Wagner, J.B. and Wagner, C., J. Chem. Phys., 1957, vol. 26, p. 1602. [54] Miyatani, S., J. Phys. Soc. Jpn., 1959, vol. 14, p. 750. [55] Mathieu, H.J. and Rickert, H., Z. Phys. Chem. (Frankfurt/ Main, Ger.), 1972, vol. 79, p. 315. [56] Leushina, A.P. and Simonova, M.V., Zh. Fiz. Khim., 1975, vol. 49, p. 1218. (in Russian). [57] Leushina, A.P., Kolesnikov, L.A., Makhanova, E.V., and Zlomanov, V.P., Trudy VII soveshchaniya “Fundamental’nye problemy ioniki tverdogo tela” (Proc. VII Conf. Fundamental Issues in Solid-State Ionics), Chernogolovka, 2004, p. 30. ( in Russian). [58] Alcock, C.B., Zador, S., and Steele, B.C.H., Proc Br. Ceram. Soc., 1967, vol. 8, p. 231. [59] Schmalzried, H. and Tretyakov, Yu.D., Ber. Bunsen-Ges. Phys. Chem., 1966, vol. 72, p. 180. [60] The Growth of Single Crystals; Crystal Growth Mechanisms: Energetics, Kinetics, and Transport, Laudise, R. and Parker, R., Eds., New York: Prentice-Hall, 1970. [61] Condif, R.H., Kinetics of High Temperature Processes, New York: Wiley, 1959, p. 97. [62] Herzog, F., Corros. Anticorros., 1959, vol. 7, p. 281. [63] Nikitina, V.G., Orlov, A.G., and Romanenko, V.N., in Protsessy rosta poluprovodnikovykh kristallovi plenok (Growth of Semiconductor Crystals and Films), Novosibirsk: Nauka, 1981, vol. 6, p. 204.(in Russian). [64] Men’, A.N., Bogdanovich, M.P., Vorob’ev, Yu.P., et al., Sostav–defektnost’–svoistva tverdykh faz. Metod klasternykh komponentov (Composition–Perfection–Properties of Solids: Method of Cluster Components), Moscow: Nauka, 1977. (in Russian).

In: Intermetallics Research Progress Editor: Yakov N. Berdovsky, pp. 175-212

ISBN: 978-1-60021-982-5 © 2008 Nova Science Publishers, Inc.

Chapter 4

SEMICONDUCTING INTERMETALLIC COMPOUNDS ---WITH SPECIAL INTEREST IN SILICIDES AND RELATED COMPOUNDS Yoji Imai National Inst of Advanced Industrial Science and Technology (AIST) AIST Tsukuba Central 5, Higashi 1-1 Ibaraki 305-8565, Japan

1. INTRODUCTION Though intermetallic compounds composed of metallic elements may be expected to be metallic, there are several semiconducting intermetallic compounds composed of transition metals (Fe, Ru, Ir, etc) or alkaline earth elements (Mg, Ca, Sr, Ba) and p-block elements (Al, Ga, In; Si, Ge, Sn, Pb; As, Sb, Bi; Se, Te, etc.). Main advantages of them, especially of silicides, exist in capability of finer band gap tuning compared to the elemental semiconductors (Diamond, Si, Ge, alpha-Sn) and in abundance in natural resources and in less toxicity compared to the III-V compound semiconductors (GaAs, GaSb, etc). In this paper, our recent studies on semiconducting intermetallic compounds using firstprinciple electronic structure calculations based on the density-functional theory (DFT) are reviewed and the future prospects are described. The target of the studies includes transition metal silicides, alkaline earth metal silicides and pnictides, and transition metal aluminides and gallides. However, the main interest will be focused on silicides since there has been an increasing attention to the semiconducting silicides [1]. The reason of the recent interest in silicides exists in that, (1), they are composed of non- or less toxic and naturally abundant elements in the earth’s crust, and (2), some of their band gaps are favorable for applications to photoelectronic and thermoelectric devices. It should be pointed out that there exists a problem in predicting physical nature by the calculation using DFT employing local density approximation (LDA) or its improved methods. That is underestimation of the band gap of most semiconductors and insulators. One of the possible reasons was thought to be the inaccurate exchange-correlation functional.

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However, this can be improved by taking into account the charge density gradient, which has been used in most of the present calculations. Another possible reason for the incorrect prediction of the gap value is the fact that the Kohn-Scham eigenvalues are not the quasiparticle energies in the excited states. Although it is customary to interpret the difference between the highest occupied and the lowest unoccupied DFT eigenvalues as the true quasiparticle band gap (Eg), this differs in principle from the former (DFT gap) by Δ , the discontinuity in the exchange-correlation potential when an electron is added to the system. The discrepancy between the DFT gap and Eg is known to be large when the Coulomb repulsion of electrons is large as in the case of the transition metal oxides, Mott-Hubbard insulators. However, we present the results obtained by DFT calculations since the ground state properties, such as the lattice constants and relative stability of various phases, are well reproduced, as stated below.

2. SILICIDES, OVERVIEW Most of metal elements make various compounds with silicon. Many of these compounds have been synthesized by sintering the fine powder from a crushed massive material obtained by (1)direct fusion method of the metal and silicon, (2) high temperature reduction of mixed powder of metal oxide and SiO2 by carbon, or (3) reduction of metal oxide by silicon. Recently, thin films or needle-like single crystals have come to be obtained using vapor processes or liquid processes. The list of the known binary compounds of metals and silicon upto now is shown in Figure 1. Most of them are "metal" and some of them show excellent electronic conductivity and durability against high temperature oxidation, which is favorable for an electrode material in high temperature. They are also used as a coating material for the high temperature oxidation in the air of 1500 or more. However, there are several compounds which show semiconducting-like behavior with a monotonous decrease in electric resistivity. Though some of them are not real ‘band’ semiconductor and ’hopping conduction’ of electrons is considered as a cause of this semiconductor-like behavior, there are real band semiconductors such as -FeSi2, BaSi2 and so on. In the following sections, results of their electronic structure calculations will be described. Transition metal silicides and alkali-earth metal silicides will be described separately because of the following reason. In transition metal silicides, the electronegativity of metal and silicon is not different so much and the structural change can be roughly understood by considering the so-called “valence electron concentration (VEC)”, number of valence electrons per metal atom. The structures whose density-of-states (DOSs) at their Fermi level is the least would be an energetically stable among stoichiometrically possible structures in most cases. This suggests that metal silicides with the same group metal elements will have the same structure, or at least, will have nearly the same local configuration of atoms.

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Figure 1. List of binary compounds of metal-Si. Chemical formulae of compounds described here are those conventionally used, but there is room for discussion. For example, ReSi2-x may be described as ReSi1.75 or Re4Si7. B14Si is often described as BnSi, because Si atoms replace part of boron atoms in boron frame found in pure β-boron and also occupy interstitial sites and it is a non-stoichiometric compound. α-Fe2Si5 is the compound usually described as α-FeSi2, the high-temperature modification of disilicides but is considered to have Fe vacancies and the stoichiometric ratio of Fe:Si is nearly equal to 2:5.

On the contrary, electronegativity of alkali (A) and alkali-earth (AE) metal is very weak compared to that of Si. They form silicides which have peculiar characteristics such as, 1)high melting point, sometimes significantly greater than the constituent elements, 2)narrow homogeneity width (i.e. line compounds), 3) high heat of formation, 4)poor conductivity, 5)greater brittleness, 6)most of them are diamagnetic. They have saltlike properties. AE silicides with high ratio of Si to AE are the typical examples of “Zintl” phases where AE donates its valence electron to Si so as to complete the various Si-network. The form of network depends on the size of metal atom to be accommodated in that network and therefore the structure varies with the promotion of the metal atom to the heavier elements. The structure is also affected by pressurization as will be expected.

3.TRANSITION METAL DISILICIDES Most of transition metal （TM） elements form disilicides, MSi2, where M denotes a transition metal. Correlation between the crystal structures of MSi2 and the location of M in the periodic table of the elements is shown in Figure 2.

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Figure 2. Correlation between the crystal structures of transition metal disilicides (MSi2) and the location of M in the periodic table of the elements.

As shown, the number of d-electrons in TM disilicides brings about their structural change from the TiSi2- or ZrSi2-type (disilicides of the 4th group metal), the CrSi2- or MoSi2type (the 5th and the 6th groups), the -FeSi2-type (the 8th group), to the CaF2- type (the 9th and 10th groups) structures. This structural change with increase in number of d-electrons can be roughly summarized as the change from stacking of MSi2 layers of nearly hexagonal arrangement found in the 4th , 5th , and 6th group elements to the nearly cubic coordination of M by Si found in 8th , 9th and 10th group elements, as described later. The 7th group elements (Mn, Tc, Re) do not form stable disilicides but form the compounds of MSi2-x. Among them, CrSi2 and 8th group element (Fe, Os) disilicides are known to be semiconducting. The 8th group element (Ru, Os) also form semiconducting sesquisilicides, M2Si3, as described later. Here, main emphasis will be placed on FeSi2 and the related compounds which are attracting recent attention for possible photoelectronic and thermoelectric devices.

3.1. FeSi2 The Fe-Si phase diagram is composed of five intermetallic compounds (Fe2Si, Fe5Si3, FeSi, FeSi2-low and FeSi2-high), and three solutions (A2 for random bcc, B2 for the CsCltype ordered structure, and DO3 for the BiF3-type ordered structure). Among them, FeSi and β-FeSi2, the lower temperature modification of FeSi2, are semiconductors. β-FeSi2 has attracting an increasing attention since this has a suitable band-gap for applications to photoelectronic devices, a band gap of ca 0.75eV, corresponding to the infrared region (1.65 μm) which is useful for optoelectronic devices integrated on wellestablished Si-technology [2]. It has also been investigated as a thermoelectric energy conversion device at mid temperatures (～500℃)[3] because of its relatively high Seebeck coefficient and stability in high-temperature oxidizing atmosphere.

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β-FeSi2 belongs to the space group of Cmca (No.64) with orthorhombic symmetry. There are two Wyckoff positions for Fe atoms, 8d (0.2146, 0, 0) and 8f (0, 0.8086, 0.1851), and also two Wyckoff positions for Si atoms, 16g (0.1283, 0.2746, 0.0512) and 16g (0.3727, 0.0450, 0.2261). Therefore, the unit cell contains sixteen formula units and the stoichiometric description of the unit cell is Fe16Si32. The unit cell of β-FeSi2 is shown in Figure 3(a) but can be reduced to the primitive cell composed of 24 atoms.

Figure 3. Crystal structures of β-FeSi2, γ-FeSi2 and α-FeSi2. Open circles and closed circles denote Si and Fe, respectively.

This crystal structure looks quite complex but can be regarded as a distorted CaF2-type structure[4]. The disilicides of the neighboring transition metal elements in the periodic table, Co and Ni, are known to have this CaF2-type structure, belonging to the space group of Fm3m with cubic symmetry, but FeSi2 with the CaF2-type structure can exist only in the ultrathin film on Si(111) [5]. This is sometimes referred to as γ-FeSi2 but is not present as an equilibrium phase. In Figure 3, crystal structure of γ-FeSi2 and α-FeSi2, the high temperature modification of FeSi2, are also presented.

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The local atomic configuration around Fe atoms in β-FeSi2 and γ-FeSi2 are compared in Figure 4. Both are surrounded by eight Si atoms; Fe atoms in γ-FeSi2 are located in the center of the cubic of Si but Fe atoms in β-FeSi2 are surrounded by an irregular hexahedron. The structure of α-FeSi2 is much different from β- and γ−FeSi2. The structure of α-FeSi2 is characterized by the presence of Si-Si bonding in the unit cell.

Figure 4. Local atomic configuration around Fe atoms （shown by closed circles）in γ-FeSi2 and βFeSi2 Open circles denote Si atoms.

Figure 5 shows the calculated band structures (BSs) along several high-symmetry lines in the Brillouin zone of β-FeSi2 near their Fermi levels (EF). The energies are shifted so that the top of the valence band is aligned with zero. Plotted in the BS Figure are the numbers which express the order counted from the bottom of the valence band. Because the reduced unit cell of β-FeSi2 contains eight Fe atoms and sixteen Si atoms, 128 valence electrons (eight electrons from each Fe atom and four electrons from each Si atom) are contained in the unit cell, and therefore, 64 bands are fully occupied because there is no overlap in energy between the 64th band (and below) and the 65th band (and above). The valence band maximum of β-FeSi2 is located at Y(-1/2 1/2 0) and a conduction band minimum is located between Γ (0 0 0) and Z (0 0 1/2). The indirect band gap between them was calculated to be 0.79eV which is close to the observed value [6]. The rather flat nature of the BS diagram especially at the conduction band edge was considered to be the reason of the relatively large effective masses. However, observed mobilities for holes and electrons in β-FeSi2 produced by conventional techniques is of the order of several tenths cm2/Vs for electron and of several cm2/Vs for hole at room temperature, much smaller than those expected from the BS diagram and this very poor mobility was regarded as the most important obstruction factor for the practical use of βFeSi2. Now, the reason is considered to be due to scattering by ionized impurities as well as strong electron-phonon scattering and recent elaborate preparation techniques have increased the mobility by magnitude of order of 2 or more [7] and the application has become hopeful.

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Figure 5. Band structure of β-FeSi2. The energies are shifted so that the top of the valence band is aligned with zero. Plotted in this and suceeding band structure (BS) diagrams are the numbers which express the order counted from the bottom of the valence band. The arrow in BS diagrams show transition from the top of the valence band to the bottom of the conduction band.

Comparison of the electronic energies of α-, β- and γ-FeSi2 is shown in Figure 6. The energies shown here were calculated using the density functional theory with the local density approximation with a norm-conserving nonlocal pseudopotential description of electron–core interactions. The calculations have been done for varied volumes of unit cells assuming, (a), the unchanged ratios of the lengths of the unit cell edges parallel to each reference axis, (b), the unchanged interaxial angles, and (c), the unchanged fractional coordinate of each atom, from the observed crystal structure of each phase. Among these phases, β- FeSi2 is correctly predicted to be the lowest in energy. The following is α-phase. The energy minimum is obtained at the equilibrium volume of β-FeSi2 (=37.6x10-3nm3/BaSi2). This is consistent with the phase diagram which shows that α-phase is stable at higher temperature, where entropy term becomes important in free-energy. The contribution of atomic configuration to the entropy term in β- FeSi2 with the complex

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structure will be smaller than that in α-FeSi2 with simpler structure in case the contribution of the lattice vibration are nearly the same.

Figure 6. Comparison of the electronic energies of α-, β- and γ-FeSi2：Variation of their electronic energies with the cell volume. The arrow in the Figure shows the equilibrium cell volume of β-FeSi2 (=37.6x10-3nm3/FeSi2).

The reason of the different total energies of FeSi2’s is demonstrated by Figure 7 which presents the densities of states (DOS) of these phases. In contrast to the semiconducting β-FeSi2, the Fermi level of γ-FeSi2 with the undistorted CaF2 structure is located at the local maximum in the DOS. In β-FeSi2, the gap has opened as a consequence of splitting of the peak of DOS of the fluorite–type structure; a Jahn-Teller distortion of the fluorite–type structure opened the gap [8]. DOS value of α-phase is also small at the Fermi level and electronic energy of α-phase will be lower than that of γ-FeSi2, the DOS of which has a sharp peak at the Fermi level.

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Figure 7. The densities of states of β-, α- and γ-FeSi2. The energies are shifted so that the Fermi level is aligned with zero.

The partial DOSs (PDOSs) calculated for Fe3d,4s,4p and Si3s,3p components for β-FeSi2 are shown in Figure 8. Since there are two inequivalent sites of Fe and Si in β-FeSi2, all the angular momentum projection (s, p, d,･･) on all the atoms are performed but the site dependence of the PDOS of the same kind of atoms can be roughly ignored. As shown in the Figure , the valence band and the conduction band are mainly composed of Fe3d state hybridized with the Si3p state. This can be compared to the alkaline-earth (AE) metal silicides stated later, where contribution of AE d-state to the bands near the Fermi level is smaller even if there is. From the DOS curve and the band structure diagram, β-FeSi2 is an intrinsic semiconductor. However, it is known that not intentionally doped β-FeSi2 is a p-type semiconductor. Therefore, defects in β-FeSi2 seems to play an important role on this nature. To elucidate the effect of defects on the type of conduction, the DOSs of non-stoichiometric β-FeSi2 was calculated.

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Figure 8. Total and partial DOSs of β-FeSi2.

The calculated DOS of β-FeSi2 with Si-vacancies and that with Fe-vacancies near the gap are shown in Figure 9 with that of stoichiometric β-FeSi2. As shown in the Figure s, the Fermi level, shown by the arrow, of Si-deficient β-FeSi2 (Fe32Si63 ) is located a bit higher than the top of valence-band, though some defect levels are formed between the gap. On the contrary, the Fermi level of Fe-deficient β-FeSi2 (Fe31Si64 ) is located at the defect levels formed between the gap. Thus, p-type conduction would be caused by Si-defects. However, the energetic evaluation of defect formation is left for future studies.

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Figure 9. DOS curve of β-FeSi2 with Si-vacancies （Fe32Si63), that with Fe-vacancies （Fe31Si64）, along with that of stoichiometric β-FeSi2. The arrows in the Figure indicate the position of the Fermi level in each.

Also left for future studies is the effect of intentional doping of β-FeSi2. The preliminary studies on the doping effect on the DOS curves are shown in Figure 10. It is known that replacement of Fe in β- FeSi2 by Cr or Mn gives p-type conduction and that by Co or Ni does n-type conduction [9]. These effects can be understood using the rigid band model, where the electronic structures are fixed and different degrees of electron filling are allowed in the band and DOS curves. Co or Ni substituting Fe will supply excessive electrons to fill the gap and will cause the n-type conduction. Substitution of Fe by Cr or Mn will supply deficient electrons to fill the gap and will cause the p-type conduction. However, the ‘ hydrogen-atom model ’ shown below gives the positions of the impurity level too close to the band edge.

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Figure 10. DOS curves of Cr-, Mn-, Co-, and Ni-doped β-FeSi2. The arrows in the Figure indicate the position of the Fermi level in each.

(m0/m*)・(ε-2)・13.6（eV） where m0 is the free electron mass, m* is the effective mass of electron or hole, andε is a static dielectric constant of the semiconductor matrix. If we assume the following values of

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m*≒1.0
m0 [10] and ε =61.6 [11], the above terms mean the generation of impurity levels at about 4 meV higher than the top of the valence band or lower than the bottom of the conduction band. On the contrary, the predicted position of the Fermi level (and shrinkage of band gap accompanied by generation of impurity levels) is closer to the observed behavior [12] though calculated position depends on k-point sampling and has a rather arbitrary nature.

3.2. OsSi2 and Possible RuSi2 Osmium (Os), belonging to the 8th group as well as Fe, forms OsSi2 with the β-FeSi2 type structure which is a semiconductor with wider band-gap than β-FeSi2. Therefore, Os is a candidate doping material to widen the band-gap of β-FeSi2. However, the toxicity of Os limits its applicability. Instead, ruthenium (Ru) is expecting and the Ru-doped β-FeSi2 can be prepared by, for example, sputtering deposition method [13] but the electric properties have not been determined yet. From the viewpoint of band-gap engineering, perfect solid solution of FeSi2-RuSi2 will be hopeful but pure RuSi2 is not present in the Ru-Si system as an equilibrium phase. Ru2Si3 is present as an equilibrium phase, which will be described later. In the Ru-Si system, RuSi2 does not appear and Ru2Si3 is present. In the Fe-Si system, FeSi2 does appear and Fe2Si3 does not. In the Os-Si system, both of OsSi2 and Os2Si3 are present. These should be understood by considering the relative stability of MSi, M2Si3, and MSi with reference to M and Si, which will be published elsewhere.

3.3. TiSi2, CrSi2, MoSi2 and the 7th Group Element Defect-Disilicides TiSi2 has an orthorhombic symmetry, belonging to the space group F ddd (No.70) and a unit cell consists of 24 atoms (Ti8Si16). CrSi2 has a hexagonal symmetry, belonging to the space group P 6222 (No.180) and a unit cell contains 18 atoms (Cr6Si12). MoSi2 has a tetragonal symmetry, belonging to the space group I 4/mmm (No.139) and a unit cell contains 6 atoms (Mo2Si4). Though their structures shown in Figure 11 look complicated, these have a common structural feature, that is, nearly hexagonal M-Si2 layers, and they are generated by changing the stacking sequence of neighboring M-Si2 layers: The TiSi2–type structure contains four layers in an ABCD stacking sequence, the CrSi2 type structure contains three layers, ABC, and the MoSi2-type structure consists of two layers with AB stacking. Since their local atomic configurations are alike, their DOS curves may be nearly the same. The d-states of T, the transition metal atom, will be filled with 10 electrons and the sp state of the Si atoms will be filled by four electrons, 14 valence electrons per T atom (usually referred to as a ‘ valence electron concentration (VEC) ’ )are considered to be just enough to fill these bands when there is no overlap of bonding and antibonding states. If this idea is appropriate, CrSi2, MoSi2 and WSi2 will be semiconductors. However, the band structure calculation shows that CrSi2 is a real semiconductor while MoSi2 and WSi2 are not.

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Figure 11. Crystal structures of TiSi2, CrSi2, and MoSi2. Open circles and closed circles denote Si and Ti (or Cr or Mo), respectively. The solid lines connecting Si atoms show hexagonal arrangement of Si atoms.

Figure 12. Band structures of CrSi2 and MoSi2.

Figure 12 shows the band structure (BS) of CrSi2 and MoSi2. As is shown, there exists definite energy gap in the BS diagram of CrSi2 with the indirect nature, while energy dispersion curve of MoSi2 cross the energy zero (the Fermi level) near P (1/4 1/4 1/4).

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Therefore, MoSi2 is not a semiconductor. Since the calculated DOS curve has a minimum at the Fermi level, it will act as semimetallic conductor. In the end of this section, it should be mentioned here about the 7th group element silicides. Re was previously believed to form ReSi2 and considered to have the MoSi2-type structure. Recent structural investigation by Gottlieb [14] suggests that the stable phase has Si vacancies and that the composition should be described as ReSi1.75 or Re4Si7, which results in the valence electron concentration as (7x4+4x7)/4=14. The calculation showed that the Fermi level exist near the minimum of DOS curve if we assume the stoichiometric ratio of Re to Si is 1:1.75, though clear energy gap could not be obtained. If we take the random distribution of Si vacancy into account, the so-called Anderson localization of wavefunctions will occur and the electric conduction will be determined by variable range hopping of carriers. Semiconducting-like behavior of a monotonous decrease in resistivity with temperature would be observed. Mn is known to have a series of silicides with the formulae of MnSi2-x, which are described in the following section.

4. CHIMNEY-LADDER COMPOUNDS A family of compounds known as Nowotny chimney-ladder (CL) phases are characterized by the composition of TnXm ( m and n are integers with 2>m/n>1.25, T is a transition metal element belonging to the 4th to the 9th group such as Ti, V, Cr, Mo, Mn, Ru, Os, Rh, and Ir, which is in a tetragonal β-Sn arrangement(chimney). X is the 13th or 14th group elements such as Al, Ga, Si, Ge, and Sn) in a coupled helical arrangement (ladder). Compounds belonging to this family have been proposed as advanced thermoelectric energy conversion materials (TE materials) because they have low lattice heat conductivity because of their complex structures [15]. The ‘14 valence electron concentration (VEC) rule’ stated above is sometimes, but not always, valid for CL compounds for predicting semiconducting behavior as stated later. Though compounds with tetragonal symmetry are really CL compounds, compounds such as Ru2Si3 and Ru2Ge3 in low temperature modification with orthorhombic symmetry are also included in this category since their structure is closely related to the CL structure in that two unit cells of Ru2Sn3 placed side by side gives the unit cell of the Ru2Si3-type structure. Both have nearly the same position of the transition elements and the difference between them exists in the Si and Sn ( Ge) position[16]. The structural relationship between the tetragonal phase and orthorhombic phases can be seen, for example, in Figure 1 of the paper by Simkin et al [17]. The band structure Ru2Si3 is shown in Figure 13(a). Since the unit cell is composed of 16 Ru atoms and 24 Si atoms, 224 valence electrons (8 electrons from each Ru atom and 4 electrons from each Si atom) are contained in the unit cell. The gap is being formed between the 112th and the 113th bands, as shown in Figure 13(a). It is characterized by a direct transition at the Γ point of the Brillouin zone, but the conduction band minimum located at Y has neary the same energy and the difference between Γ113 and Y113 is quite small. As for the cases in the Ru2Sn3 type structure, which is properly grouped with the chimney-ladder structure, the unit cell contains 8 Ru atoms and 12 Sn atoms. 112 valence

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electrons (8 electrons from each Ru atom and 4 electrons from each Sn atom) are contained in the unit cell. The gap is being formed between the 56th and the 57th bands. The band structure of Ru2Ge3 in the high temperature modification, which belongs to this type of structure, is shown in Figure 13(b). As is revealed, the band gap is located at the Γ point. The energy band gap decrease in the heavier elements semiconductor results in the closure of the gap of Ru2Sn3. A small overlapping of the conduction band and the valence band at Γ would be responsible for the metallic character of Ru2Sn3 [18]. As for the 6th , 7th and 9th group elements, CL compounds are present which do not necessarily obey the 14 VEC rule. The 6th group elements (Cr and Mo) form CL compounds of Cr11Si19 and Mo13Ge23, the VECs of which are 12.9 and 13.1, respectively. Thus, the Fermi level would be located at a place before the gap of the DOS curve, as shown in Figure 14(b) and (c), and they are metallic. Mn, the 7th group element, forms a series of defect silicides of Mn11Si19 (MnSi1.727), Mn26Si45 （MnSi1.730）Mn15Si26 (MnSi1.722), and Mn27Si47 (MnSi1.741) and they are usually written as MnSi1.75-x. The unit cell of these Mn compounds can be represented as a chain of sublattices extended along the direction of the [001] axis. In all these sublattices the Mn atoms occupy the same position, whereas the coordinates of the Si atoms are of a variable nature.

Figure 13. Band structures of (a), Ru2Si3 and (b), Ru2Ge3 in the high temperature modification.

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Figure 14. DOS curve of Mn11Si19,(a), Cr11Si19, (b), Mo13Ge23, (c), Rh10Ga17, (d), and Rh17Ge22, (e). The energies are shifted so that the Fermi level is aligned with zero.

As shown in Figure 14(a), the Fermi level (EF) of Mn11Si19, is located just below the gap of about 0.7eV. Mn11Si19 is reported to be not a metal but behaves like a p-type

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semiconductor with the band gap of 0.4eV. [19]. Generation of localized energy levels between the gap and random distribution of Si defects would cause the localization of the wavefunction, which result in semiconductor-like conduction as in the case of rhombohedral boron. Iridium (Ir) in the 9th group form CL compounds with Ga and Ge, Ir3Ga5 and Ir4Ge5, the VECs of which are equal to 14. However, the BS diagram of Ir3Ga5 shown in Figures 15(a) and (b). We find intersections of the bands of Ir3Ga5 with the Fermi level, which indicates its whereas the metallic property. As for Ir4Ge5, the conduction band minimum exists at valence band maximum exists at a point between M and . Overlap of the valence and the conduction band is limited near these points, suggesting its semiconducting (or, at least, semimetallic) nature if tendency of underestimation of band gap by the present densityfunctional calculation is allowed. Rhodium (Rh) which also belongs to the 9th group forms Rh10Ga17 and Rh17Ge22 whose VECs exceed 14. The total DOS of these are shown in Figures 14(d) and (e). In contrast to the case of Mn11Si19, their Fermi levels are located at the place of the upward slope which is past the gap of the DOS curve. The value of the DOS at their Fermi levels are of the same order as Mn11Si19, and therefore they may display n-type semiconductor-like behavior if the energy levels near their Fermi levels are fully isolated. However, the experimental data have not been obtained to our knowledge.

5. TRANSITION METAL MONOSILICIDES 5.1. Monosilicides, Overview Most of transition metal elements form monosilicides, MSi, where M denotes a transition metal. Among them, FeSi and RuSi are known to be narrow-gap semiconductors and CoSi to be semimetallic. Crystal structures of transition metal monosilicides are either of five following types; the FeB-type, the CrB-type, the FeSi-type, the MnP-type, or the CsCl-type. The FeSi structure, usually referred to as a B20 structure, is described as a pairing distortion of a face-centered-cubic (fcc) structure (rocksalt structure) in which Fe and Si are displaced along the <111> direction. This displacement reduce the space group symmetry from F m3m to P 213. Both the Fe and Si atoms are locate at the 4a-type sites in the simple cubic unit cell with position coordinates (u,u,u), (1/2+u, 1/2-u, u), (u, 1/2+u,1/2-u) and (1/2-u, u,1/2+u). For FeSi, u(Fe)=0.1358 and u(Si) =0.844 [20]. In passing I might mention that the atom-position parameters of rocksalt structure correspond to the value of u(Fe)=0.25 and u(Si)=0.75, respectively. The CrB-type and the FeB-type structure are characterized by (1)the silicon atoms form zig-zag chains, and (2)the metal atoms have six silicon neighbors and lie in octahedral symmetry. The zig-zag chain in the CrB- type and FeB-type exist on one plane, say the x-y plane. The difference exists in that the phase of the zig-zag chain is coherent in the alternate layer in the z direction in the CrB-type whereas a lag in the half-period exists in the alternate layer in the FeB-type structure.

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The MnP-type structure can be described as the distorted the NiAs-type structure. The transition metal atoms also have six silicon neighbors and lie in octahedral symmetry but the zig-zag chain formed by Si atoms does not exist on one plane. Correlation between the crystal structures of MSi and the location of M in the periodic table of the elements is shown in Figure 16. Monosilicides with the CrB- or the FeB- type structures appear in the earlier part of the transition element. Monosilicides with a MnP-type structure appear in the latter part of the transition metals Transition metals such as Cr, Mn, Fe, and Co, which have medium number of d-electrons, form monosilicides of the FeSi-type of structure. CsCl-type monosilicide appears as the high-temperature modification of RuSi. Their structural trend can be understood qualitatively from the principle that the ‘ DOS at Fermi level would be hopefully smaller in an energetically- favored structure ‘, as shown below. Figure 17 show the position of the Fermi level of the compounds, MSi, written on the DOS curve of the CrB-type, the FeB-type, the FeSi-type and the MnP-type structure, assuming that the ‘rigid band approach’ is valid. Underlined elements mean that the equilibrium structure of MSi has the corresponding structure. As shown, ScSi with the CrB type, TiSi with the FeB type, FeSi and CoSi with the FeSi type, and NiSi with the MnP-type structure have smaller DOS values at their Fermi level, compared to other types of structures. MnSi with the FeSi-type structure have relatively large DOS value but a calculation where the spin polarization is taken gives the split of the DOS curve at the Fermi level, though not shown here, and the system reduces the energy by ferromagnetic spin configuration, which can partly explain the helical spin structure observed.

Figure 15. Band structure of Ir3Ga5 and Ir4Ge5.

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Figure 16. Correlation between the crystal structures of transition metal monosilicides (MSi) and the location of M in the periodic table of the elements.

5.2. FeSi In the preivious section, the structure of FeSi was qualitatively discussed in comparison with other possible structures. The more quantitative analysis for FeSi is given in Figure 18. This presents the total energies of FeSi’s （ε−FeSi, hypothetical FeSi with the NaCl-type structure, and hypothetical FeSi with the CsCl-type structure） calculated using a normconserving nonlocal pseudopotential. Among these phases, ε-FeSi is correctly the lowest in energy. The following is hypothetical FeSi with the CsCl-type structure. The reason of the different total energy is clearly demonstrated by Figure 19 which presents the densities of states (DOSs) of these phases. FeSi wit undistoted NaCl type structure have definite value of DOS at its Fermi level but the distortion stated above cause the perfect split of DOS to open the gap and the shift of the Fermi level to just in the gap of DOS, to make FeSi semiconductor. CsCl-like configuration also makes gap of DOS and total energy of this structure is not so high compared to ε-FeSi. In fact, RuSi have this type of structure at elevated temperatures where entropy effect is more favorable for simpler atomic configurations. The band structure near the Fermi level for FeSi is plotted in Figure 20. Here, each band is two-fold degenerate. Forty-eight electrons per cell, eight from each Fe atom and four from each Si atom, are sufficient to fill the lowest 24 valence bands and the valence band maximum exits along the MΓ, ΓR, or at X, and the conduction band minimum at X , along MΓ or along ΓR. The minimum indirect gap is very close to the minimum direct gap occurs along ΓM.

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Figure 17. Position of the Fermi level of transition metal monosilisides on the DOS curve of the CrB-, FeB-, FeSi- and MnP- type structure assuming the regid band model. Underlined elements mean that the equilibrium structure of MSi has that structure.

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Figure 18. Variation of the electronic energies of FeSi with the ε−FeSi type, the hypothetical NaCltype, and the hypothetical CsCl-type structure with the cell volume. The arrow in the Figure shows the equilibrium cell volume of ε-FeSi (=22.6x10-3nm3/FeSi).

However, the band gap predicted here is much broader than the observed value(～0.05eV). The reason for that is not clarified but the value of the gap would be significantly changed when the spin-orbit coupling is taken into account, where the degeneracy above stated is lifted. FeSi is known to behave similary to the strongly correlated electron systems. Nevertheless, the ground sate properties such as lattice constants are wellreproduced by the band calculation here, as shown by arrows in Figure 18.

6. ALKALINE EARTH METAL DISILICIDES 6.1. Alkaline Earth Metal Disilicides,Overview Hereafter, we describe the results for alkaline earth (AE) metal silicides. Most of the AE disilisides crystallize in either of four structure types that differ characteristically in their silicon sublattices [21].

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A) Isolated Si-tetrahedra separated from each other by more than 1.5 times as large as Si-Si bond distance is the most prominent feature of the orthorhombic BaSi2 type structure (P nma, No.62). BaSi2 has this type structure at normal pressure. The unit cell of BaSi2 is shown in Figure 21 As shown, there are two crystallographically inequivalent sites for Ba (BaI, BaII) and three inequivalent sites for Si (SiIII, SiIV, and SiV). The unit cell contains eight formula units and the stoichiometric description of the unit cell is Ba8Si16. Atoms are distributed over 4 BaI, 4 BaII, 4 SiIII, 4 SiIV, and 8 SiV sites. BaSi2 transforms into the cubic SrSi2 type structure at higher pressure in low temperature below ca 1000 K.

Figure 19. Comparison of the densities of states of FeSi with the ε−FeSi type, the hypothetical NaCltype , and the hypothetical CsCl-type structure.

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Figure 20. Band structure of ε-FeSi. It should be noted that each band (for example, the 23rd and the 24th, the 25th and the 26th , is two-fold degenerate.

B) Three–dimensional (3-D)three－connected network of Si is found in SrSi2 type structure. All Si atoms have three equidistant neighbors in flat trigonal pyramids, but twisted against each other. SrSi2 have this structure (P 4332, No.212) at ambient condition. C) Corrugated layers of three-connected Si atoms with equidistance bonds and equal bond angles are found in this CaSi2 type structure (R 3m, No.166). This is composed of the alternative layer-by-layer packing of the hexagonal Ca layer and the Si layer. D) SrSi2 and CaSi2 transform into the tetragonal ThSi2 type structure (I 41/amd, No.141) at high pressure. Another type of Si network is found, where each silicon atom has three neighbors. They are in planar arrangement and the Si4 groups are twisted alternatively by 90°in the direction of the tetragonal c-axis

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These observed facts imply that the relative stability of these structures has close correlations with the atomic volume of these structures. Therefore, energy variation of these structures with the change of the atomic volume was calculated. The calculated total energy curves of CaSi2 with the CaSi2-type, ThSi2-type, SrSi2 type and BaSi2-type structures are shown in Figure 22 by squares, triangles, circles and crosses, respectively. The energy minima appear in the order of the ThSi2-type, SrSi2-type, CaSi2type, and BaSi2-type. The ThSi2- and SrSi2-type, (3-D network of Si atoms), are favorable for tight packing of the atoms. The layered structure in the CaSi2-type is the next and the BaSi2type, characterized by isolated Si-tetrahedra, is unfavorable to the dense packing of the atoms. This order of the volumes at energy minima is almost common to the other AE disilicides, as will be seen later. The value of the total energy is almost in the order of the BaSi2-, ThSi2-, SrSi2-, and CaSi2-type, though their dependences on the cell-volumes are different.

Figure 21. Crystal structure of BaSi2.

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The broken arrows in the Figure show the values of the volume experimentally determined for the structures of CaSi2-type at normal pressure (65.6x10-3nm3) and ThSi2-type at higher pressure (62.0x10-3nm3, prepared at 4GPa). These values are a bit larger than the volumes at energy minima of the total energy curves of each phase (about 63x10-3nm3 for CaSi2-type and about 60x10-3nm3 for ThSi2-type), as is consistent with general tendency that DFT calculation is likely to underestimate the cell volume. The energy of CaSi2-type structure has the largest negative value among the structures considered at that volume (65.6x10-3nm3, shown by a closed square), and this agrees with the fact that CaSi2 is the stable phase at normal pressure. On the contrary, the energy of ThSi2-type at the volume of 62.0x10-3nm3 shown by a closed triangle was about 0.05eV larger than CaSi2-type, which disagrees with the fact that ThSi2-type is stable at higher pressure.

Figure 22. Calculated variation of the electronic energy of CaSi2 with the CaSi2 type (□,■), ThSi2 type ( , ▲), SrSi2 type(○) and BaSi2 type(ｘ) structures. The arrows in the Figure show the values of the volumes experimentally determined for CaSi2-type structure at normal pressure and ThSi2-type at higher pressure (prepared at 4GPa, 1273 K ). The closed symbols mean the energies at the equilibrim volume experimentally determined.

However, it should be noted that the energy minimum of the ThSi2-type structure is located at the cell volume of about 60x10-3nm3 and the total energy of ThSi2-type at that cell volume is more negative than that of CaSi2-type. Small discrepancy between the predicted cell volume and the observed cell volume may lead to the erroneous conclusion in case such a small energy difference among the different crystal structures is the matter. Figures 23 and 24 give corresponding relation for SrSi2 and BaSi2, respectively. They give relatively reliable results for prediction of the phases which appear under ambient and high pressures, though the cell volumes predicted from the energy minima are a bit smaller than the experimental values.

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Figure 23. Calculated variation of the electronic energies of SrSi2 with the CaSi2 type(□), ThSi2 type ( , ▲), SrSi2 type(○, ●) and BaSi2 type(x) structures. The arrows in the Figure show the values of the volumes experimentally determined for SrSi2-type structure at normal pressure and ThSi2-type at higher pressure (prepared at 4GPa, 1273 K). The closed symbols mean the energies at the equilibrium volume experimentally determined.

Figure 24. Calculated variation of the electronic energies of BaSi2 with the CaSi2 type(□), ThSi2 type ( ), SrSi2 type(○, ●) and BaSi2 type(x) structures. The arrows in the Figure show the values of the volumes experimentally determined for the BaSi2-type structure at normal pressure and the ThSi2-type at higher pressure (prepared at 4GPa, 1273 K). The closed or bold symbol mean the energy at the equilibrim volume experimentally determined.

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6.2. BaSi2 and SrSi2 Figure 25 shows the band structures along several high-symmetry lines in the Brillouin zone of BaSi2 near their Fermi levels. Plotted in the BS Figure are the numbers which express the order counted from the bottom of the valence band.

Figure 25. Band structure of BaSi2. The energies are shifted so that the top of the valence band is aligned with zero.

Because the unit cell of this alloy contains eight Ba atoms and sixteen Si atoms, 80 valence electrons (two electrons from each Ba atom and four electrons from each Si atom) are contained in the unit cell, and therefore, 40 bands are fully occupied because there is no overlap in energy between the 40th band (and below) and the 41st band (and above).

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The valence band maximum of BaSi2 is between Γ (0 0 0) and Y (0 1/2 0) and a conduction band minimum is located at T (0 1/2 1/2). The indirect band gap between them was calculated to be 0.72eV, 60 % of the observed value (1.3 eV) and this is a typical example which indicate the underestimation of the gap by DFT calculation. Figure 26 shows the calculated total DOS of BaSi2 and its angular momentum projection to give the partial DOS(PDOS) near the Fermi level. The site dependence of the PDOS of the same kind of atoms can be roughly ignored. .As shown, the valence band edge is mainly composed of Si 3p .. The conduction band edge is mainly composed of Si3p hybridized with the Ba 5d.

Figure 26. Total and partial DOSs of BaSi2.

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Figure 27. Band structure of SrSi2.

BaSi2 thin film is expected as a good candidate for high-efficiency thin-film solar cells [22]. Its band gap value (Eg) is closer to the ideal value (ca 1.4eV) than silicon (Si, Eg is 1.1eV) which is now predominantly used for solar cell materials. In addition, BaSi2 has also much higher optical absorption coefficient than Si. The band structure of SrSi2 is shown in Figure 27. The top of the valence band, the 20th band, is located between Γ and X . The energy minimum of the lowest conduction band, the 21st band, is located between Γ and M . The unit cell (Sr4Si8) contains 40 valence electrons and, therefore, 20 bands are fully occupied. The energy difference between the top of the 20th band and the bottom of the 21st band was calculated to be 3meV, which is much lower than the observed value of 35meV [23], and again the gap is underestimated However, the

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decreasing tendency of the gap by pressurization [24] is known to be well reproduced by the calculations, though not shown here.

7. ALKALINE EARTH METAL HALF SILICIDES Though alkaline earth metal monosilicides (CaSi, SrSi and BaSi) are metallic, half silicides of Mg2Si, Ca2Si and Sr2Si.are semiconductors. Mg2Si has an anti-CaF2 type structure (F m3m, No.225) but Ca2Si and Sr2Si has the structure belonging to the space group of P nma, No.62 with orthorhombic symmetry. This structure is sometimes referred to as the Co2Si-type or the anti-PbCl2 type but we call this the Ca2Si-type here for simplicity.

Figure 28. Band structure of Mg2Si. The energies are shifted so that the Fermi level is aligned with zero.

Calculated band structures of Mg2Si and Ca2Si are presented in Figures28 and 29, respectively, in parallel with the DOS curves. As seen from the Figure s, Mg2Si is predicted to have an indirect band gap from Γ to X of 0.28eV, which is less than half of the observed value, 0.77eV. Ca2Si are predicted to have a direct band gap of 0.36eV., which is much less than observed value of 1.9eV. Again calculated values are much lower than the observed

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values but shows anyhow that Ca2Si is a semiconductor. Sr2Si, which has the same crystal structure with Ca2Si, has nearly the same band structure with Ca2Si and have a bit wider direct band gap of 0.402eV at Γ.

Figure 29. Band structure of Ca2Si.

8. ALKALINE EARTH METAL PNICRIDES Recently, Kajikawa et al. proposed that semiconducting Mg pnictides can be better thermoelectric (TE) materials than Mg2Si-Mg2Ge alloy, which has been investigated as a promising TE material, because they are composed of elements heavier than Si or Ge and would have lower lattice thermal conductivities [25]. Mg is known to form a series of intermetallic compounds with the 15th group elements (Pnicogens (Pn); N, P, As, Sb and Bi), the formulas of which are expressed as Mg3Pn2. Mg3Pn2 are known to have either the crystal structure of a), a cubic structure of the Mn2O3

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type or b), a hexagonal structure of the La2O3 type. The unit cell of the former is composed of 80 atoms, 48 Mg and 32 Pn, and belongs to the space group of I a3 (206), which can be reduced to the primitive cell composed of 40 atoms. The unit cell of the latter is composed of 5 atoms, 3 Mg and 2 Pn, and belongs to the space group of P 3m1 (164). Mg3N2 and Mg3P2 are known to have the Mn2O3-type structure. Mg3As2 also has this type of structure at ambient temperature, but changes to the La2O3-type structure at about 1323Ｋ. On the contrary, Mg3Sb2 has the La2O3-type structure below 1203 K, but has the Mn2O3-type structure above that temperature. Mg3Bi2 has also La2O3-type structure at the ambient temperature.

Figure 30. Band structure of Mg3Sb2.

Figure 30 shows the band structure (BS) of Mg3Sb2 along the high symmetry directions of the Brillouin zone near the Fermi level. The gap value is about 0.41eV. The bottom of the conduction band, the 9th band, is located at K. The band gap is indirect with the top of the valence band (the 8th band) at Γ. The gap value between them is about 0.41eV. There seems to be no recent measurements of the band gap of crystalline Mg3Sb2. However, Verbrugge and Zytveld [26] estimated the gap of the liquid phase of Mg3Sb2 as 0.8eV.

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The band structure of Mg3As2 in the high-temperature modification, not shown here, indicates that both of the top of the valence band and the bottom of the conduction band are located at Γ and the energy gap between Γ8 and Γ9 is estimated to be 1.1eV. However, the energy difference between the Γ, K and the state along the line M-L of the 9th band is about 0.05eV or less and it is difficult to state definitely that the gap is direct or indirect. In the band diagram of Mg3Bi2, we find contact of the valence band maximum and the conduction band minimum at Γ , and it is predicted to be a semimetal. Therefore, the turn of the band gaps of these are as follows: Mg3As2 > Mg3Sb2 > Mg3Bi2.

Figure 31. Band structure of low-temperature modification of Mg3As2. The energies are shifted so that the top of the valence band is aligned with zero.

Figure 31 shows their calculated band structure of Mg3As2 (low temperature phase) with the Mn2O3 type structure.

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As are shown, that is a semiconductors with the direct band gap of 1.57eV. The same can be said for Mg3N2and Mg3P2 with the gap values of 1.64eV (Mg3N2) and 1.73eV (Mg3P2). Reckeweg et al. [27] determined the energy gap of Mg3N2 to be 2.8eV using optical diffusereflectance spectra. Our result for Mg3N2 is about 60% of the observed value, as is often the case when using the density functional method. As for Mg3As2, our value calculated is about 70% of the observed value of 2.2eV [28]. There are no available data for the observed gap value of Mg3P2 as a comparison. One may assume that a monotonic shift for a band gap in the systematic calculations going from Mg3N2 to Mg3P2 and to Mg3As2 would be natural as in the case of Mg3Pn2 with the La2O3-type structure. The reason for the difference in the expected tendency and the calculated result is not clear at present, but there are several factors which may influence the gap value. For example, Larson et al.[29] carried out systematic calculations of the electronic structure of YNiPn where Pn is a pnicogen element. A decrease in the gap was observed as one goes from As to Bi. On the contrary, broadening of the band gap upon going to heavier elements is observed in the series of transition metal disilicides and sesqui-silicides, which may be caused by the enhanced effect of hybridization in the heavier elements for which the energy difference between higher orbitals is smaller. The apparent complex tendency of the gap broadening in the present case may be caused by these opposite factors. In addition, relativistic effect (massvelocity term and Darwin term) will predict complex effect on the band structures of the heavier element compounds [30] though the present calculations do not treat that explicitly but through the pseudopotentials.

9. IRON GROUP ALUMINIDES AND GALLIDES (FEGA3) The 8th group elements (Fe, Ru and Os) make semiconducting aluminides, Gallides and Indiumides. They are classified into two groups; chimney-ladder compounds which has been described above and compounds of the FeGa3-type structure. RuAl2 and RuGa2 belong to the former, which obey the 14 VEC rule. FeGa3, RuGa3, OsGa3, and RuIn3 belongs to the latter. Though they were considered to have the CoGa3-type structure and belong to the space group of P4n2 (No.118) [31,32], recent studies describe them as belonging to the space group of P 42/mnm ( No.136) [33. 34]. Energetic consideration supports the latter type of structure for semiconducting compounds [35]. Here, their band structures are described assuming that they have the latter crystal structure. Figure 32 shows the BS diagram of FeGa3. The valence band maximum occurs at A and the conduction band minimum occurs at a point between Z and Γ. The band gap of the FeGa3 structure is 0.496eV. The observed band gap by Häussermann et al. [36] is 0.3eV and that by Amagai et al. [37] is 0.26 eV Their value is smaller than the value predicted by the present calculation. It is contrary to the general tendency that DFT calculation will give narrower gap than the observed value. The reason is not clarified but study of the precise structure refinement of the prepared samples will be necessary since slight deviations from stoichiometric ratio due to defects or small amount of impurity would cause a shift of the Fermi level into the conduction band or the valence band and they can be the possible reason for the discrepancy between the calculated gap values and observed values.

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As for other compounds, OsGa3, RuGa3, and RuIn3, the band structure diagrams have almost the same features; the valence band maximum occurs at A or at a point near A between A and R or between A and Z. The conduction band minimum occurs at a point between Z and Γ. The gap values are calculated to be 0.68eV for OsGa3.,0.26eV for RuGa3, and 0.30eV for RuIn3.

Figure 32. Band structure of FeGa3.

12. SUMMARY In this paper, results on electronic structure calculation of intermetallic semiconductors have been presented. The compounds taken are transition metal silicides, chimney ladder compounds, alkaline earth metal silicides, alkaline earth metal pnictides, and iron group element aluminides and gallides. These are attracting since they have favorable band gaps and

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this gap can be controlled by alloying with the same group element, though little can be described here. Recent investigation clarified, for example, possibility of band gap tuning of BaSi2 by alloying with Sr to increase the efficiency of solar energy conversion. However, realization of these techniques is still in the early stage and there seems to be much room for investigation. In addition, there are many intermetallic semiconductors not included in this article such as a Half-Heusler alloy. This has the MgAgAs-type structure and composed of transitition metals and a sp metal such as Al and Sb. It has been clarified that the idea of valence electron concentration (VEC) is also important for judging its semiconductivity. Alloys with VEC=18 are attracting intention for thermoelectric materials to be used at relatively low temperature since this is a narrow band-gap semiconductor whose electronic properties can be changed by fine tuning of band gap using a partial substitution of constituent metal atoms. These examples show broad capability of intermetallic semiconductors.

REFERENCES [1]

International symposium on semiconductingt silicides have been performed since 1999 and the manuscripts presented there were published in Thin Solid Films Vol.381 (2001) 171-302 and in Vol. 461 (2004) 2-226, and will be in July 2007. [2-1] J.Derrien, J.Chevrien, V.Le Thanh, J.E.Mahan, Appl. Surface. Sci. 56 (1992) 382, and references therein. [2-2] E.Arushanov, E.Bucher, Ch.Kloc, O.Kulikova, L.Kulyk, A.Siminel, Phys. Rev., B52 (1995). [3] See, for review of thermoelectric behaviors of FeSi2, U.Birkholz, E.Gross, in “Thermoelectrics” ed. by M. Rowe, (CRC press, 1994) p.287. Also see many papers related to the thermoelectric energy conversion published in “International Conference on Thermoelectrics” held at Dresden in 1997, Nagoya in 1998, Baltimore in1999, Cardiff in 2000, Beijing in 2001, Long Beach in 2002, La Grande-Motte in 2003, Adelaide in 2004, Clemson in 2005, and Vienna in 2006. [4] P. Y. Dusausoy, J. Protas, R.Wandji, B.Roques, Acta Crystallogr. B27, 1209 (1971). [5] N. Onda, J. Henz, E. Muller, K. A. Mader, H. von Kanel, Appl. Surf. Sci., 56, 421 (1992). [6-1] C. A. Dimitriadis, J. H. Werner, S. Logothetidis, M.Stutzmann, J. Weber, R. Nesper, J. Appl. Phys. 68, 1726 (1990). [6-2] H. Lange, Phys. Stat. Sol. B201 (1997) 3 and references therein. [7] K. Takakura, H. Ohyama, K. Takarabe, T. Suemasu, F. Hasegawa, J. Appl. Phys., 97 (2005) Article No.093716. [8] N. E. Christensen, Phys. Rev. B 42: (1990) 7148. [9] M. Komabayashi, K. Hijikata, S. Ido, Jpn. J. Appl. Phys., 30 (1991) 331. [10] E.Arushanov, Ch. Kloc, E.Bucher, Phys. Rev., B50 (1994) 2653. [11] U. Birkholz, H. Finkenrath, J. Naegele, N.Uhle, phys. stat. sol., 30 (1968) K81. [12] D.Panknin, E.Wieser, W.Skorupa, W.Henrion, H. Lange, Appl. Phys., A62 (1996) 155. [13] T. Tsunoda, M. Mukaida, Y. Imai, Thin Solid Films, 381 (2001)296.

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[14] U. Gottlieb, B. Lambert-Anderson, F. Nava, M. Affronte, O. Laborde, A. Rouault., R. Madar., J. Appl. Phys. ; 78 (1995) 3902. [15] T. Caillat,.J. –P.. Fleurial , A. Borshchevsky, J. Alloys Compounds., 252 (1997) 12. [16] D. J. Poutcharovsky E. Parthe , Acta Cryst, B30 (1974) 2692. [17] B. A. Simkin, A. Ishida, N. L. Okamoto, K. Kishida, K. Tanaka, H. Inui, Acta Materialia, 54 (2006) 2857. [18] C. P. Susz, J. Muller, K. Yvon,E. Parthe, J. Less Common Met., 71 (1980) P1. [19-1] Nishida I, J. Mat. Sci.,;7(1972) 435. [19-2] Nikitin EN., Tarasov VI, Tamarin PV, Soviet Physics - Solid State, 11(1969) 187. [20] H.Watanabe, H.Yamazaki, K.Ito, J. Phys. Soc. Jpn, 18 995(1963) 13. [21] See, for example, Wells, A. F., “Structural Inorganic Chemistry” 5th ed., (1984, Oxford University Press, Oxford, UK) p.987-991. [22] Morita K. Inomata Y. Suemasu T. Thin Solid Films 508 (2006) 363. [23] Imai M, Naka T, Furubayashi T, .Abe H, Appl. Phys. Lett, 86 (2005) 32102. [24] M. Imai, T. Naka, H. Abe, T. Furubayashi, Intermetallics 15 (2007) 956. [25] T. Kajikawa, N. Kimura, T.Yokoyama, Proc. 22nd Int, Conf.Thermoelectrics, (2003) 305-308nd. [26] D. M. Verbrugge, J. B.Van Zytveld, J. Non-Crystalline Solids, 156-158 (1993) 736 [27] O. Recheweg, C. Lind, A. Simon, F. J. DiSalvo, Zeit fur Naturforschung B –J. Chem.. Sci., 58 (2003) 159. [28] K. Pigon, Helv. Phys. Acta 41 (1968) 1104. [29] P. Larson, S. D. Mobanti, Phys. Rev. B59 (1999) 15660. [30] See, for example, G. M. Fehrenback, H. Bross, Eur. Phys. J., B 9 (1999) 37. [31] K. Schubert, H. L. Lukas, H. –G. Meissner,S. Bhan, Zeit. Metallkunde, 50 (1959) 534. [32] C. Dasarathy , W. Hume-Rothery , Proc. Ｒoy Soc London Ser A, 286 (1965) 141. [33] C. Tao-Fan , L. Ching-Kwei , Chinese J. Phys, 22 (1966) 952. [34] S. S. Lu, L. Ching-Kwei, Chinese J. Phys., 21 (1965) 1079. [35] Y.Imai, A.Watanabe, Intermetallics 14 (2006) 722. [36] U. Häussermann, M. Boström, P. Viklund, ö. Rapp, T. Björängen, J. Solid State Chem., 165 (2002) 94. [37] Y. Amagai , A. Yamamoto,T. Iida, Y. Takanashi, J. Appl. Phys. 96 .(2004) 5644.

In: Intermetallics Research Progress Editor: Yakov N. Berdovsky, pp. 213-235

ISBN: 978-1-60021-982-5 © 2008 Nova Science Publishers, Inc.

Chapter 5

DUCTILE, STOICHIOMETRIC B2 INTERMETALLICS Alan M. Russell∗ Materials Science and Engineering Department, and Materials Engineering Physics Program, Ames Laboratory, USDoE Iowa State University, Ames, IA, 50011, USA

ABSTRACT A growing number of B2 intermetallic compounds has been reported to exhibit high room temperature tensile ductility in the polycrystalline form when tested in normal room air at ambient temperature. These are noteworthy findings, since poor room temperature ductility and low fracture toughness are major impediments to wider engineering use of intermetallic compounds [1]. Most intermetallic compounds can achieve high tensile ductility at room temperature only by means of one or more “contrivances”, such as testing single crystals, testing in an ultra-dry atmosphere, testing specimens with a metastable disordered crystal structure, or testing compositions that are off-stoichiometry or to which third elements have been added. The first of these inherently ductile compounds, AgMg, was reported in the early 1960’s to have good room temperature tensile ductility without the need for any of these contrivances. A few years later, even greater room temperature ductility was reported for another B2 compound, AuZn. Within the past few years, similar reports have been made for B2 CoZr and a large family of rare earth B2 intermetallics (DyCu, YAg, YCu, and several others). Most of these compounds share several common characteristics: substantial differences in the atomic radii and electronegativities of the two constituent elements; existence in the binary equilibrium phase diagram as a Daltonide, linecompound with no perceptible deviation allowed from precise equimolar stoichiometry; the absence of stress-induced twinning or shape-memory-type phase transformations; and a positive temperature dependence of yield strength above room temperature. This chapter describes the experimental findings reported for these materials; the factors thought to contribute to their high ductility; the commonly observed yield strength maxima at elevated temperatures; the strain aging effects seen in some of these materials; the potential applications these materials may have; and the possibilities that “lessons

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Alan M. Russell learned” from their study may suggest ductilizing strategies that could be applied to other intermetallic compounds.

1. INTRODUCTION AND EXPERIMENTAL FINDINGS 1.1. Background Information on Ductility in Intermetallics As a general rule, intermetallic compounds have low tensile ductility and low fracture toughness at room temperature. If struck with a hammer, they shatter rather than dent. There are numerous exceptions to this rule, but these exceptions typically involve one or more special circumstances or contrivances that must be invoked to achieve ductility. These contrivances include: •

Tensile tests performed on single crystals – Tensile ductility in single crystal intermetallic compounds can be quite high, even in materials with little or no polycrystalline tensile ductility. If a material has even one active slip system and the tensile specimen is oriented to give a reasonably high Schmid factor for that slip system, dislocations can glide relatively unimpeded over long distances, resulting in substantial elongation before fracture occurs. For example, polycrystalline NiAl has at most 1 to 2% tensile elongation [2]. Yet NiAl single crystals have been reported to elongate as much as 16 to 28% in tension at room temperature; the larger elongations occur in crystals pre-strained in compression to clear dislocations from large subgrain regions [3,4].

The reason for the large disparity between polycrystalline and single crystal ductilities was described by von Mises 80 years ago. In a polycrystalline metal, shape changes are required in almost every conceivable direction in each deforming grain to prevent void generation at grain boundaries that leads to rapid fracture. In his seminal paper on ductility in polycrystalline metals [5], von Mises stated that five independent slip systems must operate in a plastically deforming polycrystalline metal to accommodate the complicated strain requirements imposed by grain boundaries. This requirement has come to be known as the von Mises criterion. In this context a slip system is defined to be independent of other slip systems if its operation changes the shape of the crystal in a way that cannot be duplicated by combinations of slip on the other slip systems [6,7]. Thus, by von Mises’ definition, an FCC crystal deforming by <110>{111} slip possesses not just one slip system, but all five of the independent slip systems required (Table 1). In the case of NiAl, room temperature slip is restricted to only the <100> directions; this means that the crystal cannot be directly elongated or compressed in a <100> direction because the Schmid factors are all zero for such slip. As a result, NiAl possesses only three of the required five independent slip systems, and polycrystalline NiAl fractures after little or no tensile elongation. •

Compositions that are “off-stoichiometry” – Many binary intermetallics can maintain the crystal structure of the stoichiometric compound even when the composition deviates by several atomic per cent from stoichiometry. This is accomplished by substituting atoms of the “wrong” element on some lattice sites

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(anti-site defects) or by leaving some lattice sites vacant. For many compounds, tensile ductility increases sharply as composition deviates from stoichiometry. For example, polycrystalline Co3Ti, an L12 structure compound, will elongate 58% before fracture when the composition is Co0.80Ti0.20, but ductility approaches zero as composition approaches Co0.75Ti0.25 [8]. Several other intermetallics behave similarly. Table 1. Slip systems and independent slip systems as defined by von Mises, for B2 compounds [7] Slip Families {011}<100> {011}<011> {011}<100> + {011}<110> {100}<011> {011}<100> + {100}<011> {011}<111> {112}<111> {111}<110>

Number of Physically Distinct Slip Systems 6 6 12 6 12 12 12 12

Number of Independent Slip Systems (von Mises) 3 2 5 3 3 5 5 5

It might seem that the remarkable improvement in ductility sometimes seen in offstoichiometric intermetallics solves the brittleness problem, thereby permitting wider use of these materials in engineering applications. But, regrettably, some of the other properties that make intermetallic compounds so appealing to the design engineer (e.g., high strength and high creep resistance) degrade sharply as compositions depart from stoichiometry. •

•

Compositions that have a third element added – Ternary intermetallics often possess better ductility than binary intermetallics. For example, polycrystalline NiAl has near zero tensile elongation at room temperature, but addition of Fe, Co, or Cr substantially raises room-temperature tensile ductility by introducing a ductile FCC solid solution phase at the B2 grain boundaries [9]. Tensile tests performed in vacuum or ultra-dry atmospheres – A number of intermetallic compounds display much higher tensile ductility when they are tested in atmospheres devoid of H2O vapor. The so-called environmental embrittlement effect in intermetallics exposed to water vapor is believed to result from reactions on the material’s surface of the type: 2Al + 3H2O → Al2O3 + 6H

The H produced by this reaction is then thought to diffuse rapidly along grain boundaries, weakening them and causing intergranular fracture. For example, tests of two compositions (24 at.% Al and 23.5 at.% Al) of boron-free, recrystallized Ni3Al performed in air showed 2.5% tensile elongation, while tests of the same materials in ultra-dry oxygen produced 7-8% tensile elongation [10]. Fracture toughness also improves markedly in H20-free environments.

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KJmax values in off-stoichiometric iron aluminides more than double when tested in ultra-dry oxygen rather than in room air [11]. •

Specimens that have been quenched from high temperature to preserve a metastable, disordered crystal structure – The ordered crystal structures of intermetallics increase yield and ultimate strengths, improve creep resistance, and slow diffusion, but they also tend to lower ductility because dislocation motion is inhibited by the ordered structure. Many intermetallics have a transformation temperature, above which the ordered crystal structure is replaced by a random solid solution. Material quenched from above this transformation temperature can often retain its disordered structure as a metastable phase at room temperature, and such disordered alloys generally have greater ductility than material of the same composition with the equilibrium ordered structure.

The β−β’ transformation in Cu-Zn, for example, occurs at 460˚C. Above this temperature, β phase is a ductile, disordered BCC solid solution; below this temperature β' has the ordered B2 (CsCl-type) structure and is brittle at room temperature. Metastable β quenched to room temperature is ductile at 20˚C. •

•

Specimens tensile tested under high hydrostatic pressure to suppress fracture – The dominant failure mode for brittle intermetallics is Mode I crack propagation. Since large hydrostatic pressures act to push cracks closed, brittle intermetallics display greater tensile elongations if they are tensile tested under high hydrostatic pressure. For example, NiAl has almost no tensile ductility at ambient temperature and pressure, but when tensile tested at 20˚C under 300 MPa hydrostatic pressure the ductility increases to 4.6% elongation, and at 500 MPa pressure to more than 10% elongation [12]. This ductility increase is attributed to (1) pressure-generated formation of mobile dislocations at grain boundaries and second-phase boundaries, and (2) suppression of void nucleation and crack propagation by the applied external pressure. Materials that display superelasticity (i.e., shape memory effect) due to stressinduced transformations between two different crystal structures – A small number of intermetallic compounds have stress-induced phase transformations that allow them to deform extensively by transforming to another crystal structure. As soon as the stress is removed, however, the metal reverts to its original crystal structure and the geometry it had prior to deformation (the “shape memory effect”). The bestknown of these compounds is the NiTi compound (NITINOL), which has a B2 crystal structure at higher temperatures and a distorted tetragonal structure as the product of its stress-induced martensitic transformation [13]. NITINOL has seen numerous applications in eyeglass frames, stents, and related devices.

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1.2. Ductility in the B2 AgMg Intermetallic Compound Until recently, very few reports existed of intermetallics that are inherently ductile at room temperature without relying upon one of more of the above contrivances. The first such report was published by Wood and Westbrook in 1962 for AgMg [14]. AgMg is a B2 ordered compound at all temperatures below its congruent melting point (820˚C). It tolerates large deviations from stoichiometry, retaining a one-phase B2 structure by substitutional defects over the range of 41 to 53 at.% Mg at 300˚C. Wood and Westbrook reported [14] that AgMg deforms by dislocation glide between room temperature and about 400˚C, with solute-dislocation interactions (e.g., yield point drops, large strain rate sensitivity) becoming quite pronounced in the temperature range 150˚ to 350˚C. Tensile ductilities at fracture were not reported, but many specimens were strained to 8% elongation without fracture, which is a much greater elongation than would typically be observed for a polycrystalline, stoichiometric B2 material at room temperature. Measurements of the stored energy in AgMg specimens deformed at room temperature show greater amounts of stored energy in AgMg than would be seen in most other metallic materials. This is thought to result from the disordering effect of plastic deformation in AgMg [15]. Stoichiometric AgMg also displays substantial ductility in torsion at room temperature [16]; torsion strains of 0.045 are tolerated at room temperature in 50.1 at.%Mg-49.9 at.%Ag (torsion strain is expressed by the dimensionless parameter nd/L, where n is the number of turns of a wire specimen (360˚ of torsional rotation around the wire centerline being one turn), d is the wire diameter, and L is the gauge length deforming in torsion). The ductilebrittle transition in stoichiometric AgMg occurs near room temperature. Off-stoichiometry AgMg (44.2 at.%Mg-55.8 at.%Ag) is ductile at room temperature and also at cryogenic temperatures, tolerating a torsion strain of 0.045 at 195 K and 0.022 at 77 K. The degree of strain-induced disorder is estimated to be about 3% in stoichiometric AgMg cold-worked 4% [16]. Recovery in plastically deformed, stoichiometric AgMg is slow at room temperature, but can be completed in 15 minutes at 160˚C. Recovery is thought to begin by vacancy migration, but dislocation motion becomes an important contributor to removing disorder as recovery progresses. Recovery occurs gradually at room temperature in cold-worked 44.2 at.%Mg-55.8 at.%Ag, suggesting that room temperature deformation should be considered "warm-work" for that composition. The active slip system in AgMg was reported by Rachinger and Cottrell [17] to be {321}<111>. In addition, {211}<111> and {110}<111> slip were reported by Westbrook and Wood [14]. These three slip systems, of course, are the slip systems active in simple BCC metals such as Fe, and <111> slip satisfies the von Mises criterion for polycrystalline ductility. Mobile <111> dislocations are consistent with high ductility, but they seem somewhat surprising in an intermetallic compound of Ag and Mg. Dislocation motion would either have to occur by dislocations with a full <111> displacement for the Burgers vectors or by superdislocation pairs, which create an anti-phase boundary (APB) between two 1/2<111> dislocations gliding in tandem (Figure 1). Since dislocation line tension scales as the square of Burgers vector length, a full <111> dislocation would be expected to have a much higher energy than dislocations moving in other slip directions, such as the more commonly seen {110}<001> and {100}<001> slip in B2 crystals. Ag and Mg differ appreciably in both electronegativity (eN=0.7 Paulings) and atomic radius (0.016 nm or 10%), so the APB energy

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associated with having atoms on the “wrong” sites might be expected to be significant in this material. However, that observation is seemingly contradicted by the large deviations AgMg tolerates from equi-molar stoichiometry, which Jena, et alia, report to be accommodated by anti-site substitutional atoms [16].

Figure 1. The B2 crystal structure with ½<111> and <001> dislocation Burgers vectors marked. The {001} and {110} slip planes are shaded. (Atoms drawn disproportionately small for clarity).

Figure 2. Stress-strain plots at various temperatures for AgMg ( εÝ= 2(10-4) s-1) and NiAl ( εÝ= 1.4(10-3) s-1). Redrawn from [18] and [19].

The ductility of stoichiometric AgMg is clearly superior to that of most B2 intermetallics. However, room temperature appears to be near the ductile-brittle transition temperature of

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AgMg, and room temperature is 27% of AgMg’s 1093 K melting temperature. For comparison (Figure 2), the well-studied NiAl B2 intermetallic shows 4% tensile elongation when tested at 25% of its 1912 K melting temperature and 30% elongation when tested at 35% of its melting temperature [18]. It is noteworthy that none of the various papers on AgMg mechanical properties reported XRD results on the degree of ordering, which leaves open the possibility that the materials were not fully ordered. For these reasons, AgMg is considered an interesting ductile intermetallic, but its room temperature ductility is partially attributable to its somewhat low melting point, and it does not appear to be a “breakthrough” discovery in intermetallic ductility.

1.3. Ductility in the B2 AuZn Intermetallic Compound High room-temperature ductility was reported in 1970 for polycrystalline β'-AuZn, a compound with the B2 crystal structure at all temperatures below its congruent melting point (725˚C). Although room temperature is 30% of AuZn’s melting temperature, AuZn is ductile at less than 10% of its melting temperature, which defines a much lower homologous temperature ductility range than is seen in AgMg. AuZn tolerates significant deviations from stoichiometry, retaining a one-phase B2 structure by substitutional anti-site defects over the range of 47.5 to 52 at.% Au at 20˚C [20]. A study by Causey and Teghtsoonian [21] of the tensile ductility of various AuZn compositions reported high ductility in stoichiometric, polycrystalline AuZn over the temperature range 77 to 533 K (Figure 3). Room temperature ductility was 33% elongation, and even at liquid nitrogen temperature the tensile elongation was 13%. Failure occurred by intergranular fracture. Serrated yielding was observed in non-stoichiometric AuZn specimens at room temperature, but serrated yielding was not observed in the stoichiometric specimens. Deformation twinning is not seen in AuZn, which is consistent with theorists’ predictions [22] that such twinning is unlikely to occur in ordered compounds.

Figure 3. Tensile elongation of AuZn intermetallic at various temperatures ( εÝ= 1.6(10-3) s-1). Redrawn from [21].

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AuZn specimens display a high work hardening rate. The θ/G ratio (where θ is the work hardening rate and G is the shear modulus) is about 50 times greater for AuZn than for most ordinary metals. The high work hardening rate is attributed to dislocation intersections resulting from dislocation motion on two active slip systems. Deformation occurring by slip in both <001> and <111> directions would be expected to cause frequent dislocation intersections, which is consistent with the high work hardening rate observed. Study of single crystal AuZn [23] indicated that slip at room temperature occurs primarily in the <001> direction, but that slip occurs on the {211}<111> slip system when the specimen is oriented with the tensile axis nearly parallel to the <001> direction, a "hard" orientation that produces small Schmid factors for <001> slip. AuZn presumably slips mostly in the <001> direction, but <111> slip occurs near grain boundaries to provide many of the geometrically necessary dislocations to avoid intergranular fracture. This is supported by observations that wavy slip lines are most commonly seen near grain boundaries in plastically deformed polycrystalline AuZn [23]. The combination of {110}<001>, {100}<001>, and {211}<111> slip satisfies the von Mises criterion and appears to explain the ductility. Although AuZn has long been known to be a shape memory material, its low martensitic transformation temperature (65K) [23-25] suggests that the shape memory effect is probably not the primary cause of AuZn's room temperature ductility. The AuZn B2 intermetallic involves two elements with substantially different electronegativities (ΔeN = 0.8 Paulings) and atomic radii (0.011 nm or 7.6%), so the presence of <111> slip in AuZn poses the same questions about dislocation motion as were previously discussed for AgMg. It is perhaps significant that AuZn, like AgMg, accommodates deviation from equi-molar composition at equilibrium by creating anti-site defects in the B2 structure. This suggests that, notwithstanding differences in electronegativities and radii, these materials can tolerate the local disorder associated with an APB formed between superdislocation pairs with 1/2<111> Burgers vectors. In fact, as with the reports on the AgMg compound, none of the papers on AuZn mechanical properties reported XRD results on the degree of ordering, which leaves open the possibility that the materials were not fully ordered.

1.4. Ductility in B2 CoZr Intermetallic Compound In the 1970's the first reports of limited room-temperature tensile ductility were made for B2 CoZr. CoZr is a Daltonide (line) compound (i.e., no appreciable variation from equi-molar stoichiometry at equilibrium) with a melting point of 1670 K. CoZr’s room temperature ductility is greatly enhanced by Ni substitutions for Co to produce ternary alloys with the general formula Zr50Co(50-x)Nix [26]. Tensile elongation of 20% is observed when x = 4, and elongation reaches a maximum value of 34% at x = 12 [27]. However, early studies [26-27] reported only a few percent tensile elongation in binary CoZr. In 2005 Yamaguchi, Kaneno, and Takasugi at Osaka Prefecture University reported 7.5% tensile elongation at room temperature in polycrystalline CoZr [28]. At the time of publication, this value of tensile elongation was the highest reported for binary CoZr. Although it was the intent of this study to produce equi-molar, one-phase CoZr, it is difficult to achieve a completely single-phase specimen of a line compound. The material studied contained small amounts of dispersed C15-type Laves phase Co2Zr, indicating that it was

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slightly Co-rich. The arc-melted specimens were homogenized at 1100˚C for 24 hours, furnace cooled, hot rolled at 1000˚C to a 60% reduction, hot rolled at 700˚C to an additional 60% reduction, then annealed at 1000˚C for one hour. This thermomechanical process achieved hot breakdown of the arc melted grain structure and a recrystalled grain structure (average grain size 13 μm) containing second phase elongated dispersoids of Co2Zr aligned parallel to the rolling direction. The microstructure developed with this processing treatment presumably enhances ductility. The 7.5% tensile elongation of CoZr was somewhat difficult to explain since TEM analysis showed that the dislocations activated by room temperature deformation during tensile testing were mostly <001>-type. Slip limited to the <001> direction provides only three of the five independent slip systems required by the von Mises criterion. The authors speculated that one reason for the high ductility was the large number of "punch-out" dislocations at CoZr-Co2Zr interfaces that are present as plastic flow begins during the tensile test, a phenomenon previously observed in NiAl-based materials [29]. In 2007 Kaneno, et alia, reported a more detailed examination of the ductility of CoZr [30]. In this study, five compositions of CoZr were prepared containing 49.0, 49.5, 50.0, 50.5, and 51.0 at.% Zr. The equimolar composition had 20% tensile elongation at room temperature in normal room air. The fracture surfaces of these tensile specimens showed a mixture of the dimpled, transgranular fractures characteristic of ductile failure plus intergranular fracture surfaces. The equi-molar specimens tolerated 70% reduction by cold rolling without serious cracking. The off-stoichiometry compositions contained the expected Co2Zr or CoZr2 Laves phases, and these compositions were somewhat less ductile and slightly stronger than the equi-molar specimens. These materials had low yield strengths and high ultimate strengths (Figure 4), similar to the high work hardening rate behavior observed in AgMg and AuZn. In the 2007 report, TEM analysis of the dislocations in CoZr showed only <001>-type Burgers vectors. By the von Mises criterion, polycrystalline material deforming only by <001> dislocation motion would be expected to be brittle unless some other factor(s) act to enhance ductility.

Figure 4. Tensile stress-strain plots for equi-molar CoZr tested in vacuum at various temperatures ( εÝ= 1.6(10-4) s-1). Vacuum testing is necessary at the higher temperatures to avoid oxidation; CoZr does not display environmental embrittlement. Redrawn from [30].

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Such factors could include deformation twinning or a stress-induced phase transformation, but no evidence of either has yet been reported in CoZr. It is also conceivable, of course, that some other slip mode is actually operating in this material but was not detected in the TEM foils examined. Like most B2 compounds, CoZr is comprised of two elements with a significant difference in electronegativities (in CoZr, ΔeN = 0.4 Paulings) and atomic radii (in CoZr, 0.034 nm or 21%) [31]. Unlike AgMg and AuZn, CoZr is a line compound that will not accommodate any deviation from equi-molar composition at equilibrium. CoZr also differs from AgMg and AuZn in that no evidence has yet been reported for <111>-dislocation motion in CoZr; thus, the source of its ductility remains undetermined.

1.5. Ductility in Rare Earth B2 Intermetallic Compounds Approximately 130 binary rare earth intermetallic compounds have the B2 structure. These compounds share the general formula RM (where R = a rare earth element, M = an element from Groups 2, 8-13). In 2003, Gschneidner, et alia, published the first of several reports on the mechanical properties of RM B2 compounds [32]. Fifteen RM compounds were examined and determined to have good room-temperature ductility; two (TbCu and YZn) were found to have little or no tensile ductility. DyCu, YAg, and YCu have been most extensively studied [33-35]; all three compositions display tensile ductility of 11 to 20% elongation (Figure 5). Some, but not all, specimens’ stress-strain plots show heavily serrated plastic flow that suggests a strain aging effect. The fracture toughnesses of these three compounds were measured and found to be quite high for intermetallics: 12.0 MPa√m for YCu, 19.1 MPa√m for YAg, and 25.5 MPa√m for DyCu [36]. For comparison, the fracture toughness of polycrystalline NiAl has been reported as 5.1 to 6.4 MPa√m [37]. Most RM compounds also display good tensile ductility at 77 K. Tensile tests performed on polycrystalline YCu at elevated temperatures revealed an ultimate-tensile-strength maximum at approximately 400˚C. Strain rate tensile jump tests have been performed on several RM compounds at both room temperature and 77 K; all these tests showed little or no strain rate sensitivity, which suggests that deformation is occurring by ordinary dislocation glide rather than diffusionbased processes. Slip trace analysis of single crystal RM compounds [34,35] show slip on {110}<001> and {100}<001>, two slip systems that together provide only three of the five independent slip systems required for tensile ductility in polycrystalline material. Some RM studies [32] report <110> dislocations to be present, but these may not result from <110> slip, but may instead be junction dislocations formed by the collision of two gliding <001>-type dislocations. TEM examination of these same single-crystal specimens also showed smaller numbers of <111> dislocations, but it was not until 2007 that slip traces caused by <111> dislocations were reported [33]. Thus, at least some RM compounds appear to satisfy the von Mises criterion. Neutron diffraction experiments performed on YCu specimens during tensile and compression testing have found no mechanical twinning and no stress-induced phase transformations. The neutron diffraction experiments have, however, shown a peculiar effect in which all diffraction peaks increase in intensity as plastic deformation progresses. Since texturing effects cannot raise the intensity of all peaks simultaneously, this phenomenon has

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been attributed to an extinction effect resulting from a change in mosaic (subgrain) size as dislocation density increases during deformation.

Figure 5. Tensile stress-strain plots for DyCu, YAg, and YCu tested in room air ( εÝ= 2(10-4) s-1). Redrawn from [36].

Single-crystal tests also revealed a curious anomaly in the RM compounds; the yield strengths of these materials are often lower in polycrystalline specimens than in single-crystal specimens. Although other possible causes for the low yield strengths in polycrystalline specimens (e.g., interstitial and substitutional impurity differences between sample batches) need to be examined, it suggests the possibility that some sort of grain boundary dislocation source mechanism may be operating in these materials. TEM studies on DyCu, TbCu, and YCu showed that the specimens contain a few volume percent of an orthorhombic phase in the B2 matrix (Figure 6). Electron diffraction has shown that in DyCu this phase has lattice parameters of a0 = 0.38 nm, b0 = 1.20 nm, c0 = 0.40 nm. These lattice parameters do not correspond to any equilibrium phase in the Dy-Cu binary system. _ In DyCu, TbCu, and YCu, the orthorhombic–B2 interface has a _ (110)[111]B 2 || (111)[101]ORTHO orientation. Since plastically deformed and as-arc-melted material show similar amounts of the orthorhombic phase, it does not appear to be a stressinduced transformation product. The appearance of the orthorhombic phase does not change in TEM foils from cryogenic temperatures to 700˚C. There are some indications that this orthorhombic material may be a H-stabilized phase, but, whatever its source, it does not appear to be directly related to the high ductility since it has not been observed in the majority of RM materials, including YAg, the most ductile RM compound found to date. From the perspective of atomic radii differences, the ductility of RM compounds seems more surprising than do the ductilities of AgMg, AuZn, and CoZr. The RM compounds have atomic radii differences of 22% (for YAg) to 37% (for YCu and DyCu); these differences are greater than the differences between Ag and Mg in AgMg (10%), Au and Zn in AuZn (7.6%), and Co and Zr in CoZr (21%). The differences in atomic radii for these systems are consistent

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with the degree to which their B2 structures will tolerate equilibrium deviations from stoichiometry. Lattice strain from anti-site defects becomes severe when atomic radii differ greatly.

Figure 6. Orthorhombic second phase (darker regions) in DyCu after tensile testing to 5% elongation.

The AgMg and AuZn compounds, whose size differences are modest, maintain a singlephase microstructure over ranges of several atomic percent from exact equi-molar stoichiometry. By contrast, CoZr and RM compounds, whose size differences are large, are line compounds. If 1/2<111> dislocation motion is necessary forductility in these materials, then the material's ability to form APB's between 1/2<111> dislocation pairs becomes a key factor. Large atomic radii differences would seem likely to raise APB energies due to the lattice strain that occurs from juxtaposing like atoms in the B2 structure. From this perspective the RM compounds seem the least likely to be highly ductile because they seem poorly suited to forming low-energy APB's.

2. FACTORS CONTRIBUTING TO TENSILE DUCTILITY AND FRACTURE TOUGHNESS With the exception of CoZr, all the materials described in §1 have been observed to deform by slip systems involving <111> slip directions that satisfy the von Mises criterion. No evidence has been reported for mechanical twinning, stress-induced phase transformations, or similar processes that might enhance the ductility of these materials. With the possible exception of CoZr, the ductility seems to originate from <111> slip. Thus, there is a major difference in the slip systems active in the ductile B2 compounds compared to those in brittle B2 intermetallics, such as NiAl. Interest then naturally shifts to the question of why these materials allow <111> slip at room temperature when most ordered intermetallics with substantial differences in the A and B atom sizes and electronegativities do not. To date, the ductility of the RM compounds has attracted the most attention from theorists.

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2.1. Anisotropy Effects One factor that has been suggested to explain the ductility in the RM compounds is the location of the RM B2 compounds on a plot of (anisotropy ratio)-1/2 vs. Poisson ratio of the type shown in Figure 7 that was introduced by Yoo, et alia [38]. The anisotropy ratio is defined by the elastic constants of the material: A = 2c44/(c11-c12) When A = 1, the material is isotropic, and the prospects for ductility are maximized; when A1/2 and the Poisson ratio deviate outside the bounds marked by the dashed lines on Figure 7, the material is predicted to be less ductile. The three RM compounds plotted in Figure 7 (DyCu, YAg, YCu) are all located near the elemental BCC metals, rather than with ionic or intermetallic compounds. Although the predictive value of this type of plot is imperfect, the location of the three RM compounds is interpreted to mean that the bonding in these RM compounds is more like that of metallic elements than ionic or intermetallic compounds.

Figure 7. Plot of the (anisotropy ratio)-1/2 vs. Poisson ratio for several B2 compounds. RM compounds are depicted with circles; note that they are located near elemental BCC metals such as W, Ta, and V. Redrawn from [32].

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The nearly isotropic behavior of the RM compounds' elastic constants also appears to facilitate dislocation motion in these materials. Chen and Biner [39] calculated the line tensions for <111> screw dislocations in YAg, YCu, and YZn and found (Figure 8) that they have positive line tensions for all values of θ (θ = the angle between the dislocation's Burgers vector and the dislocation line) and that dislocations are stable for all θ values in these three materials. This contrasts with the behavior of B2 NiAl, which has unstable dislocations for 38˚<θ<59˚ and negative line tensions within the central portion of that range (41˚<θ<52˚). (Negative line tension is a sufficient, but not necessary condition for instability.) These results suggest that all straight dislocations in NiAl with 38˚<θ <59˚ can lower their energy by transforming into V-shaped or zigzagged bends. Similarly, dislocations in the offstoichiometry B2 compound Fe-25%Al are unstable for 24˚<θ <76˚ and have negative line tension for 37˚<θ <60˚. Both NiAl and Fe-25Al in polycrystalline form at room temperature are almost completely brittle and show no evidence of <111> slip.

_

Figure 8. Polar plots of 1/K, where K is the energy factor for (110)[111] glide loop dislocations, versus θ, where θ is the angle between the dislocation line and its Burgers vector in (left) NiAl and Fe25%Al and (right) YAg, YCu, and YZn. In NiAl and Fe-25%Al, the dislocation loop is unstable over substantial ranges of θ values (where the plot appears concave), but the loop is stable for all θ values in YAg, YCu, and YZn. Redrawn from [39].

2.2. Ab Initio Calculations of Defect Properties Morris, et alia, have performed ab initio calculations to predict defect energies in YAg and YCu [40]. (RM compounds containing Y pose less daunting computational challenges than RM compounds containing lanthanides, because Y has no 4f subshell.) The calculations were performed with the full-potential linearized augmented plane wave (FLAPW) code WIEN97, an all-electron total-energy electronic structure code. The calculations predict large APB energies for these materials (Table 2), as would be expected from the large atomic radii mismatches between Y atoms and the Cu or Ag atoms; however, the energies of stacking faults are much lower than in NiAl.

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Table 2. Calculated APB energies and unstable stacking fault energies in three B2 materials. APB = anti-phase boundary; γsf = stacking fault

YAg YCu NiAl

{110}1/2<111> APB energy (mJ/m2) 745 1030 815

{112}1/2<111> APB energy (mJ/m2) 680 1090 995

{010}1/2<100> γsf energy (mJ/m2) 560 700 1835

{011}1/2<100> γsf energy (mJ/m2) 315 325 1290

High ductility in polycrystalline RM material apparently requires <111> dislocation motion to satisfy the von Mises criterion. Ab initio calculations show that for {110}1/2<111> and {112}1/2<111> slip, APB energies in YAg are only moderately less than those of NiAl, which is brittle. They also show that APB energies in YCu are actually greater than in NiAl. Thus, these results provide no obvious explanation for how <111> dislocation motion occurs at room temperature in RM compounds while not occurring in NiAl. The ab initio calculations do, however, predict much lower stacking fault energies for <100> slip in the RM compounds vis-a-vis NiAl. The B2 structure has long been thought to have only unstable stacking faults, but the unstable stacking faults replicate the atom positions mid-way through a dislocation displacement. The lower values for the RM compounds are consistent with the observation that RM compounds have lower critical resolved shear stresses for <100> slip (13 MPa in YAg, 18 MPa in YCu) than does NiAl (30 MPa) [41]. Morris' calculations also indicated that the bonding in YAg and YCu is less directional than in NiAl and that there is less charge rearrangement in YAg and YCu than in NiAl. Thus, the bonding in RM compounds is more like that of ordinary metals than intermetallic compounds.

2.3. Environmental Effects Many intermetallic compounds, including some B2 compounds, display much greater ductility and fracture toughness when tested in vacuum or ultra-dry atmospheres than they do in ordinary air of normal humidity [11,42,43]. As discussed in §1, this environmental embrittlement is thought to result from the reaction of the material with atmospheric water vapor, which feeds H atoms into the material's grain boundaries where it lowers bond strength across the grain boundaries and promotes intergranular fracture. It has been suggested that the presence of reactive rare earth atoms in the RM compounds may form rare earth hydrides that block the H-induced grain boundary embrittlement seen in other intermetallics. Rare earth metals absorb H to form RHx (where 2 ≤ x ≤ 3). These hydrides are brittle, but it is conceivable that they form in a manner that inhibits rather than promotes intergranular fracture. If that were the case, then the RM intermetallics might display the high ductility and fracture toughness in ordinary humid air that other intermetallics can achieve only in high vacuum or ultra-dry atmospheres. CoZr shows no environmental effect on ductility [28]. Zr also forms stable hydrides, and it is conceivable that the same mechanism is active in CoZr to increase its ductility. However, if that were the case, one would still face the challenge of explaining why other B2 intermetallics containing Zr are brittle.

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The effect of H in the RM compounds clearly needs further study. Investigators of RM compounds have sometimes observed that "old" material that has been stored for several months or years seems sometimes to be less ductile than "fresh" material. This sort of behavior would be consistent with material that gradually becomes saturated with H until the "protective effect" of hydride formation is finally overwhelmed, allowing environmental embrittlement to degrade mechanical properties after long exposure to H2O vapor. It would be desirable to test this qualitative observation with quantitative experiments such as deliberately doping RM compounds with varying quantities of H, then testing mechanical properties and searching for hydrides at fracture surfaces and in TEM foils.

3. YIELD STRENGTH ANOMALIES AND STRAIN AGING IN B2 COMPOUNDS 3.1. Yield Strength Anomalies Some B2 compounds (e.g., CoFe, CoHf, CoTi, FeAl, FeTi, NiTi, RuAl) display a yield strength anomaly (Figure 9) in which the yield strength rises if the material is tested above room temperature, reaching a maximum value at an elevated temperature (often about 0.4Tm.pt.) before finally decreasing at still higher temperatures. Investigators have suggested several possible explanations for the yield strength anomaly, including: •

• •

The <001>-type screw dislocations cross slip from {110} to {100} and become sessile on their new slip planes by a thermally activated spreading process, thereby inhibiting further dislocation motion [44]. Slip systems change at the temperature of the yield strength maximum [45]. In incompletely ordered compounds, the imperfect long-range order permits the motion of single dislocations to dominate slip, but those single dislocations encounter increasing resistance as the degree of order is increased by higher temperatures. As the degree of long-range order approaches complete ordering, slip is increasingly dominated by superlattice dislocations, causing strength to decrease [46].

In the case of Fe-40%Al, George and Baker presented convincing experimental evidence that the yield strength maximum matches the behavior expected from the hardening effect of the increased numbers of thermal vacancies that form as temperature rises (for T<σy,max) and from the softening effect of vacancy-enhanced dislocation creep (for T>σy,max) [47]. To observe the maximum, specimens must be given long annealing treatments at temperatures low enough to avoid biasing the results with vacancies quenched-in from higher temperatures. Above T = σy,max, the yield strength is controlled by a vacancy-enhanced dislocation creep phenomenon so the strength is strain-rate dependent. Kaneno, et alia [30], report a yield strength anomaly in off-stoichiometry CoZr, but only a small strength anomaly was observed in stoichiometric Co-50.0at.%Zr specimens (Figure 10). These investigators attributed the yield strength anomaly to the core <100> dislocations' transition from glissile to sessile behavior under the influence of temperature and applied stress. All three of the CoZr compositions shown in Figure 10 display an ultimate tensile

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strength anomaly at the same temperature as the yield strength anomaly, and ductility increases sharply at temperatures above T = σy,max.

Figure 9. Plot of yield strength vs. tensile test temperature for B2 Fe-40%Al. The circles represent experimental values; the curve represents the prediction of the George-Baker vacancy hardening model ( εÝ= 1(10-4) s-1). Redrawn from [47].

Figure 10. Yield strength as a function of tensile test temperature for CoZr specimens of three different compositions ( εÝ= 1.7(10-4) s-1). Redrawn from [30].

AgMg does not display a yield strength anomaly [14]. AuZn displays an ultimate tensile strength anomaly near 240K; however, yield strengths show no maximum [21]. YCu displays an ultimate tensile strength anomaly (Figure 11), but no yield strength data are available for YCu [48]. Due to the unusually low yield strengths (often 10 to 15 MPa at 22˚C) of

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polycrystalline RM's, yield strength values are difficult to measure accurately at elevated temperature. Further study is needed to determine whether yield strength anomalies exist in the RM compounds.

Figure 11. Plot of ultimate tensile strength vs. tensile test temperature for B2 YCu ( εÝ= 1(10-3) s-1).

3.2. Strain Aging Phenomena in B2 Intermetallics The term “strain aging” covers several phenomena observed during mechanical properties testing, including: • • • • •

yield point drops serrated stress-strain curves maxima in work hardening rates (θ = Δσ/Δε) minima in strain rate sensitivity (s = Δ σ Δ (ln εÝ) reduced tensile elongations within certain strain rate or temperature ranges

These strain aging effects are caused by interstitial impurity atoms diffusing to dislocations to form an “atmosphere” around the dislocations. The lattice near interstitial impurity atoms is typically in a state of residual compressive stress because the impurity atoms are too large to fit easily into the available interstitial spaces. Since the lattice near dislocations contains regions of residual tensile stress, there is a natural tendency for interstitial atoms to remain near dislocations so their strain fields can partially cancel one another. When the material is stressed sufficiently to move those dislocations, the dislocations break away from their interstitial impurity atmospheres and, once in motion, can glide at lower shear stress levels than were required to start their motion, creating yield point drops during tensile or compressive testing. If diffusion is rapid enough to allow the impurity atoms to quickly reform atmospheres around dislocations as deformation progresses, serrated yielding is observed as dislocations repeatedly break free from impurity atmospheres and then form new atmospheres during brief pauses in their glide.

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Strain aging phenomena have been observed in B2 materials such as CoTi, FeAl, NiAl, and RuAl. Polycrystalline NiAl displays a room-temperature yield point, a maximum in work hardening rate near 800 K, strain rate sensitivity minima near 350 K and 650-800 K, and serrated flow near 800 K [49]. These appear to be caused by C impurities, possibly augmented by Si impurities. Additions of reactive metals such as Ti appear to have a “gettering” effect, forming carbide precipitates that reduce the amount of C available to drive strain aging effects. In single-crystal Fe-39.5 at.%Al and Fe-43 at.%Al, similar manifestations of strain aging are seen [50-51]. Yield stress reaches a maximum value around 800 K in this material, which is also the temperature at which the dominant slip direction switches from <111> superdislocations to <001> dislocations. Morris, et alia, attribute the dynamic strain aging behavior of this material to vacancies rather than to impurity atoms; however, Yoshimi, et alia, do not support this conclusion. Nandy, et alia, studied polycrystalline RuAl deformed in compression and observed serrated flow, a flow stress plateau, maxima in the rate of work hardening, and minima in the strain-rate sensitivity [52]. The investigators concluded that C is the likely cause for these phenomena in RuAl. More ductile B2 intermetallics also show strain aging behavior. Westbrook and Wood [14] reported a marked yield point and a range of discontinuous yielding in AgMg specimens deformed between 150˚ and 350˚C, and they suggested that this behavior might be the result of dissolved O or N. Terry and Smallman [19] did not observe a yield point in AgMg in that same temperature range. AuZn showed serrated flow at room temperature in the nonstoichiometric compositions one or two percent on either side of the equimolar composition [21]. No strain aging behaviors were reported in CoZr [28,30]. The RM compounds sometimes display small yield points and serrated yielding; in some cases the serrations are quite pronounced, particularly in compression (Figure 12).

Figure 12. Compression stress-strain plot for single crystal YCu. Redrawn from [35].

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In some RM compounds, the energies of the B2, B27, and B33 phases are all nearly equal, which suggests the possibility that a stress-induced phase transformation may cause the serrated yielding. However, as previously stated, in situ neutron diffraction performed on YCu during tension and compression testing reveals no phases other than B2 during room temperature testing, nor does it indicate any twin formation. The numerous observations of strain aging phenomena in both ductile and brittle B2 compounds suggest that these effects are incidental to the ductility issues and probably do not play a central role in determination of ductility.

4. POTENTIAL APPLICATIONS FOR DUCTILE B2 COMPOUNDS AND PROSPECTS FOR “DUCTILIZING” OTHER INTERMETALLIC COMPOUNDS 4.1. Potential Applications At present all the ductile B2 intermetallics (AgMg, AuZn, CoZr, and the RM family) are of scientific interest only; none of these materials is used for engineering applications. The high costs of Ag and Au discourage any structural uses of the first two intermetallics. One might think CoZr would have potential value for elevated temperature applications since both Co alloys and Zr alloys are noted for formation of self-protective oxide layers; however, binary CoZr shows mediocre high temperature oxidation resistance, and its melting point (1400˚C) is not particularly high. The RM compounds possess some appealing attributes for possible engineering service. YMg has been shown to display surprisingly good elevated temperature oxidation resistance [53]; YMg gains only about 60 mg/dm2 when exposed for 24 hours to flowing air at 800˚C. This material may have value as a coating on Mg (or possibly even Y) components exposed to oxidizing environments at elevated temperatures. The RM compounds where M = Au have attracted interest from the jewelry industry to meet the growing demand for black gold. Current black gold pieces are produced by electrodeposition of black Rh or Ru, by a chemical vapor deposition process using amorphous carbon, or by a controlled oxidation process of Au containing Cr or Co. All of these processes are based on surface coatings that are vulnerable to scratching or abrasion that would allow the characteristic yellow color of the underlying alloy to show through. Moreover, some of these products have poor ductility. Three RAu intermetallics (ScAu, YAu, and LuAu) possess the B2 structure at all temperatures below melting. Nine more compositions possess a high-temperature B2 phase that transforms to an orthorhombic phase at lower temperature; in these nine compositions it may be possible to retain the ductile B2 phase as a metastable structure at room temperature by quenching. In these materials a scratch in the black surface oxide will appear bright for only a few hours or days before the underlying metal re-forms a new black surface layer; thus, the material regenerates the black surface film if damaged. Finally, more speculative possibilities exist, such as use of RuSc (Tm.pt. = 2200˚C) or AlSc (low density and good oxidation resistance) in aerospace and engine components; however, the ductility of those particular RM compounds has yet to be confirmed, and the costs of both Ru and Sc are exceptionally high.

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4.2. Prospects for “Ductilizing” Other Intermetallic Compounds Although the potential uses for ductile intermetallics based on AgMg, AuZn, CoZr, and the RM family appear quite limited (§4.1), it may be that insights into the mechanism(s) that confer their ductility could be applied to intermetallics with more appealing costs and engineering attributes (e.g., NiAl, FeAl). If, for example, the presence of a reactive metal such as Zr or a rare earth inhibits environmental embrittlement, then it might be possible to produce variations of intermetallics with the reactive metal located near free surfaces and grain boundaries to suppress environmental embrittlement and deliver the superior mechanical performance that is seen in vacuo or in ultra-dry atmospheres when these materials are used in ordinary air.

CONCLUSION High ductilities have been reported in room temperature tensile tests performed on polycrystalline specimens of B2 intermetallic compounds: AgMg, AuZn, CoZr, and a large family of rare earth compounds. In most cases (all but CoZr), this unusually high ductility has been shown to be associated with <111>-dislocation glide. Although <111> dislocations have been observed to glide at room temperature in numerous B2 intermetallics, they are usually observed to move in compounds with low ordering energies (e.g., CuZn). Since most of the ductile B2 compounds listed above are thought to have high ordering energies, their ability to move <111> dislocations is somewhat surprising. Several of these ductile compounds display yield strength anomalies and strain aging effects, but there appear to be no clear correlations between those factors and the materials’ high ductilities. Useful first steps have been taken to provide theoretical insights into the cause(s) of the high ductility, but key questions in this area remain unanswered. The potential engineering applications for these materials appear quite limited at present, but further study of these materials continues, spurred by the prospect of (1) better fundamental understanding of deformation mechanisms in intermetallic compounds, and (2) the possibility that these materials may suggest ductilizing strategies that could be applied to other intermetallic compounds to improve their mechanical properties.

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8]

Russell A.M. Adv. Eng. Mater. 2003, 5, 629-639. Hahn, K.H; Vedula, K. Scripta Metall. 1989, 23, 7. Levit, V.I; Bul, I.A.; Hu, J.; Kaufman M.J. Scripta Mater. 1996, 34, 1925-1930. Ebrahimi, F; Shrivastava, S. Acta Mater. 1998, 46(5), 1493-1502. von Mises, R; Z. Ang. Math. Mech. 1928, 8(3), 161-185. Groves, G.W; Kelly, A. Philos. Mag. 1963, 8, 877-887. Cotton, J.D; Kaufman, M.J; Noebe, R.D. Scripta Metall. 1991, 25, 2395. Takasugi, T; Masahashi, N.; Izumi, O. Acta Metall. 1987, 35, 381.

234 [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]

[33] [34] [35] [36] [37] [38] [39] [40] [41] [42]

Alan M. Russell Ishida, K; Kainuma, R; Ueno, N; and Nishizawa, T. Metall. Trans. A 1991, 22, 441446. Liu, C.T. Scripta Metall. Mater. 1992, 27, 25-28. Ko, S.H; Gnanamoorthy, R; Hanada, S. Mater. Sci. Eng. A 1997, A222, 133-139. Margevicius, R. W; Lewandowski, J. J. Scripta Metall. Mater. 1991, 25, 2017-2022. Huang, X; Ackland, G.J; Rabe, K.M. Nat. Mater. 2003, 2, 307-311. Wood, J; Westbrook, J. Trans. AIME 1962, 224, 1024. Robinson, P; Bever, M. Acta Metall. 1965, 13, 647. Jena, A.K; Westbrook; J.H; Bever, M.B. ASM Trans. Q, 1969, 62, 784-793. Rachinger, W.A; Cottrell, A.H. Acta Metall. 1956, 4, 109-113. Vedula, K; Hahn, K.H; Boulogne, B. Mater. Res. Soc. Proc. 1989, 133, 299-304. Terry, J.C; Smallman, R.E. Philos. Mag. 1963, 8, 1827. Causey, A.R; Ph.D. dissertation, Univ. British Columbia, 1967. Causey, A.R; Teghtsoonian, E. Metall. Trans. 1970, 1, 1177-1183. Marcinkowski, M.J; Fisher, R.M. J. Appl. Phys. 1963, 34, 2135. Schulson, E.M.; Teghtsoonian, E. Philos. Mag. 1969, 19, 155. Pops, H; Massalski, T.B. Trans. Metall. Soc. AIME 1965, 233, 728. Lashley, J.C; Ledbetter, H; Darling, T.W; Saxena, A; Malinowski, A; Hundley, M.F; Smith, J.L; Thoma, D.J. Mater. Trans. JIM 2006, 47, 587-593. Lall, C; Loretto, M.H; Harris, I.R. Acta Metall. 1978, 26, 1631-1641. Hossain, D; Harris, I.R. J. Less Comm. Metals, 1974, 37, 35-57. Yamaguchi, T; Kaneno, Y; Takasugi, T. Scripta Mater. 2005, 52, 39-44. Yang, W; Dodd, R.A; Strutt, P.R. Metall. Trans. A 1972, 3, 2049. Kaneno, Y; Asao, K; Yoshida, M; Tsuda, H; Takasugi, T. J. Alloys Compd., 2007 (in press). Dwight, A.E in Intermetallic Compounds, Westbrook, J.H.; Ed.; John Wiley and Sons: New York, NY, 1967; pp 166-179. Gschneidner, K.A; Russell, A.M; Pecharsky, A.O; Morris, J.R; Zhang, Z; Lograsso, T.A; Hsu, D.K; Lo, C.H.C; Ye, Y; Slager, A.J; Kesse, D.C. Nat. Mater 2003, 2, 587– 591. Cao, G.H; Shechtman, D; Wu, D.M; Becker, A.T; Chumbley, L.S; Lograsso, T.A; Russell, A.M; Gschneidner, K.A. Acta Mater. 2007, 55, 3765-3770. Russell, A.M; Zhang, Z; Lograsso, T.A; Lo, C.H.C; Pecharsky, A.O; Morris, J.R; Ye, Y.Y; Gschneidner, K.A; Slager, A.J. Acta Mater. 2004, 52, 4033-4040. Russell, A.M; Zhang, Z; Lograsso, T.A; Gschneidner, K.A; Pecharsky, A.O; Slager, A.J; Kesse, D.C. Intermetallics, 2005, 13, 565-571. Zhang, Z; Russell, A.M; Biner, S.B; Gschneidner, K.A; Lo, C.H.C, Intermetallics 2005, 13, 559-564. Kim, T; Hong, K.T; Lee, K.S. Intermetallics, 2003, 11, 33. Yoo, M.H; Takasugi, T; Hanada, S; Izumi, O. Mater. Trans. JIM, 1990, 31, 435-442. Chen, Q; Biner S.B. Acta Mater. 2005, 53, 3215-3223. Morris J.R; Ye Y.Y; Lee Y.B; Harmon B.N; Gschneidner K.A; Russell A.M. Acta Mater. 2004, 52, 4849-4857. Brunner, D; Gumbsch, P. Mater. Sci. Eng. A 2001, 319-321, 653-658. Liu, C.T; Lee, E.H; McKamey, C.G. Scripta Metall. 1989, 23, 875.

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[43] Baker, I; Wu, D; Kruijver, S.O; George, E.P. Mater. Sci. Eng. 2002, A329-331, 729733. [44] Takasugi, T; Hanada, S. Philos. Mag. 1995, A71, 347. [45] Baker, I; Gaydosh, D.J. Mater. Sci. Eng. 1987, 96, 315. [46] Stoloff, N.S; Davies, R.G. Acta Metall. 1964, 12, 473–485. [47] George, E.P; Baker, I. Philos. Mag. A 1998, A77, 737. [48] Barnard, D.J. unpublished data, private communication. [49] Weaver, M.L; Noebe, R.D; Kaufman, M.J. Intermetallics 1996, 4, 593-600. [50] Morris, D.G; Joye, J.C; Yoo, M.H. Philos. Mag. A 1994, 69, 961. [51] Yoshimi, K; Hanada, S; Yoo, M.H. Acta Metall. Mater. 1995, 43, 4141-4151. [52] Nandy, T.K; Feng, Q; Pollock, T.M. Intermetallics 2003, 11, 1029-1038. [53] Stumphy B.D; Mudryk Y; Russell A.M; Herman D.M; and Gschneidner, K.A. “Oxidation resistance of B2 rare earth-magnesium intermetallic compounds”, J. Alloys Compd. accepted May, 2007 (in press).

In: Intermetallics Research Progress Editor: Yakov N. Berdovsky, pp. 237-259

ISBN: 978-1-60021-982-5 © 2008 Nova Science Publishers, Inc.

Chapter 6

ULTRA SLOW DYNAMICS IN INTERMETALLIC THIN FILMS Marcus Rennhofer∗ Scattering and Spectroscopy Group Faculty of Physics, University of Vienna Strudlhofgasse 4, A-1090 Wien, Austria

ABSTRACT Diffusion studies on the mesoscopic and macroscopic scale were done up to now via radiotracer technique for a wide range of diffusivities. Nevertheless, the resolution of diffusion depths is limited by the detector efficiencies and sputtering resolving power. On the other hand scattering methods with atomic resolution like quasielastic Mössbauer spectroscopy, nuclear resonant scaterring and quasielastic neutron scattering have very limited range of accessible diffusion coefficients, especially for slow diffusion at low temperatures. We advantageously applied grazing incidence nuclear resonant scattering (GINRS) of synchrotron radiation for the study of iron self-diffusion in technically most promising intermetallic thin films (L10-FePt, L10-FePd and B2-FeSi). The investigations are non-destructive and non-contaminating. It is possible to measure very low rates of diffusion of about . The diffusion coefficients accessible for investigation can be tuned in a certain range. The application of GINRS gives no direct access to jump frequencies and jump vectors of the diffusing atoms. Nevertheless, combining the method with results from "order-order" dynamics or Monte Carlo simulations allows the determination of the diffusion model.

1. INTRODUCTION This chapter is devoted to the studies on diffusion in ordered intermetallic thin films. The presented results were achieved by means of nuclear resonant scattering (NRS). To study the ∗

E-mail: [email protected]

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self diffusion of Fe in thin films with high spatial resolution we used a method [1] exploiting the grazing incidence nuclear resonant scattering (GINRS) of synchrotron radiation [2, 3]. For metals and alloys, diffusivity (like e.g. self-diffusion, impurity diffusion, chemical diffusion) is an important parameter for various problems of solid state physics. It is of tremendous importance for high-temperature applications, structural alloys and semi conductor industry. Up to now, it was possible to study bulk diffusivities in solids only by a few methods. Recently, a new method was established opening a window for diffusion measurements in the range of very slow diffusion below 10-21 m2 s-1 [4]. Further, it enables investigations of metastable systems, ultra thin films or amorphous solids [5]. In this chapter we will show recent results for diffusion in L10-ordered FePt, L10-ordered FePd and shortly report on first attempts to measure iron self diffusion in metastable B2-FeSi. While FePt and FePd are main candidates for next generation data-storage devices, their physical properties regarding diffusion are nearly unknown. Various experiments with bulk FePt and FePd [6, 7, 8, 9] dealing with diffusion and ordering have been performed. Moreover, no diffusion data except for radio-tracer data and chemical diffusion data in the high-temperature range and in the disordered fcc phase exist [6, 7, 9] (see figure 1). We will discuss the graph in detail later in section 5. For FePt and FePd the L10 phase has a large magnetocrystalline uniaxial anisotropy which makes them ferromagnetically stable (the highest values are reached for FePt in the range between 7 Jcm-3 [11] and 80 Jcm-3 [12]). Therefore, FePt and FePd are of high technological interest for applications like data-storage devices [13, 14].

Figure 1. Arrhenius plot for iron diffusion in FePt and FePd. (■) and (■) are radio-tracer data for iron diffusion in bulk FePt along the a-and c-direction, respectively [6]. Chemical tracer data are shown as (■), a-direction, and (△ ), c-direction, for iron diffusion in bulk FePt [7]. The dashed line shows results from interdiffusion via diffusion couples in polycrystalline FePt [10]. The solid line represents self diffusion of iron in disordered bulk FePd [9].

The magnetocrystalline and thermal stability makes these compounds suitable for ultrahigh density recording. A detailed knowledge of the dynamic and diffusion processes is

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essential for selectively designing alloys with different physical properties for technical applications. The FeSi system for a long time has been in the center of interest regarding diffusion studies with a remarkable fast diffusion of iron in Fe3Si [15]. Recently, it has become possible to grow the technically important c-phase of FeSi [16, 17]. The c-FeSi phase is metastable and exists only in thin epitaxial films. Up to now, the low transition temperature to the ε -phase made it impossible to investigate diffusion via conventional nuclear resonant scattering in this system. The thin film c-FeSi is used in various applications for investigation of magnetic structures as multilayers, or ferromagnetic and antiferromagnetic coupling, see e.g. [18]. For these and for the design of layered structures with magnetical spacers the growth conditions are of essential importance and, therefore, also the exact knowledge of the dynamics in c-FeSi.

2. METHODOLOGY The radio-tracer technique is used to study mesoscopic and macroscopic diffusion dynamics. For an overview see [19]. The radio-tracer technique gives access to a wide range of diffusion constants. It is applicable to almost all elements and can (especially if applied for stable isotopes investigated by mass spectroscopy deal with high diffusivities (near the melting point) as well as low diffusivities, due to the possibility to adjust the annealing time of the specimen [19]. The main drawback of tracer methods is that it deals with radioisotopes and the measurement is destructive. Further, the resolution of diffusion depths is limited by the detector efficiencies and sputtering resolving power. It is clearly above the range of atomic distances, i.e. the elementary diffusion jump is not resolvable. On the atomic scale, scattering methods as quasielastic Mössbauer spectroscopy (QMS), nuclear resonant scattering (NRS) and quasielastic neutron scattering (QNS) have shown their excellence [15, 20]. Scattering methods allow to distinguish diffusion lengths with atomic resolution, i.e. they enable to resolve jump vectors and jump frequencies. The disadvantage of all scattering methods is the very limited range of accessible diffusion coefficients. Usually, the specimen has to be heated close to the melting point. There also were approaches made to use isotopic layer structures for diffusion studies, where the layer profile was probed via secondary ionmass spectrometry (SIMS) [21, 22]. While the regarding experiments gave access to rather low diffusivities, the method was nevertheless destructive. Combining the principles of the two above mentioned methods, i. e. tracer atoms to investigate the diffusion length of nuclei and nuclear resonant scattering to resolve isotopes, we obtain a powerful tool for studying dynamical processes on the nanometer scale. Very early DuMond and Youtz have shown that it is possible to use X-ray scattering contrast of a deposited multilayer structure of chemically different elements to measure interdiffusion [23]. Cook and Hillard laid the theoretical background using the method for studying interdiffusion coefficients [24]. Recently, the method was adapted for synchrotron radiation and neutron scattering [5, 25, 26]. In this chapter we will report on the method used in in combination with synchrotron radiation. The Mössbauer isotope 57Fe with its nuclear resonance transition at 14.4 keV allows to study diffusion coefficients below 10-24 m2s-1 in thermodynamical equilibrium and with high 57

resolution of the diffusion length [1]. The Mössbauer transition of Fe can be used in GINRS

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by monochromatising the synchrotron radiation to the designated resonant energy. Therefor, experiments using GINRS allow to achieve detailed information about the sample structure and its hyperfine parameters. Further, it provides information about the depth structure and chemical composition of the sample. In a nuclear resonance experiment the sensitivity is extended from chemically different elements to different isotopes. In a typical experiment in GINRS geometry three types of spectra are collected simultaneously (except for special timing modes of the synchrotron): electronic reflectivity, nuclear resonant reflectivity (so called ’delayed reflectivity’) and nuclear resonant scattering in the time domain (so called ’time spectra’), for an introduction see [27], for an overview [2, 3]. We will focus on the first two, i.e. reflectivity curves of electronic and nuclear scattered X-rays. The experiments with GINRS are performed on isotopic multilayers composed of alternating layers containing nuclear resonant (57Fe) and nonresonant (56Fe or Fe of natural abundance of about 2 at.%) nuclei, see figure 2. The preparation of such isotopic multilayers is rather demanding (we give a detailed description in 4.1), but has advantages: 1. The full power of the isotope sensitivity of GINRS can be used to achieve high spatial resolution of the diffusion length below the nm-range. 2. The sample structure stays in chemical equilibrium during the experiments, i.e. self diffusion can be measured. The multilayer is composed of a bilayer structure which is repeated N times and is grown on an appropriate substrate. The bilayer contains one intermetallic layer enriched with 57Fe, and another non enriched. It can be enriched with 56Fe, but usually it is easier to use only natural iron, which has abundance of 2.14% 57Fe. This is sufficient for most experiments. The over all structure then has a step-like concentration profile c(57Fe), see the right side of figure 2. The chemical structure is just one homogenous thick layer, as for an ideal prepared multilayer the electronic density is homogenous through the layer structure. For the detailed calculation, the restriction to an isotopic multilayer system influences only the delayed reflectivity. The time spectra and the electronic reflectivity are not influenced by the isotopical composition of the multilayer. Note, that this is only true for the ideal structure without variations in chemical composition, hyperfine field or roughness at interfaces [28]. When X-rays are reflected from the periodically modulated structure, e.g. from the repeated isotopic bilayer structure, superstructure peaks (so called nuclear Bragg peaks) occur at angles corresponding to the layer periodicity. The electronic reflectivity will show no superstructure peaks, but only the thickness oscillations corresponding to the total thickness of the multilayer [3, 29]. As self-diffusion of iron atoms occur during annealing for a defined time at a constant temperature, the isotopic bilayer structure is smeared out, see figure 3. In consequence, the spectra show a decrease of the nuclear Bragg peak intensity. Due to the high sensitivity of GINRS, this dependency gives access to low diffusivities.

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Figure 2. Sketch of an isotopic multilayer on arbitrary substrate. The curve at the right side corresponds to the concentration profile of 57Fe. The multilayer is chemically homogenous.

3. THEORY 3.1. Grazing Incidence Nuclear Resonant Scattering For the general properties of grazing incidence nuclear resonant scattering we discuss first only pure electronic reflectivity. GINRS is a form of X-Ray reflectivity (XRR). In XRR the geometry is chosen like in figure 4. A beam of synchrotron radiation of wavelength λ, energy E0 and wave vector kI =2π/λ irradiating a thin film sample with an angle ϑ. For NRS we have E0 = 14.4 keV λ =0.86 Å -1

kI =7.3 Å A part of the radiation is reflected and part is transmitted, depending on ϑ and the refractive index n of the thin film. The incident wave vector, kI , the wave vector of the

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reflected beam, kR with angle ϑ, and the wave vector of the transmitted beam, kT with angle ϑ lie in one plane, the scattering plane, see figure 4.

Figure 3. Principle of access to diffusion measurement with GINRS. The row shows the concentration profile of the isotopic multilayer. Due to annealing-induced diffusion the profile is smeared out.

Figure 4. Geometry of XRR and GINRS. The wave vectors of the incident, the reflected and the transmitted beam, kI , k R and k R lie in one plane. The momentum transfer is Δk. In GINRS geometry the reflective index n for X-rays is complex and smaller than unity. The angle of the incoming and outgoing beam is very small (usually

).

The momentum transfer of the scattering process is Δk = kR - kI . In this geometry (angles of incident and reflected beam are the same) only the depth modulations in z-direction of the sample contribute to the scattered intensity. The scattered signal is not sensitive to a lateral

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modulation from the surface, i.e. in the x-y-plane. Analytically this can be seen in the the scattering vector Δk, which has only a z-component. From the graph it is clear that it is identical to the z-component of the incident beam. With k0 = kI follows (1) The scattered intensity decreases fast for increasing incident angles (I ~ kz 4 . This restricts the method to small angles and therefor small kz values. The lateral resolution in this geometry can not resolve atomic distances. For small angles ϑ < 1 and using Snell’s law we get: (2)

In GINRS the beam is scattered at the sample under the grazing angle Depending on the setup, the beam hits the sample in air or vacuum with It is refracted corresponding to the refraction index for X-rays of the thin film sample: (3) with (4)

and (5)

where is the density of electrons, Å the scattering amplitude per electron, and µ the absorption length [27]. As can be seen from the formula the refractive index for X-rays is smaller than unity, the transmitted beam is broken from the orthogonal, compare figure 4. This results in the phenomenon of total external reflection, i.e. total reflection to the optical ’thinner’ medium [27]. While δ is of the order of 10-6, it is clear, that the range of GINRS, lies in the order of mrad near the angle of total reflection ϑc. ϑc can be calculated via Snell’s law with (6)

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From equations (4) and (6) one can see, that ϑc increases with the electronic density in the sample and decreases linearly with the energy of the radiation. Now we introduce the delayed reflectivity, i.e. we exclude electronic reflectivity and only focus on nuclear resonant scattered quanta. In this case, in grazing incidence geometry the index of refraction of a material containing resonant nuclei is related to the nuclear forward scattering amplitude f0 [30, 31] via: (7)

Here λ is the wavelength of the synchrotron radiation and η the atomic density, and f0 is

(8) Here P is the enrichment of resonant nuclei, fLM the Lamb-Mössbauer factor, α the internal conversion coefficient for the gamma quanta in the nuclei, jex and jgr the momentum of the exited and ground state of the resonant nuclei, Γ the natural linewidth, a the broadening of the line, ΔE the deviation in energy from the resonance (i.e. resolution of the monochromatisation) and ˆi the complex unity. For the index of refraction it follows:

(9)

Putting this in equation (2) the Fresnel coefficients Rij(ϑ) for reflection of the beam at the boundary between two media i and j is

(10)

with

(11)

And we find the simple correspondence (12)

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Here Rij is calculated for perfect plane interfaces. Corrections for non-perfect interfaces can be found e.g. in [31]. The calculation of the reflected amplitude for the layer j of the thickness dj now is given by [32]

(13) Recursive application of equation (13) gives the reflected amplitude of any multilayer structure. Formula (13) is an analytical representation of the measured signal from an isotopic multilayer sample for idealised experimental conditions.

3.2. GINRS and Diffusion Access to physical properties of this films may be achieved by various methods, as -20

2 -1

described in section 2. Measuring very slow diffusivities (below ~ 10 m s ) in thin films is only possible with a method sensitive to the corresponding diffusion length. As described, the method dedicated to this problem is an application of grazing incidence nuclear resonant scattering (GINRS) of synchrotron radiation [2, 3]. The derivation of the diffusion coefficient combines those of DuMond and Youtz [23] and Cook and Hillard [24], using up-to-date diction regarding diffusion and reformulated for resonant nuclei. Let ρFe’ (x, t) and ρFe(x, t) be the mass of iron atoms, Fe’ =^57Fe and Fe =ˆ56Fe or natural iron per unit volume of the intermetallic alloy in an isotopic multilayer at the position x and time t. Further VFe' and VFe be the volume fraction occupied by Fe’ and Fe per unit mass of the intermetallic alloy, respectively. Then the mass fraction of atoms of type Fe’ and Fe of the multilayer are Viρi(x, t) with i ε {Fe’,Fe} which must be preserved in the multilayer

(14) From the definition of ρFe’ (x, t) and D being the concentration independent diffusion coefficient, the diffusion equation holds:

(15) As for the isotopic multilayer ρFe’ (x, t) is a periodic function with period L (bilayer period), it can be expanded in a Fourier series with period L. When diffusion starts the concentration profile (and so the sharp periodicity) decay exponentially with time t. The series can be written as

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(16)

where σn and γn are constants. The series then represent the artificially modulated isotopic periodicities. Substituting this into equation (15) and comparing the coefficients one gets

(17) The density distribution of Fe’ (57Fe) atoms in space decays with time t, i.e. is smeared out with an exponential dependence exp[-4Dπ2n2t/L2]. As the amplitude of the nuclear Bragg peaks is calculated from the layer periodicity it shows a similar exponential behavior:

(18)

Note that here m denotes the order of the nuclear Bragg peak. From (18) it is clear that higher order Bragg peaks decay faster with an order of 2. For the experiment this means that for most multilayers only the first order nuclear Bragg peak can be used. In the measurement only the intensity I is observed, where I ~|A|2. By calculating the logarithmic ratio between the intensity at time t and at time zero, ln[I(t)/I(0)], for the nuclear Bragg peaks we get the time dependent dynamics in the system. Further, for the time derivative, this yields the relation for the determination of D

(19)

Equation (19) means, that by calculating the logarithmic ratio of the intensities for successive annealing steps, one can determine the diffusion coefficient D for one annealing temperature T. An exemplary plot is shown for results on the FePt thin films in figure 5. For different annealing tem- peratures Ti an Arrhenius plot D versus 1/T can be obtained. The activation energy E for the single diffusion jump of the iron atom can be derived via

(20)

with kB the Boltzmann constant and D0 the pre-exponential factor. Resulting from the geometry of the GINRS setup (compare figure 4) and the orientation of the isotopic multilayer structure (see figure 2), experiments give exclusive access to

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diffusion along crystallographic axis perpendicular to the thin film surface. The scattering vector and a specific axis of the thin film are both perpendicular to the sample surface.

Figure 5. Logarithmic ratio ln[It/I0] for the FePt thin films. The Bragg peak intensities versus the total annealing time are plotted at 773 K (circles), 823 K (squares), 848 K (triangles) and 873 K (diamonds). The lines are linear regressions. The slopes correspond to the diffusion coefficients D(T ).

3.3. Limitations of the Method Compared to other NRS experiments [15, 20], determining directly elementary jump processes, the method presented in this chapter gives no information about elementary jump processes or direct access to jump models. Jump models have to be revealed indirectly in combination with other methods. We want to stress that the power of the presented method is studying diffusion on nanoscale systems. The diffusion coefficients accessible for investigation can be tuned by choosing the temperature for the successive annealing steps. To avoid too fast or slow mixing of the layer structure, i.e. the decrease of the nuclear Bragg peaks, the annealing time can be adjusted appropriately. This gives unique access to very low diffusion coefficients. The technique is particularly appropriate to study thin film layers of metals and alloys. It can be applied to alloys that are difficult to obtain as bulk single crystals, but may be grown as thin films. The same holds for metastable systems. The important information for choosing GINRS in this way for diffusion measurements is to check, wether the diffusivities in question may fall in the ’window’ accessible. For this we can estimate a lower and upper limit of accessible diffusion coefficients. It is feasible to orient this on the experimental experience. A rough determination of the limits can be based on the assumption, that a decrease of the nuclear Bragg peak intensity can only be followed, if the decrease is measurable, or not yet completed. We can estimate:

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−

In a rather conservative estimation the upper limit is reached, if about 90% of the Bragg peak decay after about 1/2 h. This values come from the idea that a few annealings are needed to determine one diffusion coefficient, and with heating up and cooling, annealing times below 5 min may cause experimental problems. The lower limit is reached, if no changes of the nuclear Bragg peak intensity occur larger than about 5% after 1 h annealing. The idea is, that the determination of the intensities for a proper evaluation have to be clearly more accurate than the change of the intensity due to diffusion. The time comes from the simple fact, that at a synchrotron during a beam time there is not time to do annealings of very long time periods.

Feeding this assumptions in equation (19) lead to the following limits of the method: (21)

Of course the limits are only benchmarks. The upper limit can be pushed by well defined short annealing times (it seems possible to anneal down to 120 s with small errors with a well constructed furnace). The lower limit can easily be pushed by using more furnaces. For even smaller diffusion constants an ensemble of samples can be pre-annealed for long times and simply measured with GINRS post-annealed.

4. SAMPLE PREPARATION 4.1. Preparation Procedure We will in the following describe briefly the details about sample preparations for the investigated thin films. The samples were deposited using molecular beam epitaxy (MBE) on MgO(001) crystals.

L10-FePt Figure 6 (a) shows a sketch of the L10 structure. The two atomic species form monoatomic planes with a distance of c/2, where c is axis of the elementary cell perpendicular to the monoatomic planes. The structure is tetragonally distorted resulting in the high ordering energy of this phase. In a sample structure order with the c-axis out of plane of the sample surface is called c-variant, whereas ordering with c-axis in plane (i.e. a-axis out of plane) is called a-variant. They are clearly distinguishable via X-Ray Diffraction (XRD), see figure 7. The FePt alloy form a L10 phase for a wide range of concentrations around stoichiometry from 33 at.% Pt to 55 at.% Pt at 873 K. The temperature of the "order-disorder" transition is 1553 K. Clearly the quality of FePt thin films strongly depends on the modification of the preparation conditions such as deposition temperature [33], buffer-layer material and thickness [34]. A problem of preparation via epitaxial growth with MBE is the lattice misfit between the sample and the substrate. For FePt on MgO(001) this is about 9% but only 1.6% on a Pt

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buffer [34, 35]. Therefore a Pt-buffer layer relaxing the stress of the lattice misfit is usually used when preparing thin FePt films. On the other hand, the use of buffer layers can easily induce growth of L10-ordered FePt islands, where the height and width of the islands strongly depends on the deposition temperature and buffer layer thickness [34, 36]. To avoid the island growth and to guarantee a flat film, no buffer was used. Following [34], the stress in the L10 structure can then be reduced only by formation of micro twins destroying the perfect singlecrystalline order. Recent characterisations with transmission electron microscopy (TEM) show a quite different behavior for the preparation conditions described here, see section 4.2.

Figure 6. Sketch of crystalline structures of (a) L10 structure of FePt and FePd with alternating monoatomic planes of Fe and Pt or Pd, respectively, and (b) B2 (CsCl) structure of c-phase FeSi.

Figure 7. XRD image of a L10-ordered poly-crystalline bulk FePt. The peaks at 46.9(1)° and 48.6(1)° correspond to domains of c-variant and a-variant, respectively.

The multilayer was prepared as

with the isotopic bilayer. The FePt layers were deposited at

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623 K in a vacuum better than 1.3x10-10 mbar at the K.U. Leuven. A capping layer of 20 Å Pt deposited at room temperature prevented oxidation of the multilayer. The moderate deposition temperature was chosen to guarantee a well ordered L10 structure [33, 36] but, simultaneously, to prevent the isotopic multilayer structure from mixing during the deposition process. Moreover, the low deposition temperature prevent the formation of islands [36].

L10-FePd The range of formation of the L10 phase lies for FePd at concentrations from 50 at% Pt to 62 at% Pt at 473 K. The temperature of the "order-disorder" transition (TOD) significantly lower than for FePt with 1063 K at 57 at%. From this, and remembering also the lower melting temperature (for FePt TSL = 1830 K, whereas for FePd TSL = 1583 K) it is clear that the magnetocrystalline uniaxial anisotropy is smaller. As the anisotropy causes the preferential formation of the c-variant this makes it much more difficult to grow pure cvariant L10-ordered FePd thin films [37, 38]. Nevertheless, the similarity of the structural and physical features drives the over all characteristics of the L10-FePd system. So again micro twinning is found as mechanism for stress reduction at the interface film substrate [37], as the formation of islands was reported [39]. The TOD and the diffusion data for the disordered fcc-phase [9] mean for the preparation temperature, that the compromise of ordering in cvariant L10 structure (due to high mobility of atoms at the surface during the evaporation process) and slow enough long range diffusion (to avoid mixing of the isotopic multilayer) is harder to be balanced. The layer structure was

with

. The FePd layers were deposited at 620 K in a vacuum better than 1.3x10-10 mbar at the KFKI in Budapest. The Pd-cover was again deposited to avoid oxidation, the Pd-buffer layer and the Cr-seed layer were deposited to improve the formation of c-variant FePd. The concentration was chosen off-stoichiometric, as stoichiometric composition showed bad ordering at the low growth temperature.

c-FeSi Around an iron concentration of 50 at.% the B20 cubic ε -phase is formed as bulk material [40]. For thin films of stoichiometric composition of 50 at.% iron grown epitaxially on MgO(100) substrates FeSi grows in the non-magnetic B2 cubic phase (c-phase) instead of thr ε -phase [16, 17]. The c-phase is only stable up to temperatures of about 548 K [41] and then undergoes a transition to the ε -phase. The growth of the c-phase is rather difficult, as the stoichiometry range of the phase is only about 1 at.%. The preparation has to be done at very low temperatures. The right order is achieved due to the choice of substrate. The multilayer structure prepared at the K.U. Leuven with MBE technique. The structure was [57FeSi(30 Å) / FeSi(40 Å)]x10 / Fe(30 Å)/MgO(100). The deposition temperature was kept as 423 K at a pressure below 1.3x10-10 mbar. Growth rates of 0.052 Å/s and 0.088 Å/s were used for Fe and Si, respectively. No cover layer was used, as the FeSi is resistent against oxidation at room temperature. A sketch of all the layer structures for FePt, FePd and FeSi are shown in figure 8.

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Figure 8. Layer structure of thin film samples for c-variant L10-FePt, (a), c-variant L10-FePd (b) and cphase B2-FeSi (c). The elements, forming the layers are written to the left of each multilayer.

4.2. Characterisation The characterisation of thin films can be done by various methods. We used for all samples XRD, to check crystalline sample structure. Exemplary spectra for the L10 and B2 structure are shown in figure 9. The characterisations were done for Cu-Kα radiation. To examine the hyperfine structure of the samples, conversion electron Mössbauer spectroscopy (CEMS) was done, see figure 10. For the thin film of FePt the composition was checked post-annealed via Rutherford backscattering (RBS) and was Fe50Pt50 with an accouracy of 1 at.%. Furthermore, the RBS yield that the layer remains uniform after annealing (no islanding), and maintains its good crystalline quality. The isotopic stoichiometry was determined by secondary ion mass spectroscopy (SIMS). The disturbance in the layer periodicity (the third bilayer consisted of natural iron only) leads to a splitting of the nuclear Bragg peaks. this effect was not our intention and produced experimental problems, but the evaluation of the data was possible. The long-range order parameter S for the FePt thin film was determined from X-ray diffraction spectra. S was as high as 0.77(5) at 623 K and increases to S=0.94(6) at 877 K in this case. The CEMS spectrum in figure 10 (a) shows the magnetic order of the thin film. From the weights of the spectral lines (1st and 6th line to 2nd and 5th) one can determine the amount of c-variant in the sample (here not less than about 98%). The width of the lines (i.e. the field distribution of the magnetic field) provides information about the local order (nearestneighbor surrounding of the individual iron atoms). The thin films were recently characterised via (TEM) regarding their defect structure, finding a nearly perfect single crystalline c-variant order. The thin films reduce the misfit on the substrate by formation of edge-dislocations at the interface film-substrate in periodic distances.

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Figure 9. X-ray diffraction image of L10-FePt (a) and B2-FeSi (b) as prepared at 623 K and 423 K. The structural reflexes indicating good order can be seen for FePt and FeSi. The peak broadening in (a) is due to poor collimation of the X-rays.

The FePd thin films were checked with CEMS on their magnetic sample structure. As can be seen in figure 10 (b) the structure is not as good as for FePt. This is due to the physical characteristics of the system and the growth conditions, as described above. The samples were of about 78% c-variant with high amount of other oriented domains. The local order was not as good as for FePt, as was found from the distribution of the magnetic field. The c-FeSi was characterised via XRD. From figure 9 the well ordered B2 crystalline sample structure can be seen. Further the isotopic stoichiometry was determined by secondary ion mass spectroscopy (SIMS). CEMS characterisation showed also the non-magnetic structure of the c-phase, see figure 10 (c). The amount of c-phase for 423 K was 100%. The stability of the thin film was tested before the GINRS experiments for long annealing and up to 623 K. The stability was given up to 523 K for annealings of several hours which is clearly above the values reported in [41], but is obviously due to the use of a different substrate.

5. APPLICATION TO INTERMETALLIC THIN FILMS The presented GINRS method for low diffusivities was applied for the intermetallic thin film systems in several beam times at the beamlines ID18 and ID22N of the ESRF [2]. The annealing was accomplished in a quartz-tube furnace in a vacuum of about 10-6 mbar. The GINRS spectra of electronic and nuclear reflectivity for the thin film samples were taken in air at room temperature after successive annealing steps. The delayed nuclear scattered intensity and the prompt electronic reflectivity are measured simultaneously (usually between 10 s and 50 s per point for a scan). A possibility to prove the hyperfine structure of the sample during the successive annealing procedure is collecting time spectra of forward scattered intensity. Exemplary spectra for the as-prepared FePd isotopic multilayer is shown in figure 11. The electronic reflectivity shows a beat (Kiessig beats [29]) pattern corresponding to the total film thickness. The angle of the total reflection ϑc is slightly above 0.25°. It can be seen in the electronic (upper curve) and nuclear (lower curve) reflectivity. For covered films there can be a shift to a smaller value of ϑc than for the pure bilayer structure due to a thick cover

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layer. The position of the total reflection peak is indicating the chemical composition of the sample (except for instabilities of the experimental setup). Its angular stability is therefor a measure of the chemical composition changes during the annealing. Only the nuclear reflectivity shows the characteristic nuclear Bragg peaks of 1st and 2nd-order at angles corresponding to the bilayer periodicity. The 2nd-order Bragg peak of more than 10 times lower intensity than the 1st-order peak, even for the as prepared state and will decay due to annealing as given by equation (18). This shall illustrate the difficulty of determining diffusion coefficients using the 2nd-order Bragg peaks. The logarithmic ratio of the peak intensities versus total annealing time was plotted versus Dt. The slope of the exponential function is the diffusion coefficient D(T), for the annealing temperature T. For the FePt the layered structure lead to a splitting of the nuclear Bragg peaks. The data is normalized for the synchrotron-beam intensity. The small-angle X-4

ray scattering (SAXS) background with its q angular dependence was found to be negligibly small for all measurements and was therefore not taken into account. For the general evaluation the 1st-order nuclear Bragg peaks were fitted by Gaussians. The diffusion coefficients D(T) at the corresponding temperatures were calculated from the intensity loss of the nuclear Bragg peaks via equation (19) (with m =1). exact isotopic structure allowed to fit this behaviour of the nuclear reflectivity data satisfactorily. The results for the annealing temperatures of 773 K, 823 K, 848 K and 873 K are summarized in table 1. The diffusion coefficients follow Arrhenius behavior. The plot of the activation energy is shown in figure 12 (circles), and is compared to high temperature radio-tracer data (triangles showing up and down) and interdiffusion data (squares and diamonds). The slope of the Arrhenius plot corresponds to an activation energy of with the constant The data from nuclear resonant scattering give exclusively information about the iron diffusion along the c-direction in the thin film. There exists no nearest-neighbor jump vector to iron sites in this direction. The next-nearest-neighbor jumps are energetically less favorable than diffusion along the a-direction, i.e. in the layers of pure iron. Nevertheless, the activation energy for diffusion in the low temperature region, obtained by GINRS, is significantly lower than the activation energies from high-temperature radio-tracer data in bulk crystals [6, 7] (for a detailed discussion see [42]). For the L10-structure we have the rare possibility to compare our result to comparative methods like residual resistivity measurements (REST). The GINRS results are in agreement with the activation energies for "order-order" relaxations from REST measurements on Fe50Pt50 bulk polycrystalline sample and in-situ resistivity measurements of the FePt thin film (the same we used in the NRS experiment) [8]. The activation energy achieved by these methods represents the activation energy for migration of Fe in c-direction of the film (i.e. change of order due to antisites), as change in resistivity is not sensitive to the migration of iron atoms along the a-direction (i.e. in the plane of iron no change of order takes place) [43]. This agreement is only valid for the special case of the L10 structure, due to the monoatomic planar formation of the thin film. Resistivity measurements and Monte Carlo simulations [44, 45] indicate that the mechanisms of atomic ordering in intermetallic compounds are very similar to the mechanisms of diffusion and both phenomena operate via the same defect structure [43]. Therefore, it was proposed that each mechanism might be driven by Fe antisites on the Pt lattice via nearest-neighbor jumps of Fe atoms [42]. In different structures (e.g. L12) the correspondence would not be straightforward like for L10 as

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nearest-neighbor jumps within one sublattice separate migration processes from elementary "order-disorder" processes [43]. Effects on the iron diffusivity in FePt regarding surface effects, anti-phase boundaries (APB), or high volume fraction size of the micro twins could be excluded [42]. Recently also the exact defect structure was investigated via TEM, see section 4.2. The recent results achieved for the FePd are of quite different significance. The procedure is the same as for FePt. The temperature range of choice for the GINRS easurements was predetermined from the extrapolation of the high temperature data [9], shown in figure 1. The estimation corresponds to the comparison of the TOD of FePd to FePt. Both indicate a higher diffusivity for the same temperature range for iron self diffusion in FePd than in FePt. This fact may be simply due to the local defect structure, which might allow the iron to diffuse easier in FePd. The measurements were successful at 798 K and 823 K. The Arrhenius plot in comparison with iron diffusivities in FePt at this temperature range is shown in figure 13 the results in table 1. The fact, that only two points were measured, disables the identification of the activation energy. Moreover, the investigations and their interpretation turned out to be rather complicated due to the fact that the complicated sample structure starts to change during annealing. This can be, e.g., interdiffusion of the isotopic layers in the buffer or cover. A re-orientation of FePd to a-variant and disordered domains was found for post-annealed samples. The amount of c-variant shows a drastic decrease, differing at the two temperatures. The amount of a-variant and domains with random magnetic orientation were increased. Note, that the diffusion for iron in a L10 structure is much faster along the a-axis (within monoatomic planes of iron, i.e. without change of the sublattice), as found for FePt [6], than along the c-axis. It follows, that the a-variant domains form diffusion channels along which the iron atoms can easily diffuse. This leads to the effect, that the over all diffusion coefficient is a mixture of the diffusion coefficient along the a-axis and the c-axis of the L10-FePd. The isotopic multilayer then mixes much faster than with diffusion in pure c-variant FePt thin films. As the formation of the a-variant could not be checked during the experiment, the time dependence is not known. Further, the formation need not to be the same for different samples. Therefore, we have to assume that the diffusivities are uncertain. Nevertheless they indicate the approximate range of diffusivity for iron in c-variant FePd. The investigations of FeSi of c-phase did not show any effect of decay of the nuclear Bragg peak at temperatures <= 543 K. This means that the diffusivity is smaller than the sensitivity of the method for annealing times up to 14 h. It was not clear, if the transition of the metastable low temperature c-phase to the ε -phase is of martensitic type or diffusive type. It was suggested that it is martensitic [46]. Nevertheless the transition appears to be rather slow. Further an intermediate phase is formed, growing much faster than the ε -phase, even at temperatures below the transition point [46]. This would indicate a diffusive transition. From that it was assumed that the diffusivity might be measureable even at temperatures below 543 K, as for an diffusive phase transition the mobility of the atoms have to be increased. The extrapolated diffusivities of the ε -phase lie below 10-40 m2s-1 [40]. The iron diffusivities in c-FeSi are situated between this values and the lower limit of the method, see section 3.3 and table 1. The lower limit of diffusivity in cFeSi was checked with a GINRS spectrum taken for a sample annealed at 523 K twice as the original measurement time. Neverthesless, no diffusion could be measured. The GINRS results therefore, might be interpreted as a prove for a martensitic phase transition. It might

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also be, that the diffusivities are close to the limit and can be determined for pre-annealed samples of 10x - 20x longer annealing times.

Figure 10. CEMS spectra for thin films of L10-FePt (a), L10-FePd (b) and c-FeSi (c), note the different velocity scale of (c).

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Figure 11. Electronic (upper curve) and nuclear (lower curve) reflectivity for the as-prepared FePd isotopic multilayer.

Figure 12. Arrhenius plot for iron diffusion in FePt. The NRS data for diffusion along the c-direction in the thin film are indicated by circles (circles), whereas (triangles down) and (triangles up) are radiotracer data for iron diffusion in bulk FePt along the a-and c-direction, respectively [6]. Chemical tracer data are shown as (■), a-direction, and (▲), c-direction, for iron diffusion in bulk FePt [7].

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Figure 13. Arrhenius plot for iron diffusion in FePd. The GINRS data for iron diffusion in FePt thin films are indicated by circles, whereas (■) shows the FePd data. The short dashed and long dashed lines show the extrapolation from high temperature trace data for FePt and FePd, respectively.

Table 1. Annealing temperatures and Diffusion coefficients for the annealing procedure of the FePt, FePd and FeSi thin films system FePt

FePd FeSi

sample / T [K] P 1 / 823 P 2 / 873 P 3 / 773 P 4 / 848 P d / 798 P d / 823 ≤ 543

D [10−24 m2s−1] 20 ± 6 101 ± 2 6.9 ± 2.5 76 ± 11 ~ 150 ± 30 ~ 240 ± 50 < 1.0

CONCLUSION We wanted to show the potential of GINRS applications in determining low and very low diffusivities in intermetallic alloys. The method was successively applied to diffusion studies in well-ordered alloys and gives access to very small diffusion lengths. In combination with complementary methods, the results can provide detailed information about diffusion processes in crystalline ordered structures. We showed the great importance of proper sample preparation and characterisation by various methods. Limits and difficulties of the method were presented and experimental examples given. Finally we want to stress again, that the technique is particularly appropriate to study thin film layers of metals and alloys. It can be applied to alloys which are difficult to obtain as bulk single crystals, but may be grown as thin films. The same holds for metastable systems.

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ACKNOWLEDGEMENTS We thank the European Synchrotron Radiation Facility for provision of synchrotron radiation facilities. We kindly acknowledge the financial support from the Austrian ministery, bm:bwk GZ 45.529/2-VI/B/7a/2002 (MDN) and the 6th framework program of the European Union no. 001516 (DYNASYNC). We kindly thank B. Laenens, N. Planckaert and J. Meersschaut (K.U. Leuven) for the preparation and characterization of the FePt and FeSi isotopic multilayer. We kindly thank D. Merkel and L. Bottyan (KFKI Budapest) for the preparation and characterization of the FePd isotopic multilayer. We thank B. Sepiol (University of Vienna) for many fruitful discussion about the interpretation of the results.

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[20] Vogl G. In Diffusion in condensed matter; Heitjans P., Kärger P.; Ed.; Springer: Berlin Heidlberg, EU, 2005; pp 65. [21] Bracht H., Nicols S.P., Walukiewicz, W., Silveira J.P, Briones F., Haller E.E. Nature 2000, 408, 69-72. [22] Fuchs H.D., Walukiewicz W., Haller E.E., Dondl W., Schorer R., Abstreiter G., Rudnev A.I., Tikhomirov A.V., Ozhogin V.I. Phys. Rev. B. 1995, 51(23), 16817-16821. [23] DuMond J., Youtz J.P. J. Appl. Phys. 1940, 11, 375-365. [24] Cook H.E., Hilliard J.E. J. Appl. Phys. 1969, 40(5), 2191-2198. [25] Wang W.H., Bai H.Y., Zhang M., Zhao J.H., Zhang X.Y., Wang W.K. Phys. Rev. B. 1999, 59(16), 10811-10822. [26] Schmidt H., Gupta M., Geckle U., Bruns M. Def. and Diff. Forum 2007, 263, 51. [27] Smirnov G.V. Hyp. Int. 1996, 97-98, 551-588. [28] Andreeva M.A., Lindgren B. Phys. Rev. B. 2005, 72, 125422. [29] Kiessig H. Ann. Phys. 1993, 10, 769. [30] Hannon J.P., Hung N.V., Trammell G.T., Gerdau E., Mueller M., Rueffer R., Winkler H. Phys. Rev. B. 1985, 32(8), 5068. [31] Roehlsberger R., Witthoff E., Gerdau E., Luecke E. J. Appl. Phys. 1993, 74(3), 19331937. [32] Born M., Wolf E. In Principles of Optics; Pergamon: New York, US, 1977. [33] Endo Y., Kikuchi N., Kitakami O., Shimada Y. J. Appl. Phys. 2001, 89(11), 7065-7067. [34] Hong M.H., Hono K., Watanabe M. J. Appl. Phys. 1998, 84(8), 4403-4409. M. Rennhofer. [35] Kim M.G., Shin S.C., Kang K. Appl. Phys. Lett. 2002, 80(20), 3802-3804. [36] Kim M.G., Shin S.C. J. Appl. Phys. 2001, 90(5), 2211-2215. [37] Halley D., Auric P., Bayle-Guillemaud P., Gilles B., Marty A., Jalabert D. J. Appl. Phys. 2002, 91(12), 9757-9763. [38] Issro Ch., Pueschl W., Pfeiler W., Rogl P.F., Soffa W.A., Acosta M., Schmerber G., Kozubski R., Pierron-Bohnes V. Scripta Mater. 2005, 53, 447-452. [39] Revenant C., Leroy F., Lazzari R., Renaud G., Henry C.R. Phys. Rev. B. 2004, 69, 035411. [40] Salamon M., Mehrer H. Phil. Mag. A 1999, 79(9), 2137-2155. [41] Fanciulli M., Weyer G., Svane A., Christensen N.E., vonKänel H., Müller E., Onda N., Miglio L., Tavazza F., Celino M. Phys. Rev. B. 1999, 59(5), 3675-3687. [42] Rennhofer M., Sepiol B., Sladecek M., Kmiec D., Stankov S., Vogl G., Kozlowski M., Kozubski R., Vantomme A., Meersschaut J., Rüffer R., Gupta A. Phys. Rev. B. 2006, 74(10), 104301. [43] Kozubski R., Kozlowski M., Pierron-Bohnes V., Pfeiler W. Z. Metallkde. 2004, 95(10), 880 887. [44] Kozubski R., Czekaj S., Kozlowski M., Partyka E., Zapala K. J. Alloys Comp. 2004, 378, 302-307. [45] Oramus P., Kozlowski M., Kozubski R., Pierron-Bohnes V., Cadeville M.C., Pfeiler W. Mat. Sci. and Engin. 2004, A365, 166-171. [46] Fanciulli M., Weyer G., Chevallier, J., vonKaenel H., Deller H., Onda N., Miglio L., Tavazza F., Celino M. Europhys. Lett. 1997, 37(2), 139-144.

In: Intermetallics Research Progress Editor: Yakov N. Berdovsky, pp. 261-277

ISBN: 978-1-60021-982-5 © 2008 Nova Science Publishers, Inc.

Chapter 7

CRYSTALLIZATION BEHAVIOR AND MAGNETIC PROPERTIES OF FE-BASED BULK METALLIC GLASSES Mihai Stoica1, Stefan Roth2, Jürgen Eckert1,3 and Gavin Vaughan4 IFW Dresden, 1Institute for Complex Materials 2 Institute for Metallic Materials, Dresden, Germany 3 TU Dresden, Institute of Materials Science, D-01062 Dresden, Germany 4 European Synchrotron Radiation Facility (ESRF), 38402 Grenoble, France

ABSTRACT The expression “glass” in its original sense refers to an amorphous or non-crystalline solid formed by continuous cooling of a liquid, while a solid is defined somewhat arbitrarily as any body having a viscosity greater than 1014 Pa·s. A glass lacks threedimensional atomic periodicity beyond a few atomic distances. It is characterized by a limited number of diffuse maxima in X-ray, electron and neutron diffraction and no sharp diffraction contrast in high-resolution electron microscopy. The glass-forming tendency varies widely. Some oxide mixtures form a glass at normal slow cooling rates of ~1 K/min, while monoatomic metals with possible incorporation of impurities require rates as high as ~1010 K/s. During the solidification no essential change in spatial atomic configuration occurs. A glass may be considered as a solid with frozen-in liquid structure. It is in general not in an internal equilibrium state and thus relaxes structurally to a more stable equilibrium state whenever atoms attain an appreciable mobility. Furthermore, a glass is metastable with respect to crystalline phase(s) and transforms to the latter upon heating through nucleation and growth. As a result of the requirement for rapid cooling, amorphous alloys have usually been prepared in form of thin sheets with a thickness below 0.1 mm. In the last 10-15 years it was found that a number of transition metal-based alloy systems may form bulk metallic glasses (BMGs). These alloys require much lower cooling rates for amorphization or bypassing crystallization upon cooling. Fe-, Co- or Ni- based metallic glasses are good candidates for application as soft magnetic materials because of the lack of crystal

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Mihai Stoica, Stefan Roth, Jürgen Eckert et al. anisotropy. Fe-based alloys able to form magnetic BMGs are of the type transition metal – metalloid and often contain 5 or more elements. Usually, the metalloid content is around 20 at.%. In some cases, the magnetic properties of such BMGs can be enhanced by partial devitrification upon heating at a constant rate or by isothermal annealing. The change in magnetic properties is due to structural changes induced upon heating/annealing. Usually, the Fe-based BMGs form intermetallic metastable phases at elevated temperatures, which finally transform into crystalline stable phases if the heating goes further. Despite several studies published in the literature about Fe-based BMGs and their magnetic properties, just few of them deal with crystallization behavior and crystallization kinetics. The aim of this work is to present the crystallization behavior of some Fe-based BMGs and to link the structural changes with modification of the magnetic properties.

INTRODUCTION In common practice, the term “glass” refers to an amorphous (non-crystalline) oxide, made up mostly of silica (SiO2) and oxides of metals like Al, Ca, Mg, K, Na etc. In general “glasses” are characterized as “hard, brittle and transparent” substances, used for window materials and household glassware. They are prepared by rapid cooling of the molten mixture of silicates and metallic oxides in order to prevent crystallization. During this progressive transition from liquid to solid, which takes place upon fast cooling, the atoms in the liquid do not rearrange themselves into a regular periodic three dimensional structure, i.e. crystalline solid. Thus it is possible to say that the atomic arrangement in the glass is similar to that of the liquid with the same composition and hence sometimes this state of matter is termed “supercooled liquid” [1]. By analogy, the term “metallic glass” refers to an amorphous metallic alloy prepared by rapid solidification of a molten metallic alloy. Hence, it lacks the long-range order symmetry and results in an amorphous liquid-like structure sometimes called as “supercooled metallic liquid” at room temperature. Since the discovery of the first “metallic glass” of composition Au75Si25 in 1960 by Duwez et al. [2] at the California Institute of Technology, Pasadena, USA, it has become a very interesting topic for metallurgists and material scientists to study rapidly solidified alloys all over the world. They used splat-quenching or gun technique to produce amorphous material in form of thin foils. In this process, a small liquid globule is propelled into small droplets by means of a shock wave and the droplets were sprayed on a cold copper substrate. Though it was an unexpected and surprising development, the properties of metallic glasses were found to be better than for crystalline alloys of identical composition [3]. The cooling rate required to produce these glasses was of the order of 106 K/s, thereby restricting the specimen geometry to thin ribbons, foils and powders [1]. The required cooling rate for producing metallic glass was too high in order to suppress normal solidification, because the latent heat of solidification for metals, i.e. the thermal energy released during the phase transformation from the liquid to the solid phase, was very high [1]. The earliest technique applied for the fabrication of metallic glasses in shape of wires or tapes for technical applications was reported by Chen and Miller in 1970 [4]. In this technique a molten alloy is put into the gap between a pair of rapidly rotating rollers which creates very high cooling rates. But the most commonly used process for the fabrication of amorphous alloy in form of ribbon is the well known technique patented by Strange and Pim in 1908 [5],

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in which the molten stream is cast onto the outer surface of a copper wheel rotating at very high speed. The quenching rates achieved by these techniques are on the order of 106 K/s and hence are widely used as industrial manufacturing process as well as for laboratory research and allows to continuously produce glassy ribbons of 20-100 μm thickness and a width in the centimeter range [1]. Generally, Fe-based glassy alloys are well known for their good magnetic properties like soft ferromagnetic or hard ferromagnetic behavior depending on composition, type of constituents and subsequent heat treatment of the alloy [6]. The Fe-based bulk metallic glasses (BMGs) have soft magnetic properties because of the absence of crystalline anisotropy [6,7]. Since the preparation of amorphous alloys in Fe-metalloid system which exhibit good soft-magnetic properties in 1974 [8,9], a large number of studies on the development of softmagnetic amorphous alloys has been carried out for the subsequent decade. However, the shape and dimension of the Fe-based amorphous magnetic alloys has been limited to thin ribbon form with thicknesses below 30 μm because of the necessity of a high cooling rate of almost 106 K/ s for the formation of an amorphous phase [10]. More recently, since 1988, A.Inoue, and his group have succeeded in finding new multicomponent alloy systems with much lower critical cooling rates in Mg-, Ln-, Zr-, Fe-, Pd-CuPd-Fe-, Ti- and Ni-based alloy systems [11]. This fact opens the possibility of other preparation routes like copper mold casting, together with other experimental methods employed for the investigation of the amorphous structure. In 1995, a distinct glass transition before crystallization was found for rapidly solidified Fe72Al5Ga2P11C6B4 [12], and an Fe73Al5Ga2P11C5B4 ferromagnetic bulk metallic glass (BMG) was synthesized through the stabilization of the supercooled liquid [13]. Subsequently, a variety of Fe-based ferromagnetic BMGs have been developed because of their potential magnetic applications [14,15]. Now, the development of Fe- and Co-based BMGs with high glass-forming ability (GFA) has become a very hot research topic not only because of the soft-magnetic properties [16,17] but also of the high fracture strength (σf) of the glass [18,19]. The Fe-based amorphous alloys found in the last decade by Inoue et al. [20-22] typically exhibit a large supercooled liquid region between the glass transition temperature Tg and the crystallization temperature Tx visible upon constant-rate heating to elevated temperatures. Because of the lack of crystal anisotropy, they have good soft magnetic properties characterized by low coercive force and high permeability [13,23-25]. The high glass-forming ability of this kind of alloys allows the formation of bulk glassy samples [26-28]. Such alloys can be directly cast in form of bulk specimens, which can be used for magnetic cores using different techniques, such as copper mold casting or water quenching [11,14]. However, the critical cooling rate of about 102 K/s required for glass formation is higher than the value of about 1-10 K/s characteristic for alloys with very good glass-forming ability [29,30]. Thus, the maximum achievable diameter of these Fe-based alloys is limited to only a few millimeters [31]. The other hindrance that can influence bulk glass formation is the presence of impurities in the melt [14,32] that can be removed using fluxing techniques [33,34], or of crystalline inclusions that can form upon solidification of the melt. In the case of FeCrMoGaPCB alloys, Shen and Schwarz [14] used the flux-melting technique to remove the oxide inclusions from the melt and subsequent water quenching allows to produce rods with 4 mm diameter. From this class of alloys, the nominal composition Fe65.5Cr4Mo4Ga4P12C5B5.5

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was chosen because glass with this composition shows the best thermal stability and soft magnetic properties [14]. On the other hand, bulk amorphous samples with various sizes and shapes can be prepared by mechanical alloying or ball milling of amorphous ribbons combined with subsequent consolidation of the resulting powders in the viscous state at temperatures within the supercooled liquid region [35,36]. High-energy ball milling induces stresses, which can be successfully reduced by annealing the powders at temperatures below the onset of crystallization [27,37]. The enhanced coercivity of ball milled powders in comparison with melt-spun ribbons is not only due to the mechanical stress induced upon milling, but it may be caused also by the presence of nonmagnetic oxide phases formed during milling on the reactive surface of the powder particles [27]. The consolidation process can be combined with annealing in order to obtain bulk specimens with amorphous structure. This can yield bulk amorphous specimens with larger dimensions than those achievable by slow cooling from the melt [38]. By applying such powder metallurgical methods pellets were prepared with 10 mm diameter and 3-5 mm thickness, i.e. larger dimensions than those achievable in case of copper mold casting [39]. By definition, BMGs are alloys in a metastable state. Upon annealing at elevated temperatures, comparable or higher than Tx, new metastable crystalline phases with specific magnetic properties may be promoted. Such kind of bulk nanocrystalline soft magnetic alloys can be produced only by devitrification from their amorphous precursors. The present work will summarize the preparation routes employed to obtain soft magnetic BMGs of different particular compositions (Fe65.5Cr4Mo4Ga4P12C5B5.5 and Fe66Nb4B30) [38-40]. Their magnetic properties will be discussed as well, pointing at the correlation of structure and magnetic properties.

EXPERIMENT Regardless of the preparation procedure, at first master alloys with nominal composition were produced. While Fe66Nb4B30 was simply produced by arc-melting together Fe lumps (99.9% purity), Nb lumps (99.98% purity) and crystalline boron (99.99% purity), and remelting the resulting ingot several times in order to assure homogeneity, the preparation of Fe65.5Cr4Mo4Ga4P12C5B5.5 required more steps and more carefulness, which is basically due to the very high difference in melting temperatures of the constituents. In a first step, induction melting of Fe with B, Fe with C (99.9% purity) and Fe with Ga (99.7% purity) allowed to produce Fe-B, Fe-C and Fe-Ga pre-alloys. Mechanical alloying of Fe powder (99.9% purity, less than 10 microns particle size) with amorphous red P (99% purity, less than 100 microns particle size) in a SPEX 8000 ball mill using hardened steel balls and vial and a ball-to-powder weight ratio of 3:1, followed by consolidation of the resulting powders by cold pressing and subsequent induction melting was employed to obtain the Fe-P prealloy. All materials were handled in a glove box under purified argon atmosphere (less than 1 ppm O2 and H2O). Finally, the Fe65.5Cr4Mo4Ga4P12C5B5.5 master alloy ingots were prepared by induction melting Fe-B, Fe-C, Fe-Ga, Fe-P pre-alloys and lumps of Mo (99.4% purity) and Cr (99.95% purity). The balance of Fe content was realized by controlling the FeP pre-alloy composition. In fact, X-ray diffraction studies combined with chemical analysis (not shown

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here) confirmed that upon 5 hours of milling in the SPEX mill, the entire P powder reacted with Fe powder and the output consisted only of a mixture of α-Fe and Fe2P. Amorphous rods with diameters of 1.5, 2, 2.5 and 3 mm and a length of 70 mm, discs with 10 mm diameter and 1 mm thickness, as well as ribbons (10 x 0.03 mm) were prepared from the Fe65.5Cr4Mo4Ga4P12C5B5.5 master alloy. The rods were obtained by induction melting under argon atmosphere at a pressure of 80x103 Pa and injection into a copper mold under an applied pressure of 3x105 Pa. The ribbons were prepared by single-roller melt spinning under argon flow on a copper wheel at 24 m/s tangential velocity of the wheel. The oxygen content of the master alloys and the pre-alloys was checked by hot extraction using a C436 LECO analyzer. We found values of 50 ppm for Fe65.5Cr4Mo4Ga4P12C5B5.5, 180 ppm for Fe-P and 130 ppm for the other pre-alloys, respectively. The amorphous structure of the samples was checked by X-ray diffraction (XRD) using a Phillips PW 3020 diffractometer with Co-Kα radiation (λ = 0.17889 nm). For the XRD measurements, the cast samples were crushed into small pieces and bonded into amorphous resin in order to have good resolution. The powder metallurgical route was employed in order to obtain bulk amorphous alloys with larger geometrical dimensions than those achievable by copper mold casting. The experimental procedure consisted of two steps: in the first step, the amorphous ribbons or flakes produced by melt spinning were milled in a planetary ball mill until complete conversion to powder. The second step was the hot pressing of these powders. The amorphous ribbons produced by melt spinning were cut into small pieces of about 1 cm length and were introduced into hardened stainless steel milling vials. The vials were also charged with 10 mm diameter hardened steel balls to give a ball-to-flakes mass ratio of about 15:1. For a typical batch of about 25 g of flakes, 90 balls were used. The sample handling was performed in a glove box under a purified argon atmosphere (< 1 ppm O2 and H2O). The milling was performed in a RETSCH PM 4000 planetary ball mill. The milling experiments were done for three different velocities (200, 250, and 300 RPM, respectively) while keeping the milling time constant (3 hours). An unaxial hydraulic press was used to carry out powder consolidation experiments in a controlled atmosphere, in order to produce bulk glassy samples from the as-milled amorphous powders. The press was equipped with a 10 mm inner diameter Ni-base superalloy die and an induction coil wound around the die. A thermocouple fixed in a dedicated cavity within the die ensured a permanent monitoring of the compaction temperature. Typical consolidation experiments were performed in a vacuum of 10-3 mbar, with a constant load of about 500 MPa. The samples were held isothermally in the press under the applied load for 2 min. The compacting temperature was chosen to be in the temperature range of the supercooled liquid region, just above Tg. The resulting compacted samples were discs with 10 mm diameter and about 3-5 mm thickness. The master alloy with composition Fe66Nb4B30 was fluxed with B2O3 to remove oxide impurities as complete as possible. The fluxing was performed under vacuum in an induction furnace. Several BMGs of the fluxed alloy were cast by injecting the molten alloy into machined copper mold to obtain rods with a diameter between 1 and 2mm. The total length of the rods was 4 cm. The glassy nature of the BMGs, as well as their crystallization behavior, was examined by X-ray diffraction in transmission configuration using a high intensity monochromatic synchrotron beam (wavelength 0.015527 nm) at the ID11 station of the European Synchrotron Radiation Facility at Grenoble. The thermal stability, as well as the melting and solidification behavior of all samples was examined by differential scanning calorimetry (DSC) at a constant heating or cooling rate

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of 20 K/min. The DC magnetic properties were determined using a Faraday magnetometer, a Foerster coercimat and a vibrating sample magnetometer (VSM).

Fe65.5Cr4Mo4Ga4P12C5B5.5 Cast Samples Figure 1 shows typical diffraction patterns for Fe65.5Cr4Mo4Ga4P12C5B5.5 samples. Generally, the patterns consist only of a broad diffraction maximum centred at 2θ = 51°, which is characteristic for an amorphous phase. However, it is rather difficult to exclude the existence of a small volume fraction of nanoscale crystalline precipitates, which may be present in the glassy matrix. For example, there are additional diffraction peaks with weak intensity superimposed on the broad diffraction maximum of the amorphous phase for the Fe65.5Cr4Mo4Ga4P12C5B5.5 cast rod with 3 mm diameter. A better physical understanding is given by the wave vector Q, which is related to the wavelength λ and to the diffraction angle θ by:

Q = 4π

sin θ

λ

.

(1)

In extenso, taking into account the Bragg equation for the first-order reflexion, the wave vector becomes

Q=

2π , d

(2)

where d is the spacing between the atomic distances of the material. For amorphous samples of the composition Fe65.5Cr4Mo4Ga4P12C5B5.5, the first broad diffraction maxima are at 2θ = 51.5° ± 0.14°, which corresponds to a wave vector Q = 30.51 ± 0.08 nm-1. As was already mentioned, in the case of the 3 mm diameter rod (Figure 1), two crystalline peaks with weak intensity are superimposed on the broad diffraction maximum of the amorphous phase. The corresponding values of the wave vector are 30.13 nm-1 and 30.90 nm-1, respectively. The first peak is characteristic of a Fe3C-type structure and it is marked in Figure 3.1 by an open circle. The second peak is related to an α-Fe phase with bcc structure and is marked by a black circle. It is worth to mention that the first crystalline reflections cannot be attributed to one single phase. This demonstrates that complex atomic rearrangements are necessary for crystallization upon cooling the melt. Table 1 summarizes the coercivity, saturation magnetization and Curie temperature for Fe65.5Cr4Mo4Ga4P12C5B5.5 as-cast samples. The values are different for samples with different shape or diameter. The lowest coercivity value was found for ribbons and it increases in the case of bulk samples. The coercivity for the ribbon is 1.7 A/m. For rods, Hc increases to 62 A/m for a 3 mm diameter rod, but not monotonically with the sample diameter: 5 A/m for a rod with 1.5 mm diameter, 3 A/m for a rod with 2 mm diameter, 9 A/m for a rod with 2.5 mm diameter or 6 A/m in the case of the disc. The same trend was observed also in the case of similar compositions [38]. The coercivity does not increase monotonically with increasing diameter of the rods, i.e. it does not depend on the geometry of the sample, but is probably

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most sensitive to residual stress induced during the casting and to crystalline inclusions. For glassy samples without crystalline inclusions, the coercivity is typically lower than 10 A/m. The coercivity increases by one order of magnitude when some (nano)crystals are present in the samples and it is expected to depend on the volume fraction of such crystalline inclusions. The 3 mm diameter rod, which shows the highest value of coercivity, it is not fully amorphous - as presented also in Figure 1. The values of the saturation magnetization for different samples and compositions, measured using the VSM, are summarized in Table 1. It can be seen that the saturation is almost the same for all samples. The weak variation of the values of a few percent is within the error of the measurements. The Curie temperature was measured using the Faraday balance, following the procedure described in [41]. As a general trend it is observed that the Curie temperature is larger for rod samples in comparison to ribbon samples, and it increases with increasing rod diameter.

Fe65.5Cr4Mo4Ga4P12C5B5.5 Intensity, [a. u.]

z

- bcc α -Fe  - Fe C-type 3 rod φ 3 mm z

rod φ 2.5 mm rod φ 2 mm rod φ 1.5 mm ribbon 20

30

40 50 60 70 Scan angle, 2θ [degrees]

80

90

Figure 1. X-ray diffraction patterns of as-cast Fe65.5Cr4Mo4Ga4P12C5B5.5 samples.

Table 1. Hc, Ms and TC of as-cast Fe65.5Cr4Mo4Ga4P12C5B5.5 samples Sample ribbon φ 1.5 mm φ 2 mm φ 2.5 mm φ 3 mm disc

Hc [A/m] 1.7 5 3 9 62 6

Ms [Am2/kg] 92.5 91.3 86.8 88 88 90.2

TC [K] 435 451 454 457 460 N.A.

Such a variation of the Curie temperature is due to a more relaxed amorphous structure of the rods with larger diameter in comparison with the ribbons. However, the values corresponding to the rods are close to each other, while the Curie temperatures measured for

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ribbons are 15 K lower. Such behavior may also arise for a small difference in composition between the ribbons and the rods. In one of the glassy Fe65.5Cr4Mo4Ga4P12C5B5.5 discs a hole was introduced by using the spark erosion method. The exact dimensions of the resulting ring were: external diameter 9.90 mm, inner diameter 3.55 mm and thickness 1.04 mm. Around the ring two different windings were attached, corresponding to a primary and a secondary winding, and the resulting toroidal transformer was connected to the B-H loop tracer. Figure 2 shows the hysteresis loops recorded for a maximum applied field of 15 A/cm, with the toroid immersed in water at room temperature (293 K) or in liquid nitrogen (77 K). At saturation, the magnetic flux density B reaches 0.77 T at room temperature and increases up to 1 T when the sample is cooled to 77 K. The values are in the same range as the values obtained from VSM measurements (for this alloy, if one considers the density of 7.057 g/cm3, 1 T corresponds to 112.76 Am2/kg). The initial permeability μi can be determined from the slope of the magnetization curve in the limit HÆ0. In this case,

μ i = lim

H →0

B = 8100 μ0 H

(3)

The low temperature behavior, from room temperature to 100 K, was also investigated using the VSM with a low temperature cryostat mounted on it. Several hysteresis loops were recorded in intervals of 5 K, starting from room temperature down to 100 K,.

Magnetic flux density, B [T]

1.0

77 K 293 K

0.5 0.0 -0.5

Fe65.5Cr4Mo 4Ga4P12C5B5.5 glassy ring

-1.0 -20

-10 0 10 Applied field, H [A/cm]

20

Figure 2. Hysteresis loops for an Fe65.5Cr4Mo4Ga4P12C5B5.5 glassy ring at room temperature and liquid nitrogen temperature.

Crystallization Behavior and Magnetic Properties of Fe-Based …

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2

Magnetization, M [Am /kg]

120 Fe65.5Cr4Mo4Ga4P12C5B5.5 disc φ 10 x 1 mm

115 110 105 100

annealed

95 90

as-cast

85 80 0

50

100 150 200 250 Temperature, T [K]

300

Figure 3. Variation of saturation magnetization with temperature for as-cast and annealed Fe65.5Cr4Mo4Ga4P12C5B5.5 glassy samples (open symbols). The solid lines show the fitting of the experimental data.

In Figure 3, the values of the saturation magnetization are plotted as a function of temperature (symbols), together with the fitting according to a power series of T 3/2 (solid lines), for as-cast samples and samples annealed for 10 min at 723 K. At room temperature, the annealed sample exhibits a slightly larger value of the saturation magnetization (85.96 Am2/kg) than the as-cast sample (85.24 Am2/kg). It increases with decreasing temperature, in a similar way for both samples and without noticeable events. The experimental data presented in Figure3 were fitted using equation 4 [42]:

M (T ) = M (0) ⋅ (1 − B ⋅ T 3 / 2 − C ⋅ T 5 / 2 − ...)

(4)

The parameters M(0), B and C corresponding to Fe65.5Cr4Mo4Ga4P12C5B5.5 glassy samples are listed in Table 2.

as-cast

and

annealed

Table 2. Parameters describing the low temperature dependence of the saturation magnetization for as-cast and annealed Fe65.5Cr4Mo4Ga4P12C5B5.5 glassy discs Fe65.5Cr4Mo4Ga4P12C5B5.5 sample as-cast glassy disc annealed glassy disc

M(0) [Am2/kg] 112 ± 0.05 112 ± 0.09

B [K-3/2] (2.4 ± 0.05)·10-5 (1.7 ± 0.09)·10-5

C [K-5/2] (7.3 ± 0.01)·10-8 (8.9 ± 0.02)·10-8

Generally, the low temperature behavior of the saturation magnetization of crystalline ferromagnetic materials can be described within reasonable error by the first two terms from equation (5):

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M (T ) = M (0) ⋅ (1 − B ⋅ T 3 / 2 )

(5)

For the bulk glassy samples studied here, the fitting using equation (5) gives a high deviation from the experimental curves. The final fitting, as presented in Figure 3 by solid lines, also took the term T5/2 into account. This behavior was analyzed in detail by Bhagat et al. [43] for Fe30Ni45Al3P16B6, Fe29Ni49P14B6Si2 and Fe37.5Ni37.5Al3P16B6. If the range of the exchange interaction is rather high (for example, the Fe-Fe nearest-neighbor distance is = 2.5 Å [44] in pure crystalline α-Fe), i.e. if the exchange interactions take place at a large distance, the B constant from equation (5) can no more be treated as a constant [43]. B is related to the stiffness constant D by [42]:

μ g ⎛ k ⎞ B = 2.612 B ⎜ B ⎟ M (0) ⎝ 4πD ⎠

3/ 2

(6)

where μB is Bohr’s magneton, kB the Boltzmann constant, g the gyromagnetic factor and M(0) is the saturation magnetization at 0 K. The stiffness constant D is also temperature-dependent:

D(T ) = D(0) ⋅ (1 − T )υ

(7)

with 2 ≤ ν ≤ 3 [42]. The assumption that the exchange interactions take place at a larger distance than in crystalline ferromagnetic materials also explains the rather low values of the Curie temperature (around 450 K- see Table 1-, in comparison to 1044 K for bcc α-Fe). The average magnetic moment per iron atom calculated from the fitting at 0 K, <μ>, is 0.73μB, in comparison to 2.2μB for bulk crystalline Fe. This is also an indication that the magnetic interactions take place at a rather large distance.

Fe65.5Cr4Mo4Ga4P12C5B5.5 Compacted Samples In order to prepare bulk samples with larger dimensions, the powder metallurgy route was employed. The experimental procedure was already described in the experimental part. The initial ribbons, named R1, R2 and R3, were identically from the structural point of view (completely amorphous – see Figure 4). The X-ray diffraction experiments performed for the powders (P1, P2 and P3 describe the powders of ribbons R1, R2 and R3, which were milled at 200, 250 and 300 RPM, respectively), revealed also a fully amorphous structure (Figure 5). The relative densities of the pressed pellets were calculated as the ratio between the actual density and the theoretical density (7057 kg/m3) of the alloy and were in the range of 75-80%. The broad maxima, characteristic for an amorphous phase, are centered at 2θ = 51.5° (Q = 30.51 nm-1) in the case of melt-spun ribbons. Upon milling, the maxima shifted towards higher values: Q = 30.58 nm-1 for powder P1, 30.59 nm-1 for powder P2 and 30.62 nm-1 for powder P3, respectively. As published recently [45,46], the higher values of Q can be attributed to an increase of the free volume content in the material. The amount of free volume, which is generated upon milling, is proportional to the milling intensity: the higher

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the velocity of the colliding balls as given through the rotational velocity of the milling plate, the higher is the amount of excess free volume in the glass. This agrees well with free volume generation during heterogeneous plastic deformation of metallic glasses [47]. After milling, a small quantity of each as-milled powder was mixed with an amorphous resin and dried. The samples prepared in this way were measured with the coercimat. The values of the coercivity are listed in Table 3 under the name of “coercivity of as-milled powders”.

Intensity [a. u.]

Ribbon flakes used as precursors for milling

R1 R2 R3 30

40

50 60 70 80 Scan angle, 2θ [degree]

90

100

Figure 4. XRD patterns of amorphous Fe65.5Cr4Mo4Ga4P12C5B5.5 ribbons before milling.

Milled Powders Intensity [a.u.]

P1

P2 P3

30

40

50 60 70 80 Scan angle, 2θ [degree]

90

100

Figure 5. XRD patterns of powders prepared by milling Fe65.5Cr4Mo4Ga4P12C5B5.5 ribbons: P1 at 200 RPM, P2 at 250 RPM and P3 at 300 RPM.

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Table 3. Coercivity of Fe65.5Cr4Mo4Ga4P12C5B5.5 powder samples and of the initial ribbon used as precursor. The estimated relative density values are also given Sample Hc [A/m] as-milled Hc [A/m] as-compacted Hc [A/m] annealed Relative density of compacted pellets

P1 1090 50 23 80.6 %

P2 1260 60 37 79.4 %

P3 1500 190 135 76.8 %

Ribbon – 1.7 <1 100 %

The rest of each powder batch was compacted and the resulting pellets were also measured with the coercimat. Next, the as-compacted pellets were annealed for 10 min at a temperature corresponding to Tg for each powder sample, i.e. P1 at 746 K, P2 at 743 K and P3 at 733 K, respectively (the thermal stability data are not presented here). Table 3 shows the coercivity values for powder samples at each stage: as-milled, as-pressed and after annealing. The corresponding values for ribbons are also given. After hot compaction, the samples show a lower coercivity, characteristic for soft magnetic alloys, but up to more than 100 times larger than the value of the as-quenched ribbon. A subsequent annealing can decrease these values. The final values are lower, but still at least one order of magnitude higher than those obtained for bulk cast samples (Table 1). The explanation for this behavior is related to the lower relative density, which characterizes the compacted samples, in contrast to the fully dense samples obtained by copper mold casting. The presence of pores is magnetically the same as the presence of a second nonmagnetic phase and gives rise to a stray field [48]. Thus magnetization reversal is impeded by the pores. The samples P1 and P2, with relatively close density values (80.6 % for P1 and 79.4 % for P2), exhibit also similar coercivities (23 A/m for P1 and 37 A/m for P2), but with a further decrease of the density (76.8 % for P3), the coercivity increases drastically: 135 A/m even after annealing. Another fact, which may help to explain this behavior, is the possible increase of the oxygen content with increasing milling velocity, where oxides are another non magnetic phase similar as e.g. pores and may also act as sources of stress due to different thermal expansion.

Fe66Nb4B30 Cast Samples Very recently [40], we reported that the Fe66Nb4B30 alloy may form BMG by copper mold casting. BMG specimens of this composition can be prepared in rod shape and the maximum diameter for which the alloy is still amorphous is 2 mm. DSC investigations revealed a glass transition event with an onset temperature of 845 K, followed by a first crystallization event with onset at 876 K and a second crystallization event at 1035 K. The melting takes place through a peritectic reaction. Thus, the liquidus temperature, Tliq, measured as the onset of the last melting peak, is 1530 K [49]. Figure 6 (a) shows the X-ray patterns recorded in-situ during heating with a rate of 20 K/min for an amorphous 2 mm diameter rod, while Figure 6 (b) contains in detail patterns corresponding to the room temperature amorphous state, crystallized at 1000 K (above the first crystallization event) and at 1300 K (above the second crystallization event).

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(a)

(b) Figure 6 .In-situ crystallization behavior (a) and phase identification (b) for an Fe66Nb4B30 rod with 2 mm diameter.

As is observed from Figure 6 (b), after the first crystallization some crystalline peaks appear, which are superimposed on the broad maxima characteristic of the amorphous phase. At this moment, the sample contains only nanocrystals of a metastable Fe23B6-type phase and, eventually, some residual amorphous matrix. The phase has in fact the composition (Fe,Nb)23B6, with a fcc structure and a lattice constant a = 1.076 nm. As the temperature increases further, this metastable phase transforms completely into α-Fe, Fe2B and FeNbB phases. Also, no residual amorphous matrix can be observed.

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It is interesting to follow the changes in magnetic properties as the structure changes. Figure 7 shows the variation of the saturation magnetization MS with temperature, measured at a constant heating and cooling rate of 20 K/min. At a certain temperature, the saturation drops to zero; this point can be considered to be the Curie temperature of the amorphous phase, (Fe,Nb)23B6 as TC = 550 K. As the temperature increases and approaches the point where (Fe,Nb)23B6 starts to form, the saturation increases again (inset in Figure 7), indicating that this phase is ferromagnetic. The cooling curve does not follow the heating curve, because of the presence of the crystalline magnetic phase. Due to experimental limitation, the heating did not reach 1035 K, the point where the (Fe,Nb)23B6 phase transforms completely. From the cooling curve a Curie temperature of 720 K can be determined from the point of inflection in the cooling curve of Figure 7. This Curie temperature is attributed to the residual amorphous matrix (which has another composition than the starting one). (Fe,Nb)23B6 has a Curie temperature larger than 900 K, as can be seen from the inset in Figure 7. Thus, the Curie temperature of the emerging nanocrystalline metastable (Fe,Nb)23B6 is much higher than the Curie temperature of amorphous Fe66NB4B30 and the Curie temperaure of the amorphous phase increases considerably upon precipitating the crystalline (Fe,Nb)23B6 phase. Taking into account that the saturation magnetization usually follows the trend of the Curie temperature [48], one also expects to observe an increase in saturation upon nanocrystallization. Figure 8 compares the hysteresis loops recorded for two slices cut from a 2 mm diameter rod, fully amorphous at room temperature, and annealed at 900 K and 1300 K, respectively. The annealing temperatures were chosen to match the maximum temperature attained in the case of the Curie temperature and in-situ crystallization measurements, respectively.

Figure 7. Temperature variation of the saturation magnetization recorded for a 2 mm diameter Fe66Nb4B30 amorphous rod.

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Figure 8. Hysteresis loops for Fe66Nb4B30 2 mm diameter rods crystallized upon annealing at (a) 900 K and (b) 1300 K.

For the amorphous sample, the coercivity is 1.5 A/m and the saturation magnetization 105 Am2/kg. The sample annealed at 900 K shows a larger coercivity, but still very low (85 A/m), and a 15% higher saturation (120 Am2/kg). A further increase of the annealing temperature leads to macroscopic crystallization of the amorphous sample. Even if the saturation further increases to 130 Am2/kg, the soft magnetic properties almost disappear: the coercivity is three orders of magnitude higher (5000 A/m) and the hysteresis loop is no more rectangular.

CONCLUSION Fe65.5Cr4Mo4Ga4P12C5B5.5 can be successfully prepared as BMG using different routes. The achievable geometry and dimensions, together with very attractive soft magnetic properties, make this alloy a good candidate for applications. Fe-based BMGs can be prepared also even in a ternary system and with very high metalloid content (Fe66Nb4B30) if the melt is fluxed prior to casting. This alloy also exhibits excellent soft magnetic properties. The magnetic properties are correlated with the structure of the material and are strongly influenced by the stress anisotropies induced during different preparation routes. At the same time, the magnetic properties can be enhanced by annealing treatment. If the annealing takes place at moderate temperatures, i.e. at temperatures well below the glass transition, the structure relaxes and the induced anisotropies are released. If the annealing temperature is high, a structural change can be induced, with influence on the magnetic response of the material. This particular behavior can be explained by the formation of nanocrystalline metastable ferromagnetic phases. Such kind of phases can be formed only from the

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amorphous precursors. A too high annealing temperature may be detrimental to the soft magnetic properties of the material once complete crystallization takes place.

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[8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]

Anantharaman, T.R.; Suryanarayana, C. Rapidly solidified metals: a technological overview; Trans Tech Publications: Switzerland-Germany-USA, 1987. Klement, W.; Willens, R.H.; Duwez, P. Nature 1960, 187, 869-870. Rapidly Solidified Alloys: Processes Structures, Proeprties, Applications; Liebermann, H.H.; Marcel Dekker, Inc.: New York NY, 1993. Chen, H.S.; Miller C.E. Rev. Sci. Instrum. 1970, 41, 1237-1238. Strange, E.H.; Pim, C.A. (1908) Process of manufacturing thin sheets, foil, strips, or ribbons of zinc, lead, or other metal or alloy, US Pat. 905758. Boll, R. Weichmagnetische Werkstoffe; VAC GmbH, Siemens AG: Berlin-München, Germany, 1990. Roth, S.; Ferchmin, A.R.; Kobe, S. In Magnetic Properties of Metals; Wijn, H.P.J.; Landolt-Börnstein Series - Numerical Data and Functional Relationships in Science and Technology; Springer-Verlag: Berlin-Heidelberg, Germany, 1994; Vol. III/19, pp. 144200. Fujimori, H; Masumoto, T; Obi, Y; Kikuchi, M. Jpn. J. Appl. Phys. 1974, 13, 18891890. O’Handley, R.C; Hasegawa, R; Ray, R; Chou, C.P. Appl. Phys. Lett. 1976, 29, 330-332. Cahn, W. In Rapidly Solidified Alloys; Liebermann, H.H.; Marcel Dekker: New York, NY, 1993, pp. 1–15. Inoue, A. Acta Mater. 2000, 48, 279-306. Inoue, A; Shibata, T; Zhang, T. Mater Trans. JIM 1995, 36, 1420-1426. Inoue, A; Gook, J.S. Mater. Trans. JIM 1995, 36, 1180-1183. Shen, T.D.; Schwarz, R.B. Appl. Phys. Lett. 1999, 75, 49-51. Shen, B.L.; Inoue, A. Mater. Trans. 2002, 43, 1235-1239. Pawlik, P; Davies, H.A.; Gibbs, M.R.J. Appl. Phys. Lett. 2003, 83, 2775-2777. Stoica, M; Roth, S; Eckert, J; Schultz, L; Baró, M.D. J. Magn. Magn. Mater. 2005, 290–291, 1480-1482. Inoue, A; Shen, B.L.; Yavari, A.R.; Greer, A.L. J. Mater. Res. 2003, 18, 1487-1492. Sheng, S.H.; Ma, C.L.; Pang, S.J.; Zhang, T. Mater. Trans. 2005, 46, 2949-2953. Inoue, A; Gook, J.S. Mater. Trans. JIM 1996, 37, 32-38. Inoue, A; Gook, J.S. Mater. Trans. JIM 1995, 36, 1282-1285. Inoue, A. Mater. Sci. Eng. A 1997, 226-228, 357-363. Inoue, A; Murakami, A.; Zhang, T.; Takeuchi, A. Mater. Trans. JIM 1997, 38, 189-196. Mizushima, T.; Makino, A.; Inoue, A. Mater. Sci. Eng. A 1997, 226-228, 721-725. Inoue, A.; Koshiba, H.; Zhang, T.; Makino, A. Mater. Trans. JIM 1997, 38, 577-582. Chen, H.S. Rep. Prog. Phys. 1980, 43, 353-432. Schlorke, N.; Eckert, J.; Schultz, L. J. Phys. D: Appl Phys. 1999, 32, 855-861. Mizushima, T.; Iskarashi, K.; Yoshida, S.; Makino, A.; Inoue, A. Mater. Trans. JIM 1999, 40, 1019-1022.

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[29] Inoue, A.; Kato, A.; Zhang, T.; Kim, S.G.; Masumoto, T. Mater. Trans. JIM 1991, 32, 609-616. [30] He, Y.; Shen, T.D.; Schwarz, R.B. Metall. Mater. Trans. A 1998, 29, 1795-1804. [31] Inoue, A.; Zhang, T.; Takeuchi, A. Appl. Phys. Lett. 1997, 71, 464-466. [32] Gebert, A.; Eckert, J.; Schultz, L. Acta Mater. 1998, 46, 5475-5482. [33] Kui, H.W.; Greer, A.L.; Turnbull, D. Appl. Phys. Lett. 1984, 45, 615-616. [34] Shen, B.L.; Kimura, H.; Inoue, A.; Mizushima, T. Mater. Trans. JIM 2001, 42, 660663. [35] Eckert, J.; Schlorke, N.; Miranda, C.A.R.T.; Schultz, L. In Synthesis and Processing of Light Weight Mettalic Materials II; Ward-Close, C.M. et al.; Warrendale: The Minerals Metals and Materials Society, 1997; pp. 383-394. [36] Seidel, M.; Eckert, J.; Bauer, H.D.; Schultz, L. Mater. Sci. Forum 1996, 119, 225-227. [37] Schlorke-de Boer, N.; Schäfer, R.; Eckert, J.; Schultz, L. J. Appl. Phys. 2002, 91, 66016610. [38] Stoica, M. Casting and Characterization of Fe-(Cr,Mo,Ga)–(P,C,B) Soft Magnetic Bulk Metallic Glasses, Shaker Verlag: Aachen, Germany, 2005. [39] Stoica, M.; Eckert, J.; Roth, S.; Schultz, L. Mat. Sci. Eng. A 2004, 375-377, 399-402. [40] Stoica, M.; Hajlaoui, K.; Lemoulec, A.; Yavari, A.R. Phil. Mag. Lett. 2006, 86, 267275. [41] Herzer, G. IEEE Trans. on Magn. 1989, 25, 3327-3329. [42] Handrich, K.; Kobe, S. Amorphe Ferro- und Ferrimagnetica, Akademie-Verlag: Berlin, Germany, 1980. [43] Bhagat, S.M.; Spano, M.L.; Rao, K.V. J. Appl. Phys. 1979, 50, 1580-1582. [44] Axe, J.D.; Shirane, G.; Mizoguchi, T.; Yamauchi, K. Phys. Rev. B 1977, 15, 2763-2770. [45] Yavari, A.R.; Tonegaru, M.; Lupu, N.; Inoue, A.; Matsubara, E.; Vaughan, G.; Kvick, Å. Mat. Res. Soc. Symp. Proc. 2004, 806, 203. [46] Hajlaoui, K.; Benameur, T.; Vaughan, G.; Yavari, A.R. Scripta Mater. 2004, 51, 843848. [47] Heggen, M.; Spaepen, F.; Feuerbacher, M. Mat. Res. Soc. Symp. Proc. 2004, 806, 307. [48] Kneller, E. Ferromagnetismus; Springer-Verlag: Berlin, Germany, 1962. [49] Stoica, M.; Hajlaoui, K.; Das, J.; Eckert, J.; Yavari, A.R. submitted to J. Alloys Comp. (presented at ISMANAM 2006, Warsaw, Poland).

INDEX A access, ix, 237, 239, 240, 242, 246, 247, 257 accuracy, 111, 169 acid, 25, 38, 39 activation, 17, 67, 71, 72, 73, 74, 75, 76, 77, 79, 81, 82, 83, 84, 85, 86, 87, 91, 94, 98, 101, 108, 110, 113, 123, 124, 125, 246, 253, 254 activation energy, 17, 67, 71, 72, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 98, 101, 108, 110, 113, 124, 125, 246, 253, 254 activation enthalpy, 79, 81, 87, 123, 125 activation parameters, 87, 101, 110 adhesion, 6, 7, 8, 12, 14, 24, 25, 31, 39, 43 aerospace, vii, 1, 2, 18, 232 agent, 167, 168 aggregates, 29 aging, ix, 75, 104, 213, 222, 230, 231, 232, 233 Al2O3 particles, 7, 28, 29 alkaline, 141, 175, 183, 196, 205, 210 alternative, 20, 198 alters, 150 aluminide, 2 aluminium, viii, 2, 3, 14, 17, 18, 21, 37, 40, 42, 65 aluminum, 14, 15, 36 Aluminum, 18 ammonium, 142 amorphization, x, 261 amplitude, viii, 65, 66, 67, 71, 87, 88, 91, 92, 94, 243, 244, 245, 246 Amsterdam, 127, 171, 172 analytical techniques, 136 anelasticity, viii, 65, 69, 81, 109, 127, 132 anion, 6, 30, 37, 149, 154, 155 anisotropy, x, 225, 238, 250, 262, 263 annealing, vii, x, 37, 76, 77, 81, 85, 89, 90, 98, 102, 103, 108, 110, 112, 113, 115, 118, 119, 121, 163, 166, 167, 169, 228, 239, 240, 242, 246, 247, 248,

251, 252, 253, 254, 255, 257, 262, 264, 272, 274, 275 annihilation, 71 antiphase domains, vii aqueous solutions, 19 Argentina, 69, 125 argon, 10, 28, 37, 39, 69, 264, 265 argument, 79 Arrhenius equation, 67 Arrhenius law, 73 arsenic, 165, 166 assimilation, 151, 152, 153 assumptions, 126, 248 asymmetry, 113, 124 atmosphere, ix, 16, 19, 23, 27, 28, 34, 39, 42, 69, 164, 170, 178, 213, 230, 264, 265 atomic distances, x, 239, 243, 261, 266 atomic force, 153 atomic orbitals, 150 attention, vii, viii, 1, 2, 33, 135, 142, 175, 178, 224 Austria, 237 averaging, 72, 126

B backscattering, 251 band gap, 137, 144, 145, 175, 178, 180, 187, 190, 192, 196, 203, 204, 205, 207, 208, 209, 210, 211 barriers, 37, 126, 140 behavior, viii, x, 5, 6, 7, 10, 11, 12, 16, 23, 37, 135, 145, 148, 149, 176, 187, 189, 192, 221, 226, 228, 231, 246, 249, 253, 262, 263, 265, 268, 269, 270, 272, 273, 275 Beijing, 211 benchmarks, 248 bending, 88, 89, 122 beneficial effect, 7, 11, 14, 18, 22, 23, 24, 28, 33, 37 binding, 75 binding energy, 75

280

Index

blocks, 141, 142, 150, 151, 153, 155, 156, 170 Boltzmann constant, 125, 246, 270 bonding, vii, 24, 39, 41, 150, 180, 187, 225, 227 bonds, 136, 140, 198 bounds, 225 breakdown, 4, 221 Britain, 132 British Columbia, 234 bromine, 32 buffer, 248, 249, 250, 254 building blocks, 170

C cadmium, 136, 162 California, 59, 262 calorimetry, 71, 265 candidates, x, 94, 238, 261 Capacity, 128 capsule, 37 carbides, viii, 5, 16, 68, 75, 94, 95, 97, 99, 102, 107, 135 carbon, viii, 5, 65, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 88, 94, 97, 99, 110, 111, 112, 115, 116, 118, 123, 124, 125, 126, 127, 176, 232 carbon atoms, 5, 69, 76, 79, 99, 112, 118, 125, 126, 127 carburization, viii, 2 carefulness, 264 carrier, 137, 145, 165 cast, 7, 10, 32, 33, 39, 40, 42, 89, 113, 114, 118, 119, 263, 265, 266, 267, 269, 272 casting, 9, 42, 118, 263, 264, 265, 267, 272, 275 catalytic effect, 38 cation, 8, 11, 19, 27, 37, 149, 154, 155 C-C, 74, 126, 127 cell, 149, 150, 169, 179, 180, 181, 182, 187, 189, 190, 192, 194, 196, 197, 199, 200, 202, 204, 207, 248 ceramic, 9, 19 ceramics, vii, 1, 2, 20 cerium, 5 chalcogenides, viii, 135, 148, 149, 169 channels, 155, 254 charge density, 176 chemical bonds, 136, 140 chemical composition, 7, 136, 158, 240, 253 chemical properties, 139, 145 chemical reactions, 140, 143, 145 chemical vapor deposition, 232 chemical vapour, 36 Chicago, 127 Chinese, 212

chloride, 32 chlorine, 32 chromium, 2, 3, 24, 97, 99 cladding, 35 classification, viii, 135 closure, 190 clustering, 142 clusters, 140, 149, 150, 152, 156, 158, 160 CO2, 18, 37, 69, 165 coal, 3 coatings, 13, 15, 17, 24, 34, 35, 36, 38, 39, 40, 41, 42, 232 collisions, 140 combustion, 69 communication, 235 community, 43 compatibility, 35 competition, 21 components, vii, 1, 2, 3, 20, 21, 25, 26, 75, 76, 81, 87, 89, 103, 104, 105, 136, 137, 139, 142, 143, 144, 150, 157, 159, 163, 166, 169, 170, 171, 183, 232 composites, 20, 41 compound semiconductors, 175 compounds, vii, viii, ix, 1, 2, 20, 21, 41, 43, 65, 66, 68, 72, 76, 109, 135, 136, 137, 141, 142, 143, 145, 146, 148, 149, 150, 151, 155, 156, 157, 159, 160, 161, 163, 164, 165, 166, 167, 168, 169, 170, 175, 176, 177, 178, 189, 190, 192, 193, 206, 209, 210, 213, 214, 215, 216, 219, 222, 223, 224, 225, 226, 227, 228, 230, 231, 232, 233, 235, 238, 253 computer simulation(s), 81, 124 concentration, 2, 3, 4, 5, 9, 11, 13, 14, 19, 21, 22, 26, 27, 29, 30, 32, 33, 34, 37, 39, 68, 72, 74, 75, 76, 78, 81, 82, 83, 88, 90, 91, 95, 96, 107, 123, 126, 137, 144, 145, 152, 153, 159, 169, 170, 176, 187, 189, 211, 240, 241, 242, 245, 250 condensation, 8, 13, 14 condensed matter, 258, 259 conduction, 117, 144, 145, 176, 180, 181, 183, 184, 185, 187, 189, 190, 192, 194, 203, 204, 207, 208, 209, 210 conductivity, 13, 117, 136, 169, 176, 177, 189 conductor, 189, 238 confidence, 170 confidence interval, 170 configuration, x, 126, 127, 141, 150, 152, 155, 158, 170, 176, 180, 181, 193, 194, 261, 265 congruence, 161 conservation, 3 consolidation, 17, 264, 265 constant load, 265 constant rate, x, 262

Index Constitution, 131 constraints, 163 consumption, 37, 41, 139 contamination, 5 control, 3, 13, 21, 22, 25, 29, 107, 148, 149, 160, 163, 165, 168, 169 conversion, 3, 158, 178, 189, 211, 244, 251, 265 convex, 157, 159 cooling, ix, x, 6, 8, 12, 13, 33, 78, 81, 88, 93, 100, 107, 109, 110, 111, 112, 113, 114, 116, 117, 121, 122, 123, 139, 140, 162, 170, 248, 261, 262, 263, 264, 265, 266, 274 copper, 169, 262, 263, 264, 265, 272 correlation(s), 121, 175, 199, 233, 264 correlation function, 175 corrosion, vii, viii, 1, 2, 3, 4, 5, 9, 11, 15, 19, 24, 42, 170 costs, 232, 233 Coulomb, 127, 176 couples, 238 coupling, 90, 196, 239 crack, 16, 34, 216 creep, vii, 3, 6, 7, 8, 9, 17, 18, 21, 22, 26, 215, 216, 228 critical value, 16, 32 cryogenic, 17, 217, 223 crystal growth, 140, 141, 163, 165, 166 crystal structure(s), vii, ix, 1, 2, 22, 27, 34, 40, 43, 141, 142, 153, 177, 178, 179, 181, 193, 194, 200, 206, 209, 213, 214, 216, 218, 219 crystalline, ix, x, 9, 39, 82, 92, 126, 127, 157, 207, 249, 251, 252, 257, 261, 262, 263, 264, 266, 267, 269, 270, 273, 274 crystalline solids, 127 crystallisation, 117 crystallites, 141 crystallization, vii, x, 39, 261, 262, 263, 264, 265, 266, 272, 273, 274, 275, 276 crystallization kinetics, x, 262 crystals, ix, 14, 42, 77, 91, 137, 138, 139, 140, 141, 142, 143, 145, 148, 149, 150, 151, 153, 154, 156, 162, 163, 164, 165, 166, 168, 169, 170, 176, 213, 214, 217, 247, 248, 253, 257, 267 Curie temperature, 68, 90, 93, 98, 102, 103, 120, 121, 266, 267, 270, 274 CVD, 36 cycles, 12, 36, 116 cycling, 4, 8, 9, 13, 17, 30, 33

D Daltonide, ix, 213, 220

281

damping, viii, 65, 67, 74, 77, 85, 89, 92, 93, 94, 96, 102, 107, 108, 109, 115, 124, 125 Debye, 66, 73, 74, 90, 100, 110, 112, 124, 125 decay, 69, 245, 246, 248, 253, 254 decomposition, viii, 19, 29, 90, 135, 142, 148, 151, 156, 157, 158, 160, 165 deconvolution, 87, 112, 124 defect formation, 145, 146, 156, 184 defects, vii, viii, 8, 16, 25, 42, 43, 65, 87, 90, 94, 123, 127, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 154, 155, 156, 158, 159, 170, 183, 184, 192, 209, 215, 217, 219, 220, 224 deficiency, 155 definition, 159, 214, 264 deformation, 6, 7, 12, 20, 21, 25, 34, 35, 39, 40, 87, 88, 89, 94, 216, 217, 221, 222, 223, 230, 233, 271 degenerate, 194, 198 degradation, 11, 34, 42, 145 degradation rate, 11 demand, 232 density, vii, 1, 2, 3, 8, 10, 13, 15, 18, 20, 21, 33, 34, 40, 89, 97, 102, 139, 145, 146, 149, 155, 156, 175, 176, 181, 192, 209, 223, 232, 238, 240, 243, 244, 246, 268, 270, 272 density functional theory, 181 density values, 272 deposition, 12, 24, 25, 36, 41, 163, 187, 232, 248, 249, 250 derivatives, 69 desire, 21 destruction, 28 detachment, 12 detection, 69 deviation, viii, ix, 118, 124, 135, 136, 137, 142, 144, 150, 161, 170, 213, 220, 222, 244, 270 DFT, 175, 176, 200, 203, 209 diamond, 150 Diamond, 175 diamonds, 247, 253 dielectric, 186 dielectric constant, 186 differential scanning calorimetry (DSC), viii, 65, 71, 95, 96, 100, 102, 109, 111, 115, 116, 117, 119, 120, 121, 124, 265, 272 diffraction, x, 71, 106, 109, 115, 116, 118, 119, 148, 152, 153, 155, 167, 222, 223, 232, 251, 252, 261, 264, 265, 266, 267, 270 diffusion, ix, 2, 6, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 71, 72, 76, 81, 82, 83, 84, 85, 88, 98, 108, 125, 126, 136, 139, 145, 170,

282

Index

216, 222, 230, 237, 238, 239, 240, 242, 245, 246, 247, 248, 250, 253, 254, 256, 257 diffusion process, 2, 19, 36, 43, 238, 257 diffusion region, 41 diffusivities, ix, 13, 34, 237, 238, 239, 240, 245, 247, 252, 254, 257 diffusivity, 21, 30, 31, 32, 33, 39, 77, 238, 254 diodes, 145 dipole, 72, 140 direct measure, 66 discontinuity, 116, 121, 176 discs, 265, 268, 269 dislocation, viii, 2, 34, 65, 67, 75, 86, 88, 89, 90, 94, 96, 107, 140, 165, 216, 217, 218, 220, 221, 222, 223, 224, 226, 227, 228, 233 disorder, vii, 83, 90, 102, 121, 123, 217, 220, 248, 250, 254 dispersion, 6, 8, 11, 14, 19, 188 displacement, 140, 192, 217, 227 dissociation, 37, 38, 97 dissolved oxygen, 22 distortions, 106, 150 distribution, 7, 14, 22, 23, 34, 67, 73, 75, 76, 86, 92, 101, 104, 110, 119, 123, 125, 126, 146, 149, 151, 155, 170, 189, 192, 246, 251, 252 distribution function, 146, 170 domain structure, 91, 108, 141 donors, 140 doping, 8, 14, 23, 28, 30, 39, 185, 187, 228 ductility, vii, ix, 1, 2, 3, 9, 11, 13, 15, 18, 20, 21, 22, 23, 25, 26, 33, 41, 42, 68, 89, 97, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 227, 229, 232, 233 durability, 176

E earth, ix, 6, 7, 22, 33, 75, 141, 175, 176, 177, 183, 196, 205, 210, 213, 222, 227, 233, 235 elasticity, 21, 90 electrical conductivity, 136 electrical properties, vii electricity, 169 electrochemical, 25, 169 electrochemical deposition, 25 electrodeposition, 34, 232 electrodes, 169 electrolysis, 169 electron diffraction, 153 electron microscopy, x, 71, 148, 153, 249, 261 electron paramagnetic resonance, 140 electronegativity, 176, 177, 217 electronic structure, 43, 175, 176, 185, 209, 210, 226

electron(s), x, 71, 120, 137, 139, 140, 144, 148, 153, 169, 176, 177, 178, 180, 181, 185, 186, 187, 189, 190, 193, 194, 196, 202, 204, 211, 226, 243, 249, 251, 261 electroplating, 35 elongation, 214, 215, 216, 217, 219, 220, 221, 222, 224 emission, 69 encapsulation, 166 ENDOR, 140 endothermic, 139 energy, 5, 17, 18, 21, 67, 71, 72, 73, 74, 75, 76, 77, 79, 81, 82, 83, 84, 85, 86, 90, 92, 97, 98, 101, 108, 110, 113, 117, 124, 125, 126, 127, 137, 138, 139, 140, 141, 142, 144, 146, 147, 148, 154, 156, 157, 158, 159, 160, 170, 178, 180, 181, 182, 188, 189, 190, 192, 193, 194, 199, 200, 201, 202, 204, 208, 209, 211, 217, 224, 226, 227, 240, 241, 244, 246, 248, 253, 254, 262, 264 energy consumption, 139 enthalpy, 146 enthalpy of activation, 73, 124 enthusiasm, 125 entropy, viii, 135, 144, 145, 146, 148, 149, 156, 181, 194 environment, 12, 16, 42, 139, 140, 149, 152 environmental degradation, 42 epitaxial growth, 248 EPR, 140 equilibrium, ix, x, 13, 28, 37, 43, 79, 83, 107, 113, 124, 127, 137, 139, 143, 144, 145, 146, 156, 161, 162, 163, 170, 179, 181, 182, 187, 193, 195, 196, 201, 213, 216, 220, 222, 223, 224, 239, 240, 261 equipment, 69, 169 erosion, 42, 268 ESR, 5 European, 258, 265 European Union (EU), 66, 67, 258, 259 evaporation, 32, 250 evidence, 94, 119, 155, 222, 224, 226, 228 evolution, 107 experimental condition, 245 exposure, 3, 10, 16, 18, 19, 20, 21, 23, 24, 27, 28, 31, 32, 33, 35, 39, 42, 43, 228 extinction, 223 extraction, 265 extrapolation, 93, 254, 257 extrusion, 42

F fabrication, 15, 19, 262 failure, 35, 36, 40, 43, 216, 221

Index family, vii, viii, ix, 1, 2, 65, 90, 94, 141, 189, 213, 232, 233 fatigue, vii, 29 FCC, 214, 215 Fermi level, 176, 180, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 202, 203, 205, 207, 209 ferrite, viii, 65 ferromagnetic, 92, 109, 121, 125, 193, 239, 263, 269, 270, 274, 275 ferromagnets, 142 film(s), 9, 12, 24, 25, 35, 36, 37, 38, 141, 163, 170, 176, 179, 204, 232 fine tuning, 211 flow curves, 97 fluctuations, 157, 158, 170 fluidized bed, 39 fluorine, 32 foils, 8, 222, 223, 228, 262 food, 18 Fourier, 245 fractures, 214, 221 France, 71, 107, 125, 261 free energy, 5, 21, 146 free volume, 270 friction, viii, 65, 66, 67, 72, 73, 81, 82, 83, 91, 93, 114, 122, 123, 124, 125, 126, 127, 128 fusion, 176

G gallium, 147, 150, 163, 165, 167, 168 gas phase, 32 gas turbine, 20 gases, 16 gauge, 217 Gaussian, 73, 86, 110 gel, 25 generation, 35, 140, 144, 187, 214, 238, 271 germanium, 155 Germany, 58, 69, 125, 261, 276, 277 Gibbs energy, 137, 140, 147, 148, 156, 157, 158, 159, 160, 170 glass, ix, 70, 261, 262, 263, 271, 272, 275 glass transition, 263, 272, 275 glass transition temperature, 263 glasses, x, 261, 262, 263, 271 gold, 232 grades, 15 grain boundaries, 6, 8, 10, 14, 34, 107, 108, 140, 214, 215, 216, 220, 227, 233 grain refinement, 9

283

grains, 5, 6, 7, 11, 16, 22, 26, 27, 33, 39, 89, 90, 107, 141 graph, 238, 243 grazing, ix, 237, 238, 241, 243, 244, 245 grazing incidence nuclear resonant scattering (GINRS), ix, 237, 238, 239, 240, 241, 242, 243, 245, 246, 247, 248, 252, 253, 254, 257 Great Britain, 132 groups, 22, 30, 39, 68, 102, 150, 156, 178, 198, 209 growth, x, 4, 6, 7, 8, 11, 12, 13, 14, 15, 16, 27, 28, 29, 30, 32, 34, 36, 42, 43, 85, 90, 140, 141, 142, 161, 163, 165, 166, 169, 239, 249, 250, 252, 261 growth mechanism, 6, 14 growth rate, 4, 8, 14, 28, 29, 34 growth temperature, 165, 250

H halogen, 32 Hamiltonian, 126, 127 hardness, 96, 98, 102, 106, 107, 108, 109, 140 healing, 10, 11 heat, 3, 7, 17, 21, 22, 25, 26, 33, 37, 42, 75, 78, 93, 96, 97, 109, 112, 116, 117, 118, 121, 123, 124, 137, 144, 145, 177, 189, 262, 263 heat capacity, 137 heat conductivity, 117, 189 heating, x, 27, 75, 78, 81, 89, 90, 96, 107, 109, 111, 112, 114, 115, 116, 117, 122, 123, 140, 162, 165, 248, 261, 262, 263, 265, 272, 274 heating rate, 81, 111, 116 height, 72, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 88, 100, 101, 102, 104, 106, 110, 111, 123, 249 hexagonal lattice, 118 homogeneity, viii, 135, 136, 142, 143, 145, 148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 161, 163, 164, 169, 170, 171, 177, 264 host, 72, 85, 126, 127 hot pressing, 265 humidity, 227 hybrid, 35 hybridization, 209 hydride(s), 228 hydrocarbons, 154 hydrogen, 9, 12, 73, 185 hydrostatic pressure, 216 hydroxide, 16 hypothesis, 11, 79 hysteresis, 92, 115, 117, 121, 268, 274, 275 hysteresis loop, 92, 121, 268, 274, 275

284

Index

I identification, 157, 273 images, 89 impurities, x, 13, 37, 180, 231, 261, 263, 265 in situ, 85, 106, 232 incidence, ix, 237, 238, 241, 244, 245 incubation period, 27, 28 independence, 159 indication, 69, 109, 270 indium, 162, 168 induction, 69, 264, 265 industrial application, 33 industry, 18, 20, 232, 238 inequality, 170 infinite, 140, 155 inhomogeneity, 170, 171 initial state, 144 injury, iv instability, 81, 90, 149, 157, 159, 161, 226 insulators, 175 integrated circuits, 141 integrity, 11, 17, 24 intensity, 107, 108, 118, 222, 240, 242, 243, 246, 247, 248, 252, 253, 265, 266, 270 interaction(s), viii, 42, 65, 69, 72, 74, 75, 76, 78, 79, 90, 92, 98, 99, 107, 108, 111, 124, 125, 126, 127, 130, 135, 140, 142, 151, 152, 153, 155, 156, 181, 217, 270 interface, 6, 8, 10, 12, 13, 14, 18, 19, 22, 23, 24, 25, 28, 29, 30, 31, 32, 141, 161, 223, 250, 251 intermetallic compounds, vii, viii, ix, 1, 2, 20, 21, 41, 42, 43, 65, 66, 68, 72, 76, 109, 175, 178, 206, 213, 214, 215, 216, 222, 225, 227, 233, 235, 253 intermetallics, vii, viii, ix, 1, 2, 6, 9, 40, 65, 73, 213, 214, 215, 216, 217, 218, 222, 224, 227, 231, 232, 233 internet, 129 interphase, vii interpretation, 71, 76, 79, 171, 254, 258 interval, 111, 171 intrusions, 10 investment, 9 iodine, 32 ion implantation, 12, 32, 37 ion mass spectroscopy, 251, 252 ionization, 144, 145 ions, 4, 14, 19, 31, 32, 36, 39, 138, 139, 140, 152, 153, 169 iron, vii, viii, ix, 1, 2, 3, 4, 6, 15, 42, 65, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 82, 83, 86, 94, 95, 97, 104, 106, 108, 111, 121, 158, 170, 210, 216, 237,

238, 239, 240, 245, 246, 250, 251, 253, 254, 256, 257, 270 irradiation, 138, 140 isostatic pressing, 10 isothermal, x, 6, 7, 8, 11, 15, 23, 24, 33, 34, 36, 42, 71, 83, 84, 100, 102, 163, 164, 262 isotopes, 239, 240

J Japan, 129, 131, 132, 175 Jung, 48, 60, 64

K kinetic instability, 161 kinetics, x, 15, 16, 19, 22, 23, 27, 28, 30, 41, 262 kinks, 87 Kobe, 276, 277

L lamellae, 26 laser(s), 17, 35, 141, 145 lattice parameters, 119, 223 lattices, 69, 150 laws, 136 lead, 3, 6, 7, 8, 14, 15, 31, 34, 73, 74, 75, 81, 95, 117, 123, 149, 154, 158, 169, 170, 200, 248, 253, 276 lifetime, 7, 14, 17, 29, 41, 43, 77, 140 light-emitting diodes, 145 limitation, 274 linear function, 147 liquid nitrogen, 219, 268 liquid phase, 17, 161, 207 literature, vii, viii, x, 1, 41, 65, 66, 67, 72, 73, 106, 109, 110, 118, 119, 120, 262 local configuration, 176 local order, 149, 251, 252 localization, 189, 192 location, 79, 101, 177, 178, 193, 194, 225 London, 50, 53, 57, 128, 171, 212 long distance, 214 low temperatures, ix, 10, 11, 13, 15, 26, 27, 87, 140, 142, 156, 157, 170, 237, 250 lying, 159

M magnesium, 141, 235

Index magnetic field, 69, 91, 121 magnetic materials, x, 261 magnetic moment, 121, 142, 270 magnetic properties, x, 262, 263, 264, 266, 274, 275 magnetic structure, 93, 121, 239, 252 magnetism, 121 magnetite, 152, 158 magnetization, 93, 120, 121, 266, 267, 268, 269, 270, 272, 274, 275 magnetoelastic, 115 magnetometry, viii, 65, 71, 109, 111, 118, 124 magnetostriction, 92, 115 magnetron, 35, 36, 39, 41 manufacturing, 263, 276 mass spectrometry, 239 materials science, 128, 130 matrix, 5, 19, 20, 23, 27, 31, 86, 186, 223, 266, 273, 274 MBE, 248, 250 meanings, 157 measurement, 40, 110, 117, 121, 239, 242, 246, 254 mechanical properties, vii, 1, 2, 3, 4, 7, 18, 21, 22, 25, 26, 34, 40, 41, 94, 219, 220, 222, 228, 230, 233 mechanical stress, 264 media, 16, 244 melt(s), vii, 40, 118, 137, 161, 162, 163, 165, 166, 263, 264, 265, 266, 270, 275 melting, vii, 1, 2, 9, 13, 15, 20, 21, 24, 25, 69, 117, 161, 177, 217, 219, 220, 232, 239, 250, 263, 264, 265, 272 melting temperature, 161, 219, 250, 264 memory, ix, 142, 213, 216, 220 metal oxides, 28, 148, 176 metallography, 118 metallurgy, 10, 20, 128, 270 metals, vii, viii, x, 15, 28, 41, 66, 67, 71, 72, 79, 86, 90, 97, 127, 128, 135, 140, 150, 175, 176, 193, 211, 214, 217, 220, 225, 227, 231, 238, 247, 257, 261, 262, 276 microscopy, x, 71, 116, 118, 119, 140, 148, 153, 249, 261 microstructure, viii, 1, 5, 8, 10, 22, 25, 26, 27, 28, 33, 34, 36, 41, 42, 43, 221, 224 microstructures, 12, 23, 26, 33, 34 migration, 31, 77, 79, 88, 217, 253 minerals, 141 minority, 140 mixing, 247, 250 mobility, x, 2, 8, 19, 30, 75, 86, 88, 92, 96, 107, 180, 250, 254, 261 model system, 109 modeling, 81

285

models, 120, 147, 247 modulus, vii, 1, 2, 20, 21, 41, 66, 67, 69, 80, 84, 85, 87, 90, 91, 92, 121, 123, 124, 220 moisture, 9 mold, 263, 264, 265, 272 mole, 136, 137, 159 molecular beam epitaxy, 248 molecular oxygen, 38 molecules, 136, 138 momentum, 183, 203, 242, 244 Monte Carlo, ix, 78, 126, 127, 237, 253 Monte Carlo method, 127 morphology, 7, 8, 11, 15, 23, 26, 34, 36, 40 mosaic, 141, 223 Moscow, 65, 69, 127, 128, 135, 171, 172, 173 Mössbauer, ix, 109, 121, 148, 237, 239, 244, 251 Mössbauer effect, 109 motion, 75, 86, 87, 89, 91, 92, 96, 142, 216, 217, 220, 221, 222, 224, 226, 227, 228, 230 motion control, 86 movement, 79, 89, 92, 140

N NaCl, 150, 152, 194, 196, 197 nanocrystals, 273 nanometer scale, 239 natural resources, 175 Nd, 6 negative consequences, 158 network, 141, 177, 198, 199 New York, 50, 127, 131, 132, 171, 172, 173, 234, 259, 276 New Zealand, 1 next generation, 238 nickel, vii, 1, 2, 15, 20, 35, 42 niobium, 155 nitridation, viii, 2, 38 nitrides, 16 nitrogen, 8, 19, 27, 28, 31, 37, 69, 71, 73, 75, 219, 268 nodules, 5 nonequilibrium, 142 non-magnetic, 67, 250, 252 nonstoichiometric, viii, 135, 136, 137, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 155, 156, 157, 161, 162, 163, 165, 166, 169 n-type, 19, 145, 185, 192 nuclear resonant scattering, ix, 237, 239, 240, 241, 245, 253 nucleation, x, 15, 29, 87, 89, 117, 140, 156, 158, 216, 261

286

Index

nucleus(i), 15, 140, 156, 158, 165, 239, 240, 244, 245

O observations, 8, 10, 12, 23, 25, 220, 232 observed behavior, 187 obstruction, 180 ODS, 7, 8 oil, 265 optical absorption coefficient, 204 optical microscopy, 71, 118, 119 optical parameters, 145 optical properties, 137 optimization, 3, 26 optoelectronic, 141, 178 optoelectronic devices, 178 orbit, 196 organization, 149, 156 orientation, 77, 107, 120, 141, 142, 220, 223, 246, 254 oscillation, 125 oxidation, vii, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 85, 145, 150, 176, 221, 232, 250 oxidation products, 23 oxidation rate, 4, 5, 6, 8, 10, 11, 12, 14, 16, 19, 20, 23, 24, 25, 26, 27, 28, 29, 31, 34, 35, 38, 42 oxide(s), viii, x, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 86, 135, 141, 148, 150, 155, 164, 176, 232, 261, 262, 263, 264, 265, 272 oxygen, viii, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 33, 36, 37, 38, 39, 41, 42, 72, 141, 146, 147, 150, 152, 153, 155, 158, 165, 215, 265, 272

P pairing, 192 parabolic, 4, 5, 7, 11, 16, 19, 22, 23, 39, 41, 42 parameter, 71, 72, 73, 78, 82, 85, 102, 103, 106, 107, 108, 110, 113, 116, 124, 125, 126, 140, 142, 144, 150, 217, 238, 251 Paris, 128, 129, 130 particles, 6, 8, 12, 14, 19, 28, 29, 42, 86, 119, 139, 170, 264 PDs, 158 pegging, 12 pendulum, 67, 70, 86

performance, 7, 8, 21, 233 periodicity, x, 154, 240, 245, 246, 251, 253, 261 permeability, 31, 263, 268 perovskite, 150 petrochemical, 3, 18 phase boundaries, 216, 254 phase diagram, vii, viii, ix, 16, 20, 31, 40, 43, 66, 68, 73, 77, 83, 93, 109, 111, 115, 117, 118, 119, 121, 124, 135, 161, 162, 167, 168, 178, 181, 213 phase transformation, ix, 10, 14, 15, 35, 43, 66, 68, 83, 109, 116, 117, 123, 142, 145, 157, 160, 213, 216, 222, 224, 232, 262 phase transitions, 159 phonons, 139 phosphorus, 38 photodetectors, 141 physical and mechanical properties, vii physical properties, 142, 171, 238, 239, 245 physics, 128, 131, 238 plants, 3 plasma, 19, 69 plastic deformation, 12, 21, 25, 39, 40, 87, 217, 222, 271 plastic strain, 40 plasticity, 12, 21, 140 platelets, 29, 142 platinum, 169 PM, 8, 265 point defects, 87, 90, 94, 139, 140, 143, 155 Poisson ratio, 21, 225 Poland, 277 polarization, 139, 193 polycrystalline, ix, 9, 41, 72, 213, 214, 215, 217, 219, 220, 221, 222, 223, 226, 227, 230, 231, 233, 238, 253 poor, ix, 13, 14, 23, 26, 28, 177, 180, 213, 232, 252 porosity, 19, 23 positive influences, 7 positron, 71, 77 power, ix, 3, 10, 146, 237, 239, 240, 247, 269 power plants, 3 precipitation, 3, 5, 19, 22, 170 prediction, 176, 200, 229 preference, 97 pressure, 10, 16, 32, 37, 89, 136, 144, 145, 146, 147, 156, 157, 160, 162, 163, 164, 165, 166, 169, 197, 198, 200, 201, 216, 250, 265 probe, 140, 153 production, 10, 19, 69 program, 73, 87, 258 promote, 6, 11, 14, 21, 23, 31, 32, 34 propagation, 140, 216 proportionality, 74, 111

Index protective coating, 42 p-type, 11, 145, 183, 184, 185, 191 pyrophosphate, 39

Q quanta, 244 quartz, 70, 111, 252 quasiparticle, 176

R race, 257 radiation, ix, 237, 238, 239, 240, 241, 244, 245, 251, 258, 261, 265 radio, 238, 239, 253, 256 radius, 217 rain, 85, 94 Raman, 155 rare earth, ix, 6, 7, 22, 75, 213, 222, 227, 233, 235 rare earth elements, 6, 75 reactant(s), 8, 21, 22, 33, 157 reaction rate, 157 reactivity, 16, 142 reagents, 169 recombination, 140, 145 recovery, 91, 94, 217 recovery processes, 94 recrystallization, 19, 169 redistribution, 75, 79 reduction, 5, 6, 12, 19, 73, 74, 107, 140, 153, 154, 176, 221, 250 reflectance spectra, 209 reflection, 108, 115, 141 refraction index, 243 refractive index, 241, 243 relationship(s), 22, 136, 189 relaxation, viii, 9, 12, 39, 65, 66, 67, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 82, 83, 84, 85, 86, 87, 90, 93, 94, 96, 99, 100, 101, 104, 106, 107, 108, 109, 110, 113, 115, 122, 123, 124, 125, 126, 127, 152 relaxation effect, 66, 79, 90, 94 relaxation process, 9, 67, 71, 73, 79, 104, 123, 124 relaxation times, 67, 73, 110 REM, 148 reparation, 257 resistance, vii, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 26, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 215, 216, 228, 232, 235 resolution, ix, x, 110, 148, 153, 237, 238, 239, 240, 243, 244, 261, 265

287

resources, 175 risk, 165 rods, 263, 265, 266, 267, 275 rolling, 221 room temperature, ix, 3, 9, 13, 20, 23, 39, 40, 41, 90, 107, 108, 117, 121, 124, 139, 180, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 224, 226, 227, 228, 231, 232, 233, 250, 252, 262, 268, 269, 272, 274 rotation axis, 141 roughness, 240 Royal Society, 125 Russia, 65, 69, 125, 129, 130, 132, 133, 135 ruthenium, 187 Rutherford, 140, 251 rutile, 16, 18, 19, 23, 26, 30, 31, 35, 38

S SA, 59, 72, 74, 276 safety, 42 salt, 3, 4, 150 sample, 27, 36, 37, 71, 75, 107, 111, 116, 118, 119, 167, 169, 223, 240, 241, 242, 243, 244, 245, 247, 248, 251, 252, 253, 254, 257, 265, 266, 268, 269, 272, 273, 275 sampling, 187 saturation, 92, 121, 266, 267, 268, 269, 270, 274, 275 scaling, 10, 11, 19, 28, 29, 33, 43 scanning calorimetry, 71, 265 scanning electron microscopy, 71 scanning tunneling microscopy (STM), 140, 153 scattering, ix, 140, 155, 180, 237, 239, 240, 241, 242, 243, 244, 245, 247, 253 Schmid, 214, 220 Schottky, 143, 171 science, 128, 130 screw dislocations, 86, 87, 89, 226, 228 searching, 228 seed, 166, 250 segregation, 13, 14 selecting, viii, 135, 156 self-organization, 149 semiconductor(s), 141, 175, 176, 178, 183, 186, 187, 189, 190, 192, 194, 205, 206, 209, 210, 211 sensitivity, 3, 169, 217, 222, 230, 231, 240, 254 separation, 149, 153, 154, 157, 158, 160 series, viii, 20, 135, 149, 151, 154, 159, 169, 189, 190, 206, 209, 245, 246, 269 shape, ix, 22, 73, 75, 77, 92, 100, 104, 117, 158, 165, 213, 214, 216, 220, 262, 263, 266, 272 shape-memory, ix, 213

288

Index

shear, 21, 67, 69, 80, 85, 153, 154, 155, 158, 159, 220, 227, 230 shock, 262 shoulders, 119 Si3N4, 36 signs, 119 silica, 37, 262 silicon, 176, 192, 193, 196, 198, 204 silver, 169 similarity, 250 simulation, 117, 125, 126 single crystals, ix, 14, 77, 91, 165, 176, 213, 214, 247, 257 sintering, 16, 27, 145, 176 SiO2, 3, 17, 19, 23, 25, 28, 32, 35, 36, 37, 176, 262 sites, 12, 68, 126, 137, 138, 139, 144, 149, 150, 152, 154, 155, 170, 177, 183, 192, 197, 214, 218, 253 Snoek-type, viii, 65, 69, 72, 74, 75, 76, 77, 78, 79, 80, 81, 90, 94, 95, 98, 99, 103, 104, 105, 107, 108, 109, 110, 113, 123, 124 solar cells, 141, 204 solar energy, 211 sol-gel, 25 solid phase, 136, 137, 141, 149, 161, 170, 262 solid solutions, 136, 142 solid state, 238 solidification, x, 9, 22, 24, 42, 118, 169, 261, 262, 263, 265 solubility, 11, 19, 23, 29, 30, 31, 32, 33, 39, 41, 95, 96, 97, 139, 170 solvent, 28, 85 spacers, 239 species, 11, 17, 106, 138, 144, 145, 147, 149, 163, 248 spectroscopy, viii, ix, 65, 66, 67, 69, 71, 77, 83, 94, 100, 121, 124, 127, 130, 140, 148, 167, 237, 239, 251, 252 spectrum, 76, 107, 126, 251, 254 speed, 263 spin, 120, 193, 196 sputtering, ix, 24, 34, 35, 36, 41, 187, 237, 239 St. Petersburg, 172 stability, viii, 8, 14, 17, 18, 21, 24, 29, 32, 33, 35, 40, 41, 65, 112, 116, 123, 124, 135, 149, 156, 157, 158, 159, 163, 167, 170, 176, 178, 187, 199, 238, 252, 253, 264, 265, 272 stabilization, 31, 263 stabilizers, 17 stages, 4, 6, 16, 27, 37, 90 stainless steels, 3 statistics, 117 steel, 42, 71, 264, 265

stoichiometry, vii, viii, ix, 17, 135, 136, 137, 140, 142, 144, 149, 150, 157, 164, 165, 170, 213, 214, 215, 217, 218, 219, 220, 221, 224, 226, 228, 248, 250, 251, 252 storage, 238 strain, ix, 40, 74, 78, 87, 89, 90, 127, 213, 214, 217, 218, 221, 222, 223, 224, 228, 230, 231, 232, 233 strategies, ix, 214, 233 stratification, 19 strength, vii, ix, 1, 2, 3, 5, 6, 8, 9, 11, 12, 15, 18, 20, 21, 22, 25, 26, 33, 40, 41, 66, 67, 68, 72, 83, 106, 107, 113, 123, 124, 125, 126, 140, 213, 215, 222, 227, 228, 229, 230, 233, 263 stress, vii, ix, 6, 7, 12, 15, 20, 37, 39, 67, 71, 72, 76, 79, 81, 82, 83, 85, 92, 97, 123, 213, 216, 221, 222, 223, 224, 228, 230, 231, 232, 247, 249, 250, 257, 264, 267, 272, 275 stress-strain curves, 230 structural changes, x, 151, 156, 262 structural defects, viii, 65, 127, 148, 149, 150 structural relaxation, 152 students, 125 substitutes, 30, 74 substitution, 4, 21, 30, 31, 75, 94, 102, 107, 109, 211 substrates, 3, 6, 35, 42, 141, 250 subtraction, 84, 86 sulfidation, viii, 2, 3, 4, 15, 38 sulfur, 13, 16, 165 Sun, 45, 48, 49, 52, 53, 54, 64 superalloys, vii, 1, 2, 20, 41 superconductor, 156 superlattice(s), vii, 1, 2, 155, 228 superplasticity, 7 supply, 185 suppression, 29, 120, 216 surface energy, 141 surface layer, 14, 27, 32, 36, 39, 140, 232 surface properties, 17 surface region, 24, 34, 36 surface treatment, viii, 1, 34, 36, 39 susceptibility, 5 switching, 28 Switzerland, 71, 128, 130, 276 symbols, 144, 200, 201, 269 symmetry, 34, 41, 140, 142, 149, 150, 179, 180, 187, 189, 192, 193, 202, 205, 207, 262 synchrotron radiation, ix, 237, 238, 239, 240, 241, 244, 245, 258 synthesis, viii, 135, 137, 139, 156, 157, 160, 161, 162, 165, 169 systems, vii, viii, x, 1, 2, 20, 21, 34, 35, 36, 41, 43, 66, 69, 73, 75, 95, 109, 110, 142, 149, 150, 155, 159, 163, 164, 165, 166, 196, 214, 215, 217, 220,

Index 221, 222, 223, 224, 228, 238, 247, 252, 257, 261, 263

T tantalum, 23 Tc, 156, 157, 158, 178 technology, 178 tellurium, 136 temperature annealing, 113, 118, 119, 121 temperature dependence, ix, 41, 67, 72, 75, 91, 92, 110, 121, 161, 213, 269 temperature gradient, 165 tensile strength, 3, 229, 230 tensile stress, 12, 230 tension, 91, 214, 217, 226, 232 textbooks, 66 theory, vii, viii, 72, 75, 82, 85, 135, 136, 148, 175, 181 thermal energy, 262 thermal expansion, 7, 8, 9, 86, 272 thermal stability, viii, 65, 238, 264, 265, 272 thermodynamic, viii, 21, 31, 32, 43, 135, 139, 145, 148, 149 thermodynamic calculations, 32 thermodynamic equilibrium, 43, 139 thermodynamic function, 145 thermodynamic parameters, 145 thermodynamic properties, 149 thermodynamics, 146, 147, 158 thermogravimetric, 147 thermomechanical treatment, 4, 22 thin film(s), 12, 25, 176, 204 threshold, 74 time periods, 34, 248 timing, 240 titania, 33, 36, 38 titanium, 15, 17, 18, 19, 20, 21, 31, 32, 37, 38, 41 TMP, 26 total energy, 146, 194, 199, 200 toxicity, 175, 187 TPI, 70 transformation(s), ix, 4, 10, 11, 13, 15, 27, 35, 43, 66, 68, 83, 95, 96, 99, 109, 116, 117, 123, 142, 145, 157, 158, 160, 213, 216, 220, 222, 223, 224, 232, 262 transformation product, 223 transition, viii, x, 5, 15, 16, 17, 29, 30, 31, 32, 41, 68, 79, 83, 86, 90, 92, 97, 98, 99, 100, 102, 103, 107, 108, 109, 111, 112, 115, 120, 121, 123, 135, 146, 148, 149, 156, 159, 175, 176, 177, 178, 179, 181, 187, 189, 192, 193, 194, 195, 209, 210, 217, 218, 228, 239, 248, 250, 254, 261, 262, 263, 272, 275

289

transition elements, 15, 189 transition metal, viii, x, 15, 41, 135, 175, 176, 177, 178, 179, 187, 189, 192, 193, 194, 195, 209, 210, 261 transition temperature, 5, 15, 68, 97, 98, 102, 103, 107, 108, 109, 115, 218, 239, 263 transitions, vii, 90, 102, 121, 159 transmission, 71, 153, 249, 265 transmission electron microscopy (TEM), viii, 27, 65, 71, 92, 98, 99, 103, 108, 153, 172, 221, 222, 223, 228, 249, 251, 254 transport, 4, 6, 7, 8, 13, 14, 16, 27, 32, 37, 163, 166, 167, 168, 169 transportation, 10, 28, 32 trend, 193, 266, 267, 274 tungsten, 24, 141 tunneling, 140 twinning, ix, 213, 219, 222, 224, 250 twins, 249, 254

U UK, 125, 212 uniform, 39, 251 universal gas constant, 73 uranium, 152

V vacancies, viii, 12, 14, 29, 31, 32, 65, 66, 77, 79, 81, 87, 88, 97, 102, 104, 107, 112, 113, 124, 125, 126, 137, 138, 139, 140, 144, 145, 146, 147, 149, 150, 152, 153, 158, 170, 177, 184, 185, 189, 228, 231 vacuum, 24, 35, 69, 70, 111, 215, 221, 227, 243, 250, 252, 265 valence, 29, 30, 144, 176, 177, 180, 181, 183, 184, 187, 189, 190, 192, 194, 202, 203, 204, 207, 208, 209, 210, 211 values, 15, 66, 77, 83, 90, 101, 110, 111, 117, 118, 119, 121, 123, 124, 127, 147, 171, 186, 193, 200, 201, 205, 209, 210, 216, 226, 227, 229, 230, 238, 243, 248, 252, 254, 265, 266, 267, 268, 269, 270, 271, 272 vapor, 16, 28, 136, 137, 139, 144, 147, 161, 162, 163, 164, 165, 166, 167, 168, 169, 176, 215, 227, 228, 232 variable, 18, 136, 189, 190 variation, 109, 110, 123, 199, 200, 201, 220, 267, 274 vector, 140, 217, 226, 241, 243, 247, 253, 266 velocity, 85, 209, 255, 265, 271, 272

290

Index

vibration, 73, 87, 90, 92, 182 Vickers hardness, 96 viscoelastic, 127 viscosity, ix, 85, 261

W Warsaw, 277 water vapor, 16, 28, 215, 227 wave vector, 241, 242, 266 weakness, 3 weight changes, 14 weight gain, 11, 17, 31 weight ratio, 20, 21, 264 wetting, 32 winning, 141 wires, 262

X XPS, 32

x-ray, x, 71, 85, 109, 113, 115, 118, 119, 121, 145, 148, 152, 153, 155, 167, 239, 240, 242, 243, 251, 252, 253, 261, 264, 265, 267, 270, 272 x-ray diffraction (XRD), viii, 23, 65, 71, 98, 102, 108, 110, 115, 118, 119, 120, 121, 124, 148, 152, 155, 167, 219, 220, 248, 249, 251, 252, 264, 265, 267, 270, 271

Y yield, ix, 2, 3, 9, 23, 25, 40, 41, 67, 68, 97, 109, 111, 213, 216, 217, 221, 223, 228, 229, 230, 231, 233, 251, 264

Z Zener, viii, 65, 66, 69, 71, 80, 82, 83, 84, 85, 86, 87, 94, 96, 98, 99, 100, 101, 104, 105, 106, 107, 108, 109, 113, 123, 124, 125, 127, 130 zinc, 164, 276 zinc oxide, 164 zirconia, 36 ZnO, 25