ELSEVIER CORROSION SERIES Series Editor: Tim Burstein Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, UK VOLUME 1:
High Temperature Oxidation and Corrosion of Metals – by David John Young
HIGH TEMPERATURE OXIDATION AND CORROSION OF METALS
By DAVID JOHN YOUNG
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PREFACE
Almost all metals and alloys of technological interest oxidize and corrode at high temperatures. However, the nature of the reaction products and the rates at which metal surfaces are degraded vary widely, and a capacity for prediction is highly desirable. This book is concerned with providing a fundamental basis for understanding the alloy–gas oxidation and corrosion reactions observed in practice and in the laboratory. Its purpose is to enable the prediction of reaction morphology, kinetics and rate as a function of temperature and the compositions of both alloy and gas. The term ‘‘oxidation’’ is used in a generic sense, for any chemical reaction which increases the metal oxidation state by forming a compound such as an oxide, sulfide, carbide, etc. Alloy oxidation reactions can be conceived of as occurring in three stages. Initially, all alloy components in contact with a hot gas are likely to react simultaneously. Subsequently, thermodynamically more stable compounds replace less stable ones, and a state of near equilibrium is locally approached. The reacting system can then be modelled as a series of spatially adjacent local equilibrium states which vary incrementally in reactant chemical potentials. During this stage, the reaction morphology and composition distribution are invariant with time. Ultimately, this ‘‘steady state’’ is lost, and all reactive alloy components are consumed in a final breakdown stage. Successful alloys are those which evidence lengthy periods of slow, steadystate reaction. For this reason, considerable emphasis is placed on analysing the underlying local equilibrium condition and testing its applicability to particular metal or alloy-oxidant systems. When an alloy–gas reaction is at steady state, the constant composition profile developed through the reaction zone can be mapped onto the system phase diagram as a ‘‘diffusion path’’. Frequent use is made of these paths in understanding reaction product distributions and in predicting, or at least rationalizing, reaction outcomes. Analysis of the alloy oxidation problem requires a multidisciplinary approach. Physical metallurgy, materials science and physical chemistry provide the tools with which to dissect alloy phase constitutions and their transformations, oxide properties and chemical kinetics. Deliberate emphasis is placed on the use of chemical thermodynamics in predicting oxidation products and describing solid solution phases. Equal attention is paid to the detailed understanding of defect-based diffusion processes in crystalline solids. The introductory Chapter 1 indicates how these various disciplines can contribute to the analysis. The lengthy Chapter 2 reviews the thermodynamic, kinetic and
ix
x
Preface
mechanical theories used in this book. It also contains tabulated data and refers to Appendices relevant to diffusion. Appendix A lists representative alloy compositions. After these preliminaries, the book is arranged in a sequence of chapters reflecting increasing complexity, which equates with greater system component multiplicity. An analysis of the reaction between pure metals and single oxidant gases is followed by a discussion of metal reactions with mixed oxidant gases and then, in Chapters 5–7, an examination of alloy reactions with a single oxidant. Much of this discussion is based on the early work of Carl Wagner, which still provides a good conceptual framework and in several cases a useful analytical basis for quantitative prediction. However, as will be shown, increasing system complexity is accompanied by a weakening in theoretical completeness. The problems arise from multicomponent effects and from microstructural complexity. Consider first the effect of increasing the number of alloy components. A steady-state reacting system consisting of a binary alloy and a single oxidant can be modelled in a two co-ordinate description of both thermodynamics and diffusion kinetics, provided that temperature and pressure are constant. Substantial thermodynamic and diffusion data are available for many such systems, and these are used in developing diffusion path descriptions. Increasing the number of alloy components leads, however, to chemical and structural interactions among them, rendering the experimental problem much less tractable. In the absence of the requisite extensive thermodynamic or diffusion data, the Wagner theory cannot be applied. Instead, higher order alloys are discussed from the point of view of dilute addition effects on the behaviour of binaries. Wagner’s theory is based on lattice diffusion. However, the transport properties of slow growing oxides are largely determined by their grain boundaries and, in some cases perhaps, microporosity. Additional alloy components can affect both the oxide grain size and the diffusion properties of the grain boundaries. Description of these phenomena is at this stage largely empirical. The latter part of the book is concerned with the effects of other corrodents and temperature variations. Chapters 8 and 9 deal with sulfur and carbonbearing gases. The very rapid diffusion rates involved in sulfidation and carburization makes them potentially threatening corrosion processes in a number of industrial technologies. Of fundamental interest are the complications arising out of the complex gas phase chemistries and the generally slow homogeneous gas phase reactions. It becomes necessary in discussing the behaviour of these gas mixtures to consider the role of catalysts, including the alloys in question and their corrosion products. It emerges that not only the gas phase, but also the gas–solid interface can be far removed from local equilibrium. In particular, analysis of the catastrophic ‘‘metal dusting’’ corrosion caused by carbon-supersaturated gases calls for the use of non-equilibrium models. The effects of water vapour on oxidation are discussed in Chapter 10. In many respects this is the least well-understood aspect of high-temperature corrosion. The reason for the difficulty is to be found in the multiple ways in which water molecules can interact with oxides. Preferential adsorption, hydrogen uptake,
Preface
xi
lattice defect changes, grain boundary transport property changes, gas generation within oxide pores, and scale and scale–alloy interface mechanical property changes need all to be considered. Finally, the effects of temperature cycling on oxide scale growth are considered in Chapter 11. A combination of diffusion modelling with a rather empirical scale spallation description is found to provide a reasonably successful way of extrapolating data for particular alloys. However, there is a need for development of more predictive descriptions of the relationship between spallation propensity, alloy properties and exposure conditions. Discussion is focused throughout on developing an understanding of the fundamentals of high-temperature oxidation. Frequent use is made of experimental information on real alloys in order to illustrate the principles involved. However, no attempt is made to survey the very extensive literature which exists for alloy oxidation. Thus most examples considered concern either iron- or nickel-based alloys, whereas cobalt-based alloys are largely ignored. Nickel aluminides are discussed, but other intermetallics are seldom mentioned. The scope of the book is further limited by the exclusion of some particular topics. Examples include ‘‘pesting’’ (disintegration by grain boundary attack) of silicides, and extensive oxygen dissolution by metals such as titanium and zirconium. No book of manageable proportions can ever be complete, or even fully up-to-date. It is remarkable that since the early, very substantial progress made by Carl Wagner and associates in understanding oxidation phenomena, the research effort has nonetheless continued to expand. The reason, of course, is the continuing need to operate equipment at ever higher temperatures to achieve greater efficiencies and reduced emissions. The need to develop suitable materials can be expected to drive even more research in years to come. Writing this book has been a large task, and its content inevitably reflects my own experience, as well as the ideas and results of others. I have tried to acknowledge important contributions to our understanding made by many researchers, and apologize for any omissions. My own research in this area has benefited from interaction with many talented students, research fellows and colleagues, all acknowledged by direct reference. It has also been sustained in large part by the Australian Research Council, a body to be commended for its willingness to support fundamental research. This book has benefited from colleagues from around the world who offered hospitality and/or generously gave expert commentary as I wrote: Brian Gleeson (University of Pittsburgh), Jack Kirkaldy (McMaster University), Daniel Monceau (CIRIMAT, Toulouse), Toshio Narita (Hokkaido University), Joe Quadakkers (Forschungzentrum, Julich), Jim Smialek (NASA, Lewis) and Peter Tortorelli (Oak Ridge National Laboratory). Finally, I acknowledge with gratitude and affection the inspiration provided by my mentors and friends at McMaster University, Walt Smeltzer and Jack Kirkaldy. D.J. Young August 2007
GLOSSARY OF SYMBOLS
Greek symbols
Explanation for symbol
a a a d d Zi Zg g g gi l l mi n ng nin np c r s y x x ec eik OX
Coefficient of thermal expansion Enrichment factor for metal in internal oxidation zone Ferrite, body-centred cubic metal phase Deviation from stoichiometry in oxide Thickness of gas phase boundary layer Electrochemical potential of component i Viscosity of gas Austenite, face-centred cubic metal phase Surface tension, free energy per unit surface area Activity coefficient of component i Interplanar distance, jump distance x=t1=2 , for parametric solutions to Fick’s equation Chemical potential of component i Stoichiometric coefficient in chemical reaction or compound Kinematic viscosity of gas Kinetic frequency term Poisson’s ratio Electrostatic potential Density Mechanical stress Fraction of surface sites Extent of reaction Mole fraction of oxide BO in solid solution A1x Bx O Critical strain for mechanical failure of scale or scale–alloy interface Wagner interaction coefficients for solute compounds i and k Mechanical strain in oxide
Symbol
Explanation for symbol
A ai a0o ; a00o
Surface area of oxidizing metal Chemical activity of component i Boundary values of oxygen activity at metal–scale and scale–gas interfaces Mobility of species i Concentration of component i Boundary values of concentration at metal–scale and scale–gas interfaces Diffusion coefficient Grain boundary width Intrinsic diffusion coefficient for species A
Bi Ci C0 ; C00 D D DA
xiii
xiv
Glossary of Symbols
Symbol
Explanation for symbol
DAB DA Dij
Gas phase diffusion coefficient for binary mixture A–B Tracer or self-diffusion coefficient of species A Diffusion coefficient relating flux of component i to concentration gradient in component j Chemical (or inter) diffusion coefficient Self-diffusion coefficient component B; self-diffusion coefficient for species in grain or phase boundary Self-diffusion coefficient for lattice species Diffusion coefficient for solute oxygen in alloy Diffusion coefficient for oxygen along an interface Electric field Elastic modulus of oxide Activation energy Free electron The Faraday (96,500 C) Fraction Volume fraction Total or molar Gibbs free energy Partial molar free energy Shear modulus of oxide Free energy per unit volume Volume fraction of internally precipitated oxide, BO Total or molar enthalpy Positive hole Species i adsorbed (bound) to surface site Internal oxidation zone Flux of component i Chemical equilibrium constant for reaction number n Rate constant Boltzmann’s constant Parabolic rate constant for metal consumption, corrosion rate constant Linear rate constant for scale thickening Gaseous mass transfer coefficient Surface area fraction of oxide spalled Parabolic rate constant for internal oxidation
~ D DB DL Do Do,i E EOX EA e0 F F fv G ¯ G GOX Gn gBO H h i|S ioz Ji Kn k k kc kl km ks kðiÞ p kp kw kv Kp Ksp KIC Lij L l MW mi m ; m0 n nT Ni NAV
Parabolic rate constant for scale thickening Parabolic rate constant for scaling weight gain Vaporization rate Equilibrium constant at fixed pressure Solubility product Fracture toughness, critical stress intensity factor General mobility coefficient, Onsager phenomenological coefficient Length of material over which gas flows Half thickness of alloy sheet Molecular weight Molar concentration of component i Number of charge units on lattice point defect species Number of moles Total number of moles, all species Mole fraction of component i Avogadro’s number
Glossary of Symbols
xv
Symbol
Explanation for symbol
NM, i N M;min
Mole fraction of component M at scale–alloy interface Minimum mole fraction of component M required to support growth of external MO scale Mole fraction of component M originally present in alloy Mole fraction of dissolved oxygen Mole fraction of dissolved oxygen at alloy surface (solubility at ambient conditions) Pressure DA =DB , ratio of metal self-diffusion coefficients in ternary oxide Partial pressure of component i Total pressure of gas mixture Activation energy Charge General gas constant Rate constant for indicated gas–solid reaction Entropy source term (time rate of entropy production per unit volume) Total or molar entropy Spacing of periodic microstructure Surface site Species S located on crystal lattice site M, with effective charge X Temperature Time Time at temperature in cyclic exposure conditions Total or molar internal energy Building unit in crystalline compound Volume Velocity Molar volume of phase i Weight Scale thickness Position co-ordinate Metal surface recession Steady-state scale thickness when growth balanced by evaporation Depth of internal oxidation zone Position co-ordinate for scale–alloy interface relative to the original, unreacted surface location z=zs (or x/X), position within scale normalized to its thickness Effective charge, valence Position co-ordinate in reference frame with origin at scale–alloy interface
N ðoÞ M NO N ðsÞ O p p Pi PT Q q R ri s_ S S S SX M T t t U Ui V n Vi W X x XM Xss X(i) y y Z z
ABBREVIATIONS AND ACRONYMS
CTGA CVD EBSD EDAX EELS EPMA FIB IGCC ppm ppma ppmm PVD SAD SEM SIMS TBC TEM TGA TGO XRD YSZ
Continuous thermogravimetric analysis Chemical vapour deposition Electron back scattered diffraction Energy dispersive analysis of X-rays Electron energy loss spectroscopy Electron probe microanalysis Focused ion beam Integrated gasification combined cycle Parts per million (unit of relative concentration) Parts per million by atoms Parts per million by mass Physical vapour deposition Selected area diffraction Secondary electron microscope Secondary ion mass spectrometry Thermal barrier coating Transmission electron microscope Thermogravimetric analysis Thermally grown oxide X-ray diffraction Yttria-stabilized zirconia
xvii
CHAPT ER
1 The Nature of High Temperature Oxidation
Contents
1.1. 1.2. 1.3. 1.4. 1.5.
Metal Loss Due to the Scaling of Steel Heating Elements Protecting Turbine Engine Components Hydrocarbon Cracking Furnaces Prediction and Measurement 1.5.1 Oxidation rates 1.6. Rate Equations 1.6.1 Linear kinetics 1.6.2 Diffusion-controlled processes and parabolic kinetics 1.6.3 Diffusion and phase boundary processes combined 1.6.4 Volatilization 1.6.5 Thin oxide film growth 1.7. Reaction Morphology: Specimen Examination 1.8. Summary References
1 4 5 9 10 12 15 15 16 18 18 19 22 26 26
At high temperatures, most metals will inevitably oxidize over a wide range of conditions. The practical issues of material lifetimes and corrosion protection methods therefore centre around the rate of the oxidation reaction, methods of slowing it and the means for controlling its morphology. Answers to these questions turn out to be rather interesting, involving as they do the need for a fundamental understanding of several diverse aspects of solid–gas reactions. The general nature of the problem can be appreciated from a consideration of some practical examples.
1.1. METAL LOSS DUE TO THE SCALING OF STEEL Carbon steel is produced in prodigious quantities: about 1.3 109 t worldwide in 2007. Almost all of it is cast into large pieces such as slabs, which are subsequently reheated to around 1,000–1,2001C to be formed into more useful shapes (Figure 1.1). The reheating operation is carried out in direct-fired furnaces where steelworks gases, or sometimes natural gas, are combusted with excess air. 1
2
Chapter 1 The Nature of High Temperature Oxidation
Figure 1.1 Oxidized steel slab emerging from reheat furnace (Courtesy of BlueScope Steel).
The combination of high temperature, heating times of around 2 h, and oxidizing gases leads to the growth of a thick iron oxide scale on the steel. The amount of steel consumed in this way is about 1–2% of the total. Obviously, with steel losses of 13–26 Mt in 2007, plus the added cost of removing the scale and recycling it, there is considerable economic motivation to control or slow this process. However, there are difficulties. As discussed later, and as is intuitively reasonable, the steel scaling rate depends on three variables: steel chemistry, temperature and the gas atmosphere. The first cannot be changed because it is critical to the final steel properties. Temperature is determined by steel chemistry and is therefore also fixed. Changes in gas composition should, however, be possible. The reactions producing the furnace atmospheres can be described as: 3þx x CH4 þ O2 ¼ CO þ 2H2 O þ O2 (1.1) 2 2 and 1þx x CO þ O2 ¼ CO2 þ O2 (1.2) 2 2 where x represents the surplus of oxygen above stoichiometric requirements for complete combustion. In normal practice, excess air (xW0) is used to ensure complete combustion. However, it was recognized long ago [1] that for xo0, the atmosphere would be much less oxidizing and the extent of scaling might thereby be lessened. In analysing this suggestion, we recognize that it is necessary to calculate the furnace gas partial pressure of oxygen, pO2 , as a function of x and temperature, that the possible oxides of iron must be identified, and that the ranges of pO2 values at which they exist need to be established. The necessary pO2 values can be calculated from the equilibrium of reactions (1.1) and (1.2) and those of the iron oxide formation reactions, using the techniques of chemical thermodynamics described in Chapter 2. Such an analysis shows that it is not possible to lower pO2 below the value at which iron oxidizes, and still have sufficient combustion to heat the steel. Given that steel scaling cannot be prevented, it is important to know how the rate of scale growth (and steel consumption) varies with pO2 and temperature.
1.1. Metal Loss Due to the Scaling of Steel
Alloy
MO
Gas
M2+
M
O2 (g)
e-
M→M2++2e-
3
1 O2O +2e-→O 2 2
M2++O2-→MO
Figure 1.2 Reactions and transport processes involved in growth of an oxide scale.
A schematic cross-sectional view of a growing oxide scale is shown in Figure 1.2. The overall oxidation process can be subdivided into several steps. (1) Delivery of oxidant to the scale–gas interface via mass transfer in the gas phase. (2) Incorporation of oxygen into the oxide scale. (3) Delivery of reacting metal from the alloy to the alloy–scale interface. (4) Incorporation of metal into the oxide scale. (5) Transport of metal and/or oxygen through the scale. Evaluation of the rates at which these steps occur involves calculation of the gas phase mass transfer, solid-state mass transfer or diffusion in the oxide and alloy, and consideration of the interfacial redox reactions.
Fe ¼ Fenþ þ ne
(1.3)
2e þ 12O2 ¼ O2
(1.4)
where e represents an electron. The redox reactions are rapid and do not usually contribute to rate control. Other scale–gas interactions can be dealt with using the methods of surface chemistry. Gas phase mass transfer rates can be calculated from the methods of fluid dynamics, whilst mass transfer in the solid oxide and alloy is described using diffusion theory. The principal constituent of an iron oxide scale at TW5701C is wu¨stite, FeO, in which the Fe2+ species diffuses rapidly at high temperatures. At high values of pO2 , diffusion in FeO controls the rate at which this oxide accumulates [2]. However, in a combustion gas, where pO2 can be quite low, reaction with the oxidant species CO2 and/or H2O is slower than wu¨stite diffusion, and controls
4
Chapter 1 The Nature of High Temperature Oxidation
the scaling rate [3]. Thus, it appears possible that steel scaling can be slowed by operating reheat furnaces under substoichiometric combustion conditions. Of course, the economic feasibility of this process alteration would have to be established through quantification of the actual benefit to be expected (as well as the costs). Such an exercise requires the ability to predict scaling rates as a numerical function of process variables, a principal concern of this book.
1.2. HEATING ELEMENTS The use of metals as electrical resistance heating elements is commonplace in small domestic appliances and laboratory furnaces. Of course the metals used must resist oxidation in air. Two groups of alloys are widely used for this purpose: nickel alloys containing around 20 wt% (weight percent) chromium and iron alloys containing about 20 wt% Cr and 5 wt% Al. As pure metals, each of Fe, Ni, Cr and Al oxidizes in air, but at vastly different rates. Oxidation rate measurements are discussed later in this chapter, but for the moment it is sufficient to use a comparison of different oxide scale thicknesses grown in a particular time. Data for 100 h reaction at 8001C in pure O2 at 1 atm are shown in Table 1.1. It is clear that pure iron would be quite unacceptable as a heating element, and that aluminium and chromium appear much more attractive. However, these are not practical choices: aluminium melts at 6601C and pure chromium is brittle and cannot be formed at room temperature. Nickel has neither of these deficiencies, and might have an acceptable scaling rate for some applications. However, like most metals in the pure state, nickel has quite poor high temperature strength and cannot be used. However, appropriate alloying can provide both strength and oxidation resistance. Cross-sectional views of oxidized surfaces of Ni-28Cr and Fe-20.1Cr-5.6Al0.08La alloys (all compositions in wt%) are shown in Figure 1.3. Single-phase oxides, Cr2O3 and Al2O3, respectively, grow as almost uniform scales, providing satisfactorily slow alloy consumption rates. It would be useful to be able to predict what concentrations of chromium and aluminium are required to achieve their preferential oxidation and thereby avoid reaction of the nickel or iron. To deal with this situation, it will be necessary to consider the thermodynamics of Table 1.1
a
Metal oxide scale thicknesses (t ¼ 100 h, pO2 ¼ 1 atm, T ¼ 8001C)
Metal
Scale thickness (mm)
Fe Ni Cr Ala
1.1 0.01 0.003 0.001
Measured on Ni-50Al.
1.3. Protecting Turbine Engine Components
5
Figure 1.3 Cross-sections of slow-growing protective scales (a) optical micrograph of Cr2O3 on Ni-28Cr after 24 h at 9001C; (b) bright field transmission electron microscopy view of Al2O3 on Fe-20Cr-6Al-0.08La after 400 h at 1,1501C [4]. Published with permission of Science Reviews.
competitive oxidation processes such as 2 Cr þ3NiO ¼ Cr2 O3 þ 3 Ni
(1.5)
where underlining indicates the metal is present as an alloy solute. An additional factor can be expected to complicate this prediction. Selective oxidation of a metal implies its removal from the alloy, and a lowering of its concentration at the alloy surface. Thus, it will also be necessary to consider the diffusion processes in both alloy and oxide.
1.3. PROTECTING TURBINE ENGINE COMPONENTS The gas turbine engines used to propel aircraft and to generate electric power have been developed to a remarkable extent since their invention in the midtwentieth century. As shown in Figure 1.4, fuel is combusted within a turbine to produce a large volume of hot gas. This gas impinges on angled blades in the hot (turbine) stage of the engine, causing it to rotate and drive the compressor stage, which draws in air to support combustion. Power is obtained from the engine either as rotational energy via a driveshaft, or as thrust, generated by the jet of hot exhaust gas. The efficiency of the engine, which is the proportion of the thermal energy converted to mechanical power, is related to the theoretical maximum work available, given by T To wmax ¼ q (1.6) T where q is the heat exchanged, To the ambient temperature and T the operating temperature. It is clear that the higher the turbine operation temperature, the greater is the efficiency potentially available. Since higher efficiency is the
6
Chapter 1 The Nature of High Temperature Oxidation
Figure 1.4 Schematic diagram of gas turbine engine.
equivalent of lower cost and less greenhouse gas production per unit of output, its desirability has driven a steady increase in turbine gas temperatures. However, because this temperature is limited to whatever the materials of the first hot stage components can withstand, an increase in materials capability has also been necessary. Figure 1.5 summarizes the history of developments in turbine blade materials and the temperatures at which they have operated. In addition to alloy compositional changes, the development of these materials has seen an evolution in production technology from wrought through conventional cast and directionally solidified to single crystal production. Current hot stage materials are nickelbased superalloys, which possess excellent high temperature strength. This is necessary to withstand the enormous centrifugal forces generated by the high rotational speeds, around 10,000 rpm in the case of jet engines. The metallurgical design which provides the strength of these superalloys is such that they oxidize at unacceptably rapid rates at operating temperature. This problem has been solved by providing a coating of oxidation-resistant alloy on the component surfaces. Turbine temperatures are now exceeding the capabilities of superalloy components, and it has become necessary to cool them. This is done by pumping air or steam through cooling channels running through the component interiors, and providing thermal insulation (a thermal barrier coating or TBC) on top of the oxidation-resistant coating. The whole assembly is shown schematically in Figure 1.6. The TBC is typically a ceramic made of yttria-stabilized zirconia (YSZ); the oxidation-resistant coating, known as a bondcoat, is an aluminium-rich material (several designs are possible), and the superalloys are complex, nickelbase alloys containing chromium, aluminium and numerous other elements. Some examples of superalloy and bondcoat compositions are given in Table 1.2. Further examples of superalloy compositions can be found in Appendix A. Manufacture of these sophisticated components is complex. The superalloy itself is cast, using a directional solidification process, often as a single crystal [5]. The bondcoat can be applied in various ways [6]. Chemical vapour
1.3. Protecting Turbine Engine Components
Figure 1.5 Progressive increases in temperature capabilities of superalloys for turbine engine blades. Reproduced with permission of the National Institute of Materials (NIMS), Japan.
TBC TGO Bond coat
Superalloy
Coolant flow
Figure 1.6 Cross-sectional schematic view of TBC system for gas turbine blade.
7
8
Chapter 1 The Nature of High Temperature Oxidation
Table 1.2
a
Some superalloy and coating nominal compositions (wt%)
Material
Ni
Cr
Al
Co
Mo
W
Ti
C
Other
IN738LC Rene´ N4 Rene´ N5 CMSX4 PWA 1480 PWA 1484 MC2 SRR99 NiCoCrAlYa b-NiAlb
bal bal bal bal bal bal bal bal bal bal
15.8 10.3 7.5 7.5 10 5 7.8 9.6 18 7
3.1 4.2 6.2 12.6 5 5.6 5.0 12.0 12.5 30
8.5 7.8 7.7 10.0 5 10 5.2 5.0 23 5
1.8 1.5 1.4 0.4
2.6 6.4 6.4 2.1 4 6 8.0 3.0
3.4 3.5
0.1
1.3 1.5
0.1
2.7
0.1
0.5Si, 0.8Ta 0.47Nb, 4.6Ta 7.1Ta, 2.8Re, 0.15Hf 2.1Ta, 1Re, 0.03Hf 12Ta 8.7Ta, 3Re, 0.1Hf 5.8Ta 0.9Ta 1Y
2 2.1 0.3
2
Overlay coating. Diffusion coating on Rene´ N4.
b
deposition (CVD) in which aluminium from a vapour phase species diffuses into the alloy surface, forms an aluminide diffusion coating. These coatings can be modified by the incorporation of platinum and the co-deposition of additional metals from the vapour phase. More complex coating chemistries can be achieved by physical co-deposition of various MCrAlY compositions in which M indicates Fe, Ni or Co or a mixture thereof. These coatings are deposited by sputtering, plasma spraying or physical vapour deposition, using a high-voltage electron beam to vaporize the source material. The outer surface of the bondcoat is oxidized to form a thermally grown oxide (TGO) that is the surface to which the TBC adheres. Application of the TBC is performed by either electron beam physical vapour deposition or plasma spraying [7]. At high temperatures, various interactions between these materials can be expected. Interdiffusion between the superalloy and its aluminium-rich coating can produce new phases as well as draining the coating of its essential aluminium. Some bondcoat constituents and metals diffusing from the superalloy through the bondcoat can dissolve in the TBC to form mixed oxides. Understanding and predicting these interactions requires knowledge of the phase equilibria relevant to each particular system. Finally, because the TBC is porous, oxygen from the hot combustion gas penetrates to the bondcoat surface, causing oxide scale growth. A high degree of resistance to this oxidation process is an essential function of the bondcoat. All of these processes are accompanied by volume changes which have the potential to mechanically disrupt the junction between the TBC and the underlying oxide scale. This in turn can lead to partial or even complete loss of the TBC, subsequent overheating of the substrate metal and component failure. To predict and thereby manage these consequences, it is necessary to understand the detailed mechanics of stress development within the superalloy substrate/bondcoat/TGO/TBC system, and the ways in which that stress is accommodated by deformation or fracture of one or more of the system components.
1.4. Hydrocarbon Cracking Furnaces
9
1.4. HYDROCARBON CRACKING FURNACES Many chemical and petrochemical processes are operated at high temperatures to achieve reasonable production rates or, as in cracking furnaces, to promote endothermic reactions. Cracking (or pyrolysis) furnaces are used to produce olefins such as ethylene and propylene, which are subsequently used to make the commodity materials polyethylene and polypropylene. The cracking reaction can be written as 2CH2 2CH2 2 ¼ 2CH ¼ CH2 þ H2
(1.7)
and is accompanied by carbon formation CH4 ¼ C þ 2H2
(1.8)
To slow the latter reaction, steam is added to the hydrocarbon feedstock. The hydrocarbon-stream mixture is heated by passing it through a tube which is suspended within a firebox. As seen in Figure 1.7, tube units (or coils) are large. The tubes are around 100 mm diameter, 10 mm wall thickness and about 10 m long. These tubes are expected to survive for 5 years or more whilst operating at wall temperatures ranging up to about 1,1001C. They must therefore possess adequate resistance to creep deformation (under their own weight), to oxidation
Figure 1.7 Pyrolysis tube unit being installed in steam cracker furnace.
10
Chapter 1 The Nature of High Temperature Oxidation
of their external surface by combustion gas, and to attack by both carbon and oxygen on their inner surface. The materials used for pyrolysis furnace tubes are centrifugally cast heat resisting steels or nickel-base alloys, all austenitic alloys containing high chromium levels. Process economics are enhanced by higher operating temperatures, creating a demand for improved heat-resistant alloys. This demand has driven a shift in materials selection for the centrifugally cast tubes from HK grade (25% chromium, 20% nickel) to HP grade (25% chromium, 35% nickel) steel, and more recently to alloys containing 45 or 60% nickel and around 25% chromium. These higher nickel levels are intended to achieve higher creep strength. Consideration of the process gas composition reveals that the oxygen partial pressure is controlled by the equilibrium H2 O ¼ H2 þ 12O2
(1.9)
and pO2 1024 atm at 1,0001C. The carbon activity, aC, is controlled by reaction (1.8), and has the value unity. Under these conditions, the main alloy constituent which is reactive is chromium, and all of the compounds Cr2O3, Cr7C3 and Cr23C6 are possible products. The practical findings are that an external chromium-rich oxide scale grows early in the life of the tube, but that chromium carbides precipitate within the alloy, beneath its surface, later on. The results of a laboratory simulation of the process are shown in Figure 1.8. Questions arising from these observations of what happens to the alloy might include the following. Why do the alloy constituents other than chromium apparently not react? Why are the carbides formed as dispersed precipitates and not as scale layers? Why are carbides formed beneath the oxide and not vice versa? How does carbon penetrate the oxide layer to reach the alloy interiors? Why is there a layer of apparently unreacted alloy immediately beneath the scale? In addition, and as always, we wish to know the rates at which scale growth and internal carbide precipitation occur, and how these rates will vary with changes in temperature, alloy composition and gas conditions. To answer these questions, it is necessary to consider first the chemical thermodynamics governing reactions between a metal and two different oxidants. Secondly, a description of the rates of mass transfer of chromium, oxygen and carbon within the solid phases is required. Finally, knowledge of the processes whereby precipitates nucleate and grow within metals is needed, along with an ability to predict which precipitate phases can co-exist with which alloy compositions.
1.5. PREDICTION AND MEASUREMENT It is recognized from a consideration of the examples above that it is desirable to be able to predict which reaction products result from high temperature oxidation (or carburization, sulfidation, etc.), whether those products are formed as external scale layers or internal precipitates, how fast they form and what their mechanical stability will be, all as functions of alloy composition, temperature
1.5. Prediction and Measurement
11
Figure 1.8 Cross-section of cast heat-resisting steel (HP Mod grade) after laboratory exposure to steam-hydrocarbon mixture at 1,1001C for 500 cycles of 1 h each.
and gas conditions. The theoretical bases for the requisite predictive methodologies are reviewed in Chapter 2. The necessary thermodynamic, kinetic and mechanical data is not always available for complex, multi-component systems, and further experimental investigation is often necessary. Nonetheless, theoretical prediction is still useful, as it provides qualitative indications of the expected effect of experimental variables. Even if these are no more than hypotheses, they provide a rational framework for experimental design, thereby enabling efficient planning of laboratory investigations. At the same time, it is advisable to be aware of the possibilities afforded by modern experimental techniques. Useful theories provide predictions which can be tested, and the more thoroughly we can test a theory, the more confidence we are likely to have in it. Theoretical treatments should therefore be explored with the aim not only of achieving the desired performance predictions, but also of finding other implied outcomes which can be measured. The point here is that ‘‘performance’’ in terms of component lifetime might be tens or even hundreds of thousands of hours. Other predicted results, such as compositional, microstructural or phase constitutional change in alloy or reaction product, will be evident much more rapidly. Their verification therefore provides an early indication of the probability of the desired oxidation lifetime being achieved.
12
Chapter 1 The Nature of High Temperature Oxidation
1.5.1 Oxidation rates The course of an oxidation reaction x 1 M þ 12O2 ! Mx Oy y y
(1.10)
follows a kinetic rate law dx ¼ fðtÞ dt where x is a measure of the extent of reaction at time, t. Thus, dx ¼ dnMx Oy ¼
(1.11)
dnM 2dnO2 ¼ x y
(1.12)
where ni is the number of moles of the indicated species, i. It is necessary to determine the quantitative form of the function f(t). In principle, a reaction can be followed by measuring consumption of metal or oxygen, or by observing oxide accumulation, as a function of time. If the oxide is a gas, then metal consumption can be followed continuously by attaching the metal sample to a balance of appropriate sensitivity, heating it in the reaction gas and measuring the weight loss. An apparatus suitable for this experiment is shown in Figure 1.9. In the more common case, the oxide is solid, and metal consumption cannot be directly observed in this way. Instead, a metal sample could be reacted for a time, and the amount of metal remaining after subsequent removal of the oxide measured. A series of samples reacted for different times would then yield a kinetic plot. Difficulties in removing all of the scale without damaging the underlying metal render weight change measurements of this sort
8 11
10
3
1
9 5
2 4
6
7
1. 2. 3. 4. 5. 6.
gas bottle catch bottle condenser + flask water bath for flask water pump water bath condenser 7. furnace 8. microbalance 9. specimen 10. amplifier 11. computer
Figure 1.9 Schematic view of thermogravimetric apparatus for measuring weight uptake during high temperature reaction in a controlled gas atmosphere.
1.5. Prediction and Measurement
13
inaccurate. An alternative technique is to measure the difference in metal section thickness before and after reaction. Given that the differences will be small, perhaps of order 10 mm, compared to the usual specimen thickness of some millimetre, measurement errors can be large. However, this technique has been successfully applied to the oxidation of thin foils [8]. The consumption of oxidant, dnO2 , can be followed by observing DpO2 at constant volume, or the volume change required to maintain pO2 constant. Given the vastly different densities of solids and gases, it is clear that this technique is restricted to cases of small dx, unless the oxidant can be replenished. Similar reservations apply to the use of this technique when the reaction gas is a mixture: as dx increases, the gas changes composition. By far the most common method of measuring oxidation rates is the observation of oxide accumulation with time. Gravimetric measurements can be performed continuously with a microbalance, or discontinuously by weighing a series of samples subjected to different reaction times. Continuous measurements yield a more accurate definition of Equation (1.11), but the time lapse exposure approach can be used to simultaneously react a large number of different alloys. Moreover, the multiple samples obtained for each alloy can be useful in characterizing the reaction products. When dx/dt is very small, the measurement precision provided by a high-quality microbalance is desirable, although it can be difficult to achieve. Microbalances are expensive. They must be protected against corrosion by the reaction gas by passing a counterflow of unreactive gas through the balance chamber, as shown in Figure 1.9. In the case of particularly corrosive species such as SO2 or H2S, it is advisable to use a cheap spring balance such as that shown in Figure 1.10. The elongation of a helical spring is observed as a sample suspended from it reacts and becomes heavier. The spring is usually made from silica fibre or Ni Span C wire, the latter being an alloy with an elastic modulus insensitive to temperature. The observed weight change, DW, varies with specimen surface area, A, and the measured quantity is reported as DW/A. If no metal volatilization occurs, the weight change corresponds to oxidant uptake, and it follows from Equation (1.12) that 2dnO2 1 DW ydnMx Oy ydnM ¼ ¼ ¼ 16 A A A xA
(1.13)
The loss of metal can then be expressed in terms of weight per unit surface area, DW M =A, using the atomic weight, AWM DW M dnM ¼ AWM A A
(1.14)
This loss is equivalent to a decrease in volume given by DV M 1 DW M ¼ rM A A
(1.15)
14
Chapter 1 The Nature of High Temperature Oxidation
Figure 1.10 Schematic view of spring balance assembly for observing high temperature oxidation kinetics.
where rM is the metal density. Recognizing that uniform removal of metal from a flat surface results in a recession of the surface by a depth XM ¼ DVM =A
(1.16)
it is seen that XM ¼
AWM x DW 16rM y A
(1.17)
Similarly, the thickness X of a uniform, single-phase oxide scale grown on a flat surface can be calculated as X¼
MWOX DW 16rOX y A
(1.18)
where MWOX is the molecular weight and rOX the density of the oxide. Oxide scale thicknesses can be measured directly by examining microscopic images of cross-sections such as those shown in Figures 1.3 and 1.8. This technique, which is described below, is relatively simple and economical. For this
1.6. Rate Equations
15
reason, and also because diffusion equations are expressed in terms of position coordinates, it is preferably to rephrase the general oxidation rate Equation (1.11) as dX ¼ fðtÞ dt
(1.19)
1.6. RATE EQUATIONS 1.6.1 Linear kinetics The form of Equation (1.19) reflects the reaction mechanism in effect. As seen in Figure 1.2, the reaction steps can be classified within two groups: those occurring within the scale and those outside it. It might therefore be expected that steps in the latter group take place at rates independent of X. If they control the overall scaling rate, then dX ¼ kl dt
(1.20a)
X ¼ kl t
(1.20b)
which integrates to yield where kl is the linear rate constant, and the integration constant reflects the assumed condition X ¼ 0 at t ¼ 0. An example of such a situation is oxidation at very high temperatures in a dilute oxygen gas mixture. Under these conditions, diffusion in the oxide scale can be so fast that it does not contribute to rate control. However, transfer of oxygen from the bulk gas to the scale surface will be relatively slow, occurring at a rate controlled only by the gas properties, including pO2 and temperature. As long as these are fixed, the rate of O2(g) arrival at the scale surface is constant, and Equations (1.20) hold. Surface processes, such as molecular dissociation to produce adsorbed oxygen [9] CO2 ðgÞ ! COðgÞ þ OðadÞ
(1.21)
would, if rate controlling, lead to Equations (1.20). Linear kinetics are expected whenever a planar phase boundary process controls the overall rate. As noted in connection with Figure 1.2, scale growth requires the transfer of metal and/or oxidant through the scale. If the scale is highly porous, gas phase mass transfer takes place within the pores. If the pores are large compared to the mean free path of gas molecules, their dimensions are unimportant to the rate of gaseous diffusion, and scale thickness has no bearing on the oxidation rate. Linear kinetics then result. It was pointed out by Pilling and Bedworth [10] that if the volume of oxide is less than the volume of metal consumed in the reaction, then it is likely that a porous oxide layer will result. This condition is often stated in terms of the ‘‘Pilling–Bedworth ratio’’, and the requirement for non-porous oxides is expressed as V OX 41 (1.22) xV M
16
Chapter 1 The Nature of High Temperature Oxidation
where Vi is the molar volume of the indicated species. However, a perusal of tabulated values [11] of this ratio reveals that only alkali and alkali earth metal oxides fail this test. By this criterion, all other metals should form compact scales. In fact, the situation is more complex, but it is nonetheless true that most metals of practical importance form more or less compact oxide scales.
1.6.2 Diffusion-controlled processes and parabolic kinetics The growth rate of compact scales is commonly controlled by diffusion of some species through the scale itself. A simplified analysis of this situation is now carried out to show that rate control by such a process leads to parabolic kinetics. dX kp ¼ dt X
(1.23a)
X2 ¼ 2kp t
(1.23b)
where kp is the rate constant and X ¼ 0 at t ¼ 0. The rate of diffusion in one dimension is described by Fick’s first law [12] as J ¼ D
@C @x
(1.24)
Here J is the flux, that is the net rate at which the moving component passes through unit area of a plane oriented at right angles to the diffusion direction, D the diffusion coefficient and C the concentration of a component. This equation, the physical origins of which are examined in Sections 2.5–2.7, expresses the empirical fact that, other things being equal, any mobile species will flow from a region of high concentration to one where the concentration is lower, until homogenization is achieved. The partial derivative in Equation (1.24) is now approximated by the difference in boundary values J ¼ D
DC DðC2 C1 Þ ¼ Dx X
(1.25)
where, as illustrated in Figure 1.11, C2 and C1 are, respectively, the diffusing component concentrations at the scale–gas and scale–metal interfaces. If diffusion is rate controlling, then the interfacial processes must be rapid and may be assumed to be locally at equilibrium. That is to say C1, C2 are time invariant, Equation (1.25) is seen to be equivalent in form to Equation (1.23a), and we may write kp ¼ ODðC1 C2 Þ
(1.26)
where O is the volume of oxide formed per unit quantity of diffusing species. This important result was first derived by Wagner [13], who thus showed that the scaling rate was determined by oxide properties: its diffusion coefficient and its composition when at equilibrium with metal and with oxidant. Wagner’s more rigorous treatment is described in Chapter 3. Parabolic oxidation kinetics were first demonstrated experimentally by Tammann [14] and, independently, by Pilling and Bedworth [10].
1.6. Rate Equations
M
MO
17
Gas
C1 C
C2
X
Figure 1.11 Simplified diffusion model for mass transport through growing metal oxide scale. C represents concentration of diffusing species, and C1, C2 its boundary values.
Metal recession is related to oxide scale thickness through Equations (1.17) and (1.18) VM XM ¼ x X (1.27) VOX where the molar volume, Vi, of each indicated substance is equal to MW/r. Thus, the rate equation for metal recession is X2M ¼ 2kc t
(1.28)
kc ¼ ðxV M =VOX Þ2 kp
(1.29)
with
the so called ‘‘corrosion rate constant’’. The rate constant measured by thermogravimetric analysis is given by DW 2 ¼ 2kw t A
(1.30)
For an oxide of stoichiometry MxOy , Equation (1.18) can be rewritten as X¼
VOX DW 16y A
(1.31)
Substitution in Equation (1.30) and comparison with Equation (1.23b) then yields V OX 2 kp ¼ kw 16y
(1.32)
18
Chapter 1 The Nature of High Temperature Oxidation
In this book we are concerned mainly with scale thickness and metal consumption as measures of oxidation, and usually employ kp and kc.
1.6.3 Diffusion and phase boundary processes combined Because diffusion is initially rapid, but slows with increasing scale thickness, it is possible for scale growth to be controlled in the early stages by a phase boundary reaction and later by diffusion. When the scale is thin, the scaling rate predicted from Equation (1.23a) is faster than the other processes can sustain, and the rate is instead controlled by one of them, often a phase boundary reaction. As the scale thickens, the diffusion rate eventually decreases until it becomes slower than the constant phase boundary reaction rate, and then controls the overall reaction. The phase boundary process then approaches local equilibrium. The observed kinetics will be initially linear and subsequently parabolic. This behaviour has been described [15] by the rate equation X2 þ LX ¼ kt þ C
(1.33)
where L and C are constants. It is worth noting that during the initial stage, mass transfer within the scale is nonetheless occurring via diffusion, implying that the boundary values C1 or C2 in Equation (1.25) change with time.
1.6.4 Volatilization Some metals form volatile oxides. At temperatures above about 1,3001C, tungsten reacts with low-pressure oxygen to form gaseous WO3 and WO2 species, with no solid oxide formed on the surface. If the gas composition is unchanged, metal is consumed at a constant rate. This is why incandescent light filaments, which are based on tungsten, are protected by enclosure in inert gas filled light bulbs. A less severe situation arises with chromium which undergoes two oxidation reactions in dry oxygen 2CrðsÞ þ 32O2 ðgÞ ¼ Cr2 O3 ðsÞ
(1.34)
Cr2 O3 ðsÞ þ 32O2 ðgÞ ¼ 2CrO3 ðgÞ
(1.35)
the latter reaction becoming important at temperatures above about 1,0001C at pO2 ¼ 1 atm. The scaling rate law is then made up of two terms: diffusioncontrolled accumulation and a constant volatilization loss [16] dX kp ¼ kv dt X
(1.36)
This equation predicts that the scale thickness increases to a steady-state value, Xs, where dX/dt ¼ O and Xs ¼ kp/kv . Of course, metal continues to be lost at a constant rate proportional to kv .
1.6. Rate Equations
19
1.6.5 Thin oxide film growth During the early stages of reaction, X is small. At low temperatures, where diffusion and other processes are slow, the time period over which X is ‘‘thin’’ (i.e. tens of nm) can be very long. In this regime, mass transfer through the oxide film is strongly affected by electrostatic effects. These may be understood in a qualitative way from a consideration of the schematic electron energy level diagram in Figure 1.12. In the case of a very thin oxide film, electrons can be transferred from the underlying metal to surface levels at the oxide–gas interface by quantum mechanical tunnelling through the barrier represented by the film [19]. As the film thickens, this mode of electron transport is rapidly attenuated and thermionic emission becomes the most feasible mechanism. The processes of conduction and diffusion within the film itself finally control electron transport, when scattering prevents thermionically emitted elections from crossing the film in a single step. The electron transfer processes can be the oxide growth rate limiting processes, or they can be rapid, achieving a pseudo-equilibrium state with oxygen anions on the film surface. In the latter case, movement of charged ions (Mn+ or O2) through the oxide film is likely to be rate controlling. The mobile ions migrate through the oxide under the influence of an electric field, E, the magnitude of which at the surface is given by Poisson’s equation E¼
4pqs e
(1.37)
where s is the surface concentration of species with charge q, and e the dielectric constant of the oxide. Within the oxide the field is modified by any locally
Vacuum level Conduction band
Potential Energy
Øm Ø′’O Ø
Ø′’m Ø
Fermi level
O- level
Metal
Oxide |eVX| X=0
Valence band
x=X
Figure 1.12 Approximate energy level diagram for electrons in the metal-oxide-adsorbed gas system.
20
Chapter 1 The Nature of High Temperature Oxidation
uncompensated (space) charge dE 4pr ¼ dx x
(1.38)
where r is the space charge density. The boundary conditions for this equation are supplied by the condition of overall charge neutrality Ex ¼
4pqX sX 4pqO sO ¼ þ e e
Z
X o
4pr dx e
(1.39)
where the subscripts O and X correspond to the two film interfaces. The development of an electrostatic field during oxidation has been confirmed by surface potential measurements [17]. That the oxidation rate is affected by the magnitude of the field is confirmed by experiments [18] in which an electrostatic potential difference impressed across a growing film was shown to modify the growth rate. At relatively low temperatures and high oxidant pressures, surface and gas phase processes are seldom rate controlling, and film-thickening rates will be governed by the rate of electronic or ionic transport. The transport of all charged species depends on the electric field strength, which in turn is a function of film thickness. Evaluation of the field is achieved by integrating Poisson’s Equation (1.38), for which purpose the space charge distribution must be known. This in turn can be found from a consideration of the transport equations. At the very high field strengths prevailing in thin films, of order 106 V cm1, the transport equations are non-linear, and the calculations are complex. Because this regime of behaviour is not considered in detail in this book, the reader is referred to the comprehensive treatment provided by Fromhold [19]. A more succinct account, together with a brief review of its applicability to a selection of experimental data is also available [20]. The first equation used to describe thin film growth kinetics was suggested by Tammann [14] as X ¼ k1 lnð1 þ AtÞ
(1.40)
where kl and A are constants. The various theoretical treatments reviewed in references [19, 20] do not lead to this expression (which was purely empirical) but instead yield for the case of rate control by ion transport equations of the form dX B1 ¼ A1 sinh (1.41) dt X or dX A2 B2 ¼ sinh (1.42) dt X X with Ai, Bi constants. The difficulty of distinguishing between the various models on the basis of kinetic data is illustrated in Figure 1.13, where it is seen that when the thickness
1.6. Rate Equations
21
Figure 1.13 Zinc oxidation data and regression lines found for the sinh rate Equation (1.41), the two-stage logarithmic Equation (1.43) and the parabolic rate equation. Reprinted from Ref. [20] with permission of Elsevier.
of oxide formed on zinc [21] is plotted against log (time), concave upwards curves result. This is a fairly common observation, and has led to the proposal of a two-stage logarithmic rate law [22] X ¼ k1 lnð1 þ A1 tÞ þ k2 lnð1 þ A2 tÞ þ Xo
(1.43)
on the supposition that two reaction paths operate in parallel. The data in Figure 1.13 has been curve fitted to three separate rate equations, and it is seen that their merits cannot be distinguished on this basis. It is better to test the applicability of kinetic models by seeing if the constants emerging from the fitting procedure are physically reasonable, and by verifying that the model predicts correctly the effects on reaction rate of perturbations to the system such as changes in T; pO2 and Ex. Other empirical rate laws suggested for thin film oxidation include the ‘‘inverse log law’’ 1 1 ¼ k3 logð1 þ tÞ (1.44) X X0 and the cubic rate law
X 3 ¼ k4 t
(1.45)
No physical basis exists for Equation (1.44), and only under very restricted circumstances can Equation (1.45) be justified for thin film growth [23]. However, the cubic rate equation is found to apply to alumina scale growth (Section 5.9) when oxide grain boundaries provide the means of solid-state diffusion (Section 3.9).
22
Chapter 1 The Nature of High Temperature Oxidation
1.7. REACTION MORPHOLOGY: SPECIMEN EXAMINATION As already noted, compositional, microstructural and phase constitution information are required for both the reaction product and nearby regions of the affected alloy. As seen in Figure 1.8, these quantities can vary considerably with position in the reaction zone, and analytical methods which yield average results are inappropriate. Many features of the reaction morphology are revealed in metallographic cross-sections, such as those made use of in this chapter. Reacted samples are embedded in cold setting epoxy resin by vacuum impregnation. After the resin cures, the section is ground and polished, usually to a 1/4 mm finish. Because the corrosion products are much more brittle than metals, additional effort is required at each stage of grinding and polishing to remove the damage remaining from the preceding step. For the same reason, it can be advantageous to protect the scale outer edge by depositing a layer of nickel or copper on it prior to sectioning. The procedure is to first vacuum evaporate or plasma coat a thin metal deposit onto the reacted sample surface, making it electrically conductive. The sample can then be electroplated with the desired thickness of metal. The polished cross-section should first be examined by optical microscopy, using low and high magnifications, with a maximum resolution of about 1 mm. Digital images are then analysed, using image analysis computer software, to obtain data such as scale layer thickness, precipitate sizes and volume fraction, etc. The speed of this process permits extensive sampling and the accumulation of statistically reliable data. Higher magnification images can be acquired using scanning electron microscopy (SEM) or, for very high magnifications, transmission electron microscopy (TEM). Examples of the three image types are shown in Figure 1.14. Electron microscopy provides the opportunity to acquire compositional and crystallographic information at precisely defined locations within the reaction zone. The electron beam interacts with atoms within the sample, exciting the emission of X-rays with energies characteristic of the atomic number of the atoms involved. These X-rays are collected, analysed according to energy, and counted using the technique of Energy Dispersive Analysis of X-rays (EDAX). The spatial resolution is limited by electron scattering within the solid. Depending on electron energy and their absorption by the solid, the spatial resolution is around 1–2 mm. When appropriate standards and correction procedures are used, the technique is quantitative, yielding reliable compositional analyses for metals, but only semi-quantitative results for oxygen and, at best, qualitative results for carbon. The spatial resolution of EDAX is much better in a TEM, 1–10 nm, simply because the electrons are scattered less widely during their transit of the very thin sample. The effect is illustrated in Figure 1.15. Superior analytical precision and the capability of analysis for light elements are provided by the alternative technique of electron probe microanalysis (EPMA). In this instrument, X-rays excited by an electron beam are analysed by wavelength, using single crystals as diffraction gratings. This technique provides better analytical discrimination (e.g. between molybdenum and sulfur) and much higher count rates.
1.7. Reaction Morphology: Specimen Examination
23
Figure 1.14 Sections of internally carburized Fe-Ni-Cr alloy (a) optical metallograph, (b) SEM view of deep-etched section, (c) TEM bright field view and (d) selected area diffraction pattern from (c).
Both EDAX and EPMA are used to identify reaction product and alloy compositions as a function of position. Care is necessary when analysing multiphase regions, such as scale–alloy interfaces or precipitate-matrix assemblages, because the electron beam can be sampling two phases at the same time. The difficulty is illustrated in Figure 1.15, along with the remedy: ‘‘point counting’’. The beam, or preferably the sample, is stepped at small intervals along a line intersecting the phase boundaries, and X-rays counted at each point. Only when a constant composition is measured at several successive points, and when that composition is reproduced in several sample regions, can the analysis be accepted. The point counting techniques is also valuable for measuring composition profiles in scales and in underlying alloy regions.
24
Chapter 1 The Nature of High Temperature Oxidation
Electron beam
(a) Electron beam
Concentration
(b)
x
(c) Figure 1.15 Spatial resolution of EDAX and EPMA limited by Compton scattering of electrons (a) bulk sample, (b) thin foil in TEM and (c) two-phase region with corresponding analysis.
The electron beam is diffracted by crystalline solids, and analysis of the resulting patterns provides information on the crystal structure and orientation of the diffraction region. The TEM is commonly used for this purpose, and an example is shown in Figure 1.14. This valuable technique is now being applied more frequently to oxidized specimens, since the introduction of the focused ion beam (FIB) milling technique for producing the required thin foil samples. The FIB provides thin foils in precisely determined locations, and is thus able to capture interfaces, grain boundaries, etc. The SEM can also be used to generate
1.7. Reaction Morphology: Specimen Examination
25
crystallographic information via the electron backscattered diffraction (EBSD) technique. This is particularly useful for identifying alloy and oxide grain orientations, to be correlated with other reaction morphological and kinetic features. Because SEM images can provide a large depth of field, the technique is suitable for examining rough surfaces such as the scale outer surface or the alloy surface after scale removal. The use of electron microscopy to identify reaction product phases by diffraction can be costly and time consuming. An alternative is provided by X-ray diffraction (XRD). The reacted sample is simply placed in the specimen holder of a diffractometer, so that the X-ray beam falls on the flat scale surface, and the intensity of diffracted beams measured. Matching the resulting diffraction pattern with tabulated standards then leads to phase identification. At the wavelengths and intensities normally used, X-rays penetrate only a short depth (1–3 mm) into the sample, so the technique provides information on only the near surface region. If a thin scale is being analysed, glancing angle XRD can be used to sample an extremely thin surface region. Because alloy oxidation frequently produces multiple reaction products disposed over a thick reaction zone (e.g. Figure 1.8), it is necessary to obtain diffraction data at a number of different depths. This is done by grinding away a thin surface region, obtaining an XRD pattern and repeating this process until the entire reaction zone has been traversed. This technique was used to identify the reaction products shown in Figure 1.8: an outer scale layer of MnCr2O4 with a thicker layer of Cr2O3 beneath it; internal Al2O3 precipitates (plus some SiO2); a singlephase austenite zone; finally an internal carburization zone of chromium carbide plus austenite. The XRD technique yields measurements of crystal lattice plane spacings. Comparison of this data with that of standards reveals any distortions in the lattice, corresponding to the existence of mechanical stress. Measurements can be carried out at a high temperature to estimate stress states under reaction conditions. Because the stress can change during reaction, it is necessary to make very rapid measurements, and this can be done using the high intensity X-rays available from a synchrotron [24, 25]. The electron beam techniques described above identify the constituent elements of a solid and define their crystallographic relationships. However, they are insensitive to atomic weight and cannot distinguish isotopes. One way of investigating the contribution of oxygen diffusion to scale growth is the use of isotopically labelled oxidants. For example, a metal can be oxidised first in 16 O2 and subsequently in 18 O2 , and the scale then analysed to determine the 16 O=18 O distribution. If they are found to be mixed, then oxygen diffusion has occurred, whereas the observation of an M18O layer on top of an M16O layer would indicate the absence of such a process. The necessary measurements are made by secondary ion mass spectrometry (SIMS). An ion beam is used to sputter away the scale surface, and the ejected ions are analysed by mass spectrometry. Sputtering is continued, removing successively deeper regions of oxide, until the underlying metal is reached. An example of the results obtained in this way is shown in Figure 1.16.
26
Chapter 1 The Nature of High Temperature Oxidation
Figure 1.16 SIMS analysis of scale grown on an Fe-9Cr steel in N2 1%16 O2 2%H2 18 O showing different extents of oxidation by O2 and H2O in different parts of the scale. Reprinted from Ref. [26] with permission of Elsevier.
1.8. SUMMARY As seen from the oxidation cases examined here, a diversity of oxidation reaction morphologies and rates is possible. It is important, therefore, to be able to predict under which circumstances (alloy composition and environmental state) each particular form of reaction will occur, the kinetics of the process and how the rate varies with temperature and the compositions of both alloy and gas. An understanding of these fundamental principles then permits a rational approach to materials selection (or design), and the determination of suitable operating limits for temperature, gas composition, flow rate, etc. Two basic techniques are used to approach the problem. Chemical thermodynamics are employed to predict the reaction outcome, and an analysis of mass transfer processes provides an evaluation of reaction rate. The enabling theory underlying these techniques is summarized in Chapter 2, and examples relevant to high temperature oxidation are discussed. In addition, summary descriptions are provided for interfacial processes and the effects of mechanical stress in oxide scales.
REFERENCES 1. 2. 3. 4. 5. 6. 7.
J.S. Sheasby, W.E. Boggs and E.T. Turkdogan, Met. Sci., 18, 127 (1984). L. Himmel, R.F. Mehl and C.E. Birchenall, Trans. AIME, 197, 822 (1953). V.H.J. Lee, B. Gleeson and D.J. Young, Oxid. Met., 63, 15 (2005). F.H. Stott and N. Hiramatsu, Mater. High Temp., 17, 93 (2000). Superalloys II, eds. C.T. Sims, N.S. Stoloff and W.C. Hagel, Wiley-Interscience, New York (1987). G.W. Goward, in High Temperature Corrosion, ed. R.A. Rapp, NACE, Houston (1983), p. 553. B. Gleeson, J. Propulsion Power, 22, 375 (2006).
References
8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.
27
B.A. Pint, J. Eng. Gas Turbines Power, 128, 370 (2006). F.S. Pettit, R. Yinger and J.B. Wagner, Acta Met., 8, 617 (1960). N.B. Pilling and R.E. Bedworth, J. Inst. Met., 29, 529 (1923). O. Kubaschewski and B.E. Hopkins, Oxidation of Metals and Alloys, Butterworth, London (1953). A.E. Fick, Pogg. Ann., 94, 59 (1855). C. Wagner, Z. Phys. Chem., 111, 78 (1920). G. Tammann, Z. Anorg.Chem., 111, 78 (1920). P. Kofstad, High Temperature Corrosion, Elsevier, London (1988). C.S. Tedmon, J. Electrochem. Soc., 113, 766 (1966). F.P. Fehlner and N.F. Mott, Oxid. Met., 2, 59 (1970). P.J. Jorgensen, J. Electrochem. Soc., 110, 461 (1963). A.T. Fromhold, Theory of Metal Oxidation, Elsevier, New York (1975). W.W. Smeltzer and D.J. Young, Prog. Solid State Chem., 10, 17 (1975). V.O. Nwoko and H.H. Uhlig, J. Electrochem. Soc., 112, 1181 (1965). I.M. Ritchie, Surface Sci., 23, 443 (1970). D.J. Young and M.J. Dignam, Oxid. Met., 5, 241 (1972). P.F. Tortorelli, K.L. More, E.E. Specht, B.A. Pint and P. Zschack, Mater. High Temp., 20, 303 (2003). P.Y. Hou, A.P. Paulikas and B.W. Veal, Mater. Sci. Forum, 522–523, 433 (2006). J. Ehlers, D.J. Young, E.J. Smaardijk, A.K. Tyagi, H.J. Penkella, L. Singheiser and W.J. Quadakkers, Corros. Sci., 48, 3428 (2006).
CHAPT ER
2 Enabling Theory
Contents
2.1.
Chemical Thermodynamics 2.1.1 Chemical potential and composition 2.1.2 Chemical equilibrium in gas mixtures 2.2. Chemical Equilibria Between Solids and Gases 2.2.1 Chemical equilibria involving multiple solids 2.2.2 Gases containing two reactants 2.3. Alloys and Solid Solutions 2.3.1 Dissolution of gases in metals 2.4. Chemical Equilibria Between Alloys and Gases 2.4.1 Equilibria between alloys and single oxide 2.4.2 Equilibria between alloys and multiple oxides 2.5. Thermodynamics of Diffusion 2.5.1 Driving forces 2.5.2 Point defects 2.6. Absolute Rate Theory Applied to Lattice Particle Diffusion 2.7. Diffusion in Alloys 2.7.1 Origins of cross effects 2.7.2 Kirkendall effect 2.8. Diffusion Couples and the Measurement of Diffusion Coefficients 2.8.1 Diffusion data for alloys 2.9. Interfacial Processes and Gas Phase Mass Transfer 2.9.1 Gas adsorption 2.9.2 Gas phase mass transfer at low pressure 2.9.3 Mass transfer in dilute gases 2.10. Mechanical Effects: Stresses in Oxide Scales 2.10.1 Stresses developed during oxidation 2.10.2 Stresses developed during temperature change References Further Reading
30 31 31 34 37 41 42 45 46 46 48 51 51 54 55 58 58 60 63 66 66 66 68 69 71 71 73 76 77
As seen in the previous chapter, we wish to predict which reaction products form when a particular alloy is exposed to a given gas, and the effects of temperature and pressure on the outcome. This requires the use of chemical thermodynamics, and in particular the use of phase equilibria. The rates at which the products form are usually governed by diffusion and interfacial processes, both involving crystallographic defects. Finally, the structural integrity of any solid is determined by its mechanical state. We now review these areas, focusing on their application to high temperature oxidation reactions. 29
30
Chapter 2 Enabling Theory
2.1. CHEMICAL THERMODYNAMICS The question of whether or not an oxide is formed is answered by determining the most stable state of the reacting system M þ 12O2 ¼ MO
(2.1)
At constant temperature and pressure the stability of a system is measured by its Gibbs free energy. The total Gibbs free energy, G, of a system is defined as G ¼ H TS ¼ U þ pV TS
(2.2)
where H is the enthalpy, S the entropy, U the internal energy and V the volume of the system, and p, T have their usual meanings. For a system in which compositional change through chemical reaction is possible, the reversible internal energy change is provided by the basic laws of thermodynamics dU ¼ TdS pdV þ
X
mi dni
(2.3)
i
where ni is the number of moles of component i, the summation is over all components in the system, and @U mi ¼ (2.4) @ni T;P;njai is the chemical potential. Combination of the differential form of Equation (2.2) with Equation (2.3) yields X dG ¼ Vdp SdT þ mi dni (2.5) i
An isothermal, isobaric system is at equilibrium where G is minimum, the location of which is determined by the differential dG ¼ 0 (2.6) Under these conditions, it is seen that the partial molar free energy of a component @G ¯ Gi ¼ ¼ mi (2.7) @ni T;P;njai is equivalent to its chemical potential. The overbar symbol will be used to denote partial molar quantities in general. Integration of Equation (2.5) leads to X mi ni (2.8) G¼ i
when dT ¼ 0 ¼ dp, and combination of Equations (2.6) and (2.8) yields the condition for chemical equilibrium X ni mi ¼ 0 (2.9) i
2.1. Chemical Thermodynamics
31
which is the Gibbs equation. To utilize this result it is necessary to evaluate the mi in terms of compositional variables.
2.1.1 Chemical potential and composition For an isothermal system of fixed composition, application of Equation (2.5) to component A yields ¯A @G ¯A ¼V (2.10) @p ¯ A is the partial molar volume. The latter is found for a perfect gas mixture to be where V ¯ A ¼ PV ¼ N A RT V pA ni
(2.11)
i
where N A ¼ nA =
P ni is the mole fraction. Rewriting Equation (2.10) as an exact i
differential and substituting from Equation (2.11), it is found that ¯ A ¼ N A RT dp dmA ¼ dG pA
(2.12)
Further substitution from Dalton’s law of partial pressures pA ¼ N A ; dpA ¼ N A dp p then leads to dm ¼ RT which upon integration yields
dpA pA
m ¼ m þ RT ln
pA pA
(2.13)
(2.14)
Here the arbitrarily chosen value pA ¼ pA is used to define the standard state at which the chemical potential has its standard (temperature-dependent) value of m . It is convenient to choose pA as unity, commonly 1 atm.
2.1.2 Chemical equilibrium in gas mixtures We consider reactions such as CO2 ¼ CO þ 12O2
(2.15)
H2 O ¼ H2 þ 12O2
(2.16)
with the intention of calculating pO2 . More generally, any reaction can be formulated as a summation over all chemical species involved X 0¼ Sni Mi (2.17) i
32
Chapter 2 Enabling Theory
where the Mi are the symbols for the different chemical species (CO, CO2, etc.) and the ni the stoichiometric coefficients, which are negative for reactants and positive for products. Thus for reaction (2.15) n1 ¼ 1, n2 ¼ 1 and n3 ¼ 0.5. It follows that dn1 dn2 dn3 dnm ¼ ¼ ¼ ¼ dx (2.18) n1 n2 n3 nm where again x denotes the extent of reaction. Equation (2.5) may now be written as dG ¼ Vdp SdT þ mA dnA þ mm dnm ¼ Vdp SdT þ ðnA mA þ nm mm Þdx and hence
@G @x
¼ T;P
X
(2.19)
ni mi
i
The condition for chemical equilibrium is therefore given by Equation (2.9) in the specific form X ni mi ¼ 0 (2.20) i
Substituting from Equation (2.14), we find in the case of the CO2 reaction (2.15) 1=2
0 ¼ mCO þ 0:5mO2 mCO2 þ RT ln
pCO pO2 pCO2
(2.21)
Recognizing that the standard chemical potentials are, by definition, the standard free energies per unit mole, this result is recast as 1=2
mCO þ 0:5mO2 mCO2 ¼ DG ¼ RT ln
pCO pO2 pCO2
(2.22)
where DG ¼ mCO þ 0:5mO2 mCO2 is termed the standard free energy change. Since DG is a function only of temperature, the quantity Kp, called the equilibrium constant at fixed total pressure, 1=2 pCO pO2 DG Kp ¼ exp (2.23) ¼ RT pCO2 is also a function only of temperature. Tabulated values of DG are available [1–3], allowing easy calculation of Kp. A small selection of useful values is provided in Table 2.1. If the equilibrium ratio pCO =pCO2 is known, then the oxygen partial pressure is readily found from Equation (2.23). A more commonly encountered problem is that of calculating pO2 from a knowledge of the input gas composition, i.e. before equilibrium is reached. This is dealt with using the stoichiometry of the reaction, and specifying an unknown extent of reaction to be determined. If there is initially no oxygen present and the
33
2.1. Chemical Thermodynamics
Table 2.1
Standard free energiesa of reaction [1, 2] DG ¼ A þ BT ( J mol1)
Reaction
2 1 1 3AlðlÞ þ 2O2 ¼ 3Al2 O3 1 1 1 2Si þ 2O2 ¼ 2SiO2 Mn þ 12O2 ¼ MnO Zn+12O2 ¼ ZnO 2 1 1 3Cr þ 2O2 ¼ 3Cr2 O3 23 1 6 Cr þ C ¼ 6Cr23 C6 7 23 27Cr23 C6 þ C ¼ 27Cr7 C3 3 7 5Cr7 C3 þ C ¼ 5Cr3 C2 1 2Cr þ 2N2 ¼ Cr2 N Cr2 N þ 12N2 ¼ 2CrN Fe þ 12O2 ¼ FeO 3FeO þ 12O2 ¼ Fe3 O4 2Fe3 O4 þ 12O2 ¼ 3Fe2 O3 Fe þ 12S2 ¼ FeS
3Fe þ C ¼ Fe3 C Co þ 12O2 ¼ CoO 3CoO þ 12O2 ¼ Co3 O4 Ni þ 12O2 ¼ NiO H2 þ 12O2 ¼ H2 O H2 þ 12S2 ¼ H2 S O2 þ 12S2 ¼ SO2 CO þ 12O2 ¼ CO2 2CO ¼ CO2 þ C
A
B
565,900 451,040 412,304 356,190 373,420 68,533 42,049 13,389 108,575 133,890 264,890 312,210 249,450 150,247 29,037 233,886 183,260 234,345 246,440 180,580 362,420 282,420 170,700
128 86.8 72.8 107.9 86 6.45 11.9 0.84 138 174 65.4 125.1 140.7 52.6 28.0 70.7 148.1 84.3 54.8 98.8 72.4 86.8 174.5
a Referred to pure solid metals (except liquid Al), compounds and graphite. DG values for the mole numbers shown in the chemical equations.
input gas mixture consists of a moles of CO2 plus b moles of CO, we see that x/2 moles of O2 are formed with the consumption of x moles of CO2 and the generation of x moles of CO ¼ CO2 ða xÞ
CO ðb þ xÞ
þ
1 2O2 x 2
In this system Si ni ¼ a þ b þ ðx=2Þ, and the partial pressures are given by ni p (2.24) pi ¼ ða þ b þ x=2Þ
34
Chapter 2 Enabling Theory
Thus K2p ¼
¼
p2CO pO2 p2CO2
ðb þ xÞ2 ðx=2Þ p 2 ða þ b þ x=2Þ ða xÞ
(2.25)
Although this cubic equation can be solved numerically, use can be made of the fact that x will be small, as is now seen. For reaction (2.15) DG ¼ 282; 420 86:28T J mol1 and at 1,0001C, DG1273 ¼ 172; 586 J mol1 , and therefore Kp ¼ 8:3 108 If the input gas contains nCO ¼ 0.1, nCO2 ¼ 0.9 then clearly x must be very small. Using the approximation b x a in Equation (2.25) leads to 2 0:1 x 2 15 p ¼ Kp ¼ 6:8 10 0:9 2 and if p ¼ 1 atm, we find x ¼ 1.1 1012, justifying the approximation. The value of pO2 is then given by x=2 ¼ 5 1013 atm pO2 ¼ a þ b þ ðx=2Þ It is seen that the substoichiometric combustion considered in Section 1.1 can lead to quite low oxygen partial pressures. However, to attach significance to this value, it is necessary to consider the thermodynamics of steel oxidation.
2.2. CHEMICAL EQUILIBRIA BETWEEN SOLIDS AND GASES We consider metal oxidation reactions such as (2.1), observe that they are of the general form (2.17) and note that the condition for equilibrium is therefore given by Equation (2.20). It is convenient to state this as mMO mM 12mO2 12RT ln pO2 ¼ 0
(2.26)
where the values of mMO, mM, in general depend on pressure, temperature and composition, and these dependencies have been stated explicitly for mO. However, if the metal and metal oxide are pure, immiscible solids, then their m values are independent of system composition.
2.2. Chemical Equilibria Between Solids and Gases
35
Furthermore, the chemical potentials of solids are insensitive to pressure according to Equation (2.10), because their molar volumes are small. Thus mM , mMO depend on temperature only, and Equation (2.26) can be rewritten as DG ¼ mMO mM 12mO2 ¼ 12RT ln pO2
(2.27)
DG 1 Kp ¼ exp ¼ 1=2 RT p
(2.28)
or equivalently
O2
At this precisely defined temperature-dependent value of pO2 , the metal and its oxide co-exist at equilibrium. This value is often termed the dissociation pressure, and will be denoted here as pO2 ðMOÞ. For wu¨stite formation Fe þ 12O2 ¼ FeO
(2.29a)
DG ¼ 264; 890 þ 65:4T J mol1
(2.29b)
we find from Table 2.1
and at 1,0001C, DG1273 ¼ 181; 640 J mol1 , corresponding to K2:29 ¼ 3:6 106 ;
pO2 ðFeOÞ ¼ 1:2 1015 atm
The symbol Ki will be used to denote the equilibrium constant at fixed total pressure for reaction i. For pO2 ¼ 1:2 1015 atm, iron and wu¨stite co-exist. At lower oxygen partial pressures, a clean iron surface would not oxidize and any FeO would be reduced to metal. At higher values of pO2 , iron would oxidize, a process which would continue until either the iron was consumed or, if the gas supply was limited, until enough oxygen was consumed to lower pO2 to 1.2 1015 atm. In the steel reheat furnace considered in Chapter 1, the steel can be regarded in a chemical sense as almost pure iron, and reaction (2.29a) describes its oxidation. Because fuel is continuously combusted, the ambient pO2 is maintained at a constant value. Even under the strongly substoichiometric combustion conditions leading to a 90/10 mixture of CO2/CO, this value exceeds the Fe/FeO equilibrium value. Since, moreover, the steel sections are much larger than can be consumed in the time available, reaction (2.29a) continues to form more scale. In fact, iron can form two higher oxides 3FeO þ 12O2 ¼ Fe3 O4 ;
DG ¼ 312; 210 þ 125:1T J mol1
2Fe3 O4 þ 12O2 ¼ 3Fe2 O3 ; DG ¼ 249; 450 þ 140:7T J mol1 from which we calculate for T ¼ 1,0001C pO2 ðFe3 O4 Þ ¼ 2:8 1013 atm pO2 ðFe2 O3 Þ ¼ 1:7 106 atm
(2.30) (2.31)
36
Chapter 2 Enabling Theory
Thus the supposed gas mixture of 10% CO, 90% CO2 will form magnetite (Fe3O4), but not hematite. The question as to how wu¨stite and magnetite are disposed within the scale is dealt with in the next section. Standard free energy data for metal oxidation reactions 2x 2 M þ O2 ¼ Mx Oy (2.32) y y are conveniently summarized in Ellingham/Richardson diagrams such as the one shown in Figure 2.1. Here DG is plotted as the y-axis and temperature as the x-axis. Because all reactions are normalized to 1 mol of O2, it follows that DG ¼ RT ln pO2 and an auxiliary scale in pO2 is possible. The equilibrium value of pO2 for a particular metal oxide couple is found by drawing a straight line (the dashed line in Figure. 2.1) from the point marked ‘‘O’’ (at DG ¼ 0; T ¼ 0K) through the free energy line of interest at the desired temperature, and continuing the line to its intersection with the pO2 scale on the right-hand side of the diagram. Following this procedure for Fe/FeO at 1,0001C yields the estimate pO2 1015 atm, in agreement with the earlier calculation. The justification for this procedure is seen in the equation for the straight line y ¼ a þ bx In this case, DG ¼
DGT1 T T1
where T1 ¼ 1; 273 K, and DGT1 =T 1 ¼ R ln pO2 ðT1 Þ. The auxiliary pO2 scale is seen in the diagram to be located at T2 2; 873 K. Thus the intersection of the dashed line with the pO2 scale is at DG ¼ RT 2 ln pO2 ðT1 Þ. Additional scales are provided for the CO/CO2 and H2/H2O ratios corresponding to oxidation equilibria. We consider the example of the FeO formation reaction again. A straight line is drawn from the point marked ‘‘C’’ on the left (at DG ¼ DG reaction ð2:15Þ; T ¼ 0K) to the Fe/FeO line at 1,0001C, and continued to the CO/CO2 scale on the right-hand side, yielding an estimate pCO =pCO2 41. Thus the diagram is useful for obtaining close order of magnitude estimates. Similar diagrams are available for sulfides [4] and carbides [5]. It is seen that the free energy plots in Figure 2.1 are almost straight lines. Furthermore, most of the lines are approximately parallel, apart from changes in slope corresponding to changes of state. Rewriting Equation (2.2) as DG ¼ DH TDS
(2.33)
it is deduced from the near linearity of the plots that DH and DS are almost constant. It is also seen that the positive slopes of the lines correspond to negative entropy changes. This is a consequence of the fact that the entropy of a gas is much larger than that of a solid. Thus the largest component of DS in reaction (2.32) is associated with the removal of 1 mol from the gas phase. This also explains why the slopes of the lines are approximately equal.
2.2. Chemical Equilibria Between Solids and Gases
37
Figure 2.1 Ellingham/Richardson diagram showing free energies of formation for selected oxides as a function of temperature, together with corresponding equilibrium pO2 and H2/H2O and CO/CO2 ratios. Dashed line to find equilibrium pO2 for Fe/FeO and dotted line to find pCO =pCO2 for same reaction.
2.2.1 Chemical equilibria involving multiple solids In the last section we encountered the situation where the ambient pO2 value was maintained at such a value that two different oxides, FeO and Fe3O4, could form: reactions (2.29a) and (2.30) were both favoured. Of course in the fullness of time, all the iron would be converted to magnetite, which would then equilibrate with the ambient gas. Our interest is in the earlier stages, when the reaction is still in progress, and some iron still remains. In thinking about the structure of the scale,
38
Chapter 2 Enabling Theory
it is useful to consider the metal–scale and scale–gas interfaces. At the latter, reaction (2.30) proceeds to the right at pO2 42:8 1013 atm, and we predict that the surface oxide will be magnetite. Consider now what would happen if the underlying metal was in contact with this oxide, by enquiring as to whether the reaction Fe þ Fe3 O4 ¼ 4FeO
(2.34)
will proceed. For T ¼ 1,0001C, we evaluate DG ð2:34Þ ¼ 4DG ð2:29Þ DG ð2:30Þ ¼ 57; 360 J mol1 and see that wu¨stite is more stable. It will therefore form between the iron and the magnetite, and a two-layer scale is predicted. The reasoning above is correct, but tedious. The same conclusion is reached immediately on examining the Fe–O phase diagram in Figure 2.2. This composition–temperature diagram maps the existence regions of the various possible phases. It is seen that wu¨stite is not actually ‘‘FeO’’, but is a metaldeficient oxide Fe1d O, where d varies at any given temperature. Magnetite also deviates from its nominal stoichiometry at high temperatures, but the highest oxide, hematite, is closely stoichiometric at all temperatures. The diagram also reveals that wu¨stite is unstable below 5701C. Phase diagrams summarize experimental observations of equilibrium. The Fe–O diagram informs us that for 1,370WTW5701C, iron equilibrates with
Figure 2.2 Iron–oxygen phase diagram.
2.2. Chemical Equilibria Between Solids and Gases
39
Fe1d O. At high oxygen contents, wu¨stite can co-exist with magnetite, magnetite with hematite and hematite with O2 ðgÞ. This sequence is the one in which oxide layers are disposed within a scale grown isothermally on iron, as shown in Figure 2.3. The locus of scale composition across its width, from pure iron to oxygen gas, can be mapped onto the phase diagram, as shown in the figure. The resulting line is termed a ‘‘diffusion path’’, as it shows the concentration changes which drive diffusion within the reacting system. The significance of the single-phase regions traversed by the diffusion path is clear. However, interpretation of the two-phase regions requires consideration of the phase rule. Consider a system containing C components (chemical species) and consisting of P phases. In principle, each phase can contain all C components, and its composition is specified by C1 variables. When temperature and pressure are included, the state of each phase is completely specified by C+1 variables. For the entire system we thus find that the total number of variables is P(C+1). At equilibrium, a number of equations are in effect among the variables T1 ¼ T2 ¼ Tp
ðP 1 equalitiesÞ
p1 ¼ p2 ¼ pp
ðP 1 equalitiesÞ
m1;1 ¼ m1;2 ¼ m1;p
ðP 1 equalities for component 1Þ
and a similar set of (P1) equations for each of the other components. In all, there are (P1) (C+2) equations. It is seen that the number of variables exceeds the number of equations by a number F: F¼CPþ2
(2.35)
This result is the phase rule, and F represents the number of degrees of freedom available to the system. It tells us the number of variables which can be incrementally changed without altering the number of phases present. Confusion can sometimes arise in determining the number of components, C. The usually stated rule is that C equals the smallest number of constituents whose specification suffices to determine the composition of every phase. Evaluating this number can be a non-trivial exercise in complex chemical systems, but is straightforward for alloy oxidation: C equals the number of elements involved. For a binary oxide, C ¼ 2. The need to specify both arises from the variable composition of oxide and other solid compounds, as is now demonstrated. In an isothermal, isobaric situation, such as the oxidation of iron discussed earlier, the phase rule becomes F¼CP (2.36) For the two-component Fe–O system, a single-phase region is univariant, i.e. its composition can vary. This is self-evidently the case for Fe1dO and Fe3O4 at high temperatures. Although it cannot be seen on the diagram, Fe2O3 is also capable of very small variations in composition. It is this degree of freedom which permits the development of concentration gradients, which in turn drive the diffusion processes supporting scale growth. In binary two-phase
40
Chapter 2 Enabling Theory
Fe
FeO
Fe3O4
Fe2O3
Figure 2.3 Cross-section of oxide scale grown on iron, with diffusion path mapped on phase diagram.
2.2. Chemical Equilibria Between Solids and Gases
41
regions, it follows from Equation (2.36) that F ¼ 0, and compositions are fixed. In the absence of any concentration gradient, dispersed two-phase regions cannot grow and are not found in the scale. Instead, two-phase regions consist of sharp interfaces, as seen in Figure 2.3. For the same reason, wu¨stite cannot form as particles within the iron. When pure metals are oxidized isothermally, they always grow external scales rather than forming internal oxide precipitates.
2.2.2 Gases containing two reactants Gases containing two or more oxidants are commonly encountered at high temperatures. For example, most fossil fuels contain sulfur, and combustion leads to the formation of SO2 and other gaseous species. If iron is exposed to such a gas, then the possible reactions include 1 Fe þ 12S2 ¼ FeS; K2:37 ¼ (2.37) p S2 1=2
FeO þ
1 2S2
¼ FeS þ
1 2O2 ;
K2:38 ¼
pO2
1=2
p S2
Fe3 O4 þ 32S2 ¼ 3FeS þ 2O2 ;
K2:39 ¼
Fe2 O3 þ S2 ¼ 2FeS þ 32O2 ;
K2:40 ¼
p2O2 3=2
p S2
(2.38)
(2.39)
3=2
pO 2 p S2
(2.40)
as well as reactions producing sulfates, which will be ignored here for the sake of simplicity. The gas phase reactions of importance are 1=2
SO2 ¼ 12S2 þ O2 ;
K2:41 ¼
p S2 p O 2 pSO2
(2.41)
and, at high oxygen partial pressures, SO2 þ 12O2 ¼ SO3 ;
K2:42 ¼
pSO3 1=2
pSO2 pO2
(2.42)
The ternary system Fe–S–O can be analysed thermodynamically in the same way as was done for the Fe–O system, but the multiple equilibria make the process complex. As seen from the phase rule, up to three phases can co-exist at interfaces, and two-phase scale layers can grow. Interpretation of this situation is much easier using a phase diagram, such as the one drawn in Figure 2.4 on the assumption that all solids are pure and immiscible. Logarithmic scales are used for pS2 and pO2 in order to encompass the large ranges involved, and have the advantage of linearizing the equilibrium relationships of reactions (2.37)–(2.40). Thus, for example, the phase boundary
42
Chapter 2 Enabling Theory
Figure 2.4 Thermochemical (Kellogg) diagram for Fe–S–O system at 8001C, showing three possible diffusion paths for reaction with Gas A.
between FeO and FeS is defined as a straight line by the equation log pO2 ¼ log pS2 þ 2 log K2:38
(2.43)
and has a slope equal to one. The diagram unambiguously defines the range of gas compositions in which pure iron is stable as a metal ð pO2 o1 1019 atm and pS2 o7 1010 atm at T ¼ 8001C). It also allows prediction of which of the possible reaction products can co-exist with an equilibrium gas mixture. Thus, for example, at pS2 ¼ 1 107 atm and pO2 ¼ 1 1014 atm, the surface of a scale is expected to be magnetite (point A). However, it is not possible to predict the diffusion path trajectory, from A to B, from thermodynamic information alone. Three possibilities are shown in Figure 2.4, one involving oxide, but the other two also involving sulfide. Since sulfides generally grow much faster than oxides, the question is important and is considered further in Chapters 4, 9 and 10.
2.3. ALLOYS AND SOLID SOLUTIONS Alloy phases are in general solid solutions, and the need arises to specify component activities within them. Returning to Equation (2.3) we note that the changes in composition, dni , now to be considered reflect alteration of solute concentration rather than chemical reaction. Taking the total differential of Equation (2.8) X X dG ¼ mi dni þ ni dmi (2.44) i
i
2.3. Alloys and Solid Solutions
43
and subtracting it from Equation (2.5), we obtain the Gibbs–Duhem equation X 0 ¼ Vdp SdT ni dmi (2.45) i
Again, summations are performed over all components of the system. We consider an isothermal, isobaric system in which, at equilibrium, X ni dmi ¼ 0 (2.46) i
or, dividing by the total number of component moles, nT, to obtain mole fractions X N i dmi ¼ 0 (2.47) Consistent with the approach adopted for ideal gas mixtures (Equation (2.14), the solution component activity is defined through ¯i G ¯ i mi mi ¼ RT ln ai ¼ G
(2.48)
where unit activity corresponds to the standard state in which mi ¼ mi . The choice of standard state is arbitrary, but that of pure solid is convenient. In this case, an ideal solution is defined as one in which the chemical potential of every component is related to its mole fraction by mi mi ¼ RT ln N i
(2.49)
Real solutions deviate from ideality, and are dealt with by defining an activity coefficient, gi , such that the relationship mi mi ¼ RT ln gi N i
(2.50)
holds, whatever the extent of deviation. In general, gi varies with composition, as well as with temperature and pressure. The thermodynamics of solutions can be understood from their enthalpy and entropy of mixing. At constant pressure, application of Equations (2.2) and (2.48) to a particular component in a solution of fixed composition yields ¯ i =TÞ @ðG ¯i ¼H (2.51) @ð1=TÞ and hence
@ ðmi mi Þ T ¯ i H i ¼H @ð1=TÞ
(2.52)
where Hi is the standard enthalpy per mole of unmixed component i, and overscoring indicates the partial molar quantity. Comparison with Equation (2.48) then leads to @ ln ai ¯ i H i R ¼H (2.53) @ð1=TÞ For an ideal solution, ai ¼ N i , and the partial differential in Equation (2.52) is zero, the enthalpy of the dissolved component being equal to its value in the
44
Chapter 2 Enabling Theory
unmixed state. The enthalpy of mixing is defined for the entire solution as X X ¯i Ni H N i H i (2.54) DH m ¼ i
i
DH id m
and in the ideal case, ¼ 0. If Equation (2.48) is multiplied by N i and a sum formed for all components, we obtain X X X ¯i NiG N i Gi ¼ RT N i ln ai (2.55) i
i
i
in which the left-hand side is recognized as the free energy of mixing X DGm ¼ G N i Gi
(2.56)
i
In an ideal solution, therefore, DGid m ¼ RT
X
N i ln N i
and it follows from the equation @DG ¼ DS @T P;ni that DSid m ¼ R
X
N i ln N i
(2.57)
(2.58)
(2.59)
This expression is recognized from the Boltzmann equation S ¼ k ln o where o is a measure of randomness and k the Boltzmann’s constant, as corresponding to a random mixture. This is now illustrated for a binary mixture of A and B DSid m ¼ Smix SA SB ðnA þ nB Þ! ¼ k ln ð2:60Þ nA !nB ! where ni is the number of atoms of the indicated species and o has been evaluated as the number of distinguishable configurations of the nA þ nB atoms. Expanding Equation (2.60) with the aid of Stirling’s approximation ln n! ¼ n ln n n
(2.61)
and the relationship R ¼ kN AV (with N AV equal to Avogadro’s number) leads to DSid m ¼ RðN A ln N A þ N B ln N B Þ
(2.62)
which is merely (2.59) applied to a binary system. Thus an ideal solution is a completely random mixture of constituents which experience the same thermal interaction with all neighbouring atoms, and the entropy of mixing is purely configurational.
2.3. Alloys and Solid Solutions
45
In real solutions, interactions between dissimilar atoms give rise to non-zero ¯ i and thermal contributions to S¯ i . These are conveniently described using H ‘‘excess’’ functions of the sort Gxs ¼ G Gid
(2.63)
¯ i Gi RT ln N i RT ln gi ¼ G
(2.64)
Rewriting Equation (2.46) as and substituting for RT ln N i from Equation (2.49) we find ¯ i Gi Þ ðG ¯ id RT ln gi ¼ ðG i Gi Þ ¯ i Gid ¼G i
¯ xs ¼ H ¯ xs ¯ xs ¼G i TS i Since
¯ id H i
ð2:65Þ
¼ 0, this is equivalent to ¯ i TS¯ xs RT ln gi ¼ H
(2.66)
where the deviation from ideality of component i is seen to arise from its thermal interaction with the solution and the consequent shift in ¯ xs , H ¯ xs thermal entropy. A useful tabulation of partial molar excess quantities G xs and S¯ has been provided by Kubaschewski and Alcock [1] for binary alloy systems. An alternative approach is suited to dilute solutions where the experimental finding is that ai ¼ gi N i
(2.67)
with gi a constant. This is Henry’s law. More generally, the quantity gi varies with composition, and can be expanded, as proposed by Wagner [6], as a Taylor series which to the first order yields X ln gi ¼ ln gi þ ik N k (2.68) where the gi are the Henry’s law coefficients. It can be shown that @ ln gi @ ln gk ¼ ik ¼ ki ¼ @N k @N i
(2.69)
lessening the amount of experimentation needed. Although there are many alternative solution models available, the form (2.68) is a useful one for moderately dilute solutions.
2.3.1 Dissolution of gases in metals In studying the formation of internally precipitated oxides, carbide, etc. (see Figure 1.8), it is necessary to consider the dissolution of the oxidant in the metal, e.g. 1 2O2 ðgÞ
¼O
(2.70)
46
Chapter 2 Enabling Theory
Table 2.2
Oxygen dissolution in metalsa
a w
Metal
¯ O (kJ mol1) DH
DS¯ O (J mol1 K1)
Referencew
Ni a Fe g Fe
182 155.6 175.1
107.6 81.0 98.8
[A6] [A9] [A9]
xs
Referred to Equation (2.72) with pO2 (atm) and N O (mole fraction). References in Appendix D.
Here, and elsewhere in this book, underscoring is used to denote a solute species in a solid. It is convenient to specify concentrations as mole fractions, Ni, and we write 1=2
N O ¼ K70 pO2
(2.71)
which is Sievert’s equation. It was the experimental demonstration of Equation (2.71) which proved that gaseous oxygen, nitrogen and sulfur dissolve in metals as dissociated atoms. The value of K70 is related to that of DG for Equation (2.70) in the usual way, but care is needed in specifying the concentration units and standard state for the solute. In much of the published work, concentration is expressed in wt%, and a standard state of 1 wt% is chosen. It is preferable to use mole fraction, N O , so that ¯ TDS¯ xs þ RT ln N O 1RT ln p (2.72) DGð2:70Þ ¼ DH 2
O2
Data for oxygen solubility in iron and nickel are summarized in Table 2.2, and corresponding data for carbon are provided in Table 9.4. The maximum value of pO2 applicable in Equation (2.71) is the equilibrium value for formation of the lowest metal oxide. Thus, for example, the maximum solubility of oxygen in austenitic iron is set by the Fe/FeO equilibrium. As seen earlier, at T ¼ 1,0001C, pO2 ðFeOÞ ¼ 1:2 1015 atm. Calculating K70 from the data in Table 2.2, this is found to correspond to a solubility limit of 3.7 106 mole fraction in the iron beneath an oxide scale. In the case of an alloy, if sufficient dissolved oxygen is present, it can react with an alloy metal solute to precipitate particles of oxide, a situation considered in the next section.
2.4. CHEMICAL EQUILIBRIA BETWEEN ALLOYS AND GASES 2.4.1 Equilibria between alloys and single oxide Consider a binary alloy A–B reacting with oxygen. In general DG ðAOÞaDG ðBOÞ and one of the metal oxides is more stable than the other. Referring to Table 1.1 we see that, e.g., the alloys Fe–Ni and Fe–Cr are of interest because the growth of NiO or Cr2O3 is much slower than that of FeO. We enquire as to the alloy concentration of nickel or chromium necessary to form the desired oxide. This situation can be formulated as a competitive oxidation reaction, e.g. Ni þFeO ¼ NiO þ Fe
(2.73)
2.4. Chemical Equilibria Between Alloys and Gases
The condition for chemical equilibrium, Equation (2.48) yields
P
47
ni mi ¼ 0, after substitution from
aNiO aFe (2.74) aFeO aNi For simplicity, we approximate the oxides as being pure, immiscible solids, so that aNiO ¼ 1 ¼ aFeO . The standard free energy change is evaluated from the equation DG ¼ mFe þ mNiO mNi mFeO ¼ RT ln
DG ð2:73Þ ¼ DG ðNiOÞ DG ðFeOÞ as +55,760 J mol1 at 1,0001C. Thus, at equilibrium, aNi ¼ 194 aFe
(2.75)
(2.76)
and the alloy needs a very high nickel content. Approximating the alloy as an ideal solution, and rewriting Equation (2.76) as N Ni ¼ 194 (2.77) 1 N Ni we find the solution N Ni ¼ 0:995. It is clear that alloying with nickel cannot be used as a method of achieving oxidation resistance for steel. Turning now to the Fe–Cr alloy, we formulate the competitive reaction 2 Cr þ3FeO ¼ Cr2 O3 þ 3 Fe
(2.78)
for which the equilibrium expression is aCr2 O3 a3Fe DG ð2:78Þ ¼ exp RT a3FeO a2Cr
(2.79)
Pure, immiscible oxides are again assumed so that their activities can be set to unity, and the standard free energy change is evaluated from the equation DG ð2:78Þ ¼ DG ðCr2 O3 Þ 3DG ðFeOÞ
(2.80)
as 244,590 J mol1 at 1,0001C, corresponding to a2Cr ¼ 9 1011 a3Fe
(2.81)
Assuming that in such a dilute solution aFe ¼ N Fe 1, it is found that aCr 1 105 . Data tabulated by Kubaschewski and Alcock [1] for ¯ Cr ¼ þ25; 100 J mol1 and ferritic Fe–Cr alloys show that for N Cr ! O, DH s 1 1 DS¯ Cr ¼ þ10:25 J mol K . Insertion of these values in Equation (2.66) yields the value gCr ¼ 3:1 at 1,0001C. Thus the required chromium activity of 1 105 is equivalent to N Cr 3 106 . Thermodynamically, at least, the use of chromium as a steel alloying addition for oxidation protection is seen to be very attractive. The question of whether the oxide forms as an external scale or as internal precipitates requires kinetic analysis. Assuming for the moment that internal oxidation occurs within a dilute alloy, it is seen that the reaction is one between
48
Chapter 2 Enabling Theory
solute species 2 Cr þ3 O ¼ Cr2 O3
(2.82)
The value of DG (2.82) is found from the reactions 2Cr þ 32O2 ðgÞ ¼ Cr2 O3
(2.83)
Cr ¼ Cr
(2.84)
1 2O 2
(2.85)
¼O
for which we can write DG ð2:83Þ ¼ 1; 120; 270 þ 259:83T J mol1
(2.86)
¯ Cr ð2:84Þ ¼ 25; 100 10:25T þ RT ln N Cr J mol1 DG
(2.87)
¯ O ð2:85Þ ¼ 175; 100 þ 98:8T þ RT ln N O J mol1 DG
(2.88)
where Equation (2.66) has been used to find Equation (2.87), and Equation (2.88) was calculated using data for g Fe provided by Kubaschewski and Alcock [1]. From the equation ¯ Cr ð2:84Þ 3DG ¯ O ð2:85Þ DGð2:82Þ ¼ DG ð2:83Þ 2DG we find, at equilibrium, 0 ¼ DGð2:82Þ ¼ 645; 170 16:07T 2RT ln N Cr 3RT ln N O
(2.89)
and at T ¼ 1,0001C, N 2Cr N 3O ¼ Ksp ¼ 4 1028
(2.90)
The equilibrium constant, Ksp , is known as the solubility product. The maximum value of pO2 available to a dilute Fe–Cr alloy is the level set by the Fe–FeO equilibrium because a scale forms on the alloy surface. As seen earlier, this value is 1:2 1015 atm for pure iron at 1,0001C, and results in N O ¼ 3:1 106 . It follows from Equation (2.90) that the precipitation of Cr2O3 within the alloy would leave an equilibrium value N Cr ¼ 2:8 105 . It is therefore concluded that any Fe–Cr alloy containing more than 28 ppm of chromium can form internal Cr2O3 precipitates when oxidized at 1,0001C. Whether or not an external Cr2O3 scale forms cannot be predicted from thermodynamics alone. The preceding discussion of Fe–Ni and Fe–Cr alloy oxidation has been based on the simplifying assumption that the product oxides are pure, immiscible solids. This assumption is not always valid. The Fe–Ni–O system forms a solid solution spinel phase NixFe3xO4, and the Fe–Cr–O system develops several mixed oxides. These complications are best described with the help of phase diagrams.
2.4.2 Equilibria between alloys and multiple oxides A binary alloy reacting with a single oxidant constitutes a ternary system. The phase assemblages capable of co-existing at local equilibrium at a fixed
2.4. Chemical Equilibria Between Alloys and Gases
49
temperature can be represented by an isothermal section of the phase diagram. An example for Fe–Cr–O shown in Figure 2.5 is drawn as a Gibbs composition triangle. The geometry of the equilateral triangle is such that for any point within the triangle, wherever located, the sum of the perpendiculars to the three sides is always the same. This provides a convenient means of mapping compositions where N Fe þ N Cr þ N O ¼ 1, avoiding the need to calculate the third component which would arise if normal rectangular co-ordinates were used. Single-phase existence regions are marked on the diagram. The two alloy phases are shown on the Fe–Cr binary side of the triangle: austenite, containing N Cr 0:13 and ferrite, with N Cr 0:17. The three iron oxides are shown along the Fe–O binary side and the single chromium oxide on the Cr–O side. It is seen that Fe1dO dissolves a significant amount of chromium, the solubility varying with wu¨stite stoichiometry. The spinel phase Fe3O4 dissolves large amounts of chromium, up to a terminal composition of FeCr2O4. Finally, the structurally isotypic Fe2O3 and Cr2O3 form a continuous solid solution at this temperature. As the phase rule informs us, there are two degrees of freedom within a ternary single-phase region, as is illustrated by the representation on the diagram
Figure 2.5 Isothermal section (1,2001C) of Fe–Cr–O phase diagram with alloy phases omitted for clarity.
50
Chapter 2 Enabling Theory
of single phases as areas. When two phases co-exist only one degree of freedom is available. Two-phase regions separate pairs of adjacent single phases, as shown more clearly in the enlarged schematic diagram of Figure 2.6. Each two-phase region is defined by a set of tie-lines which joins pairs of composition points along the phase boundaries. Thus, for example, compositions of wu¨stite along the line ab equilibrate with spinel compositions along the line cd. For all points on any one tie-line mFe ðWÞ ¼ mFe ðSpÞ mCr ðWÞ ¼ mCr ðSpÞ mO ðWÞ ¼ mO ðSpÞ where W denotes wu¨stite and Sp the spinel. Of course, different tie-lines correspond to different compositions of the phases, and therefore different chemical potentials. The two-phase region is univariant, and this is represented by the lines ab and cd, which define the composition of each phase in terms of a single variable. The two-phase regions bound three-phase triangles, e.g., the wu¨stite–spinel– alloy triangle bde, which represent invariants. All points within the triangle correspond to differing proportions of these three phases, always of the compositions given by the points b, d and e. Thus the relationships mFe ðWÞ ¼ mFe ðSpÞ ¼ mFe ðAlloyÞ, etc. are satisfied. As we have already seen when examining Figure 2.4, ternary phase diagrams have some utility in predicting the outcome of alloy oxidation reactions, but diffusion paths cannot be predicted without additional information. The Fe–Cr–O
d Fe3O4
c
a Fe1-δO b O
Fe e
f
Figure 2.6 Schematic enlargement of part of Figure 2.5.
Cr
2.5. Thermodynamics of Diffusion
51
diagram reveals that a necessary condition for the formation of Cr2O3 at the scale–metal interface is a surface alloy chromium concentration greater than that at the point f, i.e. N Cr 0:04. This is much higher than the value calculated from Equation (2.79) as aCr 104 at 1,2001C. The difference arises from the neglect of spinel formation in the earlier treatment. As the Fe–Cr–O diagram shows, chromium-rich spinel has a stability equal to that of Cr2O3 when N Cr 0:04 at 1,2001C. The competitive oxidation reaction is reformulated as Fe þ43Cr2 O3 ¼ FeCr2 O4 þ 23 Cr
(2.91)
for which DG ð2:91Þ ¼ 56; 690 14:0T J mol1 and 2=3
K¼
aFeCr2 O4 aCr 4=3
aCr2 O3 aFe
(2.92)
Assuming that the oxides are pure and immiscible, and approximating aFe N Fe 1, it is found that DG ¼ RT ln K ¼ 23DmCr
(2.93)
and at 1,2001C, DmCr ¼ 54; 102 J mol1. Using Equation (2.87), it is then found that the value of N Cr satisfying the equilibrium between spinel and Cr2 O3 is 0.03, in reasonable agreement with the phase diagram. Clearly the latter provides a simpler route to the answer, when available for the temperature of interest. The use of the Fe–Cr–O diagram is considered in more detail in Sections 5.3 and 7.3. However, it should be noted that the condition N Cr 40:04 is insufficient to achieve protective Cr2O3 scale formation. The main reason for this is depletion of chromium from the alloy surface by its preferential oxidation. The actual surface concentration is determined by the balance between chromium diffusion from the alloy interior and its removal into the scale.
2.5. THERMODYNAMICS OF DIFFUSION 2.5.1 Driving forces We start by considering the thermodynamic implications of matter diffusing from one part of a system to another. In an isothermal, field-free system, an amount dnA2 of component A passes from region 2 to region 1, each region being regarded as homogeneous. The changes are described using Equation (2.3) dU TdS ¼ p1 dV 1 p2 dV 2 þ ðmA1 mA2 ÞdnA2
(2.94)
and the last term reflects the fact that dnA1 ¼ dnA2 . In a slow process, the pi do not vary, and p1 dV1 p2 dV 2 ¼ dw
(2.95)
52
Chapter 2 Enabling Theory
the amount of work done on the system. From the second law of thermodynamics we have dðU TSÞodw
(2.96)
for a spontaneous process. It follows that the necessary condition for isothermal mass transfer to occur is ðmA1 mA2 ÞdnA2 o0
(2.97)
In other words, the sign of dnA2 is the opposite of the sign of ðmA1 mA2 Þ: if dnA2 is a positive transfer of component A from region 2 to region 1, the chemical potential in region 2 must be greater than in region 1. This important result informs us that diffusion actually occurs from regions of high to low chemical potential, rather than from high to low concentration. Thus the simple description given by Fick’s law for the relationship between flux and concentration gradient in Equation (1.24) J ¼ D
@C @x
can be inaccurate to the point of predicting diffusion in the wrong direction. In developing a more accurate description of diffusion, several approaches are possible. These include geometric, random walk procedures which have been applied to crystalline solids to yield an advanced theory of correlation and isotope effects [7, 8], and the application of absolute rate theory. Before developing the latter treatment, we consider a phenomenological approach based on irreversible thermodynamics. The principal concepts were developed by Onsager [9] and extended by de Groot [10] and Prigogine [11]. Their application to solid-state diffusion has been reviewed a number of times [8, 12, 13]. An essential element of the thermodynamic treatment of diffusion is the postulate that a state of local equilibrium can be adequately approximated in each region of the solid, despite the compositional variation with position within the system. The simultaneous satisfaction of these two requirements is achieved by taking a microscopic volume element which is so small that its composition can be treated as homogeneous. Because the solid is atomically dense, the element contains a statistically meaningful number of particles. A series of such elements describes the diffusion profile within the solid (Figure 3.32). The procedures of irreversible thermodynamics enable us to calculate the rate of entropy production per unit volume, s_, in terms of the various fluxes flowing within the system. The result is a bilinear expression involving the fluxes themselves and a set of thermodynamic forces, Xi, X J i Xi T_s ¼ i
These forces are thereby identified as those responsible for the fluxes, each flux being linearly dependent on all the forces. The description is applicable only to systems that are not far removed from equilibrium, and is therefore appropriate to diffusion in a solid within which the local equilibrium state is closely approached.
2.5. Thermodynamics of Diffusion
53
For isothermal diffusion in a closed, isobaric, field-free n-component system, it is found that n X J i rZi (2.98) T_s ¼ i¼1
where r indicates gradient, i.e. partial derivative with respect to position co-ordinate, and the summation covers all components. Hence the component fluxes are given by a set of linear equations n X Ji ¼ Lij rZj (2.99) j¼1
where the Lij are the Onsager phenomenological coefficients. These each relate the flux of species i to the gradient in species j, and form a square matrix of order equal to the number of system components. The driving forces are seen to be the gradients rZi , known as electrochemical potential gradients. They are defined by Z ¼ m þ qFc
(2.100)
where q is the charge of the species, F is Faraday’s constant and c the local electrostatic potential. Gradients in potential constitute fields, but these are internal to the solid and the conditions for the validity of Equation (2.98) are maintained. In the case of a metallic alloy, the constituent atoms have no effective charge, and the driving force is the chemical potential gradient, rm. This result is intuitively satisfactory in the sense that diffusion is perceived (under the conditions specified earlier) as a process that eliminates differences in chemical potential, thereby achieving equilibration. A more profound result of the irreversible thermodynamic treatment is the recognition that the flux of any component is, in general, dependent on the chemical potential gradients of all components. The Lij ðiajÞ in Equation (2.99) are referred to as off-diagonal coefficients, and represent the ‘‘cross effects’’ between components. These cross effects can arise from thermodynamic interactions (cf 2.68) or from kinetic interactions. Aspects of the latter are outlined in Appendix B for ionic solids. For the moment, we consider the situation where cross effects are small enough to ignore. For one-dimensional diffusion in a binary alloy, the approximation L12 0 yields the simple result J 1 ¼ L11
@m1 @x
(2.101)
which, upon substitution for m1 from Equation (2.50) leads to L11 RT g1 @N 1 N 1 @g1 J1 ¼ þ g1 N 1 @x @x ¼
L11 RT @ ln g1 @N 1 1þ N1 @ ln N 1 @x
(2.102)
54
Chapter 2 Enabling Theory
Noting that the change in molar concentration @C1 ¼ C@N 1 , with C the average molar concentration, it is found from a comparison of Equations (1.24) and (2.102) that L11 RT @ ln g1 D1 ¼ 1þ (2.103) C1 @ ln N 1 This makes clear that chemical diffusion is strongly dependent on the thermodynamic properties of the solid solution, even in the absence of kinetic cross effects. The shortcoming of the phenomenological description (2.99) is that it provides no information on the coefficients Lij relating the diffusion rate to the driving forces. For our present purposes, a more transparent description is provided by an absolute rate theory approach. Before developing this description it is necessary to consider the identity and nature of the diffusing species.
2.5.2 Point defects Solid-state diffusion involves the movement of individual particles (atoms or ions) that constitute the material. These particles are capable of movement because they vibrate around their mean positions and because the existence of defects in the solid crystal permits an occasional vibration to extend into a translation to an available lattice site nearby. Two common defects are illustrated in Figure. 2.7 for the case of a pure, single-component solid: a vacancy, or unoccupied lattice site, and an interstitial atom, i.e. one located between normal lattice sites. A lattice atom can move into an adjacent vacancy, exchanging sites with the defect. Movement via this vacancy mechanism is the most common way in
Figure 2.7 An individual vacancy and interstitial defect in a single-component crystal lattice.
2.6. Absolute Rate Theory Applied to Lattice Particle Diffusion
55
which diffusion occurs. Clearly, the concentration of vacancies present is important in determining the probability of atom translation occurring. The interstitial species can contribute to diffusion simply by moving into an adjacent interstitial site. This is improbable in pure metals, because the atoms are large, but operates for interstitial impurities such as C, H, N and O dissolved in metals. Whichever the mechanism, the concentration of defects is an important factor in the particle movement rates. The question of defect concentrations is now considered. Equilibrium concentrations of point defects in crystals are calculated by the methods of statistical thermodynamics. The application of these methods to crystals has been reviewed in detail by Schottky [14], and their use in diffusion calculations has been explored by several authors, notably Mott and Gurney [15] and Howard and Lidiard [8]. The Gibbs free energy for a monatomic crystal containing nn vacancies and n atoms is G ¼ GO þ nn gn kT ln
ðn þ nn Þ! n!nn !
(2.104)
where gn is the free energy of formation of a vacancy, and the logarithmic term is recognized as the configurational entropy resulting from the presence of defects. It is this term that makes vacancy formation inevitable at all temperatures above absolute zero. The free energy minimum representing the equilibrium state of the crystal defines the chemical potential of the vacancies as zero: @G ¼ mn ¼ 0 (2.105) @nn T;P;N Application of this to Equation (2.103) making use of Stirling’s approximation ðln N! ¼ N ln N NÞ, then yields g
nn Nn ¼ ¼ exp n (2.106) ðn þ nn Þ kT Equation (2.106) is recognized as an equilibrium expression of the same form as Equation (2.23). A more detailed discussion of point defect equilibria in ionic solids is provided in Chapter 3.
2.6. ABSOLUTE RATE THEORY APPLIED TO LATTICE PARTICLE DIFFUSION We turn now to the evaluation of individual particle jump frequencies, using absolute rate theory. The first applications to solid-state diffusion were reported by Wert and Zener [16] and Seitz [17], and subsequent extensions for various cases have been provided by others [18–20]. When a particle moves from one lattice position to another, it passes through an intermediate state that has a higher energy because adjacent particles must be perturbed from their mean lattice positions in order to accommodate the passage of the moving particle. During this lattice distortion, an activated complex involving the two interchanging species (e.g., particle plus vacancy) is formed.
56
Chapter 2 Enabling Theory
The activity ain of the complex is described via the equilibrium constant Kin for its formation: ain DH in DSin ¼ Kin ¼ exp exp (2.107) ai an RT R where DH in is the enthalpy and DSin the entropy of complex formation. A profile of the periodic internal energy surface in a direction parallel to that of diffusion is shown in Figure 2.8. An electrostatic field can be externally imposed, or can arise through the movement of the charged species themselves, and will in this case be aligned with the diffusion direction. The height of the energy barrier to diffusion of a charged species is modified by the field, being lower for downfield movement than for upfield movement of an appropriately charged species. It will be assumed that the field does not affect DSin . We may write for the interchange of species i and a vacancy between planes (1) and (2) separated by a distance l, as shown in Figure 2.8. DSin J ¼ mlnin exp R ( " # DU in qFðcð0Þ cð1Þ Þ ð1Þ ð2Þ ai an exp RT " #) DU in qFðcð2Þ cð0Þ Þ ð1Þ ð2Þ an ai exp RT g1 in
ð2:108Þ
where m is the volume concentration of lattice sites, nin a kinetic frequency term and gin the activity coefficient for the transition-state complex. Here q is the effective charge of the vacancy, that of the cation being zero. Superscripts in
Figure 2.8 Potential energy profile in diffusion direction: upper curve, no electrostatic field; lower curve showing effect of electrostatic field.
2.6. Absolute Rate Theory Applied to Lattice Particle Diffusion
57
parentheses represent the location in Figure 2.8 at which the quantity in question is evaluated. An alternative treatment of the particle movement kinetics might be found more appealing. The rate at which ions can move from plane (1) to (2) must be proportional to the probability of finding an ion at position (1), að1Þ i , to the availability of a vacancy for it to jump into, að2Þ , to the frequency, n , with which in n the ion approaches the intervening energy barrier, and to the Boltzmann factor giving the proportion of ions possessed of sufficient energy to surmount the barrier, expðDGin =RTÞ. The overall probability of the event occurring is then given by DGin ð1Þ ð2Þ nin ai an exp RT Calculation of the corresponding flux from this probability by multiplying by the area density of sites on plane (1), ml, and expansion of DGin leads to the first term in Equation (2.108). The net flux is then calculated by subtracting the equivalent expression for the rate at which ions return from the second plane to the first, and Equation (2.108) results. Equation (2.108) is cleared of common terms and subjected to Taylor series ð2Þ ð2Þ expansion of the terms að2Þ n and ai expðqFc =RTÞ. Retention of linear terms, in the case where the field is not inordinately high, leads to J¼
ml2 nin Kin ai an rmi rmn qFrc RT
(2.109)
which, upon substituting from Equation (2.100) becomes J¼
ml2 nin Kin ai an rZi rZn RT
(2.110)
Expressions of this sort always apply to pairwise site exchanges. For diffusion of non-charged species in a metal or an alloy, q ¼ 0, and we obtain Ji ¼
ml2 nin Kin ai an rmi rmn RT
(2.111)
If the equilibrium condition of Equation (2.105) is realized and the off-diagonal terms in Equation (2.99) are ignored, this result simplifies to Equation (2.101), with 2 ml L11 ¼ nin Kin ai an RT and therefore, in the dilute (ideal) solution approximation, it is found from Equation (2.103) that Di ¼ l2 nin exp
DHin DSin exp Nn RT R
(2.112)
58
Chapter 2 Enabling Theory
We now combine Equations (2.106) and (2.112) to determine the temperature dependence of the diffusion coefficient Q D ¼ DO exp (2.113) RT where Q ¼ DH in þ DH n with DH n the enthalpy (per mole) for vacancy formation, and the remaining constants have been collected in DO . The expected Arrhenius form is arrived at and is commonly used to interpolate or extrapolate sparse experimental data.
2.7. DIFFUSION IN ALLOYS 2.7.1 Origins of cross effects Equation (2.99) may be rewritten for atomic diffusion in an n-component system as n X Ji ¼ Lij rmj (2.114) j¼1
when it is clear that cross effects can arise through either kinetic interactions, as represented by the Onsager coefficients, Lij , or thermodynamic interactions, represented by the variation of chemical potential with composition. Experimental diffusion data is almost always collected in the form of concentration rather than chemical potential. For this reason, it is desirable to use a generalized form of Fick’s law Ji ¼
n1 X
Dij rCj
(2.115)
j¼1
where the Dij are functions of the kinetic coefficients Lij and also reflect the dependence of chemical potential on composition. A useful example is provided by the application of Wagner’s dilute solution model (Equation (2.68)). For a ternary system, it is found that D11 ¼ RT L11 ð11 þ 1=N 1 Þ þ L12 21 D12 ¼ RT L11 12 þ L12 ð22 þ 1=N 2 Þ D21 ¼ RT L22 21 þ L21 ð11 þ 1=N 1 Þ ð2:116Þ D22 ¼ RT L22 ð22 þ 1=N 2 Þ þ L21 12 In an ideal solution all ij ¼ 0, and the Dij reduce to the purely kinetic form. RTLij Dij ¼ (2.117) Nj For real solutions, if no kinetic cross effects occur, i.e. Lij ðiajÞ ¼ 0, it is clear that the diffusional cross terms Dij (i6¼j) are nevertheless non-zero. In this case the
2.7. Diffusion in Alloys
59
dilute solution limit ðN 1 ; N 2 ! 0Þ may be described by
and
D12 N 1 12 ¼ D11 1 þ 11 N 1
(2.118)
D21 N 2 21 ¼ D22 1 þ 22 N 2
(2.119)
Thus the ternary coefficients are determined uniquely by the binary ones in dilute solutions. For interstitial diffusion there are negligible correlations between crystal sublattices, so that the approximation Lij ðiajÞ ¼ 0 is valid. Practical examples are steels Fe–C–M in which M is a substitutional metal (Si, Mn, Ni, Cr, Mo, Co) and the carbon is interstitial. The variation of DCM =DCC with carbon concentration is shown in Figure 2.9, compared with the predictions of Equation (2.118) using independently measured interaction parameters [21]. Agreement is quite good. Correlations of this sort can contribute to an understanding of alloy carburization reactions. A detailed diffusion analysis employing cross terms was used by Nesbitt [22] in analysing the ability of Ni–Cr–Al alloys to supply aluminium to the surface to reheal damaged alumina scales. In the regime examined, the value of DAlCr was as high as 0:5DAlAl , leading to a significant contribution from the chromium
Figure 2.9 Variation of D12 =D11 with carbon concentration ðC1 Þ, with solid lines representing thermodynamic prediction. After Brown and Kirkaldy [21]. Published with permission from the Minerals, Metals and Materials Society.
60
Chapter 2 Enabling Theory
concentration gradient to aluminium diffusion. Cross effects between dissolved oxygen and alloy components were considered by Whittle et al. [23, 24] in analysing alloy surface behaviour as oxygen diffused inwards. This analysis revealed that the cross effect between oxygen and a selectively oxidized component was important in driving the oxygen flux. Writing the equations (2.115) as J A ¼ DAA rCA DAO rCO J O ¼ DOA rCA DOO rCO we consider their application to diffusion in the subsurface zone of alloy AB, in which A is selectively oxidized. In the case of Ni–Cr at 1,0001C, the self-diffusion coefficients of oxygen and chromium are of order 107 and 1012 cm2 s1, respectively, and rCCr rCO . Consequently, even for small values of DOA, the off-diagonal term is important, and likely predominant, in the expression for JO.
2.7.2 Kirkendall effect We now consider another way in which diffusional interactions arise between components sharing the same lattice, but possessing different intrinsic mobilities. Their experimental manifestation is known as the Kirkendall effect, and its measurement is used to evaluate a composite alloy diffusion coefficient defined below. Consider a binary alloy AB in which one-dimensional diffusion occurs via atom-vacancy exchanges, and Equation (2.111) applies to both A and B, so that DA and DB correspond to D1 and D2 in Equation (2.112). In general the fluxes are not equal and opposite. Thus, if DA 4DB in a sample initially rich in A on the left, there will be an excess flux of A from left to right over B atoms moving to the left. Consequently, the diffusion zone as a whole drifts to the left, compensating for the accumulation of matter and hydrostatic pressure that would otherwise occur on the right. Thus the lattice planes which define the frame of reference within which Equation (2.111) applies are themselves moving. Since the diffusion zone is generally a small part of a larger sample, measurements of position that are referred to the end of the sample (the laboratory reference frame) are affected by this drift, and so, in consequence, is the estimate of diffusion rate. The problem is the same as that faced by a navigator measuring the speed of a plane using its airspeed when a wind is blowing. A knowledge of the wind speed relative to the ground resolves the difficulty. Formally, the situation is dealt with by relating the two frames of reference. In the laboratory frame of the diffusion measurement, we use n X Ji ¼ 0 (2.120) i¼1
which is equivalent to a volume-fixed frame of reference if the partial molar volumes are approximately equal. In the lattice frame, where Equation (2.111)
2.7. Diffusion in Alloys
61
applies, the expression (2.120) does not. We therefore write for the lattice frame, using J 0i to denote its fluxes J 0A þ J 0B ¼ J 0V
(2.121)
If the lattice frame moves with respect to the laboratory frame with a velocity n, then J i ¼ J 0i þ Ci n;
i ¼ A; B
(2.122)
where the non-primed fluxes refer to the laboratory frame. These equations are solved using Equation (2.120) to obtain n¼
J 0A þ J 0B CA þ CB
(2.123)
or, upon resubstitution J A ¼ J B ¼ N B J 0A N A J 0B
(2.124)
In the simple situation in which the off-diagonal Onsager coefficients are set equal to zero, and local equilibrium applies ðrmn ¼ 0Þ, Equations (2.111) and (2.112) simplify to Fick’s law (1.24). Since, moreover, for an isobaric system in ¯ are equal which partial molar volumes V ¯ A þ CB Þ ¼ 1 VðC (2.125) combination of Equations (2.123)–(2.125), and (1.24) yields ¯ A DB Þ @CA n ¼ VðD @x J A ¼ ðN B DA þ N A DB Þ
@CA @x
(2.126) (2.127)
The value of n can be measured using inert markers, as is now discussed. The first demonstration of lattice drift was performed by Smigelskas and Kirkendall [25] using the diffusion arrangement shown schematically in
Figure 2.10 Lattice drift experiment of Smigelskas and Kirkendall.
62
Chapter 2 Enabling Theory
Figure 2.10. Molybdenum wires (the markers) were attached to a block of brass (Cu–Zn) and then an outer copper layer applied by electroplating. Annealing this couple at high temperature caused rapid outward diffusion of the more mobile zinc from the brass into the copper, slower inward diffusion of copper and inward drift of the molybdenum markers. The effect is quite general and is widely used in diffusion measurements. For an infinite diffusion couple (sample much larger than the diffusion zone), it can be shown that x CA ¼ CA ðlÞ; l ¼ 1=2 (2.128) t and hence n¼
DA DB dCA dl t1=2
(2.129)
Because the markers are located at a point of fixed composition and therefore at a fixed value of dCA =dl, Equation (2.129) integrates immediately to yield xm ¼ 2ðDA DB Þ
dCA 1=2 t dl
(2.130)
for the marker displacement. The quantities DA and DB are known as the intrinsic diffusion coefficients because they refer to diffusion with respect to the lattice planes in the presence of an activity gradient. It is necessary now to relate these to the measured tracer coefficients, DAn and DBn . These refer to the diffusional intermixing of different isotopes of the same atom or ion, and usually the enthalpy of mixing is small and the solution ideal. In this case, Equation (2.103) simplifies to L11 RT D1 ¼ (2.131) C1 However, the intrinsic diffusion coefficient refers to a non-ideal solution and Equation (2.103) must be used without approximation. As a result, d ln gA n DA ¼ DA 1 þ (2.132) d ln N A Using the Gibbs–Duhem equation for equilibrium in a solution (Equation (2.46)) we may write d ln gA d ln gB 1þ ¼1þ (2.133) d ln N A d ln N B then Equation (2.127) becomes with
~ J A ¼ DrN A
(2.134)
d ln g ~ D ¼ ðN B DAn þ N A DBn Þ 1 þ d ln N
(2.135)
~ is the chemical diffusion This is the Darken–Hartley–Crank equation [26, 27] and D ~ coefficient. The quantity D is also called the alloy diffusion coefficient, and is
63
2.8. Diffusion Couples and the Measurement of Diffusion Coefficients
obtained from a diffusion couple measurement (Section 2.8). If markers are used in the measurement, values of the self-diffusion coefficients DA and DB may also be obtained. This provides a powerful technique for exploring the compositional dependence of the Di . The above analysis has been extended to multicomponent systems (see e.g., Ref. [12]). The lack of balance among the intrinsic diffusive flows always leads to a compensating mass flow of material. That is to say, diffusional cross effects arise even in the absence of kinetic or thermodynamic correlations. Thus even a component with a negligible intrinsic mobility will move. The simple form of Fick’s law fails, and the generalized form (2.115) must be used.
2.8. DIFFUSION COUPLES AND THE MEASUREMENT OF DIFFUSION COEFFICIENTS In the most common diffusion measurements, the movement of a system towards homogeneity is observed and compared with the predictions of the diffusion equations. These equations, together with appropriate boundary conditions, yield solutions for the one-dimensional case of the general form Ci ¼ Ci ðx; t; DÞ
(2.136)
Thus D is evaluated by fitting the expressions to experimental data Ci ¼ Ci ðx; tÞ. We consider here diffusion couple experiments in which two different homogeneous mixtures are brought into contact at a planar interface and diffusion observed along a direction normal to it. Two types of diffusion couple are important. If sample dimensions and the period of diffusion are such that concentrations at the ends of the sample do not change, then the experiment is described as an infinite diffusion couple. These couples are used to measure chemical diffusion. In a tracer diffusion measurement, the couple consists of a homogeneous block of material and a thin film of isotopically labelled but compositionally identical material. The two types of diffusion couple are shown schematically in Figure 2.11. Predicted profiles of the form (2.136) are obtained from Fick’s law (Equation (1.24)), which is subject to the continuity condition @Ci @J ¼ i (2.137) @t @x leading to Fick’s second law @Ci @2 Ci ¼D 2 @t @x
(2.138)
where D has been approximated as constant. The solution of Equation (2.138) is required for the appropriate boundary and initial conditions. Methods and a number of solutions are available from Carslaw and Jaeger [28] and Crank [29]. The thin-film solution applies to the one-dimensional tracer diffusion experiment
64
Chapter 2 Enabling Theory
t=0 A
t>0 B
CA (a)
A*
A
CA* (b)
Figure 2.11 Diffusion couples before and after diffusion. (a) Infinite couple and (b) thin-film (tracer experiment) couple.
of Figure 2.11b: Cðx; tÞ ¼
a expðx2 =4DAn tÞ 2ðpDAn tÞ1=2
(2.139)
where a is the amount of labelled material per unit area of film. After annealing, the couple is sectioned and the tracer concentration measured as a function of position. The value of DAn is then evaluated from a logarithmic plot according to Equation (2.139). For an infinite diffusion couple consisting initially of one half containing a uniform concentration C0 and the other a concentration C1 (Figure 2.11a), after diffusion time t we have Cðx; tÞ C0 1 x ¼ 1 erf pffiffiffiffiffiffi (2.140) 2 C1 C0 2 Dt where erf is the Gaussian error function Z z 2 erf ðzÞ ¼ pffiffiffi expðu2 Þdu p 0
(2.141)
Corresponding solutions are available for ternary systems [12]. Properties of the error function together with an abbreviated table of its values are shown in Appendix C. The above solutions rely on D being constant. This will apply in the tracer diffusion case, and Equation (2.139) can be used directly. However, it is improbable in the presence of a concentration gradient, the situation obtaining for the diffusion couple described by Equation (2.140) and Figure 2.11a. Either the difference C1C0 must be kept small, or the analysis of Boltzmann [30] and
2.8. Diffusion Couples and the Measurement of Diffusion Coefficients
65
pffiffi Matano [31] must be used in this case. Here the new variable l ¼ x= t is introduced. The initial conditions for the infinite diffusion couple C ¼ C0 for xo0 and C ¼ 0 for xW 0 at t ¼ 0 are independent of x, apart from the discontinuity at x ¼ 0 (Figure 2.11a). They can be described as C ¼ C0 at l ¼ 1 and C ¼ 0 at l ¼ þ1, and the Boltzmann–Matano analysis applies. Fick’s Law can then be transformed into an ordinary differential equation l dC d dC ¼ D 2 dl dl dl which integrates between zero and a value C0 such that 0oC0 oC0 , and for a fixed value of t, to yield C¼C0 0 Z 1 C¼C dC xdC ¼ Dt 2 C¼0 dx C¼0 Noting that dC=dx ¼ 0 at c ¼ 0 and c ¼ C0 , we arrive at the final solution Z C0 1 dx 0 ~ xdC (2.142) DðC Þ ¼ 2 dC 0 with
Z
C1
xdC ¼ 0
(2.143)
C0
defining the origin of co-ordinates. Graphical or numerical evaluations of the ~ 0 Þ, differential and the integral in Equation (2.142) are used to evaluate DðC as shown in Figure 2.12. Observation of marker movement in the diffusion
Figure 2.12 Concentration profile in infinite couple after diffusion, showing how the quantities required for the Boltzmann–Matano analysis (2.142) are evaluated.
66
Chapter 2 Enabling Theory
couple then allows calculation of the self-diffusion coefficients DA and DB from Equations (2.130) to (2.135).
2.8.1 Diffusion data for alloys It is often expedient to ignore diffusional interactions, either because the necessary data are not available or because an approximate calculation is all that is required. In such cases, we rely on self-diffusion coefficients, usually measured on binary alloys. These apply to either substitutional (vacancy-exchange) diffusion of metal components or interstitial diffusion of solute oxidants. Most measurements have been carried out using tracer diffusion experiments. These are related to the intrinsic, or self-diffusion coefficients through Equation (2.132) which, in a near ideal solution approximates to DA DAn In some cases, not even tracer data are available, but a chemical diffusion ~ may have been measured. If the diffusing species of interest is both coefficient, D, dilute and highly mobile, then the expression ~ ¼ N A DB þ N B DA D can be approximated as ~ ¼ DB D A selection of self-diffusion coefficient data for binary alloys is given in Appendix D. For multicomponent systems where Equation (2.115) holds, the Matano analysis can also be applied. The origin is then defined by the condition (2.143) being simultaneously satisfied for all components. Data are available for a number of ternary alloy systems in a useful review compiled by Dayananda [32]. A rather different treatment is required for diffusion in ionic solids, where the charges on individual species must be explicitly recognized. This is dealt with in Chapters 3 and 5.
2.9. INTERFACIAL PROCESSES AND GAS PHASE MASS TRANSFER As seen earlier, linear oxidation kinetics are expected if a surface or interfacial process is rate controlling. We consider the scale–gas interface, examining first the situation where the supply of oxidizing gas is not rate determining, and gas adsorption equilibrium can be expected. The very initial reaction between gas and bare metal is not considered here. Instead, a uniform oxide scale is assumed to have already formed.
2.9.1 Gas adsorption The reaction may be written as O2 ðgÞ þ S ¼ O2 jS
(a)
2.9. Interfacial Processes and Gas Phase Mass Transfer
O2 jS þ S ¼ OjS þ OjS kc
OjS!Oxide
67
(b) (c)
where S denotes a surface site, O2 jS and OjS adsorbed molecules and atoms and kc the rate constant for the slow step (c). The pre-equilibria (a) and (b) lead to ½O2 jS ¼ ½S Ka pO2 ½OjS ¼ ð½S Kb ½O2 jS Þ
(2.144) 1=2
(2.145)
where square brackets indicate area concentration. Substitution of Equation (2.144) into Equation (2.145) leads to 1=2
½OjS ¼ ½S ðKa Kb Þ1=2 pO2
(2.146)
Assuming now that the surface area and total concentration of sites are constant M ¼ ½S þ ½O2 jS þ ½OjS and substituting from Equations (2.144) and (2.146), one obtains M i ½S ¼ h 1=2 1 þ Ka pO2 þ ðKa Kb Þ1=2 pO2
(2.147)
(2.148)
The constant M is of order 1015 cm2. Combination of Equations (2.146), (2.147) and the rate equation for reaction (c) then leads to the result 1=2
Rate ¼
kc MðKa Kb Þ1=2 pO2 h i 1=2 1=2 1 þ ðKa Kb Þ1=2 pO2 1 þ ðKa =Kb Þ1=2 pO2
(2.149)
The rate is of course constant at fixed pO2 , but varies in a complex way with oxygen potential. Three limiting cases can be seen. At sufficiently low values of pO2 , Ka pO2 1 ðKa Kb pO2 Þ1=2 so that 1=2
Rate ¼ kc MðKa Kb Þ1=2 pO2
(2.150)
At higher pO2 values, the competitive adsorption of molecular and atomic oxygen must be considered. When atomic adsorption predominates over the molecular form 1=2 Ka 1=2 pO2 1 (2.151) Kb the term in square brackets in the denominator approximates to unity. If, furthermore, the surface is saturated, i.e. 1=2
ðKa Kb Þ1=2 pO2 1
(2.152)
then the oxidation rate is simply Rate ¼ kc M
(2.153)
68
Chapter 2 Enabling Theory
and independent of oxygen partial pressure. However, if molecular adsorption predominates, the converse of Equation (2.151) is true and the rate equation becomes 1=2
Rate ¼
kc MðKa Kb Þ1=2 pO2 1 þ Ka pO2
(2.154)
If the surface is close to saturation with molecular oxygen, Ka pO2 1, then an inverse dependence of the rate on pO2 is predicted. Competitive adsorption treatments are particularly useful in analysing oxidation kinetics in more complex gases such as CO+CO2 mixtures [33], but have also been used for oxygen alone [34], where the competing species are O and O2. Adsorption equilibrium can only be supported if gas species arrive at the scale surface quickly enough to keep up with reaction (c). This may not be the case if the oxidant partial pressure is very low. Two such situations are of interest: pure oxidant at low pressure, and oxidant as a dilute component of an otherwise inert gas.
2.9.2 Gas phase mass transfer at low pressure This situation is described using the Hertz–Langmuir–Knudsen equation, which derives from the kinetic theory of gases [35]. In the ideal case, pi ki ¼ (2.155) ð2pmi kTÞ1=2 where ki is the rate, pi the partial pressure and mi the mass of a molecule of species i, and k is Boltzmann’s constant. This expression describes both the rate of arrival of a low-pressure gas at a flat surface and, equally, the rate of evaporation into vacuum of the same species. Using practical units of g cm2 s1 for ki and atm for pi, the rate is calculated as MWi 1=2 (2.156) ki ¼ 44:3 pi T where MWi is the species molecular weight. This equation can be used to investigate gas phase mass transfer inside porous or cracked oxide scales, as shown schematically in Figure 2.13. The question addressed is whether the values of pO2 expected from local equilibrium with the surrounding oxide can sustain significant mass transfer across the cavities to support oxide growth. If the oxide is FeO at 1,0001C, then the equilibrium pO2 is in the range 1 1015 2:8 1013 atm. Oxygen transfer rates calculated from Equation (2.156) are found to be 7 1015 2 1012 g cm2 s1 , corresponding to a thickness of wu¨stite grown on the inner side of the cavity at rates of about 1–100 nm per year. Thus closed pores and cracks are seen to be effective local barriers to continued scale growth if O2 is the only vapour species within them.
2.9. Interfacial Processes and Gas Phase Mass Transfer
M
MO
(1 − δ )MO + δ O2 = M 1−δ O
k O2
2
Figure 2.13
69
Gas
M 1−δ O = (1 − δ )MO +
δ 2
O2
Vapour phase mass transport inside pores within a growing scale.
2.9.3 Mass transfer in dilute gases The usual situation encountered in practice and in the laboratory is a gas mixture flowing past a metal surface. The Hertz–Langmuir–Knudsen equation cannot be used in this situation, because of the multiple collisions occurring between oxygen and other molecules. The rate of transfer is governed by the gas flow rate, the width of the gas boundary layer (which is retained by viscous drag), oxygen partial pressure and gas mixture properties. A readable account of how this problem is solved has been provided by Gaskell [35]. The flux of oxygen to a flat surface from a gas flowing parallel to it is given by km ðoÞ ðp pðiÞ Þ (2.157) RT where km is a mass transfer coefficient and pðoÞ and pðiÞ the oxygen partial pressures in the bulk gas and at the solid surface, respectively. The mass transfer coefficient is given by 4 1=6
DAB n 1=2 km ¼ 0:664 (2.158) L ng J¼
where DAB is the diffusion coefficient in a binary gas A-B, ng the kinematic viscosity, n the linear velocity of the gas and L the length of surface. The diffusion coefficient is found from the Chapman–Enskog formulation [36, 37] of the kinetic theory of gases. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1:858 103 T 3 ð1=MWA þ 1=MWB Þ DAB ¼ (2.159) Ps2AB OD;AB Here MWA and MWB are the molecular weights of the two gas species, sAB their average collision cross-section, OD;AB a collision integral and the numerical factor ˚ for s, Poise for Z arises from the use of non-SI units. These are cm2 s1 for DAB, A
70
Chapter 2 Enabling Theory
and atm for P, with a dimensionless O. Tabulations of s and data permitting calculation of OD are available [35, 38]. The kinematic viscosity is defined as Zg (2.160) ng ¼ r where r is the gas density, here in g cm3, and the viscosity, Zg , is given by pffiffiffiffiffiffiffiffi 2:669 105 MT (2.161) Zg ¼ s2 O with O a different collision integral, tabulated values of which are also available. The description is valid when the dimensionless Schmidt number n Sc ¼ (2.162) D has a value between 0.6 and 50. The oxidation of steel in reheat atmospheres considered in Section 1.1 provides an example where this description can be used. Laboratory simulations of reheat furnace gases have been used [39] to investigate the effect of combustion stoichiometry on steel scaling rates at 1,1001C. The equilibrium gas composition corresponding to combustion of methane with 1% excess air is shown in Table 2.3. Reaction of a low carbon steel with this gas produced a scale consisting of single-phase FeO, which thickened according to linear kinetics. These are not the results to be expected if local equilibrium at the scale–gas interface were achieved. In that case, the surface oxide would be Fe3O4, an additional layer of FeO would grow beneath it, and diffusion-controlled, parabolic kinetics would result. The situation at the scale–gas interface therefore requires analysis. Gas phase mass transfer rates calculated from Equations (2.157) and (2.158) are shown in Table 2.3. The measured oxidation rate corresponded to J O ¼ 2 107 mol O cm2 s1 . As is clear from the comparison, molecular oxygen was not a significant reactant species, as its gas phase mass transfer rate was too slow to keep up with the scaling rate. However, gas phase transport of H2O and CO2 was more than fast enough to sustain the observed oxidation rate. Thus it is concluded on this basis that H2O and/or CO2 were the reactants, but that gas phase transport was not rate controlling, because of the relative abundance of these species. This conclusion was confirmed by the magnitude of the activation energy for the linear rate constant, measured as 135 kJ mol1. This value is much greater than the temperature effect predicted from Equations (2.157) and (2.158). Other measurements [40] of linear steel oxidation rates in dilute O2–N2 gases, where the rate is controlled by gaseous mass transfer, yielded an apparent Table 2.3 Equilibrium partial pressures and corresponding oxygen transport rates in 101% stoichiometric combustion gas at 1,1001C [39] CO
CO2
p (atm) 9.42 10 2 1 JO (mol cm s ) 5 107
2
1.3 10
N2 6
O2
H 2O 3
0.72 1.9 10 1.2 108
H2
0.188 1.3 106 6 1 10
2.10. Mechanical Effects: Stresses in Oxide Scales
71
activation energy of 17 kJ mol1. Thus it is eventually concluded that the ratecontrolling step in the linear oxidation process observed in this combustion gas at 1,1001C is a surface reaction. As seen above, quantitative gas phase mass transfer calculations can be useful in determining the feasibility of vapour transport within closed scale voids and cracks, in identifying reactant species in gas mixtures, and in distinguishing the contributions to rate control by mass transfer and interfacial reactions.
2.10. MECHANICAL EFFECTS: STRESSES IN OXIDE SCALES Oxide scales are usually subject to mechanical stress. This is of interest, because if the oxide stress is high enough, the scale will deform or even fracture. Mechanical failure of the scale will, at least temporarily, destroy the scale’s protective function. It is desirable to be able to predict such events, and preferably to design alloys which retain their scales intact. In the absence of external loading, a compressive stress in the oxide is balanced by a tensile one in the metal. Thus the mechanical state of the oxide reflects changes occurring in both phases. It is convenient to divide these into two classes: stresses developed during oxidation and those developed during temperature change. These matters have been reviewed several times, and the reader is referred in particular to Stringer [41], Taniguchi [42], Stott and Atkinson [43], Evans [44] and Schutze [45].
2.10.1 Stresses developed during oxidation Oxidation causes volume changes which, if constrained by specimen shape or constitution, are accommodated by deformation or strain in the oxide, ox . Pilling and Bedworth [46] considered scale growth occurring by inward oxygen transport, and recognized that if the ratio V ox =V m was greater than one, the resulting expansion could put the oxide into compression, whereas if the ratio was less than unity, tension and a discontinuous oxide could result. In the practically relevant case of V ox =V m 41, if the scale grows by outward metal diffusion, new oxide is formed at the free, unconstrained oxide–gas interface, and no strain results. However, if the scale grows by inward oxygen diffusion, the volume change accompanying new oxide formation has to be accommodated at the metal–oxide interface, leading to " # Vox 1=3 ox ¼ 1 (2.163) Vm if no other stress relieving mechanism is available. If the oxide behaves elastically, the corresponding growth stress would be Eox sox ¼ ox (2.164) 1 nP where Eox is the elastic modulus and nP is Poisson’s ratio for the oxide.
72
Chapter 2 Enabling Theory
The Pilling–Bedworth description is conceptually useful, but of little quantitative use. Firstly, many oxides grow predominantly by outward metal diffusion, and the model does not apply. Even in the case of inward diffusion, the stress levels calculated from Equations (2.163) and (2.164) are found to be impossibly high [47]. The solution to this problem is proposed [45] to be mixed diffusion of both metal and oxide, leading to growth of new oxide both at the scale surface and within its interior. Mixed transport can become possible as a result of grain boundaries or microcracks facilitating oxygen access. The relative contributions of the different growth sites are expected to vary with the factors affecting individual metal and oxygen transport mechanisms (T,pO2 , oxide grain size and substrate preparation). Kofstad, in his review [48] of the extensive data available for chromium oxidation, demonstrated that the Cr2O3 scale grows by counter-current diffusion of metal and oxygen along grain boundaries. Formation of new oxide in the boundaries results in lateral stress development, deformation of the scale and its partial detachment from the metal surface. Plastic deformation increases with decreasing oxygen activity and smaller grain size. Using the assumption of elastic oxide behaviour, Srolowitz and Ramanarayanan [49] analysed the effect of new oxide growth at grain boundaries within the scale. When the grain size, d X, they find sox ¼
4Gox di 2dð1 2nP Þ
(2.165)
where Gox is the shear modulus of the oxide and di the width of new oxide grown at internal grain boundaries. Additional stresses arise when curved metal surfaces are oxidized. Consider first an infinite plane metal surface being oxidized, with V ox =VM 41. As metal is consumed, the metal–oxide interface recedes. The oxide scale, which is chemically bonded to the metal surface, remains attached and moves with the retreating metal. If scale growth is sustained wholly by metal transport, no stress results. Consider now a convex metal surface oxidizing and receding. As the oxide follows it, it is compressed tangentially into the smaller volume formerly occupied by metal. Simultaneously, a radial tensile stress develops. The differing consequences for concave and convex slopes, inward and outward diffusion and V ox =VM 4oro1 have been explored by Hancock and Hurst [50] and Christ et al. [51]. The qualitative results for V ox =VM 41 are illustrated in Figure 2.14. Oxide stresses can also be caused in other ways during oxidation. Dissolution of oxygen into metals with high solubilities (e.g., Ta, Ti) can cause large expansions [52]. Internal precipitation of oxides [53] or oxidation of internal carbides [54] in alloy subsurface regions can cause very large volume expansions and tensile stresses in external scales. Phase changes in an alloy resulting from selective oxidation also cause volume changes. In general, any deformation of the substrate metal, including that due to external loading, is transferred to an
2.10. Mechanical Effects: Stresses in Oxide Scales
73
Figure 2.14 Effects of metal surface curvature on growth stress development in oxide scales. Grey shading indicates newly grown oxide. Based on Refs [50, 51].
adherent scale, because ox ¼ M
(2.166)
for an intact scale.
2.10.2 Stresses developed during temperature change Metals and oxides can have significantly different coefficients of thermal expansion, a, as seen in Table 2.4. The stress produced in an intact, adherent scale by a temperature change, DT, is given by [55] sox ¼
Eox DTðaM aox Þ ½ðEox =EM ÞðXox =XM Þ ð1 nPðMÞ Þ þ ð1 nðoxÞ P Þ
(2.167)
where Xox and XM are the thicknesses of scale and substrate metal, nðoxÞ and nPðMÞ P are the Poisson’s ratio values for scale and metal and the values of E and a have been approximated as independent of temperature. For thin scales on thick substrates, Equation (2.167) is adequately approximated by sox ¼
Eox DTðaM aox Þ 1 nox P
(2.168)
providing that linear elastic behaviour is in effect. Clearly, the thermally induced stress is dependent on the magnitude of the temperature change and the difference between coefficients of thermal expansion. As seen in Table 2.4, values for metals are usually greater than for oxides,
74
Table 2.4
Chapter 2 Enabling Theory
Coefficients of thermal expansion (a)
Material
106 a (K1)
T (1C)
Reference
Fe FeO FeO Fe2O3 Ni NiO Co CoO Cr Cr2O3 Cr2O3 Alloy 800 12 Cr, 1 Mo steel a Al2 O3 (single xl) Kanthal
15.3 15.0 12.2 14.9 17.6 17.1 14.0 15.0 9.5 7.3 8.5 16.2–19.2 10.8–13.3 5.1–9.8 15
0–900 400–800 100–1,000 20–900 0–1,000 20–1,000 25–350 20–900 0–1,000 100–1,000 400–800 20–1,000 20–600 28–1,165 20–1,000
[59] [60] [59] [59] [59] [59] [59] [59] [59] [59] [60] [45] [45] [61] Kanthal AB
and rapidly cooling an oxidized metal from high temperature will put the scale in compression. If the resulting stress is high enough, the scale suffers mechanical failure. The tabulated data explains why such failure is rare for oxide scales on nickel and cobalt, but common for Cr2O3 scales on austenitic chromia-forming materials such as Alloy 800. The development of stresses, both during oxidation and during temperature change, has been described here in terms of linear elastic behaviour. Thus it has been assumed that no stress relief mechanisms are in effect. This is, in fact, not the case, and a variety of outcomes can be arrived at. Stress can be relieved by plastic deformation, a process which occurs at low temperatures by dislocation movement, and at high temperature by creep. The latter is a time-dependent material flow resulting from lattice diffusion (Nabarro–Herring creep [56, 57]) or grain boundary diffusion (Coble creep [58]). Creep processes are strongly dependent on grain size and impurities, and in oxides to some extent on oxygen activity. An example where the stresses at a sample corner have been relieved by creep in the alloy is shown in Figure 2.15. If the stresses in an oxide scale develop to levels larger than can be accommodated by elastic strain, and if plastic deformation is insufficient to relieve the stresses, mechanical disruption of the system results. Depending on its stress state, properties and microstructure (which can change with temperature) the scale can fracture, form multiple microcracks, disbond from the metal (or separate along scale layer interfaces) or spall. Spallation means the separation and ejection of fragments from the scale, and is illustrated in Figure 2.16. The situation is analysed using a fracture mechanics approach, on the highly probable assumption that small defects are always present in the scale.
2.10. Mechanical Effects: Stresses in Oxide Scales
Figure 2.15
75
Deformation of cast, heat-resisting steel sample corner during oxidation at 1,1001C.
Figure 2.16 Partial spallation of alumina scale from a platinum-modified nickel aluminide coating system resulting from temperature cycling between 1,2001C and 801C.
76
Chapter 2 Enabling Theory
The energy available from releasing the stress by growing a crack is compared with the energy required to form the newly created surfaces. In the linear-elastic regime, the critical stress, sc , is found in a simple calculation to be given by pffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi sc pa ¼ Gc E0 (2.169) where a denotes the geometric dimensions of a pre-existing defect (length of a surface crack or half length of an internal crack), Gc the energy needed to create new surface and E0 the effective elastic modulus. The left side of Equation (2.169) represents the stress intensity factor, and the right side the fracture toughness of the material. Measured values of the latter are found [44] to be of order 1 MPa m1/2 for oxide scales. For a much more detailed discussion of the mechanical properties of oxide scales, the reader is referred to the book by Schu¨tze [45]. Mechanical failure of scales leading to their spallation, and the consequential acceleration in alloy failure rates are discussed in detail in Chapter 11. Alloy design strategies for minimizing spallation are considered in Section 7.5.
REFERENCES 1. O. Kubaschewski and C.B. Alcock, Metallurgical Thermochemistry, 5th ed, Pergamon Press, Oxford (1979). 2. I. Barin and G. Platzki, Thermochemical Data of Pure Substances, VCH, Weinheim (1995). 3. JANAF Thermochemical Data., Army-Navy-Airforce Thermochemical Panel, Dow Chemical Co., Midland, MI (1962–1963). 4. S. Mrowec and K. Przybylski, High Temp. Mater. Proc., 6, 1 (1984). 5. S.R. Shatynski, Oxid. Met., 13, 105 (1979). 6. C. Wagner, Thermodynamics of Alloys, Addison-Wesley, Reading, MA (1952). 7. J.R. Manning, Diffusion kinetics of atoms in crystals, Van Nostrand, Princeton, NJ (1968). 8. R.E. Howard and A.B. Lidiard, Rep. Prog. Phys., 27, 161 (1964). 9. L. Onsager, Phys. Rev., 37, 405; 38, 2265 (1931). 10. S.R. de Groot, Thermodynamics of Irreversible Processes, North Holland, Amsterdam, (1952). 11. I. Prigogine, Introduction to Thermodynamics of Irreversible Processes, C.C. Thomas, Springfield, IL (1955). 12. J.S. Kirkaldy and D.J. Young, Diffusion in the Condensed State, Institute of Metals, London (1987). 13. P.G. Shewmon, Diffusion in Solids, 2nd ed, Minerals, Metals and Materials Society, Warrendale, PA (1989). 14. W. Schottky, in Halbleiterprobleme, ed. W. Schottky, Fr. Viewig, Braunschweig (1958), Vol. 4. 15. N.F. Mott and R.W. Gurney, Electronic Processes in Ionic Crystals, Clarendon Press, Oxford (1940). 16. C.A. Wert and C. Zener, J. Appl. Phys., 21, 5 (1950). 17. F. Seitz, Acta Cryst., 3, 355 (1950). 18. A.B. Lidiard, Phil. Mag., 46, 1218 (1955). 19. M.J. Dignam, D.J. Young and D.W.G. Goad, J. Phys. Chem. Solids, 34, 1227 (1973). 20. D.J. Young and J.S. Kirkaldy, J. Phys. Chem. Solids, 45, 781 (1984). 21. L.C. Brown and J.S. Kirkaldy, Trans. AIME, 230, 223 (1964). 22. J. Nesbitt, J. Electrochem. Soc., 136, 1518 (1989). 23. D.P. Whittle, D.J. Young and W.W. Smeltzer, J. Electrochem. Soc., 123, 1073 (1976). 24. W.W. Smeltzer and D.P. Whittle, J. Electrochem. Soc., 125, 1116 (1978). 25. A. Smigelskas and E. Kirkendall, Trans. AIME, 171, 130 (1947).
References
26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61.
77
L.S. Darken, Trans. AIME, 184, 175 (1948). G.S. Hartley and J. Crank, Trans. Faraday Soc., 45, 801 (1949). H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, Clarendon Press, Oxford (1959). J. Crank, The Mathematics of Diffusion, Oxford University Press, Oxford (1970). L. Boltzmann, Ann. Phys., 53, 960 (1894). C. Matano, Japan Phys., 8, 109 (1933). M.A. Dayananda, in Diffusion in Metals and Alloys, Landolt and Bernstein, ed. H. Mehrer, Springer-Verlag, Berlin (1991), Ser. III, Vol. 26, p. 372. F.S. Pettit and J.B. Wagner, Acta Met., 12, 35 (1964). D.J. Young and M. Cohen, J. Electrochem. Soc., 124, 775 (1977). D.R. Gaskell, An Introduction to Transport Phenomena in Materials Engineering, Macmillan, New York (1992). D. Enskog, Arkiv. Met. Astronom. Fyz., 16, 16 (1922). S. Chapman and T.G. Cowling, The Mathematical Theory of Non-uniform Gases, Cambridge University Press (1939). R.A. Svehla, Estimated Viscosities and Thermal Conductivities of Gases at High Temperatures, NASA Technical Report R-132, NASA Lewis, Cleveland, OH (1961). V.H.J. Lee, B. Gleeson and D.J. Young, Oxid. Met., 63, 15 (2005). X.H. Abuluwefa, R.I.L. Guthrie and F. Ajersch, Oxid. Met., 46, 423 (1996). J. Stringer, Corros. Sci., 10, 513 (1970). S. Taniguchi, Trans. ISIJ, 25, 3 (1985). F.H. Stott and A. Atkinson, Mater. High Temp., 12, 195 (1994). H.E. Evans, Int. Mater. Rev., 40, 1 (1995). M. Schu¨tze, Protective Oxide Scales and their Breakdown, Institute of Corrosion and Wiley, Chichester (1997). N.B. Pilling and R.E. Bedworth, J. Inst. Met., 29, 529 (1923). D.J. Baxter and K. Natesan, Rev. High Temp. Mater., 5, 149 (1983). P. Kofstad, High Temperature Corrosion, Elsevier Applied Science, London (1988). D.A. Srolowitz and T.A. Ramanarayanan, Oxid. Met., 22, 133 (1984). P. Hancock and R.C. Hurst, in Advances in Corrosion Science and Technology, eds. M.G. Fontana and R.W. Staehle, Plenum, New York (1974), Vol. 4, p. 1. W. Christ, A. Rahmel and M. Schu¨tze, Oxid. Met., 31, 1 (1989). R.E. Pawel, J.V. Cathcart and J.J. Campbell, J. Electrochem. Soc, 110, 551 (1963). J. Litz, A. Rahmel and M. Schorr, Oxid. Met., 30, 95 (1988). N. Belen, P. Tomaszewicz and D.J. Young, Oxid. Met., 22, 227 (1984). J.K. Tien and J.M. Davidson, in Stress Effects and the Oxidation of Metals Proc. TMS-AIME Fall Meeting, ed. J.V. Cathcart, TMS-AIME, New York (1975), p. 200. F.R.N. Nabarro, in Rep. Conf. on the Strength of Solids, Physical Society, London (1948), p. 15. C. Herring, J. Appl. Phys., 21, 437 (1950). R.L. Coble, J. Appl. Phys., 34, 1679 (1963). R.F. Tylecote, J. Iron Steel Inst., 196, 135 (1960). J. Robertson and M.I. Manning, Mater. Sci. Technol., 6, 81 (1990). J.K. Tien and J.M. Davidson, Adv. Corros. Sci. Technol., 7, 1 (1980).
FURTHER READING 1. Chemical Thermodynamics and Phase Equilibria 1. K. Denbigh, The Principles of Chemical Equilibrium: With Applications in Chemistry and Chemical Engineering, 4th ed, Cambridge University Press (1981). 2. D.R. Gaskell, Introduction to the Thermodynamics of Materials, 4th ed, Taylor and Francis, Washington, DC (2003). 3. C.H.P. Lupis, Chemical Thermodynamics of Materials, North-Holland, New York (1983).
78
Chapter 2 Enabling Theory
4. O. Kubaschewski, C.B. Alcock and P.J. Spencer, Materials Thermochemistry, Pergamon Press (1993). 5. R.A. Swalin, Thermodynamics of Solids, 2nd ed, Wiley-Interscience, New York (1972). 6. H.B. Callen, Thermodynamics and an Introduction to Thermostatics, 2nd ed, Wiley, New York (1985). 7. M. Hillert, Phase Equilibria, Phase Diagrams and Phase Transformations, Their Thermodynamic Basis, Cambridge University Press (1998). 8. M. Hansen, Constitution of Binary Alloys, McGraw-Hill, New York (1958), 2nd ed; See also First supplement, R.P. Elliott (1965); Second supplement, F.A. Shunk (1969). 9. E.M. Levin, C.R. Robbins and H.F. McMurdie, Phase Diagrams for Ceramists, American Ceramic Society, Inc., Columbia, OH (1969), 2nd ed. See also supplements (1969, 1975).
2. Diffusion in Solids 1. N.F. Mott and R.W. Gurney, Electronic Processes in Ionic Crystals, Oxford University Press (1940). 2. J.H. Holloway, Atom Movements ASM, Cleveland (1951). 3. R.M. Barrer, Diffusion in and through Solids, Cambridge University Press (1951). 4. P.G. Shewmon, Diffusion in Solids, 2nd ed, Minerals, Metals and Materials Society, Warrendale, PA (1989). 5. J. Philibert, Atom Movements: Diffusion and Mass Transport in Solids, Les Editions de Physique (1991). 6. H. Mehrer, Diffusion in Solids: Fundamentals, Methods, Materials, Diffusion Controlled Processes, Springer, Berlin (2007). 7. I. Kaur and W. Gust, Fundamentals of Grain and Interphase Boundary Diffusion, 2nd ed, Ziegler Press, Stuttgart (1989). 8. J.S. Kirkaldy and D.J. Young, Diffusion in the Condensed State, Institute of Metals, London (1987).
3. Point Defects in Solids 1. N.F. Mott and R.W. Gurney, Electronic Processes in Ionic Crystals, Clarendon Press, Oxford (1940). 2. F.A. Kro¨ger, The Chemistry of Imperfect Crystals, 2nd ed, North-Holland, Amsterdam (1973). 3. P. Kofstad, Nonstoichiometry, Diffusion and Electrical Conductivity in Binary Metal Oxides, Wiley-Interscience, New York (1972). 4. C.P. Flynn, Point Defects and Diffusion, Oxford University Press (1972). 5. H. Schmalzried, Chemical Kinetics of Solids, VCH, Weinheim (1995). 6. J. Maier, Physical Chemistry of Ionic Materials: Ions and Electrons in Solids, Wiley, Chichester (2004).
4. Mass Transfer in Fluids 1. D.R. Gaskell, An Introduction to Transport Phenomena in Materials Engineering, Macmillan, New York (1992). 2. R.B. Bird, W.E. Stewart and E.N. Lightfoot, Transport Phenomena, 2nd ed, Wiley, New York (2002). 3. R.A. Svehla, Estimated Viscosities and Thermal Conductivities of Gases at High Temperatures, NASA Technical Report R-132, NASA-Lewis, Cleveland, OH (1961).
References
79
5. Mechanical Behaviour of Scales 1. M. Schu¨tze, Protective Oxide Scales and their Breakdown, Institute of Corrosion and Wiley, Chichester (1997). 2. Mechanical Properties of Protective Oxide Scales, Special Issue of Mater. High Temp., 12 (1994).
CHAPT ER
3 Oxidation of Pure Metals
Contents
3.1. 3.2. 3.3. 3.4. 3.5. 3.6. 3.7.
Experimental Findings Use of Phase Diagrams Point Defects and Non-Stoichiometry in Ionic Oxides Lattice Species and Structural Units in Ionic Oxides Gibbs–Duhem Equation for Defective Solid Oxides Lattice Diffusion and Oxide Scaling: Wagner’s Model Validation of Wagner’s Model 3.7.1 Oxidation of nickel 3.7.2 Oxidation of cobalt 3.7.3 Oxidation of iron 3.7.4 Sulfidation of iron 3.7.5 Effects of oxidant partial pressure on the parabolic rate constant 3.7.6 Effect of temperature on the parabolic rate constant 3.7.7 Other systems 3.7.8 Utility of Wagner’s theory 3.8. Impurity Effects on Lattice Diffusion 3.9. Microstructural Effects 3.9.1 Grain boundary diffusion 3.9.2 Multilayer scale growth 3.9.3 Development of macroscopic defects and scale detachment 3.10. Reactions Not Controlled by Solid-State Diffusion 3.10.1 Oxidation of iron at low pO2 to form wu¨stite only 3.10.2 Oxidation of silicon 3.11. The Value of Thermodynamic and Kinetic Analysis References
82 84 85 89 91 93 96 97 98 101 104 107 109 111 112 113 115 116 122 124 127 127 131 133 135
Reaction of a pure metal with a single oxidant (oxygen, carbon, nitrogen, sulfur or a halogen) is considered. Most metals present in alloys used at high temperature form solid oxides, carbides or nitrides, but sulfides have lower melting points than the corresponding oxides, and liquid formation must sometimes be considered. We commence by surveying a selected set of experimental findings. The goal is to follow the development of a theoretical framework devised to provide an understanding of those findings, and which can be used as a predictive basis for corrosion rates under different conditions. 81
82
Chapter 3 Oxidation of Pure Metals
3.1. EXPERIMENTAL FINDINGS Cross-sections of oxide scales grown on iron, nickel and chromium are compared in Figure 3.1, and the complex sulfide scale grown on nickel is shown in Figure 3.2. All of these scales were found to thicken according to parabolic kinetics. X2 ¼ 2kp t
(3.1)
a result seen earlier to correspond to rate control by diffusion through the scale. It is to be expected then that the relative rates would correspond to the nature of the oxides. Representative values of kp are summarized in Table 3.1. Under the
Figure 3.1 Cross-sections of oxide scales on Fe reprinted from [1] with permission from La Revue de Metallurgie, Ni [3]. Reproduced by permission of The Electrochemical Society and Cr [4] with kind permission from Springer Science and Business Media.
Figure 3.2 Fracture cross-section of sulfide scale on Ni [5]. With kind permission from Springer Science and Business Media.
3.1. Experimental Findings
83
conditions examined, the scale grown on iron is approximately 95% FeO, 4% Fe3O4 and 1% Fe2O3 [1]. To a reasonable approximation, then, the kp value for iron oxidation represents the growth of the FeO layer. Noting that FeO, CoO and NiO all have the same crystal structure (isotypic with face-centred-cubic NaCl) it is seen that their growth rates, nonetheless, differ widely. The Cr2O3 phase has a hexagonal crystal structure, and is therefore not to be compared on this basis with the cubic oxides. Finally, it is seen that iron sulfidises much more rapidly than it oxidizes. The rate constant values in Table 3.1 are for specific temperatures and pressures. It is common that the temperature dependence can be described by the Arrhenius relationship Q kp ¼ kO exp (3.2) RT where Q is a constant known as the effective activation energy and kO is also a constant. As seen in Table 3.2, values of Q and kO differ widely from one metal to another. In some cases, different values apply for the same metal in different temperature regimes. An example of the oxygen pressure effect on kp is shown in Figure 3.3. The linearity of the log–log plots demonstrates the applicability of the relationship 1=n
kp ¼ kO pO2
(3.3)
where kO and n are temperature independent constants.
Table 3.1
Selected scaling parabolic rate constants, kp(cm2s1)
Metal
Gas
Fe Co Ni Cr Fe Co
Table 3.2
kp
T (1C)
Air (1 atm) O2 (1 atm) O2 (1 atm) O2 (1 atm) S2 (1 atm) S2 (1 atm)
Reference 7
1,000 1,000 1,000 1,000 900 700
2 10 3.3 109 9 1011 6 1014 7 106 2 107
[1] [2] [3] [4] [5] [6]
Arnhenius activation energy (Equation 3.2) for oxide scale growth
Metal/gas
T (1C)
Q (kJ mol1)
Reference
Fe/O2 Co/O2
700–1,000 800–950 950–1,150 600–1,100 1,100–1,400 980–1,200
164 230 150 120 240 243
[1] [2]
Ni/O2 Cr/O2
[3] [4]
Chapter 3 Oxidation of Pure Metals
log10 (kp /mg2cm-4h-1)
84
1100 °C
1000
100 950 °C
10 0.01
0.1
1 log10 (pO2 /atm)
10
100
Figure 3.3 Oxygen partial pressure effects on kp for cobalt. Data from [2].
To account properly for these observations, it is necessary to analyse more carefully the diffusion processes which support scale growth and determine their rates. Such an analysis was first carried out by Wagner [9], and we follow his treatment here, rephrasing it in terms of the Kroger–Vink description [10] of the defect solid state. A central assumption of Wagner’s theory of scale growth is that the process is supported by diffusion of crystalline lattice species through the scale. Thus the oxide is considered to be compact and free of pores and cracks. Any effect of grain boundaries and other extended defects is ignored, and attention is focused on the movement of individual lattice site, or ‘‘point’’, defects. The nature of these defects is considered first, and the relationship between defect concentration and oxide non-stoichiometry is developed. A technique of grouping point defects as ‘‘structural units’’ is used to relate micro- and macroscopic levels of thermodynamic description. Point defect diffusion is then described, and its use in the classical Wagner treatment explored. The utility of this description in accounting for experimental observations is then examined. Finally, the limitations of this treatment are identified, and their consequences for scale growth kinetics are examined.
3.2. USE OF PHASE DIAGRAMS The Wagner theory describes steady-state kinetics, controlled by diffusion within a scale under fixed boundary conditions. Thus the chemical potential of diffusing species at the metal–scale, scale–gas and any intermediate interfaces are supposed to be time invariant. In this event, local equilibrium will be in effect at those boundaries, which should therefore correspond to boundaries defined by
3.3. Point Defects and Non-Stoichiometry in Ionic Oxides
85
the metal-oxidant phase diagram. A first step in verifying that a scaling reaction is diffusion controlled is to test the validity of this proposition. We saw earlier that the three-layered oxide scale grown on iron at temperatures above 5701C was as predicted from the Fe–O phase diagram (see Figure 2.2). A more quantitative test is possible with sulfides, because EPMA can be used to measure both metal and oxidant concentrations at precisely defined (71 mm) locations within a scale. Results obtained by Bastow and Wood [7] for the nickel sulfide scale are compared with the Ni–S phase diagram in Figure 3.4, where agreement is seen to be good. In the case of reaction products with significant deviations from stoichiometry, their composition will vary with position within the scale, from the metalrich to the oxidant-rich sides of the oxide field defined by the phase diagram. This is easier to measure in sulfides than in oxides, because of the greater sensitivity of the EPMA technique to the high atomic weight sulfur. Results for an Fe1dS scale in Figure 3.4(c) show that the expected compositional gradient was indeed developed.
3.3. POINT DEFECTS AND NON-STOICHIOMETRY IN IONIC OXIDES For isothermal diffusion in the absence of external fields, there is no net flow of charge. Any physically realistic mechanism must therefore involve the movement of groups of species which conserve charge and, of course, sites. As will be demonstrated in the next section, such groups fit the definition of ‘‘relative building units’’ conceived of by Schottky [9] and Kroger et al. [10] in the development of a thermodynamic description of point defect equilibria. Since these units can be used to represent both diffusion and equilibrium, they form an appropriate link between the transport properties and local equilibrium state of a solid. In what follows, we employ the defect notation of Kroger and Vink [9] wherein the oxide lattice species are represented by the symbol SX M . Here the subscript represents the normal occupancy in a perfect crystal of the site in question, and the principal symbol represents the species actually occupying the site. The superscript represents the charge of the species relative to normal site occupancy with a prime indicating a negative, a dot positive and a cross zero charge. Thus, for example, the principal lattice species in magnesio–wu¨stite, X X (Fe,Mg)O, are the two cations FeX Fe , MgFe and the anion OO . Defect species are now introduced. Following the early work of Frenkel [11], Schottky and Wagner [12] and Jost [13], we consider first the lattice defects which can arise in a homogeneous, crystalline ionic solid. Firstly, individual lattice sites can be vacant. In a binary 0 00 oxide MO, the possibilities are V X M ,V M and V M , representing different ionization X states, on the cation sublattice, plus V O , etc. on the anion sublattice. In addition, interstitial species, e.g. Mi and O00i are possible, with the subscript i denoting an interstitial lattice site. Interstitial oxygen is unusual, because its large size makes interstitial occupancy energetically improbable in most oxides. The
86
Chapter 3 Oxidation of Pure Metals
Figure 3.4 (a) Phase diagram for Ni–S system; (b) microanalysis of compositional variation in sulfide scale on Ni at 4481C [7] (with kind permission from Springer Science and Business Media); (c) microanalysis of deviation from stoichiometry in Fe1dS scale grown on Fe at 7001C [8]. Reproduced by permission of The Electrochemical Society.
3.3. Point Defects and Non-Stoichiometry in Ionic Oxides
87
formation of charged defects always occurs in matching sets, to balance electrostatic charge. Schottky defects consist of cation and anion vacancies, e.g. V 00Ni þ V O in nickel oxide. Frenkel defects consist of matched vacancies and X interstitials, e.g. V 00Cd þ Cdi in CdO and V X O þ Oi in UO2. As seen in Section 2.2, defects of this sort always exist at temperatures above 0 K. However, their existence does not account for non-stoichiometry in oxides, for example the large deviations from stoichiometry observed in Fe1dO (see Figure 2.2). In fact, that particular system is complicated by interactions between the highly concentrated defects. We consider instead deviations from stoichiometry in a model oxide M1dO in which it is assumed fully ionized cation and anion vacancies can form. Using equilibrium expressions of the form of Equation (2.106) we write the Schottky reaction 0 ¼ V 00M þ V O
(3.4)
for which nVM nVO (3.5) N2 with KS the Schottky equilibrium constant and N ¼ n+nv , the total number of sites on each sublattice, N M and N O , which are here taken as equal for a divalent metal oxide. Deviations from stoichiometry are achieved by interchange of matter, usually oxygen, with the surrounding environment. In the metal-deficit (dW0) range KS ¼
1 2O2 ðgÞ
00 ¼ OX O þ V M þ 2h
(3.6)
and KP ¼
nVM n2h 1=2
N 3 pO2
(3.7)
while in the metal excess (do0) range 0 1 OX O ¼ V O þ 2e þ 2O2 ðgÞ
(3.8)
1=2
KN ¼
nVO n2e pO2
(3.9) N3 Here KP and KN are equilibrium constants, e0 an electron and h a positive hole: the metal excess oxide exhibits n-type semiconductivity and the metal-deficit oxide shows p-type behaviour. It is noted in formulating these equations that sites can be created or destroyed, as in Equation (3.6), but the crystalline phase is preserved by maintaining the site ratio N M =N O constant, unity in this case. Mass is conserved, effective charge is conserved and the electroneutrality of the compound is always preserved. Note also that adoption of the ‘‘effective charge’’ description means that charge is associated only with defect species. This avoids the clumsiness of counting ions, and comparing large numbers (B1022 cm3) to arrive at very small differences.
88
Chapter 3 Oxidation of Pure Metals
The relationship between intrinsic disorder, i.e. the concentration of defects when d ¼ 0, extent of non-stoichiometry and pO2 is of interest. The deviation from stoichiometry is nVM nVO (3.10) d¼ N The vacancy concentrations are found from Equations (3.7) and (3.9) using the approximations nh ¼ 2nVM
(3.11)
ne ¼ 2nVO
(3.12)
for charge balance in the relevant regimes, and their substitution into Equation (3.10) yields 1=3 1=3 KP KN 1=6 ð1=6Þ d¼ pO 2 pO 2 (3.13) 4 4 This is the desired relationship between non-stoichiometry and pO2 . We now relate it to the conditions for stoichiometry. Defining pðoÞ O2 as the equilibrium partial pressure at which the compound is stoichiometric, d ¼ 0, we find from Equation (3.13) that KN ¼ KP pðoÞ O2
(3.14)
When d ¼ 0, it follows from Equations (3.5) and (3.10) that the intrinsic disorder, D, is given by nðoÞ nðoÞ 1=2 V VM ¼ O ¼ KS N N Combination of Equations (3.5), (3.7) and (3.9) leads to D¼
KP KN ¼ KS K2e
(3.15)
(3.16)
where Ke ¼ nh ne corresponding to the electron–hole pair formation equilibrium 0 ¼ h þ e 0 Substitution from Equations (3.14) and (3.16) into Equation (3.13) yields 8 !1=6 ! 9 1=3 < ðoÞ 1=6 = p p K e 1=6 O2 O2 d ¼ KS : pðoÞ ; 4 pO2
(3.17)
(3.18)
O2
which upon substitution from Equation (3.15) leads to 8 !1=6 !1=6 9 = pðoÞ DKe 1=3 < pO2 O2 d¼ : pðoÞ ; 4 pO2 O2
(3.19)
89
3.4. Lattice Species and Structural Units in Ionic Oxides
As pointed out by Greenwood [14], this general description reveals that the greater the intrinsic disorder, D, of the stoichiometric compound, the smaller is the relative partial pressure change required to produce a given deviation from stoichiometry. Conversely, oxides which are close to stoichiometric have low D values. This is true despite the fact that compounds with the same defect type will evidence the same functional relationship between d and pO2 . The applicability of equations like (3.19) is, of course, limited to the oxide phase field, and can be of even narrower applicability if defect interactions become important. It is clear from Equation (3.19) that an oxygen potential gradient across an oxide scale gives rise to a defect gradient. It is this gradient which provides the mechanism for diffusion through an oxide scale bounded on one side by metal and on the other by oxygen gas. An example is shown in Figure 3.4(c).
3.4. LATTICE SPECIES AND STRUCTURAL UNITS IN IONIC OXIDES Consider a p-type oxide MO, containing fully ionized vacancies and positive holes, under isothermal, isobaric conditions. The lattice species are X 00 MX M ; V M ; h ; OO
and thus outnumber the single thermodynamically independent compositional variable available to the binary oxide. The removal of the dependencies among the set is accomplished by the application of the physical constraints which exist for the species. In a crystalline solid the ratio of cation to anion sites is fixed X 00 nðMX M Þ þ nðV M Þ ¼ nðOO Þ
(3.20)
and, in the absence of a field, the system is charge neutral 2nðV00M Þ þ nðh Þ ¼ 0
(3.21)
The use of these relationships has been explored by Kroger et al. [15] in arriving at their definition of building units. Building units are groups of lattice species having such a composition that the requirements Equations (3.20) and (3.21) are met when the group is added to the crystal. The obvious unit for MO is X fMX M þ OO g. A subset of building units is comprised of ‘‘relative building units’’. These are defined relative to the perfect crystal and consist of the difference between a lattice species and the lattice species corresponding to normal site occupancy. Thus relative building units represent a change in composition X resulting from the replacement of one species with another, e.g. fBX M AM g in a substitutional solid solution. Since relative building units represent compositional change they can be used X to describe diffusion. It is clear that a flux of units fBX M AM g corresponds to interdiffusion of cations A and B via a site-exchange process. The formulation of suitable relative building units emerges from the flux constraints which are analogous to the site and charge density constraints Equations (3.20) and (3.21). In the case of one-dimensional diffusion in the model system under discussion,
90
Chapter 3 Oxidation of Pure Metals
these constraints are, for a ternary oxide JA þ JB þ JV ¼ 0 ¼ J0
(3.22)
2J V ¼ J h
(3.23)
where the fluxes, J, are measured within the solvent-fixed reference frame provided by an immobile anion lattice. It follows that movement of a vacancy must be accompanied by movement of positive holes and is associated with an opposing flux of cations. Relative building units, U i , which describe these exchanges are: 00 U 1 fAX M V M 2h g
(3.24)
00 U 2 fBX M V M 2h g
(3.25)
X U 3 fBX M AM g
(3.26)
of which one unit is seen to be redundant. A further unit not contributing to diffusion but necessary to complete the structure is 00 U 4 fOX O V M 2h g
(3.27)
It is clear that combination in the appropriate proportions of units 1, 2 and 4 yields a solid (A,B)O of any desired degree of substitution and nonstoichiometry. Thermodynamic meaning is now attached to the relative building units by considering the reactions which lead to the introduction of point defects into the compound AðgÞ þ V00M þ 2h ¼ AX M
(3.28)
BðgÞ þ V00M þ 2h ¼ BX M
(3.29)
00 1 OX O þ V M þ 2h ¼ 2O2 ðgÞ
(3.30)
These equilibria are described by their corresponding Gibbs equations which, under isothermal field-free conditions, may be written in terms of molar concentrations, m, and electrochemical potentials, Z, as X Zi dmi ¼ 0 i
in each case. Since the dmi are related via the reaction stoichiometry coefficients, v, we may write X n i Zi ¼ 0 (3.31) i
whence mA ¼ ZðAM Þ ZðV 00M Þ 2Zðh Þ ¼ mðU 1 Þ
(3.32)
mB ¼ ZðBM Þ ZðV00M Þ 2Zðh Þ ¼ mðU 2 Þ
(3.33)
3.5. Gibbs–Duhem Equation for Defective Solid Oxides
1 2mO2
¼ ZðOO Þ þ ZðV00M Þ þ 2Zðh Þ ¼ mðU 3 Þ
91
(3.34)
and the potentials of U 1 ; U 2 and U 4 are seen to be the chemical potentials of the constituent elements, mi . The electrochemical potentials of individual lattice species cannot be measured. Moreover they depend on the local electrostatic potential, c, through the definition ZðSZ Þ ¼ mðSZ Þ þ ZFc where Z is the effective charge of the species and F the Faraday. The value of c is also inaccessible to measurement. It is apparent that appropriate grouping of species leads to the avoidance altogether of the need to consider directly the electrostatic potential or individual species’ chemical potentials. These quantities are indeterminate within the formalism, just as they are experimentally inaccessible. Since it is not possible to add, or remove, or diffuse lattice species other than in a way which conserves charge and lattice sites, the use of relative building units is entirely consistent with the fact that the thermodynamics and diffusion kinetics of ionic crystals can always be described in terms of elemental chemical potentials. Relative building units provide a link between the macroscopic thermodynamic/kinetic properties and the point defect structure.
3.5. GIBBS–DUHEM EQUATION FOR DEFECTIVE SOLID OXIDES For an isothermal, isobaric and chemically equilibrated system, the Gibbs– Duhem equation X ni dmi ¼ 0 (2.46) i
relates the chemical potentials of the constituent elements. The relationship applies to an open system, i.e. one which can exchange matter with its surroundings. It is therefore appropriate to the case of a solid oxide which achieves equilibrium via the transfer of oxygen to or from the ambient gas phase. As we have seen, such an oxide is generally non-stoichiometric, its composition varying continuously with oxygen activity. Such an oxide may be regarded as a solution composed of an oxide of chosen reference composition and an excess amount of one constituent. We consider here a pure binary metal-deficit oxide of composition M1dO. It is frequently convenient, if not always realistic, to adopt as a reference the stoichiometric composition MO. The formation of the metal-deficit oxide solution may then be represented as d ð1 dÞMOðsÞ þ O2 ðgÞ ¼ M1d OðsÞ 2 Although one cannot write a Gibbs equilibrium equation for this, or any other, solution formation process (because the composition of the product
92
Chapter 3 Oxidation of Pure Metals
varies with aO ), the Gibbs–Duhem equation is clearly of the form ð1 dÞdmMO þ d dmO ¼ 0
(3.35)
This result informs us that the chemical potential of the reference composition oxide varies with oxygen activity. Alternatively, one might consider the solution M1dO as being formed from its elements and write ð1 dÞdmM þ dmO ¼ 0
(3.36)
The alternative expressions given by Equations (3.35) and (3.36) are linked via the statement of equilibrium for formation of the reference oxide MðsÞ þ 12O2 ðgÞ ¼ MOðsÞ the Gibbs equation for which is dmM þ dmO ¼ dmMO
(3.37)
Since the Gibbs–Duhem equation represents the means of removing redundancy among a set of chemical potentials, it need not have a unique form. The several different, but equivalent, forms of the equation are related by the equilibria which exist among the various chemical species. Similarly, it is possible to write the Gibbs–Duhem equation in terms of lattice and defect species because the electrochemical potentials of the species are related via the appropriate building units to the chemical potentials of the elements. Thus substitution of the relationships of Equations (3.32) and (3.34) for doubly changed vacancies in a binary oxide MO into Equation (3.36) leads immediately to X 00 ð1 dÞ dZðMX M Þ þ dZðOO Þ þ ddZðV M Þ þ 2ddZðhÞ ¼ 0
(3.38)
It follows from the site and charge balances of Equations (3.20) and (3.21) that d¼
nðV 00M Þ nðOX OÞ
1d¼
nðMX MÞ X nðOO Þ
(3.39)
(3.40)
Substitution from Equations (3.39), (3.40) and (3.21) into Equation (3.38) then yields X X X 00 00 nðMX M ÞdZðMM Þ þ nðOO ÞdZðOO Þ þ nðV M ÞdZðV M Þ þ 2nðh ÞdZðh Þ ¼ 0
(3.41)
which is the form appropriate to individual species. The elemental form (3.36) and the lattice species form (3.41) of the Gibbs–Duhem equation are completely consistent. This is a necessary consequence of the imposed condition of local equilibrium expressed through Equations (3.32) and (3.34). Similar analyses can be performed for other defect types, with the same general conclusion being reached [17].
3.6. Lattice Diffusion and Oxide Scaling: Wagner’s Model
93
3.6. LATTICE DIFFUSION AND OXIDE SCALING: WAGNER’S MODEL Wagner’s original treatment [9, 16] was of critical importance in providing an understanding of the particle (atomic or ionic) processes occurring within a growing oxide scale, thereby leading to a capacity to predict the effects on oxidation rate of changes in temperature, oxide chemistry, etc. The treatment is based on the assumption that lattice diffusion of ions or the transport of free carriers (electrons or positive holes) controls scaling rates. For diffusion to be rate controlling, the scale boundaries must achieve local equilibrium. This requires that the processes occurring at the metal–scale and scale–gas interfaces are so fast that they do not contribute to rate control, and may be regarded as at equilibrium. Although this will not be the case at the very beginning of reaction, equilibrium is quickly established once a continuous scale is formed, providing that the supply of gaseous oxidant is abundant. If diffusion by lattice species is to be rate controlling, then no other diffusion process can contribute significantly to mass transfer. Thus the scale must be dense (i.e. non-porous) and adherent to the metal, so that gas phase transport within the scale is unimportant. Furthermore, the scale must contain a relatively low density of grain boundaries and dislocations so that their contribution to diffusion is unimportant, and the oxide lattice (or volume) diffusion properties dictate mass transfer rates. The Wagner model is illustrated in Figure 3.5 for the more common case of cation transport. Oxygen anion transport can sometimes occur, usually via vacancy movement. In his original model, Wagner proposed that ions and electronic species migrated independently. This is correct only to the extent that (a) charge separation can be sustained within the oxide and (b) the oxide is
Metal
Oxide Scale
Gas
ao
JV′′ Jh•
M + 2h• + VM′′ = M×M Figure 3.5
1
2
O 2 = O×O + VM′′ + 2h•
Schematic view of Wagner’s diffusion model for cation vacancy transport.
94
Chapter 3 Oxidation of Pure Metals
thermodynamically and kinetically ideal, so that the cross-terms in a complete diffusion description (see Equation 2.99) can be ignored. The latter point has been made by Wagner [18] and others [19, 20]. Wagner solved the transport problem by writing two equations, for ionic and electron species, in terms of their electrochemical potential gradients. These were of the form (2.99) without cross terms and written in terms of mobilities, Bi : J i ¼ Ci Bi rZi
(3.42)
Here the species mobility is defined as its drift velocity under an electrochemical potential gradient of unity. Comparison of Equations (3.42) and (2.99) yields L11 ¼ C1 B1
(3.43)
when cross terms are ignored. If, furthermore, the system is field free (as in, e.g. a tracer diffusion experiment) and thermodynamically ideal, we have from Equation (2.103) L11 RT (3.44) D1 ¼ C1 whence B1 RT ¼ D1
(3.45)
a form of the Nernst–Einstein relationship between diffusion and mobility. Consider the growth of a p-type (metal deficit) binary oxide scale sustained by metal vacancy diffusion. Writing Equation (3.42) explicitly, one obtains @mi þ 2FE (3.46) J V ¼ CV BV @x @mh FE (3.47) J h ¼ Ch Bh @x where the electrostatic field dc (3.48) dx and the effective charges ZV ¼ 2 and Zh ¼ 1 have been inserted. The difficulty is that the local electrostatic field cannot be measured. Recognizing that any field developed by charge within the oxide would affect the flux of other charged species, Wagner resolved the problem by invoking the condition of zero net electric current (3.23). In this way the unknown quantity E is eliminated between Equations (3.46) and (3.47) via the result 1 @m @m E¼ BV V B h h (3.49) ðBh þ 2BV ÞF @x @x E¼
Resubstitution in Equation (3.46) leads to JV ¼
CV BV Bh @mV @m þ2 h Bh þ 2BV @x @x
(3.50)
95
3.6. Lattice Diffusion and Oxide Scaling: Wagner’s Model
The expression in braces is related to thermodynamic variables via the local equilibrium Equation (3.34), rewritten for a fixed anion lattice as dmo ¼ dZV þ 2dZh
(3.51)
Since ZV ¼ 2Zh , the electrostatic potential terms on the right-hand side cancel, and Equation (3.50) becomes JV ¼
CV BV Bh dmo Bh þ 2BV dx
(3.52)
As the mobilities of free carriers are usually very much greater than those of ions, Bh BV (and Be BMi ) this result is well approximated by J V ¼ CV BV
¼
dmo dx
CV DV dmo RT dx
¼ CV DV
d ln ao dx
(3.53)
which is one form of Wagner’s original solution. The algebra leading to Equation (3.53) is tedious and, in more complex systems, quite time consuming. A simpler procedure is afforded by a description of diffusion in terms of relative buildingunits (Section 3.4). The unit of relevance 00 to a binary metal-deficit oxide is U 1 ¼ MX M V M 2h . As described earlier, the diffusion of these units necessarily satisfies site and charge balance, and is equivalent to cation diffusion through the oxide. J M ¼ JðU 1 Þ @ 00 ZðMX M Þ ZðV M Þ 2Zðh Þ @x Substitution from Equation (3.32) leads immediately to ¼ CM BM
dmM dx which is transformed via the Gibbs–Duhem Equation (3.36) to J M ¼ CM BM
(3.55)
CM BM dmo 1 d dx
(3.56)
CM DM d ln ao ð1 dÞ dx
(3.57)
JM ¼ JM ¼
(3.54)
Recognizing that because of site conservation CV DV ¼ CM DM
(3.58)
it is seen that Equations (3.53) and (3.57) are equivalent at low values of d.
96
Chapter 3 Oxidation of Pure Metals
The remaining step in this description is the relating of scale thickening rate to diffusive flux through kp dX ¼ JM VM ¼ dt X
(3.59)
where VM is the volume of oxide formed per mole of metal. It follows from Equations (3.57) and (3.59) that kp ¼
DM d ln ao 1 d dy
(3.60)
where y is the normalized position co-ordinate, y ¼ x/X. Upon integration from x ¼ 0 to x ¼ X (i.e. from one side to the other of the scale), this yields Z a00o 1 d ln ao kp ¼ DM (3.61) i 1 d ao where a0o and a00o represent the boundary values of the oxygen activity at the metal–scale and scale–gas interfaces. Use of the relationship for vacancies ZM 1 ¼ jZo j ð1 dÞ leads to the form Z
a00o
kp ¼
DM a0o
ZM d ln ao jZo j
(3.62)
which was Wagner’s original equation for metal oxidation. In the case of very small deviations from stoichiometry, d1, and ZM =jZo j is constant. In this case, Equation (3.62) can be expressed with the help of Equation (3.58) as Z 00 ZM ao kp ¼ DV CV d ln ao (3.63) jZo j a0o This useful form corresponds to Equation (1.25) as is seen below.
3.7. VALIDATION OF WAGNER’S MODEL Considerable effort has been expended in testing both the qualitative and quantitative accuracy of the Wagner description of scale growth kinetics. In the event, quantitative success was achieved in a satisfactory number of important cases: the oxidation of iron, nickel, cobalt and copper and the sulfidation of iron and silver. A review of the practically important cases of FeO, NiO, CoO and FeS scale growth is instructive.
3.7. Validation of Wagner’s Model
97
3.7.1 Oxidation of nickel Nickel forms only one oxide, NiO, which exhibits a small range of nonstoichiometry, ca. 103 at.% on the metal-deficit side. Although NiO scales are formed over a wide temperature range, it is only at temperatures above 9001C that the oxide grain size is sufficiently large for lattice diffusion to predominate over grain boundary transport. Defect concentration, electrical and diffusional properties of NiO have been interpreted in terms of non-interacting cation vacancies 1 2O2 ðgÞ
0 ¼ OX O þ V Ni þ h
V 0Ni ¼ V 00Ni þ h
Thus if V 0Ni V00Ni , the charge balance for the system is
0 VNi ¼ ½h
(3.64) (3.65)
and the equilibrium (3.64) yields 1=4
V 0Ni ¼ KpO2
Conversely, if V 00Ni V 0Ni , we have
1=6 2 V 00Ni ¼ ½h ¼ ð2K0 Þ1=3 pO2
(3.66)
(3.67)
Several investigations [21–23] have shown that the defect properties of 1=4 1=6 NiO are functions of oxygen pressure between pO2 and pO2 . For example, the self-diffusion coefficient of nickel in NiO was shown by Volpe and 1=6 1=4 Reddy [21] to be proportional to pO2 at 1,2451C and pO2 at 1,3801C, as shown in Figure 3.6. The values of DNi given in Figure 3.6 can be used in Equation (3.62) to predict scaling rate constants. The procedure is the same for any oxide for which ZM =jZO j can be approximated as constant, and the form (3.63) used. Setting 1=n
CV ¼ KpO2
(3.68)
and hence 1=n
where
DoNi
DV CV ¼ DoNi pO2
(3.69)
is the self-diffusion coefficient at pO2 ¼ 1 atom, we obtain Z a00o 1=n kp ¼ DoNi pO2 d ln pO2
(3.70)
a0o
¼
DoNi
which upon integration yields kp ¼ nDoNi
Z
a00o a0o
p00O2
1=n1
pO 2
1=n
dpO2
1=n p0O2
(3.71)
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Chapter 3 Oxidation of Pure Metals
Figure 3.6 Self-diffusion coefficient of nickel in NiO (a) at 1 atm pressure as a function of temperature and (b) as a function of oxygen pressure. Reused with permission from Milton L. Volpe and John Reddy [21], copyright 1970, American Institute of Physics.
Rates measured at pO2 ¼ 1 atm are compared in Figure 3.7 with values predicted from Equation (3.71) using the DoNi temperature dependence provided by Volpe and Reddy [21]. Thus quantitative success was achieved with a model based on mass transport via individual point defect species. It should be noted, however, that the Volpe and Reddy diffusion description employed here could not define the relative contributions of the singly and doubly charged vacancies. More seriously, the model fails badly at temperatures below 9001C, as seen in Figure 3.7.
3.7.2 Oxidation of cobalt The monoxide CoO is also of the metal-deficit type, and shows a much larger deviation from stoichiometry than NiO, about 1 at.%. A higher oxide, Co3O4 forms at sufficiently high pO2 , but values greater than 1 atm are required at TW9001C. Growth of a single phase CoO scale occurs via cobalt diffusion, as DoB103DCo. Fisher and Tannhauser [24] and Carter and Richardson [25, 26] studied the parabolic oxidation kinetics and the self-diffusion of cobalt in CoO as a function of temperature and oxygen pressure. Diffusion data found from tracer experiments is shown in Figure 3.8. The value of D is proportional to a constant power of pO2 at each temperature, but the power changes with temperature from 0.27 to 0.35 in the range investigated. Assuming, therefore, that the ionization of
3.7. Validation of Wagner’s Model
99
Figure 3.7 Parabolic rate constant for NiO scale growth: continuous lines calculated from diffusion data; individual points are measured values. Reprinted from Ref. [33] with permission from Elsevier.
cobalt vacancies varies with temperature, the authors wrote 1 2O2
m0 ¼ OX O þ V Co þ mh
If the charge balance can be approximated as
m V m0 Co ¼ h then
mþ1 1=2 mm V m0 ¼ KpO2 Co
(3.72) (3.73)
(3.74)
K being in this instance the equilibrium constant for Equation (3.72). To ease the integration of Equation (3.62) which lies ahead, it is expedient at this point to take
100
Chapter 3 Oxidation of Pure Metals
Figure 3.8 Tracer diffusion coefficient of cobalt in CoO [25, 26]. With permission of TMS.
Table 3.3 Measured and calculated parabolic oxidation rate constants for cobalt to cobaltous oxide [26, 29] Pressure: (1 atm) T (1C)
1,000 1,148 1,350
kw (g cm2 s1/2) Experimental 4
1.56 10 3.05 104 8.85 104
Calculated 4
1.65 10 3.35 104 8.26 104
kw(exptl)/kw(calcd)
0.90 0.88 1.16
the logarithmic differential of Equation (3.74) with Cv ¼ V m0 Co d ln pO2 ¼ 2ðm þ 1Þ d ln Cv Equation (3.63) then integrates immediately to yield 1=2ðmþ1Þ 1=2ðmþ1Þ o 00 p0O2 kp ¼ ðm þ 1ÞDCo pO2
(3.75)
(3.76)
where DoCo is the diffusion coefficient at pO2 ¼ 1 atm. The experimental and calculated values are in approximate agreement, as shown in Table 3.3. A more extensive examination of CoO scale growth kinetic measurements has been provided by Kofstad [27], who concluded that the Wagner model describes high temperature (TW9001C) cobalt oxidation well, with m 1.
3.7. Validation of Wagner’s Model
101
A disadvantage of the integration procedure leading to Equations (3.71) and (3.76) is the treatment of n (or m) as a constant, whereas in general it varies as the relative concentrations of V0m and V 00m change. The difficulty was dealt with by Fueki and Wagner [28] by expressing Equation (3.62) in differential form DCo ¼
jZo j dkp ZCo d ln ao
(3.77)
This equation was used by Mrowec et al. [29, 30] in a careful study of cobalt oxidation kinetics. Values of DCo found from the application of Equation (3.77) to rate data were in good agreement with directly measured values [26, 31]. Gesmundo and Viani [32] considered further the variation of m with oxygen activity, and hence with position in the scale. They achieved an improved match with the experimental pO2 kp relationship by replacing the right-hand side of Equation (3.62) with the sum of two such terms, one for vacancies and one for cobalt interstitials, the latter being significant at low pO2 values near the oxide–cobalt interface.
3.7.3 Oxidation of iron At temperatures above 5701C, iron can form three oxides, wu¨stite, magnetite and hematite. The Fe–O phase diagram and Arrhenius plots for diffusion in the various phases are shown in Figures 2.2 and 3.9. As already seen (Section 2.2), the iron–oxygen diffusion couple resulting from high temperature oxidation develops a scale consisting of inner, intermediate and outer layers of wu¨stite, magnetite and hematite, respectively. The thickness of the wu¨stite layer would be predicted to be much greater than the others, because the phase field and iron diffusion coefficients for FeO are orders of magnitude larger than for the higher oxides, if the reaction is controlled by solid-state diffusion with local equilibria established at phase interfaces. Scaling kinetics determined by Paidassi [1] are shown in Figure 3.10 to be parabolic after a brief initial period of non-steady-state reaction, indicating diffusion control. The relative thicknesses of the different oxide layers quickly attain steady values, as expected for diffusion controlled oxidation. Furthermore, their values (Figure 3.11) display the expected relative magnitudes. It is clear from the Fe–O phase diagram that the approximation d 1 is inapplicable, and the simplified integral (3.63) should not be employed. Himmel et al. [35] used the radioactive tracer technique to measure DFe in wu¨stite, obtaining the results shown in Figure 3.12. As would be expected from Equation (3.58), DFe increases with departure from stoichiometry. These data were used, together with information on the variation of composition (effectively, d) with oxygen activity to carry out a graphical integration of Equation (3.57) for growth of the wu¨stite scale layer in the temperature range 800–1,0001C at pO2 ¼ 1 atm. As seen in Table 3.4, agreement with experiment is good. Similar agreement is found [36] at pO2 ¼ 3.3 106 atm. A simplified analysis has been provided by Smeltzer [40], and is perhaps more transparent. Assuming that the only defects in Fe1dO are divalent cation
102
Chapter 3 Oxidation of Pure Metals
Figure 3.9 Iron and oxygen self-diffusion coefficients in iron and iron oxides. Sources: O in Fe [34], Fe in FeO [35], Fe in Fe3O4 [37], Fe [38] and O [39] in Fe2O3. Reprinted from Ref. [33] with permission from Elsevier.
vacancies and equivalent concentrations of positive holes, and approximating Fick’s first law by a linear vacancy concentration gradient, he obtained.
DV C00V C0V J¼ (3.78) X and therefore
kp ¼ V Fe DV C00V C0V (3.79) Values for DV were obtained from the tracer diffusion data for iron in wu¨stite, using Equation (3.58). Estimates of CV ðXÞ were available from Engell [41], who coulometrically titrated the positive holes as a function of thickness in scales quenched from reaction temperature, by equating C00V ¼ 12 Ch . Rate constants calculated from Equation (3.79) are compared with experimental results in Figure 3.13, where good agreement over a wide temperature range is evident.
3.7. Validation of Wagner’s Model
103
Figure 3.10 Parabolic plots for isothermal scaling of iron in air. Reprinted from [1] with permission from La Revue de Metallurgie.
Figure 3.11 Relative amounts of iron oxides in scales grown in air. Reprinted from [1] with permission from La Revue de Metallurgie.
The apparent success of Equation (3.79) and the implied validity of its assumption of diffusion via individual, doubly charged vacancies in wu¨stite are illusory. Figure 3.14 shows the measured non-stoichiometry of wu¨stite as a function of oxygen potential at a number of temperatures. If the degree of non-stoichiometry
104
Chapter 3 Oxidation of Pure Metals
Figure 3.12 Iron tracer diffusion coefficient in wu¨stite [35]. With kind permission from Springer Science and Business Media. Table 3.4 Measured and calculated parabolic rate constants for oxidation of iron to wu¨stite [35] Pressure: (1 atm) T (1C)
800 897 983
kw (g cm2 s1/2) Experimental 4
2.3 10 5.0 104 8.2 104
Calculated 4
2.3 10 4.8 104 7.7 104
kw(exptl)/kw(calcd)
1.0 1.04 1.07
were in fact equivalent to the vacancy concentration, and the defects exhibited ideal or Henrian solution behaviour, then a log–log plot such as those of Figure 3.15 would be a straight line of slope 1/6 or 1/4 for doubly or singly charged vacancies. The real plots are curved, showing that the assumed basis for Equation (3.79) is a rather crude approximation. This failure is to be expected for the large vacancy concentrations present in wu¨stite, where vacancy interactions such as cluster formation [45, 46] should be taken into account. The diffusion coefficient used in Equation (3.79) is some sort of average, representing the participating species. It must therefore be concluded that although it provides an empirically successful means of predicting the growth of wu¨stite, the model provides only limited insight into the defect nature of this oxide or its diffusion mechanism.
3.7.4 Sulfidation of iron The iron sulfidation reaction has been studied intensively as a test case for the applicability of Wagner’s theory. A review [47] of the work serves also to illustrate the considerable differences between oxidation and sulfidation reactions.
3.7. Validation of Wagner’s Model
105
Figure 3.13 Calculated (curves) parabolic rate constants for wu¨stite growth on iron compared with measured values [41–43]. Reprinted from Ref. [40] with permission from Elsevier.
The Fe–S phase diagram in the Fe1dS region, is shown in Figure 3.15. As seen, the non-stoichiometry is a strong function of temperature and pS2 , and can range up to ca. 25 at.%. The material is always metal-deficit, the principal defects being metal vacancies. Usually a much larger degree of non-stoichiometry is found in sulfides than in the analogous oxides. Factors which contribute to this are the larger anion size and lower lattice energy of the sulfides. Thus point defects are more easily created and deviation from stoichiometry thereby arrived at. What is important from the point of view of metal sulfidation is that a material containing a high density of lattice defects will evidence a high diffusion rate and therefore form only a poorly protective scale. At temperatures below that of the Fe–S eutectic, pure iron sulfidises to form, in the relatively short term, a compact, tightly adherent scale. When the value of pS2 is sufficiently high (see Figure 3.15) the scale consists of a thin surface layer of FeS2 over a thick layer of Fe1dS, but at lower values of pS2 only the monosulfide phase is formed. Since the rate of formation of FeS2 is orders of magnitude less than for Fe1dS, attention is focused on the monosulfide formation reaction.
106
Chapter 3 Oxidation of Pure Metals
Figure 3.14 Non-stoichiometry of wu¨stite at several temperatures. Reprinted from Ref. [44] by permission of The Electrochemical Society, and Ref. [45], published with permission from La Revue de Metallurgie.
Figure 3.15 Phase diagram for Fe–S in the Fe1dS region with equilibrium sulfur partial pressure isobars in kPa.
The compact monosulfide scale grows according to parabolic kinetics, suggesting that the process is controlled by solid-state diffusion. Since the electron conduction characteristics of Fe1dS are metallic in nature and since the self-diffusion coefficient of sulfur, DS, is much less than that of iron, DFe,
3.7. Validation of Wagner’s Model
107
then Wagner’s theory predicts that the flux of iron supports sulfide scale growth rate Z a00 S 1 d ln aS kp ¼ DFe (3.80) 0 1 d aS The variation of the tracer diffusion coefficient of iron with stoichiometry has been measured by Condit et al. [48] in single crystal Fe1dS as Q DFe ¼ Do d exp (3.81a) RT with Q ¼ 81 þ 84d kJ mol1
(3.81b)
where Do has the values 1.7 102 and 3.0 102 cm2 s1 for diffusion in the a and c directions, respectively. The way in which d varies with T and pS2 was determined by Toulmin and Barton [49], permitting the numerical integration of Equation (3.80). Fryt et al. [50, 51] found very good agreement between rates calculated in this way and measured values over wide ranges of temperature (600–9801C) and pS2 (5 1011–2 102 atm). A comparison of Fe1dO and Fe1dS scaling rates is informative. At a temperature of 8001C, a wu¨stite layer grows at 1 108 cm2 s1, whereas Fe1dS grows at 1 105 cm2 s1 when PS2 ¼ 0:01 atm. The value of d (measured by chemical analysis) at the Fe1dO/Fe3O4 interface is B0.1, and at the Fe1dS scale– gas interface B0.12. Thus the reason for the large difference in rates lies in the diffusion coefficients rather than the degree of non-stoichiometry. In wu¨stite at 8001C, DFe ¼ 107 cm2 s1, whereas in Fe1dS it is B105 cm2 s1. These differences reflect the different crystal structures (Fe1dS has the hexagonal NiAs structure rather than the cubic NaCl structure of Fe1dO) and lattice spacings of the two iron compounds.
3.7.5 Effects of oxidant partial pressure on the parabolic rate constant Wagner’s treatment of diffusion-controlled scale growth explicitly recognizes the effect of oxidant partial pressure by relating the flux of diffusing species to chemical potential gradients in the scale. Local equilibrium at the metal– scale interface for the case of negligible deviation from stoichiometry may be written M þ 12O2 ¼ MO 1 (3.82) K and fixes a0m ¼ 1 and a0o ¼ 1=K. Changing the ambient gas cannot change these values. However, at the scale–gas interface, the oxidant partial pressure can be a0m a0o ¼
108
Chapter 3 Oxidation of Pure Metals
varied, and then a00m ¼
1 1=2
KpO2
(3.83)
Thus the gradients in both metal and oxidant activity are affected by changes in the ambient atmosphere, as are the diffusive fluxes within the scale. For a metal-deficit oxide such as Fe1dO, CoO or NiO, Equation (3.63) applies if deviations from stoichiometry can be ignored. If, furthermore, DV afðao Þ, the integral is evaluated using the point-defect equilibrium (3.72) to provide the change of variable given by (3.75) resulting in (3.76). Because p00O2 is usually orders of magnitude greater than the scale–gas equilibrium value p0O2 , we can write 1=2ðmþ1Þ
kp ¼ ðm þ 1ÞDoM pO2
(3.84)
where DoM is the metal diffusion coefficient at pO2 ¼ 1 atm. Fueki and Wagner [28] tested the applicability of Equaton (3.84) to the oxidation of nickel, and found m to vary from 2 at 1,0001C to 0.75 at 1,4001C. They concluded on this basis that doubly charged vacancies, as identified in Equation (3.72), were predominant at 1,0001C, but that singly charged vacancies became more important at higher temperatures. The effect of pO2 on kp for cobalt oxidation is shown in Figure 3.3. At lower pO2 values, only CoO is formed, and Equation (3.84) describes well the variation in kp with oxidant activity, with m 1. When an outer layer of Co3O4 is formed at higher oxygen activities, it is rather thin, and the measured total weight gain corresponds essentially to CoO layer growth. As seen in Figure 3.3, the rate does not vary with pO2 in this regime. This is a consequence of the fact that the boundary value of ao at the CoO outer interface is set by the equilibrium 3CoO þ 12O2 ¼ Co3 O4
(3.85)
and is therefore unaffected by changes to the gas atmosphere. A more detailed study of the effect of pO2 on CoO scale growth was undertaken by Mrowec and Przybylski [30] who showed that 2(m+1) varied from 3.4 at 9501C to 3.96 at 1,3001C. They attributed the deviation from the value 4 expected for singly charged vacancies to a contribution from intrinsic Frenkel defects. However, when much lower pO2 values were investigated [52], the defect properties of CoO were found not to conform with the continuous power relationship of Equation (3.75). Study of the pO2 dependence of wu¨stite layer growth is difficult because the oxygen partial pressures required are so low. At 1,0001C, Fe3O4 forms on top of the wu¨stite layer at pO2 ¼ 1012 atm. As seen earlier (Figure 3.11), wu¨stite continues to constitute the majority of the scale, and measured reaction rates correspond essentially to that of Fe1dO layer growth. Since the boundary values of oxygen activity at the metal–scale and Fe1dO/Fe3O4 interfaces are fixed by the phase equilibria at these surfaces, the diffusive flux supporting wu¨stite layer growth is independent of the ambient pO2 value. The low pO2 values necessary to grow Fe1dO alone can be achieved using CO/CO2 or H2/H2O atmospheres.
3.7. Validation of Wagner’s Model
109
Pettit and Wagner [53] and Turkdogan et al. [54] have oxidized iron in such atmospheres, and found the reactions to be controlled initially by surface processes involving CO2 or H2O. Eventually parabolic kinetics take over, at the rates predicted from Wagner’s theory. Growth rates of metal excess, n-type oxides show interesting oxidant pressure effects. Consider formation of interstitial cations (e.g. in Zn1+dO)
0 1 MO ¼ Mm i þ me þ 2O2 ðgÞ
(3.86)
If the charge balance can be written Ce ¼ mCMi
(3.87)
then CMi ¼
1=ðmþ1Þ K 1=2ðmþ1Þ pO2 m
(3.88)
where K is the equilibrium constant for Equation (3.86). As expected, adding more oxygen to a metal excess oxide reduces the deviation from stoichiometry. Logarithmic differentiation then yields d ln pO2 ¼ 2ðm þ 1Þ d ln CMi and integration of Wagner’s rate expression leads to 1=2ðmþ1Þ 1=2ðmþ1Þ kp ¼ ðm þ 1ÞDMi p0O2 p00O2
(3.89)
(3.90)
In the usual case where p00O2 p0O2 , the negative exponent makes the second term in the braces much less than the first, and 1=2ðmþ1Þ (3.91) kp ¼ ðm þ 1ÞDMi p0O2 Since p0O2 is established by the metal-oxide equilibrium at the base of the scale, it is independent of the gas composition. Thus the rate of growth of a metal excess oxide is usually independent of pO2 . A similar argument can be developed for metal-excess oxides in which anion vacancies are the principal defects [27]. The correctness of this prediction for the growth of Zn1+dO was demonstrated by Wagner and Grunewald [55], who obtained essentially the same oxidation rate at oxygen partial pressures of 1 and 0.02 atm, and a temperature of 3901C. The rate at which iron sulfidises varies in a complex manner with pS2 [50, 51]. This is a consequence of vacancy interactions at the high concentrations involved, and Wagner’s kinetic analysis cannot be used to provide insight into the defect properties of Fe1dS.
3.7.6 Effect of temperature on the parabolic rate constant The rate constant for growth of a metal-deficit oxide given by Wagner’s theory (3.61) is dependent on temperature in three ways. The diffusion coefficient is thermally activated, DM ¼ Do expðQ=RTÞ. The boundary value of the oxygen
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Chapter 3 Oxidation of Pure Metals
activity, a0o , which is one of the limits of integration, is set by the temperature dependent metal-oxide equilibrium (3.82), whence, through Equation (2.28): þDH ðMOÞ DS ðMOÞ 0 ao ¼ exp exp (3.92) RT R Finally, the functional relationship between non-stoichiometry and a0o is itself temperature dependent through the temperature effect on intrinsic disorder (3.18). This last effect is significant if the degree of non-stoichiometry is large, and must be dealt with by numerical integration, as has been done for Fe1dO [35] and Fe1dS [47]. Usually, however, it is ignored. The importance or otherwise of the temperature effect on a0o depends on the nature of the oxide. For a metal-deficit oxide, we have seen that the integrated form in Equation (3.76) can be simplified on the basis a00o a0o to the form of Equation (3.84). Thus the temperature dependence of a0o is unimportant. The activation energy for the scaling rate constant is in this case the same as that of the metal diffusion coefficient. A different conclusion is reached for metal excess oxide, where the defect concentration is inversely proportional to some power of pO2 . In the usual situation where a00o 4a0o it follows that 1 1 00 (3.93) 0 ao ao and the integrated form of the rate expression is given by Equation (3.91). Rewriting this to show the temperature effect explicitly, we obtain Q DH ðMOÞ DS ðMOÞ exp exp (3.94) kp ¼ ðm þ 1ÞDo exp RT ðm þ 1ÞRT ðm þ 1ÞR thus observing that the activation energy for kp is given by ½Q þ DH ðMOÞ=ðm þ 1Þ . In the foregoing discussion of temperature effects, we have assumed that the scale was a single phase, and that its outer surface was in contact with gas at 1=2 some fixed value of a00o ¼ pO2 . However, if an additional layer develops, as in the cases of iron and cobalt (Figure 3.1), then a00o is set by the interfacial equilibrium between the two oxides, as expressed, e.g. by Equation (3.85). The temperature effect on the rate of CoO growth is then found from Equation (3.76) as Q DH DS kp ¼ ðm þ 1ÞDo exp exp exp (3.95) RT ðm þ 1ÞRT ðm þ 1ÞR where DH and DS refer to the CoO ! Co3 O4 reaction (3.85). Kofstad’s compilation [27] of cobalt oxidation rate data is reproduced in Figure 3.16. At high temperatures, where only CoO is formed, the activation energy is equal to that of DCo at 160 kJ mol1. At lower temperatures, a thin layer of Co3O4 forms on top of the CoO, but the measured overall oxidation rate corresponds closely to the growth of the majority CoO layer, and is given to a good approximation by Equation (3.95). Taking DH ð3:85Þ ¼ 183 kJ mol1, the activation energy for scaling is then predicted to be 160+183/2 ¼ 252 kJ mol1. This is in reasonable
3.7. Validation of Wagner’s Model
111
Figure 3.16 Temperature effects on cobalt oxidation rates in 1 atm O2. Reprinted from Ref. [27] with permission from Elsevier.
agreement with the experimental finding of 230 kJ mol1. The rate of CoO growth is ‘‘decreased’’ at lower temperatures because a00o , as established by the CoO/Co3O4 equilibrium, is much lower than the gas phase value of 1 atm.
3.7.7 Other systems Wagner’s theory has been shown to be successful in describing the oxidation of copper to form metal-deficit Cu2O. This first demonstration is of historic interest, as it was performed by Wagner himself [55]. It is also unusual in that the transport properties of Cu2O were measured electrochemically. Later results on copper oxidation have been reviewed [27, 33] and are considered to indicate that the defect nature of Cu2O is more complex than the neutral vacancy model 1 2O2 ðgÞ
X ¼ 2V X Cu þ OO
(3.96)
deduced by Wagner. The high temperature oxidation of silicon is important in solid-state device technology, and it has accordingly been studied intensively. The reaction product is amorphous or glassy SiO2, which is highly protective. The early kinetic
112
Chapter 3 Oxidation of Pure Metals
investigations of Deal and Grove [56] led to the parabolic-linear rate equation X2 þ AX ¼ kp ðt þ tÞ
(3.97)
for reaction in dry oxygen. Here kp =A is a linear rate constant related to phase boundary reactions and t a correction to allow for the non-zero oxide film thickness at the commencement of reaction. The magnitude and activation energy of kp were shown [56, 57] to agree with those of oxygen diffusion through glassy silica. The Wagner equation for oxygen diffusion control is simply Z p00 O kp ¼ Do d ln pO2 (3.98) p0O
2
and for Do independent of oxygen activity, this integrates to yield h i kp ¼ Do p00O2 p0O2 Do p00O2
(3.99)
thus accounting for the original observation [56] that kp / pO2 , and indicating that the diffusing species are oxygen molecules. Very different results are obtained at high temperature and low pO2 values, because volatilization of SiO(g) becomes important. This situation is discussed in Section 3.10. A few other systems have been used to test the validity of the Wagner approach: silver sulfidation and bromination and CuI formation. Scaling rates were found to be in good order of magnitude agreement with predictions based on the transport properties of the relevant compounds [58–60].
3.7.8 Utility of Wagner’s theory Wagner’s equations express succinctly the parameters affecting oxidation rates: the material properties of the oxide, oxidant partial pressure and temperature. Consider the relative rates at which Fe1dO, CoO and NiO grow at 1,0001C (see Table 3.1). All three oxides have the same crystal structure and contain cation vacancies. To a first approximation, we ignore differences in atomic weights, lattice spacing and, most importantly, defect interactions, and suppose that DV has the same value in each oxide. This approximation can be tested, using DM ¼ DV CV on the assumption of uncorrelated diffusion, and measured values of D and d ¼ CV . As seen in Table 3.5, DV values calculated in this way are in fact within an order of magnitude. To this degree of approximation then, the Table 3.5
Comparative data for metal deficit oxides at 1,0001C
Oxide kp (cm2 s1)
Fe1dO CoO NiO
Calculated Dv (cm2 s1)
Measured data
7
2 10 3.3 109 9 1011
DM (cm2 s1) 7
8 10 1.2 109 1 1011
Cv (fraction)
0.13 0.01 105
6.2 106 1.2 107 1 106
3.8. Impurity Effects on Lattice Diffusion
113
differences in metal self-diffusion coefficient can be attributed directly to oxide non-stoichiometry. Recalling the earlier result for metal-deficit oxides in Equation (3.84) 1=2ðmþ1Þ
kp ¼ ðm þ 1ÞDoM pO2
then at pO2 ¼ 1 atm, kp is 1, 2 or 3 times DoM for vacancy charges of 0, 1 or 2, respectively. The rate data for cobalt and nickel at 1,0001C and pO2 ¼ 1 atm in Table 3.5 is in reasonable accord with this prediction for m ¼ 2. In the case of iron, pO2 has the value set by the FeO/Fe3O4 equilibrium and, for m ¼ 2, the value of kp predicted from Equation (3.84) is 2 108 cm2 s1, an order of magnitude lower than the measured quantity. Nonetheless, the widely different growth rates of these three oxide scales can be understood, and semi-quantitatively predicted, simply from a knowledge of their non-stoichiometry. It was the achievement of Wagner and the other early investigators in Germany to recognize that non-stoichiometry corresponded to the existence of lattice defects, and that furthermore these defects provided the mechanism of diffusion and scale growth. Wagner’s theory has been shown to be quantitatively successful in a convincing number of cases. A principal reason for the limited utility of the theory is the lack of sufficient data to permit accurate integration of rate equations like Equation (3.61). From a practical point of view, it is easier to measure a parabolic rate constant than to predict it by determining diffusion coefficients and deviations from stoichiometry as functions of oxygen activity. The real value of the theory is in providing a fundamental understanding of the oxidation mechanism. As we have seen, the thermodynamic and diffusional analysis leads to an understanding of and the ability to predict the effects of temperature and oxidant partial pressure. Despite the intellectually satisfying nature of the Wagner analysis, it is prudent to bear in mind its limitations. As we have seen, the theory works well for a moderately non-stoichiometric oxide like CoO, but fails to reveal the complexities of diffusion in highly disordered solids like Fe1dO and Fe1dS. More seriously, it cannot be used to predict the growth rates of slow growing (and therefore important) oxides like Cr2O3 and Al2O3. These oxides have immeasurably small deviations from stoichiometry, and their diffusion properties are not well understood. These difficulties result from the nature of the oxides. Firstly, the native lattice defect concentrations are so small that even low concentrations of impurities can dominate the oxide. Secondly, and for the same reason, diffusion via pathways other than the oxide lattice are usually important. We now consider these effects.
3.8. IMPURITY EFFECTS ON LATTICE DIFFUSION In reality metals are seldom anywhere near pure. Even so-called high-purity metals usually contain impurities at concentrations in the parts per million (ppm) range. One exception to this generalization might be silicon, which is routinely
114
Chapter 3 Oxidation of Pure Metals
zone-refined to very high purity levels, in order to avoid unwanted dopants which would affect semiconductor properties. The presence of impurity ions of valence different from that of the solvent species can change the defect concentration through their effect on charge balance. Consider the dissolution of chromium in NiO X X 00 2Cr þ 3ðNiX Ni þ OO Þ ¼ 2CrNi þ V Ni þ 3OO þ 3Ni
(3.100)
Cr2 O3 ðþNiOÞ ¼ 2CrNi þ V00Ni þ 3OX O ðþNiOÞ
(3.101)
or, equivalently
The different effective charge of the impurity, or dopant, is seen to be accommodated by an adjustment in the number of cation vacancies. In the first formulation, chromium metal is oxidized by NiO, displacing nickel metal, as would be predicted from the relative stabilities of Cr2O3 and NiO. In the second formulation, the NiO lattice is extended by the dissolution of some chromia. In writing these equations it is assumed that chromium is dissolved substitutionally onto the normal cation sublattice. Moreover, the cation to anion site ratio of the solvent oxide is maintained, as its crystallography is unchanged. To formulate the equations it is necessary, of course, to know the natural defect type of the solvent oxide. Consider now the cation vacancy concentration when the doped oxide is at equilibrium with a gas. In addition to Equation (3.101), we have 1 2O2 ðgÞ
00 ¼ OX O þ V Ni þ 2h
1=2
CV C2h ¼ KpO2
(3.102) (3.103)
if only doubly charged vacancies can form. The charge balance is now written 2CV ¼ CCr þ Ch
(3.104)
Substitution for Ch from Equation (3.103) then lends to 1=4
2CV ¼ CCr þ
K1=2 pO2 1=2
CV
! (3.105)
Thus doping with a higher valent cation has the effect of increasing the vacancy concentration and making it less sensitive to oxygen partial pressure. The effects on kp are predicted to be qualitatively similar. Nickel containing low concentrations of chromium has been found [61, 62] to oxidize faster than pure nickel, in agreement with this prediction. Using similar reasoning, it is found that dissolution of a lower valence cation in a metal-deficit oxide decreases the concentration of vacancies, and hence the oxidation rate. In the case of a metal excess oxide like ZnO, where the ionic defects have a positive charge, the effects of aliovalent doping are reversed. Consider the
3.9. Microstructural Effects
115
incorporation of a higher valent cation such as Cr3+ 0 1 Cr2 O3 ðþZnOÞ ¼ 2CrZn þ 2OX O þ 2e þ 2O2 ðgÞ
(3.106)
Because formation of a cation vacancy is energetically unfavourable in an n-type oxide, site balance is instead maintained via the ejection of gaseous oxygen and the formation of free electrons. If the interstitial zinc species are fully ionized, we have also ZnO ¼ Zn€ i þ 2e0 þ 12O2 1=2
(3.107)
K ¼ CZni C2e pO2
(3.108)
2CZni þ CCrZn ¼ Ce
(3.109)
and the charge balance becomes Combination of Equations (3.108) and (3.109) then yields 2CZni þ CCrZn ¼
K1=2 1=2 1=4
CZni pO2
(3.110)
and the addition of chromium is seen to decrease the concentration of zinc interstitials and would therefore be expected to decrease the zinc oxidation rate. The various combinations of higher or lower valent dopants with stoichiometric oxides (both Schottky and Frenkel type) or non-stoichiometric compounds (metal excess or deficit, lattice or interstitial species) have been considered in detail, as they are important to the study of solid-state chemistry [63]. However, the value of dopant chemistry in understanding or predicting oxidation behaviour is far from clear. Consider even the simple case of chromium doping NiO to the extent where Equation (3.105) can be approximated as CV ¼ 12CCr The rate expression Equation (3.63) then becomes Z a00o kp ¼ D V CCr d ln ao
(3.111)
(3.112)
a0o
and to proceed further we require knowledge of the chromium concentration profile within the scale. Information of this sort is not available. Moreover, the ideal or Henrian solution (Section 2.3) behaviour implicit in equilibrium concentration relationships like Equation (3.103) is highly unlikely to apply in the presence of dopants.
3.9. MICROSTRUCTURAL EFFECTS Wagner’s theory assumes the oxide scale to be continuous, coherent, perfectly bonded to the substrate metal and to be capable of diffusion only via lattice defects. As seen in the preceding sections, these assumptions can be successful, particularly at high temperatures in systems containing large concentrations of lattice defects. At lower temperatures and in oxides with less defective lattices,
116
Chapter 3 Oxidation of Pure Metals
they can fail. Nickel oxidation (Figure 3.7) provides an example of agreement between theory and experiment at high temperatures, but measured rates are much higher than predicted at low temperatures. As is clear from the measurements, the activation energy has a smaller value at lower temperatures, and a different mechanism must be in effect. That mechanism has been shown to be grain boundary diffusion.
3.9.1 Grain boundary diffusion Oxide scales are polycrystalline, and grain size can vary considerably. As seen in Figure 3.1, the NiO grain size in a scale grown at 1,1001C is tens of microns. In oxide grown at 8001C, the columnar grains seen in Figure 3.17 are about 1 mm across. At lower temperatures, the grains are even finer, and show evidence of coarsening with time (Figure 3.18). Grain boundary diffusion is often more important than lattice diffusion at low temperatures. A principal reason for this is the lower activation energy of the boundary process, corresponding to the more disordered structures in the boundaries [66]. A second reason is the usually finer grain size and hence more numerous boundaries encountered at lower temperatures, as illustrated above for NiO. The additional possibility of impurity species segregation to grain boundaries is considered in Sections 4.4, 7.5 and 10.4. A useful way of describing diffusion in a polycrystalline material was proposed by Hart [67] and adapted by Smeltzer et al. [68] to the nickel
Figure 3.17 SEM view of cross-section through NiO scale [64]. With kind permission from Springer Science and Business Media.
3.9. Microstructural Effects
117
Figure 3.18 Average grain size in NiO scales as a function of oxidation time. Reprinted from Ref. [65] with permission from Elsevier.
oxidation case. An effective diffusion coefficient is defined as a weighted sum of lattice and boundary contributions Deff ¼ DL ð1 f Þ þ DB f
(3.113)
where f is the fraction of diffusion sites within the boundaries and DL and DB the self-diffusion coefficients for the bulk lattice and boundaries, respectively. Using the linear approximation to the oxidation rate equation dX DC ¼ VDeff dt X and integrating, one obtains X2 ¼ 2VDL DC
Z t DB 1þ f dt DL o
(3.114)
(3.115)
so that the effective rate constant for fixed f and predominant boundary diffusion is kp ¼ VDCDB f
(3.116)
More complex kinetics result if the oxide grains grow during the scaling reaction [64, 65, 68]. If the density of rapid diffusion sites decays according to first order kinetics [68] f ¼ f expðktÞ
(3.117)
f DB X2 ¼ 2kp t þ ð1 ekt Þ kDL
(3.118)
then
where f is the initial value of f. If, on the other hand, the decay in f is due to recrystallization and grain growth in the oxide [64] f ¼ 2d=Dt ; D2t D2o ¼ Gt
(3.119)
118
Chapter 3 Oxidation of Pure Metals
and Equation (3.118) becomes (
" #) 1=2 2 ðD GtÞ D 4D d B o o X2 ¼ 2kp t 1 þ DL G t
(3.120)
Here, the grains are modelled as cubes of edge Dt, which have grown from an original size Do with a growth constant G, and the boundaries have a width, d. Low temperature nickel single crystal oxidation rates have been successfully described [64] using Equation (3.120) with a value for kp calculated for lattice diffusion from Wagner’s theory. The success of this procedure can be seen in Figure 3.19. The reaction was controlled by boundary diffusion in the temperature range 500–8001C. Assuming d ¼ 1 nm and using measured grain sizes, the activation energy was estimated at 130–145 kJ mol1, compared with 255 kJ mol1 for lattice diffusion of nickel and for kp. Graham et al. [69] estimated the activation energy for boundary diffusion as 169 kJ mol1, using first order kinetics (3.117) for the decrease in boundary density, in approximate agreement. A review [33] of correlations of oxide microstructures with oxidation rates of several metals confirms that boundary diffusion is an important component of
Figure 3.19 Experimental results and curves calculated from Equation (3.120) for the growth of NiO scales on a (100) Ni face. Reprinted from Ref. [64] with permission from Elsevier.
119
3.9. Microstructural Effects
Table 3.6
Activation energies for parabolic oxidation kinetics and for oxide lattice diffusion [33]
Metal/oxide
T (1C)
Oxidation activation energy EA (kJ mol1)
Diffusion activation energy Q (kJ mol1)
EA/Q
Cr/Cr2O3 Ni/NiO Cu/Cu2O Zn/ZnO Ti/TiO2 Zr/ZrO2
700–1,100 400–800 300–550 440–700 350–700 400–860
157 159 84 104 122 134
330 254 151 305 251 234
0.48 0.62 0.56 0.34 0.49 0.57
scale growth. This is evident in Table 3.6 where activation energies for oxidation at intermediate temperatures are compared with the corresponding quantity for cation lattice diffusion. The former are around half the magnitude of the latter, as is typical of grain boundary diffusion. Isotope diffusion measurements in growing NiO scales [70] have demonstrated that boundary diffusion is dominant at 5001C and 8001C. The success of the grain growth model (3.119) was demonstrated by Atkinson et al. [71, 72], who used independently measured values for lattice, dislocation and grain boundary diffusion to predict low temperature nickel oxidation rates in agreement with experimental results. The intensively studied nickel oxidation reaction has been shown conclusively to be dominated by grain boundary diffusion at temperatures below about 9001C. It seems likely that the same will be true for all oxides, in an appropriate temperature regime, and that the lower the value of DL , then the higher the temperature range in which boundary diffusion will be the predominant mechanism of mass transport. An example of practical importance is Cr2O3. Lattice diffusion has been measured in single crystal Cr2O3, and found to be extremely slow. Several investigators [73–75] found that DCr was independent of 3=4 pO2 over a wide range, but increased with pO2 at high oxygen potentials, ð3=4Þ and perhaps [27] with pO2 at low potentials. The oxygen potential effects are not well understood, although Kofstad [27] has suggested that Cr2O3 shows metal-deficit behaviour at high pO2 and metal excess behaviour at low pO2, and that the intermediate range where DCr afðpO2 Þ may reflect intrinsic behaviour. The most important finding, however, is the very low magnitude of DCr , 1016 cm2 s1 at pO2 ¼ 1 atm and 1,1001C. The activation energy for lattice diffusion of chromium is about 515 kJ mol1. Chromium oxide scaling studies are restricted to relatively low temperatures, to avoid volatilization of both metal and oxide CrðsÞ ¼ CrðgÞ; Cr2 O3 þ 12O2 ¼ 2CrO3 ;
DG ¼ 396; 000 224 T J mol1
(3.121)
DG ¼ 561; 730 357 T J mol1
(3.122)
Metal evaporation becomes important at temperatures above about 1,0001C and CrO3 formation at pO2 ¼ 1 atm is significant above 9001C. Even when
120
Chapter 3 Oxidation of Pure Metals
consideration is restricted to low temperatures, the thermogravimetric kinetic data shows a remarkable degree of scatter (Figure 3.20). Caplan and Sproule [76] showed that much of the observed variation is due to the diversity of scale microstructures developed. These authors were able to use rather high temperatures by surrounding their samples with Cr2O3, to saturate the gas with CrO3. As seen in Figure 3.21, the scale grown on an etched polycrystalline chromium surface varied considerable, with thin oxide growing on some grains and thick oxide on others (and at grain boundaries). Figure 3.21 compares SEM views of scale fracture sections taken from oxidized samples of etched and electropolished chromium. The latter is made up of multiple layers of detached, convoluted finely polycrystalline Cr2O3, whereas the former appears to be a single crystal of Cr2O3, still attached to the metal surface. The authors attributed these different outcomes to the very thin oxide left by the electropolishing procedure being finely polycrystalline, and nucleating a scale of
Figure 3.20 Comparison of reported rate constants for chromium oxidation [76]. With kind permission from Springer Science and Business Media.
3.9. Microstructural Effects
121
Figure 3.21 Fracture cross-sections of chromia scales grown at 1,0901C on (a) etched Cr and (b) electropolished Cr [76]. With kind permission from Springer Science and Business Media.
similar microstructure [84]. The different morphological evolutionary paths of the two structures shown in Figure 3.21 was accounted for in terms of their different diffusion mechanisms. The polycrystalline oxide grew rapidly, and developed compressive stresses, leading to convolution and eventual detachment form the metal. The compressive stresses were attributed to new oxide formation within the scale resulting from simultaneous metal and oxygen diffusion along grain boundaries. The single crystal oxide scale grew slowly and developed no significant compressive stress because, in the absence of grain boundaries, only lattice diffusion of chromium occurred. In this case, new oxide would form at the free outer surface, generating no stress. The difference in observed weight change kinetics is clearly related to the different scale morphologies. However, the rate of single crystal scale growth was not quantitatively correlated with the lattice value of DCr , there being no single crystal diffusion data available at that time. Because the diffusion coefficient is so small, data is still scant. If the value measured [75] at pO2 ¼ 1 atm and 1,1001C of DCr ¼ 1016 cm2 s1 is used in Equation (3.84) with pO2 ¼ 1 atm, a value of kp ¼ (m+1) 1016 cm2 s1 is predicted. The value measured by Caplan and Sproule at 1,0901C corresponds to kp ¼ 2 1013 cm2 s1, three orders of magnitude faster. Moreover, the measured activation energy for oxidation was 240 kJ mol1, compared with 515 kJ mol1 for diffusion. It would be concluded on this basis that lattice diffusion via cation vacancies cannot support the observed rate of chromia scale growth, even when no grain boundaries are present, and presumably lattice diffusion is important. Consider now the possibility of scale growth supported by interstitial cation diffusion, in which case Equations (3.90) and (3.94) should apply. We formulate
122
Chapter 3 Oxidation of Pure Metals
the interstitial defect equilibrium m 0 3 X 3 CrX Cr þ 2OO ¼ Cri þ me þ 4O2 ðgÞ
(3.123)
along with the charge balance Ce ¼ mCCri obtaining ð3=4ðmþ1ÞÞ
CCri ¼ Constant pO2
(3.124)
The value of pO2 is that given by the Cr/Cr2O3 equilibrium. Using the value (see Table 2.1) DH ðCr2 O3 Þ ¼ 746 kJ mol1 of O2, and Kofstad’s [27] value of 515 kJ mol1 for the diffusion activation energy, we find from Equation (3.94) that the activation oxidation energy for oxidation is [550+746 3/4(m+1)] kJ mol1. If the interstitial species is singly charged, then the predicted activation energy is 236 kJ mol1, in close agreement with the 240 kJ mol1 measured by Caplan and Sproule. Thus the data is consistent with lattice diffusion via chromium interstitials. However, in the complete absence of diffusion data for the relevant regime of T and pO2 , it would be unwise to view this agreement as conclusive. The very low oxygen pressures needed to explore the behaviour of chromia near the Cr/Cr2O3 equilibrium can only be controlled by using H2/H2O or CO/ CO2 mixtures. Unfortunately, these molecular species have their own interactions with Cr2O3 [85–89], and these may obscure the oxygen effects which are relevant to chromia scales grown in pure oxygen. Data obtained [88] in H2/H2O atmospheres at 9001C corresponded to growth of Cr2O3 as the only reaction product under conditions where volatilization would be slow. In this gas, pO2 ¼ 1 1019 atm and the rate constant was 8.6 1011 g2 cm4 s1. Reference to Figure 3.20 shows that this value is of the same order as other measurements made at pO2 ¼ 1 atm, and much faster than the single crystal rate measured by Caplan and Sproule [76]. The fast rate is consistent with grain boundary diffusion, and the lack of pO2 dependence indicates that chromium interstitials are the mobile species.
3.9.2 Multilayer scale growth As we have seen in Sections 2.2 and 3.2, multilayered scales can form during metal oxidation, and the scale structure is qualitatively predictable from the relevant phase diagram. Because local equilibrium is in effect at each of the interfaces, the values of ao are fixed at these boundaries. Accordingly, we expect that the diffusion flux in each layer is inversely proportional to its thickness. However, we cannot evaluate layer-thickening rates directly from these fluxes, because there is an additional mass transfer process at each interface. This problem has been treated by a number of authors [27, 90–95]. Consider the growth of a duplex scale (Figure 3.22) made up of MOa and MOaþb . Under steady-state conditions, the thickness of each layer increases
3.9. Microstructural Effects
M
Gas
Moa+b
MOa
CM
123
a/b
CM
b/a
CM
x=0
Figure 3.22
x =X1
x=X2
Schematic view of two-layered scale growth.
parabolically with time X2i ¼ ki t
(3.125)
where ki is a rate constant (which is not equal to kp ) and the subscript indicates the layer identity. The values of ki depend on the diffusional fluxes in the oxide, and on the interface reaction b b (3.126) MOaþb þ M ¼ 1 þ MOa a a This situation can, in principle, be dealt with from a mass balance point of view. If metal is the only diffusing species
dX1 b=a a=b J1 J2 ¼ CM CM (3.127) dt b=a a=b where J i is the metal flux in the indicated layer and CM and CM the concentrations of metal in the outer and inner oxide, respectively, both at the MOa =MOaþb interface. Evaluation of the J i is difficult, and it is useful instead to relate the ki values to other, simpler reactions. If a single layer of MOa is grown at pO2 ða; bÞ, the equilibrium value for Equation (3.126), the rate constant can be evaluated from Wagner’s theory, assuming only metal diffuses, as Z pa=b ð1Þ O2 Z M Dð1Þ ka ¼ (3.128) M d ln pO2 0 j j Z o pO 2
The rate constant kb is defined in terms of growth of a higher oxide layer on the surface of lower oxide, in the absence of any base metal and therefore of diffusion from it, but exposed at its outer surface to pO2 ðgÞ4pO2 ða=bÞ. This rate is related to k2, the rate of outer layer thickening when both layers grow simultaneously on
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Chapter 3 Oxidation of Pure Metals
the metal, via the volume change accompanying the phase transformation (3.126). Thus X2 V MOaþb (3.129) kb ¼ 1 þ k2 X1 VMOa Z kb ¼
ðgÞ
pO
2
ða=bÞ
pO
2
Zð2Þ M Dð2Þ d ln pO2 jZo j M
(3.130)
Recognizing that in the duplex scale relative layer thicknesses reflect the fractions of the metal flux consumed in growing each of them, it can be shown that ka ðX1 Þ2 1 þ aðða=ða þ bÞÞðX2 =X1 ÞÞ ¼ 1 þ ð1=aÞðX1 =X2 Þ kb ðX2 Þ2
(3.131)
where a ¼ V MOa =V MOaþb . Thus the ratio of the layer thicknesses in a duplex scale is related to the ratio of the rate constants for the exclusive growth of the individual layers. Finally, the overall rate constant kov which describes the rate of total scale thickness increase is related to the layer growth rates by
2 1=2 1=2 kov ¼ k1 þ k2 (3.132) The applicability of this description to the growth of FeO+Fe3O4 scales on iron has been demonstrated by Garnaud and Rapp [96], who used independently measured values of ka and kb to predict XFe3 O4 =XFeO ¼ 0.041 at 1,1001C. This value is in good agreement with that of 0.053 derived from Paidassi’s metallographic observations [1].
3.9.3 Development of macroscopic defects and scale detachment As discussed in Section 2.10, oxide scale growth by outward metal transport leads to new oxide formation at the free outer surface, and no growth stresses result. However, as the metal surface recedes, the scale can maintain contact with it only if it is free to move. In the case of a flat sample of limited size, a rigid scale would be constrained at specimen edges and therefore unable to maintain contact. Even when the oxide has limited plasticity, growth of a sufficiently thick scale will eventually lead to detachment from the metal, starting at the edges. An example of the effect [97] is shown for a silver sufide scale in Figure 3.23. The cross-section reveals that the sulfide had remained in contact with the flat sides of the specimen, forming a thick, compact scale as metal was consumed. Much less silver was reacted at the specimen edges, where geometrical constraints had prevented the sulfide from maintaining good contact. As seen in the figure, a porous reaction product had developed, rather than an empty gap. This interpretation was confirmed by the ‘‘pellet’’ experiment [98, 99] shown schematically in Figure 3.24. A pellet of the same material as the scale was placed in contact with the metal specimen. A tube containing the oxidant (liquid sulfur in this case) was placed on top of the pellet and held there under load.
3.9. Microstructural Effects
125
Figure 3.23 Cross-section of initially flat silver sample after sulfidation at 4441C for 9 min [97].
Load
S(l)
S(l) tube
Ag2S
Ag2S
Ag2S
Ag2S
Ag
Porous Ag2S Ag Rigid support
Figure 3.24
Schematic illustration of Rickert’s [98, 99] pellet experiment. Description in text.
Heating the whole assembly was found to cause growth of more scale up into the tube (confirming outward diffusion of silver in Ag2S). As the metal was consumed, the pellet and loaded tube moved downward, maintaining contact with the metal. No region of porous sulfide developed. However, if at some time after commencement of the reaction, the metal and tube of sulfur were each independently clamped in position, porous sulfide formed at the pellet-metal interface. The development of porous material was described by Mrowec and co-workers [97] using their dissociation mechanism. Once local scale–metal separation occurs, the metal activity at the underside of the scale can no longer be maintained. Metal continues to diffuse outward, driven by the oxidant chemical potential gradient, and aM decreases. Consequently, as seen from Equation (3.82),
126
Chapter 3 Oxidation of Pure Metals
as increases, and gas phase transport commences from the underside of the scale to the underlying metal surface. A porous product grows under gaseous mass transfer control, until it bridges the gap between metal and separated scale, whereupon outwards metal transport resumes. As calculated in Section 2.9 (and as pointed out by Gibbs [100]) the oxidant partial pressures prevailing at metal–scale interfaces are usually too low to support any significant transport. However, as diffusion through the scale takes place, the ao value at the scale underside will rise and gaseous mass transport could thereby be enabled. Birks and Rickert [101] showed that in the case of NiO growth, the likely pO2 values were sufficient to account for the observations. Furthermore, most metals contain carbon impurities which will oxidize. As shown by Graham and Caplan [102], the resulting CO/CO2 mixture occupies the voids. In this case, the gas can act as an oxygen carrier via the reactions CO þ MO ¼ CO2 þ M taking place in different directions on opposite sides of the cavity (Figure 3.25). Finally, it will be recalled that real oxide scales are polycrystalline, and inward oxygen diffusion via grain boundaries can occur. Atkinson et al. [70] used 18 O tracer studies to show that oxygen did not penetrate NiO scales during their initial growth, but that long-term penetration occurred when an inner, porous NiO scale sublayer developed. This transport of oxidant molecules is suggested to take place through microchannels or pores developed in the outer layer. Mrowec and co-workers [97] have proposed that the underside of a separated scale will dissociate preferentially at oxide grain boundaries, where outward diffusion of metal is fastest. This process could then create microchannels along favourably oriented boundaries, allowing subsequent inward transport of molecular oxidant. The possibility of molecular species penetrating scales is discussed in Chapters 4, 9 and 10.
Gas
JM
MO
CO + MO →CO2 + M
CO
CO2
CO2+M →CO+MO
Figure 3.25 Action of CO/CO2 couple within a void accelerating oxygen transport.
3.10. Reactions Not Controlled by Solid-State Diffusion
127
3.10. REACTIONS NOT CONTROLLED BY SOLID-STATE DIFFUSION As observed in Section 1.6, parabolic scaling kinetics are not invariably observed at high temperatures, and processes other than solid-state diffusion can control the reaction rate. For pure metals, this will be the case if either an interfacial process or gas phase mass transfer is slower than diffusion in the scale. The principles involved are discussed here with reference to the oxidation of iron and silicon at low oxygen potentials.
3.10.1 Oxidation of iron at low pO2 to form wu¨stite only Linear scaling kinetics have long been reported [103] for the oxidation of iron at low oxygen potentials where only Fe1dO forms. In order to obtain the low pO2 values required, gas mixtures of CO–CO2 or H2–H2O are used. Because the pO2 values are so low (1015–1013 atm at 1,0001C), molecular oxygen is far less abundant than the CO2 or H2O species. Given that the homogeneous gas phase dissociation reactions of both CO2 and H2O are rather slow at these temperatures, it is clear that the relevant species of importance are CO2 and H2O. In the case of CO2, the linear rate was found to depend on pCO2 and the total pressure of CO+CO2 mixtures [53, 104–110]. It was concluded that the rate was controlled by the reaction CO2 ðgÞ þ S!COðgÞ þ OjS
(3.133)
where, as before, S represents a surface adsorption site, and the net rate can be written Rate ¼ kf pCO2 yv kr pCO ð1 yv Þ
(3.134)
with kf and kr denoting the forward and reverse rate constants for reaction (3.133), and yv the fraction of surface sites empty. At the Fe/FeO equilibrium oxygen activity, ano , the net rate is zero. Substituting from the CO/CO2 equilibrium expression (2.15) p ano ¼ Kc CO2 (3.135) pCO into Equation (3.134), we obtain from the zero rate condition the general result kr ð1 yv Þ ¼ kf yv
ano Kc
enabling us to rewrite Equation (3.134) as ano Rate ¼ kf yv pCO2 pCO Kc
(3.136)
(3.137)
In gas mixtures containing only CO and CO2, the total pressure is PT ¼ pCO þ pCO2
(3.138)
128
and
Chapter 3 Oxidation of Pure Metals
an an Rate ¼ kf yv PT N CO2 1 þ o o Kc Kc
(3.139)
where N CO2 ¼ pCO2 =PT . As seen in Figure 3.26, the data of Pettit et al. [104] confirms the dependence on both total pressure and CO2 mol fraction, providing that yv is constant. A similar expression has been shown to apply for the linear kinetics of wu¨stite scaling in H2/H2O atmospheres [53]. Grabke [111] showed that the linear rate constant values in CO/CO2 atmospheres agreed with those obtained for surface exchange of oxygen on wu¨stite equilibrated with iron. As the wu¨stite scale thickens, diffusion through it slows until a thickness is reached at which diffusion becomes rate-controlling and the kinetics parabolic [53]. It has been noted [106, 108] that reaction at high pCO2 values produces scales of wu¨stite only, although the equilibrium pO2 values calculated from Equation (2.15) exceed the value for Fe3O4 formation. Clearly the supposed gas phase equilibrium is not in effect, and instead the local CO/CO2 ratio is set at the gas–scale boundary. As noted by Kofstad [27], parabolic scaling in H2/H2O gases is faster than in CO/CO2 gases of the same calculated equilibrium oxygen potential. Again this indicates that the scale–gas boundary conditions cannot be calculated from the CO–CO2 equilibrium. Part of the reason for this is the rapid rate at which oxygen is incorporated into the fast growing scale. As shown in Section 2.9, the oxidation of low-carbon steels in substoichiometric combustion gases leads to wu¨stite scale formation according to linear kinetics. Mass transfer calculations showed that gas phase mass transfer did not control the rate, but a surface reaction process did. A regime of behaviour was
Figure 3.26 Dependence of initial linear iron oxidation rate on composition and total pressure in CO/CO2 mixtures. Reprinted from Ref. [104] with permission from Elsevier.
129
3.10. Reactions Not Controlled by Solid-State Diffusion
0.24
k1 (mg cm-2 min-1)
0.22 0.2 0.18 0.16 0.14 0.12 0.1 8.8
8.9
9.1
9
9.2
9.3
9.4
9.5
102 pCO2 (atm)
Figure 3.27 Linear scaling rates for a low-carbon steel in simulated reheat furnace gas, T ¼ 1,1001C [112]. With kind permission from Springer Science and Business Media.
found for low carbon, low silicon steel [112] in which a small fractional change in oxidant partial pressure led to a relatively large change in rate, as shown in Figure 3.27. The expression in Equation (3.139) cannot be used because ðpCO2 þ pCO Þaconstant. Even Equation (3.138) is unreliable, because yv can vary, and a different treatment of the surface processes is to be preferred. The surface reactions are reformulated as CO2 ðgÞ þ S ¼ CO2 jS OjS þ COðgÞ
CO2 jS k2
OjS!OX o þS
(a) (b) (c)
in order to track vacant surface sites. Assuming a fixed concentration of surface sites M ¼ ½S þ ½OjS þ ½CO2 jS
(3.140)
defining Ka as the adsorption equilibrium constant for reaction (a), and using the rate constants ki specified in (b) and (c), we formulate the steady-state approximation for the surface concentration ½OjS : d½OjS ¼ 0 ¼ k1 ½CO2 jS k1 ½OjS pCO k2 ½OjS (3.141) dt It is found by substituting Ka pCO2 ½S for ½CO2 jS in Equations (3.140) and (3.141), followed by elimination of [S], that ½OjS ¼
k1 Ka MpCO2 Ka pCO2 ðk1 þ k1 pCO þ k2 Þ þ k1 pCO þ k2
A similar scheme can be proposed for reaction with H2O.
(3.142)
130
Chapter 3 Oxidation of Pure Metals
The rate of the oxygen uptake reaction (c) is proportional to [O|S], given by Equation (3.142). It is concluded then that k2 is not the dominant term in the numerator (because the reaction rate is not proportional to pCO2 ) and the reverse of reaction (b) must therefore be significant. Similarly, it can be concluded that the surface is not saturated with adsorbed CO2, as the rate does change with changing gas compositions, and therefore Ka pCO2 cannot be large. Proceeding on the assumption that, in fact, Ka pCO2 is small, Equation (3.142) is approximated as ½OjS ¼
k2 Ka MpCO2 k2 k1 pCO
and the oxidation rate expression becomes pCO2 kl ¼ a þ b pCO
(3.143)
(3.144)
where a and b are constants. This expression was found to fit the data well [112] with a ¼ 0.375 mg1 cm2 s atm and b ¼ 27.3 mg1 cm2 s. The large change in pCO had a much greater effect than did the very small one in pCO2 . Yet another regime of behaviour is found for iron oxidation in the case of exposure to dilute oxygen-bearing gases. Abuluwefa et al. [113] oxidized a lowcarbon, low-silicon steel in N2–O2 mixtures containing 1–16% O2, at temperatures of 1,000–1,2501C. They found initially linear rates, followed by steady-state parabolic kinetics. The linear rate constant was directly proportional to pO2 , and displayed a very small activation energy, 17 kJ mol1. The observed scaling rates were in good agreement at low pO2 values with predictions made for gas phase diffusion control using Equation (2.157), as shown in Figure 3.28. The small
Figure 3.28 Comparison of measured rates for carbon steel oxidation at 1,2001C with values calculated from Equation (2.157) [113]. With kind permission from Springer Science and Business Media.
3.10. Reactions Not Controlled by Solid-State Diffusion
131
activation energy is also consistent with such a mechanism. The difference between this situation and the combustion gas oxidation discussed above was the larger total oxidant partial pressures of the latter, leading to higher gaseous transfer rates.
3.10.2 Oxidation of silicon As seen earlier, scales of amorphous SiO2 are extremely slow growing and provide excellent protection. However, volatile species can form at elevated temperatures, causing wastage of silicon. Partial pressures of the various possible gas species are shown in Figure 3.29, where pSiO is seen to reach a maximum near the Si/SiO2 equilibrium oxygen partial pressure. At lower values of pO2 , SiO(g) forms and, in the absence of a protective silica scale, silicon is lost through this volatilization process. Wagner [58] analysed this phenomenon, which he called ‘‘active’’ oxidation, in terms of gas phase mass transfer. Because oxygen is consumed at the silicon surface, a diffusion gradient is established in the gas mixture near the surface (Figure 3.30). Thus the value at the surface, pnO2 , could be below the minimum necessary for solid SiO2 formation, even with a pO2 (gas) value above it. It is recognized that the initial value of pO2 (gas) necessary to passivate the silicon surface is therefore higher than the equilibrium Si/SiO2 value. The critical value can be calculated from a consideration of gas phase mass transfer. Most situations of practical interest involve the viscous flow regime, and Equations (2.157) and (2.158) apply. To use them, we need boundary values for both pO2 and pSiO , which are related via local equilibrium at the silicon–gas interface SiðsÞ þ 12O2 ðgÞ ¼ SiOðgÞ
(3.145)
pnSiO ¼ KðpnO2 Þ1=2
(3.146)
4 SiO2(s)
Si (s)
0 -4
Si (g)
log pSixOy
-8
SiO (g) SiO2(g)
-12 -16 -20 -24 -28 -44
Figure 3.29
-40
-36
-32
-28
-24 -20 log pO2
-16
-12
-8
-4
Equilibrium vapour pressures in the Si–O system at T ¼ 1,1271C.
0
132
Chapter 3 Oxidation of Pure Metals
SiO2 Gas
Si
) pO(gas 2
pO∗ 2 ∗ pSiO ∗ pSiO ≈0
δ
Figure 3.30 Filamentary SiO2 growth on silicon at high temperatures, showing gas phase partial pressure gradients.
From Equation (2.157) J O2
kO2 pO2 DO2 pO2 ¼ RT dO2 RT
(3.147a)
DSiO pSiO dSiO RT
(3.147b)
J SiO ¼
where d is the thickness of the boundary layer (Figure 3.30). The steady-state condition for SiO volatilization is J SiO ¼ 2J O2 (3.148) and therefore pO2 ¼ 12
dO2 DSiO p dSiO DO2 SiO
It can be shown [114] that for a laminar boundary layer dSiO DSiO 1=2
dO2 DO2 and Equation (3.149) becomes
DSiO 1=2 pO2 ¼ 12 pSiO DO2
(3.149)
(3.150)
(3.151)
Consider now the critical condition for protective SiO2 formation 1 1 2SiðsÞ þ 2SiO2 ðsÞ
¼ SiOðgÞ
(3.152)
3.11. The Value of Thermodynamic and Kinetic Analysis
133
Figure 3.31 Silica nanofibres formed by oxidation of silicon at 1,1301C in CO/CO2 [118]. With kind permission from Springer Science and Business Media. Eq
which defines an equilibrium value, pSiO . The critical value of pO2 is therefore given by DSiO 1=2 Eq pO2 ðcritÞ ¼ 12 pSiO (3.153) DO2 If the gas phase pO2 is higher, then protective SiO2 forms. If it is lower, pnSiO adjusts through Equation (3.146), and volatilization or active oxidation results. A similar analysis can be made for the molecular flow regime, using Equation (2.155). Its effectiveness in predicting the transition between active and protective oxidation has been verified experimentally [115–117]. Behaviour in the viscous flow regime is more complex, however, because when solid SiO2 does form, it can be in the form of a non-protective, fast growing deposit. Hinze and Graham [118] observed three regimes of behaviour in Ar–O2 mixtures at 1,2271C: linear weight loss at low pO2, fast linear weight gain at somewhat higher pO2, and protective oxidation at pO2 4 103 atm. The explanation for the intermediate regime was suggested to be formation of SiO2 whiskers growing from the silicon surface. The outer tips of these whiskers acted as growth sites, redefining the diffusion distance dSiO (see Figure 3.30) and explaining the rapid reaction through an accelerated SiO flux (3.147b). Improved imaging capabilities which have become available since that work have allowed the production of Figure 3.31. A highly ordered structure of SiO2 is seen to develop [119] in confirmation of the Hinze and Graham proposal.
3.11. THE VALUE OF THERMODYNAMIC AND KINETIC ANALYSIS In this chapter we have explored the application of thermodynamic and kinetic analysis techniques to the simplest high temperature oxidation situation: reaction
134
Chapter 3 Oxidation of Pure Metals
of a pure metal with a single oxidant. It is clear that the usual hypothesis of local equilibrium at interfaces between contacting phases is commonly correct. Thus the oxide (or sulfide, etc) predicted to be at equilibrium with the gas is usually found at the scale surface; the oxide shown by the phase diagram to equilibrate with the metal is found to grow in contact with the metal. When this is not so, it can be concluded that solid-state diffusion does not control the reaction rate, and that instead either a gas phase process or a surface reaction is rate controlling. Calculation of gas phase mass transfer rates has been found to be quantitatively successful in determining when these processes are capable of controlling the rate. More importantly, the model of local equilibrium within the growing oxide scale is also successful. The state of a scale interior is well described as a series of microscopic local equilibrium regions, each incrementally different (in the growth direction) from adjacent regions, as shown schematically in Figure 3.32. This allows the use of the diffusion path description and justifies the application of irreversible thermodynamics to the diffusion problem. In a very large number of cases, scale growth is controlled by solid-state diffusion. The Wagner treatment of this situation is found to succeed when adequate information on oxide defect properties is available. This success provides proof that lattice diffusion of point defect species can support scale growth in a number of cases. It leads to very useful predictions as to how scaling rate will vary with oxide type (degree of non-stoichiometry and lattice species mobility) and with oxidant activity and temperature. It also succeeds in predicting qualitatively the effect of dilute oxide solute impurities on scaling rates. The value of the Wagner treatment is less obvious in the case of slow-growing oxides such as Cr2O3 and Al2O3. Our knowledge of the defect properties of these oxides, and the effect of oxygen potential upon them is very limited, and testing the Wagner model is in this sense difficult. Morever, as will be discussed in M
MO
O2(g)
aO″ aO aO′
Figure 3.32 The local equilibrium description: a series of very small regions each of which can be approximated as homogeneous.
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Chapter 7, the diffusion properties of these oxides are often dominated by grain boundary transport. As seen in Section 3.9, grain boundary diffusion can lead to oxidation rates very different from those predicted by Wagner, and even to different kinetics when microstructural change occurs with time. Nonetheless, the mechanism is still one of diffusion, and the basic concepts underlying Wagner’s theory still provide insight and a basis for experimental design. To obtain value from the theory, however, it is essential to add to it a detailed description of microstructural phenomena. Arriving at a definitive version of such a description is a continuing pre-occupation in high temperature corrosion research. For this reason, microstructural evolution receives considerable attention in the remainder of this book.
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T. Norby, Advan. Ceram., 23, 107 (1987). T. Norby, J. Phys. IV, 3, 99 (1993). X.G. Zheng and D.J. Young, Oxid. Met., 42, 163 (1994). W.J. Quadakkers, J.F. Norton, S. Canetoni, K. Schuster and A. Gil, Proc. 3rd Conf. Microscopy of Oxidation, p. 609 (1996). G. Valensi, Rev. Metall., 45, 205 (1948). C. Wagner, Acta Met., 17, 99 (1969). G.J. Yurek, J.P. Hirth and R.A. Rapp, Oxid. Met., 8, 265 (1976). F. Gesmundo and F. Viani, Corros. Sci., 18, 217, 231 (1978). H.S. Hsu, Oxid. Met., 26, 315 (1986). G. Wang, B. Gleeson and D.L. Douglass, Oxid. Met., 31, 415 (1989). G. Garnaud and R.A. Rapp, Oxid. Met., 11, 193 (1977). S. Mrowec and T. Werber, Gas Corrosion of Metals, US National Bureau of Standards, Nat. Center Sci. Tech. Economic Information, Warsaw (1978). H. Rickert, Z. Phys. Chem. N.F., 21, 432 (1959). H. Rickert and C. Wagner, Z. Phys. Chem. N.F., 31, 32 (1961). G.B. Gibbs, Oxid. Met., 7, 173 (1973). N. Birks and H. Rickert, J. Inst. Met., 91, 308 (1962). M.J. Graham and D. Caplan, J. Electrochem. Soc., 120, 843 (1972). K. Fischbeck, L. Neundeubel and F. Salzer, Z. Elektrochem., 40, 517 (1934). F. Pettit, R. Yinger and J.B. Wagner, Jr., Acta Metall., 8, 617 (1960). K. Hedden and G. Lehmann, Arch. Eisenhu¨ttenwes., 35, 839 (1964). W.W. Smeltzer, Acta Metall., 8, 377 (1960). H.J. Grabke, Ber. Bunsenges. Phys. Chem., 69, 48 (1965). P. Kofstad and R. Bredsen, Proc. 9th Int. Congr. on Metallic Corros. National Research Council of Canada, Ottawa, June (1984), Vol. 1. p. 12. W.W. Smeltzer and A.G. Goursat, Rev. High Temp. Mater., 1, 351 (1973). K. Hauffe and H. Pfeiffer, Z. Metallkunde, 44, 27 (1953). H.J. Grabke, Proc. 3rd Int. Congr. Catalysis, Amsterdam (1964), Vol. 2, p. 928. V.H.J. Lee, B. Gleeson and D.J. Young, Oxid. Met., 63, 15 (2005). H. Abuluwefa, R.I.L. Guthrie and F. Ajersch, Oxid. Met., 46, 423 (1996). C. Wagner, Corros. Sci., 5, 751 (1965). E.A. Gulfransen and S.A. Jansson, Oxid. Met., 4, 181 (1972). J.E. Antill and J.B. Warburton, Corros. Sci., 11, 337 (1971). C. Gelain, A. Cassuto and P. De Goff, Oxid. Met., 3, 139 (1971). J.W. Hinze and H.C. Graham, J. Electrochem. Soc., 123, 1066 (1986). P. Carter, B. Gleeson and D.J. Young, Oxid. Met., 56, 375 (2001).
CHAPT ER
4 Mixed Gas Corrosion of Pure Metals
Contents
4.1. Introduction 4.2. Selected Experimental Findings 4.3. Phase Diagrams and Diffusion Paths 4.3.1 Scaling of chromium in oxidizing–nitriding and oxidizing–carburizing gases 4.3.2 Scaling of chromium in oxidizing–sulfidizing–carburizing gases 4.3.3 Scaling of iron in oxidizing–sulfidizing gases 4.3.4 Scaling of nickel in oxidizing–sulfidizing gases 4.4. Scale–Gas Interactions 4.4.1 Identity of reactant species 4.4.2 Rate determining processes in SO2 reactions 4.4.3 Production of metastable sulfide 4.4.4 Independent oxide and sulfide growth in SO2 4.5. Transport Processes in Mixed Scales 4.5.1 Effect of pre-oxidation on reaction with sulfidizing– oxidizing gases 4.5.2 Solid-state diffusion of sulfur 4.5.3 Gas diffusion through scales 4.5.4 Scale penetration by multiple gas species 4.5.5 Metal transport processes 4.6. Predicting the Outcome of Mixed Gas Reactions References
139 140 147 147 150 150 151 154 154 156 159 163 168 169 172 172 174 175 175 181
4.1. INTRODUCTION Atmospheres encountered in practice are very rarely constituted of a single oxidant. Even in the case of air, both oxygen and nitrogen can react with a base metal such as chromium. Examples of more complex gases are frequently encountered. A common example is provided by combustion gases which invariably contain carbonaceous species, usually water vapour and commonly sulfur species deriving from the impurities present in most fossil fuels. Another example is the production of synthesis gas. The two processes used to produce hydrogen on a large scale are steam reforming CH4 þ H2 O ¼ CO þ 3H2
(4.1) 139
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Chapter 4 Mixed Gas Corrosion of Pure Metals
and coal gasification C þ H2 O ¼ CO þ H2
(4.2)
Clearly both processes involve handling gases which, at the necessarily low oxygen potentials, are likely to be carburizing as well as oxidizing. In general, it is necessary to consider the possibility of more than one oxidant reacting with the metal. After a brief review of selected experimental findings, the use of phase diagrams and diffusion paths to arrive at an understanding of scale constitutions is examined, and surface processes are analysed. The mechanisms of mass transport are then considered in a discussion of scaling rates. Much of the literature in the area of mixed gas corrosion is of an applied nature, involving complex engineering alloys and simulated, multicomponent process gases. Although of obvious practical utility, this literature provides little in the way of fundamental understanding. Fortunately, a substantial number of model studies involving pure metals are also available, particularly for sulfidizing–oxidizing gases [1–7]. The behaviour of a number of metals in gases containing both oxygen and sulfur was studied rather intensively in the 1970s and 1980s, in the aftermath of sudden oil price increases, when alternative routes to liquid fuels were being sought. The matter is becoming of renewed interest, as oil prices rise again, and the combustion of high sulfur content coals for power generation increases. Attention is focused here on the behaviour of chromium, iron and nickel in mixed gases.
4.2. SELECTED EXPERIMENTAL FINDINGS Key questions in the case of mixed gas corrosion concern whether or not reaction products other than oxide form, and to what extent they are harmful. Iron exposed to SO2 or SO2–Ar can form a lamellar mixture of sulfide plus oxide [9, 10] or a two-phase mixture overlaid by oxide alone [8, 9, 11–14] as shown in Figure 4.1. Layered structures as shown in Figure 4.2 can be formed on nickel [8, 15–17] and sometimes on cobalt [18, 19] although results reported for cobalt are not all in agreement. More complex gas mixtures of CO/CO2/SO2/N2 have been used to simulate aspects of combustion gas corrosion, and to permit independent control of pS2 and pO2 . The earlier literature concerns reaction in pure SO2 or in diluted SO2/Ar mixtures. In these gases the equilibrium SO2 ¼ 12S2 þ O2
(4.3)
requires that pS2 ð1=2ÞpO2 , if SO3 formation can be neglected. Values of DG (4.3) are given in Table 2.1. In the CO/CO2/SO2/N2 mixtures, Equation (4.3) still holds, but the equilibrium CO2 ¼ CO þ 12O2
(4.4)
4.2. Selected Experimental Findings
141
Figure 4.1 Oxide–sulfide scales grown on iron in different SO2/CO2/CO mixtures at 8001C. Grey phase is oxide, light phase sulfide.
Figure 4.2 Layered sulfide–oxide scale grown on nickel in SO2 at 6001C [33]. With kind permission from Springer Science and Business Media.
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can be used to control pO2 , and the value of pS2 is then given by 1=2
pS2 ¼ K4:3 pSO2 =pO2
(4.5)
Additional species such as COS and CS2 can be important under some conditions. In these cases equilibrium calculations are best carried out using numerical free energy minimization procedures, for example those in software packages such as ThermoCalc or FACTSage. A practical difficulty arises from the rather slow rates of the homogeneous gas phase reactions involved, and it is essential that laboratory gas mixtures be brought to equilibrium by passing them through a heated catalyst bed (such as alumina-supported platinum) before contacting the experimental specimen. The effect is illustrated in Figure 4.3 for manganese exposed at 8001C to a gas mixture of inlet composition 23-CO2, 45-CO, 22-SO2, 10-N2 vol.%. The calculated equilibrium composition contained pS2 ¼ 8:6 106 atm and pO2 ¼ 5:7 1016 atm. As seen in the figure, the catalysed gas produced a scale of MnO plus MnS, but the non-catalysed gas led to a scale which evolved with time from a two-phase mixture to almost single-phase MnO. The formation and behaviour of Cr2O3 in mixed gases have been the subject of many research programs because of the protective nature of the Cr2O3 scale, upon which many technologically important alloys depend. In the presence of secondary oxidants, chromia scales have been found to behave in a diversity of ways. For example, a sublayer product of Cr2N has often been found growing underneath an outer Cr2O3 scale on pure chromium after heating in air [21–26]. Pre-oxidation for 2.5 h in oxygen (pO2 ¼ 40 kPa) was found not to stop the
Figure 4.3 Scales grown on manganese in CO2/CO/SO2/N2 mixture at 8001C (light phase sulfide, grey phase oxide) (a) gas passed over Pt catalyst, (b) gas uncatalysed [20]. At equilibrium, MnS is stable with respect to MnO. (With kind permission from Springer Science and Business Media).
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4.2. Selected Experimental Findings
Table 4.1 Gas no. 1 2 3 4 5
Carburizing–oxidizing–nitriding gas mixtures reacted with chromium [27] Starting gas composition (vol.%) CO 96.6 62.2 49.7 12.4
CO2
H2
H 2O
Reaction potentials (9001C) N2
P(O2) (atm)
P(N2) (atm)
19
3.40 2.20 17.6 44.0 56.5
2.30
35.6 32.7 43.6 41.2
1 10 1 1019 1 1017 1 1015 1 1019
0.36 0.33 0.44 0.41
ac 0.5 0.5 0.04 0.001
nitridation of chromium during subsequent exposure to nitrogen (pN2 ¼ 40 kPa), indicating that the previously established oxide film does not constitute an effective barrier to nitrogen ingress. Obviously the oxide scale formed under these conditions was not impermeable to gas penetration, and nitrogen from the air had reached the chromium. When exposed at 9001C to a CO/CO2 mixture (Table 4.1), chromium is found [27] to develop a two-layered scale (Figure 4.4) consisting of a Cr2O3 outer layer and an inner layer of Cr7C3 containing finely distributed oxide particles. Adding N2 to CO–CO2 results in a three-layered scale (Figure 4.4). The outer layer is again pure Cr2O3. The intermediate layer, now thicker than the chromia, is a mixture of Cr7C3, oxide and a small amount of Cr2N. The innermost layer is pure, compact Cr2N. In a gas mixture of H2/H2O/N2 corresponding to the same equilibrium pO2 value as the CO/CO2/N2 gas, and a closely similar value of pN2 , chromium grows a single layer of pure Cr2O3, and no nitride develops. Addition of SO2 to the gas (Table 4.2) leads to sulfide formation and suppresses nitridation [28]. The resulting scale is shown in Figure 4.4 to be multilayered. The outermost layer is principally Cr5S6 with a Cr2O3 content varying from 1 wt% at the scale–gas interface to 12 wt% near its inner boundary. This two-phase mixture consists of a fibrous structure aligned approximately normal to the metal substrate surface. The underlying scale region is highly porous. Its outer region is largely oxide with a small sulfur content, but its inner region is principally Cr5S6 with minor amounts of Cr2O3 and Cr7C3. The innermost layer is mainly Cr7C3 and Cr2O3 with very little sulfide. Lower pSO2 values have less effect [28]. The gas composition represented by point B in Figure 4.10 produces a thick compact scale of Cr2O3 containing about 24 wt% Cr5S6 as finely dispersed particles. Gas C (Figure 4.10) produces an outer, buckled layer of Cr2O3 containing 0.5 wt% S. A thin sublayer made up of Cr7C3 with oxide dispersions also forms adjacent to the metal. Rather different observations have been reported for reaction of chromium in pure SO2. An early investigation [29] reported the simultaneous growth of CrS and Cr2O3, whereas later work [30] using the same gas led to the finding that only oxide formed, containing 1 wt% S. However, scaling rates in SO2 were found to be 2–3 orders of magnitude faster than in oxygen at 800–1,0001C. The reaction of chromium with H2/H2O/H2S gases at 9001C has also been studied [31]. These gases were such that Cr2O3 was stable with respect to sulfides, but two-phase
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Figure 4.4 Scales grown on chromium exposed at 9001C to (a) CO/CO2 and (b) CO/CO2/N2 [27] (with kind permission from Springer Science and Business Media); (c) SO2/CO2/CO/N2 (reprinted from Ref. [28] with permission from Elsevier).
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4.2. Selected Experimental Findings
Table 4.2 Gas
Sulfur-bearing gas mixtures reacted with chromium [28] Input gas composition (vol.%) CO
A B C
74.7 62.2 74.6
CO2
2.56 2.18 2.63
N2
22.7 35.6 22.8
SO2
0.039 0.010 0.0039
Reaction potentials (atm) at 9001C P(O2)
P(S2) 19
1 10 1 1019 1 1019
7
3 10 3 108 3 109
P(N2)
ac
0.23 0.36 0.23
0.6 0.5 0.6
Figure 4.5 Initial linear and subsequent parabolic kinetics: Fe reacted with dilute Ar2SO2 at T ¼ 8001C [9]. Published with permission of Taylor and Francis Ltd., http:// www.informaworld.com.
oxide-plus-sulfide scales formed at low H2O/H2S ratios. At intermediate ratios, the two-phase product was overgrown by oxide, and at high ratios only oxide was formed. Scaling kinetics and rates can vary considerably as the nature of the reaction product changes with gas composition. When iron is reacted with dilute Ar–SO2 mixtures, an initial period of linear reaction is followed by parabolic kinetics as shown in Figure 4.5. Flatley and Birks [9] demonstrated that the linear rate constant was proportional to both pSO2 and the gas flow rate, and concluded that gas phase diffusion of SO2 was rate controlling in this regime. The reaction product was a lamellar oxide–sulfide mixture, like that shown in Figure 1a. The subsequent parabolic stage of reaction reflected the onset of solid-state diffusion control in the thicker scale. At low pSO2 values this scale consisted of a coarse FeO+FeS outer
146
Chapter 4 Mixed Gas Corrosion of Pure Metals
layer on top of the first formed lamellar structure. Reaction rates were reported to be faster than those for the oxidation of iron in pure oxygen. At high pSO2 values, the initially formed FeO+FeS structure was overgrown by pure oxide, and the parabolic rate constant was equal to that for the oxidation of iron in pure O2 [10]. The same result was found for reaction in CO/CO2/SO2/N2 gases [20]. Chromium scaling kinetics in the gas mixtures of Tables 4.1 and 4.2 are shown in Figures 4.6 and 4.7. Formation of additional carbide and nitride layers augments the rate, and sulfide formation increases the rate by up to an order of magnitude, depending on the sulfur partial pressure.
Figure 4.6 Chromium scaling kinetics at 9001C in gases of Table 4.1 [27]. With kind permission from Springer Science and Business Media.
Figure 4.7 Chromium scaling kinetics at 9001C in gases of Table 4.2 [32]. Published with permission from Trans Tech Publications Ltd.
4.3. Phase Diagrams and Diffusion Paths
147
4.3. PHASE DIAGRAMS AND DIFFUSION PATHS Thermochemical diagrams of the sort described in Section 2.2 provide a useful basis for analysing and rationalizing the morphologies of scales grown in dual oxidant gases. However, as we now discuss, they seldom provide a means of predicting the outcome of a particular reaction. The essence of this approach is simple: calculate the partial pressures of the two oxidants, locate the co-ordinates on the thermochemical diagram (Section 2.2) and thereby define the reaction product. Even if this calculation is successful, it provides no information as to which compounds will exist within the scale interior, where the oxidant activities are not the same as in the gas. More seriously, the prediction often fails even at the scale–gas interface, where one might hope to predict the equilibrium phase, as is done in the case of a single oxidant (Section 3.2). One reason for such a failure was illustrated in Figure 4.3. In the absence of a catalyst, the gas phase was far removed from equilibrium and a completely different reaction product resulted. Even in pure SO2 this can be a problem because the additional reaction SO2 þ 12O2 ¼ SO3
(4.6)
can, depending on temperature, affect the value of pO2 by orders of magnitude [30]. Unfortunately, much of the early work on reaction with pure or diluted SO2 failed to employ a catalyst for the SO3 reaction. If the scaling reaction is rapid and the reactant species is dilute or at low pressure, then it will be depleted from the gas at the scale surface. In the absence of a catalyst at this surface, the gas composition will be different from that of the bulk gas. Furthermore, the kinetics of the solid–gas reactions can lead to changes in the relative oxidant activities, a point which is discussed in Section 4.2 with reference to oxidation–sulfidation of nickel, cobalt and iron. We consider first the reactions of chromium with oxygen–carbon and oxygen– nitrogen gases, where scaling rates are slow and the complications described earlier should be avoided.
4.3.1 Scaling of chromium in oxidizing–nitriding and oxidizing–carburizing gases The Cr–O–C and Cr–O–N phase diagrams are shown in Figure 4.8, with the equilibrium oxidant potentials for the gases in Table 4.1 marked. The carbon activity, aC, is defined through Equation (2.48), with pure solid graphite as reference state. The oxide is much more stable than both carbide and nitride, and is predicted to form in contact with these gases. As seen in Figure 4.4, the prediction is borne out. Unfortunately, however, the protection expected of a chromia scale is not realized in the CO/CO2-based gases, or even in air, as carbides and/or nitrides form beneath the oxide. As will be shown subsequently, the inner carbide and nitride layers continue to grow as the chromia layer thickens, showing that carbon and nitrogen are diffusing through the oxide.
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Figure 4.8 Thermochemical diagrams for Cr–O–C and Cr–O–N at 9001C. Points correspond to equilibrium for gases in Table 4.1. Dashed lines show diffusion paths for oxide–carbide and oxide–nitride scales. Dotted line represents equilibrium C þ 21 O2 ¼ CO at fixed pCO.
A schematic diffusion path for the oxide over nitride layered structure grown in air [21–25] is shown in Figure 4.8, where the Cr2O3/Cr2N phase boundary is seen to correspond to the interface between the two scale layers. A diffusion path for the oxide over carbide+oxide layered structure developed in CO/CO2/Ar is shown in Figure 4.8. The transit of the path through the inner, two-phase layer is represented by the line along the carbide– oxide phase boundary. Although the activity ratio, ao/ac, is defined at this boundary (assuming pure, stoichiometric compounds), the individual values are
4.3. Phase Diagrams and Diffusion Paths
149
not. Put another way, the three-component system has a degree of freedom in the two-phase region, and the activity gradients necessary for mass transfer and scale growth can and do develop. The compositions of all the above gases were such that chromium oxide was stable with respect to chromium carbide and nitride. However, the gas phase carbon and nitrogen activities were high enough to react with chromium in the absence of oxygen. The observed sequence of reaction products in the scales is in accord with thermodynamic prediction. Thus, at the scale surface where the chromium activity is lowest, the most stable product, oxide, is formed. At the scale base where the chromium activity is highest and oxygen activity at a minimum, the least stable product, nitride, is located (when it forms). The intermediate stability phase Cr7C3 is found in the middle regions of the scale. The formation of the lower stability phases implies an ability of the secondary oxidants to penetrate the Cr2O3. Schematic activity profiles for these cases are shown in Figure 4.9. The thermodynamic analysis leaves many questions unanswered. Most obviously, the reason for development of an inner Cr2N layer in air and CO/CO2/N2 but not in H2/H2O/N2 gas is not revealed. The ao/aN values of the
aC O CrCr 7O73+3 +Cr O Cr 2O23 3
Cr
Cr2O3
aO
aCr (a)
aC
aN
aO Cr
Cr2O3 Cr2N Cr7C3+Cr2O3 +Cr2N
aCr
(b)
Figure 4.9 Schematic activity profiles representing the penetration of (a) carbon and (b) nitrogen and carbon through a Cr2O3 layer.
150
Chapter 4 Mixed Gas Corrosion of Pure Metals
two are almost identical and the thermodynamic driving forces for oxide and nitride formation are the same in each gas. The difference is one of reaction kinetics. This raises the more general questions as to how the secondary oxidants can penetrate the oxide layer, and what the mass transfer processes are in the inner layers. These questions are considered in Section 4.4.
4.3.2 Scaling of chromium in oxidizing–sulfidizing–carburizing gases The Cr–O–S phase diagram is shown in Figure 4.10. In all the gas mixtures shown, the oxide is stable with respect to sulfide. The appearance of chromium sulfide at the scale–gas interface (Figure 4.4c) thus demonstrates that the scale surface was not at equilibrium with the bulk gas composition. Carbide grew beneath the oxide developed in the gas, just as in the sulfur-free gases. However, no nitride ever formed in the SO2-containing gases, although it did in sulfur-free CO/CO2/N2. Clearly this complex pattern of behaviour cannot be predicted from the thermochemical diagrams.
4.3.3 Scaling of iron in oxidizing–sulfidizing gases The Fe–S–O phase diagram is shown in Figure 4.11, with a number of different gas compositions marked on it. These compositions were controlled using CO/CO2/SO2/N2 mixtures. In the more commonly reported experiments, a gas of pure SO2 or SO2 diluted with N2 or Ar is used. In this case, the sulfur and oxygen pressures are given by the equilibrium (4.3) plus the stoichiometric
Figure 4.10 Thermochemical diagram for Cr2O2S at 9001C. Dotted line shows diffusion path for sulfide forming under oxide.
4.3. Phase Diagrams and Diffusion Paths
151
Figure 4.11 Thermochemical diagram for Fe2O2S at 8001C [48]. Numbered points represent equilibrium compositions for reaction gases. Dashed line represents pSO2 ¼ 7:9 102 atm. With kind permission from Springer Science and Business Media.
requirement pS2 ¼ ð1=2ÞpO2 . Values corresponding to pSO2 ¼ 7:9 102 atm are marked in Figure 4.11. The Fe–S–O diagram reveals that scales in equilibrium with pure SO2 at 1 atm should consist of oxide only at the scale–gas interface. This prediction is in fact borne out [9, 10], at least in the long term, when the reaction products had the appearance of the scale in Figure 4.1b. However, scales grown in diluted SO2 varied in their phase constitution with pSO2 . At pSO2 ¼ 7:9 102 atm, the scale had the same appearance as at pSO2 ¼ 1 atm. At lower pSO2 values, scales were two-phase lamellar mixtures of oxide and sulfide [9, 14]. Gases corresponding to points 7 and 8 (pSO2 ¼ 2 104 atm) corroded iron to produce the scale shown in Figure 4.1a. Evidently local equilibrium at the scale–gas interface might be achieved at high pSO2 values, but not at low values, where sulfide apparently can exist despite the fact it is in contact with a gas in which the reaction FeS þ 12O2 ¼ FeO þ 12S2
(4.7)
is thermodynamically favoured. Furthermore, sulfide has been found to form in gases 7 and 9, which contain equilibrium pS2 values below the minimum necessary for FeS formation in the absence of oxygen. Similar difficulties have been found in the much-studied Ni–S–O system, which is now briefly reviewed.
4.3.4 Scaling of nickel in oxidizing–sulfidizing gases The Ni–O–S phase diagram is shown in Figure 4.12 for T ¼ 6001C. The point labelled X represents the equilibrium oxygen and sulfur potentials in pure SO2 at
152
Chapter 4 Mixed Gas Corrosion of Pure Metals
Figure 4.12 Thermochemical diagram for Ni2O2S at 6001C. Point X represents equilibrium in pure SO2 at 1 atm. Diffusion path for oxide+sulfide layer over Ni3S2 layer.
1 atm. It is clear that the only nickel reaction product stable in contact with this gas is the oxide. However, the experimental findings do not conform with this prediction. The reaction of nickel with pure SO2 in the temperature range 500–1,1001C almost always produces a scale consisting of an inner layer of singlephase sulfide surmounted by a thick layer of duplex NiO+nickel sulfide mixture [8, 15–17, 33–36]. The inner sulfide is the one stable in equilibrium with nickel: Ni3S2 for To5331C, Ni37dS2 for 533oTo6371C and Ni–S liquid at higher temperatures. The phase Ni37dS2 ranges in stoichiometry from metal deficit to metal excess (Figure 3.4a). The sulfide in the duplex layer formed at about 6001C has been identified as Ni37dS2 [17, 34], but that found in scales grown at higher temperatures has not been directly identified. Scales grown in SO2/argon mixtures [17, 34, 35] had the same morphologies. The only exceptions to this pattern are the observations of a scale of NiO only at 1,0001C and pSO2 ¼ 0:01 atm [16], and at the same temperature in an SO2-50% Ar mixture [38]. The detailed morphology of the duplex layer varies with temperature. The concentration of sulfur in the inner part of this layer is very low at To5251C [37],
4.3. Phase Diagrams and Diffusion Paths
153
while at around 6001C it is lower than in the outer part of the layer [17, 33]. At these lower temperatures, the sulfide precipitates in the outer part of the duplex layer are large and irregular [15, 37] and because of their shape (Figure 4.2) are described as ‘‘flames’’. As the temperature increases, the flames are replaced by a finer distribution. A duplex layer grown at 6031C was found to have a high electrical conductivity at room temperature, suggesting the presence of a continuous path made up of the metallic conductor Ni37dS2 within the oxide matrix [17]. At higher temperatures, 700–8001C, the duplex scale morphology is quite complex, reflecting a tendency for the liquid sulfide to be extruded from the inner region to form protrusions at the scale–gas interface where they are subsequently oxidized [16, 33]. At still higher temperatures, the overall sulfur content of the duplex layer is much reduced and the sulfide particles are coarser and more isolated [15, 33, 37]. The kinetics of nickel reaction with pure and diluted SO2 are correspondingly complex, as shown in Figure 4.13. Rapid rates correspond to the existence of a continuous sulfide network in the two-phase layer, and slow kinetics are observed when the sulfide content of the layer becomes small. The high diffusion coefficient of the sulfide explains these observations [17]: an interconnected sulfide network provides a continuous rapid mass transfer medium, whereas a discontinuous distribution contributes much less to mass transfer. Reaction kinetics in the temperature range 600–8001C, where sulfide-rich layers grow, have been described as linear [16, 37], protective [15] or irregular [36, 39]. Linear rate constants were reported [16, 34] to be approximately proportional to pSO2 . In SO2/Ar mixtures, the kinetics at 6031C showed an initial linear stage, a second stage of increasing rate, and were finally parabolic [17]. Complex kinetics in SO2/Ar were also reported by Wootton and Birks [37].
Figure 4.13 Scaling kinetics for Ni exposed to SO2 [33]. With kind permission from Springer Science and Business Media.
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Chapter 4 Mixed Gas Corrosion of Pure Metals
Reaction of nickel in SO2/O2 gas mixtures conducted at To6371C to avoid liquid sulfide formation, led to closely similar structures: an inner layer of singlephase sulfide, and an outer oxide-plus-sulfide mixed layer [8, 39–45] except when the gas was strongly oxidizing, and only a small amount of sulfide formed at the scale–metal interface [8, 44]. After extended periods of reaction, the scale layers started to separate, and the outer layer was converted to NiO. When separation became extensive, and nickel mass transfer was interrupted, the reaction essentially stopped and a thin outermost layer of NiSO4 was formed [43]. The SO2/O2 reaction with nickel follows kinetics which are initially linear and then parabolic until the onset of scale separation [43]. Other investigators [37, 40, 41] have described the kinetics as approximately parabolic. For so long as the duplex scale is produced, its growth rate is independent of pO2 and pSO2 , but decreases as pSO3 increases. A schematic diffusion path is shown in Figure 4.12 for a duplex oxide-plussulfide outer scale layer and Ni37dS2 inner layer. Although showing clearly that the phase diagram provides no predictive capacity in dealing with the Ni+SO2 reaction, it serves to identify the problems confronting us in understanding the scale morphology. Firstly, what are the scale–gas interaction processes which apparently permit sulfide to exist in contact with a gas which is oxidizing to sulfide? Secondly, what are the processes within the scale which constrain the diffusion path to lie along the oxide–sulfide phase boundary? Thirdly, how does the inner sulfide layer form? We consider the scale–gas interactions first.
4.4. SCALE–GAS INTERACTIONS It can usually be assumed that the bulk gas has been catalysed and brought to equilibrium with respect to the otherwise slow reactions (4.3) and (4.6). However, this does not mean that the gas has its equilibrium composition at the scale surface. If a minority species such as SO3 or O2 is a reactant, then it will be consumed at the sample surface. In the absence of a catalyst at this location, the SO3 or O2 cannot be replenished from the gas phase, and its activity is consequently lower than the equilibrium value. The question of just what are the reactant species is seen to be important.
4.4.1 Identity of reactant species The idea of slow transport within the gas coupled with rapid selective removal of some gas species into the scale leading to a different gas composition at the interface was proposed by Birks [9, 46] to explain the formation of both oxide and sulfide at the scale surface under conditions where the sulfide is not stable. It was proposed that reaction of metal at a high activity reduced the local oxygen activity in the gas to the equilibrium value with respect to oxide formation, a very low value. As a result, the sulfur activity would rise through readjustment to maintain the SO2 dissociation equilibrium (4.3), thereby stabilizing the sulfide. Although qualitatively appealing, the mechanism fails quantitatively.
4.4. Scale–Gas Interactions
155
The low pO2 values proposed (about 1019 atm for the Fe–FeO equilibrium at 8001C) are simply too small to support a measurable oxidation rate. The concept of gas phase depletion is nonetheless correct, and likely to succeed when applied to less dilute species. Consider the situation in pure SO2 and dilute Ar–SO2. Equilibrium values of pS2 and pO2 at 8001C, calculated from Equation (4.5), neglecting SO3 formation, are shown in Table 4.3. Fluxes of the various gas species to a sample surface can be calculated for the viscous flow regime (Section 2.9). Taking representative values for laboratory experiments of sample length 1 cm and gas flow rate 0.5 m/min, we calculate the molecular fluxes shown in Table 4.3. A comparison of these values with measured weight uptake rates during corrosion in SO2 gases is revealing. The weight uptake rates in Table 4.4 correspond to two-phase oxide and sulfide growth on nickel (Figure 4.2), chromium (Figure 4.4) and cobalt, and to single-phase oxide outer layer growth on iron (Figure 4.1b). In all two-phase cases, the measured rates far exceed the calculated fluxes of molecular oxygen and/or sulfur. It could be concluded on this basis that the reactant species was SO2 and not oxygen or sulfur. However, it might be argued that catalysis of reaction (4.3) by the scale surface itself, if it occurred, could rapidly replenish gaseous sulfur and oxygen which could, therefore, act as the real reactants. The question has been resolved experimentally in the cases of iron and manganese. Gas mixtures of CO/CO2/SO2/N2 have been used [20, 48, 49] to independently control two of the three variables of interact (pS2 , pO2 and pSO2 ), the third being set by the equilibrium (4.5). Referring to Figure 4.11, it is seen that gases 4–6, 9 and 10 all fall very close to the dashed line corresponding to pSO2 ¼ 0:079 atm. Reaction of iron with all of these catalysed gases led to the same Table 4.3
Partial pressures and mass transfer fluxes in SO2 gases (8001C)
Gas
pSO2
pO2
pS2
SO2 1 7.3 1010 3.6 1010 Ar-7.9%SO2 0.079 1.3 1010 6.5 1011
Table 4.4
a
JSO2
JO2
JS2
3.2 102 2.5 103
6 1012 5 1012 1 1012 1 1013
Scaling rates in SO2 at 8001C
Metal
pSO2 (atm)
Scale surface
Ni Co Fe
1 1 0.2 0.01 0.04
Oxide+sulfide (l) Linear Oxide+sulfide Parabolic Oxide Parabolic Oxide+sulfide Linear Oxide+sulfide Parabolic
Cra
Fluxes (g cm2 min1)
Equilibrium composition (atm)
In CO/CO2/SO2.
Kinetics
Weight uptake rate after 1 h (mg cm2 min1)
Reference
1.0 0.2 0.015 1.5 0.6
[31] [47] [9] [9] [28]
156
Chapter 4 Mixed Gas Corrosion of Pure Metals
results: an initially two-phase oxide and sulfide reaction product which was overgrown with oxide at extended times. This evolution of structure is illustrated in Figure 4.14. Reaction kinetics were in all cases parabolic after an initial period of more rapid reaction. Typical data are shown in Figure 4.15. At this temperature and pSO2 value, the kinetics of reaction with catalysed gas became parabolic after about 36 min, when the outer oxide layer was established. The parabolic rate constants corresponding to oxide growth were 3.270.7 mg2 cm4 min1 for all gases. Thus all gases produced the same reaction products at the same rate, despite the fact that pS2 varied from 1010 to 103 atm and pO2 from 1013 to 1011 atm. It is therefore concluded that SO2 was the reactant. Further support for this conclusion is provided by the results of reaction with gases 1, 5 and 8. All these involve essentially the same value of pS2 ¼ 106 atm, but vastly different levels of pSO2 and pO2 . Experiment 1 led to a complex, fourlayered sulfide and oxide scale which grew according to slow parabolic kinetics. Experiment 8 led to a lamellar two-phase scale (Figure 4.1a) which grew according to rapid parabolic kinetics with kp ¼ 7.8 mg2 cm4 min1. This variation in product morphology and growth rate demonstrates that the gaseous sulfur activity was not the controlling factor. Similarly, experiments 6 and 7 were carried out at the same pO2 ¼ 1011 atm, but different pSO2 and pS2 levels. Whereas experiment 6 produced the oxide overgrowth shown in Figure 4.1b, experiment 7 led to the lamellar structure of Figure 4.1a and linear, rather than parabolic kinetics. Clearly the gas phase oxygen activity was not the important factor. In only one case, experiment 3, was SO2 not the reactant species. In this case the equilibrium value of pS2 ¼ 8:6 102 atm was even higher than the equilibrium pSO2 ¼ 1:2 102 atm. The reaction product was almost pure FeS, which grew according to rapid parabolic kinetics, with kp ¼ 5 103 g2 cm4 min1, a rate which could be sustained by the high partial pressure of molecular sulfur. Thus the SO2 species ceases to be the important reactant only when its partial pressure is significantly exceeded by that of another chemically reactive species.
4.4.2 Rate determining processes in SO2 reactions The possibility of gas phase mass transport being the rate controlling process was considered briefly earlier. It was recognized that the high stability of SO2 (g) with respect to O2 (g) and S2 (g) means that the latter species are necessarily in the minority. As seen in Table 4.3, the rates at which they reach a reacting sample surface are negligibly small, and cannot support observed reaction rates. However, in dilute SO2 gas mixtures, the rate at which the SO2 species diffuses to the surface is, at 8001C, in order of magnitude similar to the scaling weight uptake rates reported in Table 4.4 for 1 h of reaction. In the case of parabolic kinetics, corrosion rates would be faster at earlier times and, at some point, too high for the gas phase process to keep up. At short times then, linear rates controlled by gaseous diffusion are predicted. Such a situation was reported by Birks [9, 46] and Rahmel [11] and later confirmed by Kurokawa et al. [10] in the case of iron reaction with SO2 gases. It was shown that the linear rate constant for mixed sulfide-plus-oxide scale growth on iron was proportional to both the flow
4.4. Scale–Gas Interactions
157
Figure 4.14 Evolution of sulfide–oxide scales on Fe in catalysed gas 5 (Figure 4.11). (a) 4 min; (b) 36 min; (c) 144 min and (d) 400 min. [48]. With kind permission from Springer Science and Business Media.
158
Chapter 4 Mixed Gas Corrosion of Pure Metals
Figure 4.15 Kinetics of Fe reaction with gas 5 of Figure 4.11, illustrating the effect of gas phase catalysis [48]. With kind permission from Springer Science and Business Media.
rate of an SO2/Ar gas mixture and its pSO2 value. As seen in the equations for viscous flow mass transfer (2.157 and 2.158), these are almost the dependencies expected for a rate controlled by gas phase transfer. The gas mixtures used in these experiments were such that, at equilibrium, oxide was stable with respect to sulfide. Mixed oxide–sulfide scales grown in gas mixtures where, at equilibrium, sulfide was stable with respect to oxide, have also been shown [50] to thicken according to linear kinetics, attributed to gas phase mass transfer control. In these latter experiments, the gas mixtures were based on CO/CO2/COS, containing rather high pCOS values, and COS was the reactant species. The reaction of manganese with SO2 gas mixtures is very similar in morphological evolution to that of iron [3, 20] when the gas compositions fall in the oxide stability field: an initial period of dual-phase oxide-plus-sulfide scale growth is succeeded by development and thickening of an oxide outer layer. However, the kinetics of both reaction stages are parabolic, with SO2 the dominant reactant species in both cases. Obviously, neither gaseous mass transfer nor an interfacial reaction, each of which leads to linear kinetics, could be involved. Instead, it must be concluded that both stages are diffusion-controlled. The way in which a solidstate diffusion-controlled process can occur under non-equilibrium conditions (in which a metastable sulfide phase grows) is discussed in the next section. Reactions of nickel with SO2 gas mixtures are difficult to study because of the changes of reaction product stabilities with both temperature and gas composition. Nonetheless, it is clear that the growth rates of two-phase (oxideplus-sulfide) scales are strongly dependent on pSO2 . Linear kinetics are attributed [16, 34] to surface reaction rate control. A similar conclusion has been reached
4.4. Scale–Gas Interactions
159
for the growth of two-phase oxide-plus-sulfide scales on cobalt, based on the dependence of scaling rate on pSO2 and flow rate [51, 52]. To summarize, then, when SO2 is the reactant gas species, the reaction kinetics can be controlled by (a) solid-state diffusion, leading to parabolic kinetics, (b) surface reactions leading to linear kinetics or (c) gas phase mass transfer, also leading to linear kinetics. Parabolic kinetics can be associated with either twophase scale growth or oxide layer overgrowth. Linear kinetics appear always to be associated with a two-phase reaction product. All these findings apply to gas compositions such that oxide is stable with respect to sulfide (although they can in some cases apply to other regimes). To dissect these reaction mechanisms, it is clearly necessary to understand first how reaction with SO2 can produce a thermodynamically unstable product.
4.4.3 Production of metastable sulfide As we have seen, pure SO2, SO2+O2 or SO2/CO/CO2 gases very commonly provide environments in which the stable reaction product is oxide. The observation of parabolic kinetics is indicative of steady-state diffusion control in the scale, and might therefore be expected to correspond to the achievement of local equilibrium at its surfaces, and the formation of oxide in contact with the gas. However, both oxide and sulfide are commonly found at the scale surface after reaction of nickel and cobalt with oxidizing–sulfidizing gases, and also for iron at short times or low pSO2 values. Clearly, in these cases the scale surface is not at equilibrium with the gas. In a gas in which SO2 is the only reactant species, possible reactions at the scale surface include 2M þ SO2 ¼ 2MO þ 12S2
(4.8)
M þ SO2 ¼ MS þ O2
(4.9)
3M þ SO2 ¼ 2MO þ MS
(4.10)
If local equilibrium for reactions (4.8) and (4.9) is reached, their combination is thermodynamically equivalent to the formation of oxide and sulfide from the elements at their equilibrium partial pressures. In this event, the two reactions can occur simultaneously only if the gas composition falls exactly on the oxide– sulfide equilibrium line in the stability diagram. The possibility of this occurring is remote, and, as suggested long ago [9, 11, 50], the direct reaction (4.10) must be considered. Reaction (4.10) can produce a mixture of oxide and sulfide, even if one of them is not in equilibrium with the bulk gas, provided that the metal activity at the scale–gas interface, asM , is larger than the equilibrium value for reaction (4.10), að10Þ M . The latter is seen from the reaction stoichiometry to be given by ð1=3Þ
að10Þ M ¼ K 10
ðpSO2 Þð1=3Þ
(4.11)
160
Chapter 4 Mixed Gas Corrosion of Pure Metals
where K10 is the equilibrium constant. Under these circumstances (which amount to a steady, although non-equilibrium, state), the unstable sulfide can form, even though not at equilibrium with the gas phase sulfur potential. However, even though molecular oxygen and sulfur are kinetically irrelevant, equilibrium could nonetheless be achieved via destruction of the sulfide through reaction with SO2: 2MS þ SO2 ¼ 2MO þ 32S2
(4.12)
As always, the reason for failure to achieve equilibrium lies in the kinetics of the situation. The sulfide will grow and be perpetuated if the rate of reaction (4.10) exceeds that of reaction (4.12). If it does not, then sulfide will be eliminated, and true equilibrium is established between an oxide scale and the gas. The metastable equilibrium (4.10) is sustained by surface activities of sulfur and oxygen which lie on the sulfide–oxide equilibrium line of the stability diagram. If the SO2 dissociation reaction is also at equilibrium on the surface, then the surface state is defined. Consider the example of iron reacting with pSO2 ¼ 0:079 atm depicted in Figure 4.11. The intersection of the dashed line 1=2 (representing pO2 pS2 ¼ 0:079K3 ) with the oxide–sulfide phase boundary represents the supposed metastable equilibrium. It also defines the minimum value of að10Þ Fe necessary at the scale surface for this equilibrium to be sustained. If, as a result of depletion, the effective value of pSO2 at the interface is less than in the surrounding gas, a steady state can nonetheless be maintained, providing that a higher asFe value is available. There remains the significant question as to just how this remarkable metastable state is arrived at. The surface state corresponds to a higher sulfur activity, but lower oxygen activity than in the gas. This has been explained [3, 53] on the basis of selective removal of oxygen from the adsorbed layer gas into the scale. At first sight, this is difficult to accept because it is the simultaneous reaction of both oxygen and sulfur we are trying to explain. We turn aside for a moment to question whether the stoichiometry of reactions such as (4.10) is actually achieved. A convincing demonstration is available in the case of iron reacting with dilute CO/CO2/SO2 gases of particular compositions [49]. The scale shown in Figure 4.16 is a lamellar mixture of FeO+FeS, with a sublayer of Fe3O4+FeS near the surface. It contains a sulfide volume fraction, fS, measured as 0.4870.06. The reaction appropriate to the equilibrium gas composition is 5Fe þ 2SO2 ¼ Fe3 O4 þ 2FeS
(4.13)
which would form sulfide and oxide in a molar ratio of 2:1. Subsequent conversion of magnetite to wu¨stite via the reaction within the scale Fe3 O4 þ Fe ¼ 4FeO
(4.14)
leads to a molar ratio of 1:2 for FeS to FeO. Using standard density data, it is calculated that the resulting value of fS would be 0.42. The good agreement of the measured value shows that, at least under the parabolic scaling conditions of this experiment, SO2 is reacted with the stoichiometry shown in reaction (4.13). It should be noted for later reference that at lower pSO2 values, where two-phase
4.4. Scale–Gas Interactions
161
Figure 4.16 Scale grown on iron in CO/CO2/SO2/N2 (gas 7 of Table 4.5) at 8001C.
scales grow according to linear kinetics, the observed sulfide volume fractions are significantly lower, indicating a different mechanism. Returning to the question of sulfur enrichment on the scale surface, we recognize that preferential sulfur adsorption will account for the observations, providing that surface concentrations are insensitive functions of activity. When kinetics are parabolic, as in the case of the scale in Figure 4.16, the boundary conditions are fixed, and it can be assumed that SO2 exchange between the surface and the surrounding gas is faster than SO2 incorporation into the scale. In other words, gas adsorption is expected to approach equilibrium with respect to SO2 (g), but not with the minority species S2(g) and O2(g). Given that two solid phases are present at the scale surface, adsorption of SO2 can be represented formally as taking place on the oxide (4.15) SO2 ðgÞ þ X ¼ S X þ 2OX þ 2V X o
and on the sulfide
M
X SO2 ðgÞ þ 2Y ¼ 2O Y þ SX s þ VM
(4.16)
together with the surface exchange processes SjX þ Y ¼ SjY þ X
(4.17)
OjY þ X ¼ OjX þ Y
(4.18)
Here X and Y represent surface adsorption sites on the oxide and sulfide, respectively, and cation vacancies have been assumed neutral for the sake of simplicity. If oxygen incorporation via Equation (4.15) is favoured over sulfur incorporation, then the adsorbed phase becomes enriched in sulfur. Such a
162
Chapter 4 Mixed Gas Corrosion of Pure Metals
situation, coupled with a low probability of sulfur desorption, can lead to the non-equilibrium surface activities required for simultaneous oxide and sulfide formation. These non-equilibrium activities can exist in a situation where both oxide and sulfide grow together. The growth of each phase involves consumption of vacancies, V X M , and the incorporation of additional sulfur or oxygen. If these growth processes proceed in parallel, then the balance between adsorbed sulfur and oxygen activities is preserved. The situation is thus seen to be self-sustaining for so long as several conditions are met: (a) The value of pSO2 is much greater than those of pS2 and pO2 . (b) The metal activity at the scale surface is no less than the minimum required for reactions such as (4.10), given by Equation (4.11), or the equivalent for other stoichiometries. (c) The rate of reaction (4.10) producing the two-phase scale is faster than the sulfide oxidation reaction (4.12). (d) Solid-state diffusion within the scale is fast enough to satisfy requirements (b) and (c). As already seen, simultaneous oxide and sulfide formation can be maintained for lengthy times, and large extents of reaction, in the case of nickel and cobalt. In the case of iron, the two-phase product is quickly overgrown by oxide at high pSO2 values, but continues for long times at low pSO2. In the case of chromium, the two-phase oxide and sulfide product grows for long times at relatively high pSO2 and not at all at low pSO2. A special situation arises when the gas composition lies in the sulfate stability field. In this case, the formation of oxide and sulfide at or close to the scale surface can be explained either by the mechanism described above, or by assuming the formation of an outer layer of metal sulfate: M þ SO3 þ 12O2 ¼ MSO4
(4.19)
A two-phase scale could then form beneath the sulfate layer through the reaction 4M þ MSO4 ¼ MS þ 4MO
(4.20)
This mechanism was originally suggested by Alcock et al. [39] and subsequently adopted by Kofstad and co-workers [44, 45] in describing the nickel reaction. In that reaction, the two-phase product was found to be Ni3S2+NiO at about 6001C. Reference to Figure 4.12 reveals a difficulty in that the sulfate phase field is seen not to contact the observed Ni3S2 area. A detailed consideration of possible metastable diffusion paths has been provided by Gesmundo et al. [14]. These are based on the supposition that kinetic hindrances exist for the formation of, e.g., a single-phase NiO layer, which the phase diagram predicts would develop between NiSO4 and Ni3S2 if no other sulfide formed. Of necessity, these possibilities remain speculative. Considerable effort has been expended [32, 33, 43, 54] in seeking to determine whether the sulfate mechanism actually operates. At 6031C, sulfate formed only when the two-phase layer separated from the metal, so that the nickel flux was
4.4. Scale–Gas Interactions
163
greatly reduced, and scale–gas equilibrium perhaps more closely approached. At higher temperatures, however, small amounts of sulfate were found in the absence of major scale separation. The sulfate was present as thin (o1 mm), scattered islands [38, 44, 45] on the surface. At 6031C, the rate decreased as pSO3 increased (and pSO2 decreased), indicating that the SO2 was the reactant species. In view of the apparently marginal kinetic stability of the sulfate phase, it is uncertain whether reaction (4.19) together with 9Ni þ 2NiSO4 ¼ Ni3 S2 þ 8NiO
(4.21)
or the direct reaction 9 2Ni
þ SO3 ¼ 12Ni3 S2 þ 3NiO
(4.22)
is the more important. Both would increase in rate with pSO3 , as observed experimentally. Slightly different volume fractions of sulfide and oxide are predicted from the two stoichiometries fS ¼ 0.38 for reaction (4.22) and 0.31 for reaction (4.21). The direct reaction with SO2 7Ni þ 2SO2 ¼ Ni3 S2 þ 4NiO
(4.23)
would produce fS ¼ 0.48, a distinctly higher value. The question of relative amounts of sulfide and oxide appears not to have been investigated.
4.4.4 Independent oxide and sulfide growth in SO2 Most discussions of SO2 corrosion are based on the occurrence of reactions such as (4.10) providing the explanation for the simultaneous formation of both oxide and sulfide. As we have seen, this is equivalent to the development of a metastable surface state which is supersaturated with respect to sulfur. If such a state develops, there seems no reason why sulfide and oxide cannot form independently via reactions such as (4.8) and (4.9). This does in fact occur during reaction of iron in CO/CO2/SO2/N2 gas mixtures at 8001C, if the SO2 partial pressure is low [49]. Catalysed gas mixtures with the equilibrium compositions shown in Table 4.5 produced scales with the morphologies shown in Figure 4.17. It is clear that both the sulfide volume fraction and lamellar spacing, l, varied with gas compositions. Measured values are listed in Table 4.6, along with scaling rates and phase constitutions of the scale surfaces. At pSO2 ¼ 2:2 102 atm, the two-phase product was overgrown with oxide. Two-stage parabolic kinetics were observed (Figure 4.18) with the second stage kw ¼ 1.6 mg cm2 min(1/2). This rate is in reasonable agreement with the value of 1.8 mg cm2 min(1/2) reported [55] for iron oxidation in pure oxygen at 8001C. In both experiments the bulk of the oxide is FeO, under thin external layers of Fe3O4 and Fe2O3 and the growth kinetics will therefore reflect largely the accumulation of wu¨stite. The diffusional flux responsible for the growth of this layer is determined by the boundary conditions at its inner and outer solid–solid interfaces, and is therefore independent of gas composition. Thus at high SO2 partial pressures, the reaction is ultimately one of oxidation only [9, 10, 50, 57].
164
Table 4.5
Chapter 4 Mixed Gas Corrosion of Pure Metals
Equilibrium gas compositions (p/atm) used in FeS volume fraction study at 8001C [49]
Gas
pN2
pCO2
pCO
pSO2
pS2
pO2
1 2 3 4 5 6 7 8 9 10 11
0.12 0.12 0.12 0.12 0.24 0.26 0.24 0.24 0.12 0.12 0.12
0.88 0.88 0.88 0.88 0.76 0.73 0.76 0.76 0.88 0.88 0.88
5.3 104 1.7 104 5.3 104 1.7 104 4.6 105 4.4 105 4.6 105 1.5 104 2.3 104 3.0 104 9.5 105
2.2 105 2.2 105 2.2 104 2.2 104 2.2 104 2.2 102 2.2 103 2.2 103 1.2 104 3.5 104 6.9 105
1.2 1013 1.2 1015 1.2 1011 1.3 1013 1.2 1015 1.2 1011 1.2 1013 1.2 1011 1.2 1013 3.2 1012 1.2 1015
1.0 1012 1.0 1011 1.0 1012 1.0 1011 1.0 1010 1.0 1010 1.0 1010 1.0 1011 5.5 1012 3.2 1012 3.2 1012
At pSO2 ¼ 2:2 103 atm, rapid parabolic kinetics (Figure 4.18) accompanied the formation of a lamellar oxide and sulfide scale (Figure 4.16). The sulfide volume fractions (Table 4.6) are in good agreement with the value fS ¼ 0.42 calculated earlier for stoichiometric uptake of SO2 via reactions (4.13) and (4.14). Thus direct reaction with SO2 produced a metastable surface state, providing a fixed boundary condition, so that diffusion-controlled parabolic kinetics resulted. The reason for the more rapid rate is discussed in the next section. At low pSO2 values in the range 2.2 105–3.5 104 atm, two-phase oxide and sulfide scales grew according to linear kinetics. Although the value of pSO2 in gases 3, 4 and 5 was 10 times higher than in gas 1, the rate was increased less than two-fold. Accordingly, it can be concluded that gas phase mass transfer, which is proportional to pSO2 , was not in effect. The reaction must therefore have been controlled by a surface process, but this was not reaction (4.10) or (4.13), as shown by the diverse values of the sulfide volume fraction fS (Table 4.6). Assuming that iron was delivered to the scale–gas interface by rapid diffusion in a process which did not control the rate, but instead led to a steady-state surface iron activity, the accumulation rates of FeO and FeS may be written from reactions (4.8) and (4.9) as dnFeS ¼ k8 pSO2 dt
(4.24)
dnFeO 1=2 ¼ k9 pSO2 dt
(4.25)
1 k9 1 ¼1þ N FeS k8 p1=2
(4.26)
and for time-independent rates
SO2
Figure 4.17 Scales grown on iron in CO/CO2/SO2/N2 gas mixtures 1, 5, 9 and 10 of Table 4.5 [49]. With kind permission from Springer Science and Business Media.
4.4. Scale–Gas Interactions
165
166
Chapter 4 Mixed Gas Corrosion of Pure Metals
Figure 4.18 Parabolic scaling kinetics for iron exposed to CO/CO2/SO2/N2 gases (Table 4.5) at 8001C [49]. With kind permission from Springer Science and Business Media.
Table 4.6
Iron oxide+sulfide scale constitutions and growth rates at 8001C [49]
Gas kw (mg cm2 min1/2)
k1 (mg cm2 min1)
Phases at surface fS
l (mm)
1 2 3 4 5 6 7 8 9 10 11
0.035
FeO/FeS Fe3O4 FeO/FeS FeO/FeS Fe3O4/FeS Fe2O3/Fe3O4 Fe3O4/FeS Fe2O3/FeS FeO/FeS Fe3O4/FeS FeO/FeS
8
1.0 0.063 0.064 0.064 5.2, 1.6 4.15 4.51 0.054 0.102 0.046
0.0870.02 0.0370.02 0.1370.05 0.1770.04 0.4070.05
2.7 2.4 2.5
0.4870.06 0.3670.09 0.2170.06 0.3270.11 0.1870.06
o1 o1 3.6 o1 3.4
Here n denotes mole number and N mole fraction. This is expressed in terms of volume fraction, using the molar volume ratio, as 1 k9 1 ¼ 1:68 þ 0:68 fS k8 p1=2
(4.27)
SO2
Data for FeO/FeS scales plotted in Figure 4.19 are seen to be in only rough agreement with this prediction. The slope implies that k8 2k9 .
4.4. Scale–Gas Interactions
167
Figure 4.19 Variation in scale sulfide volume fraction with pSO2 for (FeO+FeS) scales [49]. With kind permission from Springer Science and Business Media.
For the reaction to continue, iron must be available at a sufficient activity at the surface of both phases. If diffusion of iron through FeS and perhaps along phase boundaries predominates over diffusion through FeO, then lateral diffusion of iron must occur at the scale–gas interface in order to sustain the two-phase morphology. Treating the growth of a lamellar sulfide–oxide scale as a cellular (co-operative) phase transformation, it is recognized that the lamellar spacing, l, would therefore be inversely dependent on scaling rate [56]. Basically, a rapid scale growth rate allows time for only a closely spaced microstructure to develop because of the need for lateral mass transfer on the scale surface. Conversely, when scale growth rates are relatively slow, and both gas and surface diffusion are fast, a widely spaced microstructure which lowers the overall surface energy will develop. For a unidirectional co-operative or cellular phase transformation propagating at a velocity, v, kD (4.28) l where k is a constant which includes the driving force for reaction and D the diffusion coefficient for lateral mass transfer on the scale surface. If k is approximately independent of pSO2 , then v varies inversely with l at fixed temperature. v¼
168
Chapter 4 Mixed Gas Corrosion of Pure Metals
Figure 4.20 Variation of lamellar spacing with scale surface growth velocity for (FeO+FeS) scales [49]. With kind permission from Springer Science and Business Media.
Values of v (calculated from kl, fS and molar volumes) are shown plotted according to Equation (4.28) in Figure 4.20 for FeO/FeS scales. Agreement is good in the range examined, but the relationship fails at very large lamellar spacings. In the latter case the principal phase is wu¨stite, the sulfide is discontinuous and the basis for Equation (4.28) no longer exists. It is therefore concluded that the linear kinetic regime of the Fe–SO2 reaction is supported by two independent scale–gas reactions (4.8) and (4.9), which control the relative amounts of sulfide and oxide formed. However, the spacing of the resulting lamellar mixture of phases is controlled by delivery of the other reactant, iron, which diffuses to the surface via FeS or phase boundaries, and then laterally to the reacting oxide. These results provide experimental support for the notion of a co-operative or cellular reaction hypothesized in the past [3, 59].
4.5. TRANSPORT PROCESSES IN MIXED SCALES Two very different patterns of morphological evolution have been observed: on the one hand, continued growth of multiple scale layers and on the other, accretion of different layers, reflecting successive stages of reaction. The first is illustrated by the growth of multiple layers on chromium (Figure 4.4), the kinetics of which are seen in Figure 4.21 to be parabolic, reflecting diffusion control. An example of the second is provided by the reaction of iron with gases containing high levels of SO2 (Figure 4.14). In this case, a two-phase reaction product grows in the initial reaction, but is then overgrown by single-phase oxide, and no further growth of the buried oxide-plus-sulfide layer occurs.
4.5. Transport Processes in Mixed Scales
169
Figure 4.21 Kinetics of layer growth for scale shown in Figure 4.4 [27]. With kind permission from Springer Science and Business Media.
It is clear that carbon and nitrogen must penetrate the outer Cr2O3 scale layer in the first case, whereas this is evidently not so for sulfur in the case of iron oxide. Further information on this matter is available from pre-oxidation studies.
4.5.1 Effect of pre-oxidation on reaction with sulfidizing–oxidizing gases Many investigations into the effect of a preformed pure oxide scale on subsequent reaction with sulfur-containing gases have been reported. The practical aim of this work was to slow the damaging sulfidation process by using a compact, adherent oxide layer as a barrier to reaction. The results are relevant to an understanding of the transport processes involved. Unfortunately, data for iron is limited to that of Rahmel and Gonzalez [58] who studied the reaction of pre-oxidized iron with CO/CO2/COS gases of high sulfur and low oxygen potential at 8001C and 9001C. These gases were in the sulfide phase field and had pO2 values less than the Fe/FeO equilibrium value. A preformed FeO scale did inhibit subsequent reaction, to an extent which increased with oxide thickness. An outer layer of FeS developed during reaction with CO/CO2/COS. Depending on gas composition, the FeS layer was in direct contact with FeO, or an intermediate layer of Fe3O4 developed for a short time, and then disappeared. The outer part of the FeO layer and the intermediate Fe3O4 layer developed stringers of FeS. Thus sulfur penetration of the oxide took place to only a limited extent.
170
Chapter 4 Mixed Gas Corrosion of Pure Metals
Considerably more information is available for nickel. Alcock et al. [39] showed that NiO layers of submicron thickness slowed the subsequent reaction with SO2+O2 gas, but did not prevent sulfide formation. Pope and Birks [59] pre-oxidized nickel at pO2 ¼ 1 atm and 1,0001C, exposing it to CO/CO2 mixtures and finally to CO/CO2/SO2. Sulfide formed beneath the preformed oxide after an incubation period. Subsequent work [60] in which pSO2 was varied led to formation of sulfide beneath the oxide, except when pSO2 was too low for reaction (4.10) to be thermodynamically possible. Similar results were obtained by Kofstad and Akesson [61], who showed that the induction period was longer for thicker NiO scales. Worrell and Rao [32] showed that pre-oxidation in air at 8001C for a day to produce NiO layers of 5–10 mm provided protection against attack by SO2 for up to 14 days. A detailed study [62] of the effect of porosity in the initial NiO layer on subsequent corrosion in SO2 or SO2/O2 was revealing. Samples with high porosity reacted with SO2 according to rapid linear kinetics, quickly forming an inner sulfide, then filling the pores with nickel sulfide and finally developing a two-phase product on top of the preformed oxide. Samples with low porosity reacted significantly more slowly, and those with ‘‘extremely low’’ porosity reacted according to parabolic kinetics with a rate constant lower than that observed in pure oxygen. Subsequent reaction with SO2/O2 was different. The initial porosity was less important because the initial NiO reacted with this gas to form a surface layer of NiSO4 and then oxide and sulfide product on top of the sulfate together with sulfide channels through the underlying oxide. Information is also available on the practically important question of chromium pre-oxidation. Labranche et al. [63] pre-oxidized chromium in H2/H2O gases at 9001C and exposed it immediately to H2/H2O/H2S atmospheres with a composition in the Cr2O3 stability field. No sulfide was detected after 20 h, although about 1 wt% of sulfur was found in the chromia. However, chromium sulfide was found mixed with oxide through the entire scale thickness after 111 h of reaction. Similar results were found [64] for reaction in CO/CO2/N2-based gases. Preoxidation at 9001C produced an adherent Cr2O3 layer of 3 mm thickness, with underlying sublayers containing carbide and nitride, similar to the scale shown in Figure 4.4b. Additions of SO2 to the gas were designed to yield compositions in the Cr2O3 phase field, with sulfur potentials higher than the Cr/CrS equilibrium value. Reaction in these SO2-bearing gases led to formation of a layer of Cr3S4+Cr2O3 on top of the oxide (Figure 4.22) at pS2 ¼ 3 107 atm, and a dispersed Cr3S4 phase at the surface of porous Cr2O3 which had grown over the preformed chromia at pS2 ¼ 3 108 atm, while no surface sulfide formed at pS2 ¼ 3 109 atm. Addition of sulfur to the gas led to the disappearance of the Cr2N layer, although the Cr7C3+Cr2O3 sublayer continued to grow, and incorporated particles of Cr2N. No sulfur was found beneath the preformed oxide when pS2 ¼ 3 107 atm, a significant level (ca. 8 atm%) accumulated in this region when pS2 ¼ 3 108 atm, and less than 1% was found after reaction at pS2 ¼ 3 109 atm.
4.5. Transport Processes in Mixed Scales
171
Figure 4.22 Scales produced on chromium by exposure at 9001C to CO/CO2/SO2/N2 after pre-oxidation in CO/CO2/N2 (a) pS2 ¼ 3 107 atm, (b) pS2 ¼ 3 108 atm and (c) pS2 ¼ 3 109 atm. Reprinted from Ref. [64] with permission from Elsevier.
172
Chapter 4 Mixed Gas Corrosion of Pure Metals
It is clear that sulfur can penetrate NiO and Cr2O3 under at least some conditions where the oxides should be thermodynamically stable in contact with the gas in question. This problem has been discussed many times in the literature, usually in connection with sulfur transport in scales formed without pre-oxidation [46, 51, 59, 60, 65, 66].
4.5.2 Solid-state diffusion of sulfur An obvious possible method of sulfur penetration is via dissolution in and diffusion through the oxide lattice. Little information is available on either of these processes. Analytical measurements of sulfur solubility in NiO and CoO have been reported by Pope and Birks [59], who measured maximum values at 1,0001C of 0.026 wt % in NiO and 0.050 wt % in CoO. Sulfur has been found to diffuse more rapidly than oxygen in NiO, but much slower than nickel [67–69]. In NiO single crystals, it is reported [70] that Ds ¼ 5.4 1013 cm2 s1, Do ¼ 8 1014 cm2 s1 and DNi ¼ 1011 cm2 s1 at 1,0001C. However, the combined values of sulfur solubility and diffusivity in NiO are too small to account for the sulfidation rate of nickel in mixed atmospheres [71]. In summary, there appears to be no evidence that solid-state diffusion of sulfur through metal oxide can ever account for the penetration by sulfur of preoxidized scales. However, sulfur can diffuse at significant rates in the sulfides of nickel and cobalt [16, 34, 39–41, 72, 73] thereby accounting for the inward growth of the sulfide layer which develops at the interface between these metals and their scales.
4.5.3 Gas diffusion through scales A second mode of sulfide formation beneath single-phase oxide could be via gas diffusion of sulfur or its compounds. As seen earlier (Tables 4.3 and 4.4), however, sulfur pressures in SO2 atmospheres are generally too low to support the observed reaction rates, and the question of molecular S2(g) diffusion is therefore probably irrelevant. However, if transport occurs via the much more abundant SO2 (or SO3 in oxygenated gas), a viable mechanism is available. Inward transport of sulfur by this means has been considered in detail by Birks [46, 51, 59, 60, 65], who proposed that gas compositions within scale cracks could change by reaction with the scale. Lowering the oxygen potential to values at equilibrium with the scale interior would then lead to an increase in sulfur potential through the equilibrium relationship (4.5). In this way, sulfide formation could become thermodynamically possible within the scale. The interface between a crack surface and the gas phase is equivalent to that between the scale exterior and the gas, so the discussion provided in Section 4.4.3 is equally applicable. In particular, the condition that the thermodynamically favoured reaction (4.12) be kinetically hindered applies in this situation. Diffusion of SO2 molecules provides a satisfactory explanation of the observations reported for reaction of pre-oxidized nickel with SO2-bearing gases.
4.5. Transport Processes in Mixed Scales
173
The improved resistance to sulfur penetration of a NiO scale with increased thickness and decreased porosity is an obvious consequence. Direct information on iron oxides is very limited. However, the observation during reaction without pre-oxidation that the first formed oxide and sulfide layer ceases to grow once an oxide layer forms on top indicates that FeO and perhaps Fe3O4 are more resistant to SO2 diffusion than NiO. The much larger grain size of FeO, and the consequently reduced availability of grain boundaries, could be a factor. The greater plasticity of FeO and hence its lower frequency of cracking during growth could also be important in limiting the availability of pathways for molecular diffusion. The behaviour of Cr2O3 scales when exposed to sulfurous gases is interestingly complex. At a high sulfur potential and high pSO2 , chromium sulfide nucleated at the oxide–gas interface (Figure 4.22). Sulfide formed at both the surface and beneath the oxide at an intermediate sulfur potential (and pSO2 value), whereas at a low sulfur potential and low pSO2, some enrichment of sulfur developed beneath the oxide, but not on top. These observations are not readily understood on the basis of inward SO2 diffusion and the diffusion path shown in Figure 4.10. The diffusion path illustrates the ideas first articulated by Stringer and Whittle [74] and by Stringer [75] in connection with mixed gas corrosion. In essence, it was proposed that the reduced oxygen activity within and beneath the oxide allowed an increase in as through the SO2 dissociation equilibrium. The line A-X in Figure 4.10 follows such a path. This effect, together with the relatively high chromium activity can then stabilize the sulfide with respect to the oxide. The activity gradients for sulfur, oxygen and chromium within the two-phase layer (along the path XY) are all appropriate for its growth. A disadvantage of the description is the strong sulfur gradient within the single-phase oxide layer, along the path X-A in a direction appropriate to outward sulfur diffusion. This can be rationalized on the basis that such a process would be kinetically hindered by the low solubility of sulfur in the oxide phase. However, a more fundamental difficulty exists with the inability of the description to cope with the reaction morphology of Figure 4.22. This is overcome by applying again the description of a sulfur-enriched surface-adsorbed layer given earlier (Equations (4.15)–(4.18) in Section 4.4.3). It must be recognized that the lowering of oxygen activity relative to that of sulfur can occur both within and beneath an oxide as well as at its surface, by preferential adsorption. The line segment AX of the diffusion path in Figure 4.10 represents both cases, providing no information on the spatial location. It thus provides no ability to predict whether sulfur enrichment occurs between an (oxide) scale surface and its interior, or between the bulk gas and an adsorbed layer. It is recognized that the diffusion path description lacks utility in this situation. The case of pre-oxidized chromium reacting with SO2 illustrates very clearly how surface processes can displace the location at which oxidant activity changes occur. The oxide shown in Figure 4.22a was obviously gas permeable, as evidenced by the continued growth of the carbide subscale. The failure of sulfur
174
Chapter 4 Mixed Gas Corrosion of Pure Metals
to penetrate this material was due to its immobilization in an outer Cr3S4 layer. At a lower pSO2 value (Figure 4.22b), sulfur permeated the preformed oxide more freely because the surface sulfide formed in this gas was discontinuous. At a still lower pSO2 value (Figure 4.22c), no surface sulfide at all was formed, and sulfur slowly permeated the oxide, enriching beneath it. Assuming that a separate sulfide phase was formed in the third gas, we see that all three cases can be described, at least in part by the diffusion path of Figure 4.10. The differences in the path segment X-Y are due to (surface) processes other than diffusion. We see that a difference arises in the case of the high pSO2 gas (Figure 4.22a) where a single-phase oxide sublayer still exists. Given the failure of equilibrium thermodynamic phase diagrams to predict scale surface constitutions in the case of SO2 reaction, and the inability of diffusion paths to cope with surface reactions, it is reasonable to ask how predictive capacity could be arrived at. Unfortunately, only qualitative statements can be made, as will be seen in Section 4.6.
4.5.4 Scale penetration by multiple gas species As has been experimentally demonstrated, and discussed in some detail earlier, SO2 molecules can both react at scale surfaces and penetrate oxides to react in the scale interior. Scales which are permeable to one gas species might be expected to transmit others, and this is indeed the case. As seen earlier (Figure 4.4) nitride and carbide can form beneath a Cr2O3 scale during exposure to mixed gases. As is clear from Figure 4.21, carbon and nitrogen continue to penetrate the oxide layer, supporting diffusion-controlled growth of the underlying carbide and nitride layers throughout the observed reaction. Gas phase ac and aN values were high enough to stabilize the carbide and nitride at high aCr values, and the schematic activity profiles of Figure 4.9 illustrate the diffusional steady-state. The exception to this pattern was the single-phase oxide scale grown in H2/H2O/N2 gas, which was obviously not permeable to nitrogen. It is known [76] that carbon solubility in Cr2O3 is negligible, and it seems likely that the same would be true of nitrogen. Neither of these species could penetrate the oxide by lattice diffusion, and molecular transport via scale imperfections is indicated. Diffusion along these imperfections must be rather slow to produce the activity gradients corresponding to the layered scales which result. Accordingly, it is proposed that the transport mechanism is one of diffusion of adsorbed gas molecules along grain boundaries or similar internal surfaces. Competitive adsorption processes give rise to interactions among the diffusing species. Thus the non-polar N2 molecules are displaced by relatively strongly adsorbing H2O, and the absence of any nitride layer underneath Cr2O3 grown in H2/H2O/N2, despite its thermodynamic stability, is thereby explained. However, nitrogen is able to diffuse along these internal surfaces if the oxidant is CO2 and the corresponding adsorbed species is CO. As seen earlier (Section 4.3.2), addition of SO2 to the CO/CO2/N2 gas also suppressed the expected nitride formation, even when the pSO2 value was too low to form external surface sulfide. Under these circumstances, the rate of inner
4.6. Predicting the Outcome of Mixed Gas Reactions
175
carbide growth was slowed, but not stopped. Obviously, these effects would not be possible if the mechanism of penetration by secondary oxidants was one of gaseous diffusion through large defects. Again it is concluded that mass transport involved much smaller defects, such as internal surfaces. Preferential adsorption of sulfur on oxide boundaries would be expected. It seems that the more reactive CO molecule can adsorb to some extent on the sulfur-poisoned grain boundaries, whereas the unreactive N2 cannot.
4.5.5 Metal transport processes In a two-phase scale such as the examples shown in Figures 4.1a, 4.2 and 4.4c, metals can diffuse as cations in the lattices of both phases and along the boundaries between them. If these phases are continuous, in the sense of providing an unbroken diffusion pathway between metal and the scale–gas interface, then the flux of metal in each phase is described by Equation (3.62). However, as has become abundantly clear, the boundary conditions at the scale–gas interface are far from equilibrium, and unknown. This makes the application of Equation (3.62) impossible. Moreover, the diffusional properties of phase boundaries such as those between oxide and sulfide, which can be so abundant, are unknown. In the absence of basic data, it is appropriate to assess the contributions of the different diffusional processes by comparing scaling rates. Table 4.7 lists rate constants for oxidation, sulfidation and reaction with SO2 for several metals at particular temperatures. Most values refer to reaction with the relevant gas at a pressure of 1 atm. The comparison is not ideal because the pS2 and pO2 values in effect at a scale–SO2 gas interface will be much less than 1 atm. However, as the effect of oxidant partial pressure on reactions involving only one species (Equations (3.76) and (3.90)) is small, the values shown are sufficient for our purposes. Corrosion in SO2 is seen to be faster than oxidation in pure O2 whenever a two-phase product is formed. The difference for iron and manganese is only moderate, at about an order of magnitude, because both FeO and MnO have large concentrations of defects, and oxidation is in any case rapid. Conversely, the difference for nickel and chromium is very large. The sulfidation rates of both metals are many orders of magnitude faster than the oxidation rates because the sulfides possess much more defective structures. The formation of a continuous sulfide phase in the scales developed by these metals therefore provides an alternative, much more rapid diffusion pathway for cations.
4.6. PREDICTING THE OUTCOME OF MIXED GAS REACTIONS The corrosion reactions examined in this chapter exhibit a diversity of outcomes, and an attempt to arrive at a unified view is worthwhile. As we have seen, the use of solid–gas thermodynamic equilibrium in predicting scale surface constitutions is successful in some cases (oxidation–carburization–nitridation of
800
800
600 900
Fe
Mn
Ni Cr
[30] [79] [81]
1.6 109
1.0 1013 2 1013
5.5 10
[55]
Reference
8
kw
O2
6
9 107 8 107
3.2 109
8.1 10
kw
Notes: (a) Single-phase oxide scale surface and (b) two-phase oxide+sulfide scale surface.
T (1C)
Metal S2
[80] [80]
[78]
[77]
Reference 8
(a) 4 10 (b) 3 107 (a) 3 109 (b) 1.1 108 (b) 2.5 106 (b) 1.1 108
kw
Table 4.7 Values of kw (g2 cm4 s1) for reaction in O2 (1 atm), S2 (1 atm) and SO2 (p indicated)
2
2.2 10 2.2 103 7.3 102 2.5 104 1.0 3.9 102
p (atm)
SO2
[49] [49] [20] [20] [17] [28]
Reference
176 Chapter 4 Mixed Gas Corrosion of Pure Metals
177
4.6. Predicting the Outcome of Mixed Gas Reactions
chromium, sulfidation–oxidation of iron and manganese under certain condition) and is without value in other situations, notably the sulfidation–oxidation of nickel and chromium. Among the factors leading to these different outcomes are the differing stabilities of the reaction products, the existence of heteronuclear molecules appropriate to biphase solid production and the relative rates at which secondary, metastable reaction products can be incorporated into the scale or destroyed by interaction with gas species. Selected DG values for reactions of interest are shown in Table 4.8. We consider first the question of why chromium carbide and nitride develop beneath Cr2O3 scale layers, but never at the surface, whereas chromium sulfide and oxide can develop at both locations. Appropriate gas molecules for simultaneous formation of two products exist in all cases: CO, NO and SO2. However, the feasibility of the various reactions differs greatly. Firstly, the species NO is present at only very small concentrations, as can be seen from the equilibrium 1 2N2
þ 12O2 ¼ NO; DG ¼ 90; 136 12:4 T ðJ mol1 Þ
(4.29) 5
At 9001C, for example, a gas mixture containing pN2 ¼ 1 atm and pO2 ¼ 10 atm has an equilibrium value pNO ¼ 2 107 atm. This is far too low to support a surface reaction, and the process (e) in Table 4.8 is kinetically irrelevant. The same evaluation is arrived at for other nitrogen oxides, and we conclude that no reaction is available for the formation of metastable nitride at a Cr2O3 surface. Chromium nitride can only develop by inward diffusion of nitrogen to a zone where the oxygen activity is low and chromium activity is high. The question of nitride formation on iron or nickel at high temperatures does not arise, as no stable compounds exist. A similar situation exists with carbides. No nickel carbide is stable, and the iron carbide, Fe3C, is of marginal stability. In fact it is metastable below 7481C, where values of acW1 are required for its formation. Although Fe3C is formed on iron in strongly carburizing gases (see Chapter 9), the simultaneous formation of both carbide and oxide on pure iron has not yet been reported. However, elemental carbon can be deposited in the inner parts of an iron oxide scale grown in CO2 at low temperatures, about 400–5001C [84, 85]. Gas molecules diffuse inwards through the oxide and the CO/CO2 ratio alters according to CO2 ¼ CO þ 12O2 Table 4.8
(4.30)
Selected mixed gas reaction free energies [82, 83]
Reaction
T (1C)
DG1 (kJ mol1)
(a) 3Fe+SO2 ¼ FeO+2FeS (b) 72Ni þ SO2 ¼ 12Ni3 S2 þ 2NiO (c) 3Cr þ CO ¼ 13Cr7 C3 þ 13Cr2 O3 (d) 73Cr þ SO2 ¼ CrS þ 23Cr2 O3 (e) 83Cr þ NO ¼ Cr2 N þ 13Cr2 O3
800 600 900 900 900
195 92 124 536 379
178
Chapter 4 Mixed Gas Corrosion of Pure Metals
as the oxygen activity of the scale decreases towards the metal–scale interface. As pCO rises, the Boudouard reaction 2CO ¼ CO2 þ C
(4.31)
becomes favoured (providing the temperature is low) and carbon deposition results. This is analogous to the formation of chromium carbide beneath a Cr2O3 scale, the difference being that no iron carbide can form and instead graphite precipitation results. A significant volume expansion accompanies reaction (4.31), and the resulting compressive stresses lead to oxide ‘‘bursting’’. Chromium carbides are significantly more stable (Table 2.1) and the possibility of simultaneous Cr7C3+Cr2O3 formation is now considered. As seen in Table 4.8 their formation by reaction (c) with CO is thermodynamically favourable, but the driving force is rather small, at only 42 kJ mol1 of chromium. The reaction 2Cr þ 3CO2 ¼ Cr2 O3 þ 3CO (4.32) with DG ¼ 274 kJ mol1 at 9001C is much more favourable at gas component activities near unity. The possibility of the energy barrier to surface carbide formation being overcome by oxygen depletion and consequent carbon enrichment via CO ¼ C þ 12O2
(4.33)
is remote. If this reaction dominated the surface (and CO2 processes could be neglected), the situation could be represented by the line AB in Figure 4.8. It is seen that oxygen depletion at constant pCO would lead to carbon precipitation, but not to carbide formation. We therefore conclude that formation of carbide at a Cr2O3 scale surface is not thermodynamically favoured. Instead, carbide can form beneath the oxide, where the oxygen activity is low and chromium activity high. The situation is quite different when SO2 is the reactant species, as seen in Table 4.8. The simultaneous formation of Cr2O3 and CrS in contact with the gas via reaction (d) is strongly favoured, with DG ¼ 230 kJ mol1 of metal at T ¼ 9001C and pSO2 ¼ 1 atm. The alternative reaction 2Cr þ 32SO2 ¼ Cr2 O3 þ 32S2
1
(4.34) 1
has DG ¼ 399 kJ mol at 9001C, corresponding to 200 kJ mol of chromium at unit activity of gas components. Although the reaction is favoured even at low pS2 values, a mechanism for sulfur enrichment on the surface (represented by the shift from A to B in Figure 4.10) is available. The combination of a strong driving force plus a mechanism for selective adsorption makes two-phase product formation on chromium much more favoured thermodynamically in SO2 than in CO. As is now clear, the greater stability of metal sulfides compared to that of carbides and nitrides is the fundamental reason that metastable surface sulfide formation is sometimes possible in sulfidizing–oxidizing gases. The question of interest then is why in some cases the formation of two-phase scale continues for long reaction times, whereas in others it ceases after a short time. The situation
4.6. Predicting the Outcome of Mixed Gas Reactions
179
was described earlier in terms of competing reactions for two-phase product formation (4.10) and for sulfide oxidation (4.12). Whereas the latter is purely a surface reaction, the former is controlled at least partially by the rate of metal transport through the scale. Thus, the faster the rate of scale growth, the less likely it is that sulfide formed at the surface will be oxidized. On this basis (Table 4.7) it would be predicted that sulfide formation would continue for longer times in the case of nickel, but for shorter times in the case of iron, manganese and chromium. The analysis is qualitatively successful for manganese, iron and nickel, but not for chromium, and a further factor must be involved. It has been suggested [3] that an important factor is the metal activity at the ð2-phaseÞ surface required for two-phase scale formation through reaction (4.10), aM , relative to the activity required for true local equilibrium of reaction (4.8), aðoxideÞ . m The ratio of metal activities required for these competing processes is 1=6
ð2phaseÞ
aM
aðoxideÞ M
¼
1=2 K8 pSO2 1=3
1=4
K10 pS2
(4.35)
Thus lower values of pSO2 and higher values of pS2 lower the metal activity level required to form a two-phase scale rather than the oxide. The metal activity at the scale–gas interface is high during the initial stages of reaction and presumably decreases progressively as the scale thickens, until its value is below the minimum of Equation (4.35). This accounts satisfactorily for the observed behaviour of iron, which forms a two-phase product for long times at low pSO2 values, but quickly converts to an oxide-only outer layer at high pSO2 . It is also broadly consistent with observations on the chromium reaction. When reacted at pSO2 ¼ 1 atm, chromium formed only oxide [30] but at pSO2 ¼ 0:04 atm it developed a two-phase product at the scale–gas interface [28]. However, the latter gas when fully equilibrated would have contained pSO2 ¼ 1010 atm, a value too low to be kinetically significant, but pCOS ¼ 4 104 atm. In short, a different surface mechanism was in effect, and the utility of Equation (4.35) cannot be tested. The value of aM at the scale–gas interface is certainly an important parameter. As noted by Gesmundo et al. [3], any pre-oxidation treatment carried out at a high pO2 would result in a low surface aM value, and an inability of the scale to form any oxide-plus-sulfide product when subsequently exposed to SO2. As seen earlier, pre-oxidation of nickel at high pO2 (air or pure oxygen) produced scales which resisted sulfide formation at the surface, and eventually formed sulfide beneath the oxide when exposed to SO2. This is to be contrasted with the continued growth of oxide-plus-sulfide on nickel exposed to SO2 without preoxidation, where a higher surface aNi value must have been available. An analogous effect has been observed [64] in the reaction of chromium. As discussed earlier, chromium reacts with CO/CO2/N2/SO2 gas mixtures to form an outer layer of Cr2O3+Cr5S6. If, however, the metal was first pre-oxidized and then exposed to the same oxidizing–sulfidizing gas mixture, the sulfide formed at the scale surface was identified as Cr3S4. The Cr5S6 phase is not stable at the reaction temperature of 9001C, being formed during cooling from the high
180
Chapter 4 Mixed Gas Corrosion of Pure Metals
temperature Cr1dS phase. The growth of the lower sulfide indicates that a higher surface aCr value was available. Pre-oxidation depressed asCr , allowing the higher sulfide to form. The experimental data for both nickel and chromium provide qualitative support for the proposal that surface sulfide formation is favoured by high surface aM values, and that these can be lowered by suitable pre-oxidation treatments. High surface aM values are supported by rapid diffusion of metal through the sulfide phase, or along interphase boundaries. However, despite these successes, Equation (4.35) is not universally applicable. Evaluation of the relevant equilibrium constants using the data in Table 4.8 leads to the prediction that formation of a two-phase product requires a higher activity of nickel than of iron. Despite this, a sulfide-plus-oxide scale persists on nickel whereas on iron it is soon overgrown by oxide. Here the kinetic factors outweigh the thermodynamics because diffusion in the nickel sulfides is fast enough to maintain high asNi values. As will be discussed in Chapter 7, further complexities arise in the mixed gas corrosion of alloys. It is sufficient therefore to conclude that the formation of additional reaction products (carbides, nitrides and sulfides) during oxidation of metals is governed by both thermodynamic and kinetic factors as well as gas adsorption processes. In general, thermochemical diagrams are successful in predicting the phases formed in contact with carburizing–oxidizing and nitriding–oxidizing gases. This success is attributable to the low stability of carbides and nitrides compared to that of oxides. However, the diagrams frequently fail to predict scale constitutions formed in contact with sulfidizing–oxidizing gases. One reason for this failure is the higher stability of metal sulfides which can be sufficient to enable a metastable oxide-plus-sulfide mixture to form. Another reason is the ability of sulfur to adsorb preferentially on the scale surface, resulting in a surface richer in sulfur than the gas phase. The differences between the scales grown on different metals exposed to oxidizing–sulfidizing gases cannot be rationalized in terms of phase stabilities alone. The ability of the scale to support rapid metal diffusion, thereby maintaining high surface metal activities is an important factor in promoting two-phase product formation in direct reaction with SO2. In this respect, the behaviour of nickel is unique, as a result of its formation of high diffusivity Ni37dS2 (DNiE105 cm2 s1 at 6001C) at temperatures of 533–6351C, and liquid sulfide at higher temperatures. For this reason, the formation of mixed oxide-plus-sulfide on nickel continues for very long times, and metal destruction is extensive. The use of diffusion paths to describe phase distributions within reaction product scales is only sometimes of value. Inward diffusion of gaseous species adsorbed on internal surfaces can be represented by diffusion paths in the cases of oxidation–carburization and oxidation–nitridation of chromium. However, interaction between diffusing species (e.g. CO, N2, SO2) via competitive adsorption can prevent the diffusion of nitrogen and slow the transport of carbon, changing the diffusion paths. The diffusion path concept is of even less value in describing sulfidation–oxidation reaction. In the case of nickel and chromium,
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SO2 usually reacts at the scale surface rather than penetrating the oxide. In the case of iron, SO2 reacts at the surface initially, but cannot penetrate the iron oxide outer layer once it is formed. A very large research effort into mixed gas corrosion reactions has yielded a substantial body of descriptive knowledge, an appreciation of the multitude of factors involved and a capacity to interpret and understand the results. However, our predictive capacity is at best qualitative. Nonetheless, the understanding which has been developed does provide a rational basis for experimental design to use in any future research. This may prove to be of considerable value as new technologies for fossil fuel processing are developed to improve efficiencies and reduce greenhouse gas emissions.
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33. F. Gesmundo, C. DeAsmundis and P. Nanni, Oxid. Met., 20, 217 (1983). 34. M. Seiersten and P. Kofstad, Corros. Sci., 22, 497 (1982). 35. W.L. Worrell and B.K. Rao, in Proc. Int. Conf. High Temperature Corrosion, ed. R.A. Rapp, NACE, Houston, TX (1983), p. 295. 36. N. Jacobson and W.L. Worrell, in Proc. 3rd Int. Conf. Transport in Nonstoichiometric Compounds, eds. G. Simkovich and V.S. Stubican, Plenum Press, New York (1984), p. 451. 37. M.R. Wootton and N. Birks, Corros. Sci., 12, 829 (1972). 38. H. Nakai, K. Okada and Y. Kato, in Proc. 3rd JIM Int. Symp. High Temperature Corrosion of Metals and Alloys, Japan Institute of Metals, Sendai (1983), p. 427. 39. C.B. Alcock, M.G. Hocking and S. Zador, Corros. Sci., 9, 111 (1969). 40. V. Vasantasree and M.G. Hocking, Corros. Sci., 16, 261 (1976). 41. M.G. Hocking and V. Vasantasree, Corros. Sci., 16, 279 (1976). 42. K.L. Luthra and W. Worrell, in Proc. Symp. Properties of High Temperature Alloys, eds. Z.A. Foroulis and F.S. Pettit, Electrochem. Soc., New York (1976), Vol. 1, p. 318. 43. K.L. Luthra and W.L. Worrell, Met. Trans. A, 10A, 621 (1979). 44. B. Haflan and P. Kofstad, Corros. Sci., 23, 1333 (1983). 45. P.K. Lillerud, B. Haflan and P. Kofstad, Oxid. Met., 21, 119 (1984). 46. N. Birks, in Proc. Symp. High Temp. Gas-Metal Reactions in Mixed Environments, eds. S.A. Jansson and Z.A. Foroulis, Met. Soc. AIME, New York (1973), p. 322. 47. K. Holthe and P. Kofstad, Corros. Sci., 20, 919 (1980). 48. G. McAdam and D.J. Young, Oxid. Met., 37, 281 (1992). 49. J. Unsworth and D.J. Young, Oxid. Met., 60, 447 (2003). 50. A. Rahmel and J.A. Gonzalez, Werkst. Korros., 22, 283 (1971). 51. P. Singh and N. Birks, Oxid. Met., 12, 23 (1978). 52. N.S. Jacobson and W.L. Worrell, J. Electrochem. Soc., 131, 1182 (1984). 53. P. Kofstad, High Temperature Corrosion, Elsevier, London (1988). 54. V. Guerra-Brady and W.L. Worrell, in Proc. 10th Int. Symp. Reactivity of Solids, eds. P. Barret and L.C. Dufour, Materials Science Monographs, 28A, Elsevier, Amsterdam (1985), p. 61. 55. M.H. Davies, M.T. Simnad and C.E. Birchenall, Trans. AIME, 191, 889 (1951). 56. M. Hillert, ed., ‘‘The Mechanisms of Phase Transformations in Crystalline Solids, Institute of Metals, London (1969). 57. N. Birks and G. Meier, Introduction to High Temperature Oxidation of Metals, Edward Arnold, London (1983). 58. A. Rahmel and J.A. Gonzalez, Corros. Sci., 13, 433 (1973). 59. M.C. Pope and N. Birks, Oxid. Met., 12, 173 (1978). 60. P. Singh and N. Birks, Werkst. Korros., 31, 682 (1980). 61. P. Kofstad and G. Akesson, Oxid. Met., 13, 57 (1979). 62. W.L. Worrell and B. Ghosal, in Proc. 3rd JIM Int. Symp. High Temperature Corrosion of Metals and Alloys, Japan Institute of Metals, Sendai (1983), p. 419. 63. M.H. La Branche, A. Garrat-Reed and G.J. Yurek, J. Electrochem. Soc., 130, 2405 (1983). 64. X.G. Zheng and D.J. Young, Corros. Sci., 38, 1877 (1996). 65. N. Birks, in Proc. Symp. Properties of High Temperature Alloys, eds. Z.A. Foroulis and F.S. Pettit, Electrochemical Society (1976), Vol. 1, p. 215. 66. K.N. Strafford and P.J. Hunt, in Proc. Int. Conf. High Temperature Corrosion, ed. R.A. Rapp, NACE, Houston, TX (1983), p. 380. 67. D.R. Chang, R. Nemoto and J.B. Wagner, Met. Trans. A, 78A, 803 (1976). 68. W.Y. Howng and J.B. Wagner, J. Phys. Chem. Solids, 39, 1019 (1978). 69. P. Dumes, A. Fauvre and J.C. Colson, Ann. Chim. Fr., 4, 269 (1979). 70. J.S. Choi and W.J. Moore, J. Phys. Chem., 66, 1308 (1962). 71. J.B. Wagner, Oxid. Met., 23, 251 (1985). 72. B. Gillot and D. Garnier, Ann. Chim. Fr., 5, 483 (1989). 73. J. Gillewicz-Wolter and K. Kowalska, Oxid. Met., 22, 101 (1984). 74. J. Stringer and D.P. Whittle, Rev. Int. Htes Temp. et Refract., 14, 6 (1977).
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75. J. Stringer, in Proc. Int. Conf. Behaviour of High Temperature Alloys in Aggressive Environments, eds. I. Kirman, J.B. Marriott, M. Merz, P.R. Sahm and D.P. Whittle, Metals Society, London (1980), p. 739. 76. I. Wolf and H.J. Grabke, Solid State Comm., 54, 5 (1985). 77. S. Mrowec, in Proc. 8th Int. Conf. Metallic Corrosion, Dechema, Frankfurt (1981), Vol. 3, p. 2110. 78. K. Nishida, T. Narita, T. Tassi and S. Sesaki, Oxid. Met., 14, 65 (1980). 79. E.A. Gulbransen and K.F. Andrew, J. Electrochem. Soc., 101, 128 (1954). 80. S. Mrowec and K. Przybylski, High Temp. Mater. Processes, 6, 1 (1984). 81. D. Caplan and G.I. Sproule, Oxid. Met., 9, 459 (1975). 82. O. Kubaschewski and C.B. Alcock, Metallurgical Thermochemistry, 5th ed, Pergamon, Oxford (1983). 83. T. Rosenquist, J.I.S.I., 176, 36 (1954). 84. Corrosion of steels in CO2, Proc. British Nuclear Energy Society Int. Conf. Reading University, eds. D.R. Holmes, R.B. Hill and L.M. Wyatt, British Nuclear Energy Society, London (1974). 85. G.B. Gibbs, Oxid. Met., 7, 173 (1973).
CHAPT ER
5 Oxidation of Alloys I: Single Phase Scales
Contents
5.1. 5.2. 5.3. 5.4. 5.5.
Introduction Selected Experimental Results Phase Diagrams and Diffusion Paths Selective Oxidation of One Alloy Component Selective Oxidation of One Alloy Component Under Non-Steady-State Conditions 5.6. Solid Solution Oxide Scales 5.6.1 Modelling diffusion in solid solution scales 5.7. Transient Oxidation 5.7.1 Transient behaviour associated with alumina phase transformations 5.8. Microstructural Changes in Subsurface Alloy Regions 5.8.1 Subsurface void formation 5.8.2 Scale–alloy interface stability 5.8.3 Phase dissolution 5.8.4 New phase formation 5.8.5 Other transformations 5.9. Breakdown of Steady-State Scale 5.10. Other Factors Affecting Scale Growth References
185 187 193 196 202 206 209 216 219 226 226 229 230 235 236 237 241 243
5.1. INTRODUCTION Most metallic materials of practical importance are alloys. Even mild steel invariably contains some level of carbon, and usually small amounts of other elements. The alloys and coatings employed for heat resisting applications are usually based on iron, nickel or cobalt and contain chromium and/or aluminium to provide protective oxide scales. The choice of chromium and aluminium is based on the slow rate at which their oxides grow (see Table 1.1) and the fact that these oxides are considerably more stable than those of iron, nickel or cobalt (see Table 2.1). Thus Cr2O3 and Al2O3 are thermodynamically favoured and will form preferentially if this is kinetically possible. Alloy additions of silicon would seem to meet the same
185
186
Chapter 5 Oxidation of Alloys I: Single Phase Scales
criteria, and to possess the added advantage of being readily available in the economic form of ferrosilicon. However, the use of silicon as an alloying additive is limited by metallurgical constraints. Since silicon decreases the weldability and toughness (or impact resistance) of steels and nickel-base alloys, its concentration is limited to such low levels that formation of a silica layer alone cannot be achieved. However, silica scales play a protective role in the high temperature performance of a number of non-oxide ceramics, e.g. MoSi2, SiC and Si3N4. A very large research and development effort has led to the production of present-day heat-resisting materials, and is continuing in the search for better ones. The literature in this field is consequently vast, and no attempt will be made to review it here. Instead, the focus will be on developing an understanding of the different modes of alloy oxidation, finding ways of predicting the circumstances under which each of these modes operates, and calculating the rate of alloy consumption in each case. This chapter is concerned principally with the factors which determine whether an alloy forms a protective scale of the desired low diffusivity oxide (usually Cr2O3 or Al2O3) or some other reaction products. The number of possible outcomes is large and increases with alloy complexity, each additional alloy component providing an additional degree of thermodynamic freedom, as seen in Equation (2.35). Even a simple binary alloy can develop two-phase regions within the scale and/or form non-planar interfaces between adjacent phases. It can also precipitate oxide of its more reactive component inside the alloy in the process of internal oxidation. Alloy components will form oxides of different stabilities. Moreover, the component metals will generally have differing mobilities in each relevant phase, alloy and oxides, as well as varying intersolubilities. The situation can be further complicated by the existence of multiple phases within the alloy (e.g. ferrite+Fe3C in steel; g þ g0 in superalloys; etc.), the formation of ternary product phases, and occasionally the development of low-melting eutectics such as FeO–Fe2SiO4 on silicon steels. In addition, the distribution of reaction product phases, that is to say the reaction morphology, will usually change with time. In an initial, transient stage, all reactive alloy components oxidize, yielding a product with essentially the same relative proportions of metallic constituents as the parent alloy. Subsequently, local equilibrium is achieved at alloy–scale and scale–gas interfaces, and steady-state reaction follows. During this stage, the scale morphology and composition are invariant with time, and the phase diagram ‘‘diffusion path’’ description applies. Heat resisting alloy design is directed towards achieving a slow growing oxide scale during the steady state. Ultimately, the alloy component responsible for protective oxide formation is exhausted or ceases to be available, and a final breakdown stage ensues. Eventually, of course, the final oxidation product contains reactive alloy components in the same proportions as did the original alloy. We consider first some experimental results for alloy oxidation selected to illustrate the diversity of reaction product morphologies. Attention is then concentrated on the situation in which a single-phase oxide is the only reaction product. Its possible morphologies, growth rates and protective value are then
5.2. Selected Experimental Results
187
investigated, drawing heavily on the extensive theoretical treatments developed by Wagner and added to by others. Finally, some consideration is given to predicting the lifetime of an alloy component forming a protective scale in the steady-state regime. For detailed descriptions of the oxidation behaviour of individual alloys, the reader is referred to the proceedings of the many conferences addressing the topic. Some have been established as regular international conference proceedings [1–3]. In addition, a useful summary of commercial alloy performance in various high temperature environments has been provided by Lai [4].
5.2. SELECTED EXPERIMENTAL RESULTS Many high temperatures alloys are designed to form protective chromia (Cr2O3) scales. Examples include stainless and heat-resisting steels, and nickel-based alloys such as Incoloys and some Inconels. Compositions of some representative alloys are given in Table 5.1. A larger collection is found in Appendix A. The range of possible steady-state behaviour of chromia forming alloys is shown in Figure 5.1. A model binary alloy of Fe–28Cr (all compositions in wt%) is seen in Figure 5.1a to form an external scale of Cr2O3 alone when reacted with oxygen at 9001C. The scale grows slowly, with kp ¼ 1.4 109 cm2 s1, Table 5.1
a
Nominal compositions of some heat resisting alloys (wt%)
Alloy
Fe
Ni
Cr
Si
Mn
P91
bal
0.3
9
0.4
304L 310 347 253MA 353MA 800 HP (cast) 601 617
bal bal bal bal bal bal bal 14 1.5
8–12 20 11 11 35 31 35 bal bal
18–20 25 18 21 25 21 25 23 22
1 1.5 1.0 1.7 1.6 1.8
0.2
0.5
0.5
214 Kanthal A Kanthal AF MA956 PM2000
3
bal bal
0.5 0.5
bal bal bal
16 0.2 20.5–23.5 0.7 21 20 19
JA13
bal
16
0.1
Reactive element metals.
Al
C
Other
0.4
0.10
1Mo, 0.2V
2 2.0 2.0 0.8 1 r2.0
0.03 0.25 0.08 0.08 0.06 0.07 0.44 0.06 0.07
1.4
0.3
4.5 5.3 5.1 4.5 5.8
0.05 0.08 0.01 0.01
5.0
0.03
Nb (8 %C) 0.08Ce REMa 0.25Al, 0.35Ti 0.8Nb 0.5Ti 12.5Co, 9Mo, 0.3Ti, 0.2Cu 0.01Y 0.08Ti, 0.06Zr 0.5Ti, 0.5Y2O3 0.5Ti, 0.2Ni, 0.5 Y2O3 0.3Y
188
Chapter 5 Oxidation of Alloys I: Single Phase Scales
10m
(a)
(b)
MCr2O4 Cr2O3
20μm (c)
(d)
Figure 5.1 (a) External Cr2O3 scale grown on Fe–28Cr at T ¼ 1,0001C, (b) iron-rich scale grown on Fe–7.5Cr at T ¼ 8501C in pure O2, (c) simultaneous external Cr2O3 scale growth and internal Al2O3 precipitation, alloy IN 601 at T ¼ 1,0001C and (d) two-layered scale of spinel and Cr2O3 together with internal attack on HP35 cast, heat resisting steel oxidized in steam at 1,0001C.
representing the desired outcome of single-phase protective layer growth. However, when the alloy chromium content is too low, this protective layer does not form. A model alloy of Fe–7.5Cr reacted with oxygen at 8501C to form a fastgrowing iron-rich scale, as shown in Figure 5.1b. Dilute alloys can fail to form a protective scale even if the oxygen partial pressure is too low to oxidize any component except chromium. As will be seen in Figure 6.1, Cr2O3 is internally precipitated within an Fe–5Cr alloy reacted at 1,0001C, in a low pO2 atmosphere. Oxygen had dissolved in the alloy, diffusing inwards to react with solute chromium and precipitate its oxide. It is obviously desirable to be able to predict the minimum alloy chromium level required to form external rather than internal Cr2O3, and thereby protect the alloy iron base from oxidation. Commercial chromia-forming alloys can be even more complex in their reaction morphologies. Oxidation of Inconel 601, which contains a low level of
5.2. Selected Experimental Results
189
aluminium in addition to 23% Cr (Table 5.1), is seen in Figure 5.1c to form an external Cr2O3 scale and internal Al2O3 precipitates. A cast heat-resisting steel (HP grade, 25Cr–35Ni) oxidized in steam at 1,0001C to form a two-layered scale (Figure 5.1d). A continuous chromia inner layer formed, but a manganese-rich spinel (MCr2O4 with M a mixture of Mn, Fe and Ni) layer grew on top. Clearly it is necessary to establish the conditions under which the desired oxide scale can prevent the oxidation of other alloy components. In the example of Figure 5.1d, the chromia layer had allowed outward diffusion of manganese to form a surface layer of spinel. The chromia scale shown in Figure 5.1c had allowed oxygen to diffuse into the alloy, precipitating alumina. In these particular cases, the chromia scale nonetheless protected the alloy iron and nickel from reaction. Alloy oxidation can also lead to changes within the alloy itself. We have already encountered the example of internal oxidation, which reflects the inward diffusion of oxidant. Microstructural changes in the alloy can also result from outward diffusion of alloy components. A common example is decarburization. Figure 5.2 shows a cross-section of a tube wall from a failed boiler superheater unit. Overheating of this tube led to rapid oxidation, tube wall thinning and subsequent mechanical failure as the steam pressure inside the tube ruptured its wall. The tube metal was a 1¼Cr–1Mo steel which has a microstructure of ferrite plus pearlite. The pearlite (a mixture of lamellar Fe3C and ferrite) is seen in the lower part of the wall cross-section to have coarsened and spheroidized. In the upper part of the cross-section, near the rapidly oxidizing external surface,
Figure 5.2 Cross-section of tube wall (1¼Cr+1Mo steel) from failed boiler superheater unit, showing decarburization beneath the outer (upper) surface.
190
Chapter 5 Oxidation of Alloys I: Single Phase Scales
the carbide has almost completely disappeared. Here the solute carbon from within the ferrite was oxidized at the steel–scale interface via the reaction: C þFeO ¼ Fe þ COðgÞ
(5.1)
DG1 ¼ 147; 760 150:1T J mol1
(5.2)
for which
The resulting CO(g) escaped through the porous scale. As a result, the carbon activity in the steel at the surface was lowered, causing the cementite to dissolve: Fe3 C ¼ 3Fe þ C
(5.3)
Solute carbon diffused from the interior carbide dissolution front to the steel– scale interface, there to be oxidized and removed. Selective oxidation of an alloy constituent lowers its concentration within the alloy. If alloy diffusion is rapid compared with the scaling rate, then the change in alloy concentration is averaged over a large region, and the concentration change at the alloy–scale interface will be small. However, if alloy diffusion is relatively slow, replenishment of the selectively removed metal is hindered, and the concentration of that element is depleted in the subsurface zone, as illustrated schematically in Figure 5.3. When the concentration of one component is decreased, the concentrations of others are increased. The extent to which they are enriched is governed by the rates at which they diffuse away from the surface O2 (g)
BO
Alloy AB
NA NB
Figure 5.3 Depletion of selectively oxidized alloy component and enrichment of non-oxidized component in binary alloy.
191
5.2. Selected Experimental Results
into the alloy interior. These changes in subsurface composition can cause alterations in the phase constitution of this region. A simple example of practical importance is the precipitation of a copper-rich phase at the surface of steel during hot working [5]. A significant quantity of steel is produced by remelting scrap. Most scrap impurities are removed during the steelmaking process, but some, such as copper and tin, remain. Several successive cycles of steelmaking and recycling as scrap lead to an increase in the concentration of ‘‘residuals’’ such as copper to levels far above those found in steel produced from iron ore. Oxidation of steel is inevitable during hot working (reheating, rolling, etc.), producing a scale of iron oxide, but leaving the copper unreacted. The resulting increase in copper concentration in the steel beneath the scale can exceed the solubility limit, precipitating a copper-rich Cu–Fe phase. An example is shown in Figure 5.4. If the temperature is above about 1,1001C, this phase is liquid, and penetrates the steel grain boundaries. Mechanical working of the steel in this state causes cracking, a phenomenon known as ‘‘hot shortness’’. The selective removal from an alloy of a metal by its preferential oxidation can drive other phase changes within the subsurface zone. An example is shown in Figure 5.5, where selective oxidation of aluminium from a two-phase g-Ni plus gu-Ni3Al alloy led to dissolution of the aluminium-rich gu-phase, as aluminium diffused out of the subsurface zone. Selective oxidation of aluminium from b-NiAl does not at first cause a phase change, but it does lead to the development of cavities at the alloy–scale interface, as shown in Figure 5.6. Taking as a measure of success the ability of an alloy to form a single-phase scale of the desired oxide, it is desirable to be able to predict the conditions (alloy composition, pO2 and temperature) under which this will be the result. As seen in this preliminary examination, it is necessary to predict not only when the desired
100
FeO
Steel
Cu
Concentration (at%)
90
Fe
80 70 60
O
50 40 30
Cu
20 10
Sn
0 0
2
4
6 8 10 Distance (μm)
12
Figure 5.4 Copper enrichment beneath iron oxide scale grown on a 0.47Cu steel at T ¼ 1,1001C. Left: SEM view of cross-section and right: EPMA scan.
14
16
192
Chapter 5 Oxidation of Alloys I: Single Phase Scales
γ
γ + γ’
100µm Figure 5.5 Dissolution of gu-Ni3Al in subsurface region of g+gu model alloy (Ni–23Al) due to selective aluminium oxidation at 1,2001C.
Al2O3
Figure 5.6 FIB image showing cavity formation at b-NiAl surface due to selective aluminium oxidation at 1,2001C.
193
5.3. Phase Diagrams and Diffusion Paths
oxide will form preferentially, but also when it forms as an external layer rather than an internal precipitate. Further, it is necessary to predict the effect of the external layer on the oxidation of other alloy components and on microstructural changes in the alloy subsurface region. We consider first the utility of phase diagrams in predicting diffusion paths and thereby reaction morphologies.
5.3. PHASE DIAGRAMS AND DIFFUSION PATHS During the steady-state period of alloy oxidation, the scale morphology, i.e. the identity and spatial arrangement of phases in the reacting system, is timeinvariant. This situation is conveniently represented by a diffusion path mapped onto the relevant phase diagram on the assumption that local equilibrium is in effect. The general nature of the problem is examined using the Ni–Cr–O isothermal section [6] shown in Figure 5.7. In this particular system, two simple oxides, NiO and Cr2O3, and a ternary spinel, NiCr2O4, can exist, and the degree of miscibility or intersolubility of the
O
NiCr2O4(S) Cr2O3 NiO NiO+S +Alloy
O3 Cr 2 + S
+
loy
Al
Alloy+ Cr2O3
Ni
Figure 5.7 Isothermal section of Ni–Cr–O phase diagram at T ¼ 1,0001C [6]. With kind permission from Springer Science and Business Media.
Cr
194
Chapter 5 Oxidation of Alloys I: Single Phase Scales
oxides is very limited. As seen from the diagram, all three oxides can co-exist at equilibrium with pO2 ¼ 1 atm, as can also two-phase mixtures of NiO+NiCr2O4 and NiCr2O4+Cr2O3. Thus specifying the ambient conditions is insufficient to determine the oxide which will be stable at the surface of a growing scale. Obviously, at least the alloy composition is required as well. Local equilibrium at the alloy–scale interface is specified by the tie-lines joining alloy composition points to the corresponding oxides. According to Figure 5.7 then, all Ni–Cr alloys containing N Cr 0:03 should form the desired oxide Cr2O3 at 1,0001C. However, experimental investigations of alloy reactions with pure oxygen and other oxidizing gases [7–10] have shown that a minimum chromium level of 10–20% is required to ensure the selective formation of Cr2O3. The major reason for the discrepancy is chromium depletion in the alloy subsurface zone. The chromium concentration at the alloy–scale interface is reduced (by its selective oxidation) to a value significantly lower than that of the bulk alloy. To relate the alloy chromium mole fraction value, NCr, to the interfacial value, NCr,i, it is necessary to analyse the alloy diffusion process. The same difficulty arises in the case of Fe–Cr alloy oxidation. An isothermal section of the Fe–Cr–O phase diagram is shown in Figure 2.5. As discussed earlier, the minimum value of NCr necessary to thermodynamically stabilize Cr2O3 formation is about 0.04. Experimental observations [7, 11], however, put the critical alloy concentration at about 14% at 1,0001C. Again, a principal reason for the difference is a lowering of the value NCr,i as a result of relatively slow alloy diffusion. The Co–Cr system exhibits an even greater extent of depletion, requiring up to 30% chromium to provide the critical interfacial value, estimated as N Crit 0:01, required for Cr2O3 formation. The question of how to deal with the alloy depletion problem is addressed in the next section. Returning now to the different reaction morphologies shown in Figure 5.1, we see that they are consistent with the phase diagram, once allowance is made for surface alloy depletion. Thus the Fe–28Cr has enough chromium to sustain N Cr; i 4N Cr; Crit , and a Cr2O3 scale results. A small degree of depletion in the Fe–7.5Cr alloy is sufficient to lower NCr,i below the critical value and the diffusion path shown in Figure 5.8 results. It is noted that the Fe–28Cr alloy develops a convoluted alloy–scale interface, at which voids are nucleated. Neither effect is predictable from the phase diagram without detailed knowledge of the local diffusion processes. Reaction morphologies depend on oxygen partial pressure as well as alloy composition. The internal precipitate morphology of Figure 6.1 was produced in a gas with pO2 too low to oxidize iron, so that Cr2O3 was the only stable reaction product. The formation of internally precipitated Cr2O3 corresponds to the development of a two-phase region, as shown by the diffusion path in Figure 5.8. For comparison, a diffusion path is shown for external (single-phase) Cr2O3 formation at a higher alloy NCr value. Both paths terminate at the same oxygen potential, but at different mCr and mFe values. It is obviously not possible to predict from the phase diagram alone which of the two morphologies will result for a particular alloy composition. Again, a diffusional analysis will be required.
5.3. Phase Diagrams and Diffusion Paths
195
Figure 5.8 Diffusion paths on Fe–Cr–O phase diagram corresponding to (a) depletion and iron-rich oxide growth, (b) internal, (c) combined internal and external and (d) external chromium oxidation.
As already mentioned, even when an external single-phase Cr2O3 layer forms in contact with the alloy surface, there remains the possibility of additional oxide formation. Formation of a spinel layer on top of the chromia, as illustrated in Figure 5.1d, is a common result for heat resisting steels. A schematic diffusion path for this type of scale morphology is shown for the Fe–Cr–O system in Figure 5.8. Clearly the outer layer can develop only if the second metal is soluble in Cr2O3 and can diffuse through it at a sufficient rate. We return to this question in Chapter 7. The complex reaction morphologies shown here are all consistent with steady-state local equilibrium having been established within the reacting systems. This was shown experimentally in each case by the observations that the morphologies were time invariant as the extent of reaction increased. It is also evident from the fact that the sequence of phase assemblages making up the morphology can in each case be represented by a diffusion path on the relevant phase diagram. It is clear that phase diagrams of the type A–B–O can be used to describe the oxidation morphologies of binary alloys, AB. However, diffusion within the alloy
196
Chapter 5 Oxidation of Alloys I: Single Phase Scales
in general leads to surface concentrations which differ from those of the bulk alloy. To predict alloy oxidation behaviour it is necessary to be able to calculate these concentration changes. We now consider the diffusion processes supporting growth of a single-phase scale on a binary alloy. In general, such an oxide can contain both alloy components, depending on the intersolubility of AO and BO, and their relative stabilities. We consider first the simplest case, where one alloy component remains completely unoxidized, and a pure binary oxide results from selective oxidation of the other.
5.4. SELECTIVE OXIDATION OF ONE ALLOY COMPONENT Selective oxidation will occur if only one oxide is stable. This is the case for alloys consisting of a noble metal such as Pt, Ag or Au, which does not form an oxide under normal conditions, and a reactive metal which does. An example of this alloy class is Pt–Ni, which was analysed by Wagner [12]. It is also the case for more practically relevant alloy systems such as Fe–Cr and Ni–Cr if the ambient oxygen potential is below the minimum necessary to form any iron- or nickelbearing oxide, but still above the value required for Cr2O3 formation. In the case of exclusive scale formation, it is of interest to know whether the scaling rate is controlled by diffusion in the scale or in the alloy. In a formal sense this question lacks meaning, as the rates at which B diffuses in the alloy and the scale must be in balance for a steady state to exist. However, it is reasonable to classify the process as being controlled by scale diffusion if the scale grows at the same rate as it does on pure B metal. Conversely, scaling is described as being controlled by alloy diffusion if the rate at which BO grows on the alloy is significantly less than on pure B metal. We therefore compare scaling rates on the two materials. The growth rate of a NiO scale on a Pt–Ni alloy is proportional to the nickel cation flux in the oxide, given by Equation (3.71), rewritten here as ðiÞ 1=6 ½ðp00O2 Þ1=6 ðpO Þ 2 (5.4) ¼ Constant X ðiÞ where, as before, p00O2 is the ambient oxygen partial pressure and pO the value at 2 the alloy–scale interface. Doubly charged cation vacancies have been assumed, but a different charge can be accommodated by changing the exponent of pO2 . Scale growth on pure nickel is related to the corresponding flux expression
J NiO Alloy
ðeqÞ
½ðp00O2 Þ1=6 ðpO2 Þ1=6 (5.5) X ðeqÞ Here pO2 represents the partial pressure for equilibrium between pure nickel and its oxide. The ratio of the two fluxes at a given scale thickness is therefore J NiO Metal ¼ Constant
a¼
J NiO Alloy J NiO Metal
¼
1=6 ðp00O2 Þ1=6 ðpðiÞ O2 Þ ðeqÞ
ðp00O2 Þ1=6 ðpO2 Þ1=6
(5.6)
The boundary value oxygen pressures are next related to nickel concentrations.
5.4. Selective Oxidation of One Alloy Component
197
The equilibrium condition for the reaction 2 Ni þO2 ¼ 2NiO
(5.7)
is written ðeqÞ
a2Ni pO2 ¼ K1 7 ¼ pO2
(5.8) ðeqÞ pO 2
has the where pure nickel is the reference state, for which aNi ¼ 1 and standard equilibrium value. If the alloy is assumed to be ideal, we can write for the alloy–scale interface ðeqÞ
ðiÞ N 2Ni;i pO ¼ pO2 2
(5.9)
where N Ni;i denotes the nickel mole fraction at the alloy–scale interface. Since platinum is unreactive, it is possible to identify an alloy nickel level, N Ni;e , which will equilibrate with NiO and an oxygen partial pressure equal to the ambient value, p00O2 ðeqÞ
N 2Ni;e p00O2 ¼ pO2
(5.10)
00 Substitution in Equation (5.6) for pðiÞ O2 and pO2 from Equations (5.9) and (5.10) leads to
a¼
1 ðN Ni;e =N Ni;i Þ1=3 1 ðN Ni;e Þ1=3
(5.11)
Values of N Ni;e are very low in the case of Pt–Ni alloys. Wagner [12] calculated values of 6 107 and 6 105 at 8501C and 1,1001C, for p00O2 ¼ 0:21 atm. According to Equation (5.11), then, a 1 and oxidation is controlled essentially by diffusion in NiO, if N Ni;i 0:01. To make use of this finding, it is necessary to relate the interfacial mole fraction N Ni;i to the original alloy level N ðoÞ Ni . The concentration at the interface is established by the diffusion of nickel towards the interface from the alloy, and away from it into the oxide. Assuming ~ is independent of composition, Fick’s that the alloy diffusion coefficient, D, second law applies 2 @N Ni ~ @ N Ni ¼D @t @x2
(5.12)
where x is the distance from the alloy surface and the initial condition N Ni ¼ N ðoÞ Ni
for t ¼ 0;
x40
(5.13)
applies. The problem is simplified considerably if movement of the alloy surface can be ignored. This will be a reasonable approximation if only a very thin oxide scale is formed, and alloy surface recession is consequently small. Diffusion within the alloy is then treated as the semi-infinite case (a limiting case of Equation (2.140) in which Ci ¼ (C0+C1)/2) with a fixed boundary, leading to the steady-state solution ! x ðoÞ pffiffiffiffiffiffi N Ni ¼ N Ni; i þ N Ni N Ni; i erf (5.14) ~ 2 Dt
198
Chapter 5 Oxidation of Alloys I: Single Phase Scales
The analysis is continued by enquiring as to what interfacial nickel concentration corresponds to an alloy flux sufficient to sustain NiO scale growth. The flux of nickel towards the alloy surface is given by ~ @N Ni D J AB ¼ (5.15) V AB @x x¼0 where V AB is the alloy molar volume. The differential is evaluated from Equation (5.14), recalling the error function definition (see Appendix C) Z z 2 erf ðzÞ ¼ pffiffiffi expðZ2 ÞdZ (5.16) p o and obtaining
!2 1 @N Ni 2 x ðoÞ ¼ N Ni N Ni; i pffiffiffiffiffiffi pffiffiffi exp pffiffiffiffiffiffi @x p ~ ~ 2 Dt 2 Dt
(5.17)
Evaluation at x ¼ 0, followed by substitution into Equation (5.15) then yields ~ 1=2 N ðoÞ N Ni;i Ni D (5.18) J AB ¼ VAB pt To sustain external scale growth, this flux must equal the rate at which nickel is incorporated into the growing scale, dðnNi =AÞ (5.19) dt where nNi =A represents the number of moles of nickel in the scale per unit surface area. This rate is found from scale thickening n X Ni d (5.20) ¼d VNiO A J AB ¼
and since X2 ¼ 2kp t,
2 kp dðnNi =AÞ 1 ¼ dt VNiO t
Combining Equations (5.18), (5.19) and (5.21), we obtain 2 V AB pkp ðoÞ N Ni N Ni;i ¼ ~ V NiO D
(5.21)
(5.22)
Wagner pointed out that the maximum flux available from the alloy was delivered if N Ni;i 0, and this enables the calculation from Equation (5.22) of a minimum level of N ðoÞ Ni necessary to sustain external scale growth. This point is discussed further below. The approximation used above of a zero rate of scale–alloy interface movement can be avoided and the moving boundary incorporated into the description. The interface movement is related to the scaling rate by Equation (1.29), using V AB in place of V M . The position of the alloy–scale interface relative
5.4. Selective Oxidation of One Alloy Component
199
to its original location, DxM , is given by DxM ¼ ð2akc tÞ1=2 kc
(5.23) kc =kc .
is the corrosion rate constant for pure nickel and a ¼ The mass where balance of Equations (5.21) and (5.22) is then replaced by a balance for platinum, which is rejected from the oxide and diffuses from the scale–alloy interface into the alloy. The amount of platinum (per unit surface area) made available when the interface advances by an increment dy is equal to ð1 N Ni; i Þdy. The rate at which that occurs is equated to the diffusion rate, which is given by Fick’s first law, evaluated at the interface. Thus dy @ð1 N Ni Þ ~ ¼ D ð1 N Ni;i Þ (5.24) dt @x x¼y assuming that the alloy molar volume is independent of composition. Wagner found the result 1=2 N ðoÞ kc Ni N Ni;i ¼F ~ 1 N Ni;i 2D
(5.25)
where the function F(u) is defined by FðuÞ ¼ p1=2 uð1 erf uÞ exp ðu2 Þ
(5.26)
Thus N Ni;i and a can be found from the simultaneous solution of Equations (5.11) and (5.25). It is useful to observe that when uc1, F(u)E1 and when u{1, FðuÞ p1=2 u. If kc is small enough, then u{1. In this case of negligible interface recession, the solution (5.25) reduces to the form Equation (5.22), obtained on the basis that the interface movement can be ignored. In any event, the analysis predicts that scale growth is controlled by oxide diffusion ðkc ¼ kc Þ if N Ni 4N Ni;min , and by alloy diffusion if N Ni oN Ni;min . In the former case, a ¼ kc =kc is independent of ðoÞ ðoÞ N Ni and in the latter case a decreases as N Ni is lowered. ðoÞ Comparison of experimental results [13] for the dependence of a on N Ni with Wagner’s predictions for the Pt–Ni system showed that the latter were reasonably successful in the regime where N ðoÞ Ni o0:5 and alloy diffusion controlled the scaling rate (ao1). However, at higher nickel levels, the measured rates were significantly slower than predicted. As a result, the predicted critical values of N oNi at which rate control should transfer to scale diffusion (0.7 at 8501C and 0.6 at 1,1001C) were ~ lead to incorrect. However, the significant errors in measured values of kc and D ~ and the accurate calculation of Equation (5.25) large compounded errors in kc =D, is therefore difficult. Moreover, the assumption that NiO scale growth is controlled by lattice diffusion is not applicable at temperatures lower than about 9001C, where grain boundary diffusion is more important. ~ 1=2 1, i.e when scale–alloy interface moveIn the case where u ¼ ðkc =2DÞ ment is slow compared to alloy diffusion, then FðuÞ p1=2 u
(5.27)
200
Chapter 5 Oxidation of Alloys I: Single Phase Scales
Substitution into Equation (5.25) then yields 1=2 pkc ðoÞ N Ni ~ 2D N Ni;i ¼ 1=2 pkc 1 ~ 2D
(5.28)
This approximation is not applicable to the Pt–Ni alloy situation, because the NiO growth rate leads to relatively high kc values. It might be appropriate, however, for slower growing oxides such as Cr2O3 and Al2O3. Data on several alloys collected by Whittle et al. [14] is reproduced in Table 5.2, along with data for Ni–Al [15, 16]. It is seen that the condition u{1 is met in these cases. Interface concentrations calculated from Equation (5.28) are also shown in the Table. The extent of depletion predicted from Equation (5.28) is, in fact, unrealistically small. Chromium concentration profiles measured in an Fe–32Cr alloy after selective formation of a Cr2O3 scale are shown in Figure 5.9. These confirm that depletion occurs, but show that the effect is much greater than predicted. Given the sensitivity ~ this is perhaps not surprising. We note in of the calculation to errors in kc and D, ~ particular that D will normally be a function of alloy composition (see Section 2.7). Bastow et al. [18] showed that an interfacial value N Cr;i ¼ 0:19, in approximate agreement with their EPMA measurement, was consistent with a rate constant kc ¼ 3.9 1012 cm2 s1, a value three times faster than the rate they actually observed. This discrepancy has led to a more detailed examination of the relationship between alloy and scale diffusion, which we discuss below. First, however, an examination of qualitative trends revealed by the data in Table 5.2 is useful. Comparing iron- and nickel-based chromia forming alloys, it is seen that the ~ is somewhat greater for the latter. This reflects mainly the fact that ratio kc =D diffusion in austenite is slower than in ferrite. Consequently, the chromium concentration at the alloy–oxide interface will be depleted to a lower value in a Ni–Cr alloy than in an equivalent Fe–Cr alloy under the same conditions. ~ is much smaller Comparing Fe–Cr and Fe–Al alloys, it is seen that the ratio kc =D Table 5.2 Alloy
Kinetic parameters for alloy diffusion and selective scale growth [14] NðoÞ A
Ni–28Cr 0.30
T (1C)
1,000 1,200 Fe–28Cr 0.29 1,000 1,200 Fe–4.4Al 0.087 1,000 1,200 Fe–12Al 0.22 1,000 1,200 Ni–10Al 0.19 1,200
D~ AB (cm2 s1)
kc (cm2 s1)
u
NA;i (Equation 5.28)
4.1 1011 3.9 1010 4.1 1010 3.9 109 8.4 109 2.1 106 8.4 109 2.1 106 1 109 [16]
1.2 1013 7.2 1013 1.2 1012 3.9 1012 2.6 1016 1.4 1013 2.0 1018 6.4 1016 4.0 1013 [15]
3.8 102 3.0 102 3.8 102 2.2 102 1.8 104 1.8 104 1.2 105 1.2 105 1.4 102
0.24 0.26 0.24 0.26 0.087 0.087 0.22 0.22 0.17
5.4. Selective Oxidation of One Alloy Component
201
Figure 5.9 Chromium depletion in Fe–32Cr measured by electron probe microanalysis after selective oxidation of chromium at T ¼ 9771C. Reprinted from Ref. [17] with permission from Elsevier.
in the alumina forming alloys, because the oxidation rate is much slower and alloy diffusion is faster. As a result, Fe–Al alloys are predicted to maintain rather flat aluminium concentration profiles, with N Al;i N ðoÞ Al . This has been verified [19] for Fe–Cr–Al alloys under circumstances where a scale of alumina only forms. Microprobe analysis, with a spatial resolution of 1–2 mm, showed no detectable variation in the alloy aluminium level from the alloy interior to the alloy–scale interface. Thus any depletion zone was of thickness less than 1–2 mm. ~ values lower than either Ni–Cr or Fe–Cr, leading to a The Ni–Al alloys have kc =D reduced extent of depletion. In comparison to Fe–Al alloys, however, Ni–Al is subject to significantly more depletion. Values of the minimum concentration, N B;min , of scale-forming element necessary to support external scale growth were calculated from Equation (5.22) and are listed in Table 5.3. Comparison with experimental observations of N B;min , however, reveals that these predictions are not useful. As already noted, one reason for this lack of success is the sensitivity of the calculation to error in the ~ An example is shown in Figure 5.10, where calculations basic data used, kc and D. ~ which differ by a factor of 2 are seen to [18] for Fe–Cr assuming two values for D result in values of N Cr;i which differ by 0.05, i.e. 40%. A further reason for its lack of quantitative success in predicting values of N B;min , is that Wagner’s treatment was designed to assess the minimum alloy concentration necessary to supply a flux to the surface sufficient to sustain the growth of a single-phase scale presumed to have formed already. Thus the theory does not provide guidance on
202
Table 5.3
a
Chapter 5 Oxidation of Alloys I: Single Phase Scales
Values of NB,min to support selective oxide scale growth
Alloy
Scale
T (1C)
Predicted (Equation 5.25)
Observed
Reference
Ni–Cr Fe–Cr Ni–Al Fe–Ala
Cr2O3 Cr2O3 Al2O3 Al2O3
1,000 1,000 1,200 1,300
0.07 0.07 0.02 104
0.15 0.14 0.12–0.24 0.02–0.04
[7] [7] [15, 20, 21] [22]
Observed on Fe–Cr–Al alloys growing scales of Al2O3 only.
Figure 5.10 Chromium depletion profiles calculated for (1) DFeCr ¼ 1 1012 and (2) 2 1012 cm2 s1 [18]. With kind permission from Springer Science and Business Media.
how much of the alloy component is required to form this scale in the first place. Before returning to this question we consider again the depletion profiles in Figure 5.9.
5.5. SELECTIVE OXIDATION OF ONE ALLOY COMPONENT UNDER NON-STEADY-STATE CONDITIONS Although concentration measurements near a phase boundary are subject to error, it seems from Figure 5.9, that N Cr;i first decreases then increases with time.
5.5. Selective Oxidation of One Alloy Component Under Non-Steady-State Conditions
203
Although N Cr;i ultimately reaches a constant value, the steady-state assumption of fixed boundary conditions is apparently inapplicable for a significant period at the commencement of reaction. The steady-state assumption is the basis for Wagner’s analytical solution (5.25), which could for this reason be inapplicable. The non-steady-state situation has been analysed for Fe–Cr oxidation, by Whittle et al. [14], Wulf et al. [17] and Bastow et al. [18], using a finite difference method. In this numerical approach, it is possible to allow for a compositiondependent alloy diffusion coefficient, but this has been shown to have little effect on the interfacial concentration in Fe–Cr alloys. The possible variation in N Cr;i with time is reflected in the mass balance for chromium at the alloy–scale interface. The situation is shown schematically for a binary alloy AB in Figure 5.11, where C represents concentration (moles/ volume), and an average value, CB;OX , is specified for B in the scale of BOn. The general statement of mass balance at a moving interface is written 0 J AB J OX B ¼ nðCB;OX CB;i Þ
J OX B
(5.29)
where is the flux of B away from the interface into the oxide, n the velocity of the interface and C0B;OX the boundary value of CB in the oxide at the interface. All of J AB , J OX B and n must be defined in the same frame of reference (see Section 2.7). The choice is arbitrary, but solution of the diffusion profile in the alloy is
Figure 5.11
Mass transfer at moving scale–alloy interface.
204
Chapter 5 Oxidation of Alloys I: Single Phase Scales
facilitated by using a reference frame with its origin at the original alloy surface, marked by a dashed line in Figure. 5.11. The displacement of the scale–alloy interface from its origin is specified as xc , and hence n ¼ dxc =dt. The flux of B from the alloy towards the interface is given by @CB (5.30) J AB ¼ DAB @x x¼xc
Component B also diffuses away from the interface through the scale, allowing it to grow. This is normally expressed with respect to a reference frame with its origin at the metal–scale interface. Defining the scale thickness as zs , then 0 V BOn ð J OX B Þ ¼
dzs dt
(5.31)
or dzs (5.32) dt where the prime is used to denote the different frame of reference, z. This is transformed to the desired reference frame, x, using the relationship 0 ð J OX B Þ ¼ CB;OX
OX 0 J OX B ¼ ð J B Þ þ CB;OX v1;2
(5.33)
where n1;2 is the velocity of the oxide frame with respect to the original alloy surface n1;2 ¼
dxc dt
Combination of the Equations (5.29) to (5.34) leads to @cB dzs dxc dxc ðCB;OX CB;i Þ CB;OX D ¼ @x x¼xc dt dt dt where the approximation C0B;OX CB;OX has been used. Noting that VBOn xc zs ¼ V AB it is found from Equation (5.35) that @cA dxc V MOn ¼ CB;OX CB;i DAB @x x¼xc dt V AB
(5.34)
(5.35)
(5.36)
(5.37)
Numerical solution of Equations (5.15) and (5.37) together with an expression for the alloy recession rate dxc V AB dzs ¼ dt V BOn dt
(5.38)
coupled with a rate law zs ¼ fðtÞ then reveals the alloy depletion profiles. Whittle et al. [14] proposed that an appropriate formulation of the rate law was z2s ¼ 2kp t þ k
(5.39)
205
5.5. Selective Oxidation of One Alloy Component Under Non-Steady-State Conditions
which differs from that of Wagner. Their evaluation of the change with time of the interfacial concentration relative to the bulk alloy value, N B;i y ¼ ðoÞ (5.40) NB is shown in Figure 5.12 for a model alloy. It is seen that a rapid decrease in N B;i occurs in the initial stages of reaction, when the oxide growth flux, (and rate at which B is withdrawn) is maximal. This initial decrease is followed by an increase, until a steady-state value is reached. This theoretical prediction is in agreement with experimental observation for the Fe–Cr system. Thus we conclude that the steady state assumed by Wagner is in fact arrived at, but that during an initial period this is not the case. The existence of a steady state is actually a pre-requisite for parabolic kinetics to be in effect. As seen in Section 3.7, diffusion controlled scale growth leads to parabolic kinetics only if the boundary conditions are fixed with time. The boundary values in a scale are related to the alloy interfacial composition through a local equilibrium condition such as Equation (5.10). More generally 2 2 B þO2 ¼ BOn ; DG41 (5.41) n n DG41 2=n aB pO2 ¼ K41 ¼ exp (5.42) RT If the activity coefficient for B is denoted by g, then K41 pðiÞ O2 ¼ ðgN B;i Þ2=n
(5.43)
and, in general, rate expressions such as Equation (5.4) lead to parabolic kinetics only if N B;i afðtÞ. Conversely, the observation of parabolic kinetics is an indication
1.0
θ
0.75
0.5
0.25
0
2.5
5 7.5 10 Dimensionless time
12.5
×10-3
Figure 5.12 Calculated variation of interfacial concentration with time during non-steadystate oxidation. Reprinted from Ref. [14] with permission from Elsevier.
206
Chapter 5 Oxidation of Alloys I: Single Phase Scales
00 that N B;i is constant. However, if pðiÞ O2 pO2 , the effect on oxidation rate of transient variation in N B;i could be small, as seen from Equation (5.4). The initial time dependence of N B;i predicted by Whittle et al. [14] was a consequence of their use of Equation (5.39) to describe scaling kinetics. As seen from the differential form
kp dzs ¼ dt ð2kp t þ kÞ1=2
(5.44)
the deviation from parabolic kinetics is greatest in the early stages of reaction, when 2kp tok. A non-zero value for k is realistic, reflecting as it does the existence of an oxide film on the metal surface before commencement of the high temperature reaction. Even in the absence of such a pre-formed oxide, strictly parabolic kinetics cannot obtain at extremely short times. If k ¼ 0, then dzs/dt is predicted to approach infinity as t approaches zero, an impossibility, as diffusion from the alloy is limited. It is recognized that the very initial kinetics cannot be parabolic, just as the exclusive oxidation of only one alloy component when the ambient pO2 is sufficient to oxidize others is initially impossible. This initial period of reaction, referred to as ‘‘transient’’ because it precedes the establishment of steady-state conditions, is discussed further in Section 5.7. Other oxidation morphologies result if selective oxidation of one component to form an external scale does not occur. Their natures vary with the reactivity of other alloy components. If no other alloy metals are reactive at the oxidant activity and temperature in question, and the one reactive component cannot reach the surface quickly enough to develop a scale, then internal oxidation results. This situation is considered in Chapter 6. Another reactive alloy component will oxidize simultaneously. Oxides which have limited intersolubility develop as separate phases, a situation described in Chapter 7. However, if the degree of intersolubility is large, it is still possible that a single-phase external scale of solid solution oxide can result. The questions of interest then concern the nature of this scale, its growth rate and how these properties vary with alloy composition.
5.6. SOLID SOLUTION OXIDE SCALES Pairs of binary oxides, AOn1 þ BOn2 , will dissolve in one another to an extent which is greater if (a) n1 ¼ n2 , (b) the oxides are crystallographically isotypic, (c) the cations A2nþ and B2nþ are similar in size and polarisability and (d) the stabilities of the oxides are not too different. The oxides MnO, FeO, CoO and NiO, all of which have the face-centred cubic NaCl structure, form ternary solid solutions A1x Bx O in which O x 1. Similarly, a-Fe2O3 and Cr2O3, both of which have a hexagonal crystal structure, are completely miscible at high temperatures. In the same way, FeS and NiS are fully intersoluble, as are FeS and CoS, all three monosulfides having the hexagonal NiAs structure. In general, the ratio N A =N B ¼ ð1 xÞ=x in the oxide differs from the corresponding alloy ratio
5.6. Solid Solution Oxide Scales
207
because the more reactive metal enters the scale preferentially. Furthermore, as the cation self-diffusion coefficients in the oxide, DA and DB , will differ, the cation ratio will vary with position in the scale. To calculate the scale growth rate as a function of alloy composition, it is necessary to know the distributions of the two metals within the scale. This problem has been analysed by Wagner [23] and the results extended by Coates and Dalvi [24]. The co-ordinate systems shown in Figure 5.11 are again employed. The z frame, attached to the alloy–scale interface, is used to describe transport in the oxide; the x frame, with its origin at the original alloy surface describes transport in the alloy. Of course it is understood that the oxide concentration profile will in general not be flat. The molar flux of each cation species in the oxide, J i , is given by @ ln ai (5.45) @z where i is A or B, and kinetic cross-effects are ignored. The Gibbs equation (2.9) relates the chemical potentials of the binary oxides and their constituents zA moA þ RT ln aA þ ðmoO þ RT ln ao Þ ¼ moAOn þ RT ln aAOn (5.46) zO J i ¼ Di Ci
with a similar equation for BOn. Assuming for the sake of simplicity that the valences, zi , are related by (5.47) zA ¼ zB ¼ j zO j ¼ 2 so that n ¼ 1, one obtains from Equations (5.45) and (5.46) DA ð1 xÞ @ ln aAO @x @ ln ao JA ¼ V OX @x @z @z DB x @ ln aBO @x @ ln ao JB ¼ V OX @x @z @z
(5.48)
(5.49)
It is supposed that V OX does not vary with x and that @ ln aAO =@x and @ ln aBO =@x are known from the solution thermodynamics of the mixed oxide. The scale-thickening rate is then found from ð J A þ J B ÞVOX ¼
dzs kp ¼ dt zs
(5.50)
where zs is the instantaneous scale thickness. Because diffusion control is in effect, the system is in a steady state, and both x and ao can be expressed in terms of a normalized position parameter z y¼ (5.51) zs Substitution from Equations (5.48), (5.49) and (5.51) into Equation (5.50) yields @ ln aAO @x @ ln ao @ ln aBO @x @ ln ao þ þ DA ð1 xÞ þ DB x ¼k (5.52) @x @y @y @x @y @y
208
Chapter 5 Oxidation of Alloys I: Single Phase Scales
Application of the continuity condition for the diffusion of one component on the basis again that x and ao are functions of y only leads to @x d @ ln aBO @x @ ln ao DB x yk ¼ (5.53) @y dy @x @y @y Each of Equations (5.52) and (5.53) apply only within the scale. Within the alloy phase, the distribution of component B is found by solving Fick’s second law @N B @2 N B ¼ DAB @t @x2 assuming DAB to be a constant. Using the Boltzmann transformation x l ¼ 1=2 t we obtain the ordinary differential equation
(5.54)
(5.55)
d2 N B l dN B ¼0 (5.56) þ 2 dl dl2 Solution of the three simultaneous Equations (5.52), (5.53) and (5.54) requires appropriate boundary conditions. These are provided by the initial conditions DAB
N B ¼ N ðoÞ B
for
x40;
t ¼ 0;
x ¼ 1;
t40
(5.57)
and ao ðy ¼ 1Þ ¼ a00o
(5.58)
together with the thermodynamic relationships xðy ¼ 1Þ ¼ f 1 ða00o Þ
(5.59)
xðy ¼ 0Þ ¼ f 2 ðN B;i Þ
(5.60)
a0o ¼ f 3 ðx0 Þ
(5.61)
and the mass balances which apply at the scale interfaces. The mass balance for B at the scale–gas interface is J B ðy ¼ 1Þ ¼
x00 dzs V OX dt
(5.62)
which, upon substitution from Equations (5.51), (5.52) and (5.53), becomes @ ln aBO dx d ln ao ¼ x00 k (5.63) DB x @x dy dy y¼1 Similarly, a mass balance for B at the scale–alloy interface (y ¼ 0) is used to evaluate x0 . Wagner treated this by relating the average mole fraction of B in the scale, xAV to the amount consumed from the alloy.
5.6. Solid Solution Oxide Scales
209
Using the valences of Equation (5.47), his result can be written 23=2 DAB V OX dN B N B;i þ dl l¼xs =t1=2 k1=2 VAB DB x @ ln aBO dx d ln ao ¼ k @x dy dy y¼0
(5.64)
Coates and Dalvi extended the range of applicability of this treatment by including dissolution of oxygen in the alloy and its diffusion into that phase. Even without that complication, it will be appreciated that solution of the simultaneous Equations (5.52), (5.53) and (5.54) together with the mass balances of Equation (5.63) and (5.64) represents a substantial undertaking. Since, moreover, the diffusional properties of the oxide can be expected to vary with both x and ao , a solution is essentially impossible without a relatively simple diffusion model.
5.6.1 Modelling diffusion in solid solution scales A fruitful approach was proposed by Dalvi and Coates [25] using the data [26] shown in Figure 5.13 for the distribution of nickel and cobalt in a (Ni,Co)O scale grown on a binary alloy. The mixed oxide is a nearly ideal solution d ln aCoO ¼1 d ln x
(5.65)
and the Gibbs–Duhem equation can be written as d ln aNiO ¼
x d ln aCoO 1x
(5.66)
Substitution from these thermodynamic equations into Equation (5.52) leads to ðDNi DCo Þ
dx d ln ao ½ð1 xÞDNi þ xDCo ¼ k þ dy dy
(5.67)
Investigations into the NiO–CoO solid solution by Zintl [27, 28] revealed that the vacancy mole fraction, NV, decreased almost exponentially with additions of NiO. Based on this finding and the vacancy model for each of CoO and NiO 1 2 O2 ðgÞ
¼ OXO þ V 00M þ 2h
(5.68)
Wagner [29] suggested that NV in the solid solution oxide could be modelled as 1=6
x N V ¼ N NiO V b pO 2
(5.69)
reflecting a law of mixtures for the free energy of vacancy formation via Equation (5.68), i.e. DGV ¼ ð1 xÞðDGV ÞNiO þ xðDGV ÞCoO
(5.70)
210
Chapter 5 Oxidation of Alloys I: Single Phase Scales
Figure 5.13 Distribution of CoO in CoO–NiO solid solution scale grown on Ni–10.9Co at 1,0001C. Experimental data [26] is compared with model curve calculated [25] from Equations (5.77) and (5.78) [25]. With kind permission from Springer Science and Business Media.
Here N CoO V (5.71) N NiO V is the vacancy mole fraction in the indicated binary oxide at and N MO V pO2 ¼ 1 atm. Recalling that for substitutional diffusion with NME1, DM ¼ DVNV, it was further suggested [29] that diffusion in the ternary oxide could be described by ! NV o DCo ¼ DCo (5.72) N CoO V b¼
and DNi ¼
DoNi
NV N NiO V
! (5.73)
5.6. Solid Solution Oxide Scales
211
where DoM denotes the diffusion coefficient of the indicated metal in its pure binary oxide at pO2 ¼ 1 atm. Combination of Equations (5.69), (5.72) and (5.73) with the definition p¼
DNi DCo
(5.74)
then leads to 1=6
(5.75)
1=6
(5.76)
DCo ¼ DoCo bx1 pO2
DNi ¼ pDoCo bx1 pO2
Substitution from Equations (5.75) and (5.76) into Equation (5.67) yields ( ) k0 dx ðp 1Þ 1=6 dy bx1 pO2 d ln ao ¼ ½p ðp 1Þx dy
(5.77)
where k0 ¼ k=DoCo . Application of this diffusion model to the scale–gas interface mass balance (5.63) yields, after some algebra, a differential equation describing the variation within the scale of x with normalized position y
2 d2 x 1 dx y 2þ 1 ðp 1Þ þ y ln b dy 6 dy
þb
x00 x
)
00 1=6 ( p 1 ð1=6Þ yy2 ao dx dx ¼0 dy y¼1 dy ao x00 ð1 x00 Þðp 1Þ
(5.78)
where y ¼ p ðp 1Þx. Simultaneous solution of Equations (5.77) and (5.78) using measured values of p and b then yields x and ao as functions of y. It was found expedient to treat the exponent of oxygen activity appearing in the defect equilibrium (5.69) as a variable. 1=5
When pO2 was used, the calculated composition profiles shown in Figure 5.13 were found to fit the experimental data very well. The index 1=5 was interpreted as corresponding to a mixture of singly and doubly charged vacancies. The cobalt enrichment at the scale surface resulted from the fact that p ¼ DNi =DCo 0:5. Single-phase (Fe,Mn)O scales grow according to parabolic kinetics on Fe–Mn alloys oxidized in CO2–CO atmospheres [30]. Microprobe concentration profiles showed that the scale compositions were rather uniform, and approximately the same as the alloy compositions. This reflects the fact that diffusion in the oxide was about 104 times faster than in the alloy. The relatively flat, linear gradients in the scale could be approximated by dx ¼b dy
(5.79)
212
Chapter 5 Oxidation of Alloys I: Single Phase Scales
and the ideality of the FeO–MnO solution [31] allowed use of Equation (5.65). In this case, Equations (5.53) and (5.63) yield the simple result kx00 ðp 1Þð1 x00 Þ (5.80) b after elimination of @ ln ao =@y. This yielded a value of p ¼ 0.99, consistent with the lack of segregation of the metals within the scale. The diffusion coefficient of iron in wu¨stite is proportional to the oxide non-stoichiometry [32] and an equation analogous to Equation (5.72) applies to the (Fe,Mn)O scale. Values of DFe deduced from the alloy scaling rates were used (in Equation (5.72)) to calculate the non-stoichiometry of the mixed oxide. Figure 5.14 compares the calculated results with those measured for powdered oxide after equilibrating with the gas. The good agreement provides additional support for the validity of the diffusion model. Similar analyses have been carried out for solid-solution oxide scales developed on Co–Fe [33, 34] and Ni–Fe [35] alloys, and for monosulfide scales on Fe–Ni [36, 37] and Fe–Co [38, 39]. An unusual pattern of component segregation was found in the (Co,Fe)O scales, where at low ambient pO2 values, the more mobile iron was enriched towards the scale surface, as seen in Figure 5.15a. However, at high pO2 values, a maximum in iron concentration developed in the scale interior (Figure 5.15b). The explanation for this is the DMn ¼ pDFe ¼
Figure 5.14 Non-stoichiometry of (Fe,Mn)1dO: points deduced from alloy scaling rates and Equation (5.72); dashed curves measured by equilibrating powdered oxides with gas [30] Reproduced by permission of The Electrochemical Society.
5.6. Solid Solution Oxide Scales
213
ξ ξ
(a)
(b)
(c)
Figure 5.15 (a), (b) Compositional profiles in (Co,Fe)O scales at low and high pO2 values [36, 37, 41] and (c) DFe/DCo as a function of pO2 [40]. Reproduced by permission of The Electrochemical Society.
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Chapter 5 Oxidation of Alloys I: Single Phase Scales
curious variation in p ¼ DFe =DCo with ao , as measured by Crow [40] and shown in Figure 5.15c. Incorporating this information into the numerical solution procedure for Equations (5.77) and (5.78) allowed Narita et al. [41] to calculate the scale concentration profile successfully (Figure 5.15a and b). The reason for the change in p with ao is not apparent. It has been suggested by Whittle and coworkers [42] that correlation effects can lead to variation of p with vacancy concentration, and hence with ao . However, even this model cannot account for the reversal in relative mobilities of iron and cobalt evident in Figure 5.15. Sulfide scales provide the investigator with the advantage of being able to measure accurate concentration profiles for the oxidant species using an electron microprobe. Results for an (Fe,Ni)1dS scale are shown in Figure 5.16, where the sulfur concentration varies with position in a non-monotonic fashion. The mixed sulfide grew at a faster rate than Fe1dS scales grew at the same pS2 on pure iron. The indicated enhancement in DFe could arise either through a decreased activation energy for diffusion, or from an increase in defect concentration above that predicted for an ideal solution. The former possibility may be rejected on the basis of self-diffusion data [43–46] for Fe1dS and Ni1dS. The latter possibility is supported by the concentration profiles in Figure 5.16 as is now discussed. Recognizing that the deviation from stoichiometry is given by NM d¼1 (5.81) NS
0.150
53
0.125
52
0.100
51
0.075
50
0.005
0
100 200 Distance from scale-alloy interface/μm
atomic % S
NNi /NNi + NFe
it is clear that d varies with position in an unusual fashion in the (Fe,Ni)1dS scale. The values of d calculated in this way range up to 0.04, much greater than the value of 0.02 reported [47] for Fe1dS under these conditions. Since Ni1dS has a smaller deviation from stoichiometry than Fe1dS, it is obvious that the solution is
49
Figure 5.16 Compositional profiles in (Fe,Ni)1dS scale grown on Fe–41Ni at T ¼ 6651C [37]. Reproduced by permission of The Electrochemical Society.
215
5.6. Solid Solution Oxide Scales
not ideal with respect to the defect species nor, equivalently, to sulfur. The conclusion that a ternary solid solution may be close to ideal with respect to its component binary compounds but deviate strongly from ideality for the electronegative species is a common one. If it is assumed that the psuedobinary solution FeS–NiS is ideal, that deviations from stoichiometry can be ignored and that p ¼ DFe =DNi is constant, independent of composition and as , then Equation (5.67) can be rewritten as ð1 pÞ
dx d ln as kp þ ð1 x þ pxÞ ¼ dy DFe dy
(5.82)
If it is further assumed that the relationship between DFe and N V (or d) in the (Fe,Ni)1dS scale is the same as that given by Condit et al. [43] for Fe1dS ð81 þ 84dÞ kJ mol1 DFe ¼ DO d exp (5.83) RT then Equation (5.82) can be applied to the data in Figure 5.16 for x and d as functions of y. This procedure permits the evaluation of the gradient d ln as =dy, and p can then be varied to match the sulfur activity profile to the boundary values. The results of this calculation are shown in Figure 5.17, where it is seen
Figure 5.17 Sulfur activity profile in (Fe,Ni)1dS scale (y ¼ x/X) calculated from Equations (5.82) and (5.83) [37]. Reproduced by permission of The Electrochemical Society.
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Chapter 5 Oxidation of Alloys I: Single Phase Scales
that d ln as =dy is constant throughout the scale, despite the unusual behaviour of N S . The value found for p was 0.4, consistent with the observed enrichment of nickel towards the scale surface. The methods of calculating solid solution scale compositions and growth rates are complex, and require a great deal of information on the thermodynamic and kinetic properties of the oxide. It is therefore much easier to measure scaling rates than it is to model them. Nonetheless, the experimental validation of the scaling theory has led to useful conclusions. The growth of single-phase, solid solution scale layers is controlled by diffusion, and parabolic kinetics result. Scale compositions vary with position within the scale, but are time invariant during steady-state reaction. The average scale composition is related to the ability of an alloy to deliver metal by diffusion to the scale–alloy surface. A useful form of this relationship has been provided by Bastow et al. [42] Z 1 N ðoÞ N B;i xAV ¼ þ N B;i x dy ¼ B (5.84) FðuÞ 0 where FðuÞ is as defined in Equation (5.29) and, as before, 1=2 kc u¼ 2DAB
(5.85)
If scaling is much faster than alloy diffusion, the situation for the MO and MS scales examined so far, then N B;i N ðoÞ B and the scale has the same average metal ratio as the alloy. If the reacting system is not at steady state, then N B;i changes with time, as must therefore xAV . If an alloy becomes depleted in one component, then the other component will become enriched in the scale. If that component is the faster diffusing one, then its further enrichment at the scale surface may lead to the formation of a new oxide phase. The subsequently changed oxide constitution and morphology can be associated with loss of protective behaviour, as is discussed in Section 5.9 and Chapter 7.
5.7. TRANSIENT OXIDATION Discussion so far has been focused on the growth of an external scale under steady-state conditions. However, the time taken to achieve this steady state could be lengthy, in which case considerable scale would accumulate. The situation where only one oxide is stable was considered in Section 5.4, where we concluded that the scale–alloy boundary conditions (and therefore the scaling rate) changed with time only if the kinetics were non-parabolic. Gesmundo et al. [48, 49] have investigated this situation further, noting that a more realistic description of the early stage transient kinetics should involve a contribution to rate control by the scale–gas interaction processes. Thus scaling kinetics are expected to show a transition from an initial linear form to subsequent parabolic behaviour as the scale thickens and eventually diffusion becomes slower than the scale–gas interfacial process. It was shown that under these conditions the value
5.7. Transient Oxidation
217
of N B;i decreased monotonically from N ðoÞ B to the steady-state value, with no minimum of the sort suggested by Whittle et al. [14]. The different conclusions were consequences of the different kinetic models used for the transient stage. The consequences of the transient oxidation stage are potentially more significant in the case where more than one oxide can form, and the oxides have limited intersolubility. An example is provided by the oxidation of binary Cu–Zn alloys, studied long ago by Dunn [50] and subsequently by others. Relative oxidation rates of these alloys are indicated by the data in Figure 5.18. Alloys containing up to 10% Zn react at 8001C according to parabolic kinetics at essentially the same rate as pure copper, producing a Cu2O scale with inclusions of ZnO [51]. If the alloy zinc level is 20%, the oxidation rate is orders of magnitude less, independent of N ðoÞ Zn , and corresponds to the growth mainly of the more stable ZnO. Wagner [12] calculated the value of N Zn;min from Equation (5.25), modified to take into account the variation of DZn with composition [52]. The resulting values for N Zn;min of 0.14, 0.15 and 0.16 at 7251C, 8001C and 8001C are in reasonably good agreement with experimental observation (Figure 5.18). Alloys containing intermediate zinc levels of 10–20% showed wide deviations from parabolic kinetics [53], as seen in Figure 5.19. The rate was initially similar to that of pure copper, but subsequently decreased significantly as a ZnO layer developed at the base of the scale. If the reaction was interrupted by a 1-h anneal under argon, the ZnO layer developed during this time. When oxidation was resumed, slow parabolic kinetics were observed, and the rate was characteristic of high zinc content alloys. This pattern of behaviour can be understood in terms of an initial, transient reaction period during which both Cu2O and ZnO nucleate on the surface [54, 55]. The faster growing Cu2O overgrows the ZnO, which remains as slow-growing
Figure 5.18 Oxidation of Cu–Zn alloys: weight uptake after 5 h reaction at pO2 ¼ 1 atm [51]. With permission of TMS.
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Chapter 5 Oxidation of Alloys I: Single Phase Scales
3.0 (a)
2.0
(ΔW/A/mgcm-2)2
1.0
0 (b) 2.0
1.0
0
0
40
80
120 Time, min
160
200
Figure 5.19 Oxidation kinetics observed for Cu–15Zn at T ¼ 7001C and pO2 ¼ 1 atm (a) continuous (b) interrupted by 1 h anneal in Ar [53]. Reproduced by permission of The Electrochemical Society.
particles at the scale–alloy interface (Figure 5.20). During this stage, the overall scaling kinetics are similar to those of single-phase Cu2O layer growth, since this phase constitutes the majority of the scale. This initial stage of preferential copper oxidation leads to zinc enrichment at the alloy–scale interface, and the reaction Zn þCu2 O ¼ ZnO þ 2Cu
(5.86)
commences. This process is thermodynamically favoured, with DG ¼ 164 kJ mol1 at 8001C, corresponding to a2Cu ¼ 9:6 107 aZn
(5.87)
Thus, at local equilibrium, aZn 108 , and the transient formation of Cu2O is a consequence of the reaction kinetics. Whereas Cu2O growth is rapid, the displacement reaction (5.86) is slow. Eventually, however, the displacement
5.7. Transient Oxidation
Cu+
Cu2O ZnO Cu-Zn
Zn2+ Cu-Zn
219
Cu2O ZnO Cu-Zn
Figure 5.20 Schematic view of transient Cu2O overgrowing ZnO and eventually being isolated from Cu–Zn alloy as the ZnO layer becomes complete.
reaction becomes kinetically favoured, and the alloy surface area fraction covered with ZnO increases to unity, as shown schematically in Figure 5.20. Once coverage with ZnO is complete, further Cu2O growth ceases because copper is essentially insoluble in the zinc oxide. Further scale growth then consists of ZnO layer thickening under steady-state diffusion control. Wagner [12] carried out a similar analysis for the oxidation behaviour of Cu–Ni alloys. Using Equation (5.25), he calculated that for exclusive NiO formation a value of N Ni;min ¼ 0:75 was required at 9501C. This was in satisfactory agreement with the change in alloy oxidation rate observed by Pilling and Bedworth [56] at a value of about 0.7. However, scaling rates in the range 0:7oN ðoÞ Ni o1 were greater than for pure nickel, increasing with the level of copper. As with the Cu–Zn system, the high diffusion coefficient of Cu2O meant that regions of this oxide remaining from the initial transient stage of oxidation continued to grow fast. Evidently the displacement reaction Ni þCu2 O ¼ NiO þ 2 Cu
(5.88)
is slow and regions of Cu2O persist at the scale–alloy interface for long times [53, 57]. It may be that nucleation of new NiO regions at the Cu2O/alloy interface is energetically unfavourable, and that the lateral spreading of original surface NiO nuclei is also slow. Transient oxidation processes occurring before the establishment of steadystate protective scales of Cr2O3 or Al2O3 are rather different from the Cu–Zn and Cu–Ni systems described earlier. The much greater stability of chromia and alumina makes internal precipitation of these oxides more likely. Discussion is therefore postponed until internal oxidation processes are considered in Chapter 6. Even when only one metal is oxidized, non-steady-state oxidation can take place in an initial transient period associated with phase transformations in the oxide. The technologically important example of alumina scale formation is now considered.
5.7.1 Transient behaviour associated with alumina phase transformations Alumina exists in a number of crystalline forms only one of which, the hexagonal a-phase, is thermodynamically stable [58]. However, the other phases retain their crystalline forms indefinitely below certain temperature limits [58] as shown
220
Chapter 5 Oxidation of Alloys I: Single Phase Scales
γ
(a)
θ
γ
(b)
500
δ 700
900
α
θ+α
θ
α
1100
Figure 5.21 Approximate Al2O3 transformation temperatures observed [58] on bulk material used for catalyst supports (a) g-Al2O3+3% Pt (b) g-Al2O3. Reproduced with the permission of The American Ceramic Society.
approximately in Figure 5.21. The long-term existence of these metastable phases arises from the difficulty of achieving the transformations through which the material must pass to reach the stable a-phase. Activation barriers may, of course, be overcome thermally, but the magnitude of the barriers may also be altered by the presence of foreign phases, either gaseous or solid [59, 60], and by dissolved impurity species [61]. As seen in Figure 5.21, the presence of platinum in contact (as a dispersed catalyst) with g-Al2O3 alters the sequence of its phase transformations, and generally lowers the temperatures at which they occur. Nickel has also been shown [62] to accelerate transformation to a-Al2O3 at temperatures of 8501C and 9501C. As discussed later in this section, chromium and iron also affect the transformation. Oxidation of alumina forming alloys at temperatures below about 1,2001C often leads initially to formation of transient, metastable alumina scales [63–88]. This is significant, because the metastable aluminas grow much more rapidly than a-Al2O3 [63–88]. A comparison of scaling rates for y and a-Al2O3 in Figure 5.22 illustrates this point. An example of the transition from fast transient oxidation to slow, steady-state a-Al2O3 growth observed by Rybicki and Smialek [64] for the intermetallic b-NiAl containing 0.05 at. % Zr is shown in Figure 5.23. The metastable aluminas have lower densities than a-Al2O3 and transformation is accompanied by a 13% reduction in volume. The higher growth rates of the metastable oxides are related to their different crystal structures (g-Al2O3 has a cubic spinel type structure [66], the structure of d-Al2O3 is the subject of some disagreement [67] and y-Al2O3 is monoclinic) and looser packing than the a-Al2O3 structure of hexagonal close packed oxygen with aluminium occupying octahedral interstitial sites. The different morphologies developed by the alumina phases also contribute to their differing growth rates: whereas a-Al2O3 is a dense layer, the metastable forms tend to develop as blades and whiskers. Considerable information is available for the oxidation of the intermetallic bNiAl. This material has good oxidation resistance due to its ability to form scales which are exclusively Al2O3 [15]. It has been studied intensively because it is the principal constituent of diffusion coatings grown on nickel base superalloys to provide protection against oxidation. The transient oxide grown on b-NiAl+Zr at 9001C was found to have a blade or platelet structure. The oxide was identified by XRD as y-Al2O3. At 8001C and 9001C, the first formed oxide was g-Al2O3 but was replaced by y-Al2O3 after
5.7. Transient Oxidation
221
Figure 5.22 Rates of y-, g- and a-Al2O3 scale growth on b-NiAl+Zr [65]. Reprinted from Ref. [65] with permission from Elsevier.
Figure 5.23 Transition from fast transient oxidation to steady-state a-Al2O3 growth on b-NiAl+Zr [64]. With kind permission from Springer Science and Business Media.
about 1 h [68]. At these temperatures, the y-phase persisted for at least 100 h. At 1,0001C and 1,1001C, however, the y-phase was replaced by a-Al2O3, which nucleated in the prior y-Al2O3 scale. These nuclei grew laterally, until they impinged to form grain boundaries [68, 69], the transformation to a-Al2O3 then being complete. Shrinkage cracks within the grains resulted from the volume
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Chapter 5 Oxidation of Alloys I: Single Phase Scales
change accompanying the y–a transformation. The grain boundaries formed where the a-Al2O3 islands met provided pathways for rapid diffusion, leading to the development of oxide ridges, as proposed by Hindam and Smeltzer [20]. Plan and cross-sectional views of the ridge structure are shown in Figure 5.24. The ridges remain on the surface, but do not continue to grow in proportion to the underlying scale thickness. The nucleation sites for a-Al2O3 formation are of interest. On the basis of their TEM observations, Doychak et al. [69] suggested that nucleation commenced preferentially at the oxide-gas surface. Smialek and Gibala [71] concluded that the transient oxidation of Ni–Cr–Al alloys was ended by nucleation of a-Al2O3 at the scale–alloy interface. Both of these investigations relied upon TEM examination in which the electron beam was transmitted through the scale thickness, and the location of the a-nuclei was therefore ambiguous. Subsequent observations [72] of fracture sections of scales grown on b-NiAl, reproduced in Figure 5.25, show that the a-phase grew at the metal–scale interface. Minor alloy additions to the b-NiAl can affect the rate at which steady-state a-Al2O3 growth is achieved. Both zirconium and ion-implanted yttrium slow the transformation from y- to a-Al2O3 [73, 74]. Fine oxide dispersions in the alloy can also affect the transformation. Pint et al. [75] showed that dispersed Y2O3, ZrO2, La2O3 and HfO2 all delayed slightly the y- to a-Al2O3 transformation during initial oxidation of b-NiAl at 1,0001C. However, dispersions of a-Al2O3 and TiO2 both accelerated the transformation. The delays caused by Y, Zr, La and Hf oxides were attributed to the effect of dissolution into the transient oxide. According to Burtin et al. [61] larger ions inhibit the y–a transformation. It was suggested that such dopants could interfere with both the surface area reduction and the diffusionless transformations required to convert y-Al2O3 blades to dense a-Al2O3. The accelerating effect of a-Al2O3 inclusions was presumably simply one of nucleation. Alloy additions of chromium can also accelerate the transformation through initial formation of Cr2O3 which, being isotypic with a-Al2O3, promotes its nucleation [76]. Ferritic FeCrAl alloys such as Kanthal (Table 5.1) are also alumina formers. At temperatures of 1,0001C and higher, the a-phase is quickly formed, providing good protection. This is thought to be due to transient formation of Fe2O3 which is also structurally isotypic with a-Al2O3, and promotes its nucleation. Confirmation of this has been provided by N’Dah et al. [77], who oxidized commercial FeCrAl alloys in Ar–H2–H2O atmospheres at 1,1001C and 1,2001C. If the H2O(g) level was high enough to yield a pO2 value above the Fe2O3/FeAl2O4/ Al2O3 equilibrium value, a scale of 100% a-Al2O3 was obtained. However if the water vapour level was lower, a mixture of a- and y-Al2O3 resulted. At lower temperatures, the scales formed on FeCrAl alloys can contain metastable aluminas, and consequently provide poor protection [78–80]. Figure 5.26 shows a TEM cross-sectional view [81] of the scale grown on Kanthal AF (Table 5.1) at 9001C in an atmosphere of O2+40%H2O. An EDAX line scan across the scale revealed a narrow central region rich in chromium. This was a residue of the initial stage of transient oxidation in which Fe, Cr and Al all oxidized. The iron had subsequently diffused into the outer scale region, where oxygen
5.7. Transient Oxidation
223
30µm
whiskers
ridge
Al2O3
β cavities
2µm
Figure 5.24 Ridges of a-Al2O3 developed on b-NiAl where islands of a-Al2O3 had met: upper: SEM plan and lower: FIB cross-section views. Localized spallation visible in plan view [70]. Reproduced by permission of the Electrochemical Society.
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Chapter 5 Oxidation of Alloys I: Single Phase Scales
Figure 5.25 SEM view of fracture section of alumina scale grown at 1,1001C on b-NiAl, showing a-grains at the scale–alloy interface [72]. Published with permission from Science Reviews.
Figure 5.26 TEM cross-sectional view of scale grown on Kanthal AF at 9001C [81]. Bright material in the middle of scale is chromium-rich remnant from transient oxidation. Published with permission from Science Reviews.
activities were higher. The outer layer was g-Al2O3 whereas the inner layer was a-Al2O3. The latter had nucleated at the chromium-rich region and grown inwards and laterally to form a protective layer. Before that layer was complete, the outer g-Al2O3 layer developed. Its stability was thought to be enhanced by the presence of water vapour. An increase in the amount of transient oxidation of a variety of alumina forming alloys when exposed to humid air has also been reported by Maris-Sida et al. [82]. The more rapid growth of transient metastable aluminas can cause more severe depletion of the alloy aluminium. Pragnell et al. [83] studied the oxidation of commercial FeCrAl foils of nominal thickness 50 mm at 9001C. They observed rapid initial growth of transient y-Al2O3 which was transformed only slowly to
5.7. Transient Oxidation
225
a-Al2O3. The total weight uptake after 72 h was B0.4 mg cm2, much more than that corresponding to protective a-Al2O3 scale growth. Measurements of alloy aluminium concentrations (Figure 5.27) show that the depletion levels were consequently significant. A strongly beneficial effect of titanium in promoting a-Al2O3 formation has been reported. As noted earlier, dispersed TiO2 in b-NiAl accelerated transformation of transient alumina to the a-phase. Comparisons [84] of the oxidation kinetics of different FeCrAl grades at 850–9251C have shown that Kanthal AF reached steady-state a-Al2O3 growth the fastest. This grade contains nominally 0.1% Ti. Prasanna et al. [85] showed that titanium from the alloy was incorporated into the oxide scale, possibly accelerating the y–a transformation. The application of a slurry of TiO2 to the FeCrAl surface before oxidation has also been shown [81, 86] to accelerate a-Al2O3 formation. Since TiO2 was used by one set of investigators [81] in the form of rutile and by the other [86] as anatase, it seems that the chemical rather than the structural nature of TiO2 was important. Finally, oxidation of g-TiAl alloys produces a-Al2O3 along with TiO2 at temperatures where other alumina formers develop transient oxides [87]. Pint et al. [75] have suggested that the accelerating effect of titanium is consistent with the findings of Burtin et al. [61] in that the Ti4+ ion is of similar size to Mg2+, which has been found also to be a phase change accelerator. It seems that the transient behaviour of alumina scales is affected by a large number of variables, and that information is still being collected. Nonetheless, it also seems that ways of accelerating the phase transformations, and thereby lessening the amount of transient oxidation, are being developed. Quantification of alumina transformation kinetics under various circumstances is highly desirable. Temperature–time–transformation plots, such as those in Figure 5.28 due to Andoh et al. [88] provide a useful representation of such data. 6
Al concentration / wt%
5 4 3 2 Measured Predicted
1 0
0
20
40
60
80 100 X distance / μm
120
140
160
Figure 5.27 Aluminium depletion caused by rapid transient oxidation of FeCrAl at 9001C [83]. Published with permission from Science Reviews.
226
Chapter 5 Oxidation of Alloys I: Single Phase Scales
Figure 5.28 Temperature–time–transformation plots for alumina formed on Fe–20Cr–5Al [88]. Published with permission from Trans. Tech. Publications.
5.8. MICROSTRUCTURAL CHANGES IN SUBSURFACE ALLOY REGIONS As is by now clear, scale growth almost always leads to the development of compositional changes in the alloy subsurface as the result of the different rates at which alloy components are oxidized. The diffusion processes involved can lead to volume changes, breakdown in the morphological stability of the scale–alloy interface, depletion and dissolution of minority phases, precipitation of new phases and other transformations resulting from the compositional changes, as discussed later. The additional possibility of inward oxygen diffusion leading to internal oxide precipitation will be dealt within Chapter 6.
5.8.1 Subsurface void formation An example of void formation within b-NiAl beneath an alumina scale was shown in Figure 5.6. The alloy surface revealed by scale removal shows the voids to be faceted, and of varying aspect ratios. The cross-sectional view shows that the Al2O3 undersurface is flat, the void having developed in the metallic phase. There are several possible ways in which such voids could form. Growth of an external scale by outward metal transport means that new oxide is formed at the scale–gas interface, and cannot in any direct sense fill the space vacated by the reacted metal. However, plastic deformation of the scale can allow it to retain contact with the retreating metal surface, if scale movement is unconstrained. To the extent that plastic deformation is not available, void space develops somewhere within or beneath the scale. In the case of a completely rigid scale, the total void volume would equal the volume of metal consumed by
5.8. Microstructural Changes in Subsurface Alloy Regions
227
oxidation. The location of the voids depends on the detailed transport mechanisms in effect. In solid solution alloys, mass transport occurs via vacancy diffusion, and the origins and sinks for these defects must be considered. It is assumed [89–91] that vacancies are injected at the scale–metal interface, as metal atoms move into the scale. If these are annihilated at dislocations, they cannot cause void formation within the metal, but nonetheless the reacting metal shrinks. If, as is being supposed, the oxide scale is unable to conform with the shrinking metal core, void space must be generated elsewhere by the creation of new vacancies. These can be emitted from dislocations in the reverse of the annihilation process. Thus dislocations serve as very rapid pathways for the transmission of vacancies and thereby of void space. Voids develop where vacancies can aggregate, i.e ‘‘coalesce’’ or ‘‘condense’’, in what must be a nucleation process. Preferred sites for void nucleation will therefore be phase interfaces and alloy grain boundaries. Moreover, the development of a vacancy concentration gradient from a maximum at the scale–alloy interface to a minimum in the alloy interior will lead to a greater number of voids nucleating immediately beneath the scale than deeper into the alloy. This was the experimental finding of Hales and Hill [89] in the case of pure nickel. Of course, the vacancy injection, transport and condensation model is applicable to both metals and alloys. Alloys are subject to an additional effect, arising from the different mobilities of the constituent metals. Consider the case of b-NiAl forming an external scale of pure Al2O3, and voids at the alloy–scale interface [92–95]. Brumm and Grabke [96] have investigated void formation on a series of b-NiAl compositions within the homogeneity range of this phase (20% at 1,2001C). They found that void formation decreased with increasing alloy N Al =N Ni ratio. This was explained using the diffusion data [97] shown in Figure 5.29. As seen from the figure, DNi =DAl 3 for N Al 0:5. The selective oxidation of aluminium from b-NiAl necessarily depletes aluminium from the alloy surface, and enriches nickel, as shown schematically in Figure 5.3. In the case of nickel-rich alloys, the high value of DNi =DAl means that the inward flux of nickel exceeds the outward flux of aluminium. Such a situation of unbalanced material flows is known as the Kirkendall effect, and was analysed in Section 2.7. In that discussion it was assumed that the lattice was free to move, and its resulting drift rate, n, reflected the different metal self-diffusion coefficients n ¼ V AB ðDA DB ÞrCA
(5.89)
In the case of b-NiAl oxidation, however, the alloy surface is anchored to an almost rigid alumina scale, and is not free to move. The vacancy flux induced by the imbalance between J Ni and J Al therefore leads to void formation rather than lattice drift. Evidently void nucleation at the alloy–surface interface is energetically favoured over other sites within the bulk alloy. In aluminium-rich NiAl, however, diffusion of aluminium is the dominant process (Figure 5.29), and the Kirkendall effect ceases to drive vacancies towards the alloy surface [98, 99]. The voids continue to enlarge with time as NiAl oxidation proceeds, despite the gaps developed between alloy and oxide. At 1,2001C, the vapour pressure of aluminium above the depleted alloy is sufficient to transport Al(g) across the
228
Chapter 5 Oxidation of Alloys I: Single Phase Scales
Figure 5.29 Interdiffusion and self-diffusion coefficients in b-NiAl. Reprinted from Ref. [97] with permission from Elsevier.
cavity to the scale, sustaining its continued growth [22, 96]. At temperatures below 1,0001C, the value of pAl is too low, according to Equation (2.155), to maintain the observed oxide scaling rate. Some other transport mechanism, perhaps surface diffusion, must be involved [96]. The development of the interfacial voids obviously weakens scale adhesion, making scale loss more likely. Platinum is added to NiAl to improve its scale adherence [100]. The improvement is associated with a reduction in cavity formation [101], an effect thought to result from interactions within the alloy increasing DAl and/or decreasing DNi . Gleeson et al. [102] have confirmed that platinum increases DAl in b-NiAl. A completely different mechanism of void formation is available in cases where the alloy contains carbon. Inward diffusing oxygen can react with solute
5.8. Microstructural Changes in Subsurface Alloy Regions
229
carbon to form bubbles of CO2, as has been shown experimentally [103–105]. Fracture of oxidized specimens in a vacuum chamber attached to a mass spectrometer revealed the presence of CO2. The extent of void formation was shown to increase with carbon content, and could be suppressed by decarburization before oxidation. This mechanism can operate in both alloys and single metals.
5.8.2 Scale–alloy interface stability The additional degree of freedom available in a binary alloy plus oxygen system permits the development of a two-phase region in a diffusion zone, unlike the case of pure metal oxidation, where such zones are thermodynamically impossible in the absence of capillarity effects. For this reason, pure metal–scale interfaces are stable. However, no such thermodynamic constraint applies to alloy–scale interfaces, the shapes of which are kinetically controlled. An example of an unstable interface is shown in Figure 5.1a. The general nature of the problem is rather simple, as shown in Figure 5.30, where a perturbation in an otherwise flat alloy–scale interface is represented. If such a perturbation grows, the interface is unstable; if it decays, the interface is stable.
Figure 5.30 Schematic view of growth or decay of perturbation at alloy–scale interface, according to which phase is the slower diffusing.
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Chapter 5 Oxidation of Alloys I: Single Phase Scales
The effect of the perturbation is locally to decrease the scale thickness from X to Xu and increase the alloy depletion depth from XD to X0D . Clearly, if scale growth is controlled by scale diffusion, i.e. dX=dt ¼ kp =X, then growth is faster at the site of the perturbation. Accordingly metal is consumed faster at this site than on the flat surface, a process which continues until a uniform scale thickness is restored. It is seen that the interface is stable when scale diffusion is rate controlling. Consider now the situation where alloy diffusion is rate controlling, ~ AB =XD . Clearly this and to a first approximation, the flux of B is proportional to D flux is slowest at the site of the perturbation shown in Figure 5.30, because X0D 4XD . Thus oxidation of the flat part of the interface is faster than at the perturbation, causing the flat surface to recede faster than the locally perturbed region. In this case, the irregularity grows and the interface is unstable. The conditions under which diffusion in the alloy controls scaling rates were examined by Wagner [12], as discussed in Section 5.3. Wagner [106] extended that analysis to consider the possibility of morphological breakdown, assuming that no oxygen dissolved in the alloy and that surface capillarity effects can be neglected. He found from a two dimensional analysis of diffusion at a sinusoidal scale–alloy interface that the condition for interface stability is N B;i DAB VOX 41 (5.90) 1 N B;i DB V AB where now N B;i represents alloy composition at the average interface location. When, however, the interface is unstable, it is likely that particles of the more noble metal will be occluded into the oxide. Whittle et al. [107] have examined the effect of relaxing the assumptions of negligible oxygen solubility in the alloy and of the more noble metal in the oxide. They found that internal precipitation of BO behind the alloy–scale interface was a likely outcome under the supposed conditions.
5.8.3 Phase dissolution The situation considered is that of a two-phase alloy in which a precipitate phase rich in the more reactive solute element acts as a reservoir for the continued exclusive growth of the solute metal oxide scale. A schematic representation is shown in Figure 5.31, using the example of an Ni–Si alloy. The concentration profile of reactive metal B is defined by the original alloy mole fraction N ðoÞ B , the solubility limit in the matrix phase, N aB , and the alloy–scale boundary value. It is assumed that precipitate dissolution is fast enough to maintain local precipitatematrix equilibrium. If diffusion of B through the solute-depleted subsurface alloy region is also fast enough, then N B;i will be approximately constant, and steadystate parabolic kinetics result. Diffusion analysis [108] yields the concentration profile of B in the single-phase dissolution zone. Approximating the scale–alloy interface as immobile, one finds from a mass balance for B that u N ðoÞ þ p1=2 u erf ðgÞ (5.91) B N B;i ¼ g exp ðg2 Þ
5.8. Microstructural Changes in Subsurface Alloy Regions
231
Figure 5.31 Selective oxidation of two-phase alloy AB causing dissolution of B-rich phase and diffusion through depletion zone.
where u¼
kc ~ 4DAB
1=2
g¼
Xd 1=2 ~ AB t 4D
(5.92)
(5.93)
and Xd represents the precipitate dissolution depth. A slightly more accurate description is obtained by taking scale–metal interface movement into account [108]. Application of (5.91) to the kinetics of precipitate dissolution zone widening during oxidation of Ni–Si alloys consisting of a g-matrix and b-Ni3Si precipitates, and of Co–Si alloys containing a-Co2Si precipitate led to successful prediction [109] of depletion depths (Figure 5.32). Two questions arise when considering the selective oxidation of protective scale-forming metals from two-phase alloys. Firstly, will the precipitates dissolve fast enough to maintain the solute level at its equilibrium value N aB ? Secondly, will diffusion through the depleted zone be fast enough to maintain N B;i at a high enough level to sustain selective scale growth? The second problem is similar to
232
Chapter 5 Oxidation of Alloys I: Single Phase Scales
300
250
Xd [μm]
200
150
100
50
0 0
50
100
150
200
250
300
350
t1/2 [s1/2]
Figure 5.32 Depletion zone deepening kinetics for Ni–16Si (’) and Co–19Si (~). Continuous lines predicted from Equation (5.91). Reprinted from Ref. [109] with permission from Elsevier.
the situation of diffusion from a single-phase alloy considered by Wagner [12], and discussed here in Section 5.3. In both cases, diffusion through a single-phase, ~ AB subsurface alloy zone delivers B to the scale–alloy interface, and the ratio kc =D is a key factor. This has been demonstrated [110] by comparing austenitic and ferritic modifications of a series of cast iron–chromium carbide alloys. The software package THERMO-CALC [111] was used to predict how alloying additions would affect the phase constitution and to calculate alloy and precipitate compositions and weight fractions. The base alloy chosen for investigation was Fe–15Cr–0.5C at 8501C, where it is austenitic. Alloy compositions are listed in Table 5.4 along with their predicted phase constitutions. Matrix chromium contents were around 11 wt.% and the coarse interdendritic carbides varied in volume fraction from 6% to 10%. Adding silicon to the iron-based alloy altered its phase constitution to a+M7C3. To study the chemical effect of silicon in isolation from its effect on the matrix crystal structure, another alloy was designed to retain the austenite structure by using nickel as an austenite stabilizer. To complete the iron-based alloy set, an a+carbide steel was produced to investigate the effect of changing matrix to ferrite without simultaneously introducing silicon. Molybdenum was chosen as the ferrite stabilizer. To verify that the molybdenum had no major effect other than producing a ferrite matrix, a molybdenum-bearing austenitic alloy was designed, again using nickel as the austenite stabilizer. Measured oxidation rates and observed reaction morphologies (Table 5.4) fell into two classes. Either a protective chromium-rich oxide scale developed in association
5.8. Microstructural Changes in Subsurface Alloy Regions
Table 5.4
233
Oxidation of cast ferrous alloys in oxygen at 8501C Phase constitution
Reaction morphology
kp ðg2 cm 4 s1 Þ
Fe–15Cr–0.5C
g þ M23 C6
2.5 108
Fe–15Cr–0.5C–3Mo
a þ M23 C6
Fe–15Cr–0.5C–3Mo–3Ni
g þ M23 C6
Fe–15Cr–0.5C–1Si
a þ M7 C3
Fe–15Cr–0.4C–1Si–1Ni
g þ M23 C6
Iron oxide scale Carbides engulfed Cr2O3 scale Carbide dissolution zone Iron oxide scale Carbides engulfed Cr2O3 scale Carbide dissolution zone Cr2O3 scale Carbide dissolution zone
Composition (wt%)
1.4 1011
9.3 109 1.3 1012
1.4 1012
with subsurface alloy carbide dissolution, or a fast-growing iron oxide scale engulfed the carbide phase. Whereas the ferritic materials always formed protective chromia scales, the austenitic alloys formed non-protective, rapidly growing iron oxide scales except in the case of the austenite containing silicon. The discussion will return to this last observation after consideration of the alloy diffusion processes. Carbide dissolution depths were measured metallographically and chromium concentrations by electron probe microanalysis, leading to the results shown in Table 5.5. Values for kc were calculated from the weight gain kinetics using measured scale compositions. Values for DCr were then calculated from Equation (5.91) leading to the results shown in Table 5.5. Examination of these values reveals that DCr calculated for ferritic alloys are of the order of those reported in the literature. Chromium diffusion in austenitic alloys was slower, as expected, but not as slow as independently measured diffusion coefficients would suggest. Subsequent use of high temperature XRD to identify the surface phase constitution of reacted alloys confirmed that decarburization of this region had transformed it from austenite to ferrite. Whether the alloy was ferritic to begin with, or was converted to ferrite in its subsurface zone, the relatively rapid lattice diffusion of chromium to the alloy surface sustained a protective Cr2O3 scale. The effect of silicon on the oxidation behaviour of cast Fe–Cr–C was very strong. Adding 1% to the base alloy made it ferritic and led to growth of a protective Cr2O3 scale. Even with an austenitic matrix, which resulted from the further addition of nickel, the silicon-bearing alloy developed a Cr2O3 scale. It was concluded that the effect of silicon on oxidation was related not to the change it produced in alloy diffusion, but rather its ability to alter the scale–alloy interface. Variation in carbide size was important to the reaction morphology [110, 112]. Whereas the base alloy Fe–15Cr–0.5C developed a thick iron oxide scale when reacted in its cast and annealed form, the same alloy formed a protective Cr2O3
234
Chapter 5 Oxidation of Alloys I: Single Phase Scales
Table 5.5
Calculated DCr values for Cr2O3-forming alloys at 8501C
Alloy
Matrix
Xd (mm)
NiCr
DCr (cm2 s1)
Fe–15Cr–0.5C (forged) Fe–15Cr–0.5C–1.0Si Fe–15Cr–0.4C–1.0Si–Ni Fe–15Cr–0.5C–3.0Mo
g a g a
35 22 25 45
0.06 0.10 0.10 0.07
6 1012 4 1011 1 1011 4 1011
Cr23C6 particles b
Figure 5.33 Oxide scales grown at 8501C on g-Fe–15Cr–0.5C (a) as cast (b) forged, demonstrating effect of carbide size on chromium release [110]. With kind permission from Springer Science and Business Media.
scale after hot forging (Figure 5.33). The value of kp in this latter case was 6.8 1012 g2 cm4 s1. The volume fraction of chromium-rich carbide was the same in both alloy forms, but the precipitates were much smaller (around 1 mm) in the forged material than the 3–5-mm interdendritic carbides typical of the cast alloys. Thus precipitate size as well as volume fraction is important in achieving delivery of scale-forming metal to the alloy surface. In the literature on multiphase oxidation, frequent reference is made to the 1974 study performed by El Dahshan et al. [113] on Co–Cr–C alloys. This work was the basis of the subsequent suggestion [114] of using a minority alloy phase as a ‘‘reservoir’’ of scale-forming metal. Additions of up to 2 wt% carbon to Co–25Cr caused precipitation of large quantities of chromium-rich carbide and consequently lower chromium content in the metal matrix of these alloys. Nonetheless, the alloys oxidized protectively at 1,0001C in pure oxygen. Formation of a protective chromium-rich oxide scale was accompanied by dissolution of the chromium-rich carbides within a shallow alloy subsurface region. It was therefore concluded that localization of much of the alloy chromium content into precipitates had no effect on oxidation performance, as rapid carbide dissolution yielded the chromium required to form the protective scale. Viewed in the light of the findings for Fe–Cr–C alloys discussed earlier, the conclusions reached by El Dahshan et al. are surprising. Their cast, cobalt-based
235
5.8. Microstructural Changes in Subsurface Alloy Regions
alloys had coarse carbides which would be expected to dissolve slowly. Furthermore, the austenitic alloys might not provide the rapid diffusion required to sustain Cr2O3 growth on a Co–Cr alloy. A re-examination [115] of Co–25Cr–C oxidation at 1,0001C has demonstrated that their protective behaviour was in fact due to the presence of silicon contamination, as suggested by Jones and Stringer [116]. Silicon was incorporated into the alloys during annealing in evacuated SiO2 ampoules. The silicon was thought to promote rapid chromia formation through a surface nucleation effect.
5.8.4 New phase formation The example of copper hot shortness was described in Section 5.1. Accumulation of a layer of copper-rich phase results from noble metal rejection at the scale–alloy interface, just as in the Pt–Ni case investigated by Wagner [12], coupled in this case with a limited solubility for copper in iron. The concentration profile for copper in the reacting system is represented schematically in Figure 5.34, where the steel is represented as a binary Fe–Cu alloy, and the solubility of copper in FeO is set at zero. At low temperatures, diffusion in the alloy can be neglected, and the thickness of the copper-rich layer can be estimated from a simple mass balance ðoÞ ¯ yCðoÞ Cu ¼ xðCCu CCu Þ
(5.94)
where C¯ Cu is the average copper concentration in the copper-rich layer and the distances x and y are defined in Figure 5.34. Combination with Equation (5.36) Fe(Cu)
Cu(Fe)
FeO
CCu
y
(0)
CCu x
z
Figure 5.34 Schematic concentration profile for copper in oxidized copper-bearing steel, neglecting diffusion into substrate. Dashed line shows location of original alloy reference.
236
Chapter 5 Oxidation of Alloys I: Single Phase Scales
then leads to x¼
CðoÞ Cu
VFeCu z ðoÞ V ¯ ðCCu CCu Þ FeO
(5.95)
where the scale is approximated as being entirely wu¨stite. Under steady-state conditions of parabolic scale growth, the copper layer also thickens according to ¯ Cu estimated from the parabolic kinetics. If V FeCu is approximated as VFe and C Fe–Cu phase diagram, then for a 0.47 wt% copper steel, we calculate x ¼ 2:83 103 z. Measured [117] rates of copper layer accumulation were found to be in agreement with values predicted from scaling rates at 1,1501C, using the above mass balance. However, measured copper layer thicknesses were less than predicted at 1,2501C, particularly in the early stages. This occurred because diffusion of copper into the substrate steel cannot be neglected at high temperatures, as seen in the measured concentration profile in Figure 5.4. Another example of new phase formation is provided by the technically important alloys based on g-TiAl. These have an attractive combination of high temperature strength and low density, but their high temperature oxidation performance needs improvement. Initial selective oxidation of aluminium leads to formation of the z-phase (approximately Ti50Al30O20) as a layer at the alloy surface [118, 119]. Examination of the diffusion path in Figure 5.35 shows that little titanium diffusion is involved, but inward oxygen diffusion through the z-phase matches the outward aluminium diffusion. This steady state is not maintained with continued oxidation. Instead, slow aluminium diffusion in the parent g-phase towards the Z/g interface leads to its local depletion, morphological breakdown of the interface and ultimately precipitation of oxygen-rich a2, as shown in Figure 5.35. The accompanying volume change leads to cracking of both the z-layer and Al2O3 scale, followed by TiO2 formation and loss of protective behaviour.
5.8.5 Other transformations Alloys of three or more components are obviously capable of a greater diversity of phase changes than the relatively straightforward binaries considered so far. An example of practical importance is the Ni–Cr–Al systems, which forms the basis of a number of heat resisting alloys and coatings. An isothermal section at 1,1501C of the phase diagram for this system is shown in Figure 5.36 [120]. Isothermal oxidation of three-phase (a-Cr+b-NiAl+g-Ni) alloys led to selective aluminium removal from the alloy, and development of a transformed subsurface region [121], as shown in Figure 5.36. The phases present were identified by electron probe microanalysis: the bright white phase is a-Cr, the mid-grey phase b-NiAl the light grey one g-Ni. As seen from the schematic diffusion path in Figure 5.36, depletion of aluminium from the three-phase alloys must lead eventually to single g-phase formation. Dissolution of the b-phase is immediately understandable in terms of the large gradient in aluminium activity developed by the selective oxidation process.
5.9. Breakdown of Steady-State Scale
237
(a)
(c)
(b)
(d)
Figure 5.35 Oxidation of g-TiAl at T ¼ 1,0001C (a, b) initial protective behaviour and (c, d) after a2 precipitation at g–Z interface. Reprinted from Ref. [119] with permission from Elsevier.
Dissolution of a-Cr, however, was driven by smaller, local gradients in aCr resulting from the increased solubility for chromium in g-Ni developed as the aluminium concentration decreased. For this reason an alloy with a large N ðoÞ Cr value formed a subsurface g+a region whereas a chromium alloy formed single-phase g-Ni.
5.9. BREAKDOWN OF STEADY-STATE SCALE When a protective scale of slow growing oxide can no longer be maintained, other alloy components start to oxidize and alloy consumption is accelerated.
238
Chapter 5 Oxidation of Alloys I: Single Phase Scales
30μm Figure 5.36 Isothermal section at 1,1501C of Ni–Cr–Al phase diagram [121] and metallographic section of oxidized alloy, showing diffusion path for selective Al2O3 formation on three-phase alloy.
This phenomenon of breakdown or breakaway oxidation becomes inevitable when the interfacial concentration N B;i decreases to a value lower than the minimum necessary to maintain the exclusive growth of the desired BOn scale. It may even become possible at higher values of N B;i , which are adequate to maintain growth, but insufficient to reform a new scale if the existing one is damaged or removed. Although there is no satisfactory way of predicting the latter value, it can be measured experimentally. The problem then becomes one of predicting when the capacity of the alloy to supply B to the interface is exhausted. Similar considerations apply in the case of a scale with some solubility for a second alloy component. Taking the example of an Fe–Cr alloy, it is clear
5.9. Breakdown of Steady-State Scale
239
that as N Cr;i decreases, N Fe;i increases and the iron content of the scale also rises. If in the oxide DFe =DCr 41, iron is increasingly enriched towards the scale–gas interface until an iron-rich oxide precipitates. The ability of an alloy to supply the desired metal to its surface obviously ~ varies with N ðoÞ B , DAB and t, along with the total amount of B in the alloy specimen. Assuming the specimen to be a large, thin sheet so that edge effects can be neglected, the problem is one of diffusion in a single dimension, normal to the oxidizing surfaces. We consider first the situation where scale growth is very slow, but alloy diffusion rapid, as will be the case with ferritic alumina formers. In this event, the N Al profile in the alloy will be almost flat, and the value of N Al;i is equal to the average value N Al remaining after aluminium is withdrawn from the alloy into the scale. Clearly, the change in N Al with time is significant only if the sheet is extremely thin. This is, in fact, a situation of practical interest because thin sheet material is used in some heat exchangers and as catalyst supports. This problem has been treated by Quadakkers and Bongartz [122] on the basis that the small movement of the scale–alloy interface can be ignored. The materials examined were Fe–20Cr–5Al and oxide dispersion strengthened (ODS) versions of this and similar alloys. Their oxidation weight gain kinetics are not strictly parabolic [123], obeying instead a power law DW ¼ k t1=n (5.96) A where n 3. The approximately cubic rate law results from the fact that mass transfer in the scale is predominantly via grain boundary diffusion, and the density of grain boundaries changes with time [124] (see Section 3.9). The corresponding amount of aluminium withdrawn from each side of the sheet is DW Al ¼ 1:125kt1=n (5.97) A where the dimensionless numerical factor is the Al/O weight ratio in Al2O3. Setting the alloy sheet thickness at 2l, we find for the reduction in alloy aluminium content, DCAl (mole/volume) 1:125kt1=n (5.98) 27l with 27 the atomic weight of aluminium. If the critical value for breakaway is CCrit , the time taken to reach it, tB is therefore !n ðoÞ 27l CAl CCrit tB ¼ (5.99) 1:125 k ðoÞ CAl CAl ¼ DCAl ¼
Quadakkers and Bongartz [122] examined sheets of several ferritic alumina formers oxidized at 1,2001C, and verified that the concentration profiles of aluminium were essentially flat. Using a critical aluminium level of 1.3 wt% for breakdown of the alloy MA956, they predicted from Equation (5.99) the times for breakdown of different sheet thicknesses, shown in Figure 5.37 as the line
240
Chapter 5 Oxidation of Alloys I: Single Phase Scales
Figure 5.37 Lifetime limits for breakdown of Al2O3 scales on MA956 sheet. Straight lines predicted from Equations (5.99) and (5.101), and points observed experimentally [122]. Published with permission from Wiley-VCH.
labelled ‘‘no spalling’’. Agreement is seen to be good, as would be expected of a simple mass balance. At greater sheet thicknesses, and longer lifetime, the times to failure are seen to be shorter than predicted. This was attributed to repeated scale cracking and spallation, which occurred at regular intervals. After each of these events, alumina grew again, according to the same kinetics until the next scale spalled. Assuming equal amounts of aluminium are lost in each spallation event, DW n ¼ 1:125kðtn Þ1=n (5.100) A where t is the time between spallation events and DW n the corresponding aluminium loss, then ðoÞ 27l ðCAl CCrit Þ DW n n1 (5.101) tB ¼ 1:125 A kn The dashed line in Figure 5.37 shows behaviour times calculated from Equation (5.101) on the basis of the observed average DW n =A ¼ 2 mg cm2 . Again the simple mass balance prediction is seen to be successful. The more difficult question of predicting when scale spallation will occur is deferred to Chapter 11. Diffusion in austenitic alloys is significantly slower, and the above description does not apply. Instead, the diffusion profile inside the alloy must be found by solving the general diffusion equation (5.12). Because the interface concentration N B;i becomes a function of time as breakdown is approached, no analytical solution is available. However, a simpler approach is to assume that the surface
5.10. Other Factors Affecting Scale Growth
241
concentration remains constant until the depleted zones on the two sides of the sheet meet in the middle. At that stage, the surface concentration starts to decrease and breakdown follows. For diffusion out of a thin, plane sheet –loxol in which the concentration is initially CðoÞ B and the interfacial concentration is fixed at CB;i the solution is quoted by Crank [125] as 1 CB CB;i 4X ð1Þn Dð2n þ 1Þ2 p2 t ð2n þ 1Þpx (5.102) exp ¼ cos 2 ðoÞ p 2l 2n þ 1 4l CB CB;i n¼0 for fixed interfaces. As shown by Carslaw and Jaeger [126], diffusion depletion reaches the middle of the sheet when Dt 0:05 (5.103) l2 The subsequent decrease in CB;i with time has been treated approximately by Whittle [127] on the assumption that N B;i 1. Whittles’ solution was " ! !# 1 pkc 1=2 X 2nl þ x 2ðn þ 1Þl x ðoÞ erfc N B;i ¼ N B þ erfc (5.104) 2DAB 2ðDAB tÞ1=2 2ðDAB tÞ1=2 n¼0 For the specific example of Ni–20Cr oxidized at 1,2001C, with ~ AB ¼ 2 1010 cm2 s1 , kc ¼ 2 108 cm2 s1 and 2l ¼ 0.25 mm, he set x ¼ 0, D and calculated N Cr;i ¼ fðtÞ. If the critical interface concentration necessary to prevent spinel formation is N Cr ¼ 0:03, then a breakdown time of 6 105 s would be predicted. This compares with a value of 2 105 s predicted from Equation (5.103) for the time at which depletion reaches the sample centre. Consistent with these predictions, Douglass and Armijo [128] showed that NiCr2O4 had started to form beneath the chromia scale on this alloy in less than 444 h at 1,2001C. Evans and Donaldson [129] have demonstrated that the approximate solution (5.104) for diffusion out of a thin plane sheet describes the remnant chromium profile reasonably well. The above analyses are of at least indicative value for thin alloy sections, where consumption of the scale-forming metal can occur in a reasonable time. For larger sections, the predictions are optimistic. At 1,1001C, a 5-mm section of MA956 (Table 5.1) is predicted from Equation (5.101) to last for more than 105 h. At 1,0001C (a realistic maximum for a chromia former), a 5-mm section of Ni–20Cr is predicted on the conservative basis of Equation (5.103) to last for 8 107 h. However, the latter estimate is based on the benign assumption that the Cr2O3 scale never cracks or spalls. Moreover, as will be described in later chapters, other modes of failure become likely before the alloy is exhausted of chromium.
5.10. OTHER FACTORS AFFECTING SCALE GROWTH When alloys scale under steady-state conditions, the identity of the oxide in contact with the alloy is determined by the metal composition at this interface.
242
Chapter 5 Oxidation of Alloys I: Single Phase Scales
This composition is related to the original alloy composition and can be calculated from Wagner’s analysis of diffusion in the alloy and scale, assuming the latter to be a single phase, continuous layer. The ratio kc =DAB is found to be critical in determining interfacial concentrations and, therefore, the minimum original alloy concentration of a component necessary to sustain the exclusive growth of its oxide scale. Quantitative application of the theory yields limited success, because of its ~ AB . Although the sensitivity to error in experimental measurements of kc and D theory has been extended to cover solid solution scales, the complexity of their solution thermodynamics and diffusion behaviour means that an even larger body of experimental information is required to permit predictions of scale composition and growth rate. Nonetheless, the theory has been verified in a number of cases, and can clearly be relied upon in a qualitative sense. In describing N B;i in terms of kc and DAB , the theory successfully accounts for differences between ferritic and austenitic alloys, and between chromia and alumina scales. It also succeeds in relating the spatial distribution of components within solid solution scales to the relative oxide stabilities and mobilities. These successes are of use in interpreting and to some extent predicting scale breakdown. The values used for the alloy diffusion coefficient have been assumed in this chapter to be those characteristics of bulk or lattice diffusion. Whereas this is reasonable at very high temperatures, it will often be an underestimate at low and intermediate temperatures, where other diffusion pathways such as grain boundaries and dislocations can be more important. The surface finish given to an alloy component before placing it into service can affect the density of grain boundaries and dislocations in the subsurface region. Any low-temperature mechanical working of the surface, such as machining, grinding, blast cleaning, shot peening, etc deforms the subsurface metal, introducing large numbers of dislocations. As the alloy is heated, the deformed metal recrystallizes, forming a generally finer grain and subgrain structure. These subsurface defects will be present during the transient stage of oxidation, and will persist for long times at low temperatures. The consequently higher effective alloy diffusion coefficient is obviously of benefit in rapidly achieving and maintaining protective steadystate growth of chromia or alumina. Several experimental studies [8, 130–132] have demonstrated the more rapid formation of Cr2O3 on cold-worked alloy surfaces. Diffusion theory allows calculation of the minimum concentration of an alloy component necessary to sustain the exclusive growth of its oxide. However, this concentration may not be sufficient to achieve such a steady state. In the initial, transient oxidation stage of reaction, essentially all alloy components capable of forming oxides do so. The subsequent development of scale morphology then depends on the competition between continued growth of fast diffusing oxides and replacement of less stable oxides by more stable, but slow growing ones at the oxide–alloy interface. Because this morphological evolution is controlled in part by nucleation and solid–solid interfacial processes, it cannot be described by diffusion alone.
References
243
The presence of minority components in the alloy can be critical in their effect on the transient reaction. As discussed in Section 5.6, the phase transformations leading to a-Al2O3 formation can be accelerated by many alloy additions, either by their chemical doping of alumina or by providing isostructural oxides which act as ‘‘templating’’ sites for a-phase nucleation. Similarly, the addition of cerium to Fe–Cr alloys has been shown [133, 134] to promote Cr2O3 nucleation. Several metals which form very stable oxides (e.g. Ce, La, Y, Hf, etc.) are for this reason known as ‘‘reactive elements’’. Their addition to chromia and alumina forming alloys often affects the strength of the scale–alloy interface, the scale microstructure and the mass transfer mechanisms governing scale growth. These effects are discussed in Chapter 7.
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29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70.
71. 72. 73. 74. 75.
Chapter 5 Oxidation of Alloys I: Single Phase Scales
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CHAPT ER
6 Oxidation of Alloys II: Internal Oxidation
Contents
6.1. Introduction 6.2. Selected Experimental Results 6.3. Internal Oxidation Kinetics in the Absence of External Scaling 6.4. Experimental Verification of Diffusion Model 6.5. Surface Diffusion Effects in the Precipitation Zone 6.6. Internal Precipitates of Low Stability 6.7. Precipitate Nucleation and Growth 6.8. Cellular Precipitation Morphologies 6.9. Multiple Internal Precipitates 6.10. Solute Interactions in the Precipitation Zone 6.11. Transition from Internal to External Oxidation 6.12. Internal Oxidation Beneath a Corroding Alloy Surface 6.13. Volume Expansion in the Internal Precipitation Zone 6.14. Success of Internal Oxidation Theory References
247 248 255 260 267 273 278 284 290 299 301 305 306 311 312
6.1. INTRODUCTION As recognized in Chapter 5, when an alloy component is selectively oxidized but cannot reach the surface quickly enough to develop a scale, then internal oxidation results. Furthermore, an alloy which initially contains sufficient of the reacting metal to form a scale can become depleted in that component to the extent that internal oxidation commences. Under some circumstances, internal oxidation and external scaling can occur simultaneously. It is emphasized that ‘‘oxidation’’ means forming a compound (oxide, carbide, nitride, etc.) of the reactive alloy solute metal, and the description given here applies to internal oxidation, carburization, nitridation, etc. Internal oxidation is the process in which a gas phase oxidant dissolves in an alloy and diffuses inward, reacting with a dilute solute metal to form dispersed precipitates of metal oxide or metal carbide, etc. This class of precipitation reactions is distinguished by its dependence on gas–solid interaction, and the formation of a reaction product zone adjacent to the alloy surface. It does not
247
248
Chapter 6 Oxidation of Alloys II: Internal Oxidation
include homogeneously distributed phase changes, such as carbide precipitation occurring during alloy aging. The practical reality [1] is that a large percentage of high-temperature corrosion failures involve internal oxidation. The internally precipitated reaction products cause embrittlement and dilation of the alloy subsurface region, which can cause the affected zone to flake off. Because the process is supported by diffusion of interstitial species (dissolved oxygen, carbon, nitrogen or sulfur), it is rapid. Internal oxidation is a very destructive process. Both chromia and alumina formers can be attacked by internal oxidation, even when the alloys contain sufficient chromium or aluminium to sustain external scale growth according to Wagner’s criterion (5.22). Just what leads to this outcome is obviously of interest. It is important to establish not only the conditions under which this mode of attack occurs, but also the rate of the process and how it varies with alloy composition and ambient conditions. The general features of internal oxidation reactions were first established by Smith [2, 3], Rhines et al. [4, 5] and Meijering and Druyvesten [6, 7]. Many subsequent investigations have added to our descriptive knowledge of the process. We consider first some experimental results, with the aim of relating reaction morphologies to the phase diagrams which describe the phase assemblages encountered. The conditions under which these morphologies develop are then established, and the kinetics described using Wagner’s diffusion analysis [8] and its explication by Rapp [9]. These descriptions are then extended to other, more complex situations, where the simplifying assumptions adopted by Wagner are no longer applicable. As always, our purpose is to understand the mechanisms of the processes, develop means of calculating their rates and ultimately arrive at means for their mitigation.
6.2. SELECTED EXPERIMENTAL RESULTS Typical reaction morphologies of internally oxidized alloys are shown in Figure 6.1, where chromium-rich oxide has precipitated inside an Fe–5Cr alloy reacted in Ar/H2/H2O atmospheres where the ambient pO2 value was too low for FeO to form. Clearly oxygen had dissolved in the alloy and diffused inwards to react with alloy solute chromium, precipitating its oxide. The depth of the precipitation zone, XðiÞ , is seen in Figure 6.1 to increase according to parabolic kinetics X2ðiÞ ¼ 2kðiÞ p t
(6.1)
where kðiÞ p is the internal oxidation rate constant. This is an almost universal observation [11, 12] and indicates that the process is diffusion-controlled. The effect of alloy chromium content is shown in Figure 6.2. Dilute alloys form only internal oxide, Fe–10Cr forms both external and internal oxide and Fe–17Cr forms only an external scale. A schematic phase diagram in Figure 6.3 illustrates diffusion paths corresponding to the steady-state morphologies of
6.2. Selected Experimental Results
249
Figure 6.1 Internal oxidation of Fe–5Cr at pO2 ¼ 8:7 1017 atm in Ar–H2–H2O; kinetics at 1,0001C. Reproduced from Ref. [10] by permission of The Electrochemical Society.
Figure 6.2a–d. The diagram has been constructed on the basis that pO2 is too low for any iron-bearing oxide, such as FeCr2O4, to form. Thus pure iron equilibrates directly with oxygen. Paths (a) and (b) show variation in oxygen content at a ~ AB , where oxygen fixed NCr/NFe ratio, and correspond to the situation DO D diffuses into the alloy so fast that chromium diffusion can be neglected. These paths represent local equilibrium situations, and do not encompass the supersaturation zones necessary to drive precipitate nucleation (Section 6.7). Path (c) represents simultaneous internal and external oxidation, and path (d) shows external scaling only. The chromium oxide precipitates shown in Figures 6.1 and 6.2 are dispersed and generally spheroidal in shape, although non-uniform in size. Moreover, the volume fraction of precipitate appears to vary somewhat with depth at higher temperatures, although it is approximately constant at 9001C. A very different
250
Chapter 6 Oxidation of Alloys II: Internal Oxidation
Figure 6.2 Change in oxide morphology with composition of Fe–Cr alloys exposed to pO2 ¼ 8:7 1017 atm in Ar–H2–H2O at 1,0001C. Reproduced from Ref. [10] by permission of The Electrochemical Society.
precipitate shape is obtained by internal nitridation, as seen in Figure 6.4. Lamellar precipitates of Cr2N have grown into the alloy, aligned approximately normal to the sample surface, i.e. in a direction parallel to that in which the reaction is proceeding. Clearly the competition between precipitate nucleation and growth has led to very different outcomes in the oxidation and nitridation reactions. It was observed in Chapter 5 that cold working an alloy surface by grinding introduced subsurface defects which accelerated alloy diffusion, making external scale formation by the selectively oxidized component more likely at moderate temperatures. As seen in Figure 6.5, Incoloy 617 (Table 2.1) forms a protective Cr2O3 scale when surface ground before reaction. However, when the deformed region is removed by chemical polishing, both internal and external oxidation develop during subsequent reaction. Of further interest is the finding that internal oxidation occurs preferentially at grain boundaries, rather than within the grains. Penetration along the grain boundaries involved oxidation of alloy
6.2. Selected Experimental Results
251
Figure 6.3 Schematic phase diagram for Fe–Cr–O with Cr2O3 as the only stable oxide. Diffusion paths (a)–(d) correspond to the reaction morphologies in Figure 6.2a–d.
Figure 6.4 Optical micrograph of lamellar Cr2N precipitates formed in Fe–20Ni–25Cr reacted at 1,0001C in N2–10%H2.
carbides, and was remarkably fast. It turns out that internal oxidation at grain boundaries is common in austenitic alloys. In a number of alloys, the selectively reacted component can form more than one product phase. A frequently encountered example is the precipitation of
252
Chapter 6 Oxidation of Alloys II: Internal Oxidation
(a)
(b)
Figure 6.5 Oxidation of IN 617 at T ¼ 7001C, pO2 ¼ 1 1023 atm in Ar–CO–CO2. (a) Grain boundary precipitation of Cr2O3 in material prepared by chemical polishing and (b) external Cr2O3 scale on material prepared by surface grinding.
chromium-rich carbides during carburization of heat-resisting alloys. Figure 6.6 shows a cross-section of carburized Fe–37.5Ni–25Cr where two precipitation zones have been revealed by their different response to stain etching. The carbides in the near-surface zone are chromium-rich M7C3, and those in the deeper zone are chromium-rich M23C6. Carburization reactions are discussed in detail in Chapter 9. As already indicated, diverse precipitate morphologies are possible. Further examples are shown in Figure 6.7. Strongly directional growth of alumina precipitates in the diffusion direction has occurred, Widmansta¨tten plates of
6.2. Selected Experimental Results
253
Figure 6.6 Internal carburization of Fe–37.5Ni–25Cr at 1,0001C in gas with ac ¼ 1, in H2–C3H6. Near-surface zone contains Cr7C3 precipitates and deeper zone contains Cr23C6. Etched with Murakami’s reagent.
Cr2N have developed and apparently lamellar, chromium-rich M23C6 has grown into an Fe–25Cr alloy. Questions of interest concern the factors controlling the predominance of precipitate growth over nucleation, what controls the orientation of the precipitate with respect to the metal matrix and the diffusion direction, and whether or not the aligned precipitate–matrix interfaces can provide preferred diffusion pathways for the oxidant, thereby accelerating the corrosion rate. Alloys can contain more than one component capable of internally precipitating an oxide. Oxidation of a model alloy Ni–3.5Cr–2.5Al led to the internal precipitation of both chromium- and aluminium-rich oxides, as shown in Figure 6.8, a cross-sectional image obtained by SEM. The image brightness is related to the average atomic number of the material being imaged. Thus the metal matrix, which is mainly nickel, is bright, the chromium-rich oxide is grey and the aluminium-rich oxide appears dark. Clearly, the more stable aluminiumrich oxide is precipitated to greater depth than the chromium-rich oxide. This reflects the gradient in oxygen activity from its maximum at the alloy surface to a minimum in the alloy interior. The conditions under which internal oxidation is possible can be specified in a general way, and are formulated here for a binary alloy AB. Internal precipitation of BOn can occur if this oxide is more stable than that of metal A, per mole of oxygen. Precipitation will occur if oxygen can dissolve in the alloy and diffuse inward so as to achieve an activity high enough to stabilize BOn , but not AO. The precipitates will be distributed internally rather than aggregating to form a scale if NB is sufficiently low. It is desirable to be able to specify the critical value of NB
254
Chapter 6 Oxidation of Alloys II: Internal Oxidation
Figure 6.7 Diverse precipitate morphologies resulting from internal oxidation reactions. (a) Oxidation of Ni–2.5Al at T ¼ 1,0001C, pO2 ¼ 4:6 1011 atm, in Ar–H2–H2O; (b) nitridation of Ni–15Fe–25Cr in N2–10%H2 at 1,0001C and (c) carburization of Fe–25Cr at 1,0001C in H2–C3H6 gas with ac ¼ 1, showing internal reaction front.
6.3. Internal Oxidation Kinetics in the Absence of External Scaling
255
Figure 6.8 Simultaneous internal oxidation of chromium and aluminium in Ni–3.5Cr–2.5Al at T ¼ 1,0001C, pO2 ¼ 9:8 1013 atm, in Ar–H2–H2O. Grey oxide is chromium-rich and dark oxide aluminium-rich. A pure nickel layer is present at the surface.
separating these two regimes of oxidation. As always, we wish to predict the rate of the process, and how it varies with material properties and environmental factors. As seen from the brief survey of experimental results, a full description of the process also involves predicting precipitate size, shape, orientation and distribution. The kinetics of internal oxidation are considered first, and a number of simple limiting cases are identified. The factors affecting precipitate nucleation, growth, morphology and distributions are then considered. Predictions for the transition between internal and external oxidation are then compared with experimental data. Finally, the effects of the volume expansion accompanying internal oxide precipitation are discussed.
6.3. INTERNAL OXIDATION KINETICS IN THE ABSENCE OF EXTERNAL SCALING We consider an alloy AB exposed to an oxygen potential high enough to react with B, but not with A, and suppose that alloy diffusion is negligible compared with inward oxygen movement. Internal oxidation will result if the oxygen solubility in the B-depleted alloy, expressed as a mole fraction, N ðsÞ O , and its diffusion coefficient, DO , are high enough. If, furthermore, the precipitate BOn is extremely stable, then the reaction zone is assumed to consist of precipitates embedded in a matrix of almost pure A. This assumption is based on the thermodynamics of the reaction B þn O ¼ BOn ;
DGP
(6.2)
256
Chapter 6 Oxidation of Alloys II: Internal Oxidation
discussed in Section 2.4. The solubility product for local equilibrium between precipitate and matrix DGP N B N nO ¼ Ksp ¼ exp (6.3) RT with DGP ¼ DGf ðBOn Þ DH B nDH O
(6.4)
is very small for a high-stability precipitate. Although it is not necessarily so, it was originally assumed [8, 9], and is often the case, that both N B and N O are very low throughout the precipitation zone, as represented in Figure 6.9. Thus oxygen diffuses through a metal matrix of almost pure A, between the BOn precipitates which have already formed, to reach the reaction front at a depth X(i), where more B is available for reaction. An approximate estimate of the internal penetration rate can be made from a mass balance at the reaction front. Reformulating the standard expression (5.29) for mass balance at a moving boundary in terms appropriate to the development of a two-phase zone, we can write ioz all all J ioz O J O ¼ nðCO CO Þ
(6.5)
where the superscripts ioz and all refer to the internal oxidation zone and the base alloy, and Cioz O the overall oxygen concentration in the oxide-plus-matrix two-phase region. Given the assumption that the oxygen concentration at the reaction front is zero, it follows that all Call O ¼ 0 ¼ JO
(6.6)
Approximating further that the oxygen flux J ioz O ¼ DO Gas
Alloy
NBOυ
CðsÞ CðXÞ @CO O DO O @x XðiÞ Gas
NB(0)
(6.7) Alloy
NBOυ (0 NBB(0)
N0(s) N0
N0(s) N0
(a)
Xi
(b)
Figure 6.9 Schematic representation of internal precipitation of a very stable oxide and the reactant concentration profiles: (a) component B immobile and (b) both oxygen and B diffuse.
6.3. Internal Oxidation Kinetics in the Absence of External Scaling
257
where the superscripts (s) and (X) denote the boundary values of the oxygen concentration at the surface and internal limit of the precipitation zone. Setting ðXÞ CO ¼ 0 (Figure 6.9) and substituting Equation (6.7) in Equation (6.5) yields DO CðsÞ dXðiÞ iox O C ¼ XðiÞ dt O
(6.8)
Integration of Equation (6.8) and substitution from the stoichiometric relationship ðoÞ Ciox O ¼ nCB
where with
CðoÞ B
(6.9)
is the original alloy concentration of B, then leads to Equation (6.1), kðiÞ p ¼
DO CðsÞ O
(6.10)
nCðoÞ B
It is usually assumed that the molar volumes of the alloy and the matrix A are the same, and hence kðiÞ p ¼
DO N ðsÞ O
(6.11)
nN ðoÞ B
This simple result is intuitively reasonable in that it reflects the fact that the penetration rate is proportional to oxygen permeability, N ðsÞ O DO , and inversely proportional to the concentration of reactant metal. It should be noted that it has been assumed that the oxide precipitates do not interfere with inward oxygen diffusion. A more rigorous and less restrictive analysis has been provided by Wagner [8, 9], allowing for the possibility that component B also diffuses. The diffusion model is shown schematically in Figure 6.9b. Again it is assumed that Ksp is extremely small, and that both N O and N B are vanishingly small at the reaction front. The problem then is to solve the diffusion equations for both B and O: @N i @2 N i ¼D 2 @t @x
(6.12)
for the boundary conditions N O ¼ N ðsÞ O NO ¼ 0
t40
(6.13)
x XðiÞ ;
t40
(6.14)
for x40;
t¼0
(6.15)
x XðiÞ ;
t40
(6.16)
for
N B ¼ N ðoÞ B NB ¼ 0
x ¼ 0;
for
for
The solutions are NO ¼
N ðsÞ O
pffiffiffiffiffiffiffiffiffi erf x=2 DO t 1 erf g
(6.17)
258
Chapter 6 Oxidation of Alloys II: Internal Oxidation
( NB ¼
N ðoÞ B
1
pffiffiffiffiffiffiffiffi) erfc x=2 DB t erfcðgf1=2 Þ
for parabolic kinetics, where Equation (6.1) applies, with !1=2 kðiÞ p g¼ 2DO
(6.18)
(6.19)
and f¼
DO DB
(6.20)
Wagner dealt with the mass balance at the reaction front ðx ¼ XðiÞ Þ by supposing that all precipitation took place at this location, and therefore the fluxes of O and B towards the interface were equivalent: @N O @N B DO ¼ nDB (6.21) @x x¼XðiÞ @x x¼XðiÞ þ Here e is a very small increment in x, used to indicate that the fluxes are evaluated very close to, but on opposite sides of the reaction front. Substitution from Equations (6.17) and (6.18) into Equation (6.21) leads, after differentiation, to N ðsÞ O N BðoÞ
¼
expðg2 Þerf g f1=2 expðg2 fÞerfcðgf1=2 Þ
(6.22)
The quantity g, and hence kp , can be evaluated numerically from this equation. In the special case where N ðsÞ DB O 1 DO NB
(6.23)
then g 1 and gf1=2 1, and Equation (6.22) can be accurately approximated by !1=2 N ðsÞ O (6.24) g 2nN ðoÞ B Substitution of this result into Equation (6.19) then yields the simple result (6.11). Inspection of Equation (6.23) reveals that the required condition amounts to a high oxygen permeability relative to any B diffusion, which was the basis for the derivation of Equation (6.10), and is represented by Figure 6.9a. If, however, diffusion of B is important, another special case can arise if N ðsÞ O N ðoÞ B
DB 1 DO
(6.25)
In this case, g 1 and gf1=2 1, and Equation (6.22) can be approximated by g
p1=2 f1=2 N ðsÞ O 2nN ðoÞ B
(6.26)
6.3. Internal Oxidation Kinetics in the Absence of External Scaling
which, when combined with Equations (6.19) and (6.20), yields ! ðsÞ 2 p DO N O ðiÞ kp ¼ DB 2nN ðoÞ B
259
(6.27)
This is the situation represented by Figure 6.9b, and corresponds to enrichment of B within the precipitation zone as a result of its rapid diffusion from within the alloy towards the surface. In distinguishing the two limiting cases represented by Equations (6.11) and (6.27) it is necessary to evaluate the oxidant permeability N ðsÞ O DO and the corresponding alloy quantity, N BðoÞ DB . The oxidant solubility is related to the surface oxygen activity via Sievert’s Equation (2.71). The maximum value of pO2 available to a bare alloy surface is that at which component A forms an external scale. Thus, for example, internal oxidation of Fe–Cr is limited to a maximum N ðsÞ O value given by 1=2 N ðsÞ O ¼ K½pO2 ðFeOÞ
(6.28)
where K is the Sievert’s law constant for O in iron. To avoid the complications of scale formation (see Section 6.12), it is common to study internal oxidation by controlling pO2 at the level set by the A/AO equilibrium. This is conveniently done using a ‘‘Rhines pack’’ [4]: a sealed, evacuated capsule containing a large quantity of powdered metal A mixed with its lowest oxide, along with the AB alloy sample. Alloy solubility data for oxygen shown in Table 6.1 are calculated from Table 2.2. Their use is based on the supposition that all of the reactive alloy components are precipitated near the surface, and oxygen solubility in the remaining, almost pure iron or nickel is set by the Rhines pack condition. Data for both ferritic and austenitic iron are provided, for reasons which are now discussed. Table 6.1 Alloy
Fe–Cr
a
Permeability data for internal oxidation in Rhines packsa T (1C)
1,000
Fe–Al
1,000
Fe–Si
1,150
Ni–Cr Ni–Al Ni–Si
1,000 1,200 1,000
In alloy ABb
In matrix A NðsÞ O
DO (cm2 s1)
4.5 106(a) 3.3 106(g) 4.5 106(a) 3.3 106(g) 1.5 105(a) 9.0 106(g) 4.8 104 9.4 104 4.8 104
3.5 106(a) 7.3 107(g) 3.5 106(a) 7.3 107(g) 9.3 106(a) 3.9 107(g) 9.1 109 7.5 108 9.1 109
DB (cm2 s1)
NðoÞ B
0.054 1.5 1011(g) 4.2 1010(a)
0.020
3.0 1.9
6.3 109(a)
0.016
1.4
7.2 1012 1.0 109 3.9 1011
0.056 0.043 0.016
10.8 1.6 7
Described in Section 6.3. Alloy compositions chosen to match examples studied experimentally.
b
ðoÞ NðsÞ O DO =NB DB
260
Chapter 6 Oxidation of Alloys II: Internal Oxidation
Diffusion in ferritic alloys is complicated at certain temperatures by the appearance of a gðfccÞ-phase. Reference to the phase diagrams for Fe–Cr, Fe–Al and Fe–Si in Figure 6.10 shows that all alloys, when sufficiently dilute, are austenitic at temperatures of about 900–1,4001C. Consider, for example, an alloy of original composition Fe–15Cr, which at T ¼ 1,0001C is ferritic. Internal oxidation removes most of the chromium from the metal phase, shifting its composition into the g-region. If the small concentration of dissolved oxygen can be ignored, the diffusion path in the metal region of the reacting alloy is as shown in Figure 6.10a. For this reason, it is appropriate to consider oxygen dissolution and diffusion through austenite. The a ! g transformation can be suppressed [13] by the addition of an unreactive ferrite stabilizer such as tin, and data for ferrite is also provided in Table 6.1. Similarly, data for DB (calculated from data in Appendix D) in both a- and g-Fe are provided, where available. ðoÞ It is seen in Table 6.1 that for the conditions chosen, DO N ðsÞ O 4DCr N Cr and the conditions for Equations (6.24) and (6.11) are met. Even in the case of much more mobile silicon and aluminium, the conditions are close to being realized, and (6.11) is expected to provide a reasonable approximation. In this situation, the internal oxidation process is controlled by inward oxygen diffusion, and counter diffusion of the alloy solute metal can be ignored. If, however, counter diffusion of the reacting metal is important, then it will enrich in the internal oxidation zone as additional oxide precipitates. Such a situation can be expected during oxidation at very low pO2 values, when the oxygen permeability is consequently lowered. Wagner [8] also calculated the degree of solute enrichment in the precipitation zone. Defining f BO as the mole fraction of BOn precipitate in the internal oxide zone, an enrichment factor a¼
f BO N ðoÞ B
is identified, and was evaluated by Wagner as h i1 a ¼ p1=2 u expðu2 Þerfc u
(6.29)
(6.30)
with u ¼ gf1=2 . Under the limiting conditions of Equation (6.25), this result can be approximated as a ¼ p1=2 u ¼
2nN ðoÞ B DB pN ðsÞ O DO
(6.31)
6.4. EXPERIMENTAL VERIFICATION OF DIFFUSION MODEL As already mentioned, internal oxidation almost invariably follows parabolic kinetics. The applicability of the simple form (6.11) is first investigated. One obvious and useful prediction from this equation is that for a given solvent A, the rate of internal oxidation is independent of the chemical identity of B, and is
6.4. Experimental Verification of Diffusion Model
Figure 6.10 Phase diagrams for (a) Fe–Cr, (b) Fe–Al and (c) Fe–Si showing g-phase regions, and diffusion path in metallic part of internally oxidized Fe–Cr (see text).
261
262
Figure 6.10
Chapter 6 Oxidation of Alloys II: Internal Oxidation
(Continued ).
determined solely by the permeability of oxygen in A, together with the oxide stoichiometry. If correct, this provides a method for measuring oxygen permeability. Alloys based on silver provide a good test of this possibility, because Ag2O is unstable at high temperatures, and reliable, independent measurements of N ðsÞ O and DO are available [14]. Values of DO N ðsÞ O derived from measurements of X i as a function of time (Equations (6.1) and (6.11)) have been collected by Meijering [11] and are compared in Figure 6.11 with independent permeability measurements [14] which yielded 107:2 kJ mol1 ðsÞ 4 N O DO ¼ 2:4 10 exp (6.32) cm2 s1 RT Agreement is seen to be good. It may be concluded that, at least for the dilute alloys involved here, the assumption that oxide precipitates do not interfere with oxygen diffusion is reasonable. The internal oxidation of silver alloys is of more than academic interest: the process is used to provide hardness in silver-based electrical contact materials. Good-quality data for oxygen permeability in nickel have been provided by Park and Altstetter [22], using solid-state electrochemical techniques to measure independently 164 kJ mol1 DO ¼ 4:9 102 exp (6.33) cm2 s1 RT
6.4. Experimental Verification of Diffusion Model
263
Figure 6.11 Permeability of oxygen in silver deduced from internal oxidation kinetics in 1 atm O2 of: ’ Ag–1.3Zn [6], & Ag–1.0Mg [6], K Ag–1.75Mg [15], Ag–1.8Al [15], E Ag–1.0Cd [15], B Ag–0.95Cd [16], Ag–4.8Cd [17], X Ag–1.7Li [18], + Ag–0.3Pb [19] and J Ag–In alloys [20]. Continuous line represents Equation (6.32). Published from Ref. [11] with permission from Wiley.
4
2 N ðsÞ exp O ¼ 8:3 10
7
55 kJ mol1 RT
(6.34)
for pO2 set by the Ni/NiO equilibrium. Internal oxidation kinetics for various nickel-based alloys have been used to deduce the oxygen permeability values shown in Figure 6.12. Agreement with Equations (6.33) and (6.34) is seen to be reasonable. It should be noted that permeabilities deduced from internal ðoÞ oxidation of Ni–Al alloys were in fact a function of N Al , as will be discussed later. The values shown in Figure 6.12 were obtained [21] by extrapolating to ðoÞ N Al ¼ 0. Another prediction available from Equation (6.10) is that for a given matrix A, and fixed T and pO2 , the rate constant for internal oxidation is inversely proportional to N ðoÞ B . Internal oxidation rates for a series of Fe–Cr alloys [23] are seen in Figure 6.13 to vary with 1=N ðoÞ Cr as predicted. Internal oxidation depths observed in Ni–Cr [21] and Cu–Si [24] alloys are seen in Figure 6.14 to vary as predicted from Equations (6.1) and (6.11), i.e. X2ðiÞ / 1=N ðoÞ B . As we have seen, the Wagner diffusion theory achieves considerable success in quantitatively accounting for internal oxidation rates. The theory also applies
264
Chapter 6 Oxidation of Alloys II: Internal Oxidation
log10(N0(s)D0 /cm2s-1)
-10
-11
-12
-13
-14
6
7
8 104K/T
9
10
Figure 6.12 Permeability of oxygen in nickel deduced from internal oxidation kinetics under Rhines pack conditions: ’ Ni–Cr [21], Ni–Al [21], J Ni–0.12Al [11]. Continuous line represents NðsÞ O DO according to Equations (6.33) and (6.44). Published from Ref. [11] with permission from Wiley.
3
Figure 6.13 Internal oxidation rates for Fe–Cr alloys at pO2 ¼ 8:7 1017 atm (E) and 2.6 1026 atm (’) values [23]. Published with permission from Trans Tech Publications.
to internal attack by other oxidants, although reaction rates can be very different because of the different permeabilities. Some comparative data in Table 6.2 illustrate this point. The corresponding internal precipitation reaction rates are shown in Table 6.3. The data are plotted according to Equation (6.10) in Figure 6.15, using logarithmic scales to encompass the large ranges of values. The slope is close to unity, confirming that Equation (6.10) provides a very useful predictive tool.
6.4. Experimental Verification of Diffusion Model
265
24 20
10−3(Xi / m)2
16 12 8 4 0 0
20
40
80
60 (0) 1/ NCr (a)
100
100
10-10kp (cm2s-1)
80
60
40
20
0 0
200
400
600
800
1000
1200
1/Nsi(0) (b)
Figure 6.14 Internal oxidation depth as a function of alloy solute content. (a) Ni–Cr alloys in Rhines pack at 1,0001C for 10 h [21] (Published with permission from Taylor & Francis Ltd., http://www.tandf.co.uk/journals). (b) Cu–Si alloys in Rhines pack at 7501C for 100 h [24] (Published with permission from The Minerals, Metals & Materials Society).
Table 6.2 Comparative permeabilities (cm2 s1) for different oxidants at 1,0001C: oxygen in Rhines packs, carbon at ac ¼ 1 and nitrogen at pN2 ¼ 1 atm
a
Solvent metal
NðsÞ O DO
Ni g-Fe
4.3 1012 2.4 1012
a
Oxygen permeability data from Chapter 2.
NðsÞ N DN
NðsÞ C DC
1.5 1011 [25, 26] 1.6 1011 [25, 26]
3.1 109 [27, 28] 1.4 108 [27, 28]
266
Chapter 6 Oxidation of Alloys II: Internal Oxidation
Table 6.3 Comparative internal oxidation, nitridation and carburization rate constants 2 1 at 1,0001C kðiÞ p /cm s Oxidationa
Nitridationb
Carburizationc
a-Fe–5Cr 5 1010 (8.7 1017 atm) [23] 2.4 107 [23] 10 11 (4.7 10 atm) [29] g-Ni–5Cr 1 10 g-Fe–20Ni–25Cr 6.6 109 [30] 1.1 107 [30] a
At indicated pO2 values. At pN2 ¼ 0:9 atm. c At ac ¼ 1. b
-6
C
Ferrite
log 10(kp(i))
-7
Austenite
N
-8
-9
C
O O
-10
-11 -11
-10
-9
-8
-7
-6
log 10(Ni(s)Di/υNCr (0))
Figure 6.15 Internal precipitation reaction rates for different oxidants in ferritic and austenitic alloys under reaction conditions specified in Table 6.3.
Despite the considerable successes of the Wagner diffusion model in describing internal precipitation reactions in the absence of any external scale, its applicability is limited by the assumptions on which it is based. The assumptions which may prove incorrect for some reacting systems are as follows: (a) The precipitate is extremely stable, and both N O and N B are vanishingly small within the precipitation zone. (b) As a consequence of (a), f BO is constant throughout the precipitation zone, and changes discontinuously to zero at the reaction front. (c) Precipitate nucleation and growth have no effect on overall reaction kinetics. (d) Mass transfer within the internal oxidation zone occurs solely via lattice (bulk) diffusion, is unaffected by the presence of precipitates and is not subject to cross-effects resulting from kinetic or thermodynamic interactions with other solutes.
6.5. Surface Diffusion Effects in the Precipitation Zone
267
We consider first the effect of precipitates, and microstructure in general, on oxidant diffusion, while retaining the assumptions of a highly stable precipitate, and a matrix which is strongly depleted in reactive solute B.
6.5. SURFACE DIFFUSION EFFECTS IN THE PRECIPITATION ZONE As seen in Figures 6.1 and 6.5, internal oxidation can be favoured at alloy grain boundaries. The situations in the two cases depicted are quite different. Although the precipitates formed on grain boundaries in Fe–Cr are larger, the penetration depth is the same as within the grains themselves, and the overall reaction kinetics are not affected. The austenitic alloy IN 617, however, has undergone rapid, preferential intergranular attack, forming a continuous internal oxide network along the grain boundaries. Preferential intergranular penetrations of internal oxide have been observed for Ni–Al [31–34] and Ni–Cr alloys [35, 36], to an extent which becomes more marked at lower temperatures and higher N ðoÞ B values. Intergranular morphologies of internal oxidation were reported earlier for Fe–Al [37], tin-based alloys [5] and copper-based alloys [4]. A related phenomenon is the in situ oxidation of prior interdendritic carbides in cast materials [38] shown in Figure 6.16. Intergranular oxidation can be much faster than the rate at which the intragranular precipitation front advances. The parabolic rate constant for intergranular oxidation in Ni–5Cr at 1,0001C is found [21] to be about 103 times the value of kðiÞ p . Similarly, the rate of in situ carbide oxidation in cast heatresisting steels (Figure 6.16) is observed [38, 39] to be much faster than intragranular precipitation. Clearly, these rapid rates cannot be sustained by volume (lattice) diffusion of oxygen, and a faster transport process must be involved. A model based on diffusion along the oxide–metal grain boundary is shown schematically in Figure 6.17 for the case of in situ carbide oxidation. A very similar situation arises when intragranular precipitates form with elongated plate or rod shapes, aligned in the growth direction (Figure 6.7). The example of elongated Al2O3 precipitate growth in dilute Ni–Al alloys has been studied intensively [21, 29, 40–46], leading to an understanding of the diffusion processes involved in the growth of these cellular morphologies. The kinetics of internal oxidation are parabolic, reflecting diffusion control, but the rate ðoÞ constant is independent of N Al . The behaviour of these alloys is compared with that of Ni–Cr in Figure 6.18. Clearly, the data for Ni–Cr alloys conform with Equation (6.11), but that for Ni–Al does not. If, nonetheless, effective oxygen permeability values are deduced from Equation (6.11), they are found [29] apparently to increase with aluminium levels ðoÞ N ðsÞ O DO ðeffÞ ¼ a þ b N Al
(6.35)
where a and b are constants. This is interpreted to mean that oxygen diffuses both through the metal matrix and along precipitate–matrix interfaces, the concentration of the latter being proportional to the original alloy aluminium content. On this basis, the effective flux of oxygen through a precipitation zone containing
268
Chapter 6 Oxidation of Alloys II: Internal Oxidation
Figure 6.16 Rapid penetration of internal oxide along prior carbide network in cast Fe–35Ni–27Cr alloy at T ¼ 1,0001C [39]. With kind permission from Springer Science and Business Media.
lath-shaped oxides oriented as shown in Figure 6.19 can be written as J eff ¼ J O AO þ J i Ai þ J OX AOX
(6.36)
where AO , Ai and AOX are the cross-sectional area fractions of alloy, alloy-oxide interface and oxide, normal to the diffusion direction. Because diffusion in Al2O3
269
6.5. Surface Diffusion Effects in the Precipitation Zone
Scale
Alloy
2 ro
Cr2O3
Cr23C6
2 rc
X
NO(s)
No (e)
NO
Figure 6.17 Schematic model for enhanced internal boundary oxidation of prior carbide in situ [38]. With kind permission from Springer Science and Business Media.
200 Ni-Al Ni-A 200
Depth (μm)
Depth (μm)
Ni-Cr
100
100
pack pack
0
0 1
2
3 4 wt % Cr (a)
5
1
2
3
4
wt % Al (b)
Figure 6.18 Extent of internal oxidation of Ni–Cr and Ni–Al alloys in Rhines packs for 20 h at 1,0001C [21]. Published with permission from Taylor & Francis Ltd., http://www.tandf.co.uk/ journals.
270
Chapter 6 Oxidation of Alloys II: Internal Oxidation
d W
XB
ξ Surface
Front of internal oxidation Allo Alloy
Figure 6.19 Schematic view of oriented Al2O3 laths in internal oxidation zone [21]. Published with permission from Taylor & Francis Ltd., http://www.tandf.co.uk/journals.
is so slow, the third term is set at zero. The effective oxygen diffusion coefficient is then defined as DO;eff ¼ DO;O AO þ DO;i Ai
(6.37)
where DO;O is the usual diffusion coefficient of oxygen in nickel and DO;i the interfacial coefficient. The area fractions and diffusion coefficients are assumed to be independent of position within the internal oxidation zone. The mole fraction of oxide, N BO , is related to the precipitate dimensions and their number density, FN. Using the dimensions w and d specified in Figure 6.19, and assuming that the precipitates are continuous across the full width of the internal oxidation zone, we write for small values of FN V All N BO ¼ FN wd (6.38) VOX and Ai ¼ 2ðw þ dÞFN di 2wFN di
(6.39)
where di is the width of the interface diffusion zone and the approximation is based on w d. The cross-section of matrix metal remaining after oxide precipitation is AO ¼ 1 Ai AOX ¼ 1 2wFN di FN wd
(6.40)
which, upon substitution along with Equations (6.38) and (6.39) into Equation (6.37) yields
DO;eff DO;i di 2 V OX 1 ¼1þ N BO (6.41) DO;O DO;O d VAll A similar result is obtained for rod-shaped precipitates [21, 29] and indeed will be found for any prismatic precipitate morphology. If no aluminium enrichment occurs, the amount of oxide corresponds to the original alloy concentration, N BO ¼ N ðoÞ Al , then the form of Equation (6.41) is seen to correspond with the experimental result (6.35). Comparison of experimentally determined values for b with the corresponding term in Equation (6.35) yields the results shown in Table 6.4.
271
6.5. Surface Diffusion Effects in the Precipitation Zone
Table 6.4
a
Interfacial and matrix oxygen diffusion in internally oxidized Ni–Al [21]a
T (1C)
DO,idi/DO,Od
DO,i/DO,O
1,100 1,000 900 800
39 85 85 173
3.9–39 102 8.5–85 102 8.5–85 102 1.7–17 103
DO,i/DO,O calculated for d ¼ 10–100 nm and di assumed to be 1 nm.
The ratios between interfacial and lattice diffusion coefficients of oxygen seem reasonable, and increase with decreasing temperature as would be expected. If the interfaces concerned are incoherent, as was assumed [21], then the chemical identity of the oxide will be of secondary importance, and a similar enhancement in oxygen diffusion can be anticipated for any oxide–austenite interface. The example of in situ oxidation of interdendritic chromium carbide (Figure 6.16) is now analysed on this basis. As is clear in the micrograph, oxygen penetration at the interdendritic locations was much faster than within the austenite grains, where only a shallow internal oxidation zone had formed. Oxidation of a rodshaped carbide is shown schematically in Figure 6.17. The chemical reaction 23 Cr23 C6 þ 69 2 O ¼ 2 Cr2 O3 þ 6 C
(6.42)
is accompanied by a volume expansion. If accumulation of chromium from the surrounding metal matrix can be ignored, the rod radii are related by rO ¼ krC where the subscripts denote oxide or carbide, and k is the ratio 11:5V OX k¼ VC
(6.43)
(6.44)
with V i the molar volume of the indicated substance. In the figure, N O denotes the local concentration of oxygen, and the zone of rapid inward interfacial diffusion is defined as an annular region, of width d, around the oxide rod. Boundary values of the oxygen concentration are set at the ðeÞ alloy–scale interface, N ðsÞ O , and by local carbide–oxide equilibrium, N O . The molar flux of oxygen, J O , per unit cross-sectional area of carbide rod is given by the linear approximation to Fick’s Law as JO ¼
ðsÞ ðeÞ dð2rO þ dÞ DO;i ðN O N O Þ VA XB r2C
(6.45)
where r is the rod radius, DB the boundary or interfacial diffusion coefficient, V A the alloy matrix molar volume and XB the boundary oxidation depth. If this oxygen is entirely consumed in reaction with the carbide rod, then the resulting oxide rod lengthens at a rate given by dXB J ¼ O VC dt 69=2
(6.46)
272
Chapter 6 Oxidation of Alloys II: Internal Oxidation
Combination of Equations (6.43)–(6.46) leads to ðsÞ ðeÞ dXB 2 dDO;i V OX N O N O ¼ 3 rC V A dt XB
(6.47)
for the case d rC . Integration of Equation (6.47) leads to X2B ¼ 2kðiÞ B t
(6.48)
where the parabolic rate constant for internal oxidation kðiÞ B ¼
2 dDO;i V OX ðsÞ ðN O N ðeÞ O Þ 3 rC V A
(6.49)
is independent of primary carbide volume fraction, but inversely proportional to carbide diameter. A similar conclusion is reached if other prismatic carbide shapes, such as uniform sheets, are chosen. Inward oxygen diffusion along phase boundaries according to Equation (6.49) explains the observation [38] that several heat-resisting alloys all had approximately the same internal oxide penetration rates, despite their considerable variations in composition. Comparing the interdendritic oxidation rate constant of Equation (6.49) with the normal bulk material value of Equation (6.10), we obtain kðiÞ B kðiÞ p
¼
N ðoÞ Cr V OX di DO;i rC V A DO;O
(6.50)
ðsÞ ðiÞ if N ðeÞ O N O . The value of kB measured for an austenitic Fe–35Ni–27Cr cast steel 11 2 1 18 at 1,0001C was 3 10 cm s compared with the value kðiÞ cm2 s1 p ¼ 6 10 expected for lattice diffusion under the same conditions. Substitution of these values in Equation (6.50) together with rC ¼ 2 mm and N ðoÞ Cr ¼ 0:29 leads to the estimate di DO;i =DO;O ¼ 800. This is similar to estimates of boundary diffusion along Al2O3–austenite interfaces (Table 6.4). As seen in Table 6.4, enhancement of oxygen diffusion at boundaries is of decreased importance at higher temperatures. Hindam and Whittle [42] showed that at 1,2001C, lath or rod-shaped precipitates (depending on N ðoÞ Al ) grew into dilute Ni–Al alloys according to parabolic kinetics, but at rates which were controlled by oxygen diffusion through the matrix. Thus it can be concluded that boundary diffusion of oxidant is not a necessary condition for the development of a cellular precipitation morphology. Because the elongated precipitate–matrix interfaces have the effect of accelerating internal attack at lower temperatures, the question of how to predict their formation is an important one to which we return in Section 6.8. Finally, it should be noted that the precipitates formed during internal oxidation of dilute chromium and aluminium alloys are in fact more complex than has been implied. In both cases a spinel phase, MCr2O4 or MAl2O4, is formed near the surface if the oxygen activity is high enough. The binary oxide, M2O3, forms in a second, deeper precipitation zone. The general question of multiple precipitation zones is discussed in Section 6.9. When the internally formed precipitates are small and disperse, their surfaces cannot provide any significant contribution to diffusion. However, their presence
6.6. Internal Precipitates of Low Stability
273
reduces the metal matrix cross-section available for diffusion, as stated in Equation (6.40). For this reason, it is common to rewrite Equation (6.10) as kðiÞ p ¼
DO N ðsÞ O nN ðoÞ B
(6.51)
where e is an empirical constant designed to take into account the diffusional blocking effect of the precipitates. The quantity e would be expected to be related to f BO , but no information is available on this point, possibly because precipitate fractions are often small, and 1.
6.6. INTERNAL PRECIPITATES OF LOW STABILITY The Wagner diffusion model assumes Ksp to be vanishingly small and both N O and N B extremely dilute within the precipitation zone, which is therefore essentially oxide embedded in pure solvent metal A. However, this is not a realistic description for many cases. Consider precipitation of chromium compounds within an alloy a Cr þna X ¼ Cra Xna
(6.52)
Ksp ¼ N aCr N na X
(6.53)
where X is a generic oxidant and Ksp the equilibrium solubility product. If Ksp is not extremely small, then the necessarily low values of N X mean that N Cr will not always be small, and the assumption of complete precipitation fails. Even for rather stable precipitates such as Cr2O3, this condition can be difficult to meet at low oxidant activities. Values for Ksp are calculated for Equation (6.52) using the free energies of compound formation and alloy dissolution Cr þ nX ¼ CrXn
(6.54)
Cr ¼ Cr
(6.55)
1 2X2
(6.56)
¼X
using tabulated values [47] for oxide and carbide formation, together with Rosenqvist’s data [48] for DGf ðCr2 NÞ. Measured carbon [28] and oxygen (Table 2.2) solubility data are available, but the situation for nitrogen is less clear. Although the expression DGN2 ðg FeÞ ¼ 5690 þ 118:6T þ 2RT ln N N J mol1
(6.57)
is available [47], it is recognized that no accurate data are available for Ni–N solutions. Following Savva et al. [49] in conjecturing a temperature insensitive solubility of 1 ppma, we find DGN2 ðNiÞ ¼ 292; 460 þ 2RT ln N N J mol1
(6.58)
274
Chapter 6 Oxidation of Alloys II: Internal Oxidation
These estimates together with partial molar free energies of solution of chromium in iron [47] lead to the precipitate stability data shown in Tables 6.5 and 6.6. The quantity N Cr;min in the tables is the minimum concentration (mole fraction) of chromium required in the matrix metal to stabilize the designated precipitate at the alloy surface where N X has its maximum value of N ðsÞ X . Clearly the assumption of complete precipitation is in considerable error for the chromium carbides and nitride. Even the rather stable oxide precipitates leaving a significant concentration of chromium in the alloy. The temperature effect is significant, both through the decreased oxide stability at higher temperature and the retrograde oxygen solubility. The calculated results of Table 6.6 correspond to greatly decreased extents of chromium precipitation at higher temperatures. This effect is apparent in the internal oxidation of Fe–Cr alloys (Figure 6.1), where the volume fraction of oxide decreases substantially at higher temperatures. It is recognized that the calculated N Cr;min values apply at the alloy surface. As depth within the precipitation zone increases, N O must decrease, and therefore the concentration of chromium in the matrix, N Cr , must increase, in order to stabilize the precipitate, according to Equation (6.53). The amount of oxide precipitated, N BO , must therefore be a function of position, decreasing from a maximum at the alloy surface to a minimum at the reaction front. In view of this, it is necessary to investigate the effect of incomplete precipitation on the practically important quantity: the rate at which the internal oxidation front advances. Qualitatively, the consequence is clear. A lower value of fBO reflects, in
Table 6.5
Chromium compound precipitate solubilities at 1,0001C in g-Fe Cr2O3
N ðsÞ X Ksp NCr,min
Table 6.6 T (1C)
Carbides (ac ¼ 1)
pO2 ¼ 8:7 1017 atm
pO2 ¼ 2:6 1020 atm
Cr7C3
3.5 106
6 108
0.066
25
1.4 10 6 105
1.4 10 0.02
25
3.8 10 0.03
Nitride
Cr23C6
Cr2N at pN2 ¼ 1 atm
1 103
0.066 15
3.6 10 0.14
27
3 105 0.17
Cr2O3 solubilities in g-Fe at low pO2 values (atm) 900
1,000
1,100
pO2 ðatmÞ
8.7 1017
2.6 1020
8.7 1017
2.6 1020
8.7 1017
2.6 1020
N ðsÞ O Ksp NCr,min
6.8 106
1.2 107
3.5 106
6 108
1.6 106
2.8 108
1.1 1027 2 106 8 104
1.4 1025 6 105 0.02
8.6 1024 1 103 0.62
6.6. Internal Precipitates of Low Stability
275
effect, a reduced availability of chromium, i.e. an effectively lower value of N BO in Equation (6.10), and hence larger values of kðiÞ p . The precipitate volume fraction varies with position, reflecting the changing values of N O and N Cr . Figure 6.20 shows schematic concentration profiles and a
M - Cr
M + Cr2N
NCr(0)
NN(s)
%N
(a)
Cr 2N
M %Cr (b)
Figure 6.20 Formation of low-stability Cr2N precipitates. (a) Concentration profiles and (b) diffusion path for DN DCr O.
276
Chapter 6 Oxidation of Alloys II: Internal Oxidation
diffusion path for the case of Cr2N precipitation. The equilibrium fraction of precipitate can be related to composition via the lever rule: N BO ¼
N ðoÞ B NB p NB NB
(6.59)
p
where N B and N B refer to local values in the precipitate and matrix, respectively, and negligible diffusion of B has been assumed. Defining a precipitate fraction r, normalized to its value at the alloy surface r¼
N ðoÞ B NB ðsÞ N ðoÞ B NB
(6.60)
and recognizing that the local equilibrium is described by combining Equations (6.53) and (6.60), we obtain NB ¼ 1 ar (6.61) N ðoÞ B with the solubility parameter a¼1
K1=a sp ðsÞ 1=v N ðoÞ B ðN X Þ
(6.62)
For Wagner’s Equation (6.10) to apply, precipitation must be uniform and complete, i.e. r ! 1 and N B ! 0. From Equation (6.61) it is seen that this requires ðsÞ an a a ! 1, a condition met when Ksp ðN ðoÞ B Þ ðN X Þ , but which will not be met for chromium carbide or nitride. The diffusional kinetics of this situation were analysed by Kirkaldy [50] and independently by Ohriner and Morral [51], and have been applied to the specific case of Cr2 N in Fe–Cr [52]. Assuming still that metal diffusion is unimportant and that KSPN 3N , one obtains
@r 4Ksp DN @ 1 @r ¼ (6.63) 3 @x @t ð1 arÞ2 @t ðN ðoÞ Cr Þ This equation can pffiffibe converted via the Boltzmann transformation (Section 2.7), l ¼ x= t, to an ordinary differential equation which upon integration yields Z 0 N ðoÞ ð1 aÞ2 dx r Cr ¼ x dr (6.64) dr o ð1 arÞ2 8DN tN ðsÞ N where r0 is the value in the interval [0, 1] chosen for evaluation. The variation in Cr2N volume fraction f n , with depth in an internally nitrided alloy is shown in Figure 6.21. The value of f n decreases approximately linearly with depth, and is everywhere much lower than the stoichiometric equivalent of N ðoÞ Cr . Also shown in the figure is the value of f n calculated from TEM-EDAX measurements of N Cr as a function of depth in the matrix of the internal nitridation zone. This calculation is based on the assumption that chromium diffusion is negligible, and the difference ðN ðoÞ Cr N Cr Þ is therefore equivalent to
6.6. Internal Precipitates of Low Stability
277
Figure 6.21 Nitride volume fractions in internally nitrided Fe–20Ni–25Cr at 1,0001C compared with stoichiometric equivalent of NðoÞ Cr , and as calculated from mass balance assuming no Cr diffusion.
the amount of nitride precipitated. Agreement is seen to be excellent, confirming that chromium diffusion can be neglected. Application of Equation (6.64) requires knowledge of several parameters. Unfortunately, the assumption of ideal solution behaviour, i.e. N ðsÞ N afðN Cr Þ is incorrect, as is discussed in Section 6.10. For the moment, however, it is 10 sufficient to use the effective permeability N ðsÞ cm2 s1 at N DN ¼ 8:8 10 1,0001C and pN2 ¼ 0:9 atm, as deduced from internal nitridation kinetics [53]. Solution of Equation (6.64) using this permeability value and the measured r ¼ rðxÞ in Figure 6.21 yields a ¼ 0.82. The corresponding value of Ksp ðCr2 NÞ is then calculated from Equation (6.62) using the nitrogen solubility N ðsÞ N . If the effect of residual chromium on nitrogen solubility is ignored, then a value of Ksp ¼ 6 107 results. The values calculated thermodynamically from the method of Equations (6.54)–(6.56) are 3 105 in g Fe and 2 108 in nickel. The agreement between the value deduced from the precipitate distribution in Equation (6.64) and the expected range for thermodynamic equilibrium is good. The semi-quantitative success of the diffusion model implies that local equilibrium in the metal matrix (as expressed by Equation (6.53)) is maintained by steady-state diffusion of dissolved nitrogen, and the local extent of precipitation is therefore controlled by the precipitate–matrix equilibrium (Equation (6.60) and Figure 6.20). In short, the precipitate distribution is controlled by the diffusion path, i.e. the diffusion coefficients and the phase diagram, and not by nucleation phenomena. The extent to which internal nitrogen penetration exceeds the predictions of Equation (6.11) depends on the deviation of r from the ideal value of 1, i.e. on a. Ohriner and Morral [51] have calculated that for a ¼ 0.8 the quantity X=t1=2 exceeds the model prediction by a factor of approximately 1.7. This corresponds
278
Chapter 6 Oxidation of Alloys II: Internal Oxidation
to an increase in kp by a factor of about 3. Experimentally measured [53] values of kp are in fact up to 5 times faster than predicted from Equation (6.11). The additional acceleration is due to higher N ðsÞ N values enhanced by a thermodynamic interaction with solute chromium. As we have seen, the Kirkaldy/Morral theory succeeds in describing the distribution of low-stability precipitates. To gain an understanding of why precipitate sizes and number densities vary with position within the internal oxidation zone, it is necessary to examine the process of precipitate nucleation and growth.
6.7. PRECIPITATE NUCLEATION AND GROWTH It has been assumed so far that the internal oxidation front corresponds to the position where the equilibrium (6.2) is just satisfied. However, new precipitates cannot form if Equation (6.3) is precisely obeyed. To nucleate a new precipitate, an excess of oxidant is required 1=n Ksp NO4 (6.65) NB to drive the nucleation event. The need for this supersaturation was recognized by Wagner [54], but it was not incorporated into his description. The need for supersaturation can be understood from a consideration of the energetics of oxide nucleus formation. For simplicity, we consider first the formation of a spherical nucleus within a homogeneous, isotropic alloy matrix and assume for the moment that the molar volume of B is the same in both oxide and alloy. The overall free energy change is DG ¼ VDGV þ Ag
(6.66)
where V is the volume of the precipitate, DGV the free energy per unit volume accompanying the chemical reaction (6.2), A the precipitate surface area and g the precipitate–matrix interfacial tension. For a spherical precipitate of radius r DG ¼ 43pr3 DGV þ 4pr2 g
(6.67)
which is represented schematically in Figure 6.22. At small values of r, the second term is more important than the first, but at larger values the reverse is true. The shape of the curve in Figure 6.22 reflects a negative value for DGV and a positive one for g. As is seen, for rorn, a nucleus will spontaneously decay, whereas for r4rn , free energy is reduced by precipitate growth. For this reason, rn is known as the critical nucleus size, and sufficient supersaturation must be present to provide DGV large enough to overcome the surface energy barrier, DGn , to nucleus formation. The assumptions underlying Equation (6.67) are unrealistic. Recognizing that precipitates may not be spherical, that their volume will generally be larger than that of the metal they replace and that nucleation sites are usually local defects
6.7. Precipitate Nucleation and Growth
279
ΔG
ΔG ∗ r r∗ ΔGr
Figure 6.22 Free energy of spherical nucleus formation according to Equation (6.67).
we write instead DG ¼ VðDGV þ DGS Þ þ
X
Ai gi DGd
(6.68)
i
Where DGS is the strain energy resulting from the volume change, Ai and gi the areas and surface tensions of the precipitate-matrix interfaces and DGd the energy associated with defect site annihilation. At equilibrium, DGV just balances the strain and surface energy barriers to nucleation. In the case of spherical precipitates, Equation (6.68) can be rewritten as DG ¼ 43pr3 ðDGV þ DGS Þ þ 4pr2 g DGd n
(6.69)
n
The critical values r and DG are found by differentiating Equation (6.69) to locate the maximum in the curve 2g (6.70) rn ¼ ðDGV DGS Þ DGn ¼
16pg3 DGd 3ðDGV DGS Þ
(6.71)
where, for clarity, the fact that DGV is of opposite sign to both DGS and g has been explicitly recognized. Thus the more stable the precipitate, the lower the barrier to nucleation. The nature of the defect at which nucleation occurs is important, as the magnitude of DGd can vary considerably. In order of increasing DGd , i.e. decreasing DGn , the sequence would be approximately: homogeneous sites, vacancies, dislocations, stacking faults, grain and interphase boundaries and free surfaces. This is evident in the frequently observed preferential precipitation of internal oxides at alloy grain boundaries, e.g. Figures 6.1 and 6.5.
280
Chapter 6 Oxidation of Alloys II: Internal Oxidation
Figure 6.23 Schematic concentration profiles for internal precipitation of BOn showing a supersaturated region ahead of the internal oxidation zone.
The effects of the supersaturation requirement on precipitate size distributions and penetration kinetics were examined by Kahlweit et al. [16, 55, 56], and their treatment has since been extended by Gesmundo et al. [57]. The diffusion model is shown schematically in Figure 6.23. A key difference between this description and that used by Wagner (Figure 6.9) is that the precipitation front is not precisely defined, but instead is spread over a small region wherein N O and N B change with time as particles nucleate and grow. This can be appreciated from a consideration of mass transfer in the region of a newly formed precipitate (Figure 6.24). For the precipitate to develop, both O and B must be delivered to its surface. In the usual case of N BðoÞ DB N ðsÞ O DO , precipitate growth is limited by the availability of the metal, which becomes depleted ahead of the precipitate. A point is reached at which the oxide particle can grow no further and the inwardly diffusing oxygen sweeps past it, deeper into the alloy. To form the next precipitate, sufficient supersaturation must be achieved to overcome the nucleation barrier. At the position, X, where this is achieved, the reactant concentrations are denoted as N nO and N nB , and N nB ðN nO Þn ¼ Sn 4Ksp
(6.72)
In contrast, the last-formed precipitate relieved the local supersaturation when it nucleated, and at that location, X0 , N 0B ðN 0O Þn ¼ Ksp
(6.73) 0
a relationship which is observed throughout the region 0 x X , i.e. most of the internal oxidation zone. For parabolic internal oxidation kinetics, the diffusion equation solutions [16] for the reactant concentrations are n pffiffiffiffiffiffiffiffiffi N ðsÞ O NO erf x=2 DO t N O ¼ N ðsÞ for xoXn (6.74) O erfðgÞ
281
6.7. Precipitate Nucleation and Growth
Figure 6.24 Mass transfer near a growing precipitate at the internal oxidation front: continuous concentration profiles at time of nucleation, dotted profiles after precipitate growth.
and N B ¼ N ðoÞ B
n N ðoÞ B NB
1=2
erfcðgf
Þ
pffiffiffiffiffiffiffiffi erfc x=2 DB t
for
x4Xn
(6.75)
with g and f as defined in Equations (6.19) and (6.20), respectively. In general [57], n N ðsÞ O NO n N ðoÞ B NB
¼n
GðgÞ Fðgf1=2 Þ
þ
N nB N 0B 0 N ðoÞ B NB
GðgÞ
(6.76)
where GðuÞ ¼ p1=2 u expðu2 ÞerfðuÞ
(6.77)
and FðuÞ ¼ p1=2 u expðu2 ÞerfcðuÞ 1=2
2
(6.78) n
with u ¼ gf . Under the limiting conditions g 1 and N O Gðg2 Þ 2g2 , and then kðiÞ p ¼
DO N ðsÞ O 0 nðN ðoÞ B NBÞ
N ðsÞ O,
then
(6.79)
replaces Equation (6.11), as found by Kahlweit et al. [16, 56]. Thus the penetration rate is greater than predicted by Wagner’s model, to the extent necessary to reach a higher solute metal concentration N 0B , where sufficient supersaturation for precipitate nucleation can be achieved.
282
Chapter 6 Oxidation of Alloys II: Internal Oxidation
The distance DX ¼ Xni X0i
(6.80)
represents the spacing between successive nucleation events, and is therefore representative of the local precipitate number density, f N 3 1 Xi 1 fN ¼ 3 (6.81) 3 DX Xi ðDXÞ Kahlweit et al. [16, 56] derived the relationship ðoÞ ðoÞ DX N nO N B N 0B N 0O N nO N oB N 0B nðN B N 0B ÞðN nB N 0B Þ ¼ ðsÞ ¼ ¼ ðoÞ n X nN nB N nB N 0B fN ðsÞ NO N ðsÞ O O ðN B N B Þ
(6.82)
ðsÞ , from which it follows that for DO ; DB and N nO ðBnB Þn independent of X and N O ðsÞ ðsÞ then ðN O DX=Xi Þ is also independent of Xi and N O . Equation (6.81) can therefore be rewritten as
fN ¼
3 kðN ðsÞ OÞ X3i
(6.83)
n n n where the constant k is a function of DO =DB ; N ðoÞ B ; K sp and N O ðN B Þ . The last is unknown, but assumed to be constant. It is then predicted from Equation (6.83) 3 that under fixed reaction conditions, f N is proportional to ðN ðsÞ O Þ , i.e.
3=2
f N ðXi Þ ¼ constant pO2
(6.84)
If, furthermore, Ksp is very small, solute enrichment is negligible ða 1Þ and the precipitates are spherical, their radius, r, is given by 4pr3 ¼ VOX N ðoÞ B 3 which upon substitution from Equation (6.83) yields !1=3 V OX N ðoÞ Xi B r¼ 4pk N ðsÞ fN
(6.85)
(6.86)
O
Bo¨hm and Kahlweit [16] tested these predictions using internal oxidation of a dilute Ag–Cd alloy at 8501C and confirmed that f N ðCdOÞ decreased with X3i and 3 increased with ðN ðsÞ O Þ . However, the assumption that K sp is very small and hence f BO afðxÞ is frequently incorrect. The predictions of Equations (6.83) and (6.86) will not be obeyed in such cases. An example of this situation is shown in Figure 6.25, where fBO decreases sharply with increasing depth. Particle size also increases with depth, but not in accord with Equation (6.86). Numerical evaluations by Gesmundo et al. [57] have shown that kðiÞ p is quite sensitive to the critical degree of supersaturation required for nucleation when Ksp is large. However, in the case of low Ksp values considered by Wagner, the predicted values of kðiÞ p are essentially unaffected. Rhines [4] pointed out that the more stable the oxide, the easier is nucleation (see Equation (6.71)) and the greater the number of precipitates which result.
283
6.7. Precipitate Nucleation and Growth
0.16 Fe-5%Cr
Oxide-Volume Fraction
Fe-7.5%Cr Fe-10%Cr
0.12
0.08
0.04
0 0
10
20
30
40
50
Depth (μm)
(a)
(b) Figure 6.25 Internal oxide. (a) Volume fraction and (b) particle radius in Fe–5Cr at 1,0001C [10]. Published with permission from The Electrochemical Society.
While this may be correct for very dilute alloys, where metal diffusion is slow, it is clearly not a useful generalization in the cases shown in Figures 6.4 and 6.7. These cellular growth morphologies are found for both a low Ksp precipitate, alumina, and high Ksp compounds, carbides and nitrides. Indeed, the Kahlweit theory of repeated supersaturation and new precipitate nucleation is clearly inapplicable to these cases where the growth of existing needle or platelet-shaped
284
Chapter 6 Oxidation of Alloys II: Internal Oxidation
precipitates is the dominant process, and nucleation is no longer important. As already noted, these morphologies can lead to faster alloy penetration by facilitating oxidant diffusion. The reasons for their development are therefore of interest.
6.8. CELLULAR PRECIPITATION MORPHOLOGIES The application of classical nucleation theory to internal oxidation developed by Kahlweit et al. [16, 55, 56] assumes that the extent of precipitate growth is limited by the local supply of reacting solute metal. Since this is usually a relatively slow process, it would seem to be a relatively good assumption. Nonetheless, the growth of rods or laths of Al2O3, Cr2N and Cr23C6 has been found to continue across virtually the complete internal precipitation zone. Other examples of these morphologies include MoS2 precipitates in internally sulfidized Ni–Mo alloys [58], Al2O3 in ferritic iron [13], In2O3 in Ag–In alloys [59], TiO2 in Co–Ti alloys [60], Cr2N in binary Ni–Cr alloys [61] and various commercial heat-resisting alloys [62, 63] and Cr23C6 in a variety of ferritic and austenitic alloys [10, 23, 64–66]. The example of Cr2N lamellar precipitate growth in austenite is now investigated. A low-magnification image of an internal nitridation zone is shown in Figure 6.4, and a high-magnification image of the precipitation front in Figure 6.26 reveals that a grain boundary had developed at the reaction front. Analysis by selected area diffraction (SAD) showed that the precipitates were Cr2N and the matrix austenite. Their orientation relationship (Figure 6.26b) was found to be
½112 :ð0002Þ
ð111Þ ½1210
(6.87) Cr2 N
g
Cr2 N
g
The same orientation relationship was found throughout the precipitation zone, and at all reaction times. The parallel orientations of the Cr2N lamellae are clear in the dark field images of Figure 6.27. The parent austenite grain ahead of the precipitation front and the product austenite grain behind the front are of different orientations. Neither the Cr2N nor the reacted austenite grain has rational orientation relationships with the parent grain. Chemical microanalysis performed by energy dispersive spectrometry in the TEM yielded results for the reaction front. A scan across the unreacted–reacted austenite grain boundary (Figure 6.28) shows a small step function decrease in N Cr at the boundary. A scan in the orthogonal direction, parallel to the reaction front, reveals a completely flat profile between precipitates. The morphology, structure and compositional variations observed at the nitridation front are characteristic of the cellular ‘‘discontinuous precipitation’’ reaction. Such a reaction is characterized by lamellar or rod-shaped precipitates growing with an orientation relationship to their matrix, a high angle boundary at the precipitate growth front where the unreacted alloy and reacted matrix are the same phase but are differently oriented, and a step function or ‘‘discontinuous’’ change in composition at the precipitation front [67]. In a closed system,
6.8. Cellular Precipitation Morphologies
285
Figure 6.26 Internal nitridation reaction front in Fe–20Ni–25Cr at 1,0001C. (a) Bright field TEM and (b) SAD pattern near precipitation front: large, bright spots show [112] zone axis of austenite, small spots show ½1120 zone axis of Cr2N.
it would be written as g ¼ gD þ P
(6.88)
with g indicating the parent austenite, gD the chromium-depleted matrix and P the precipitate. For the internal nitridation reaction we write g þ N ¼ gD þ Cr2 N
(6.89)
and show the mass transport processes schematically in Figure 6.29. Nitrogen is transported from the alloy surface to the discontinuous precipitation front by a mixture of lattice diffusion through the matrix phases and diffusion along the interfaces between the lamellae and matrix. The g=gD high angle boundary provides a mechanism for rapid lateral transport of chromium, allowing it to segregate to the advancing Cr2N lamellae tips, and for the rejection of iron and nickel from the nitride. In this situation, the rate of precipitate penetration into the alloy is controlled by the nitrogen diffusion rate, but the spacing of the precipitate lamellae is controlled by chromium diffusion at the precipitation front. If the latter process is
286
Chapter 6 Oxidation of Alloys II: Internal Oxidation
Figure 6.27 Dark field images of Cr2N precipitates 5 mm below the alloy surface and at the precipitation front (Xi ¼ 60 mm) in Fe–20Ni–25Cr after 90 min nitridation at 1,0001C.
one of grain boundary diffusion, then [68, 69] dXi kDCr;i ¼ dt S2
(6.90)
where k is a constant, DCr;i the diffusion coefficient at the g=gD boundary and S the cellular dimension defined in Figure 6.29. Equation (6.90) reflects the fact that the rate at which the precipitates advance must balance the rate at which chromium is delivered to their tips ð DCr;i =SÞ together with the requirement that the total precipitate–matrix surface area created (which is proportional to 1/S) is minimized. Precipitate lamellae spacings developed during internal nitridation of austenite are shown in Figure 6.30. The spacing at a given depth remains constant with time, and the spacing at the moving reaction front increases with depth. Calculating the reaction front speed from dXi =dt ¼ kðiÞ p =X i and the measured [70] value of kpðiÞ , the spacing data of Figure 6.30 is plotted according to Equation (6.90) in Figure 6.31. Agreement with the discontinuous precipitation theory is seen to be good.
6.8. Cellular Precipitation Morphologies
287
Figure 6.28 EDS analysis across the unreacted–reacted austenite grain boundary at the internal nitridation front of Figure 6.26. Gas
γ D+Cr2N
γ
S
JCr
JN
x= 0
x=Xi
Figure 6.29 Mass transport processes involved in discontinuous precipitation of Cr2N during internal nitridation of austenite.
There remain the questions as to why and how the discontinuous precipitation morphology is adopted by the reacting system. Two key factors are involved: the existence of a precipitate–matrix orientation relationship which can reduce surface energy, and the low stability of Cr2N with the consequently small driving force for precipitate nucleation at low N ðsÞ N levels.
288
Chapter 6 Oxidation of Alloys II: Internal Oxidation
3
precipitate spacing, µm
2.5 2 1.5
22.5 min 40 min 90 min
1 0.5 0 0
10
20
30 depth, µm
40
50
60
Figure 6.30 Variation of nitride spacing with position within precipitation zone at different reaction times for Fe–25Cr–20Ni at 1,0001C.
Figure 6.31 Test of discontinuous precipitation Equation (6.90) for internal nitridation of Fe–25Cr–Ni at 1,0001C.
The precipitates are constrained in their growth direction by the availability of chromium and nitrogen. The average direction normal to the alloy surface minimizes the nitrogen diffusion distance to where immobile chromium remains as yet unreacted. Thus a lamellar morphology is kinetically favourable, but creates a large internal surface area. The Cr2N–austenite system is able to reduce the surface energy by adopting a largely coherent precipitate–matrix orientation relationship. However, to accommodate both the preferred precipitate growth direction and the energetically favourable orientation relationship, the austenite matrix needs to adopt the appropriate orientation, which will in general be different from that of the parent grain. For this reason, the austenite undergoes reorientation at the reaction front, a process facilitated by the diffusion occurring along this high angle boundary.
6.8. Cellular Precipitation Morphologies
289
Clearly the cellular precipitation process is self-sustaining. However, it is of enduring stability only because new precipitates do not nucleate ahead of the reaction front. The primary reason for this is the low stability of Cr2N and its high solubility product (Table 6.5). The free energy barrier to nucleation (6.71) is consequently high, and the nitrogen supersaturation necessary to overcome it is not achievable when growth of the existing lamellae is supported by accelerated chromium diffusion to their tips. A similar situation arises during lamellar Cr23C6 growth, as discussed in Chapter 9. However, the formation of alumina rod and lath-shaped precipitates is apparently different. As seen in Figure 6.7, and even more clearly in Figure 6.32, the precipitates extend across the width of the internal oxidation zone. However, no grain boundary develops in the metal phase at the reaction front, no orientation relationship is established between the Al2O3 and the metal and it must be concluded that the discontinuous precipitation mechanism is not in effect. The reasons for the formation of elongated Al2O3 precipitates have not been clearly established, although it is reasonable to speculate [60] that rapid diffusion of precipitating metal to the growing particles prevents nucleation of
Figure 6.32 Rod-shaped oxide precipitates formed during internal oxidation of Ni–4Al [42], as revealed by SEM examination of deep etched samples. With kind permission from Springer Science and Business Media.
290
Chapter 6 Oxidation of Alloys II: Internal Oxidation
new ones. In that case, it would be expected that varying temperature and pO2 so as to alter DO =DAl would affect the precipitate morphology. This question appears not to have been adequately investigated.
6.9. MULTIPLE INTERNAL PRECIPITATES We consider first the case where the solute metal forms two different precipitates corresponding to different oxidation states. The example of internal carburization forming zones of Cr7C3 and Cr23C6 precipitates is illustrated in Figure 6.6. Another common example is the formation of a spinel phase together with either Cr2O3 or Al2O3. In all such cases, the existence of different precipitate zones is a consequence of the gradient in oxidant potential between its maximum at the alloy surface and minimum in the alloy interior. A diffusion path for the internal oxidation of an Ni–Al alloy is shown in Figure 6.33, drawn on the basis that DO DAl . The two reaction fronts within the internal precipitation zone correspond to the reactions 2 Al þ3 O ¼ Al2 O3
(6.91)
Al2 O3 þ Ni þ O ¼ NiAl2 O4
(6.92)
In the aluminium alloy case, precipitate growth predominates over nucleation, and the amount of oxygen supersaturation required at each interface is presumably small. The general situation of two precipitate zones was described by Meijering [11] on the assumptions that B is immobile, both precipitates have very low Ksp values and that the interface between the two zones is sharp, i.e. reaction (6.92) or its equivalent instantaneously achieve equilibrium. The diffusion model is shown schematically in Figure 6.34. The intermediate reaction front where BOn1 is further oxidized to BOn2 is located at x ¼ XI . The oxidant concentration at this point is denoted by N IO. Using the linear concentration gradient approximation in Fick’s law (as in Equation (6.7)) and utilizing the mass balances at the two reaction fronts (as in Equation (6.8)), Meijering wrote DO N IO dXi ¼ n1 N ðoÞ B Xi XI dt
(6.93)
I DO ðN ðsÞ dXi dXI O NOÞ þ ðn2 n1 ÞN oB ¼ n1 N ðoÞ B dt dt XI
(6.94)
and
It is seen that both zones widen according to parabolic kinetics. The analysis leads to the expression for total penetration X2i ¼
2DO N ðsÞ O t neff N B
(6.95)
6.9. Multiple Internal Precipitates
291
Figure 6.33 Diffusion path for internal oxidation of dilute Ni–Al at 1,0001C [42]. With kind permission from Springer Science and Business Media.
which is seen to be equivalent to Equations (6.1) and (6.11). The effective stoichiometric coefficient is given by " !# n1 ð1 þ 4mð1 mÞðn2 n1 Þ=n1 Þ1=2 1 1 neff ¼ (6.96) 2mðn2 n1 Þ=n1 m where m ¼ N IO =N ðsÞ O . While this analysis can in principle predict the ratio X I =X i , this requires a knowledge of N IO , which is indeterminate within the formalism. The practical utility of Equation (6.95) lies in its application when XI =Xi ; n1 and n2 are all known, and penetration kinetics are used to deduce the permeability N ðsÞ O DO .
292
Chapter 6 Oxidation of Alloys II: Internal Oxidation
NB
N0(s) N0
X1
Xi
Figure 6.34 Reactant concentration profiles when two precipitate zones form from a single oxidant and one solute metal.
NC(0)
NB(0)
(s)
N0
N0
Figure 6.35 Simultaneous internal oxidation of two solute metals in ternary alloy.
A somewhat similar situation can arise in the internal oxidation of ternary alloys, if two components are reactive as shown schematically in Figure 6.35. Studies of this sort date back to the pioneering work of Rhines [4] on copper alloys containing tin or zinc as well as one of the metals: aluminium, beryllium or silicon. He produced two internal oxidation zones, with the inner one containing the more stable oxide. Figure 6.8 illustrates the example of simultaneous internal oxidation of chromium and aluminium in a nickel-based alloy. A more sophisticated treatment of the simultaneous internal oxidation of two solute metals has been provided by Niu and Gesmundo [71]. However, it too fails to provide a prediction of where the reaction front for the less stable precipitate will be located. As a result, the theory cannot predict the degree of enrichment in
6.9. Multiple Internal Precipitates
293
the near-surface zone, because this is supported by diffusion of the less reactive solute metal through the inner precipitation zone. The theory was applied with qualitative success to the internal oxidation of aluminium and silicon in Ni–Si–Al, using the approximation that the intermediate SiO2 precipitation front coincided with that of Al2O3, thereby removing the uncertainty. However, Yi et al. [72] showed clearly that Al2O3 was precipitated at greater depth than SiO2. Another example of multiple internal precipitation zones arises when a dilute alloy is simultaneously attacked by two or more different oxidants. This situation also was first analysed by Meijering [11], and is shown schematically in Figure 6.36. The oxidant forming the less stable precipitate under reaction
NB N2(S)
N1(S) N2 N1
X1
X2
(a)
X1 X2
Ln ac
BC
Surface
BO B
Ln a0 (b)
Figure 6.36 (a) Concentration profiles for simultaneous internal attack on alloy AB by two oxidants, assuming essentially immobile B. (b) Corresponding diffusion path for the oxidizing–carburizing case.
294
Chapter 6 Oxidation of Alloys II: Internal Oxidation
conditions will be found in the deeper reaction zone, if it is formed. The reason for this is that the more stable precipitate forms at or near the surface if the reaction, for example, BN þ 12O2 ¼ BO þ 12N2
(6.97)
is favoured by the gas composition. Beneath the surface, N O decreases with depth, until reaching a low value at the oxide precipitation front. If diffusion of nitrogen through the near-surface oxide precipitation zone is rapid, then N N does not decrease very much, and a position is reached where N N =N O exceeds the value necessary for the reaction BO þ N ¼ BN þ O
(6.98)
where nitride precipitation commences. The Meijering analysis assumes (a) neither precipitate significantly affects the inward oxidant diffusion rates; (b) the less stable precipitate is converted to the more stable one via a displacement reaction involving dissolved oxidant (1); (c) the displacement reaction goes rapidly to completion at precisely defined oxidant activity values, i.e. no intersolubility exists between the two precipitate compounds; (d) no thermodynamic or kinetic interaction of importance takes place in the solution phase and (e) precipitates are extremely stable, and N B ffi 0 throughout the two precipitate zones. Under these conditions, the two zones grow each according to parabolic kinetics. Meijering further assumed that the alloy solute B is essentially immobile, and no solute enrichment occurs in the precipitation zone. The approximate Meijering treatment leads to the results X21 ¼ 2
X22
¼2
D1 N 1ðsÞ n1 N ðoÞ B
D1 N ðsÞ 1 n1 N ðoÞ B
þ
t
D2 N ðsÞ 2 n2 N ðoÞ B
(6.99) ! t
(6.100)
These simple forms result from the way in which the intermediate precipitation front at X1 is treated. The Meijering treatment assumes that the oxidant (2) released at this position by the displacement reaction, which is the reverse of reaction (6.98), all diffuses inward to extend the inner precipitation zone. Thus if an alloy was first reacted to internally precipitate the less stable compound, e.g. BN, and then exposed to oxygen alone, the advancing oxidation front would displace the internally nitrided zone inwards, but the thickness of the nitride zone would remain constant. In essence, therefore, the innermost precipitation zone is predicted to widen at the same rate, whether or not another precipitation zone develops near the surface.
6.9. Multiple Internal Precipitates
295
The formation of two separate precipitation zones in sequence according to thermodynamic stability has been verified [73, 74], but kinetic data have become available only recently. When heat-resisting alloys were exposed [75] to twocomponent (CO/CO2) or three-component (CO/CO2/SO2) gases, they developed discrete internal precipitation zones which each grew according to parabolic kinetics, as shown in Figure 6.37. However, the assumption of a single precipitate species in each zone, while appropriate for binary alloys, was found to be inapplicable to these multicomponent materials. The observation of chromiumrich oxide and sulfide precipitates in the same zone was common. The sulfide also contained iron. Approximating this compound as a thiospinel, one can write FeCr2 S4 þ 3 O ¼ Fe þCr2 O3 þ 4 S
(6.101)
for precipitate co-existence. Since the iron activity, aFe , can vary within the matrix of a multicomponent alloy, as and ao are independent, and the two-precipitate zone can be both thermodynamically and kinetically stable. Unfortunately, the experiments behind the data of Figure 6.37 also produced external scales, boundary conditions were uncertain and further analysis is not possible. Gesmundo and Niu [76] have relaxed the requirement that DB O, and have avoided other approximations in the Meijering treatment. However, they retained the assumption that Ksp in both precipitate zones is very small, and consequently N B O. Enrichment of precipitated element B in the internal reaction zones was found to affect the rates at which the oxidants penetrated deeper into the alloy. However, predictions made for the simultaneous internal carburization and oxidation of Ni–3.9Cr in CO/CO2 at 8211C were in poor agreement with the experimental data of Copson et al. [77, 78]. While the basic ðsÞ data used in the calculation ðN ðsÞ O ; DO ; N C ; DC ; DCr Þ were of high quality, it had
Figure 6.37 Internal precipitation zone growth kinetics for 310 stainless steel exposed to CO–CO2–SO2–N2 at 1,0001C [75]. With kind permission from Springer Science and Business Media.
296
Chapter 6 Oxidation of Alloys II: Internal Oxidation
been measured at high temperatures. Extrapolation to low temperatures, such as the 8211C used by Hopkinson and Copson, is always somewhat questionable for diffusion coefficients in view of the increasing importance of boundary and dislocation mechanisms. The simultaneous carburization and oxidation of chromium-bearing alloys is an important technical problem, leading to a form of failure known as ‘‘green rot’’ [79]. The name comes from the green colouration of fracture surfaces in the embrittled material resulting from this form of internal attack. The general reaction morphology is shown in Figure 6.38 for a Type 304 stainless steel (Fe–18Cr–8Ni base) exposed at 7001C to a CO/CO2 mixture corresponding to pO2 ¼ 1023 atm and a supersaturated carbon activity of 7. An external scale formed, but was repeatedly disrupted and spalled by regular temperature cycling. As seen in the micrograph, two internal precipitation zones were formed: oxides beneath the surface and carbides at greater depths. The oxide zone actually consisted of two regions: spinel nearest the surface, and Cr2O3 further in. The practical effect of the carburization is profound. In the absence of carbon, this alloy would form an external oxide scale rather than undergoing internal oxidation (see Section 6.11). Because carbon permeability in the alloy is so high 11 ðDC N ðsÞ cm2 s1 at 7001C) internal carburization is rapid, removing C 6 10 much of the chromium from solution. The precipitated chromium is immobilized, and is therefore unavailable to form an external oxide scale. Instead, the carbides are oxidized in situ, just as proposed by Meijering. Only in this way could the enormous oxide volume fractions seen in Figure 6.38 be formed internally. The Cr2O3 is responsible for the green colour and the expressive term, green rot.
Figure 6.38 Internal carburization and oxidation of a 304 stainless steel exposed to CO–CO2–Ar at 7001C. Reprinted from Ref. [80] with permission from Elsevier.
6.9. Multiple Internal Precipitates
297
The carburization front was found to have penetrated 520 mm in 396 h at 7001C, corresponding to ! ðsÞ DO N ðsÞ D N C O C ¼ 1:9 109 cm2 s1 2 þ ðoÞ 1:5N ðoÞ 0:344N Cr Cr according to Equation (6.100). Permeability data are not available for such a low temperature, so high-temperature data are extrapolated, yielding ðoÞ ðoÞ 18 10 DO N ðsÞ cm2 s1 and DC N ðsÞ cm2 s1 . O =1:5N Cr ¼ 2 10 C =0:344N Cr ¼ 9 10 Clearly the oxygen permeability data are not applicable to the observed internal oxidation rates, but the carbon permeability are roughly in accord with the experimental carburization depth. Alloys containing two or more reactive solute metals exposed to mixed oxidant gases can form very complex internal precipitation zones. Oxidation in air under thermal cyclic conditions (which remove scale and allow internal attack) leads to internal formation of nitrides and oxides of both aluminium and chromium [81] in Ni–Al–Cr alloys (Figure 6.39). As expected, the nitrides are located deeper within the reaction zone, reflecting their lower stability and the high nitrogen permeability. The sequence of chromium and aluminium nitrides is, however, unexpected. It can be understood in terms of thermodynamic interactions within the matrix phase, as is discussed in Section 6.10.
Figure 6.39 1,1001C.
Simultaneous internal nitridation and oxidation of Ni–Cr–Al exposed to air at
298
Chapter 6 Oxidation of Alloys II: Internal Oxidation
10 Internal penetration rates are rapid, in the range kðiÞ cm2 s1 p ¼ 1:5 5:1 10 at 1,1001C for a range of alloy compositions. The applicability of Equation (6.100) was tested using oxygen and nitrogen permeability data. For N Al ¼ 0:2, ðoÞ ðoÞ 10 10 N ðsÞ cm2 s1 and N ðsÞ cm2 s1 . The N DN =N Al ¼ 5 10 O DO =1:5N Al ¼ 3 10 overall rate constant predicted from Equation (6.100) to be 5.3 1010 cm2 s1 is in satisfactory agreement with the experimental results. The kinetic models for internal attack by multiple oxidants have a critical shortcoming. Both the approximate Meijering model [11] and the more accurate Gesmundo and Niu [76] description treat the reactant metal B as being at a negligible matrix concentration throughout the multiple precipitation zones. While this might be a reasonable approximation for oxide formation, it is nowhere near correct for carbides or nitrides (Table 6.5). A large concentration of chromium remains in the matrix of the inner carbide or nitride zone, and will react with inwardly diffusing oxygen when it arrives. Thus the description of the mass balance at the intermediate interface X1 (Figure 6.36) solely in terms of a reaction such as Equation (6.98) is in considerable error. This is illustrated in Figure 6.40 for the case of internal nitridation followed by carburization. The arrival of carbon has converted the large lamellar prior nitrides in situ to carbide,
Figure 6.40 TEM bright field view of morphology produced by sequential internal nitridation followed by carburization of a Ni–20Ni–25Cr alloy at 1,0001C.
6.10. Solute Interactions in the Precipitation Zone
299
as expected. In addition, however, it has reacted with matrix chromium to form additional fine carbides. A further complication is the appearance in this zone of CrN, a phase which is unstable at the ambient nitrogen pressure employed. The reason [82] is likely the release of nitrogen via the reaction C þ76Cr2 N ¼ 13Cr7 C3 þ 76 N
(6.102)
The saturation level N ðsÞ N corresponds in this reaction to an equilibrium value of N C ¼ 1:4 103 . However, much higher levels of N C are available from carbon dissolution, up to about 0.06, leading to higher (supersaturated) N N values according to reaction (6.102). Under these circumstances CrN is stabilized. Given all these complexities, the kinetic theory cannot be expected to provide any better than order of magnitude predictions. The further approximation in the Meijering theory that N IO ¼ 0 is an additional source of error in the case of carburization– oxidation reactions.
6.10. SOLUTE INTERACTIONS IN THE PRECIPITATION ZONE We have assumed so far that the various alloy solutes, oxidants and reacting metals, behave in an ideal fashion, each having no effect on the thermodynamic activity or diffusion of the others. Given that the oxidant and solute species interact chemically to the extent of forming a precipitate, the supposition is seen to be improbable. Nonetheless, as seen earlier in this chapter, the diffusion theories of Rhines, Wagner and Meijering have proven remarkably successful in providing at least semi-quantitative descriptions of internal penetration rates in many cases. The questions of interest therefore concern how large the solute interactions are, and when they become important. Gesmundo and Niu [83] have considered the general quaternary system A–B–C–O, in which the only oxides possible are the pure binaries. It is supposed that the stability of the oxides increases in the order AO, BO, COn, and that the oxygen potential is sufficient to oxidize only C. Assuming that Ksp ðCOn Þ 1, the situation is one of oxygen dissolving in and diffusing through a single-phase A–B matrix. The effects of B on oxygen permeability and hence internal oxidation can therefore be investigated. Ternary diffusion interactions were ignored in this analysis, and attention was focused on oxygen solubility. The model originally proposed by Alcock and Richardson [84] for oxygen solubility in liquid binary alloys was employed ln Ks ðABÞ ¼ N A ln Ks ðAÞ þ N B ln Ks ðBÞ þ N A ln gA ðABÞ þ N B ln gB ðABÞ
ð6:103Þ
where Ks ðiÞ is the Sievert’s constant (Equation (2.71)) for oxygen in the indicated solvent, and gA ðABÞ and gB ðABÞ are the metal activity coefficients in the binary alloys. Approximate ideality was assumed for the substitutional alloy solution, yielding the simplified result ln Ks ðABÞ ¼ N A ln Ks ðAÞ þ N B ln Ks ðBÞ
(6.104)
300
Chapter 6 Oxidation of Alloys II: Internal Oxidation
and the oxygen solubility in the alloy is given by 1=2
N ðsÞ O ðABÞ ¼ K s ðABÞpO2
(6.105)
The oxygen diffusion coefficient also varies with AB composition. The original model of Park and Altstetter [85] for oxygen dissolution in binary alloys DO ðABÞ ¼ DO ðAÞ
gO ðABÞ gO ðAÞ
(6.106)
was examined. However, because Ks ¼ 1=gO , this description leads to the unacceptable result DO ðBÞ ¼ DO ðAÞ
Ks ðAÞ Ks ðBÞ
To avoid this difficulty, the empirical description DO ðBÞ NB DO ðABÞ ¼ DO ðAÞ DO ðAÞ
(6.107)
(6.108)
in which the diffusion coefficient ratio is raised to the power N B, was adopted. The solutions to the diffusion equation for N O within the precipitation zone and N C in the alloy ahead of the precipitation front are the same as Equations (6.17)–(6.27). Application of this model for alloy interaction effects on oxygen permeabilities to the systems Cu–Al, Ni–Al and Cu–Ni–Al leads to the results shown in Table 6.7. While the model successfully predicts that adding nickel to Cu–Al will reduce greatly the extent of internal oxidation, it overestimates the size of the effect and is unsuccessful in relating rates to nickel concentrations. A much more detailed analysis was undertaken by Guan and Smeltzer [86] who examined the Ni–Cr–Al system. Their approach was based on the use of Wagner’s formalism (2.68) for solute interactions to evaluate N ðsÞ O (Ni–Cr), and a full solution of the diffusion equations, including cross-effects. Results for the variation of oxygen solubility with N ðoÞ Cr are shown in Figure 6.41. Such large changes in N ðsÞ would be expected to affect the rate of internal aluminium O oxidation, and perhaps limit the possibility of it occurring at all. The results of this calculation are examined in Section 7.4.
2 1 Table 6.7 Estimates [83] of kðiÞ from Equation (6.108) for internal oxidation at 8001C in p /cm s a Rhines packs
Cu–0.72Al Ni–0.54Al Cu–10.16Ni–0.76Al Cu–20.11Ni–0.79Al Cu–30.07Ni–0.80Al a
Measured
Calculated
2.0 109 1.4 1010 2.9 1011 2.5 1011 1.5 1011
1.3 108 1.4 1011 4.8 1012 6.3 1012 8.1 1012
Oxygen partial pressure controlled by Cu/Cu2O equilibrium.
6.11. Transition from Internal to External Oxidation
301
Figure 6.41 Oxygen solubility in Ni–Cr–Al as a function of NðoÞ Cr at 1,2001C [86]. With kind permission from Springer Science and Business Media.
A final example of the importance of solute interactions is provided by the internal nitridation of Ni–Cr–Ti alloys [87]. Reaction rates at nitrogen potentials high enough to react with titanium but not chromium were found to increase with N ðoÞ Cr . The effect was shown to be due to the Cr–N thermodynamic interaction which increased N ðsÞ N.
6.11. TRANSITION FROM INTERNAL TO EXTERNAL OXIDATION As is discussed in Section 5.4, if an alloy contains a sufficient concentration of its most reactive component, then the metal can form a protective external scale. Conversely, if the component is dilute, and no other alloy component is oxidized, then internal oxidation results, destroying the alloy. We now consider what concentration of solute metal is necessary to ensure external rather than internal oxide formation. Darken [88] recognized that the volume fraction of internally precipitated oxide would affect the reaction, and that internal oxidation could only occur up to a maximum value of f BO , and hence N ðoÞ B . Wagner [8] proposed that a transition from internal to exclusive external oxidation would occur when N ðoÞ B is increased to a critical value at which the internally precipitated particles reduced the oxygen flux to a sufficient extent. Since the oxide is essentially impermeable to oxygen, diffusion is restricted to the metal channels between precipitate, so that the average flux is lowered. This slows the rate at which the supersaturation needed for new precipitate nucleation can be achieved, and the outward flux of
302
Chapter 6 Oxidation of Alloys II: Internal Oxidation
component B is then of greater relative importance. If N ðoÞ B is high enough to sustain a sufficient flux for continued growth of precipitates, their enlargement leads to continuous oxide layer formation. The mole fraction of internal oxide is found by definition (6.29) to be N BO ¼ aN ðoÞ (6.109) B where a is the enrichment factor calculated from Equation (6.30). Under the limiting conditions (6.25), where metal solute diffusion is important, the limiting form (6.31) applies. Recognizing that the volume fraction of BO; gBO ; is given by VBO gBO ¼ N BO (6.110) VA we combine Equations (6.31), (6.109) and (6.110) to obtain !1=2 ðsÞ p V A N O DO ðoÞ N B ¼ gBO 2n V OX DB
(6.111)
If a critical value can be specified for gBO , then the minimum value of N ðoÞ B for external scale formation can be calculated from Equation (6.111). Rapp [89] studied the internal oxidation of Ag–In alloys at 5501C, where Ag2O is unstable over a wide range of pO2 , the conditions (6.23) were met and a ¼ 1. ðoÞ Systematic variation of N In established that the critical value for scale formation rather than internal oxidation was N InO1:5 ¼ N ðoÞ In ¼ 0:15. This corresponds to an oxide volume fraction, gBO ¼ 0:30. At low pO2 values, where N ðsÞ O is reduced, the conditions (6.25) are met, and Equation (6.111) applies. As is seen from ðsÞ this equation, the critical value of N ðoÞ B varies with N O , and hence with pO2 . Rapp determined metallographically the levels of N ðoÞ In required for scale formation at different oxygen pressures. These results are compared with theoretical predication in Figure 6.42, where agreement is seen to be quite good. We conclude that formation of a critical volume fraction of internal oxide constitutes a correct criterion for the transition to external scale formation. We also observe that oxidation at low pO2 provides a suitable way of inducing protective scale formation on dilute alloys. Providing these scales maintain their mechanical integrity, a low-pressure pre-oxidation treatment can be used to provide protection against subsequent exposure to high oxygen potential gases. We now use Equation (6.111) with gBO set at 0.3, to calculate critical alloy compositions necessary for external, rather than internal oxide formation. Results for chromia and alumina formers are calculated using oxygen solubility data from Table 2.2, and diffusion coefficients taken from Table D2 (Appendix D). Critical ðoÞ values of N ðoÞ Cr and N Al calculated on this basis are compared in Table 6.8 with minimum values estimated from the kinetic criterion (5.25) for the concentration necessary to sustain external scale growth. Similar results were obtained by Nesbitt [90], using somewhat different permeability data. It is seen that the concentrations necessary to avoid internal oxidation are greater than those required merely to support scale growth, and should therefore be preferred. As is also seen, fairly good agreement between prediction and experimental reality is achieved. Although the precision is much less than would be required
6.11. Transition from Internal to External Oxidation
303
Nln(O)*
External Oxidation
Internal Oxidation
log pO2* (atm)
Figure 6.42 Transition from internal to external oxidation of Ag–In alloys at 5501C: continuous line calculated from Equation (6.111), points measured experimentally. Reprinted from Ref. [89] with permission from Elsevier.
Table 6.8 Calculated minimum solute concentrations (mole fraction) for exclusive Cr2O3 or Al2O3 scale formation under Rhines pack conditions
a
Alloy
Scale
T (1C)
Support scaling kinetics (5.22)
Prevent internal oxidation (6.111)
Experimental
Ni–Cr g-Fe–Cr Ni–Ala Fe–Alb
Cr2O3 Cr2O3 Al2O3 Al2O3
1,000 1,000 1,200 1,200
0.07 0.07 0.02 104
0.29 0.16 0.11 0.15
0.15 0.14 0.06–0.13 0.10–0.18
gBO set at 0.2 [90]. Data for a-Fe.
b
for alloy design, it is concluded that the form of Equation (6.111) may be relied upon for semi-quantitative prediction. Of particular importance is the prediction that the critical alloying content required to avoid internal oxidation increases with N ðsÞ O and hence with ambient oxygen potential. As is clear from Equation (6.111), the competition between internal and external reaction is critically dependent on the oxidant permeability. Using the
304
Chapter 6 Oxidation of Alloys II: Internal Oxidation
representative values of Table 6.2, it is found that the minimum value of N ðoÞ B necessary to prevent internal nitridation is two to three times higher than the value required to avoid internal oxidation in austenite. Internal carburization is even more difficult to prevent, with the necessary values of N ðoÞ B 25–70 times higher than those required to form an oxide scale. This prediction is realistic only in the sense that chromia forming alloys are almost always found to carburize internally. In the absence of a protective oxide scale, internal carburization of heat-resisting steels and many alloys is unavoidable. Because, moreover, the process is also very rapid, it constitutes a serious practical problem. Carburization and related corrosion phenomena will be discussed in detail in Chapter 9. Another reaction morphology can develop during the preferential oxidation of a single alloy component: simultaneous external scale growth and internal precipitation. Wagner [91] analysed the conditions under which this could occur, by comparing the concentration product within the alloy, N B N nO , with the solubility product of the oxide, Ksp . For parabolic scale growth, Equations (5.23)–(5.26) apply. At the alloy–scale interface, the reaction B þn O ¼ BOn
(6.112)
n N B;i ðN ðsÞ O Þ ¼ K sp
(6.113)
is at equilibrium, and
The solutions to Fick’s second law for oxygen diffusion from the interface into the alloy and for diffusion of B from the alloy to the interface are Ksp 1=2 erfc½x=2ðDO tÞ1=2
(6.114) NO ¼ N B;i erfc½ðkc =2DO Þ1=2
and ðoÞ N B ¼ N ðoÞ B ðN B N B;i Þ
~ AB tÞ1=2
erfc½x=2ðD ~ AB Þ1=2
erfc½ðkc =2D
(6.115)
These solutions are then used to evaluate the gradient in the logarithm of the concentration product at the interface ðx ¼ xc Þ ~ AB Þ N ðoÞ N B;i @ ln N B N nO 1 expðkc =2D ¼ B 1=2 ~ @x N B;i ðpDAB tÞ erfc½ðkc =2DAB Þ1=2
x¼xc n expðkc =2DO Þ ð6:116Þ ðpDO tÞ1=2 erfc½ðkc =2DO Þ1=2
~ AB , we approximate the second term to Noting that DO DAB and kc D n=ðpDO tÞ1=2 . It is then found that 2 3 ðoÞ 1=2 v ð1 N B Þðkc DO Þ @ ln N B N O n 6 p 1=2 n o 17 ¼ 4 5 (6.117) 1=2 1=2 2 @x ~ ~ ðpDO tÞ x¼y N B;i nDAB 1 F½ðkc =2DAB Þ
Here the auxiliary function F(u) is as defined in Equation (6.77).
6.12. Internal Oxidation Beneath a Corroding Alloy Surface
305
If the right-hand side of Equation (6.117) is negative, the concentration product decreases in the alloy from its saturation value at the interface, and oxide precipitation is impossible. However, if it is positive, the alloy beneath the scale becomes supersaturated and internal oxidation results. Thus the condition for internal oxidation beneath a scale of the same oxide is p 1 N ðoÞ ðkc DO Þ1=2 B n o 41 (6.118) 2 N B;i nDAB 1 F½ðkc =2D ~ AB Þ1=2
and the interfacial concentration is found from N B;i ¼
1=2 ~ N ðoÞ
B F½ðkc =2DAB Þ 1=2 ~ 1 F½ðkc =2DAB Þ
(6.119)
Alternatively, the condition for avoiding internal oxidation beneath the scale may be expressed as ~ AB Þ1=2
R þ F½ðkc =2D (6.120) Rþ1 ~ AB . If kc is small enough, then kc =2D ~ AB 1 and where R ¼ ðpkc DO =2Þ1=2 =nD 1=2 ~ ~ ~ ~ 2 the F kc =2DAB ðpkc =2DAB Þ . If, furthermore, DO DAB and kc DO D AB condition (6.120) may be approximated by pkc DO 1=2 1 4 (6.121) N ðoÞ B ~ AB 2 nD N ðoÞ B 4
Simultaneous internal and external oxidation of B is predicted to occur when N BðoÞ is less than the level predicted from Equation (6.120) and greater than the value set by Equation (6.111) for external scale formation, providing that N BðoÞ is sufficient to support external scale growth (see Equation (5.25)). The range of conditions permitting both internal and external oxidation of the solute metal can be rather restricted, as demonstrated by Atkinson [92] for Fe–Si alloys.
6.12. INTERNAL OXIDATION BENEATH A CORRODING ALLOY SURFACE In many practical situations, the oxidant activity will be high and an external scale will grow. Alloys such as Ni–Cr, Ni–Al, Fe–Cr and Fe–Al will, if sufficiently dilute, form external scales of iron or nickel-rich oxides together with internally precipitated chromium or aluminium-rich oxides. A schematic view of this reaction morphology is shown in Figure 6.43. The interactions between the internal precipitates and iron or nickel oxides when they come into contact are considered in the next chapter. For the moment, our interest is in the effect of the receding alloy surface on the internal oxidation kinetics. Diffusional analyses of internal oxidation in conjunction with scale growth according to parabolic kinetics have been provided by Rhines et al. [24] and ðsÞ Maak [93]. In this situation, N O denotes the dissolved oxygen concentration at the
306
Chapter 6 Oxidation of Alloys II: Internal Oxidation
NiO
Ni+Cr2O3
Ni-Cr
NCr=NCr(0)
N0(s)
N0
Xc
Figure 6.43
Xi
Oxidation of a dilute Ni–Cr alloy at high pO2 .
alloy–scale interface, Xi the distance of the internal precipitation front from the original alloy surface and Xc the position of the scale–alloy interface with respect 1=2 to the original surface. In the common case ðkðiÞ 1 and Xc oXi , then p =2DO Þ ðsÞ pffiffiffiffiffiffiffiffi N DO (6.122) Xi ðXi Xc Þ ¼ 2 O ðoÞ F Xi =2 DB t t nN B where the function F(u) is as defined in Equation (6.78). When both Xc and DB are small, Equation (6.122) yields Equation (6.11). Experimental verification of Equation (6.122) has not been completely successful [9]. Permeability values deduced from internal oxidation kinetics under an external scale were apparently smaller than those determined from exclusively internal reactions. In view of the microstructural complexity of the scale–alloy interface (Figure 6.42), it seems quite likely that local scale separation could occur from time to time, as a result of reduced oxide plasticity. In this case, the boundary value oxygen activity, and hence N ðsÞ O , would vary with time, and (6.122) would no longer apply.
6.13. VOLUME EXPANSION IN THE INTERNAL PRECIPITATION ZONE The precipitation of internal oxides is almost always accompanied by a volume expansion. As is seen from the molar volumes listed in Table 6.9, the expansions are large. The effect of internal oxide precipitation on the molar volume of the internal oxidation zone can be calculated for a binary alloy Ni–B as ðoÞ V T ¼ V Ni ð1 N ðoÞ B Þ þ N B V BOn
(6.123)
where it is assumed that no solute element enrichment or depletion occurs. The volume increase ratio DV=V Alloy ¼ ðV T V Alloy Þ=V Alloy is then calculated for
6.13. Volume Expansion in the Internal Precipitation Zone
307
Table 6.9 Molar volumes of internal oxides; alloy expansion on internal oxidation of Ni-based alloys VOX (cm3)
SiO2a a-Al2O3 Cr2O3 a
25.8 25.6 29.2
Alloy DV/V NðoÞ B ¼ 0:01
0.05
0.10
0.026 0.008 0.011
0.13 0.04 0.05
0.26 0.08 0.11
b-Cristobalite.
various solute concentrations, leading to the results shown in Table 6.9. Similar calculations for nitridation and carburization of chromium show that resulting expansions are less, principally because of the higher densities of Cr2N and the chromium carbides, all of which are interstitial compounds. In the case of internal oxidation, the enormous volume increase generates stresses which must be relieved. Shida et al. [33, 43] suggested stress relief mechanisms of grain boundary sliding and extrusion of internal oxide-free metal adjacent to grain boundaries, in the case of intergranular oxidation at low temperature. However, internally oxidized Ni–Cr alloys were thought [36] to be able to accommodate stress by metal flow within the grains. In fact, outward transport of the more noble metal was first reported by Darken [94] in a study of Ag–Al alloy oxidation. Mackert et al. [95] found nodules of palladium and silver on the external surface of internally oxidized Pd–Ag–Sn–In alloys, and proposed that Pd and Ag diffused via the Nabarro–Herring mechanism. Guruswamy et al. [96] observed silver nodules on the surface of internally oxidized Ag–In alloys, and concluded that dislocation pipe diffusion was the mechanism of silver transport. An example of outward metal displacement during internal oxidation of Ni–Cr–Al is shown in Figure 6.8. Yi et al. [34] demonstrated that in the case of Ni–Al–Si internal oxidation, the volume of metal accumulated outside the precipitation zone was close to the equivalent of the volume increase calculated for silicon and aluminium oxidation. This result is shown in Figure 6.44, and confirms that the driving force for outward nickel displacement is the volume increase within the precipitation zone. The mechanism whereby the nickel moves is obviously of interest. Yi et al. [34] proposed that the mechanism was one of Nabarro–Herring creep [97]. In the case of internal oxidation, the volume expansion at the internal oxidation front causes compressive stress and a reduction in vacancy concentration. Thus a vacancy gradient is established between the free alloy surface, where the equilibrium concentration N v prevails, and a much reduced concentration at the reaction front. Assuming a linear gradient, we can write J Ni ¼ J V ¼
DV DN V Xi VNi
(6.124)
308
Chapter 6 Oxidation of Alloys II: Internal Oxidation
Figure 6.44 Comparison of volume of Ni transported outward with volume increase calculated for internal oxidation of Al and Si in Ni–Al–Si. Reprinted from Ref. [34] with permission from Elsevier.
where DV is the vacancy diffusion coefficient. To conserve mass, this flux must equal the rate at which nickel is displaced by newly precipitated oxide J Ni ¼
N ðoÞ 1 dXi B ðV BO V B Þ V Ni dt V Ni
(6.125)
where the amount of nickel displaced has been calculated from the volume of new materials divided by the nickel molar volume. Equating Equations (6.124) and (6.125) and integrating, we find X2i ¼ 2kðiÞ p t with kðiÞ p ¼
DV DN V VNi N BðoÞ ðV BO V B Þ
(6.126)
If the further approximation N V ðx ¼ Xi Þ O is made, then DN V ¼ N V . Recalling from Equation (3.58) that DNi DV N V , we obtain DNi V Ni kðiÞ (6.127) p ¼ ðoÞ N B ðV BO V B Þ Values of kðiÞ p predicted from Equation (6.127) are compared with experimental measurements for an Ni–4Al alloy in Figure 6.45, where agreement is seen to be good. Thus internal oxidation is, in this case, controlled by outward diffusion of nickel, although driven by inward oxygen diffusion. It is likely that the rapid
6.13. Volume Expansion in the Internal Precipitation Zone
309
Figure 6.45 Comparison of experimentally measured internal oxidation rates with predictions of Nabarro–Herring creep mechanism. Reprinted from Ref. [34] with permission from Elsevier.
oxygen diffusion associated with the fine precipitate platelets was a factor contributing to this result. The Nabarro–Herring model was found by Yi et al. [34] to be inapplicable to ðoÞ Ni–4Al–xSi alloys with x ¼ 1 or 5 wt%. Instead of decreasing with increasing N Si as predicted by Equation (6.127), the rate increased. Although the magnitude of the rate constant was satisfactorily accounted for by dislocation pipe diffusion ðoÞ of nickel, the variation of kðiÞ p with N Si was not. It is possible that increasing silicon levels led to a greater multiplicity of precipitate–matrix interfaces and consequently higher effective DO values. If dislocation pipe diffusion is sufficiently rapid, the process does not contribute to rate control, and internal oxidation kinetics are described using an expression like Equation (6.35) for the ternary alloy: ðoÞ ðoÞ N ðsÞ O DO ¼ a þ bðN Al þ N Si Þ
(6.128)
More detailed study of precipitate morphologies is required. The swelling effect caused by internal oxidation is not universally observed to cause metal ejection. For example, internal precipitation of Cr2O3 and MCr2O4 in Fe–Cr (Figures 6.1 and 6.2) or Ni–Cr [36] does not lead to external iron or nickel accumulation. The volume changes are nonetheless large (Table 6.9) and significant deformation must occur. It is possible that outward movement of nickel simply carries with it the embedded chromium-rich particles. The latter are large and spheroidal and drift with the moving nickel lattice. Alumina, however, precipitates as rods and platelets normal to the alloy surface, i.e. parallel to the direction of nickel movement. In such a configuration, it seems possible that nickel can transport past the fixed alumina precipitates, ‘‘extruding’’ to the outer surface. Even when this favourable morphology develops, nickel displacement has been found to be suppressed if an external NiO scale grows during internal Al2O3 precipitation within a binary Ni–Al alloy oxidized at pO2 ¼ 1 atm [72].
310
Chapter 6 Oxidation of Alloys II: Internal Oxidation
The suggested reason [33, 39, 72] is that growth of an external scale by outward cation diffusion leads to metal vacancies being injected into the alloy at the scale– alloy interface. These then diffuse inwards, permitting more rapid outward nickel movement. Put more simply, consumption of metal at the scale–alloy interface provides the space needed to accommodate the internally precipitated oxide. A similar situation arises during in situ oxidation of primary carbides (Figure 6.16) beneath a growing Cr2O3 scale [39]. If the carbide oxidation is described by reaction (6.42), then the weight change corresponding to oxygen consumption is given by !2 kðiÞ ðDW i =AÞ2 p f Cr23 C6 ðiÞ ¼k ¼ 576 (6.129) 2t V CrC0:261 where the mass conversion number 576 is computed on the assumption that no carbon is lost from the alloy. The volume increase due to carbide oxidation, normalized to the alloy surface area is then given by ðDV i =AÞ2 ðiÞ ðV CrO1:5 V CrC0:261 Þ (6.130) ¼ kðiÞ n ¼k 24 2t 11 The rate of the process was measured as kðiÞ cm2 s1 , corresponding p ¼ 2:9 10 ðiÞ 15 to a volume expansion accumulation rate of kn ¼ 3 10 cm2 s1 . This is to be compared with the volume consumption rate corresponding to external scale growth, DV ex . Approximating the scale as pure Cr2O3 and assuming a fixed alloy–scale interface, one finds ðDV ex =AÞ2 V Cr 2 ¼ kðexÞ ¼ kw (6.131) n 2t 24 where kw is the parabolic weight gain rate constant for scale growth. The measured value of kw ¼ 8 1012 g2 cm4 s1 leads to an estimate of kðexÞ ¼ 6:5 1013 cm2 s1 . The volume made available, if external scaling causes n injection of vacancies at the alloy surface, is very much larger that the volume required to accommodate the expansion due to interdendritic carbide oxidation. Intragranular precipitation of Al2O3 rods within Al-bearing heat-resistant steels takes place according to parabolic kinetics [39, 98] together with external chromium-rich oxide scale growth at high pO2 values. No oxide-free surface region of metal develops (Figure 6.46). This is quite unlike the extensive metal ejection observed in the absence of scaling on a dilute alloy (Figure 6.8). Measurement of internal penetration and scale thickening rates allowed calculation of the volume 14 expansion rate kðiÞ cm2 s1 and the rate of free volume generation n ¼ 6:3 10 ðexÞ by vacancy injection kn ¼ 1 1012 cm2 s1 at 1,0001C and pO2 ¼ 0:2 atm. In this instance the internal expansion corresponds to the reaction Al þ32 O ¼ Al2 O3
(6.132)
Again, the volume potentially made available by the scaling process is substantially larger than that needed to accommodate the expansion due to internal oxidation, and the absence of visible metal displacement is thereby explained.
6.14. Success of Internal Oxidation Theory
311
6.14. SUCCESS OF INTERNAL OXIDATION THEORY Internal precipitation in alloys resulting from reaction with external oxidants is a highly destructive process, frequently leading to alloy failure when it occurs. As we have seen in this chapter, these reactions can develop a diversity of morphologies, at rates which vary over orders of magnitude with oxidant identity and the alloy composition and phase constitution. However, the reactions all involve simple, solid-state precipitation processes: B þn X ¼ BXn where X is a generic oxidizing solute. Consequently, local equilibrium is closely approached at intermediate and high temperatures, and solubility product calculations work well. For this reason, the diffusion path description applies and diffusion-controlled parabolic kinetics result. In the case of the fast diffusing oxidants carbon and nitrogen, the diffusion path for the system A–B–X can usually be defined on the basis DX DB simply as a straight line from the X-corner of the ternary to the AB alloy composition. This approach correctly describes the sequence of precipitate phase constitutions, the variation in composition of mixed carbides such as (Cr,Fe)7C3, and the change in volume fraction with depth of these low-stability compounds. Even for the slower diffusing oxygen, this approach is useful. Prediction from these simplified diffusion paths is successful for multiple oxidants and multicomponent alloys, but inaccurate when fast diffusing alloy solutes such as silicon and aluminium are involved (Figure 6.46).
Figure 6.46 Internal aluminium oxidation and external chromia scale growth on 60HT heat-resisting steel (T ¼ 1,2501C, pO2 ¼ 4 1014 atm).
312
Chapter 6 Oxidation of Alloys II: Internal Oxidation
Rather simple diffusion theory usually succeeds in predicting parabolic rate constants very well for binary alloys, providing that both DX and N ðsÞ X are known. The measured permeabilities of carbon and oxygen in austenite and ferrite provide good order of magnitude predictions of the relative rates of the various internal precipitation reactions, internal carburization being almost three orders of magnitude faster than oxidation. Unfortunately, data for nitridation are scant. In the absence of such data, internal oxidation kinetic measurements can be used to evaluate permeabilities. The kinetic theory is particularly valuable in predicting the increase in rate with oxidant solubility and diffusivity, and hence with aX and temperature. It also successfully predicts the decrease in rate with increasing N ðoÞ B for cases of dispersed precipitates. However, the theory has mixed success in describing the growth of multiple precipitation zones. The total depth of attack is reasonably well predicted, but quantitative calculation of the individual precipitate zones is not yet possible. From a practical point of view, this may be unimportant to the prediction of alloy failure. However, if the reaction is to be used as a method of fabricating nanostructures, this deficiency needs to be addressed. The classical theories of internal oxidation all assume uniform distributions of precipitates. This insistence upon a strict chemical stoichiometry ignores the effects of low precipitate Ksp values, microstructure and alloy phase transformations and can lead to error. As we have seen, the competition between precipitate nucleation and growth can have important effects. It alters size distributions, and therefore penetration depths. In the extreme, it can produce cellular precipitation morphologies which are associated with rapid boundary diffusion and accelerated reaction. The alloy phase transformations or crystallographic reorientations accompanying this process have been well characterized in a number of cases, but a satisfactory description of fibrous alumina precipitate growth has not yet been arrived at. From an alloy design (or selection) point of view, the most important thing about internal oxidation is avoiding it. The diffusion-based theory provides a method for predicting how much alloy solute metal is required to ensure external scale growth rather than internal precipitation of the preferentially formed oxide. Its predictions are approximately correct, and a sound basis for alloy design is potentially available. However, for this method to be a useful design tool, we require greater accuracy. To achieve this, a much better knowledge of the solute interactions which determine thermodynamic activities and diffusivities of oxidant and alloy components is required.
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CHAPT ER
7 Alloy Oxidation III: Multiphase Scales
Contents
7.1. Introduction 7.2. Binary Alumina Formers 7.2.1 The Ni–Al system 7.2.2 The Fe–Al system 7.3. Binary Chromia Formers 7.3.1 The Ni–Cr and Fe–Cr systems 7.3.2 Transport processes in chromia scales 7.4. Ternary Alloy Oxidation 7.4.1 Fe–Ni–Cr alloys 7.4.2 Ni–Pt–Al alloys 7.4.3 Ni–Cr–Al alloys 7.4.4 Fe–Cr–Al alloys 7.4.5 Third-element effect 7.5. Scale Spallation 7.5.1 The sulfur effect 7.5.2 Interfacial voids and scale detachment 7.5.3 Reactive element effects 7.6. Effects of Minor Alloying Additions 7.6.1 Silicon effects 7.6.2 Manganese effects 7.6.3 Titanium effects 7.6.4 Other effects 7.7. Effects of Secondary Oxidants 7.8. Status of Multiphase Scale Growth Theory References
315 316 316 322 326 326 328 330 330 331 334 336 338 341 342 343 344 347 347 350 350 351 352 355 356
7.1. INTRODUCTION Practical heat-resisting alloys have multiple components (Tables 5.1 and 9.1), nearly all of which are susceptible to oxidation in a wide range of environments. When these alloys are exposed at high temperatures, an initial, transient period of reaction in which all alloy components oxidize, is followed by a steady-state reaction. The rapid development of a corrosion-resistant, steady-state scale
315
316
Chapter 7 Alloy Oxidation III: Multiphase Scales
morphology is the basis for alloy (or coating) design and selection, and is the central concern of this chapter. We wish to predict the nature of the steady-state reaction morphology as a function of alloy composition and environmental variables. Of particular interest are the conditions leading to the development of a protective, slow-growing oxide scale on the alloy surface. The ability of this scale to resist penetration by gaseous impurities such as sulfur and carbon is of obvious interest, as is also its ability to block outward diffusion of other alloy components. It turns out that diffusion through Cr2O3 scales of Fe, Ni and Mn is difficult to avoid, and simultaneous growth of two or more oxides has to be considered. As always, we wish to predict reaction rates and, ultimately, component lifetimes. The prediction of steady-state reaction morphologies is a realistic goal for single-oxidant environments, because the oxidant activity must decrease monotonically from the scale–gas interface to the alloy interior. The activity gradient provides the driving force for diffusion and interfacial mass transfer. Recognition of its existence permits the construction on phase diagrams of diffusion paths, if the alloy diffusion properties are known and concentration changes at the alloy–scale interface can be predicted. Discussions of oxidation morphologies commenced with Wagner’s analyses [1–4] of binary alloys. These distinguished alloy classes on the basis of the relative affinities for oxygen of the constituent metals. Subsequent reviews [5–7] have established a taxa of reaction morphologies for binary alloys based on the thermodynamic stabilities and transport properties of the oxidation products. Unfortunately, this systematic approach is not easily extended to multicomponent alloys. Instead, we focus here on chromia and alumina scale formation and the processes that can accompany them. A brief review of binary alloy oxidation is followed by an examination of the effect of ternary alloy additions. Minority component effects are then considered, with particular attention directed to reactive element additions. Finally, the behaviour of alloys reacted with multiple oxidants is discussed. Consideration is restricted throughout to isothermal reaction conditions.
7.2. BINARY ALUMINA FORMERS 7.2.1 The Ni–Al system Nickel-base alloys can be described using the phase diagram of Figure 7.1. The g-phase is the basis of the Inconel alloys (e.g. 601 and 617 in Table 5.1), nickel-base superalloys have the g þ g0 phase constitution and b-NiAl is a principal constituent of aluminide coatings, so this system is of considerable practical interest. The classic study of its oxidation behaviour was carried out by Pettit [8], using pure oxygen at 0.1 atm. His results are reproduced in the oxidation map of Figure 7.2, which defines regions I, II and III, corresponding to different reaction morphologies and mechanisms. The dilute alloys of region I develop external scales of NiO and internal precipitates of Al2O3 and NiAl2O4 at all temperatures
7.2. Binary Alumina Formers
Figure 7.1 Ni–Al phase diagram.
Figure 7.2 Oxidation map for Ni–Al alloys [8]. Reaction morphologies I, II and III are described in the text. Dotted line shows temperature dependence of NAl,min according to Equation (7.6). Dashed line shows variation of NAl,min in CO/CO2 gas with Al2O3 the only stable oxide.
317
318
Chapter 7 Alloy Oxidation III: Multiphase Scales
investigated. In region II, a protective a-Al2O3 scale develops initially according to slow parabolic kinetics. Subsequently, however, a thick scale containing both NiO and spinel grows more rapidly, while a discontinuous alumina layer grows at and beneath the scale–alloy interface. Increasing either temperature or N ðoÞ Al changes the behaviour to type III, in which a protective a-Al2O3 scale is the only reaction product. The broad bands separating the three regions arise through irregular behaviour which varies with alloy surface preparation. Subsequent investigations have broadly confirmed these results. Hindam et al. [9–11] also found internal precipitation of Al2O3 and NiAl2O4 beneath a scale of NiO on dilute alloys, and irregular, non-reproducible kinetics for a Ni–6Al alloy followed by the development of a three-layered scale. The innermost layer was Al2O3, the intermediate layer NiAl2O4 and the outermost layer NiO. A scale of this type is shown in Figure 7.3. Wood and Stott [12] identified the critical aluminium content necessary to form a stable Al2O3 scale at 1,0001C as being in the range 7–12.5 wt%. More recently, Niu et al. [13] determined this critical level to be N Al;min ¼ 0:1020:15 (5–7.5 wt%) at 1,0001C. At the still lower temperature of 8001C, alloys containing up to 10 wt% Al undergo internal oxidation [14]. Thus there is disagreement as to the critical level at lower temperatures. The different reaction morphologies are readily understood in terms of diffusion paths mapped onto Ni–Al–O phases diagrams, such as that of Figure 7.4. The dilute alloy situation is shown in Figure 6.33. In essence, precipitation of Al2O3 and NiAl2O4 within the alloy depletes it so severely in
Figure 7.3 Three-layered scale grown on Ni–22Al shown in FIB-milled section.
7.2. Binary Alumina Formers
319
Figure 7.4 Ni–Al–O phase diagram section at 1,0001C [15]. Reproduced by permission of The Electrochemical Society. Diffusion path for scale of Figure 7.3 mapped as dotted line.
aluminium that NiO is stable in contact with the metal. The situation for highaluminium content alloys is shown in Figure 5.24. If N ðoÞ Al is high enough, alumina forms in contact with the alloy, yielding Pettit’s Type III reaction morphology. At lower N Al (and higher N Ni ) values, the alumina scale is overlaid by spinel and NiO. This sequence reflects the relative stabilities of the oxides, as we now establish. Reactions at the interfaces shown in the schematic diagram of Figure 7.5 can be written as (a)
2 Al þ32O2 ¼ Al2 O3
(7.1)
(b)
Ni þ Al2 O3 þ 12O2 ¼ NiAl2 O4
(7.2)
(c)
Ni þ 12O2 ¼ NiO
(7.3)
on the basis that nickel diffuses through Al2O3 to form the outer layers. The oxygen activity at the scale–alloy interface clearly depends on aAl . The minimum value of aAl required to form Al2O3, rather than nickel-rich oxides, can be estimated by the methods of Section 2.4. The requisite value of aAl corresponds
320
Chapter 7 Alloy Oxidation III: Multiphase Scales
Gas
NiAl2O4
NiO
Al2O3
Alloy
Ambient NAl pO2 /atm
10-10 10-12
10-30 (d)
(c)
(b)
(a)
Figure 7.5 Schematic view of multiple layer scale grown on Ni–Al in Type II reaction. pO2 values calculated for 1,0001C, assuming aNi ¼ 1.
Table 7.1 Spinel-free energies of formation [187] DGf ¼ A þ BT ðJ mole1 Þ
Spinel
FeCr2 O4 NiCr2 O4 MnCr2 O4 FeAl2 O4 NiAl2 O4 MnAl2 O4
A
B
1,450,670 1,376,880 1,583,600 1,988,442 1,933,667 2,119,897
324 332 331 406 408 414
[8] to less than 1 ppm by weight, reflecting the very high stability of Al2O3 relative to NiO (Figure 7.4). The actual value will depend on alloy diffusion. For high N ðoÞ Al values, depletion is minimal, and pO2 values calculated from Equation (7.1) are of order 1030 atm at 1,0001C. Turning next to reaction (7.2), the local equilibrium at interface (b) can be written as h i 1=2 (7.4) aNi pO2 ¼ exp ðDGf ðNiAl2 O4 Þ DGf ðAl2 O3 ÞÞ=RT where unit activity oxides have been assumed. Again the metal component activity will be controlled by diffusion. If it is low enough, as a result of the alumina layer blocking nickel diffusions, then spinel will not form at all. However, if nickel diffuses easily through the inner layer, its activity will be close to that of the alloy, i.e. approximately unity. In this event, pO2 is calculated from Equation (7.4), using DGf ðNiAl2 O4 Þ from Table 7.1, to be of order 1012 atm. For reaction at interface (c), a value of pO2 1010 atm is calculated for aNi 1 using
7.2. Binary Alumina Formers
321
DGf ðNiOÞ from Table 2.1. Thus the oxygen activity decreases monotonically from the outside to the inside of the scale, as it must for the scale to grow. Conversely, the oxide layers can be predicted to form in this sequence on the basis of their relative stabilities. The corresponding diffusion path is shown in Figure 7.4. Whilst the oxidation morphologies can be understood on the basis of Ni–Al–O thermodynamics, the conditions under which the regimes I, II and III develop cannot. These conditions are determined largely by kinetic factors, principally diffusion in the various phases. We consider first the boundary between internal and external oxidation, i.e. between regions I and II. Wagner’s criterion [4] stated in Equation (6.111) yields the minimum aluminium level, N Al;min , necessary to form external scale rather than internal precipitate, if the critical precipitate volume fraction, g, for formation of a continuous layer is known. Nesbitt [16] set g ¼ 0:2 and found for 1,2001C, that N Al;min ¼ 0:0720:09 (4.4 wt%) at high pO2 , where NiO can form. Using the more conventional value g ¼ 0:3, and taking data for DO ; N ðsÞ O and DAl from Chapter 2 and Appendix D, we calculate the value N Al;min ¼ 0:14 at 1,2001C, equivalent to 7 wt% for these conditions. These two estimates lie within the experimental transition band between internal and external alumina formation (Figure 7.2). It is of interest to explore the effect of temperature on N Al;min , with the aim of testing the utility of Wagner’s expression in predicting the measured effect shown in Figure 7.2. Combining Wagner’s condition (Equation (6.11)) with Sievert’s Equation (2.71) for oxygen solubility, we obtain !1=2 1=2 p VA KpO2 Do n N B;min ¼ gBOn (7.5) 2n V BOn DB The temperature dependence of N B;min can therefore be expressed as R @ ln
N B;min DH O DHðO2 Þ QO þ QB ¼ @ð1=TÞ 2
(7.6)
where DH O is the partial molar heat of dissolution of oxygen in solvent metal, DHðO2 Þ the enthalpy of the interface reaction producing ½O2(g), and Qi the activation energy for diffusion of the indicated species. The transition between regimes I and II is subject to the pO2 value characteristic of the reverse of reaction (7.3), for which DHðO2 Þ ¼ 234; 000J mol1 . Taking DHO from Table 2.2 and the Qi from Appendix D, the right-hand side of Equation (7.6) is calculated as 21,828 J mol1. The predicted dependence of N Al;min on temperature is shown as a dotted line in Figure 7.2. Agreement with experiment is reasonably good for these high oxygen activity conditions. Figure 7.2 also shows results for the transition from internal to external alumina under low oxygen potentials, where only Al2O3 can form. These experiments were carried out in a CO/CO2 gas mixture of fixed composition pCO =pCO2 ¼ 0:2, so that pO2 was controlled by the reaction CO2 ¼ CO þ 12O2 , for which DHðO2 Þ ¼ 282; 420 Jmol1 . The enthalpy term in Equation (7.6) is then evaluated as 4,420 J mol1, and the value of N Al;min is predicted to increase with temperature. This is contrary to the experimental observations in Figure 7.2.
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Chapter 7 Alloy Oxidation III: Multiphase Scales
The calculated value of N Al;min at 1,2001C is 0.05 (2.4 wt%), slightly less than the observed value of 3.0 wt%. It is possible that the slow gas phase reaction led to a failure to achieve equilibrium, and the calculation for pO2 is therefore inapplicable. Despite the success of diffusion theory in accounting for the variation with temperature and N ðoÞ Al of the initial oxidation morphologies of Ni–Al alloys, it is evident from Figure 7.2 that the formation of an initial alumina scale in region II did not correspond to long-term protection. Pettit [8] attributed this loss of protection to a lowering of the interfacial aluminium content, of N Al;i , resulting from diffusion being slower than the rate of aluminium consumption by alumina scale growth. According to the Wagner description, if this was the case, no alumina scale could form in the first place. The two views are reconciled by recognizing that behaviour in regime II is not steady-state, and Wagner’s analysis therefore cannot apply. The non-steady-state behaviour is explicit in the observed transition to approximately linear kinetics when protection is lost. This could result from a change in mass transfer mechanism within the scale, any such change in the alloy being improbable. Scale diffusion mechanisms can change in response to microstructural alterations or the precipitation of new phases. The slow diffusion of nickel into the alumina scale followed by formation of spinel and even NiO appears to be the reason for this behaviour. As pointed out by Pettit, it is prevented by ðoÞ increasing either N Al or the temperature, thereby maintaining a higher value of N Al;i (and a lower N Ni;i ). The effect of N ðoÞ Al is obvious, but the temperature effect implies that the activation energy for alloy diffusion (188 kJ mol1 [17]) is greater than that of the alumina diffusion process. Tracer diffusion studies have led to activation energy estimates of 477 kJ mol1 for aluminium [18] and 460 kJ mol1 for oxygen [19] in polycrystalline Al2O3 at high oxygen pressures and temperatures above 1,4501C. However, extrapolation of these diffusion coefficients to the temperatures of oxidation experiments leads to values much lower than those implied by alumina scale growth rates. Hindam and Whittle [20] compared directly measured diffusion coefficient values with those deduced from alumina scaling rates. The results (Figure 7.6) yielded approximate agreement for scale growth controlled by grain boundary diffusion of oxygen through a fine-grained (0.1–5 mm) structure (Equation (3.113)). The effective activation energy is 130 kJ mol1, less than that of alloy diffusion, as suggested by Pettit. Before leaving the Ni–Al system, it is appropriate to note that even when a protective scale is formed in regime III, the scale is not of practical use. The problem is that the scale cracks and spalls profusely on cooling from reaction temperature. Alloy developments aimed at preventing this problem are discussed in Section 7.5.
7.2.2 The Fe–Al system An isothermal section of the Fe–Al–O phase diagram is shown in Figure 7.7, and the Fe–Al diagram is shown in Figure 6.10. The Fe–Al–O diagram is similar to
7.2. Binary Alumina Formers
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Figure 7.6 Comparison of diffusion coefficients deduced from alumina kp values with diffusion data [20]. With kind permission from Springer Science and Business Media.
that of Ni–Al–O in that Al2O3 is by far the most stable oxide in both systems, with the consequence that all alloy compositions down to extremely low levels equilibrate with this phase. Important differences exist with respect to oxide intersolubilities. The spinel and Fe3O4 form a continuous solid solution, and Al2O3 and Fe2O3 have limited mutual solubility, the extent of which increases at higher temperature. On the contrary, nickel has very little solubility in Al2O3, and the NiAl2O4 spinel is a true ternary compound of closely stoichiometric composition. Dilute Fe–Al alloys oxidize under Rhines pack conditions (in which pO2 is controlled by the Fe/Fe1dO equilibrium) to produce internally precipitated aluminium-rich oxides [23, 24]. Early work aimed at establishing aluminium levels necessary to reduce alloy scaling rates have been reviewed by Tomaszewicz and Wallwork [25]. Boggs [26] found that at To5701C and pO2 1 atm, aluminium levels of about 2.4 wt% were sufficient to form an inner scale layer of FeAl2O4 spinel. This layer acted as a partial barrier to iron diffusion, reducing the thickness of the outer Fe3O4 layer by 75%. At higher temperatures, Al2O3 appeared in the scale in increasing amounts as the temperature increased
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O
FeAl2O4 Fe2O3
Al2O3
Fe3O4 FeO
Alloy+Spinel+Al2O3
Fe
Al
Figure 7.7 Phase diagram for Fe–Al–O. Data from Refs [21, 22].
to 800–9001C. The alumina was g-phase at low temperatures, but increasingly a-phase at higher temperatures. At 8001C and 9001C, an essentially pure Al2O3 film developed after the transient stage of reaction, and oxidation rates were very low. However, protection was lost after some time, and iron-rich nodules grew through the alumina whilst aluminium was internally oxidized beneath the nodules. As seen in Figure 7.8, a transparently thin Al2O3 layer covered most of the surface, but the sporadic nodules grew quickly, causing rapid attack on the alloys. This general pattern of reaction morphologies has been confirmed by others [27–31]. The minimum value of N ðoÞ Al necessary to prevent internal oxidation is 0.048 at 5001C [26] in the range 0.038–0.048 at 8001C [27] and 0.05 at 9001C [29]. The value required to form a protective alumina scale has been estimated as more than 0.15 at 6001C [26], 0.13 at 8001C [27] and 0.14 in the range 800–1,0001C [32]. A more recent investigation [33] into the oxidation of an Fe–Al alloy with N ðoÞ Al ¼ 0:10 at 1,0001C confirmed that this was sufficient to prevent internal oxidation, but not enough to stop nodule formation after an alumina scale was established. The Fe–Al system is seen to be qualitatively similar to Ni–Al in possessing the same three regimes of behaviour. The same competition between oxygen diffusion into the alloy and aluminium diffusion to its surface determines the reaction morphology. Zhang et al. [33] have analysed the system at 1,0001C in this way, making use of Wagner’s criteria for scale formation. As noted in Section 6.3, depletion of aluminium from iron by either scale formation or internal precipitation causes the alloy a ! g transformation. Unfortunately, data for DAl in g-Fe is unavailable. Using an estimate for this quantity, they calculated an
7.2. Binary Alumina Formers
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Figure 7.8 Iron-rich nodules growing out of thin alumina film on Fe–4.9Al at 8001C, pO2 ¼ 0:92 atm [26]. Reproduced by permission of The Electrochemical Society.
N Al;min of 0.04 to be required to prevent internal oxidation. Wagner’s criterion for the N Al value required to sustain a continuous Al2O3 scale (Equation (5.22)) was found to yield 4.6 103 for a-Fe and 0.04 for g-Fe. The experimental results for ðoÞ N Al ¼ 0:10 showed that internal oxidation did not occur, as predicted, but that iron-rich nodules or a mixed scale developed, and no continuous Al2O3 scale was maintained. The same problem arises for Fe–Al as was noted for Ni–Al: Wagner’s steadystate analyses do not succeed. The same reason is in effect: neither system achieves a long lasting steady-state. In the case of Fe–Al, there is agreement that cracking of the alumina scale allows gas access to the underlying alloy. If this is depleted in aluminium, as might be the case if a subsurface g-iron layer is present, then scale rehealing would be impossible, and iron-rich nodule formation thereby explained [26, 27, 31, 34]. An alternative explanation suggested by Zhang et al. [33] is that iron oxides remaining from the initial period of transient oxidation react with the alumina, forming spinel. This decreases the Al2O3 layer thickness, balancing the growth process. If as a result the alumina layer thickness is approximately constant, aluminium metal is consumed according to linear kinetics, and depletion could be even more severe. Whether this could destabilize the alumina scale with respect to other oxides in the time scale required has not been established.
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7.3. BINARY CHROMIA FORMERS 7.3.1 The Ni–Cr and Fe–Cr systems Isothermal sections of the Fe–Cr–O and Ni–Cr–O systems are shown in Figures 2.5 and 5.7. The obvious difference between the two is the much greater intersolubility of oxides in the iron-based system. Thus a single-phase field extends between the isotypic Fe3O4 and FeCr2O4 compositions, whereas the nickel spinel is a true ternary phase. This reflects the fact that an Fe3+ cation exists but no such nickel species is formed. Similarly, a continuous Fe2O3–Cr2O3 solid solution can form, whereas the nickel solubility in Cr2O3 is extremely small. Oxidation morphologies for Fe–Cr and Ni–Cr, together with their associated diffusion paths, were discussed in Section 5.3. In both cases, the behaviour of dilute alloys is controlled by monoxide (MO) scale layer growth. Depending on temperature, internal precipitation of Cr2O3 is also observed. As the scale–metal interface advances, the Cr2O3 precipitates are incorporated into the scale and transformed into spinel. This reaction morphology is shown schematically in Figure 7.9. The volume fraction of spinel increases with N ðoÞ Cr until the Cr2O3 phase appears. The extensive compositional range of the Fe–Cr spinel allows the formation of an almost continuous spinel layer on low chromium alloys, as illustrated by the 9Cr steel in Figure 7.10. These changes in morphology are reflected in oxidation rates. A compilation by Wood et al. [36] of oxidation rate data for model alloys is reproduced in Figure 7.11. Very small additions of chromium increase the rate of nickel
Figure 7.9 Schematic view of M–Cr alloy oxidation at subcritical NðoÞ Cr levels. If M ¼ Fe, outer layers of Fe3 O4 and Fe2 O3 form at high pO2 values.
7.3. Binary Chromia Formers
327
Figure 7.10 Spinel formation in inner scale layer grown on P91 steel at 6501C. Reprinted from Ref. [35] with permission from Elsevier.
oxidation, but not that of iron. This is generally thought to be a dopant effect, due to an increase in V 00M concentration to compensate for dissolved CrM . It is not observed for Fe–Cr alloys, because Fe1dO is already highly defective. The decrease in rate observed as N ðoÞ Cr is further increased is due to a growing volume fraction of spinel particles within the MO layer. Because diffusion in the spinel phase is relatively slow, the particles effectively reduce the diffusional crosssection of the MO layer, slowing its growth. In addition, porosity develops within the MO+spinel scale layer, because the two-phase oxide is unable to deform plastically to accommodate the volume loss caused by outward diffusion of iron or nickel. Gas phase transport of oxygen within the pores is slow (Section 2.9) if O2 is the only gas species available, and pore formation also slows scale growth. The reduction in rate as alloy chromium levels are increased to about 10 wt% is much greater for Fe–Cr than for Ni–Cr. This difference is partly due to the fact that diffusion in NiO and NiFe2O4 is much slower than in iron oxides, and the basis for comparison therefore differs. It also reflects the more ready formation of a continuous spinel layer on Fe–Cr alloys. The limited intersolubility of NiO and NiCr2O4 means that the latter phase remains as dispersed particles, providing much less diffusional blocking. At higher chromium levels, continuous scales of Cr2O3 develop, and the rate constant drops sharply (Figure 7.11). The chromium levels predicted from Equation (7.5) to be necessary for chromia scale formation are shown in Table 6.8. They are in only approximate agreement with the experimental results of Figure 7.11. The slower rate of chromia scaling on nickel-base alloys is attributed to more severe chromium depletion resulting from its slower diffusion in these
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Chapter 7 Alloy Oxidation III: Multiphase Scales
Figure 7.11 Oxidation rates of M–Cr alloys in pure O2 at 1,0001C [36]. Reproduced with permission from Wiley-VCH.
alloys. Under these circumstances, alloy diffusion contributes to oxidation rate control [37], as discussed in Section 5.4. Iron-base alloys with chromium levels near the critical value N Cr;min do not achieve long-term oxidation resistance. The high solubility in Cr2O3 of iron permits its outward diffusion and the formation of iron-rich oxides at the scale surface. Chromium levels of about 25 wt% are required to prevent this. Nickelbase alloys are superior in this respect, partly as a consequence of the much lower solubility of nickel in Cr2O3, and perhaps reflecting also differences in diffusion coefficients, as is discussed below. To understand the difference between Fe–Cr and Ni–Cr oxidation in detail, and also to analyse the effects of additional alloy components it is necessary to consider diffusion in the scale.
7.3.2 Transport processes in chromia scales Much of the early data on Cr2O3 scale growth rates and mechanisms have been reviewed by Kofstad [39], who concluded that chromia scales grow by outward diffusion of chromium. Although the defect properties of Cr2O3 are not fully understood (see Section 3.9), subsequent work has shown that grain boundary
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diffusion is much faster than lattice diffusion for both chromium [40, 41] and oxygen [41–43]. These data indicate that chromia growth on simple binary alloys is supported mainly by chromium diffusion, but oxygen diffusion also contributes to overall mass transport. For spinel MCr2O4 to grow on top of the Cr2O3 scale layer, the metal M must also diffuse outwards. Lobnig et al. [44] studied the diffusion of vacuum deposited Fe, Ni, Mn and Cr into thin (1–2 mm) Cr2O3 scales, which had been grown on Fe–20Cr or Fe–20Cr–12Ni alloys. By analysing the penetration profile shapes, they determined the diffusion coefficient values shown in Table 7.2 for short diffusion times. Assuming a value for the boundary width d ¼ 1 nm, the DB values for Fe, Cr and Ni were found to be several orders of magnitude greater than the corresponding lattice diffusion coefficients. Surface roughness led to inaccuracies in the estimates of both DL and DB , but the errors were small compared with the orders of magnitude differences in the data of Table 7.2. Using Equation (3.113) to calculate effective values Deff , and for simplicity assuming cubic oxide grains, we see that Deff ðCrÞ has closely similar values in the two scales: 1015–1014 cm2 s1. Furthermore Deff ðFeÞ Deff ðCrÞ for Fe–20Cr, thereby explaining the rapid growth of an outer FeCr2O4 layer on high iron activity alloys. The values of Deff ðNiÞ are, in the Fe–20Cr scale, an order of magnitude lower that that of chromium, but in the Fe–20Cr–12Ni scale about half that of chromium. In the absence of a value for a Ni–Cr scale, the data for DðNiÞ seems inconclusive. The relatively large value of Deff ðFeÞ in Cr2O3 is relevant to the technique of ‘‘pre-oxidation’’. This is the method of first oxidizing an alloy at low pO2 so that FeO is unstable, and the selective oxidation of chromium assured. After a protective Cr2O3 scale has formed, the alloy is placed into service at what will usually be a higher pO2 value. Unfortunately, the high oxygen pressure provides a gradient in aO which constitutes a driving force for iron diffusion through the chromia scale to form iron oxide. Pre-oxidation of Fe–9Cr and Fe–7.5Cr in H2/H2O (pO2 ¼ 6 1020 atm) at 8501C produced chromia scales of about 1 mm thickness [45]. Subsequent exposure, without change in temperature, to pure Table 7.2 Values of lattice diffusion coefficient DL, grain boundary diffusion coefficient DB times boundary width d, and grain size, Dt in Cr2O3 scales at 9001C [44] Base alloy
Diffusant
DL (cm2 s1)
dDB (cm3 s1)
Dt (mm)
Fe–20Cr
Fe Ni Mn Cr Fe Ni Mn Cr
2 1014 3 1015 2 1014 1 1014 4 1015 5 1015 2 1013 7 1015
1 1016 2 1019 2 1017 1 1016 1 107
0.1 0.2 0.1 0.1 0.1 0.2 0.4 0.1
Fe–20Cr–12Ni
5 1019 – 2 1017
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oxygen at 1 atm led to continued slow growth of these scales until the rates accelerated with the precipitation of iron-rich oxide at the scale–gas interface after 2–3 weeks. Taking Deff ðFeÞ ¼ 1 1015 cm2 s1 , and estimating the iron diffusion penetration distance as X2 4Deff ðFeÞt
(7.7)
a penetration time of 29 days is calculated for a 1 mm scale. Agreement with the experimentally observed times for iron to reach the chromia scale surface can be regarded as satisfactory, given the approximate basis of Equation (7.7) and the uncertainty in the value of Deff ðFeÞ. We therefore conclude that pre-oxidation of marginal Fe–Cr alloys needs careful investigation before use. The high temperature growth of relatively thick Cr2O3 scales before service at substantially lower temperatures could nonetheless prove successful.
7.4. TERNARY ALLOY OXIDATION Our interest is in alloys for which selective oxidation of one component leads to the development of a slow-growing, protective scale. We therefore consider firstly alloys in which one component is much more reactive to oxygen than the other two, and secondly alloys in which two components are each much more reactive than the third. The first case is exemplified by Fe–Ni–Cr, the basis of heatresisting steels, and Ni–Pt–Al, the basis of a number of high temperature coatings. Examples of the second are Fe–Cr–Al (Kanthal) and Ni–Cr–Al (superalloys and Inconels). In many cases the reactive metals can be regarded as solutes in iron and/or nickel, although they may also partition to minority phases.
7.4.1 Fe–Ni–Cr alloys Single-phase Fe–Ni–Cr alloys should in principle be easily understood. However, accurate prediction of N Cr;min even for binary alloys was found to be difficult (Table 6.8). At this time it cannot even be attempted for the ternary alloys, because data for N ðsÞ O and DO in Fe–Ni binaries are not available. In the case of attack by carbon, the necessary data is available and provides a quantitative description of Fe–Ni–Cr carburization (Chapter 9). In the absence of such data for oxidation, discussion is necessarily qualitative. As seen in Figure 7.12, differences between the Fe–Cr and Ni–Cr systems are reflected in ternary alloy oxidation rates. For a given chromium level, oxidation rates decrease with increasing Ni/Fe ratio. At chromium levels less than about 10%, the differences reflect changing volume fractions of Fe1dO and the slower diffusing NixFe3xO4, and at high nickel levels, NiFe2O4 and NiO [38]. Scales formed on alloys with more than about 20% chromium consist of an inner Cr2O3 layer, overlaid by spinel. Increases in Ni/Fe ratio lead to decreases in alloy iron activity and its consequently smaller solubility in Cr2O3. This in turn affects the extent of spinel formation. The behaviour shown in Figure 7.12 is relevant to the performance of heat-resisting steels, which typically contain about
7.4. Ternary Alloy Oxidation
331
Figure 7.12 Oxidation weight gains of Fe–Ni–Cr alloys reacted in pure O2 at 1,0001C for 100 h [38]. With kind permission from Springer Science and Business Media.
10–20 wt% nickel, and are austenitic. At the higher N Ni levels, long-term protection against iron spinel formation can be achieved. Consequently, austenitic stainless and heat-resisting steels based on formulations in the range Fe–(10–20)Ni–(20–25)Cr are widely used at temperatures up to 900–1,1001C, depending on the atmosphere. Examples of alloy compositions are shown in Appendix A.
7.4.2 Ni–Pt–Al alloys It has been known for some time [46–48] that the addition of platinum to nickel aluminide intermetallics improves their oxidation resistance. Platinum-modified b-NiAl is used as a bondcoat on superalloy components in turbines [49] (Section 1.3) and new coatings based on g=g0 constitutions have recently been investigated [50–52]. An isothermal section of the Ni–Pt–Al phase diagram in Figure 7.13 shows that the solubility of platinum in each of the g; g0 and b phases is large. Copland [54, 55] has shown that substitution of platinum for nickel in these phases at constant N Al has the effect of reducing the aAl value.
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Figure 7.13 Isothermal section (T ¼ 1,1501C) of Ni–Pt–Al phase diagram. Reprinted from Ref. [53] with permission from Elsevier.
Platinum is not completely inert to oxygen at high temperatures, instead forming a volatile oxide Pt þ O2 ¼ PtO2 ; DG ¼ 164; 300 3:89TðJ mol1 Þ
(7.8)
If pO2 ¼ 1 atm, then pPtO2 values of 2 106–4 105 atm are predicted for 1,100–1,2001C. However, exposure of platinum-bearing nickel aluminides to oxygen or air leads to the growth of external scales which protect the platinum from oxidation. Oxidation of b-NiAl produces a scale of pure Al2O3. Although this behaviour is in regime III of Pettit’s classification (Figure 7.2), the reaction rate is determined by which alumina phase grows (Section 5.7) and the frequency of scale spallation. The extent of spallation, which can occur under isothermal conditions, is determined by cavity formation at the scale–alloy interface (Section 5.8) and the amount of impurity sulfur in the system [56–61]. The nature of the sulfur effect is discussed in Section 7.5. For present purposes, the important finding is that the addition of platinum to b-NiAl suppresses spallation. The cavities developed at a b-NiAl/Al2O3 interface (Figure 5.12) are observed even in the very early stages of reaction [62, 63]. The addition of platinum to the intermetallic decreases both their size and number density, whether or not sulfur is present in the alloy [64–67]. This decrease in void volume fraction is not due to
7.4. Ternary Alloy Oxidation
333
any decrease in the amount of aluminium oxidation. In fact, alumina scaling rates are accelerated by the presence of platinum [68, 69] as shown in Figure 7.14. As is discussed in Section 5.8, the cavities are Kirkendall voids, and their accumulation represents the mismatch between aluminium and nickel alloy fluxes. These fluxes are driven by the chemical potential gradients arising from the concentration profiles in the alloy (Figure 5.3): J i ¼ Ci Bi
@ ln ai @x
(7.9)
Figure 7.14 Effect of Pt on NiAl oxidation at 1,1001C for low and high sulfur alloys [69]. With kind permission from Springer Science and Business Media.
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Chapter 7 Alloy Oxidation III: Multiphase Scales
The presence of platinum depresses aAl , increasing the chemical potential gradient and hence the flux of aluminium. This accounts for the reduction of Kirkendall porosity. It also supports the more rapid alumina scale growth observed for b-Ni(Pt)Al. The increased DAl in Ni(Pt)Al has been observed directly in diffusion couple studies [51]. The decrease in cavity formation decreases the amount of bare metal surface beneath the oxide where sulfur may segregate. Somewhat similar effects are observed for g0 and g=g0 alloys when platinum is added. In the absence of platinum, these alloys fall in regime II of Figure 7.2, and are marginal alumina formers, growing NiO and NiAl2O4 on top of their alumina scales. When platinum is added to the alloys, NiO formation is decreased, and suppressed completely at high platinum levels [70]. Gleeson et al. [51, 70] ascribe this to two effects: the chemical potential gradient effect described above, and the decrease in oxygen permeability in the gphase observed with increasing platinum levels. As seen in Equation (7.5), such a decrease reduces the initial value of N ðoÞ Al required to form external rather than internal Al2O3. The addition of platinum to Ni–Al alloys can profoundly affect their oxidation behaviour, despite the fact that platinum does not participate directly in the oxidation process. The effects arise out of the strong interactions within the alloy between platinum and the other constituents. These change aAl values, and hence aluminium diffusion rates, and appear also to lower oxygen permeabilities, at least in the gphase. Faster aluminium diffusion not only helps stabilize the alumina scale, but decreases the amount of Kirkendall voidage. Attention is now directed to the technologically important M–Cr–Al alloys, where M is Fe or Ni. Whilst also important, Co–Cr–Al alloys are less commonly used, and will not be discussed here. It is important to enquire into the circumstances under which these alloys act as chromia or alumina formers. A very large and complex literature has accumulated in this area, extensive reviews of which have been provided by Wood and Stott [71] and Stott et al. [72].
7.4.3 Ni–Cr–Al alloys The phase constitutions of these alloys [73] can be seen in Figure 5.36. The g-Ni phase has extensive solubilities for both aluminium and chromium, and the Ni–Al intermetallics have smaller, but significant solubilities for chromium. The construction of a three-dimensional quaternary Ni–Cr–Al–O diagram for each temperature is unrewarding. Instead, a concise way of describing the oxidation behaviour of such a broad range of alloy compositions and correspondingly diverse set of phase assemblages is provided by oxide mapping [74–77]. Compositional regions in which particular oxides predominate in the steadystate scale are plotted onto the Gibbs triangle. The map proposed by Wallwork and Hed [75] for Ni–Cr–Al at 1,0001C is shown in Figure 7.15. Although empirical, these maps can be very useful, for example in indicating the relationship between the Ni/Cr ratio and the ability to form a highly protective alumina scale.
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7.4. Ternary Alloy Oxidation
Figure 7.15 Oxide map for Ni–Cr–Al ternaries at 1,0001C [75]. With kind permission from Springer Science and Business Media.
The thermodynamics of the oxide system are useful in understanding the development of different reaction morphologies. We enquire as to the location where chromium-rich oxides would be stable in the oxide layer sequence shown in Figure 7.5, by altering the alloy to Ni–Cr–Al, and considering the reaction 2 Al þCr2 O3 ¼ 2 Cr þAl2 O3 for which the equilibrium condition is i9 8 h < DGf ðAl2 O3 Þ DGf ðCr2 O3 Þ = aCr ¼ exp : ; 2RT aAl
(7.10)
(7.11)
Alumina is much more stable than chromia (Table 2.1), and a value of aCr =aAl ¼ 3:6 108 is calculated for 1,0001C. It is therefore concluded that Cr2O3 could be stable in contact with an alloy only if N Al =N Cr 3 109 . Put another way, the equilibrium oxygen potential at a Cr2O3–alloy interface is much higher than the value required to oxidize aluminium at any significant concentration. Thus it is concluded that alumina will form beneath a chromia layer, either as a continuous layer or as an internal precipitate. Examples are shown in Figure 5.1c and Figure 7.16. The development of these morphologies was clarified by the transient oxidation studies carried out by Pettit et al. [77, 78] on alloys containing 2–30 Cr and 1–9 Al at 1,000–1,2001C. Rapid initial reaction formed a scale principally of mixed spinel, Ni(Cr,Al)2O4, plus isolated grains of NiO and Cr2O3. The ao value corresponding to spinel–alloy equilibrium is higher than the values required to
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Chapter 7 Alloy Oxidation III: Multiphase Scales
Figure 7.16 Alumina layer (black) developing on Ni–9Fe–26Cr–2.7Al.
form either Cr2O3 or Al2O3. The more abundant chromium consequently reacted with spinel to form a continuous Cr2O3 layer. Reaction (7.10) then took place at the scale–alloy interface producing transient alumina phases. These subsequently transformed into a-Al2O3 which coalesced to form a continuous, but non-uniform layer. The remnants of NiO and Cr2O3 on the outside of the alumina layer were then isolated from the alloys, and ceased to grow. At these high temperatures, the chromia was eventually lost as vapour through reaction (1.35) and the NiO was incorporated into the scale. It is important to note that a-Al2O3 is more easily formed and maintained as an external scale on Ni–Cr–Al alloys than on Ni–Al alloys. This is explicit in the oxide maps of Figures 7.2 and 7.15. We will return to this point after first reviewing briefly the Fe–Cr–Al system.
7.4.4 Fe–Cr–Al alloys The Fe–Cr–Al system provides the basis for Kanthal and similar alloys (Table 5.1). The interesting feature of these alloys is their ability to form highly protective alumina scales at quite low N Al levels. The oxide map in Figure 7.17 shows that alloys containing more than about 20 wt% chromium require only 2–3 wt% aluminium to form a-Al2O3. This is much less than the value of N Al 40:14 (i.e. W7.5 wt%) reported [32] for a binary alloy. Because the diffusion properties of the various oxides differ so much, oxidation rates vary strongly with alloy composition.
7.4. Ternary Alloy Oxidation
337
Figure 7.17 Oxide map for Fe–Cr–Al ternaries at temperatures greater than 1,0001C [25].
Figure 7.18 Relative oxidation rates of Fe–Cr–Al and Ni–Cr–Al alloys at 1,000 and 1,2001C [71]. For identification of curves see text. Published with permission from r NACE International 1983.
Figure 7.18 compares the oxidation kinetics of several Fe–Cr–Al compositions with those of two sorts of Ni–Cr–Al alloys. The very rapid rates observed for dilute Fe–Cr–Al alloys correspond to growth of an iron-rich oxide layer above a layer of mixed oxides, and internal precipitation of aluminium and chromiumrich oxides. The intermediate curves were observed for high chromium and low
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Chapter 7 Alloy Oxidation III: Multiphase Scales
aluminium levels. They represent growth of a chromia scale, interspersed with occasional iron-rich oxide modules. Depending on N Al level, alumina precipitated internally or formed an almost continuous layer under the other oxides. The slow oxidation kinetics corresponded to alumina scale growth on alloys containing about 5 wt % aluminium. The two Ni–Cr–Al kinetic curves corresponded to chromia and alumina scaling. The initial, transient oxidation of Fe–Cr–Al is similar to that of Ni–Cr–Al, although the establishment of a protective a-Al2O3 scale is easier on the former [79]. Breakdown of the scales is more catastrophic for the iron-base alloys, simply because iron-rich oxides grow faster than their nickel equivalents. However, it is the lengthy period of steady-state oxidation following the initial transient which is of most interest. As is clear from Figure 7.18, the establishment and maintenance of an alumina scale is essential for successful performance. It is therefore necessary to understand the mechanism whereby chromium additions reduce the value of N Al;min required for alumina scale formation. This has come to be known as the ‘‘third-element effect’’ which is discussed in the next section.
7.4.5 Third-element effect The third element in question is that component of a ternary alloy which forms an oxide of stability intermediate to those of the other two metals. Thus chromium is the third element in both Ni–Cr–Al and Fe–Cr–Al (Table 2.1). Wagner [80] examined early work [81, 82] on the Cu–Zn–Al system, and noted that ternary alloys formed protective Al2O3 scales at lower N Al values than were required for Cu–Al binaries. He suggested that the explanation lay in the ability of zinc (the third element) to lower the oxygen activity at the scale–alloy interface. Consider first a dilute binary Cu–Al alloy reacted at a high pO2 so that Cu2O grows in contact with the alloy. The value of ao at the scale–metal interface is then set by the Cu/Cu2O equilibrium which corresponds to pO2 ¼ 1010 atm at 8501C, the temperature of oxidation. Now consider the effect of adding to the alloy sufficient zinc to form a surface oxide layer. Because ZnO is more stable than Cu2O, it is the former which develops at the scale–alloy interface, and pO2 is now controlled by the Zn/ZnO equilibrium. Allowing for the low aZn value in the depleted alloy, we calculate from the thermodynamic data of Table 2.1, that pO2 1021 atm. Recalling that the dissolved oxygen concentration is given by 5 Sievert’s Equation (2.71), it is seen that N ðsÞ o in copper is 10 times lower beneath a ZnO scale than under one of Cu2O. Accordingly, the balance between inward oxygen diffusion to cause internal aluminium oxidation and outward aluminium diffusion to form an external scale is altered (Equation (7.5)), and protective scale formation is more favoured. It is recognized that for such a mechanism to function, the third element must have an oxide of intermediate stability, so that it displaces Cu2O and lowers the interface pO2 value, but is not more stable than Al2O3. If it were more stable, it would form deep within the alloy or itself make up the most stable scale. This model can be tested for the Ni–Cr–Al and Fe–Cr–Al systems, assuming that a transient chromia scale controls the alloy surface oxygen activity. If the
7.4. Ternary Alloy Oxidation
339
residual aCr value is estimated as 0.1, then an equilibrium value of pO2 ¼ 1:5 1015 atm is estimated for 1,2001C. Evaluating the Sievert’s law constant in Equation (2.71) from the data in Table 2.2, one calculates N ðsÞ o equal to 2.2 107 and 6.4 106 in nickel and ferritic iron, respectively. Substitution of these values into Equation (7.5) along with estimates for DO ; DAl then leads to N Al;min estimates of 0.005 in nickel-base alloys (0.3 wt%) and 0.002 in iron-base alloys (0.1 wt%). These values are certainly much lower than those calculated for binary alloys under Rhines pack conditions (Table 6.8). Unfortunately, they are unrealistic, being also much lower than the experimentally observed requirements, summarized in Figures 7.17 and 7.19. At 1,2001C, the results of Giggins and Pettit [77] showed that N Al ¼ 0:03520:11 was required in the range N Cr ¼ 020:4. As noted in Section 7.2, the establishment of a protective Al2O3 scale on binary alloys required N Al to be high enough not only to avoid internal oxidation, but sufficient to ensure the scale was made up of alumina only, rather than a mixture of oxides. In a sense, the addition of chromium to the alloy achieves the same purpose of converting the scale from a multiphase reaction product to one of alumina only. A number of proposals have been advanced to account for this effect. The presence of a third metal will inevitably alter the thermodynamics of the alloy subsurface region where the competition between different oxidation processes takes place. In principle, the activities and effective diffusion coefficients of all components — M, Cr, Al and O — will vary with composition (Section 2.7), and affect the competition between internal and external oxidation [83]. We have already seen that the addition of even the oxygen unreactive metal platinum plays an important role in its effect on aAl . When the third element is reactive to oxygen, then it will obviously effect the activity, and hence solubility, of oxygen. The example of chromium additions decreasing N ðsÞ O in Ni–Al is shown in Figure 6.41. Such an effect would decrease inward oxygen diffusion, lessening the likelihood of internal oxidation.
Figure 7.19 Minimum NðoÞ Al for exclusive Al2 O3 scale formation at 1,2001C: continuous line measured [77], dashed lines calculated [83]. Reproduced by permission of The Electrochemical Society.
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Ternary diffusion interactions between the two oxygen reactive metals need also to be considered. Nesbitt [16] examined the effect of chromium additions on the aluminium flux in oxidizing Ni–Cr–Al alloys. Application of Equation (2.115) to this system yields @CAl @CCr DAlCr (7.12) J Al ¼ DAlAl @x @x and it is recognized that oxidation leads to a gradient in CCr in the same direction as that of CAl . Measurements by Nesbitt and Heckel [84] showed that DAlCr was positive, and varied in magnitude with composition from 20% to 50% of DAlAl in the g-phase at 1,2001C. Thus the second term in Equation (7.12) leads to an increase in J Al , and one which can be substantial. Nesbitt [16] applied Equation (7.12) to calculate the minimum value of N ðoÞ Al necessary to sustain growth of an external alumina scale, using Wagner’s criterion (Equation (5.22)). The results of the calculation are compared with measured data [77] in Figure 7.19, where agreement seems to be reasonable in the range N Cr ¼ 0:0520:20. However, neither the Dij nor kc is particularly sensitive to N Cr . The consequent insensitivity of N Al;min to the value of N Cr indicates that the basic concept is inapplicable [16]. Zhang et al. [33] have pointed out that the transition involved in achieving exclusive alumina scaling of both Fe–Cr–Al and Ni–Cr–Al is one away from formation of a multiphase scale. Thus the third-element effect envisaged by ðoÞ Wagner is not involved, there being no internal oxidation except at very low N Al values. Applying a model proposed by Niu and Gesmundo [85], suggests that the third-element effect in M–Cr–Al systems is simply due to a destabilization of the fast growing iron or nickel oxides as the value of N Cr is increased. The effect is strong, because Cr2O3 and Al2O3 are completely miscible, and the presence of chromium increases the total concentration ðN Cr;i þ N Al;i Þ at the alloy–scale interface, promoting the formation of ðAl; CrÞ2 O3 . No quantitative verification of this proposal is yet available. It seems likely that the third-element effect includes a number of factors which are simultaneously in operation. In addition to the thermodynamic and kinetic effects mentioned so far, it is also possible that the third element may, if dilute, oxidize internally, increasing the total volume of internal oxide, g, thereby promoting scale formation according to Equation (7.5). In this case, ðN B;min þ N C;min Þ should be considered, and the right-hand number of the equation becomes the sum of two terms for the two oxidizing metals. Such an approach was suggested by Boggs [86] as a basis for Fe–Si–Al alloy development, and has been explored quantitatively by Niu et al. [13] for Ni–Si–Al alloys. In the latter case, the authors calculated that the value of N Al;min at 1,0001C was reduced from 0.11 to 0.05 as N Si was increased from zero to 0.065. This prediction was in accord with experimental results obtained by these authors and others [87–89] for dilute alloys. However, an alloy with N Si ¼ 0:05 and N Al ¼ 0:20 oxidized internally [90]. This last finding illustrates one aspect of the weakness of the usual diffusion models: they ignore microstructural effects, assuming that diffusion is always via the alloy lattice, or its interstitial sites in the case of oxygen. As noted by
7.5. Scale Spallation
341
Niu et al. [13], the internal precipitation of SiO2 and Al2O3 is accompanied by very large volume changes and the formation of high dislocation densities. This favours rapid diffusion. Another factor is the frequent formation of aligned rod- and lath-shaped precipitates when aluminium and silicon oxidize internally (Figure 6.32), and the resulting rapid diffusion of oxygen along the oxide–matrix interfaces. In short, the values used for DO in Equation (7.5) are inappropriately low. Similarly, effective values of DB are enhanced if the alloy subsurface region is in a cold worked condition before service. A further weakness of the diffusion theory approach is its failure to deal with the kinetics of oxide nucleation and growth. As seen in Section 5.7, formation of Cr2O3 accelerates the rate at which the isomorphous, and highly protective a-modification of Al2O3 is formed. The greater ease of a-Al2O3 formation on Fe–Cr–Al may reflect also a similar templating effect due to Fe2O3. A detailed study of oxide nucleation and growth kinetics during the transient stages of M–Cr–Al oxidation reactions would be of value. Although predictive capacity is limited, our empirical knowledge of the oxidation behaviour of M–Cr–Al alloys is sufficient to allow the identification of appropriate compositions for alumina formation. However, none of these ternary alloys will be of practical value, because the alumina scales are prone to spallation. This important defect and the mean for its rectification are now considered.
7.5. SCALE SPALLATION Alumina scales formed on both M–Al and M–Cr–Al spall when cooled from reaction temperature. The result of scale spallation is that oxidizing gas gains access to depleted alloy surface, which might not be able to reform protective oxide. As discussed in Section 2.10, stress in the scale-alloy system results from the differential thermal contraction of the metal and oxide on cooling. The stress can be rapidly induced and therefore cannot be relieved by time-dependent creep processes. Chromia scales also fail mechanically, but are less susceptible. This generalization may reflect partly the different thermal expansion coefficients, values being particularly low for ferritic chromia formers (Table 2.4). Scale spallation, and also cracking, can sometimes occur during isothermal oxidation. These failures result from growth stresses rather than thermal ones, as discussed briefly in Section 2.10. Scale failure occurs when the magnitude of the stress and/or the strain rate are too great for the scale–alloy system to accommodate by deformation. Factors affecting the initiation of failure therefore include the microstructure, defect size and frequency, and intrinsic mechanical properties of the oxide, the alloy and the interface between them [72, 91, 92]. The topic is a large one, and no attempt is made to deal with it here. Instead, attention is directed to the factors which differentiate spallation-prone and spallation-resistant systems.
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A useful way of examining the factors contributing to scale spallation is provided by the techniques of fracture mechanics [93]. The energy released by the growth of an existing defect is compared with the work done in creating the new surfaces in, for example, extending a crack. When the energy released is large enough, the defect grows spontaneously. A major source of mechanical energy is the thermally induced stress resulting from rapid cooling after oxidation. The resulting stored elastic energy per unit area of scale–alloy interface, W n , is written as W n ¼ ð1 np ÞEOX ðDTDaÞ2 X
(7.13a)
n
and the associated elastic stress s
sn ¼
W n EOX 1 nP
1=2 (7.13b)
where the notation of Section 2.10 has been employed. Clearly, the energy available to cause mechanical damage to the scale increases with its thickness. Various modes of scale failure are possible, and can be investigated using the basic result for linear plastic deformation that crack growth occurs when pffiffiffiffiffi sc f pa Kc (7.14) where sc is the critical stress required to cause crack growth, 2a the length of a defect (crack, void, etc.), f a numerical factor related to the crack shape and precise failure mode and Kc a material property representing resistance to crack propagation. Larger values of a correspond to greater susceptibility to spallation.
7.5.1 The sulfur effect The presence of sulfur as an alloy impurity is associated with a greater tendency to scale spallation. This is true not only for b-NiAl, but also for M–Cr–Al alumina formers and a variety of chromia formers. This is made clear by the finding that ultra low (1 ppm) sulfur alloys evidence much better scale retention than do the same alloys at normal sulfur levels of tens of parts per million [94, 95]. Smialek et al. [96–100] confirmed the conclusion by demonstrating that desulfurizing alloys improved their alumina scale retention. Several workers [56, 57, 96, 101–103] have shown that sulfur from the alloy segregates to the scale–metal interface. Sigler [104] suggested that the sulfur weakens the interface in the same way as it embrittles metal grain boundaries. This would correspond to a decrease in Kc in Equation (7.14). Another view developed by Grabke et al. [105–107] is that sulfur adsorbs on free metal surfaces within voids at the scale–alloy interface. This would stabilize the voids, permitting them to grow. This corresponds to an increase in c in Equation (7.14), decreasing the critical stress required for spallation. Other impurities such as carbon or nitrogen have been suggested [104, 108–110] as playing a role in scale adhesion. Alloy desulfurizing treatments also remove carbon, so any carbon effect is masked in those experiments. However, experimental NiAl alloys with different Hf/C ratios [109] develop different
7.5. Scale Spallation
343
degrees of convolution at their scale–alloy interfaces. When the Hf/C solute atom ratio is o1, the degree of convolution increases, as does the extent of spallation. Presumably, this indicates that when insufficient hafnium is available to precipitate the carbon as HfC, the remaining carbon affects the interface. The mechanism of this interaction is not known.
7.5.2 Interfacial voids and scale detachment Voids at the scale–alloy interface or regions of scale detachment are examples of defects which can act as crack or spallation initiation sites. Their formation and growth are therefore likely preludes to scale failure. Possible explanations for such defects include vacancy injection into the alloy followed by coalescence at a suitable nucleation site, and Kirkendall porosity. Since a-Al2O3 scales grow mainly by inward diffusion of oxygen along grain boundaries, as shown by 18 O2 tracer diffusion studies [111–113], the vacancy injection model appears to be inapplicable. As discussed in Section 5.8, the Kirkendall effect accounts satisfactorily for the interfacial voids formed at the b-NiAl surface beneath an a-Al2O3 scale. However, growth of the transient aluminas, which is much faster, may be supported by grain boundary cation diffusion [114, 115]. Thus interfacial porosity could be developed by vacancy injection during the initial transient reaction period, if it were long lived. Chromia scales also grow by grain boundary diffusion (Section 3.9 and Section 7.3), and 18 O2 tracer studies have shown that chromium is the principal differing species. In this case, void nucleation at the scale–metal interface might result from vacancy injection into the metal, their supersaturation and condensation at the interface. Important features common to both Cr2O3 and a-Al2O3 scale growth are the continuation of oxidation despite the presence of voids, and the development of wrinkles in the oxide. The resulting scale appearance is shown schematically in Figure 7.20. The scales continue to grow because the vapour pressures of chromium [116] and aluminium [117] are high enough to sustain the rather slow scale thickening rates. A more interesting question concerns the driving force for wrinkle development and enlargement of the underlying voids. A frequently proposed explanation [72, 114, 118, 119] is that of oxide formation within the scale interior, causing a compressive growth stress which is relieved by wrinkling. Such a mechanism was first proposed by Rhines and Wolf [120] to explain the development of compressive stress in growing NiO scales. For this to happen, it is clear that both metal and oxygen must be delivered to the growth locations in the scale interior. As noted above, tracer diffusion measurements have shown that metal diffusion predominates in chromia growth whereas oxygen diffusion is the
Figure 7.20 Detachment of scales and the development of wrinkles.
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principal process in a-Al2O3 growth. However, they are not the only processes involved. In the case of chromia, tracer diffusion studies [121] show that there is also a contribution from inward oxygen diffusion. Similarly, a-Al2O3 scale growth involves the diffusion of metal as well as oxygen [111]. However, although mass transport of both species is evidently available, the mechanism whereby oxide precipitates within a matrix of the same oxide is not obvious. Indeed, it would be impossible if the diffusion species were lattice defects, in local equilibrium with each other via h i a2M a3O ¼ exp DGf ðM2 O3 Þ=RT (7.15) together with defect reactions such as Equations (3.123) and 1 2O2
2 000 ¼ OX O þ 3V M þ 2h
(7.16)
No mechanism for achieving the supersaturation necessary to precipitate new oxide is apparent in this case. The necessary conditions for new oxide formation can be achieved at the scale–gas and scale–alloy interfaces. They might also be achievable at grain boundaries if the mobile species are not in strict local equilibrium with the adjacent oxide. As discussed in Section 4.4, chromia scales are permeable to molecular species such as N2 and CO, presumably via grain boundary diffusion. Tracer diffusion measurements have shown [122] that H2O also penetrates chromia scales. Thus it seems likely that the O2 species can also enter the grain boundaries, enabling supersaturation with respect to Equation (7.15) to occur. The development of scale wrinkles (or rumples) need not lead to detachment if (a) no defects capable of acting as stress raisers are present and (b) the alloy can deform to remain in contact with the elongated scale. The role of sulfur impurities in stabilizing interfacial voids could therefore be important. Even in its absence, a rumpled interface develops local tensile stresses which might exceed the critical stress level necessary to create a void [123]. Most of the factors mentioned here as relevant to scale detachment and spallation are affected profoundly by the presence in the alloy of small concentrations of ‘‘reactive elements’’, i.e. metals with exceptionally strong affinity for oxygen, such as Hf, Ce, Y and La.
7.5.3 Reactive element effects An application of the reactive element effect (the addition of Ce to a Ni–Cr alloy) was patented by Pfeil [124] in 1937. Since then, reactive elements additions have become a key part of high temperature alloy design, supported by a very large research effort. Much of this activity has been reviewed by Stringer [125], Prescott and Graham [126] and Pint [127]. Reactive element additions greatly improve the ability of chromia and alumina-forming alloys to resist scale spallation. Understanding this phenomenon has been made difficult by the multiplicity of effects reactive elements have
7.5. Scale Spallation
345
on alloy–scale systems. The most obvious of these are the changes in scaling rate and mass transfer mechanisms. Tracer diffusion studies with 18 O2 [112, 121] show that the addition of reactive elements to chromia-forming alloys slows the diffusion of chromium through the scales. As a result, scale growth is due mainly to the inward diffusion of oxygen. Similar measurements on alumina formers [111, 112, 128–130] show that the transport mechanism is changed from mixed oxygen and aluminium transport to principally oxygen transport when a reactive element is present. However, because a-Al2O3 growth is in any case controlled by oxygen transport, the effect on the overall rate is less than in the chromia case. To the extent that oxide scales are made thinner, their susceptibility to spallation is predicted from Equation (7.13) to be lessened. Oxide microstructures are altered by the presence of reactive elements. Chromia scales become finer grained, with some increase in grain size in the growth direction, i.e. towards the scale–metal interface [131–133]. Alumina scales are changed by reactive elements from coarse and equiaxed to fine and columnar [118, 119, 134]. An example of this effect is shown in Figure 7.21. The oxide–alloy interface is also altered by the presence of reactive elements. Sulfur segregation to this interface is found to be suppressed [113, 119, 134, 135], wrinkling and scale detachment is decreased [103, 118, 136], oxide intrusions or ‘‘pegs’’ in some case grow into the alloy [124] and the interface is strengthened [61] in the case of a desulfurized alloy. The ways in which this multitude of effects lead to the beneficial outcome of much reduced spallation have been the subject of considerable debate. However, recent advances in instrumentation have served to resolve a number of disputes. Auger election spectroscopy experiments have proven that sulfur does indeed segregate to alloy–scale interfaces [103, 105, 137, 138], and analytical TEM work [102, 139] has shown that this occurs in regions of contact, not just in voids or cavities. A series of scanning transmission electron microscopy studies has made clear that reactive elements segregate to oxide grain boundaries, and they have also been found at the scale–alloy interface [127]. It is the enrichment of reactive elements at oxide grain boundaries which alters their transport properties. Whilst details of the mechanism are unclear, it is relevant to note that the reactive element oxides HfO2, CeO2, Y2O3, ZrO2, etc., are themselves oxygen diffusers. Reactive elements have a strong affinity for sulfur as well as oxygen. They are therefore able to desulfurize the alloy, forming sulfide or oxysulfide particles, and preventing sulfur from contaminating the scale–alloy interface. An alternative possibility is the preferential segregation of sulfur to surfaces of internal reactive element oxide particles. Removal of sulfur strengthens the scale–alloy interface, increasing its Kc value and therefore increasing spallation resistance (Equation (7.14)). In the absence of sulfur, nucleation of voids at this interface may also be more difficult. Another factor improving scale adhesion is the greatly decreased extent of rumpling. This is attributed [72, 114, 119] to the reduction in growth stresses resulting from the fact that new oxide no longer forms within the scale when only
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Chapter 7 Alloy Oxidation III: Multiphase Scales
Figure 7.21 Fracture cross-sections of a-Al2 O3 scales grown at 1,2001C on b-NiAl: (a) equiaxed oxide on undoped intermetallics and (b) columnar oxide on NiAl+Hf.
7.6. Effects of Minor Alloying Additions
347
one component diffuses. Of course this would not be relevant to the differential thermal contraction stresses generated during cooling. However, the reduced scale thickness is of benefit, as seen in Equation (7.13). Finally, it is to be observed that if reactive element additions favour inward oxygen diffusion, then oxide growth occurs at the scale–alloy interface, preventing the growth of voids there. In this case, c is very small, and according to Equation (7.14), spallation resistance is enhanced. Reactive elements also change the transient oxidation stage of reaction. Selective oxidation of chromium is promoted [140, 141], perhaps nucleated by reactive element oxide particles [142]. In the case of alumina formers, much of the transient behaviour is associated with the rapid growth of metastable y-Al2O3, the transformation of which into the a-phase is discussed in Section 5.7. Unfortunately, there appears to be no single, unified description available for the effect of reactive elements on this transformation [127]. The various reactive elements differ in effectiveness in different alloy systems. An important factor is the limited solubility of these elements, which varies with both the identity of the additive and the nature of the solvent alloy. Excessive additions can lead to the precipitation of intermetallic phases which are susceptible to internal oxidation. The effects of a number of different additives on alumina scale performance on a variety of alloys have been reviewed by Hou [143].
7.6. EFFECTS OF MINOR ALLOYING ADDITIONS A number of other elements are commonly present in heat-resisting alloys. These can derive from the processing operations used to manufacture the alloy, or can be deliberately added to enhance alloy properties. Examples of the former group are silicon, used to deoxidize steels, and manganese, used as a desulfurizer. Examples of the latter are titanium, added to steels as a carbide former and to superalloys as a g0 -Ni3(Ti,Al) former, and reactive elements. Minority element effects on chromia scaling have been reviewed by Gleeson and Harper [144], and for alumina scaling by Hou [143] and Pint et al. [145].
7.6.1 Silicon effects Because SiO2, is less stable than Al2O3 (Table 2.1) but much more stable than FeO or NiO, it acts as a ‘‘third element’’ (Section 7.4) in M–Si–Al alloys. However, silicon levels in commercial alumina-forming alloys are generally rather low, and this effect is not available. During steady-state alumina scale growth, silicon will remain unreacted in the alloy. Its role during the initial transient oxidation of alumina formers has not been studied. Silica is much more stable than Cr2O3, and forms beneath a chromia scale as internal precipitates (Figure 5.1d) or, if N ðoÞ Si is high enough and sufficient time elapses, as a more-or-less continuous layer (Figure 7.22). This layer is important in slowing the rate of chromia scale growth by acting as a partial barrier to
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Chapter 7 Alloy Oxidation III: Multiphase Scales
Figure 7.22 Oxidation of HK40 in steam cracking furnace: (a) SEM image and (b) Si X-ray image [146]. With kind permission from Springer Science and Business Media.
7.6. Effects of Minor Alloying Additions
349
diffusion [146–148]. In some cases [149, 150], the silica layer is reported to be vitreous and hence a particularly affective diffusion barrier. It also provides additional protection against attack by carbon when the alloy is exposed to carburizing–oxidizing environments (Chapter 9). However, in the absence of reactive elements, the silica layer can make the scale more susceptible to spallation [151, 152]. The transient oxidation of chromia formers is strongly affected by the presence of silicon, which promotes exclusive Cr2O3 formation. This is observed for iron-base [153, 154], nickel-base [155] and cobalt-base [156, 157] alloys, and is generally thought to be a nucleation effect, although direct experimental evidence is lacking. Silicon additions can also alter the diffusional properties of the alloy subsurface region. Johnston [158] examined diffusion in Ni–Cr–Si alloys, and found that increasing silicon levels increased DCr by around 20%. Li and Gleeson [159] measured chromium depletion profiles in oxidized Ni–28Cr and Ni–28Cr–3Si, obtaining the results shown in Figure 7.23. They deduced average values for the effective diffusion coefficient of chromium which were increased by a factor of 2 in the presence of silicon, much greater than the effect reported by Johnston. No significant gradient in silicon developed, so no diffusional crosseffects were involved. An alternative explanation is that the formation of a SiO2 layer [159] between the NiCrSi alloy and its chromia scale led to chromium diffusion being at least partly controlled by the silica, rather than by alloy diffusion.
Figure 7.23 Subsurface depletion measured by EPMA in Ni–28Cr and Ni–28Cr–3Si after 7 days oxidation in air at 1,0001C [159]. With kind permission from Springer Science and Business Media.
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Chapter 7 Alloy Oxidation III: Multiphase Scales
7.6.2 Manganese effects The oxide MnO is more stable than Cr2O3 and might be expected on that basis to form a sublayer beneath a chromia scale. This does not in fact happen, for several reasons. Firstly, the manganese spinel is stable with respect to the binary oxides at high temperatures [160] MnO þ Cr2 O3 ¼ MnCr2 O4 ; DG ¼ 51; 036 þ 0:2T ðJ mol1 Þ
(7.17)
Secondly, manganese is soluble in Cr2O3, up to a limit of 1.6% of the cation sites at 1,0001C [161]. Finally, manganese diffuses rapidly in Cr2O3, apparently via the lattice rather than grain boundaries (Table 7.2), but relatively slowly in the alloy. This results in the scale structure of Figure 5.1d. This structure can be understood from the thermodynamics of the reactions (a)
2 Cr þ32O2 ¼ Cr2 O3
(7.18)
(b)
Mn þCr2 O3 þ 12O2 ¼ MnCr2 O4
(7.19)
occurring on an M–Cr–Mn alloy. Assuming aCr ¼ 0:2, one calculates from DGf ðCr2 O3 Þ that pO2 ¼ 2 1021 atm at the Cr2O3–alloy interface for T ¼ 1,0001C. From the value of DGf ðMnOÞ, it is found that MnO will form at this interface if aMn 42 103 . In a Ni–Mn alloy, this corresponds [162] to N Mn 1 102 , a typical upper limit for many heat-resisting alloys. Given that the interfacial manganese concentration will be depleted below the bulk alloy value, the absence of MnO formation is readily understood. As noted earlier, manganese diffuses rapidly through the chromia layer. Approximating its activity as being equal to that at the alloy surface, say aMn 1 103 , and assuming unit activity oxides, one calculates for reaction (7.19) the value pO2 ¼ 1 1013 atm for the spinel–chromia interface. Thus the observed sequence of manganese spinel overlaying chromia in contact with the alloy is consistent with steady-state local equilibrium, despite the stability of the manganese oxides. At higher alloy manganese levels, spinel formation via reaction (7.19) can become favoured at the scale–alloy interface. Douglass and Armijo [151] reported that such a morphology developed on Ni–20Cr–3Mn at 1,2001C. Two-layered MnCr2O4–Cr2O3 scales are, of course, thicker than chromia scales, and are consequently more prone to spallation [144]. They are commonly observed on stainless steels and cast heat-resistant steels [147].
7.6.3 Titanium effects Compared to chromium, titanium is a ‘‘reactive element’’, forming TiO2 which has a stability comparable to that of Al2O3. It also forms a very stable carbide and sulfide. In iron-based alumina-forming alloys, titanium can function as a sulfur getter. It has also been shown [130, 133, 134, 145] to segregate to Al2O3 grain boundaries, where it may affect mass transfer. Diffusion of titanium along these
7.6. Effects of Minor Alloying Additions
351
boundaries to form titanium-rich oxides at the scale surface has been reported by Pint [127]. Finally, TiO2 promotes the transformation of transient aluminas to a-Al2O3 (Section 5.7). Some additional effects of titanium are observed in iron-based chromia formers. If TiC precipitates are present in quantity, their oxidation at locations where they intersect the surface causes a large volume change and disruption of the protective scale. Even if this effect is avoided, titanium decreases the oxidation resistance of chromia-forming alloys. It is reported [163, 164] that the titanium oxidizes both beneath the Cr2O3 scale and at its surface, indicating that titanium can penetrate the chromia layer. The oxidation sites beneath the scale are intergranular, and may result from oxidation of prior carbides. Alloy solute titanium is presumably so dilute that TiO2 cannot form via the reaction Ti þ23Cr2 O3 ¼ TiO2 þ 43 Cr
(7.20)
Thus the situation is similar to that described earlier for low levels of manganese in chromia formers. The solubility of titanium in Cr2O3 has been measured by Naoumidis et al. [161] at up to 18% of the cation sublattice at 1,0001C. Whilst no data are available for DTi in Cr2O3, the high concentrations of dissolved titanium suggest that lattice diffusion might account for the growth of outer titanium-rich oxides. Titanium also functions as a sulfur getter in iron-based chromia-forming alloys [165].
7.6.4 Other effects Chromium can be present as a minority species in nickel-based alumina formers. At low concentrations, it does not provide a third-element effect. Instead it is rejected from the alumina scale, concentrating at the scale–alloy interface [145, 166]. In the case of b-NiAl, which has limited solubility for chromium (Figure 5.36), a-Cr precipitates at the interface. The observed increase in scale spallation is attributed to the low thermal expansion coefficient of the a-Cr. A simultaneous increase in scale growth rate is unexplained. Alumina scales are often found to contain small amounts of the alloy-base metal (usually iron or nickel). This is due to the initial transient oxide, which contains iron or nickel as a major component, being incorporated into the subsequently established alumina scale. As the alumina thickens, the overall concentration of alloy-base metal in the scale decreases, but is not eliminated [143, 167]. Analytical transmission electron microscopy has shown that the iron segregates to the grain boundaries [167], a finding confirmed by Electron energy loss spectrometry (EELS) analysis [168]. Hou [143] investigated the possible effects of this segregation on mass transport which, in a-Al2O3 scales, is predominantly a grain boundary phenomenon. The resulting comparison for various alloys is shown in Figure 7.24. Despite the scatter, it was possible to conclude that nickel- and iron-based alloys reacted about 8 and 10 times faster than PtAl. The presence of chromium
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Chapter 7 Alloy Oxidation III: Multiphase Scales
Figure 7.24 Oxidation rates for Al2 O3 scale growth on Fe–Ni-and Pt-based alloys [143]. Published with permission from the American Ceramic Society.
appeared to make no difference. Thus it appears that iron and nickel at alumina grain boundaries do affect their transport properties. Chromia scales also contain small amounts of iron or nickel. However, there appears to be no direct information on possible segregation of these or other such metals to the oxide grain boundaries. Indirect evidence for such an effect is described in Section 7.7. Finally, it is noted that the beneficial effects of platinum are also available from at least some other platinum group metals. Monceau et al. [169] have shown that palladium suppresses cavity formation at the alumina/b-NiAl interface. Similar benefits have been found for the addition of iridium [170] to g=g0 Ni–Al alloys.
7.7. EFFECTS OF SECONDARY OXIDANTS Industrial gases commonly contain other reactants in addition to oxygen, those of principal concern being compounds containing carbon or sulfur. Attack by these species is discussed in detail in Chapters 8 and 9, and our focus here is on the ability of chromia and alumina scales to resist them. In view of the fact that
7.7. Effects of Secondary Oxidants
353
diffusion in these scales is principally via their grain boundaries, it is expected that these would be the sites most vulnerable to attack by foreign species. As seen in Section 4.4, chromia scales grown on pure chromium can be penetrated by each of CO, SO2 and N2 under particular circumstances. Moreover, it was concluded on the basis of interactions among the different reactions, that molecular species adsorb on grain boundaries, and are mobile to different extents within them. Such a mechanism has been confirmed in the case of H2O by tracer diffusion measurements [122]. As we have seen, other alloy components can segregate to chromia scale grain boundaries and, at least in the case of reactive elements, alter their diffusion properties. The question of practical interest is therefore whether or not this segregation affects the permeability of the scale to secondary corrodents. It turns out that the answer to this question depends on both alloy composition and the gas atmosphere in question. Fujii and Meussner [171] reacted Fe–Cr alloys containing up to 20 wt% Cr with pure CO2 at temperatures of 700–1,1001C and found that protective scales were never formed. Instead, chromium-rich carbides were internally precipitated, and the iron-plus-carbide surface oxidized to yield a two-phase inner layer of wu¨stite and iron chromium spinel. This was overgrown by an iron oxide outer layer, the constitution of which varied with temperature. This reaction morphology is consistent with the thermodynamics of the system. As oxygen activity decreases within the scale, the CO/CO2 ratio increases according to Equation (4.30), and the value of aC rises according to Equation (4.31). A schematic view of the resulting profiles is shown in Figure 7.25. Precipitation of the alloy chromium as carbide immobilizes it, and prevents the alloy forming a protective chromia scale. Higher alloy chromium levels together with measures such as cold-working the surface promote chromia scale formation, and much better protection against carbon attack is then available. Colwell and Rapp [172] reacted Fe–24Cr with CO/CO2 gases at 9501C, producing a chromia scale plus a limited amount of internal carburization.
Figure 7.25 scale.
Variation of pCO2 and pCO in local equilibrium with oxygen gradient in a growing
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Chapter 7 Alloy Oxidation III: Multiphase Scales
However, they also found that Ni–Cr alloys with sufficient chromium to form an external scale were not carburized. The slightly richer alloys Fe–28Cr and Ni–28Cr [173] developed chromia scales at 9001C in CO/CO2/N2 gas, and were not carburized. Results obtained for stainless [174, 175] and heat-resisting steels [176, 177] are difficult to interpret because of the effects of other alloy components. The role of silicon in forming a SiO2 scale sublayer (see Section 7.5) is particularly important, and makes assessment of the chromia permeability impossible. The carbon permeability of oxide scales on M–Cr chromia formers is much less than that of the scale on pure chromium (Section 4.4). Alteration of the grain boundary properties, perhaps by segregation of iron or nickel, evidently makes them less permeable to carbon. A possible mechanism is adsorption and immobilization of CO or CO2 on nickel or iron-enriched surfaces, at oxygen potentials too low to form FeO. The effects of SO2 additions to the CO/CO2 gas also differ according to whether the scale is grown on chromium metal or an M–Cr alloy [178, 179]. Carbon permeability through pure Cr2O3 was decreased, even at pSO2 values too low to form an external scale. In contrast, the carbon permeability of alloy scales was increased by the SO2 additions, and internal carburization followed. Sulfur adsorption on iron-enriched grain boundaries could prevent CO adsorption at these sites, allowing CO to penetrate the scale. The situation in these gas mixtures is complicated still further by the permeability of chromia to sulfur [178, 180]. Using radiotracer H2 35 S, Lobnig and Grabke [180] showed that the solubility of sulfur in sintered Cr2O3 was below the detectability limit of 0.1 ppm. Nonetheless, they found that sulfur penetrated chromia scales, concluding that a molecular species was involved. Alumina scales appear to be superior to chromia in their ability to exclude sulfur and carbon. Stott et al. [181] compared the resistance to sulfur of alumina scales on Fe–Cr–Al alloys with that of chromia scales on Fe–Cr materials by exposing them to H2S/H2O mixtures at 7501C. In both cases sulfides formed as iron-rich nodules on the scale surface and also beneath the oxide scale as a result of sulfur penetration. Alumina scales resisted both forms of attack for longer than did chromia, providing that scale cracking was avoided. Similar conclusions were reached by Sheybany and Douglass [182] for a variety of iron-, nickel- and cobalt-base alloys. Alumina scales are also superior to chromia in their ability to slow or prevent carburization of cast heat-resisting alloys [183]. Several investigations of Fe–Cr–Al alloys [184–186] showed that sulfur penetrated a-Al2O3 scales at local sites. The ease of penetration increased at lower temperatures, and decreased as scale adhesion was improved by alloy doping. Excessive amounts of yttrium caused precipitation of Fe–Y intermetallics particles [186], and more rapid attack occurred at sites where these intersected the surface. The limited results available for alumina scales are consistent with the hypothesis that secondary corrodents can gain access to the underlying alloy by oxide grain boundary penetration. However, this process is slow, and may be less important than mechanical failures such as cracking and spallation.
7.8. Status of Multiphase Scale Growth Theory
355
7.8. STATUS OF MULTIPHASE SCALE GROWTH THEORY From a practical point of view, the value of this theory lies mainly in its ability to guide alloy design or selection by showing how multiphase scales can be avoided, and a single-phase scale of the desired protective oxide arrived at. In this chapter, we have focused on chromia- and alumina-forming alloys, discovering that the more complex the reacting system, the weaker the theory. For binary alloys, the treatment extends that of Chapters 5 and 6 which dealt with the situation where only one oxide was thermodynamically stable. Local equilibrium and the diffusion path description are found to apply equally well to the more complex case, where oxides of different metals form layers of a scale. Providing that adequate data are available, predictions as to whether the most stable oxide forms internally or as the desired scale are reasonably successful. However, marginal alloys can fail to maintain a steady-state condition, apparently as a result of changing mass transport mechanisms in the scale. These changes can result from slow dissolution of the alloy solvent metal into the scale, or from mechanical damage. We found that ternary alloys pose a much more difficult problem, simply because data on oxygen solubility and diffusivity are so scant. Even in the case where the third metal is unreactive or only slightly reactive, its effects can be dramatic. The addition of platinum modifies the behaviour of nickel aluminides through thermodynamic interactions which reduce aAl and lower oxygen permeability. Adding nickel to Fe–Cr has the principal effect of altering metal solubilities in the chromia scale. In the absence of good data for the effects on oxygen dissolution and diffusion, the changing patterns of reaction products are best described by oxide mapping. The Fe–Ni–Cr system is the basis for many heat-resisting alloys. The consequently large body of descriptive data is the main support for oxidation resistant alloy design. Good-quality data for oxygen dissolution and diffusion in this system would be valuable. Ternary M–Cr–Al alloys, with two reactive components, are the basis for many commercial compositions. The third-element theory developed to explain the effect of chromium in reducing the levels of aluminium required to form an external scale is only qualitatively successful. This appears to be due to the strong but unquantified thermodynamic interactions between dissolved oxygen and solute metals, and perhaps also to our weak understanding of the nucleation and growth phenomena of importance during initial transient oxidation. Despite these limitations, our ability to achieve protective chromia or alumina formation by alloying is a practical reality. For these scales to be useful, however, they must be protected against cracking and spallation. This too can be achieved, by reducing alloy sulfur levels, alloying platinum group metals with nickel aluminides and, most commonly, by alloying with reactive element metals. The rather complex range of effects induced by these additions can be understood from a simple view of the fracture mechanics of scale failure. However, quantitative alloy design tools for alloying are not yet available. The results surveyed in this chapter have reinforced our perception of the importance of oxide grain boundaries in the behaviour of chromia and alumina
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scales. In addition to providing the main pathways for diffusion of the chromiaand alumina-forming species, they provide sites for reactive element segregation, access points for other gas species such as N2 and H2O and probably preferred diffusion paths for alloy iron and nickel. We will return to this point in Chapter 10, but note that a quantitative knowledge of these processes would be highly desirable.
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CHAPT ER
8 Corrosion by Sulfur
Contents
8.1. Introduction 8.2. Sulfidation of Pure Metals 8.2.1 Sulfidation kinetics and rates 8.2.2 Growth of NiAs-type sulfide scales 8.2.3 Sulfidation of manganese 8.2.4 Sulfidation of refractory metals 8.3. Alloying for Sulfidation Protection 8.3.1 Alloying with chromium 8.3.2 Alloying with aluminium 8.3.3 M–Cr–Al alloys 8.3.4 Alloying with manganese 8.3.5 Alloying with molybdenum 8.3.6 Refractory metal alloys 8.4. Sulfidation in H2/H2S 8.5. Effects of Temperature and Sulfur Partial Pressure 8.6. The Role of Oxygen 8.7. Internal Sulfidation 8.8. Hot Corrosion 8.8.1 Phenomenology of sulfate-induced hot corrosion 8.8.2 Molten salt chemistry 8.8.3 Fluxing mechanisms 8.8.4 Type I and Type II hot corrosion 8.9. Achieving Sulfidation Resistance References
361 362 363 365 365 366 367 367 371 372 373 374 376 378 381 382 383 383 384 385 389 390 391 392
8.1. INTRODUCTION Sulfur is a relatively strong corrodent (or oxidizing agent) as seen from the free energies of metal sulfide formation shown in Table 8.1. It is frequently present in fossil fuels, and causes special forms of corrosion in petroleum and petrochemical processes based on these feedstocks, as well as in combustion processes. Because metal sulfides are very different from the corresponding oxides, corrosion by sulfur is generally much more rapid, and merits separate consideration. Three situations are of interest: oxidizing environments in which sulfur is a minority species; reducing environments
361
362
Table 8.1
Chapter 8 Corrosion by Sulfur
Standard free energiesa of metal sulfide formation reactions
Reaction
T (1C)
DG ¼ A þ BTðJ mol1 Þ A
Fe þ 12S2 ¼ FeS 9 1 1 8Co þ 2S2 ¼ 8Co9 S8 4 1 1 3Co þ 2S2 ¼ 3Co4 S3 1 Co9 S8 þ 2S2 ¼ 9CoS 3 1 1 2Ni þ 2S2 ¼ 2Ni3 S2 3 1 1 2Ni þ 2S2 ¼ 2Ni3 S2x 2Ni3 S2 þ 12S2 ¼ Ni6 S5 Ni3 S2þx þ 12S2 ¼ 3NiS Ni6 S5 þ 12S2 ¼ 6NiS Cr þ 12S2 ¼ CrS 3CrS þ 12S2 ¼ Cr3 S4 2Cr3 S4 þ 12S2 ¼ 3Cr2 S3 Mn þ 12S2 ¼ MnS 2 1 1 3Mo þ 2S2 ¼ 3Mo2 S3 Mo2 S3 þ 12S2 ¼ 2MoS2 a
138–1,190 o780 780–880 460–835 460–535 535–650 400–525 560–810 400–560 900–1,100 700–900 600–900 o1,244 700–1,100 700–1,100
Reference
B
148,530 52.8 165,770 83.28 129,490 50.04 Not linear with T 165,560 78.03 140,080 34.94 102,840 40.71 159,540 118.74 111,920 62.93 204,060 56.8 226,170 169 42,719 52.0 263,380 60 179,430 75.9 179,720 82.2
[1] [1] [1] [1] [1] [1] [1] [1] [1] [2, 3] [3] [3] [4] [5] [5]
DG1 values normalized to 1/2S2(g).
where sulfur is the principal corrodent and molten sulfate salt environments which form in the presence of alkali and some other metals. The first form of sulfur corrosion is discussed in Chapter 4, and we focus here on sulfidation under reducing conditions, and molten salt induced attack, commonly described as ‘‘hot corrosion’’.
8.2. SULFIDATION OF PURE METALS The sulfidation of metals and alloys has been reviewed several times [6–10]. The widespread adoption of catalytic reforming and hydrodesulfurizing processes in the petroleum industry produced a need for improved sulfidation resistance at moderate temperatures. A renewed interest in coal gasification as a route to more efficient electric power generation has led to a number of processes, most of which have in common high temperatures and substantial concentrations of gaseous sulfur under reducing conditions [10, 11]. Each of these technological changes has led to a substantial research effort which has generated a reasonably good level of understanding. Unfortunately, however, the goal of a practical alloy possessed of superior intrinsic sulfidation resistance has proved elusive.
8.2. Sulfidation of Pure Metals
363
8.2.1 Sulfidation kinetics and rates Provided that liquid sulfide formation is avoided, most metal sulfide scales grow according to parabolic kinetics, reflecting rate control by solid-state diffusion. However, the rate constants for most metals are extraordinarily high (Table 8.2), and much faster than for the analogous metal oxidation reactions (Table 3.1). We observe in particular that the sulfidation rate of chromium is four to five orders of magnitude faster than the corresponding oxidation rate. It is evident that the major constituents of many heat-resisting alloys are on this basis predicted not to form protective scales. Examining Table 8.2 further, it is observed that MnS scales grow much more slowly than the sulfides formed on Fe, Ni and Co. In fact, manganese sulfidizes more slowly than chromium. Even slower growing scales are formed on the refractory metals Mo, W, Ta and Nb. The sulfidation rates observed for these metals are quite acceptable, being of the same order of magnitude as the rate of chromium oxidation [10]. This is quite unlike the oxidation performance of these metals: molybdenum and tungsten react to form volatile oxides; titanium and niobium dissolve oxygen and grow porous, non-protective oxides according to fast linear kinetics. These different patterns of behaviour can be understood from a brief examination of metal sulfide and oxide solid-state chemistry. The general properties of transition metal sulfides have been reviewed by Rao and Pisharody [30], and their non-stoichiometry, lattice defects and transport properties by Halstead [31], Mrowec and Przybylski [9] and Mrowec [10]. Because the sulfide ion is so much larger than the oxide (diameter 0.368 nm compared with 0.28 nm), the cation/anion radius ratios in metal oxides are smaller than in the corresponding sulfides, leading to different crystal structures. Whereas simple monoxides, MO, are usually cubic, monosulfides usually adopt the NiAs structure in which the sulfide ions occupy a hexagonal lattice. All of the chromium sulfides (CrS, Cr3S4 and Cr2S3 at high temperature) can be regarded as possessing defective NiAs structures [32, 33]. The difference in anion size leads also to M–S bond lengths longer than the corresponding M–O distances. In ionic crystals, this leads to smaller lattice energies for the sulfides. This is reflected in the lower free energies for the sulfide formation (Tables 2.1 and 8.1) and in general lower melting points of sulfides. The low melting metal/metal sulfide eutectic temperatures shown in Table 8.3 set rather restrictive upper temperature service limits for some metals. The low stabilities of the sulfides means that point defects are easily created and, as seen from Equation (3.19), deviation from stoichiometry is more easily produced. The NiAs structure sulfides of Fe, Co, Ni and Cr are seen in Table 8.3 to display large deviations from stoichiometry. In this structure, the point defect species are predominantly cationic, either vacancies, or supernumerary cations occupying otherwise empty octahedral sites between the hexagonally closepacked sulfur anions. The much lower non-stoichiometry of MnS is associated with its cubic structure and somewhat greater stability.
1:3 103 50% H2 S 1
5 109 4 103 1 1 1 1 50% H2 S
1 0.26 0.13 104 108 2 106 1 0.013 2 102 108 104 1
pS2 ðatmÞ
92 84 70 61 12 26 142 78 210 82–96 130 72 92 192 72 94 199 147 135 58
EA ðkJ mol1 Þ
Rate at 800 C; pS2 ¼ 1 atm; unless otherwise noted. Ratio of rate constants for sulphidation and oxidation, 8001C unless otherwise noted.
b
a
W Nb
Ta Mo
Ni Cr
Mn
527–697 650–800 500–700 800–1,000 800–1,000 700–1,000 550–711 420–640 800–1,000 700–900 800–1,000 850–1,050 700–950 380–980 800–1,200
650–750 700–850 650–900 600–1,000
Fe
Co
T (1C)
Sulfidation rate data
Metal
Table 8.2
6.2
5.8–6.3
2.5
5.5
5.6 6
n
8 107 ð600 CÞ 3 108 1 107 7 1010 8 1011 ð900 CÞ 7 1012 3 1010 1013
4 109
3 106
1 10
5
kwa (g2cm4s1)
[17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [28] [27]
[12] [13, 14] [15] [16]
Reference
105 ð600 CÞ 4104
E1
450
102
kw(S)/kw(O)b
364 Chapter 8 Corrosion by Sulfur
8.2. Sulfidation of Pure Metals
Table 8.3
365
Metal/metal sulfide eutectic temperatures and sulfide nonstoichiometry ranges
System
T E ð CÞ
Sulfide (T (1C))
d
Reference
Fe=FeS Co=Co4 S3 Ni=Ni3 S2 Mn=MnS
988 880 645 1,242
Fe1d S ð800Þ CoS1þd ð800Þ Ni3 S2d ð645Þ Mn1d S ð800Þ Cr1d S ð700Þ Cr3d S4 ð700Þ Cr2þd S3 ð700Þ
0 to 0.20 0 to 0.07 0.188 to 0.222 0 to 1 104 0.032 to 0.205 0.10 to 0.11 0.054 to 0.11 (tr) 0.033- (rh)
[1] [1] [1] [34] [3] [35] [3]
8.2.2 Growth of NiAs-type sulfide scales In their extensive review of pure metal sulfidation reactions, Mrowec and Przybylski [9] demonstrate that the NiAs structure sulfides invariably grow by outward metal diffusion. The high defect densities of the simple metal sulfides imply high diffusion rates and consequently rapid sulfide scaling. As shown in Section 3.7, Wagner’s diffusion model provides a quantitatively successful description of iron sulfidation. This is one of the few systems, and the only sulfidation reaction, for which sufficient information is available to perform such a calculation. The important conclusion to be drawn is that iron sulfide scale growth is supported by lattice diffusion even at quite low temperatures. It seems likely that this will be true also for other reactions forming sulfides with the NiAs structure. Sulfidation and oxidation rates, kw , are compared in Table 8.2 for metals which form NiAs-type sulfides. Although weight uptake rates reflect the different atomic weights of sulfur and oxygen, the effect is approximately compensated by the difference in compound densities, when scaling rates, kp , are calculated from Equation (1.18) or Equation (1.32). It is seen that Fe, Co, Ni and Cr all sulfidize faster than they oxidize at 8001C. The difference in the case of iron is not so large, reflecting the similar values of d in Fe1dO and Fe1dS, and a higher Dn in the sulfide (section 3.7). Data for nickel corrosion is provided for T ¼ 6001C, below the eutectic temperature for the Ni–S system. Nickel sulfidation is extraordinarily rapid, reflecting the high d values of nickel sulfides (Table 8.3) and the high defect mobilities in these compounds. Importantly for heat-resisting alloys, chromium sulfidizes much more rapidly than it oxidizes, again reflecting the difference between widely non-stoichiometric chromium sulfides and closely stoichiometric Cr2O3.
8.2.3 Sulfidation of manganese Manganese is unusual in having similar sulfidation and oxidation rates. Activation energies for the two processes are also rather similar: 88 kJ mol1 for sulfidation [21, 36] and 81 kJ mol1 for oxidation [37]. These similarities come
366
Chapter 8 Corrosion by Sulfur
about as a result of the unusual cubic structure of a-MnS, its small deviation from stoichiometry (Table 8.3) and the fact that manganese vacancies are the mobile defects in both oxide and sulfide. Of the common metals for which data is available, only manganese provides anything like acceptable sulfidation resistance. Its sulfidation rate constant is nonetheless about 4 orders of magnitude faster than that of chromium oxidation at 8001C, implying the need for a corrosion allowance about 100 times larger.
8.2.4 Sulfidation of refractory metals The refractory metals for which data is available appear to provide superior sulfidation resistance, as seen from the low scaling rates in Table 8.2. In seeking to explain this phenomenon, Mrowec and Pryzbylski [9] speculated that these sulfides, like the refractory metal oxides, might be anion diffusers. In this event, the large size of the sulfide ion might explain its low mobility. This reasoning appears to be correct for molybdenum and tungsten sulfides which have been shown in marker experiments [28] to grow by slow inward sulfur transport. The molybdenum sulfide is closely stoichiometric, with a maximum value of d o 8 105 in MoS27d between 900 and 1,1001C, although some sulfur disorder ðd 103 Þ can be achieved via stacking faults [38]. However, subsequent investigations of non-stoichiometry in other refractory metal sulfides have revealed high defect densities in the cation sublattices. Many of the refractory metal disulfides, MS2 have the Cd(OH)2 structure, made up of ‘‘sandwiches’’ consisting of two planes of sulfide ions with a plane of cations between them [30]. These sandwiches are stacked along the c-axis of a hexagonal lattice to form the crystal structure. The spaces between the sandwiches are available for occupancy by additional metal, forming lower sulfides. Thus, for example, Nb2S3 can be regarded in a structural sense as Nb1+dS2 [39] and a similar description applies to the Ti–S system [40]. The ability of these structures to accommodate different metal–sulfur ratios permits substantial deviations from stoichiometry, the defects lying within the cation sublattices. Thus the high temperature niobium sulfide NbSn exists over the range 1:4 n 1:7 at 1,0001C [41]. A defect model based on metal vacancies and interstitials [42] was shown to fit the relationship between n and pS2 at 1,0001C, and at other temperatures when point defect charges are taken into account [43]. Gesmundo et al. [43] have shown that this model matches the sulfur partial pressure dependence of kp for growth of this sulfide on niobium, if both defect species contribute to diffusion. The rather slow growth rates thus reflect very low defect mobilities. Titanium forms a series of sulfides between TiS (with a NiAs structure) and TiS2 (with a Cd(OH)2 structure [39]). Like the niobium sulfides, the titanium compounds also evidence large departures from stoichiometry. Saeki and Onoda [44] found compositional ranges for TiSn of 1:57ono1:72 and n41:82 at 9501C and high sulfur potentials. There appears to be no information available for pure titanium metal sulfidation rates.
8.3. Alloying for Sulfidation Protection
367
8.3. ALLOYING FOR SULFIDATION PROTECTION A large research effort has been devoted to the search for sulfidation-resistant alloys [7–10]. Almost all of this work was based on the design strategy which has proved so successful for oxidation resistance: selective reaction of an alloy constituent to form a slow growing protective scale. For such a strategy to succeed, the following conditions must be met: (1) The selected metal must have a sulfide much more stable than the alloy solvent metal, so that moderate alloying levels will suffice. (2) The selected metal sulfide must grow slowly. (3) The preferentially formed sulfide must act as a barrier to outward diffusion of other alloy components. There are other requirements concerning the physical and mechanical properties of the alloy and scale, but an alloy satisfying just the basic requirements has yet to be developed.
8.3.1 Alloying with chromium The difficulty of meeting the first requirement is illustrated in Figure 8.1. Comparison with analogous data for oxide formation (Figure 2.1) shows that the differences between free energies of formation of different metal sulfides are less than for the corresponding oxides. Consider the competition between chromium and iron sulfide formation: Cr þ FeS ¼ CrS þ Fe
(8.1)
DG1 ¼ 55; 530 þ 3:95 T J mol1
(8.2)
At 7001C, DGl ¼ 52 kJ mol1 , and therefore, in the case of pure, immiscible sulfide phases aFe ¼ K1 ¼ 595 (8.3) aCr In an ideal Fe–Cr solid solution, the minimum concentration of N Cr for CrS formation is therefore 0.16%. This is much higher than the value of N Cr required (o1 ppm) to thermodynamically stabilize Cr2O3 with respect to FeO on an Fe–Cr alloy (Section 2.4), but nonetheless a promising level. Unfortunately, the assumption of immiscible sulfide phases is a poor one, as seen from the Fe–Cr–S phase diagram in Figure 8.2. A minimum chromium concentration of 6 wt% ðN Cr ¼ 0:064Þ is required to stabilize the (Cr,Fe)1dS phase with respect to (Fe,Cr)1dS. Selective reaction of chromium depletes the alloy subsurface region. Diffusion paths observed for an 18.5 wt% Cr steel after sulfidation are mapped on the phase diagram of Figure 8.2 to illustrate the effect: As the value of N ðoÞ Cr is increased, a degree of protection is achieved, as greater amounts of chromiumrich sulfide (Cr,Fe)3S4 are formed [50–52]. However, an additional layer of (Cr,Fe)1dS grows on top of the (Cr,Fe)3S4. Data from Narita and Nishida for
368
Chapter 8 Corrosion by Sulfur
0
-100 MoS2 Mo2S3
-200
ΔG (kJ/mol S2)
FeS -300
CrS -400
NbS2
MnS
-500
Al2S3 Ti2S3
-600
-700 0
200
400
600
800
1000
1200
1400
T (°C)
Figure 8.1 Ellingham diagram for selected sulfides. Data sources: CrS [2], FeS [1], Mo-S [5], Ti2S3 [44], MnS [4], Al2S3 [45, 46], NbS2 [47].
reaction at pS2 ¼ 1 atm is shown in Figure 8.3. The reductions in rate achieved by chromium additions are relatively small, and decrease with increasing temperature. This is a consequence of, firstly, the rather rapid rate of chromium sulfide growth (Table 8.2) and, secondly, its evidently high permeability for iron. Both effects result from the high concentration of cation defects in Cr3S4 [35]. It should be noted that the phase diagram of Figure 8.2 is inaccurate, as it omits this important phase. Attempts to protect nickel by alloying with chromium are similarly limited in their success [26, 53–56]. Again, the explanation is to be found in the high permeability of nickel in the chromium-rich sulfides and the rapid growth of the latter. The high solubility of nickel in chromium sulfides is evident in the phase diagrams of Figure 8.4.
8.3. Alloying for Sulfidation Protection
369
Figure 8.2 Fe–Cr–S isothermal section for 7001C [48] showing diffusion paths measured on sulfidized Fe–18.5Cr–4.9Ni–2.7Mo stainless steel [49]. With kind permission from Springer Science and Business Media.
Figure 8.3 Sulfidation rates for Fe–Cr alloys reacted at pS2 ¼ 1 atm [52]. With kind permission from Springer Science and Business Media.
370
Chapter 8 Corrosion by Sulfur
Figure 8.4 Phase equilibria in the Ni–Cr–S system (a) isothermal section at 7001C [57], with kind permission from Springer Science and Business Media. (b) Sulphur potential relationships at 6001C [56], with kind permission from Springer Science and Business Media. (c) Scale cross-section grown on Ni–20Cr at 7001C [54], reproduced by permission of The Electrochemical Society.
8.3. Alloying for Sulfidation Protection
Figure 8.4
371
(Continued)
8.3.2 Alloying with aluminium Aluminium sulfide is considerably more stable than Fe1dS and the nickel sulfides (Table 8.1, Figure 8.1). The Fe–Al–S phase diagram at 7501C [58] shows, however, that a scale–alloy interface aluminium level N Al;i 0:1 is required to stabilize Al2S3. This diagram also shows the existence of a ternary compound FeAl2S4 which has been shown [59, 60] to be hexagonal in structure. Early work [61, 62] indicated that Fe–Al alloys were much more resistant to sulfidation than their Fe–Cr equivalents. Subsequent investigations [51, 63–66] of Fe–Al alloy sulfidation have led to a diversity of reports on what is apparently a very complex system. Alloys containing N ðoÞ Al ¼ 0:1 0:2 form duplex scales of Fe1dS outside Al2S3 in the short term (Figure 8.5). At higher N Al levels, an intermediate layer of FeAl2S4 forms. However, as the reaction proceeds, internal Al2S3 precipitation develops and a new layer of Fe1dS forms beneath the Al2S3. Thus the Al2S3 layer fails to prevent outward iron diffusion and eventually fails also to prevent sulfur access to the underlying alloy. Discussion is hampered by a lack of information on the defect nature and diffusion properties of the aluminium-rich sulfides. Aluminium additions to nickel are even less effective. Exposure of the intermetallic gu-Ni3Al to H2/H2S atmospheres at 8751C led to either Al2O3 formation if pS2 was too low to stabilize a nickel sulfide, or liquid sulfide when pS2 exceeded the Ni/NiSx(l) equilibrium value [67]. The b-NiAl intermetallic failed to provide selective aluminium sulfidation when exposed to high sulfur partial pressures [68]. Finally, it should be noted that Al2S3 and FeAl2S4 hydrolyse readily on exposure to humid air, producing H2S(g) and hydrated alumina. The latter disintegrates to a powder as a result of the volume expansion, and it seems
372
Chapter 8 Corrosion by Sulfur
Figure 8.5 Fracture cross-section of sulfide scale grown on Fe-10 at % Al at 7501C in H2/H2S [65]. Reproduced by permission of The Electrochemical Society.
unlikely that Al2S3 formation can ever provide a practical route to alloy protection.
8.3.3 M–Cr–Al alloys The sulfidation resistance of Fe–Cr–Al alloys has been extensively explored. In 1961, Setterland and Prescott [62] reported that alloys containing both chromium and aluminium were highly resistant to low pS2 atmospheres at 4501C. Mrowec and Wedrychowska [69] sulfidized alloys containing 18–25 wt% Cr and 1–5 wt% Al (and minority amounts of C, Mn and Ni) at temperatures of 800–1,1001C and pS2 ¼ 1 atm. Parabolic kinetics were observed, and the presence of aluminium was found to decrease the rate. Duplex scales of coarse grained Fe1dS over a fine grained, porous layer containing Fe1dS, chromium sulfides, FeCr2S4 and Al2S3 developed. Zelanko and Simkovich [70] reacted a range of ternary alloys with H2/H2S mixtures corresponding to pS2 ¼ 2 1011 atm at 5401C, obtaining parabolic kinetics in all cases. Their rate data is shown plotted as iso-corrosion contours on a composition triangle in Figure 8.6, where a rather complex interaction between chromium and aluminium effects is evident. It is seen that a typical Fe–Cr–Al composition of Fe–20Cr–5Al would be expected to perform quite well under isothermal conditions, at this admittedly low temperature. Rates have been measured at 8001C for similar composition alloys as B5 107 g2 cm4 s1 at sulfur potentials of 1 atm [69] and 107 atm [71]. These values represent a significant improvement on the rate constant for pure iron of kw 105 g2 cm4 s1 at this temperature. Scale morphologies and constitutions were similar to those reported by Mrowec and Wedrychowska, except that the outer Fe1dS layer was absent on higher alloys. The difference presumably reflects the difference in pS2 values. At both sulfur potentials, the scale inner layers were always heterophase, reflecting
8.3. Alloying for Sulfidation Protection
10
w/o Al
-10
373
-11
-9
5 -8 -7
Fe
5
10
15
20
25
w/o Cr
Figure 8.6 Iso-corrosion contours for Fe–Cr–Al alloys drawn from data due to Zelanko and Simkovich [70]. Numbers are values of log10 kw at T ¼ 5401C, pS2 ¼ 2 1011 atm.
the inability of these alloys to selectively form a single phase, protective layer. This failure is probably the result of both thermodynamic and kinetic factors. The chromium-rich sulfides are not much more stable than the chromium-doped (Fe,Cr)1dS, and the same may be true of the aluminium-rich sulfides. The rapid rates at which all sulfides grow lead to high kc values and strong depletion in the alloy subsurface zone (Equation (5.25)), making selective sulfidation more difficult. Finally, the high growth rate of Fe1dS impedes formation of a continuous, protective chromium and/or aluminium-rich sulfide. The sulfidation of Ni–Cr–Al alloys at pS2 ¼ 1 atm and 680–9501C is reported [72] to proceed according to non-parabolic and rather irreproducible kinetics, perhaps indicating liquid nickel sulfide formation.
8.3.4 Alloying with manganese Nishida et al. [22, 73] exposed iron–manganese alloys at temperatures of 700–1,0001C to elemental S2(g) at 1 atm and to H2/H2S mixtures corresponding to pS2 values of 1011 102 atm. The kinetics were always parabolic, and large decreases in rate accompanied increases in manganese levels from 11 to 64 wt%. The protective effect was associated with the formation of a Mn(Fe)S layer at the scale–alloy interface. An induction period observed in H2/H2S atmospheres was later shown [74] to be due to the slow approach to equilibrium of the gas mixtures. Unfortunately, the benefit of an MnS layer is not fully realized because FeS dissolves in it extensively, and increases somewhat the deviation from stoichiometry [22, 74]. This permits the passage of iron through the MnS, allowing growth of an outer Fe1dS layer. Even so, the benefit conferred by manganese additions is generally superior to that of chromium (Table 8.4). When Fe–Mn alloys are reacted in gases with pS2 below the Fe/ Fe1dS equilibrium, they
374
Chapter 8 Corrosion by Sulfur
Table 8.4
Sulfidation rate constants, kw ðg2 cm4 s1 108 Þ in flowing H2 =H2 S [75]
Tð CÞ
pS2 =atm Fe Fe–25Cr Fe–25Mn Fe–25Mn–10Cr
700 8
10 4.2 2.2 0.5 2.5
800 5
8 10 19 1.6 4.4 1.7
8
10 8.3 12 1.2 6.3
8 105 50 26 9 26
grow external scales and internal precipitates of MnS. Papaiacovou et al. [76] demonstrated that both processes are controlled by alloy diffusion at 700–8001C, but by scale diffusion at 9001C. Attempts have been made to improve the sulfidation of iron by alloying simultaneously with manganese and chromium [75, 77]. The ternary alloys provide better performance than Fe–Mn only if both (Mn,Fe)S and (Cr,Fe)3S4 layers are developed. The observed sequence of scale layers illustrates some of the complexities of these sulfide systems: (Fe,Mn)S, (Mn,Fe)S, Cr3S4 (when present) and (Cr,Fe)S from the scale exterior to the alloy surface. This arrangement is consistent with the relative stabilities of the pure sulfides except for the location of MnS (Table 8.1). The explanation lies in the destabilization of MnS by its approximately 0.5 mol fraction FeS content [75]. An Fe–Mn–Al alloy sulfidizes more slowly than Fe–Mn alloys at 7001C in H2/H2S atmospheres [78, 79]. In the early stages of reaction, manganese depletion from the alloy allows formation of an aluminium-rich sulfide at its surface. However, this layer does not provide long-term protection: an Fe1dS layer grows above it and the mixed hexagonal sulfide MAl2S4 develops beneath it.
8.3.5 Alloying with molybdenum The recognition that conventional alloy additions failed to provide sulfidation resistance led some years ago to a series of investigations into the effectiveness of refractory metals as alloy additives. The effects of molybdenum additions to both iron and nickel have been examined. The problem with all of these alloys is illustrated by the inert marker experiment shown in Figure 8.7. A molybdenum sulfide layer does indeed grow by inward sulfur transport, but an iron or nickel sulfide layer grows on the outside by outward cation transport. The inner layer has been reported [80, 81] to be a mixture of FeS and MoS2 at high pS2 , and the Chevrel phase FexMo6S8z at lower pS2 values. The phase diagram in Figure 8.8 illustrates the diffusion paths involved. Similar results are found for Ni–Mo alloys [83, 84]. Clearly, the alloy base metal is able to penetrate the molybdenum-rich sulfide phases rather readily, allowing continued reaction. In the case of nickelbased alloys, this can lead to liquid sulfide formation. The permeability of MoS2 to transition metals is related to its layered structure. Foreign cations can intercalate between adjacent sulfide planes, occupying some of the octahedral
8.3. Alloying for Sulfidation Protection
375
Figure 8.7 Sulfide scales grown (a) at 7501C on Fe-27 at.% Mo and (b) at 7001C on Fe–28Mo–32Mn exposed to H2/H2S (showing a Pt marker). Reprinted from [80] with permission from Elsevier.
Figure 8.8 Fe–Mo–S isothermal section at 7501C [82] showing diffusion paths for FeS layer growth over Mo-rich sulfides. Reprinted from [80] with permission from Elsevier.
376
Chapter 8 Corrosion by Sulfur
sites and, presumably, diffusing via these positions. The more reactive iron species forms the ternary Chevrel phase FexMo6S8z in which 1:15ox 1:35 and 7:70o8 z 7:90 at 1,0001C [85]. The simultaneous disorder in the iron and sulfide sublattices explains the ability of this compound to diffuse both species. The performance of Fe–Mo and Ni–Mo alloys can be improved by the addition of aluminium. Douglass et al. [86, 87] attributed the enhanced resistance to formation of the double sulfide AlxMo2S4 as part of the inner scale layer when pS2 ¼ 0:01 atm. Chen et al. [88] found Al2O3 and FeAl2O4 to be formed on Fe–Mo–Al by oxygen present as impurity H2O in their H2/H2S mixtures. He and Douglass [89] arrived at a similar conclusion for Ni–Mo–Al alloys when reacted in H2/H2S gases. The addition of manganese [80] and manganese plus aluminium [90] to Fe–Mo alloys enhances their sulfidation resistance. The manganese effect is due to formation of an intermediate Mn(Fe)S layer which slows the growth of an outermost Fe1dS layer, and the aluminium effect is as described above.
8.3.6 Refractory metal alloys The use of niobium as an alloying additive has been examined in detail by Douglass, Gesmundo and co-workers [87, 91–94]. Niobium reduces the rate of iron sulfidation only slightly, but has a strong effect on nickel sulfidation at subliquidus temperatures (Figure 8.9) during exposure to 0.01 atm of S2(g). At temperatures above 6351C, niobium levels of some 30 wt% are required to suppress Ni–S liquid phase formation. The addition of aluminium to Fe–Nb alloys depresses sulfidation rates dramatically (Figure 8.9). In all cases, the scales -5 -5.5
log10 kw/g2 cm-4
-6 -6.5
Ni-Nb
-7
Fe-Nb
-7.5 -8 -8.5 -9
Al Alloy
-9.5 -10 0
5
10
15
20
25
30
35
40
45
Wt. %Nb
Figure 8.9 Effect of Nb concentration on sulfidation in 0.01 atm S2 of Fe–Nb and Ni–Nb and Fe–30 Nb–3Al. Data points taken from [87, 91, 92].
8.3. Alloying for Sulfidation Protection
377
consist of outer layers of either Fe1dS or Ni1dS/Ni3S2 over an inner, heterogeneous, niobium-rich layer. Platinum markers are invariably found at the interface between the two layers, corresponding to the expected inward sulfur transport through niobium sulfide and outward metal transport through iron and nickel sulfides. The reduction in rate achieved by niobium alloying is caused by a slowing of iron and nickel diffusion by the inner sulfide layer. This layer is quite complex, consisting in the case of Fe–Nb alloys of Fe1dS, FeNb2S4, NbS2 and particles of intermetallic Fe2Nb. Intercalation of iron into the layered NbS2 structure and the coexistence of iron-rich sulfides in the inner layer are thought to explain the disappointing performance of these alloys. Ternary Fe–Nb–Al alloys develop similar scales, with aluminium concentrated in the inner layer. The phase constitution of these layers has not been established, and a lack of knowledge of the sulfide properties hampers discussion. It is clear, however, that the presence of aluminium affects both iron and sulfur transport, as both layers grow much more slowly. The inner layer developed on Ni–Nb alloys consists of NiNb3S6 plus NbS2. Nickel diffuses through this layer, but nickel sulfide growth is slowed considerably. Thus although the alloys are unable to form a continuous, protective NbS2 layer as a result of ternary compound formation, the diffusional blocking effect of the NbS2 particles and the presumably low value of DNi in the mixed sulfide lead to a degree of protection. Similar benefits have been obtained for Co–Nb alloys [93, 94]. Some limited information is available for titanium sulfide scaling as a result of an interesting application. Because TiO2 and Al2O3 are of comparable stability, the intermetallic TiAl provides marginal resistance to rapid TiO2 growth. However, titanium sulfides are more stable than Al2S3. Selective sulfidation of titanium has been used by Narita et al. [95–97] to form aluminium-enriched alloy surface regions on g-TiAl in order to improve its subsequent oxidation resistance. Reaction at 9001C in H2/H2S gas corresponding to pS2 ¼ 1:3 105 atm leads to growth of multilayer scales enriched in titanium. The inner layers consist mainly of TiS and Ti3S4. However, these layers also contain some aluminium, which diffuses outwards to form a mixed layer of Al2S3 and titanium sulfide in roughly equimolar proportions. Sulfidation rates are low. We conclude from the foregoing that very high alloying levels of Mo, Al, Nb and/or Mn are required to achieve any benefit in protecting iron- and nickelbased materials against high sulfur potentials. Even then, the benefit is limited by the extent to which the scale inner layers transmit alloy-based metals, allowing growth of outer iron or nickel-rich sulfides. No practical alloys have been found. However, coatings based on refractory metals and aluminium may prove to be of use in high sulfur potential environments [98, 99]. It should also be observed that the very high sulfur potentials (0.01–1 atm) used in much of the research on refractory metal alloys are seldom encountered in practice. Of more relevance to petroleum and coal conversion processes are H2/H2S atmospheres, which are now considered.
378
Chapter 8 Corrosion by Sulfur
8.4. SULFIDATION IN H2/H2S Low sulfur potentials result from the equilibrium H2 S ¼ H2 þ 12S2
(8.4)
for which the standard free energy charge is given in Table 2.1. Mixtures of H2 and H2S have often been used in laboratory reactors to control pS2 values. There is a potential difficulty with this technique at low temperatures, because the rate of H2S dissociation is slow. Darwent and Roberts [100] showed that the homogeneous gas phase reaction is bimolecular 2H2 S ¼ S2 þ 2H2 3
with a rate constant, expressed in cm mol k ¼ 2:27 10
14
1
(8.5) 1
min , of
expð217 kJ mol1 =RTÞ
(8.6)
If the furnace tube through which the gas mixture passes is modelled as a plug flow reactor [101], then the fractional conversion, y, of H2S to S2 is given for second order kinetics as 1y VT ¼ (8.7) y k½H2 S t where VT is the total volumetric flow rate, t gas residence time and ½H2 S the initial, or inlet, concentration. The maximum value of pS2 achievable may therefore be calculated. Results for H2–H2S–N2 mixtures in a typical tubular laboratory reactor are shown in Table 8.5. As expected from (8.6) and (8.7), H2S dissociation becomes slower at lower temperatures and greater gas dilution. The actual levels of pS2 reached in the gas can be very low. A simple mass balance calculation shows that the rate at which S2(g) is regenerated within the gas is too Table 8.5 Maximum pS2 values achieved by H2 S dissociationa in tubular flow reactor compared with equilibrium [102] T ð CÞ
pH2 S ðatmÞ
pS2 ðeqÞ ðatmÞ
pS2 ðmaxÞ ðatmÞ
800
1:11 101 2:4 102 3:85 101 1:43 102 1:43 102 5:7 103 8:0 101 6:0 101 4:0 101 5:0 102
6:5 106 6:5 106 6:5 106 6:5 106 3:3 109 3:3 109 6:5 106
6:5 106 9:9 107 6:5 106 6:5 106 3:3 109 2:4 109 1:6 106 2:8 107 1:3 107 7:9 1010
665
520
a
Calculated for H2 H2 S N2 mixtures at PT ¼ 1 atm, linear flow rate 2 cm s1 .
8.4. Sulfidation in H2/H2S
379
slow to keep up with observed sulfur uptake rates on many metals. The reactant species under these conditions must be H2S. In view of the fact that parabolic scaling is often observed, and that Wagner’s scaling theory applies, at least in the case of iron sulfidation, it must be supposed that H2S dissociation occurs on the scale surface. The gas adsorption and dissociation model of Section 2.9 has been applied to the case of iron sulfidation [102], leading to the prediction that the adsorbed layer approaches equilibrium at a rate which increases with pH2 S and decreases with pS2 (eq). These predictions were successful in describing non-steady-state sulfidation of both iron and Fe–Mn [74]. Data on the sulfidation of iron in H2S bearing gases illustrate the importance of recognizing this effect. Workers using high temperatures, low diluent concentrations and low values of pS2 (eq) establish a steady state relatively quickly, and commonly report parabolic kinetics [16, 17]. Conversely, workers using significant gas dilutions or low temperatures report non-steady-state behaviour [70, 102–106]. Short reaction times can fail to reveal that the sulfidation rate is increasing, and result in underestimates of scaling rates. Reaction in dilute H2/H2S gases can lead to whisker formation. An Fe–Ni alloy is seen in Figure 8.10 to have developed multiple reaction zones: an inner, compact monosulfide layer overgrown by needles of pentlandite, (Ni,Fe)9S8, which are covered in turn by whiskers of Ni7S6, covered finally by whiskers of NiS. Measured compositions are shown plotted on the Fe–Ni–S
Figure 8.10 Cross-section of reaction product layers formed on Fe–41Ni at 5201C, pS2 ¼ 1:2 109 atm, pH2 S ¼ 5 102 atm.
380
Chapter 8 Corrosion by Sulfur
Figure 8.11 Isothermal section of Fe–Ni–S phase diagram at 5201C showing diffusion path for Figure 8.10.
phase diagram in Figure 8.11, where local equilibrium is seen to be in effect. Consistent with local equilibrium, the kinetics of whisker growth were parabolic [107, 108]. The observation that the whiskers were apparently at local equilibrium is at first sight remarkable. The volume fraction of solid in the whisker zone is about 0.05. Although the whiskers are much more numerous and densely arrayed than is usual for corrosion products [109], the whisker zone is clearly permeable to gas. Despite the openness of the whisker zone, the effective sulfur activity near the base of the whiskers was much less that at their tips. In the example of Figure 8.11, the whisker tips are NiS, the mid-zone of the whisker layer is Ni7S6 and the whisker bases are pentandite. No such sulfur activity gradient could possibly exist if the gas phase were functioning as a sulfur transport medium. The explanation, of course, is that the H2S dissociation reaction does not reach equilibrium in the gas phase. The phase constitutions of the whisker zones are understandable if the whisker tips, but not their sides, are catalytically active to H2S dissociation. In this way, the effective sulfur activity is brought close to the equilibrium value at the whisker tip, and the local phase constitution is thereby determined. However, the sulfur activity along the whisker length is controlled by the outward flux of nickel along the whisker. At higher pH2 S and pS2 values, no whiskers develop and a compact nickel-rich outer sulfide layer grows instead. A final complication which sometimes arises in these gases is the dissolution of hydrogen into the sulfide. The effect is unimportant in the widely nonstoichiometric NiAs-type sulfides, but has been shown to accelerate the sulfidation of molybdenum at high temperatures [29, 110]. The variation in kp with hydrogen partial pressure at fixed pS2 values can in this case be rationalized in terms of hydride doping.
8.5. Effects of Temperature and Sulfur Partial Pressure
381
8.5. EFFECTS OF TEMPERATURE AND SULFUR PARTIAL PRESSURE Sulfide electronic conductivities are usually metallic in nature, and Wagner’s rate Equation (3.61) can be written Z a00s 1 d ln as kp ¼ DM (8.8) 1d a0s for growth of an M1dS scale. This rate constant varies with temperature through the thermal activation of DM, the temperature effect on the scale–alloy local equilibrium (which sets the integration limit a0s ) and the temperature effect on the functional relationship between d and as. The last effect is important if the degree of intrinsic disorder, and hence non-stoichiometry, is large (Equations (3.15, 3.19)). This is the case for the NiAs-type sulfides, which are the most frequently encountered in practice. A proper accounting for the effect requires numerical integration (Section 3.7), but it is usually ignored because insufficient data is available. The data in Table 8.2 show that apparent activation energies for growth of the NiAs-type sulfides differ considerably with pS2 . These sulfides contain cation defects, predominantly metal vacancies in the monosulfides. If scale growth is controlled by cation vacancy diffusion, then Wagner’s theory leads to Equation (3.84), rewritten here as kp ¼ ko p1=n s2
(8.9)
with n ¼ 2ðm þ 1Þ and m as the effective vacancy charge. The limited data in Table 8.2 is consistent with doubly charged vacancies in Fe1dS and MnS, and close to neutral vacancies in Co1dS. The apparent variation of activation energy with pS2 is therefore understandable from (8.8). At low pS2 values, d 1, and according to (8.8), kp is approximately independent of d and its temperature effect. At high pS2 values, d becomes large and its temperature-dependence effects kp. This argument succeeds for Fe1dS, but is inapplicable to cobalt which grows a multilayer scale. The different EA values reported for manganese sulfidation cannot be rationalized in this way, as d 1 at all pS2 values. Inconsistent EA values have been reported for chromium sulfidation in 1 atm S2(g). As some refractory metal sulfides grow by diffusion of sulfur, a different dependence of rate on pS2 is expected. According to Wagner’s theory, an expression like (3.90) will apply: h i kp ¼ ko ðp0S2 Þ1=n ðp00S2 Þ1=n (8.10) Since p0S2 is small, the rate is almost independent of the ambient pS2 if the latter is at high levels. This reflects the fact that sulfur vacancies are injected at the metal– sulfide interface, and their concentration at this location is unaffected by gas phase conditions. However, as p00S2 is lowered to approach p0S2 , alterations in its value will change the sulfur activity gradient and hence, kp. Study of this effect is
382
Chapter 8 Corrosion by Sulfur
complicated in the case of molybdenum, which sulfidizes in H2/H2S at faster rates than in S2(g) at the same pS2 value [29, 111], as a result of hydrogen dissolution in the sulfide. Experiments in H2–H2S–N2 gas mixtures allow investigation of the effect of variation in pH2 while pS2 is maintained constant. Results show that kp increases with pH2 , consistent with hydride dissolution [110]. The behaviour of Nb1+dS2 is interesting. Gesmundo et al. [43, 112] showed that pure niobium sulfidizes in H2/H2S at rates which increase with pS2 . This was interpreted in terms of cation diffusion. However, this mode of transport is not reflected in the sulfidation of M–Nb alloys (M ¼ Fe, Ni or Co) which form duplex scales with an inner, niobium-rich layer which grows by inward sulfur diffusion. A direct comparison is not possible, because the alloy scale layers are multiphase, containing other phases which might be responsible for the sulfur transport.
8.6. THE ROLE OF OXYGEN As noted earlier, reaction in H2/H2S mixtures invariably involves impurity amounts of H2O. Although the levels are very low, they can be sufficient to oxidize aluminium. Under these conditions, it is possible that the Al2O3 contributes substantially to protection against sulfur attack. This question has been investigated using controlled H2/H2S/H2O gas mixtures for a number of alloys. Iron–aluminium-based alloys containing various additions of titanium and/or chromium were found by Regina et al. [113] to be protected at 5001C by a thin Al2O3 scale when exposed to H2/H2S/H2O mixtures. Various workers [114–117] have shown that pre-oxidation of FeCrAl alloys provides them with a degree of protection against subsequent exposure to mixed oxidizing–sulfidizing gases. The performance improves with extent of pre-oxidation. Douglass et al. [118, 119] showed that the addition of 7 wt% aluminium to Fe–20Mo and Fe–30Mo was sufficient to form Al2S3 at 700–9801C in H2/H2S/H2O atmospheres corresponding to pS2 105 atm and pO2 1020 atm. At aluminium levels of 9–10 wt%, exclusively Al2O3 scales are formed, sulfidation being completely prevented. Qualitatively similar benefits are achieved with Ni–Mo–Al alloys in H2/H2S/H2O gases [120]. The results are complicated by the formation of the double sulfide Al0.55Mo2S4. It is clear from the work on aluminium-containing alloys that Al2O3 formation provides the best possibility of protection against sulfur corrosion. However, formation of the necessary continuous alumina layer requires a sufficiently high interfacial aluminium concentration, N Al;i . As seen from Equation (6.11), this requires both high alloy levels of aluminium and high diffusivities. At the relatively low temperatures involved in some sulfur corrosion processes, DAl will be low and the value of N ðoÞ Al required makes austenitic alloys impractical. Recognition of this problem has led to numerous investigations into the performance of metal aluminides. Iron aluminides have been shown by Tortorelli et al. [121–123] to have particularly good resistance to sulfidation as a result of
8.8. Hot Corrosion
383
their ability to develop protective Al2O3 layers. An Fe40 wt% Al alloy was found by Lang et al. [124] to exhibit excellent resistance to H2/H2S gases containing up to 9.7 v/o H2S at 900 and 1,0001C. Again, protection was due to Al2O3 formation. Nickel aluminides are much less successful, as a result of rapid nickel sulfide growth when the sulfur potential is high enough to stabilize these reaction products. Natesan [67] showed that the gu-Ni3Al intermetallic failed by sulfidation in this way at 8751C, being unable to form Al2O3. Schramm and Auer [125] demonstrated the same result for Ni–Al binaries containing 25–45 wt% Al exposed to H2/H2S/H2O at 750–9501C. The b-NiAl intermetallic also fails to develop a protective Al2O3 scale [68, 126]. The performance of several chromia and alumina forming alloys and coatings in the complex reducing, sulfidizing conditions expected of coal gasification have been explored, and the interested reader is referred to [127–130].
8.7. INTERNAL SULFIDATION Internal sulfidation is seldom studied, as the rate at which an alloy is consumed by scaling often exceeds the rate at which sulfur can diffuse into the alloy. Under these conditions, the rapidly receding scale–alloy interface sweeps up and incorporates any internal precipitates. However, if the reaction is carried out at such a low pS2 value that no external sulfide scale forms, or if a slowly growing oxide scale is penetrated by sulfur, internal sulfidation can result. Studies on model systems might provide information on sulfur permeabilities for use in predicting corrosion rates for more practical materials. Unfortunately, there are practical problems with this approach. In the first place, because sulfide stabilities are relatively low, their solubility products in iron- and nickel-based alloys are high (see Equations (2.82)–(2.90)). Consequently, the simple Wagner description of internal sulfidation kinetics leads to quantitative error. Secondly, thermodynamic interactions between solute metals and dissolved sulfur can be rather large. Finally, it has been clearly established [131–133] that sulfur diffuses preferentially along alloy grain boundaries over a wide range of temperatures, leading to intergranular sulfide precipitation. Austenitic heat-resisting steels have been found [129, 134–136] to undergo intergranular sulfidation during exposure to mixed oxidizing–sulfidizing gases, and in reaction with pure S2(g). Unfortunately, it is currently not possible to predict how the rate of this process will change with alloy composition or temperature.
8.8. HOT CORROSION The combustion of fossil fuels and the incineration of waste often produce condensed phases as well as combustion gas. Ash is generated from mineral
384
Chapter 8 Corrosion by Sulfur
components of the burning materials, and can be expected to deposit on equipment surfaces. In addition, sulfur impurities are burnt to form SO3, which reacts with alkali metals to form stable sulfates. Small amounts of salt in the air are sufficient to promote reactions such as SO3 þ H2 O þ 2NaCl ¼ Na2 SO4 þ 2HCl
(8.11)
Pure Na2SO4 has a melting point of 8841C, and can condense as a liquid on hardware exposed to the gases. (The presence of other solutes in the sulfate will change this melting point.) Liquid sulfates are ionic melts. Interactions between them and metals are therefore electrochemical in nature, involving oxidation of the metal in an anodic process such as M ¼ Mnþ þ ne
(8.12)
and reaction of salt species [137, 138] ¼ S2 O¼ 7 þ e ¼ SO4 þ SO3
(8.13)
¼ SO 3 þ e ¼ SO2 þ O
(8.14)
supported by the dissolution reaction ¼ SO3 þ SO¼ 4 ¼ S2 O7
(8.15)
This process is analogous to the electrochemical corrosion of metal in aerated water, in which the dissolved oxygen is reduced to hydroxide. As we will see, there is a further analogy in that hot corrosion is a dissolution–reprecipitation process, like the rusting of iron, in which the step (8.12) is followed by solid compound formation. Other liquid phases can be produced in combustion processes. Fuel oils can contain small amounts of vanadium which forms a series of oxides, up to V2O5 with a melting point of 6901C. Various sodium vanadates can form, with melting points around 550–7001C. The combustion of biomass together with coal can generate large amounts of Na2SO4 and/or K2SO4. Finally, waste incineration produces chemically diverse condensed phases, principally sulfates and chlorides. All of these liquid phases cause accelerated attack, or ‘‘hot corrosion’’. Attention will be restricted here to sulfate-induced hot corrosion, and the reader is referred to reviews by Paul and Seeley [140] and Rocca et al. [141] for an account of vanadium-induced hot corrosion.
8.8.1 Phenomenology of sulfate-induced hot corrosion The subject has been reviewed by Stringer [139, 142], Pettit and Giggins [143], Kofstad [144] and Rapp [145, 146]. The principal application is the accelerated corrosion of gas turbine hot stage components, a field which continues to be a focus for research. Hot corrosion in gas turbines is caused by salt deposition in the engines, a subject which has been reviewed by Bornstein and Allen [147]. The resulting damage can be severe, as seen from the example of hot corrosion damage to a diffusion coating shown in Figure 8.12.
8.8. Hot Corrosion
385
Figure 8.12 SEM view of damage to a model chromium modified nickel aluminide coating on a Rene´ 80H nickel-base superalloy after 18 h exposure at 9001C to a molten Na2SO4 film in a gas of O2–1%SO2. Porous oxide has developed along with internal sulfidation.
When sulfate-induced hot corrosion was first investigated, it was thought [148, 149] that alloy sulfidation by the salt was a necessary precursor to accelerated attack. In a series of key papers, Bornstein and De Crescente [150–152] and Goebel and Pettit [153] established the essential elements of the hot corrosion phenomenon. The role of sulfur was shown to be non-essential by the finding that oxidation of presulfidized superalloys did not lead to accelerated corrosion. Furthermore, exposure to molten Na2CO3 or NaNO3 did cause accelerated reaction, just like Na2SO4. Bornstein and De Crescente proposed that the alloy’s protective oxide scale was attacked by Na2O, the basic component of all three molten salts used. Goebel and Pettit also interpreted hot corrosion of nickel in the same way, i.e. dissolution of NiO into a basic melt, and added the additional step of NiO reprecipitation at other locations. This mechanism explained the induction period observed experimentally prior to rapid reaction. It corresponds to the time taken for dissolution of the protective oxide to occur, allowing direct access of the melt to the underlying alloy. The model was extended by Goebel et al. [154] to describe hot corrosion of alloys containing acidic oxide formers such as vanadium or molybdenum. As is discussed under Molten Salt Chemistry, the metal oxides of interest are soluble also in acidic melts. In order to evaluate oxide solubilities, it is necessary first to consider the thermodynamics and electrochemistry of the melt.
8.8.2 Molten salt chemistry The thermodynamics of oxyanion melts are conveniently described in terms of equilibrium with the oxide anion and the appropriate gas species. Thus, for a
386
Chapter 8 Corrosion by Sulfur
sulfate melt ¼ SO¼ 4 ¼ O þ SO3 ðgÞ
(8.16)
and corresponding equilibria can be written for carbonates and nitrates. In the hot corrosion literature, reaction (8.16) is conventionally written as Na2 SO4 ¼ Na2 O þ SO3 ðgÞ
(8.17)
log aNa2 O þ log pSO3 ¼ DG17 =2:303 RT
(8.18)
from which it follows that The equilibrium is described as an acid–base reaction, with Na2O (or O ¼ ) the base and SO3 the acid. At a fixed temperature, the thermodynamic state of a sodium sulfate melt is then specified by the values of the oxygen potential plus the melt basicity, defined as log aNa2 O by analogy with the pOH of aqueous solutions. The various possible states for the Na–S–O system are shown in the phase diagram of Figure 8.13. The melt stability regime is seen to be large, implying that a film of this liquid on a metal surface can sustain large gradients in oxygen potential and basicity. The diagram can be calculated from standard free energy data, using the methods of Section 2.2 [155]. The assumption of unit activity for condensed phases is used to define the phase boundaries in the diagram.
Figure 8.13 The Na–S–O phase diagram for 9001C [155]. Reproduced by permission of The Electrochemical Society.
8.8. Hot Corrosion
387
The sulfate melt phase field is shown subdivided into regions corresponding to different predominant ionic minority species. The local chemical state in any melt can be determined electrochemically [145, 146], using a ZrO2 electrode to measure oxygen activity and a sodium conducting solid electrolyte to measure aNa . The next step is to superimpose the Na–S–O phase diagram on the corresponding one for the corroding metal, following the procedure of Quets and Dresher [156]. The example of nickel is shown in Figure 8.14. As can be seen, nickel metal is stable in contact with the melt in only a very small region. Similar diagrams for iron, chromium and aluminium show that these metals have no regions of stable coexistence with molten Na2SO4. The development of new phases and the extent of their intersolubility must therefore be investigated. Nickel forms a solid sulfate (Figure 8.14), but only at very high pSO3 values. However, NiSO4 dissolves readily in Na2SO4 [157]. Its activity as a melt solute is represented by the dotted lines in Figure 8.14. In addition, Gupta and
log pSO3 -15
-10
0
-5
-5
0 NaNiO2
NiO
NiSO4
-2
-2 -4
-4
log po2
-5
Na2O
-10
NiS
Ni
Na2S 0
5
10
15
20
-log aNa2O
Figure 8.14 Phase stability diagram for Ni–S–O at 9001C in the presence of Na2SO4.
388
Chapter 8 Corrosion by Sulfur
Rapp [158] concluded (see later) that the NiO 2 anion forms, and its isoactivity lines are also shown in Figure 8.14. Rapp and co-workers [158–162], Deanhardt and Stern [163] and Misra et al. [164] measured oxide solubilities in Na2SO4 melts. Data for pO2 ¼ 1 atm and T ¼ 9271C are summarized in Figure 8.15. Most oxides are seen to exhibit two regimes of dissolution separated by a minimum behaviour which can be understood in terms of basic and acidic dissolution. Consider the example of NiO dissolution via basic dissolution 2NiO þ 12O2 ðgÞ þ O2 ¼ 2NiO¼ 2
(8.19)
NiO ¼ Ni2þ þ O¼
(8.20)
and acidic dissolution
The corresponding equilibrium expressions are used to derive the dependence of nickel solute activity on basicity: @ log aNiO¼2 1 ¼ 2 @ log aNa2 O pO2
(8.21)
@ log aNi2þ ¼1 @ log aNa2 O pO2
(8.22)
j
j
The measured [158] slopes of nickel solute concentration versus log aNa2 O were in good agreement with these predictions. Assuming that the dilute solutions were Henrian, it is concluded that the acidic and basic dissolution processes are
Figure 8.15 Measured oxide solubilities in molten Na2SO4 at 9271C and pO2 ¼ 1 atm [146]. With kind permission from Springer Science and Business Media.
8.8. Hot Corrosion
389
correctly formulated. The conclusion was reinforced by the finding that the dependence on pO2 of the basic solubility was correctly predicted. Although it has been shown that the oxides of importance to high temperature alloys will dissolve in sulfate melts, their solubilities can be rather low (Figure 8.15). The question therefore arises as to why a hot corrosion reaction does not become very slow, at least in a quiescent melt, as it becomes saturated at the oxide–sulfate interface. The answer lies, of course, in continuing mass transport within the melt.
8.8.3 Fluxing mechanisms A flux of solute metal into the salt deposits will be maintained if an appropriate activity gradient exists. Rapp and Goto [165] pointed out that this would be the case if the solubility decreased monotonically with increasing distance into the sulfate film. The mechanism is shown schematically in Figure 8.16. The greater extent of precipitation arrived at with increasing values of x means that less metal remains in solution, and therefore @ C Mþ o0 (8.23) @ x A diffusion flux results from this gradient. The required gradient in solubility cannot result from the expected gradient in ao, as shown in reaction (8.20). Alloy
MO
Fused salt film
Gas
solubility of MO
pSO3 aNa2O
Figure 8.16 Hot corrosion by dissolution and reprecipitation in a molten salt film. Based on model of [166].
390
Chapter 8 Corrosion by Sulfur
However, variation in salt basicity with position will cause gradients in solubility in both basic and acidic fluxing regimes (Figure 8.14). Basic fluxing into molten sulfate stabilized at its outer surface by the presence of gaseous SO3 is readily understood. Local penetration of the oxide scale by molten salt places the metal in contact with a low ao and high as liquid, leading to its sulfidation. Removal of sulfur from the liquid increases its basicity at the solid–molten salt interface, whereas the continuing presence of SO3 at the liquid–gas interface maintains a more acidic condition at this boundary. The required gradient in aNa2 O , and therefore in CMþ , is thereby achieved. The additional gradient in aSO3 can drive anion diffusion, maintaining a sulfidation reaction. This sequence of steps has been demonstrated in the case of pure nickel by Otsuka and Rapp [166] using electrochemical monitoring to map reaction progression on the phase diagram of Figure 8.13. The reaction morphology of Figure 8.12 is also accounted for: sulfide is formed at and beneath the alloy surface, and reprecipitated oxide forms a porous deposit rather than a compact scale. Acidic fluxing can occur if the melt is more acid at the material–melt interface than at the melt–gas surface. This can occur during corrosion of alloys, when the dissolution of one component creates the gradient in basicity necessary to flux another [167]. Dissolution of alloy components molybdenum and tungsten produces the strongly acidic oxides MoO3 and WO3, and much enhanced oxide stability through their ability to form complexes. A negative gradient in the acidic species is expected to result from its evaporation at the melt–gas interface. Both fluxing mechanisms account for the observed development of porous oxides via reprecipitation during hot corrosion. Of course, the reactive steady state implied by the model (Figure 8.16) is unrealistic. Firstly, the model ignores the effect of metal sulfide formation. As seen in Section 8.2, these sulfides are rapid diffusers, and their growth is important to the overall process. Moreover, this process consumes sulfur and destabilizes the melt unless further SO3 is supplied from the gas. Secondly, the role of the melt as an inexhaustible supply of fluxing ions to be recycled in the fluxing process can only be fulfilled if its overall chemistry remains unaltered. This requires a constancy of boundary conditions, particularly of pSO3 , seldom achieved in practice. Finally, as reaction proceeds and more porous oxide accumulates, the melt phase is attenuated and the maintenance of a continuous liquid diffusion path becomes impossible. Nonetheless, the fluxing mechanisms originally proposed by Bornstein and De Crescente [150–152] and Goebel et al. [153, 154] provide useful accounts of hot corrosion. The electrochemical measurements of Rapp et al. [158–162] have demonstrated that virtually all metals of importance to high temperature alloys are subject to attack by liquid sulfates.
8.8.4 Type I and Type II hot corrosion Two temperature regimes of molten sulfate-induced corrosion are observed for nickel and cobalt and their alloys. At temperatures around 9001C, pure Na2SO4 is
8.9. Achieving Sulfidation Resistance
391
liquid, and corrosion occurs as described earlier. This is termed Type I hot corrosion. However, hot corrosion can also occur well below the Na2SO4 melting point of 8841C. Rapid attack at temperatures of 650–6701C was found by Luthra and Shores [168] to result from formation of NiSO4–Na2SO4 or CoSO4–Na2SO4 ternary melts. The mechanism was thought to be acidic fluxing, and was observed for a series of Co–Cr, Co–Al and Co–Cr–Al alloys [169]. This is Type II hot corrosion. Under these conditions, formation of a passivating Cr2O3 or Al2O3 layer was found to be difficult. Similar results have been obtained for iron-based alloys, due to the formation of low melting FeSO4–Na2SO4 ternary salt solutions [170, 171]. The morphology of Type II hot corrosion is one of non-uniform attack, with pits of different sizes growing into the metal. Measuring the rate is therefore difficult, and lifetime predictions require complex and rather empirical statistical models [172]. The role of chromium and aluminium in providing protection against hot corrosion is seen from Figure 8.14 to be limited by the relatively high solubilities of their oxides in molten sulfate. Early electrochemical measurements by Rahmel et al. [173, 174] on nickel- and cobalt-based superalloys showed that passivation of chromia-forming alloys occurred at intermediate potentials, but not at more anodic potentials where acidic corrosion occurred. Alumina-forming alloys did not form a protective scale at all, but aluminide and platinum-modified aluminide coatings could form protective Al2O3. Later studies of superalloy hot corrosion have been numerous, and are not reviewed here. However, they are in general agreement that these alloys contain too little chromium and aluminium to resist hot corrosion. Some representative superalloy compositions are shown in Table 1.2 and Appendix A. There remain two possible routes to protection against hot corrosion when salt deposition cannot be avoided: operation at temperatures above the salt dew points, or provision of hot corrosion resistant coatings. The development of conventional metallic coatings has been reviewed by Goward [175], and that of thermal barrier coatings by Clarke and Levy [176]. The metal coatings are very rich in aluminium or contain high levels of both aluminium and chromium (Table 1.2). Thermal barrier coatings are stabilized zirconia. Modifications to metal coatings designed to improve their corrosion resistance by adding chromium or platinum group metals [177–183] continue to be investigated.
8.9. ACHIEVING SULFIDATION RESISTANCE As we have seen, most metals of practical importance react with S2(g) at unacceptably rapid rates. The reasons for this have been made clear by a large body of research: many metal sulfides contain large concentrations of rather mobile point defects, which support rapid diffusion. In addition, low melting point eutectics are formed in a number of metal–metal sulfide systems. Efforts to achieve sulfidation resistance by alloying have centred largely around the use of refractory metals, which form stable, slow growing sulfides. The resulting alloys
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do possess superior sulfidation resistance, but they are impractical as engineering materials. It is recognized, however, that dealing with pure sulfur gas is a most unusual requirement. Sulfidising environments of practical importance usually contain either H2S or SO2, depending on the process in question. Solutions to the oxidizing–sulfidizing problem are discussed in Chapter 4, and involve stable oxide-forming alloys. It is convenient to consider reducing, sulfidizing environments according to their temperatures. A good example is provided by the oil refining industry. Crude oil distillation units operate at temperatures below 3001C, and low alloy steels are sufficient to resist the organic sulfur species encountered. Hydrodesulfurization is used to remove sulfur from the process stream by converting it to H2S. Operating temperatures are in the range 300–4001C, and effective sulfur activities are low. Under these conditions, chromium-bearing steels provide adequate protection, producing slow growing sulfide scales. Subsequent higher temperature processing can then be carried out without fear of sulfur corrosion. Avoiding high temperatures is not always possible when handling H2S. Pyrometallurgical processing of sulfide ores and gasification of coal provide examples where reducing, sulfurizing gases must be handled at elevated temperatures. The materials solution in these cases is to use refractory oxide lined process vessels and gas mains in the high temperature regions of the plant. A problem arises, however, if there is a need to pass the hot gases through heat exchangers. The thermal efficiency of heat exchangers is generally best when metal surfaces are used, so high temperature sulfidation resistance will be required. As we have seen, alloys which form stable oxides provide good resistance to attack by H2S. Depending on the process, alumina formers may prove adequate in these applications. At still lower oxygen activities, coatings will be required. It is here that the fundamental research on sulfidation resistant refractory metal alloys is likely to prove of practical value. Molten sulfate accelerated corrosion is essentially an electrochemical dissolution–reprecipitation process. One practical way of achieving resistance to this form of attack involves avoiding the deposition of molten salts. This can be done by ensuring a clean gas, or by controlling the temperature of equipment surfaces so as to prevent liquid condensation. When these approaches are impossible, as for example in a waste incinerator, the materials solution is to use refractory lined equipment. A somewhat similar approach is adopted for gas turbine engines. Metal surfaces are coated with materials which either are oxides or which develop resistant oxides.
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CHAPT ER
9 Corrosion by Carbon
Contents
9.1. 9.2. 9.3. 9.4.
Introduction Gaseous Carbon Activities Carburization Internal Carburization of Model Alloys 9.4.1 Reaction morphologies and thermodynamics 9.4.2 Carburization kinetics 9.4.3 Carbide microstructures and distributions 9.5. Internal Carburization of Heat Resisting Alloys 9.5.1 Effect of carbon 9.5.2 Effect of molybdenum 9.5.3 Effect of silicon 9.5.4 Effect of niobium and reactive elements 9.5.5 Effect of aluminium 9.5.6 Alloying for carburization protection 9.6. Metal Dusting of Iron and Ferritic Alloys 9.6.1 Metal dusting of iron 9.6.2 Iron dusting in the absence of cementite 9.6.3 Effects of temperature and gas composition on iron dusting 9.6.4 Dusting of low alloy steels 9.6.5 Dusting of ferritic chromium steels 9.6.6 Dusting of FeAl and FeCrAl alloys 9.7. Dusting of Nickel and Austenitic Alloys 9.7.1 Metal dusting of nickel 9.7.2 Dusting of nickel alloys in the absence of oxide scales 9.7.3 Effects of temperature and gas composition on nickel dusting 9.7.4 Dusting of austenitic alloys 9.8. Protection by Oxide Scaling 9.8.1 Protection by adsorbed sulfur 9.8.2 Protection by coatings 9.9. Controlling Carbon Corrosion References
398 400 402 403 403 408 412 415 418 418 419 419 420 421 421 422 428 428 431 432 434 435 435 439 441 443 444 448 448 449 450
397
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Chapter 9 Corrosion by Carbon
9.1. INTRODUCTION Combustion of fossil fuels (coal, oil, natural gas) provides the basis for a major part of the world’s energy generation. This includes burning fuel to raise steam for electric power generation and combustion of liquid fuels for transportation. The combustion reactions C þ 12O2 ¼ CO (9.1) CO þ 12O2 ¼ CO2
(9.2)
CH4 þ 2O2 ¼ CO2 þ 2H2 O
(9.3)
are often carried out using excess air, so that the exhaust gases contain free molecular oxygen plus CO2 and H2O. Despite the use of excess air or oxygen, locally reducing conditions can develop and persist in large-scale combustion units. Such conditions can lead to carbon attack, as is discussed shortly. There is a continuing drive to improve the efficiency of combustion processes. Not only are temperatures being raised to achieve higher efficiencies (see Equation (1.6)), but alternative or modified technologies are being developed to reduce emissions of the greenhouse gas, CO2. The capture and sequestration of CO2 is made more feasible by using pure oxygen rather than air as oxidant, thereby eliminating nitrogen from the combustion gas. Because combustion in pure oxygen leads to excessively high flame temperatures, some of the exhaust CO2 is recirculated as a diluent for the input oxygen. As a result, the combustion zone gases contain very high concentrations of CO2 and H2O. Little is known of the behaviour of heat resisting alloys in such environments. However, given earlier observations (see Section 4.5) of carbon deposition within oxide scales exposed to CO2/CO atmospheres, there seems to be a need for research in this area. A number of other high-temperature processes are conducted under reducing conditions so as to produce hydrogen or CO, rather than their oxidation products. Steam reforming of natural gas CH4 þ H2 O ¼ CO þ 3H2
(9.4)
is widely used to produce hydrogen. This process is carried out at temperatures of around 800–9001C by passing the gases through catalyst beds in alloy tubes heated from the exterior. Somewhat similar tubular reactors are used in the Pyrolysis or ‘‘steam cracking’’ process for making ethylene or propylene, e.g. ðH2 OÞ þ C2 H6 ¼ C2 H4 þ H2 þ ðH2 OÞ
(9.5)
In this case the steam is added as a diluent in order to reduce the amount of solid carbon produced by gas phase pyrolysis. Feedstock materials, hydrocarbons, continually increase in price, and the need for improved process efficiencies has led to higher operating temperatures. Simultaneously, tube wall thicknesses have been reduced to improve heat transfer efficiency. Thus process engineering changes have led to higher tube metal temperatures and reduced load-bearing sections. These increased demands
399
9.1. Introduction
on material properties have been met by a series of advances in alloy design. The tubes are centrifugally cast, austenitic chromia formers. Their compositions (Table 9.1) have evolved from the old HK 40 grade (Fe–25Cr–20Ni), through the HP grades (Fe–25Cr–35Ni) to high nickel alloys containing 45% or even 60% Ni. The increased alloy levels have provided significant improvements in creep properties, but the alloys are still subject to corrosion by carbon. The process of coal gasification is of potential importance in achieving highefficiency electric power generation. Steam is contacted with coal at high temperature, producing synthesis gas C þ H2 O ¼ CO þ H2
(9.6)
Although coal gasification has been employed for a long time, its use on the scale and at the intensity required to support gas turbine driven power generation is relatively new. The selection of materials for handling and processing the hot carbonaceous gases produced from coal will depend on the gasification technologies chosen, and the coal impurity levels involved. However, the carbon corrosion mechanisms can be expected to be related to those observed in steam reforming and steam cracking plants. Table 9.1
Nominal heat-resisting alloy compositions (wt%) C
Si
Mn
Ni
Cr
0.4 0.4 0.44 0.09 0.53 0.46 0.45 0.44 0.42 0.40 0.43
1.3 1.8 1.5 2.2 2.1 2.1 1 1 0.1 0.0 0.1
0.6 1.1 1.5 1.1 0.3 1.2 0.4 0.5 0.1 0.2 0.1
21 35 35 36 29 45 45 45 60 61 59
25 25 25 26 30 35 19 30 25 25 25
Wrought alloys 304L 0.03 310S 0.08 800 0.1 601 0.03 625 0.02
1 1.5 0.4 0.3 0.1
2 2 0.7 0.2 0.1
8 19 32 60 60
18 24 20 22 22
690 693 602 CA
0.1 0.1 0.05
0.1 0.2 0.1
61 61 63
27 29 20
Cast alloys HK40 HP HP Mod Nb H101 30Cr Micro 35/45 45Pa 45HT 60HT(a) 60HT(b) 60HT(c)
0.02 0.01 0.2
Nb
0.8 1.5 1 1 1 0.4 0.5 1 1
0.45
Al
Other
0.1Zr, 0.2Ti
0.11Ce 2 0.5 2.4 3.6 4.8
3Mo, 0.3–1.5Hf 0–0.8Hf 0.06Y 0.05Y 0.06Y
0.3 1.4 0.4
0.4Ti 0.4Ti 9Mo, 3.4(Nb+Ta), 0.2Ti 0.2Ti 0.4Ti 0.1Ti, 0.09Y, 0.08Zr
0.2 3.2 2.3
400
Chapter 9 Corrosion by Carbon
Under combustion conditions, the oxygen potential is usually high enough to guarantee oxide scale formation. The questions of interest then concern interaction of CO2 with the oxide. In contrast, synthesis gas and other carbonaceous gases handled in the chemical and petrochemical industries are characterized by high carbon activity, aC , values and low oxygen potentials. Typically these gases are oxidizing to chromium and aluminium, but not to iron or nickel. The questions of interest therefore concern the ability of Cr2O3 and Al2O3 scales to exclude carbon from the alloy, and the consequences of oxide scale failure when carbonaceous gas species contact the metal surface. We consider first the simple case where the oxygen potential is so low that no oxide forms, and corrosion by carbon alone results. Carbon is unique among the common oxidants in that it is stable as a solid over a wide temperature range if the gas is sufficiently reducing. For this reason, the thermodynamic reference state is chosen as pure, solid graphite, for which aC ¼ 1. If the carbon activity is less than one, but large enough to stabilize a metal carbide, the reaction is described as carburization. Such reactions are rapid and destructive. However, if the gas is supersaturated with respect to carbon (aC W 1), an even greater threat emerges. If the gas can be brought to equilibrium, carbon is released from the gas phase and deposits on solid surfaces in a process described as coking. Frequently, however, the gas remains supersaturated. In this case, catalysis of carbon deposition by the metal can lead to its disruption and fragmentation in an extremely rapid corrosion process known as metal dusting. Dusting mechanisms are different for ferritic and austenitic alloys, and they are discussed separately. Alloy design strategies for slowing carburization and metal dusting are shown to be of limited value. However, alloying to achieve protective oxide formation can delay carbon access to the metal. This approach is discussed together with other surface treatments in the final section of this chapter.
9.2. GASEOUS CARBON ACTIVITIES The common gas phase processes producing carbon are the synthesis gas reaction CO þ H2 ¼ H2 O þ C
(9.7)
2CO ¼ CO2 þ C
(9.8)
CH4 ¼ 2H2 þ C
(9.9)
the Boudouard reaction and hydrocarbon cracking, e.g. Their standard free energies are listed in Table 9.2. It is necessary to recognize that all three reactions are very slow as homogenous gas phase processes. They will not reach equilibrium in a typical laboratory reactor, unless catalysed. Although many materials of practical interest — iron, nickel, cobalt and their alloys — are catalytically active to these reactions, their oxide scales are inert.
401
9.2. Gaseous Carbon Activities
Table 9.2
Gas phase equilibria relevant to carburizing [10] DGf ¼ A þ BTðJ mol1 Þ
Reaction
CO+H2 ¼ H2O+C 2CO ¼ CO2+C CH4 ¼ 2H2+C
A
B
134,515 170,700 +87,399
142.37 174.5 108.74
4 H2+CO→C+H2O 3 CH4→C+2H2
Log10(Kp)
2 2CO→C+CO2 1 0 -1 -2 300
400
500
600 700 T (°C)
800
900
1000
Figure 9.1 Equilibrium constants for gas phase carbon producing reactions.
As seen in Table 9.2 and Figure 9.1, temperature effects are very different for these carbon-producing reactions. Thus methane, and hydrocarbons in general, can produce significant carbon activities only at high temperatures. However, the synthesis gas and Boudouard reactions produce increasing carbon activities as the temperature is lowered. It is because these gases are difficult to equilibrate that they can become supersaturated with respect to carbon, i.e. aCW1. An example is synthesis gas produced in a steam-reforming unit, which will normally have aCo0.5. As the gas is cooled from reaction temperature, however, the rate of reaction (9.7) is so slow that the gas fails to adjust its composition by depositing carbon. The gas phase carbon activity calculated from K7 pH2 pCO aC ð7Þ ¼ (9.10) pH 2 O can then be much greater than unity. It is recognized that the same gas also produces carbon via reaction (9.8), and one can calculate aC ð8Þ ¼
K8 p2CO pCO2
(9.11)
402
Chapter 9 Corrosion by Carbon
In general, aC ð7ÞaaC ð8Þ, because the gas is not at equilibrium. In this situation, it is appropriate to consider the reactions (9.7)–(9.9) as separate, independent processes, as is demonstrated in Sections 9.6 and 9.7. Nonetheless, because reaction (9.7) is usually faster than reaction (9.8), it is common to calculate aC from Equation (9.10). The water vapour present in many gas mixtures is also capable of interaction with surface oxide scales, as is discussed in Chapter 10. Of course, these effects can be ignored in the reducing conditions characteristic of many carburization and dusting reactions. However, they can be important in the situation where an oxide scale is relied upon for protection against carbon attack. Some of the interactions between H2O(g) and carbon species are discussed in Chapters 4 and 10. Carburization experiments require aC 1. The use of CH4/H2 gas mixtures to control carbon activity is inadvisable at temperatures below about 1,0001C, because of the slow rate of reaction (9.9) and the usually brief residence time in a laboratory reactor. It is preferable to use mixtures of H2 and C3H6, as the latter pyrolyses readily.
9.3. CARBURIZATION Carbides are much less stable than oxides, as seen from the examples in Table 9.3. Thermodynamic data for other carbides can be found in a review by Shatynski [1]. Of the common alloy base metals, nickel and cobalt do not form carbides under the conditions of interest. Iron forms cementite, Fe3C, at temperatures below 7631C only if aCW1. Exposure of these metals to reducing carbonaceous gases at aCo1 therefore cannot cause scale formation, but leads instead to dissolution of carbon at the metal surface and its diffusion inwards. If the metal surface is at equilibrium with the gas phase, the surface concentration of dissolved carbon, N ðsÞ C (mole fraction), can be found from the relationship N ðsÞ C ¼ KaC
(9.12)
Data for carbon dissolution in iron and nickel are summarized in Table 9.4, where the carbon solubility in nickel is seen to be much lower than in g-Fe. If inward Table 9.3
Properties of metal carbides [1, 10] DGf ¼ A þ BT ðJ mol1 Þ
Carbide
Cr23C6 Cr7C3 Cr3C2 NbC SiC Al4C3 Fe3C a
A
B
411,200 174,509 84,353 130,122 113,386 266,520 29,037
38.7 25.5 11.53 +1.67 +75.7 +96.2 28.0
Volume per mole of metal.
V aMCy ðcm3 Þ
MP ð CÞ
7.91 8.26 8.98 13.47 13.70 15.24 8.31
1,580 1,665 1,895 3,480 2,700 B1,400 1,650
403
9.4. Internal Carburization of Model Alloys
Table 9.4
Carbon dissolution in metals xs
Metal
DHC ðk J mol1 Þ
DSC ðJ mol1 K1 Þ
Reference
Ni g-Fe
54 44.04
5 17.62
[3] [2]
carbon diffusion causes no phase change in the solvent metal, and if furthermore DC is independent of composition, then the resulting carbon concentration profile is found by solving Fick’s second law to obtain N C N ðoÞ x C ffiffiffiffiffiffiffiffi p ¼ erfc (9.13) ðoÞ 2 DC t N ðsÞ C NC Here N ðoÞ C represents the original carbon level in the metal before carburization. The rate at which the carburization zone widens is given approximately by X2i ¼ 4DC t
(9.14)
Using data for DC [4, 5] (see Table A2) it is found that carbon penetrates about 3 mm into each of g-Fe and Ni in 24 h at 1,0001C. We conclude that not only are Fe-, Ni- and Co-based alloys susceptible to internal attack, but that the process will be rapid. Such high rates of attack are usually averted by designing the alloy to develop a protective oxide scale. The heat resisting alloys used in contact with carbon-rich gases are usually chromia formers. As seen in Table 9.3, chromium also forms reasonably stable carbides. It is commonly observed [6–8] that exposure of these alloys to gas compositions such that no chromia scale can form leads to internal chromium carbide precipitation rather than external scale formation. The conditions under which this reaction morphology develops are now examined using model Fe–Cr, Ni–Cr and Fe–Ni–Cr alloys, for which the necessary data is available.
9.4. INTERNAL CARBURIZATION OF MODEL ALLOYS 9.4.1 Reaction morphologies and thermodynamics Chromium carbides are the expected reaction products, and their formation within the alloy is the outcome of competition between rival processes. Scale formation is favoured by rapid diffusion of chromium from the alloy to its surface, whereas internal precipitation is favoured by rapid carbon ingress. Wagner’s analysis [9] (see Section 6.11) of this situation allows calculation of the minimum value of N ðoÞ Cr at which scaling is favoured over internal precipitation !1=2 ðsÞ p V A N C DC ðoÞ (9.15) N Cr;min ¼ gCrCn 2n V CrCn DCr Here g is the critical volume fraction necessary to form a continuous layer, V A and V CrCn the molar volumes of alloy and carbide, DC and DCr the diffusion
404
Table 9.5
Chapter 9 Corrosion by Carbon
Permeability data for carburization
Alloy
T (1C)
2 1 NðsÞ C DC ðcm s Þ
DCr ðcm2 s1 Þ
g-Fe
900 1,000 1,100 900 1,000 1,100
4.3 109 1.4 108 5.5 108 7.9 1010 3.6 109 1.4 108
4.4 1013 3.7 1012 2.3 1011 8.0 1013 7.2 1012 4.7 1011
Ni
coefficients in the alloy of the indicated solutes and n the stoichiometric constant for the carbide CrCv . Choosing Nimonic 75 (approximately Ni–20Cr) as a basis for calculation, we can specify VA ¼ 6.58 cm3 mol1. Values for carbon permeability ðN ðsÞ C DC Þ and DCr listed in Table 9.5, together with V CrCn taken from Table 9.3 and the supposition gCrCn ¼ 0:3, leads to estimates of N ðoÞ Cr ¼ 15, 20 and 37 required to form scales of Cr3C2, Cr7C3 and Cr23C6, respectively, at 1,0001C. Of course values of NW1 lack physical meaning, and result from inaccuracies in the data. The conclusion is simply that Ni–Cr alloys are unlikely to form carbide scales exclusively, because the inward carbon flux is so high and the molar volumes of chromium carbides are small. The conditions necessary for carbide precipitation are now examined more closely. In the case of Cr23C6, we can write ðMÞ þ 23 Cr þ6 C ¼ Cr23 C6 ðþMÞ; DGp (9.16) the free energy change for which can be calculated from data for carbide formation 23Cr þ 6C ¼ Cr23 C6 ; DGf and alloy component dissolution Cr ¼ Cr; C ¼ C;
(9.17)
¯ Cr DG
(9.18)
¯C DG
(9.19)
in the solvent metal, M. Thus ¯ Cr 6DG ¯C (9.20) DGp ¼ DGf 23DG and we evaluate the carbide solubility product ¯ Cr 6DH ¯ CÞ ðDGf 23DH 23 6 N Cr N C ¼ Ksp ¼ exp (9.21) RT ¯ i the partial molar heat of dissolution. A similar treatment for Cr7C3 leads with H to the result ¯ Cr 6DH ¯ CÞ ðDGf 7DH N 7Cr N 3C ¼ Ksp ¼ exp (9.22) RT
9.4. Internal Carburization of Model Alloys
405
Standard values (Table 9.3) for DGf , carbon solubility data for g-Fe [2] and Ni [3] and activity coefficient data for Fe–Cr [90] and Ni–Cr [11] allow calculation of carbide solubility product values shown in Tables 9.6 and 9.7. Carbon solute levels in g-Fe and Ni in equilibrium with aC ¼ 1 are also shown in the tables, along with the corresponding minimum chromium concentrations, N Cr ðmin Þ, necessary to stabilize each carbide. Iron-based alloys are predicted on this basis to be more susceptible to internal carbide precipitation. This prediction is tested by comparing the calculated minimum N Cr values required for carbide precipitation with the experimental results for 1,0001C summarized in Table 9.8. The appearance of the carbide precipitation zones in Fe–Cr alloys is illustrated in Figure 9.2. As predicted, Fe–Cr alloys of high chromium content formed both carbides whereas Ni–Cr formed only Cr7C3. Furthermore, the prediction that no carbide should form in Ni–Cr with N ðoÞ Cr o0.13 is borne out. The success of this simple thermodynamic treatment indicates that local equilibrium is attained, and a steady-state diffusion description should therefore be applicable. However, while the assumption that the chromium carbides are pure phases — the basis for Equations (9.21) and (9.22) — is reasonable for the Ni–Cr–C system, it is a poor approximation for Fe–Cr–C. As seen in the phase diagram of Figure 9.3, iron solubilities in the carbides are high, and cannot be neglected. It is possible to calculate Ksp values for the mixed carbides (Cr,Fe)23C6 and (Cr,Fe)7C6, but a simpler approach is to construct diffusion paths representing the locus of compositions along lines through the reaction zone. Because DC 4 4DCr , these paths are constructed on the basis that only carbon Table 9.6
Calculated chromium carbide precipitationa in Fe–Cr alloys at aC ¼ 1
Alloy
9001C
N ðsÞ C ðg
0.057
FeÞ Ksp ðCr23 C6 Þ N Cr ðminÞ Ksp ðCr7 C3 Þ N Cr ðminÞ a
1,1001C
0.066 29
1 10 0.12 3 1016 0.02
0.098 27
3.6 10 0.14 3.8 1015 0.03
2.6 1024 0.17 3.4 1014 0.03
From Equations (9.21) and (9.22); NCr(min) defined in text.
Table 9.7
a
1,0001C
Calculated chromium carbide precipitationa in Ni–Cr alloys at aC ¼ 1
Alloy
9001C
1,0001C
N ðsÞ C Ksp ðCr23 C6 Þ N Cr ðminÞ Ksp ðCr7 C3 Þ N Cr ðminÞ
0.007
0.011
0.016
9.9 1026 0.29 9.8 1014 0.10
8.4 1024 0.32 9.4 1013 0.13
3.7 1022 0.34 6.5 1012 0.17
From Equations (9.21) and (9.22); NCr(min) defined in text.
1,1001C
406
Table 9.8
Carbides formed by Ni–Cr [12, 13] and Fe–Cr [14] at 1,0001C at ambient aC ¼ 1
Alloy
NðoÞ Cr
Surface carbides
Internal carbides
Reference
Ni–Cr
0.11 0.22 0.33 0.05 0.08 0.11 0.18 0.26
None Cr3C2
None Cr7C3 Cr7C3 M7C3a M7C3 M7C3 M7C3 + M23C6 M7C3 + M23C6
[12] [12] [13] [14] [14] [14] [14] [14]
Fe–Cr
a
Chapter 9 Corrosion by Carbon
Fe3C Fe3C Fe3C M7C3a M7C3
M: chromium-rich (Cr+Fe).
Figure 9.2 Internal carburization of Fe–Cr at 1,0001C (a) Fe–7.5Cr forms M7 C3 precipitates (b) Fe–17Cr forms innermost zone of lamellar M23 C6 precipitates [14]. Published with permission from The Electrochemical Society.
diffuses and hence the N Cr =N Fe ratio remains unchanged within the reaction zone. The diffusion path in Figure 9.3 for N ðoÞ Cr ¼ 0:08 is seen to cross the g þ M7 C3 two-phase region, corresponding to internal precipitation of this carbide, before entering the single-phase M3C zone, in agreement with experimental observation (Table 9.7). An alloy with N ðoÞ Cr ¼ 0:18 is seen to develop a carbon diffusion path which crosses successive two-phase regions g þ M23 C6 and g þ M7 C3 before entering the single-phase M7C3 field. Again, this corresponds with the experimental observation (Table 9.8) of two internal precipitation zones, with M23C6 forming in the inner (lower aC ) zone.
9.4. Internal Carburization of Model Alloys
407
Figure 9.3 Isothermal section at 1,0001C of the Fe–Cr–C phase diagram, with dotted lines showing carburization diffusion paths for DC 4 4DCr .
NCr/(NCr+NFe) Carbide
1
0.8
0.6
0.4
0.2
0 0
0.1
0.2 NCr/(NCr+NFe) matrix
0.3
0.4
Figure 9.4 Partitioning of Cr between precipitates and matrix in carburized Fe–Cr alloy [16] (filled symbols) and in equilibrium studies [15] (open symbols).
Because iron solubility in the carbides increases with aC , the Fe/Cr ratio in the precipitates is predicted to decrease with increasing depth within the precipitation zone. Microanalysis in a transmission electron microscope of carbides precipitated within an Fe–Ni–Cr alloy [16] revealed the partitioning of chromium between precipitate and matrix in the carburized alloy. As seen in Figure 9.4, the
408
Chapter 9 Corrosion by Carbon
results are in reasonable agreement with measured equilibrium values, and again it is concluded that local equilibrium is achieved throughout the precipitation zone. Two more important inferences can be drawn from the phase diagram of Figure 9.3. Carburization is predicted to transform the alloy matrix of a high chromium Fe–Cr alloy from ferrite to austenite as a result of chromium depletion and carbon saturation. As shown in Figure 9.2, this transformation is observed ðoÞ at the precipitation front. Secondly, if N Cr is less than about 0.4, then (Fe,Cr)3C is predicted to form at or near the alloy surface if the gas phase aC value is high enough. This is important in metal dusting reactions (Section 9.6), but can be ignored when studying carburization reactions at aC 1. Furthermore, in austenitic alloys the nickel content destabilizes Fe3C, and the phase is not observed.
9.4.2 Carburization kinetics Internal carburization is a particular form of internal oxidation, and its kinetics can therefore [6–8, 12] be described using Wagner’s theory [9], which was outlined in Chapter 6. Because (Table 9.5) carbon permeabilities are so high, N ðsÞ 4N ðoÞ C DC 4 Cr DCr , and the rate at which the carbide precipitation zone deepens is given by X2i ¼ 2kðiÞ p t kðiÞ p ¼
N ðsÞ C DC nN ðoÞ M
(9.23) (9.24)
where N ðoÞ M is the original alloy concentration of metal M which forms carbide MCn and e a diffusional blocking parameter (see Section 6.3). Thus carburization rates are predicted to vary inversely with concentration of reactive solute metal. Carburization of Fe–Cr alloys [14, 17] follows parabolic kinetics (Figure 9.5), ðoÞ ðoÞ and plots of kðiÞ p against 1=N Cr are seen to be linear except at high N Cr values. The slopes of these lines were used together with n ¼ 0.71 (for (Cr0.6Fe0.4)7C3 formed by low chromium alloys) and the assumption e ¼ 1 to calculate carbon permeabilities. Comparison in Table 9.9 with values found from N ðsÞ C [2] and DC [4] measurements shows good agreement, demonstrating the utility of Equation (9.24) in describing carburization rates. This is at first sight somewhat surprising, as Equation (9.24) is based on the assumption Ksp o o1, and the concentration of chromium in the matrix being close to zero. However, as will be seen in Section 9.4.3, Carbide microstructures and distributions, the resulting effect on carburization rates is small. A further prediction of Equation (9.24) is that carburization rates are determined by the permeability of the metal matrix, regardless of the identity of the precipitating carbide, providing that changes in the stoichiometric coefficient n are taken into account. Permeability values calculated for nickel by Allen and Douglass [12] from their carburization measurements of Ni–V, Ni–Cr and Ni–Nb alloys are seen in Table 9.10 to be in approximate agreement with
9.4. Internal Carburization of Model Alloys
409
45 40
Fe-5%Cr
Depth2 (cm2) × 10-4
35 30 25
Fe-7.5%Cr
20 15
Fe-10%Cr
10 5 0 0
50
100
150 time/min (a)
200
250
300
6
107 kp/cm2 s-1
1100°C
4
1000°C 2
900°C 0
5
10
15
20
(0)
1/Ncr
(b)
Figure 9.5 Carburization of Fe–Cr alloys (a) representative kinetics at 1,0001C [14] (published with permission from The Electrochemical Society) and (b) effect of alloy chromium content on carburization rate [17] (with permission from Trans Tech Publications, Ltd).
each other and with values found from independently measured values of N ðsÞ C [3] and DC [5]. It is concluded that internal carburization of both Fe- and Ni-based alloys is controlled by lattice diffusion of carbon through the depleted metal matrix.
410
Chapter 9 Corrosion by Carbon
Table 9.9
2 1 Carbon permeabilities N ðsÞ C DC ðcm s Þ in Fe–Cr
9001C
From carburization kinetics, Equation (9.24) From N ðsÞ C and DC
1,0001C
6.6 10
9
4.3 109
1,1001C 8
6.2 108
1.4 108
5.5 108
2.5 10
2 1 Table 9.10 Carbon permeabilities 1010 N ðsÞ C DC ðcm s Þ deduced [12] from carburization rates (9.24) of Ni-based alloys
Alloy
Ni–12V Ni–20Cr Ni–3Nb From N ðsÞ C and DC
T (1C) 700
800
900
1,000
0.40 0.21 0.30 0.19
2.2 0.8
11 8 6 7
44 55 14 36
1.6
The temperature effect on the rate is described by the empirical equation EA ðiÞ ðiÞ kp ¼ ko exp (9.25) RT According to Equation (9.24), the temperature dependence of kðiÞ p arises through the effects on N ðsÞ and D . Differentiating the logarithmic forms of Equations C C (9.24) and (9.25) with respect to temperature, and comparing the results leads to ¯CþQ EA ¼ DH (9.26) where Q is the activation energy of carbon diffusion. In the case of Fe–Cr alloys, the extent of iron dissolution in the carbides varies with temperature as does the stability of the carbides, and the simple description of Equation (9.26) cannot be expected to apply. In the case of Ni–Cr alloys, however, nickel dissolves to only a small extent in the carbides, and Cr7C3 is the only stable internal carbide over 1 a wide range of temperature for N ðoÞ Cr 0:2. The value of EA ¼ 190 kJ mol measured by Allen and Douglass [12] for Ni–20Cr agrees with the prediction of ¯ C ¼ 54 kJ mol1 [3] and Q ¼ 138 kJ mol1 [5]. Equation (9.26) based on DH Chromia-forming alloys are usually based on Fe–Ni (Table 9.1), and the applicability of Equation (9.24) to Fe–Ni–Cr model alloys is now tested. An Fe–20Ni–25Cr alloy carburized at 1,0001C and aC ¼ 1 is seen in Figure 9.6 to have developed a near-surface zone of M7C3 precipitates and an inner zone containing M23C6. Carburization kinetics of a series of Fe–Ni–Cr alloys have been found [19] to be parabolic at 1,0001C, and the rate constants are seen in Figure 9.7 to vary considerably with alloy nickel content. If nearly all the chromium is precipitated as carbide, then the reaction is sustained by carbon dissolution in and diffusion
9.4. Internal Carburization of Model Alloys
411
Figure 9.6 Carburization of Fe–20Ni–25Cr at 1,0001C and aC ¼ 1. Precipitates in the subsurface zone identified by SAD as M7 C3 and in the inner zone as M23 C6 [18]. With permission from ASM International.
7.5
109kp(i)/cm2s-1
6
4.5
3
1.5
0 0
0.1
0.2
0.3
0.4
0.5
0.6
NNi
Figure 9.7 Variation of carburization rate at 1,0001C with Ni content of Fe–Ni–25Cr alloys. Reprinted from Ref. [19] with permission from Elsevier.
412
Chapter 9 Corrosion by Carbon
Figure 9.8 Measured carburization rates of Fe–Ni–Cr alloys compared with values calculated from diffusion model. Reprinted from Ref. [19] with permission from Elsevier.
through the remaining Fe–Ni matrix. Ignoring the dissolution of some of the iron into carbide, we approximate the matrix as having the same N Ni =N Fe ratio as the parent alloy. On this basis, one can use values of N ðsÞ C measured by Wada et al. [3] for Fe–Ni alloys and for DC measured by Bose and Grabke [20] to predict carburization rates from Equation (9.24). A comparison of measurement and prediction (Figure 9.8) demonstrates the success of this procedure. We therefore conclude that the Wagner theory provides a satisfactory basis for describing the carburization of model alloy compositions close to those of commercial heat resisting alloys. Before going on to consider more practical alloys, we examine the microstructures and distributions of carbide precipitates.
9.4.3 Carbide microstructures and distributions Particles of M7C3 precipitated in austenite are globular, and develop no rational orientation relationship with the matrix. In contrast, M23C6 possesses a cubic structure and develops a strong cube-in-cube orientation relationship with the fcc g-matrix [21] ½001g ½001 : ð100Þ ð100Þ (9.27) M23 C6
g
M23 C6
Usually the M23C6 precipitates are small, cuboidal or needle-shaped particles (e.g. Figure 9.9a). The small size of the precipitates reflects the fact that they grew for only a short time: a result of the continued nucleation of new carbide particles
9.4. Internal Carburization of Model Alloys
413
Figure 9.9 Cuboidal (a) and lath-shaped (b) M23 C6 precipitates at the reaction front in Fe–20Ni–25Cr carburized at 1,0001C.
as the reaction front advanced into the alloys. This in turn was due to rapid carbon diffusion, which quickly produced sufficient supersaturation to favour homogeneously distributed nucleation. In other circumstances, the same carbide can form elongated lamellar- or lath-shaped precipitates oriented parallel to the reaction direction (Figure 9.9b). Because the value of kðiÞ p is 30–50% higher when the aligned microstructure is adopted, the reasons for its development are of interest. Lamellar or cellular M23C6 microstructures are reported to develop in ferritic alloys [14, 16, 22, 23], in high nickel austenitics [19] and in a variety of heat resisting alloys carburized at low temperatures [24, 25]. They are also observed in previously nitrided Fe–Ni–Cr alloys [19, 21]. A distinctive feature in all cases is the formation of a grain boundary at the carbide precipitation front. In the case of ferritic alloys (Figure 9.2b) the boundary corresponds to the phase transformation aðFe; CrÞ þ x C ! gðFe; CÞ þ Cr23 C6
(9.28)
In high nickel alloys, lamellar carbides develop in colonies in the alloy interior. It seems likely that they nucleated at alloy grain boundaries, and then grew into the adjacent grain in a discontinuous precipitation process which is now described. A brief period of internal nitridation can be used to form a boundary just beneath the surface of an Fe–Ni–Cr alloy (see Section 6.7). Subsequent carburization then leads to rapid inward growth of M23C6 lamellae, which advances the boundary. A high magnification view of the reaction front is shown in Figure 9.10: the dark grain on the right is unreacted austenite, the light grain on the left is chromium-depleted, austenitic matrix and the precipitates are M23C6. The selected area diffraction pattern shows the same cube-in-cube orientation relationship (9.27) between precipitate and matrix. The crystallographically oriented sides of the precipitates are always the close-packed (111) planes. No rational orientation relationships are found between unreacted austenite and either reacted austenite or carbide. Microanalysis results in Figure 9.10 show a step function change in N Cr at the austenite/depleted austenite grain boundary, but no sign of lateral diffusion within the matrix. The mechanism is that of discontinuous precipitation [18, 21] g þ C ¼ gD þ Cr23 C6
(9.29)
414
Chapter 9 Corrosion by Carbon
Figure 9.10 M23 C6 precipitation front in Fe–20Ni–25Cr after brief pre-nitridation and subsequent carburization at 1,0001C, aC ¼ 1. SAD shows precipitate/matrix coherency, and concentration profiles correspond to discontinuous precipitation [18, 21]. Published with permission from Science Reviews.
where gD denotes chromium-depleted austenite. The change in crystallographic orientation from parent g to product gD is obvious in Figure 9.10. This reorientation results from the free energy reduction achieved when the austenite forms coherent interfaces with the precipitates which grew approximately unidirectionally, parallel to the carbon diffusion direction. The incoherency of the g=gD interface is evident in its curvature, and this provides rapid chromium diffusion towards the advancing carbide precipitate tips, sustaining their growth and producing the discontinuous change in N Cr seen at the interface. We conclude that lamellar carbide precipitates develop when a grain boundary is present. The boundary provides more rapid chromium diffusion to the precipitates, favouring their continued growth rather than nucleation of new ones. As seen in Figure 9.5b, carburization rates for Fe–Cr alloys with high N Cr values are higher than predicted by Equation (9.24). These are the alloys
9.5. Internal Carburization of Heat Resisting Alloys
415
which form lamellar precipitates, and the acceleration is attributed to boundary diffusion of carbon along the multiple carbide–austenite interfaces. Because N ðsÞ C DC in austenite is in any case large, the increase in rate is relatively small: 30% faster in Fe–Cr and 30–50% faster in Fe–Ni–Cr alloys at 1,0001C. Carbide precipitate distributions are non-uniform, because Ksp is not small. Thus as depth within the precipitation zone increases, aC and N C decrease, causing N Cr to increase according to the solubility product equilibria (9.21) and (9.22). As a result, the amount of chromium precipitated is less [17]. The qualitative effect on carburization rate can be seen from Equation (9.24): because the effective value of N ðoÞ Cr is lowered, the penetration rate is faster. This effect has been analysed [26, 27] for the general case of low stability precipitates. Deviation from the Wagner assumption of vanishingly small Ksp values is expressed via a solubility parameter ! N ðsÞ Cr a¼1 (9.30) ðoÞ N Cr where N ðsÞ Cr is the matrix equilibrium chromium concentration at the surface of the reacted alloy. If a ¼ 1, Ksp ¼ 0 and the Wagner model applies; if a ¼ 0, no precipitation occurs and an error function solution describes the dissolved carbon profile. Considering Fe–Cr alloys, we find from Equation (9.22) and the data of ðoÞ Table 9.6 that N ðsÞ Cr ¼ 0:028. Taking a representative value of N Cr ¼ 0:25, then a value of a ¼ 0.9 is arrived at. For this value, Ohriner and Morall [26] calculate that kðiÞ p is increased by a factor of two above that predicted from Equation (9.24), i.e. the penetration depth is increased by about 40%. However, uncertainties ðiÞ in measured values of DC , N ðsÞ C and kp total at least this amount. A similar conclusion is reached for Cr23C6 precipitation. We therefore conclude that despite the approximate nature of its underlying assumptions, Wagner’s simple result (9.24) provides good order of magnitude prediction for model alloy carburization. A more precise prediction can be made using the numerical treatment of the Ohriner–Morall theory developed by Christ [28]. This finite difference procedure allows the incorporation of varying iron solubility in the chromium-rich carbides, as well as the variation with depth in precipitate volume fraction.
9.5. INTERNAL CARBURIZATION OF HEAT RESISTING ALLOYS Many laboratory studies of the carburization of heat resisting alloys have been reported, e.g. [6–8, 28–44]. These are in general agreement with the findings from industrial exposures (see e.g. [45]) that carburization rates vary with Fe/Ni ratio and decrease with increased levels of Cr, Nb, Si and sometimes W and Ti. The usual appearance of a cast heat resistant alloy after carburization is shown in Figure 9.11. Murakami’s etch reveals finely precipitated, cuboidal M23C6 particles in the inner zone and coarser, spherical M7C3 particles near the surface. The original cast alloy structure is seen to the right: austenite dendrites with primary interdendritic M23C6. Near the carburization front, preferential
416
Chapter 9 Corrosion by Carbon
Figure 9.11 Cast alloy 45 Pa after carburization for 24 h at 9001C and aC ¼ 1.
precipitation is seen along dendrite boundaries. Some fragmentary external carbide scale is also seen. This is usually Cr3C2 on high nickel allows and M7C3 on low nickel materials. The difference arises from the changed Fe/Cr ratios in the Fe–Cr–C system [35] (see Figure 9.3). Thus reaction morphologies are consistent with local equilibrium. Since, moreover, internal carburization kinetics are parabolic, it is clear that the process is diffusion controlled. Despite the complexity of these alloys, their relative performance under nonoxidizing conditions can be understood in terms of Wagner’s equation (9.24). The procedure is to model the heat resisting alloys as Fe–Ni–Cr ternaries, and approximate the carburization zones as chromium carbide precipitates in an Fe–Ni matrix. Carburization rates are then predicted from Equation (9.24) to change with carbon permeability, N ðsÞ C DC . This permeability shows a minimum at Ni=Fe 4 : 1 [3, 20, 46], which is seen in Figure 9.12 to be reflected in relative penetration depths of a range of alloys. Clearly the Fe/Ni ratio has a significant effect on carburization rate. However, it is desirable also to account for the effect on kpðiÞ of N M in Equation (9.24), and a more detailed calculation is required. The quantity NM, representing carbide-precipitating metal, is made up mainly of chromium. In calculating its value, the alloy chromium content must therefore be corrected for the amount already removed from the matrix into interdendritic carbide during casting. This is done on the assumption that all of the alloy carbon was precipitated as pure Cr23C6. Added contributions to NM are calculated on the basis of NbC and other MC carbide formation, as well as the molybdenum carbides (Mo2Fe)C and (CrMoFe)C. As seen earlier, the application of Equation (9.24) is nonetheless an approximation, because M7C3 and M23C6 carbides contain substantial levels of iron [15]. Consequently, the value of NM calculated as described earlier is an underestimate. However, an overestimate of NM results from the error in the mass balance underlying Equation (9.24). This latter error
9.5. Internal Carburization of Heat Resisting Alloys
417
Figure 9.12 Effect of alloy nickel content on (upper) carbon permeability in Fe–Ni and (lower) carburization extent in heat resisting alloys after 200 h at 1,1001C [47]. Published with permission from Wiley-VCH.
arises because the solubility products of Cr7C3 and Cr23C6 are large, and significant levels of chromium remain unreacted in the depleted matrix. Carburization leads to approximately equimolar amounts of M7C3 and M23C6, so a value of n ¼ 0.345 is used in Equation (9.24). No value for e is available. Predicted kðiÞ p values based on e ¼ 1 are compared in Table 9.11 with measured [40] quantities for a selection of alloys. It is seen that close order of magnitude agreement is achieved for the 30, 35 and 45Ni grades, but not for the 60Ni grades. The latter contain aluminium, and are discussed later. We consider first the effects of other alloy components.
418
Chapter 9 Corrosion by Carbon
Table 9.11
Carburization rate constants 107 kp ðcm2 s1 Þ [40] 1,0001C
1,1001C Measured Calculated
G4868 G4852 H101 Fe–35Cr–45Ni 45Pa 45HT 60HT(a)b 60HT(b)b 60HT(c)b 602 CA
1.45 0.64 0.44 0.44 0.41–0.43 0.63 0.14 0.01 0.02 0.14
2.05 2.15 1.32 0.50 0.99 0.62 0.87 0.95 0.90 0.82
a
Measured Calculated
0.13 0.28 0.17 0.10 0.13–0.22 0.10–0.15 0.04 0.01 nd 0.04
0.33 0.37 0.24 0.08 0.18 0.15 0.17 0.19 0.18 0.17
9001C a
Measured Calculateda
0.10 0.18 0.06 0.04 0.05–0.08 0.04–0.05 0.03 0.02 nd 0.03
0.11 0.10 0.06 0.03 0.034 0.023 0.03 0.03 0.03 0.03
nd: not determined. a from Equation (9.24). b Low, medium and high NAl (Table 9.1).
9.5.1 Effect of carbon As seen in Table 9.1, cast alloys usually contain high levels of carbon, which segregates as M23C6 during alloy solidification, thereby affecting NM as described earlier. The success of this description is tested by comparing carburization rates for alloys H101 and G4582, which differ in their carbon levels but are otherwise similar. At 1,0001C, the ratio kpðiÞ ðG4582Þ=kðiÞ p ðH101Þ predicted from Equation (9.24) to be 1.5 compares well with the measured value of 1.7. Agreement at the other temperatures is also good. We conclude that the method used to calculate the effect of original alloy carbon is successful. On this basis, it would follow that cast alloys have lower carburization resistance than their wrought (low carbon) equivalents. In fact, the opposite effect is found [8, 38] as a result of the overwhelming effect of rapid grain boundary diffusion of carbon in wrought alloys.
9.5.2 Effect of molybdenum Molybdenum can be added for solution strengthening of an alloy, and is also a carbide-former. Two alloys containing 24Cr, 32Ni, 0.8Nb and 0.44C, with and without additions of 3 wt% Mo were found [38] to carburize at aC ¼ 1 at different rates. The carbides Mo3C and Cr7C3 are of comparable stability, and can therefore coexist if the metals are at similar activity levels. In fact the carbides (Mo2Fe)C, (CrFeMo)C and Cr7C3 were all identified by X-ray diffraction analysis of the carburized alloy. Equation (9.24) is used to test the possibility that precipitation of molybdenum carbides slows the rate of internal carburization. A level of 3 wt% molybdenum, forming a carbide of stoichiometry Mo1.5C (an average of the two observed carbides), is equivalent in its consumption of carbon
9.5. Internal Carburization of Heat Resisting Alloys
419
to a level of 2.5 wt% chromium, forming Cr7C3. The value of N M in the alloy with 3% Mo is on this basis calculated to be 13.6% higher than for the alloy with none. Taking into account the effects of alloy compositional changes on DC , N C and N M gives predicted relative reductions in the kðiÞ p values for the molybdenumcontaining alloy of 40% at 9001C, 23% at 1,0501C and 10% at 1,1501C. The measured reductions were 44% at 9001C, 24% at 1,0501C and 16% at 1,1501C. This shows that Equation (9.24) enables the effect of molybdenum to be modelled, subject to the reliability of the N C and DC data. Furthermore, it also predicts correctly the effect of temperature on the efficacy of this element in reducing carburization.
9.5.3 Effect of silicon It has long been known [29] that silicon slows the rate of carburization, even under gas conditions where no silicon-rich oxide can form. The stability of SiC is a great deal less than that of Cr23C6 and C7C3 and no SiC will form in these chromium-rich alloys. Increasing the alloy silicon content therefore has no effect on N M . Under reducing conditions no SiO2 is formed, and the beneficial effects to be expected of silicon on carburization rates must therefore result from modification of the carbon solubility and/or diffusivity. These changes are due to thermodynamic interaction between the dissolved silicon and carbon. Silicon is known to reduce both N ðsÞ C and DC . Roy et al. [48] have examined the effect of silicon on carbon diffusion in Fe–Si–C. A comparison of carburization rates of two cast heat resisting steels which differed only in their silicon levels showed [38] that increasing the silicon level decreased the rate by more than would be predicted from Roy’s diffusion data. The other major contributory factor is the depression of carbon solubility by silicon. The effect has been measured in liquid iron alloys, where the resulting change in carbon solubility is significant, but no data directly applicable to heat resisting alloys are available.
9.5.4 Effect of niobium and reactive elements Niobium is often added to cast heat-resistant alloys for strengthening purposes. It is also found in some wrought alloys, where it improves weldability. Reactive elements such as Ce and Hf are added to modify carbide shapes and to improve oxide scale spallation resistance. All are strong carbide formers and have strong effects on carburization resistance. The benefits of niobium have been reported several times [8, 45, 49]. The variation of kðiÞ p with niobium concentrations is shown in Figure 9.13 for several heat-resisting alloys. The effect of niobium can be distinguished from variations in N ðsÞ C CC =Dm also plotted in this figure. Even if all the alloy niobium was available in solution to precipitate NbC, the effect of adding 1–2 w/o Nb on Nm is very small, much less than the substantial reductions in kðiÞ p seen at higher niobium levels. Similar effects have been noted for additions of Ce [39] and Hf [40]. These elements are present at low concentrations, typically around 0.1–1.0 wt%, and their effect on the value of N M is negligible. Nonetheless their addition is found
420
Chapter 9 Corrosion by Carbon
4 5
10-3 Kp (µm 2h-1)
3
4 36XS 3
35CW
2
2 2325Nb 1
10-3DcNc/Nm (µm 2h-1)
36X
1
0
0 0
0.5
1 w/o Nb
1.5
2
Figure 9.13 Carburization rate constants for commercial 25Cr–35Ni alloys at 1,0001C as a function of niobium content (O) compared with NðsÞ C DC =NM () [8]. With kind permission from Springer Science and Business Media.
to reduce carburization rates substantially. It is possible that carbides of Nb, Ce and Hf precipitate preferentially at sites where interference with carbon diffusion is maximal. As carbon penetration is more rapid at primary carbide/dendrite boundaries (Figure 9.11), reactive metal carbide precipitation at these interfaces could exercise a disproportionate effect on the overall rate.
9.5.5 Effect of aluminium The 60Ni alloys in Table 9.11 are predicted from Equation (9.24) to carburize at rates similar to the 45Ni alloys. At 9001C, the wrought alloy 602 CA and two cast versions react at rates close to those predicted (Table 9.11). At higher temperatures, the rates are much slower than predicted. The explanation is clear from the micrographs of Figure 9.14, where a protective, external scale is seen to form on high NAl alloys. The scale is a-Al2O3 which is thermodynamically stable at the water vapour impurity levels which are unavoidable in reaction gases. However, external scale formation is possible only when a sufficient flux of alloy solute aluminium is available, and internal oxidation can be avoided (see Equation (9.15)). This flux increases with both alloy N Al and temperature, through its effect on DAl , qualitatively accounting for the observed pattern of behaviour. When this scale forms, it functions as a barrier, limiting carbon access to the underlying metal. Thus at 9001C, no alumina forms and the 60Ni alloys all carburize at the expected rates. At 1,0001C and 11001C, alumina scales grow on all alloys, and carburization is slowed. The scale is discontinuous on the low aluminium alloys, and carburization is not completely suppressed. A minimum aluminium content of about 4 w/o is required to achieve complete protection.
9.6. Metal Dusting of Iron and Ferritic Alloys
421
40µm b (a)
(b)
Figure 9.14 Effect of Al2O3 formation on 60Ni alloys (a) low Al at 9001C and (b) high Al at 1,1001C.
9.5.6 Alloying for carburization protection The kinetics of alloy carburization are very well described by diffusion theory, and a rational approach to alloy design is therefore available. Unfortunately, however, most methods of suppressing internal attack on chromia-forming alloys are either impractical or only modestly successful. It is not possible to adjust chromium levels to achieve exclusive external carbide growth. Modifications of alloy carbon permeability through adjusting the Fe/Ni ratio or alloying with other metals yield only small improvements in carburization rates. Silicon decreases carbon solubility and diffusivity quite strongly, but metallurgical limits on alloy silicon concentrations mean that only modest improvements in carburization resistance can be obtained. The only really successful alloy additive is aluminium, and it functions by forming an oxide scale. The general question of protection against carburization by oxide scale formation is considered in Section 9.8.
9.6. METAL DUSTING OF IRON AND FERRITIC ALLOYS Metal dusting is a catastrophic form of corrosion in which metals exposed to carbon-supersaturated gas disintegrate, forming metal-rich particles (the ‘‘dust’’) dispersed in a voluminous carbon deposit. Early reports of industrial failures [50–53] were followed by the laboratory research of Hochman [54–56] concerning the dusting of iron, nickel, cobalt and chromia-forming ferritic and austenitic alloys. Subsequently, work by Grabke [57–61] quantified and extended Hochman’s observations. The description of the process, as provided by Hochman and Grabke, for pure iron is shown schematically in Figure 9.15.
422
Figure 9.15
Chapter 9 Corrosion by Carbon
Hochman–Grabke model for dusting of pure iron.
9.6.1 Metal dusting of iron When iron is exposed to carbon-rich gas at oxygen potentials too low to form iron oxide, the metal catalyses reactions such as Equations (9.7)–(9.9), but the resulting carbon is dissolved in the metal. Hochman and Grabke suggested that this leads to carbon supersaturation of the iron, and the subsequent precipitation of the metastable Fe3C phase, which they observed. The appearance of the cementite is shown in Figure 9.16. According to the proposed mechanism, once the iron surface is covered with cementite, carbon deposits on the carbide. The carbon activity at the cementite surface is then supposed to be unity (rather than the supersaturated value of the gas phase); the cementite becomes unstable and decomposes via the reaction Fe3 C ¼ 3Fe þ C
(9.31)
producing finely divided iron and carbon. The iron particles produced in this way are catalytically active, and lead to accelerated carbon deposition. The resulting conglomerate deposit of carbon- and metal-rich particles is at least 95% carbon, and is referred to as ‘‘coke’’, and the carbon deposition process as ‘‘coking’’. The kinetics of carbon deposition are observed [61] in the short term to follow the quadratic rate law DW C ¼ kC t2 (9.32) A where DW C =A is the carbon weight per unit area, before becoming approximately linear. The form of Equation (9.32) was explained by Grabke et al. [61] as being due to the generation of catalytically active particles by metal consumption in the dusting process: DW m ¼ kd t (9.33) A where DW m =A is the metal wastage expressed as a mass loss per unit area. If the catalytic particles are of uniform surface area and activity, then the rate of carbon
9.6. Metal Dusting of Iron and Ferritic Alloys
423
Figure 9.16 Cross-sectional TEM views showing Fe=Fe3 C=C interfaces after reaction in CO–H2 at 6501C [65]. Published with permission from The Electrochemical Society.
deposition is proportional to the mass of metal consumed dðDW C =AÞ ¼ k kd t (9.34) dt Integration of this expression yields Equation (9.32). In the long term, individual particles are encapsulated by carbon and deactivated as catalysts. The rate at which this happens approximately balances the rate of new particle generation, and coking rates become approximately constant. TEM [63–66] has revealed that the carbon at the cementite surface is mainly graphite, C(gr), at temperatures above about 5001C (Figure 9.16). It was suggested by Pippel et al. [63, 64] and Chun et al. [65] that the iron resulting from cementite decomposition dissolved in the graphite, diffused outwards and precipitated as metal particles which catalysed further carbon deposition. The evidence for this was the measurement by EDAX of a small concentration of iron in the graphite. However, it is difficult to understand the driving force which would cause iron to diffuse from a low activity source, the cementite, towards a high activity destination, metallic iron particles.
424
Chapter 9 Corrosion by Carbon
Coke
(10)
(001) (101)
1 μm 25 nm
(a) (b) JC Graphite
Fe3C JC
ac = 2.9
ac = 1
(c) Figure 9.17 Coke filaments with Fe3C particles at their tips (a) SEM view (b) TEM bright field image and SAD pattern and (c) mass transfer model.
Further examination of the particles by both X-ray and electron diffraction [24, 67–70] has established that they are Fe3C. As seen in Figure 9.17, much of the coke deposit is filamentary. These filaments are multiwall carbon nanotubes, and usually carry faceted Fe3C particles at their tips. The particles are oriented with their [001] direction parallel to the carbon tube axis [71]. This allows Fe3C planes in the {010} and {100} families to be parallel to the tube axis. The d-spacing of the (020) plane in 0.337 nm and that of the (300) plane is 0.169 nm. These correspond close to the (0002) and (0004) d-spacings of graphite (0.337 nm and 0.168 nm, respectively). Accordingly, it is suggested that alignment of these planes with the graphite basal planes, which form the multiple walls of the nanotube, leads to formation of low-energy graphite–carbide interfaces and a preferred growth orientation for the carbon nanotubes. A mass transport model for filamentary coke deposition is shown in Figure 9.17(c). The exposed Fe3C facets are in contact with the gas, and catalyse carbon production. This carbon diffuses through the particle to the Fe3C–graphite
9.6. Metal Dusting of Iron and Ferritic Alloys
Fe33C
C (gr)
425
Fe(C)
aC
JFe J Fe aC=1
Fig 9.25
(a) C (gr) + Fe3C
Fe3C
Fe (C)
aaC C JJC C
(b)
Figure 9.18 Mass transport models for metal dusting when cementite is formed (a) cementite decomposition and iron diffusion through graphite and (b) cementite disintegration coupled with inward graphite growth.
interface where growth of the attached carbon nanotube continues. Thus the cementite crystallites perform three functions: catalysis of the gas reaction, dissolution and transport of the resulting carbon, and provision of a template for graphite nucleation and growth. The model is analogous, with respect to the first two functions, to that originally proposed by Baker et al. [72] for catalysis of carbon filaments grown by metallic particles. There remains, however, the question of how the cementite particles are formed. If iron did in fact dissolve in graphite, it could diffuse outward if a carbon activity gradient was in effect, as illustrated in Figure 9.18(a). The iron flux would be given by @m J Fe ¼ BFe N Fe C (9.35) @x
426
Chapter 9 Corrosion by Carbon
as a result of the thermodynamic Fe–C interaction. Here BFe is the mobility of iron in graphite. When the solute iron reached a position at which aC was high enough to stabilize cementite, that phase would precipitate. To test this model, we need values for iron solubility and its diffusion coefficient in graphite, and these are lacking. It is clear that an extremely high value for DFe would be required to explain why the decomposition reaction (9.31) leads to 75 atom% iron, but produces none of that phase at the decomposition site. Studies of cementite decomposition in CH4–H2 gas mixtures [73] have shown that the reaction products are iron and graphite. In that case, however, the iron forms as a bulk phase, not as particles. The reaction is controlled by the diffusion of carbon through the product ferrite, driven by the carbon activity gradient between the high value at the Fe3C/Fe phase boundary and its value of unity at the Fe/C(gr) boundary. According to Fick’s law Rate ¼ DC ðCFe3 C=Fe CC=Fe Þ Fe3 C=C
(9.36)
C=Fe
and C are carbon concentrations at the ferrite–cementite and where C ferrite–graphite interfaces, DC the carbon diffusion coefficient in ferrite and variation in the diffusion path length is ignored. The concentration of carbon is related to its activity by a coefficient gC , with aC ¼ gC C. Approximating gC as a constant and setting aC ¼ 1 at the iron–graphite interface, we obtain ! Fe C=Fe ðaC 3 1Þ Rate ¼ DC (9.37) gC Fe C=Fe
[75], it is found that the temperature Using standard data for DC [74] and aC 3 dependence of cementite decomposition predicted by Equation (9.37) is in very good agreement with experimental observation (Figure 9.19). However, 2
4 1.5 3 1 2 0.5
1
0 450
(aC-1)xDx107
Rate of decomposition, s-1x104
5
0 550 650 750 Decomposition temperature, °C
Figure 9.19 Rate of Fe3C decomposition measured ( DC and aC in ferrite.
850
7) in H2 =CH4 and calculated (’) from
9.6. Metal Dusting of Iron and Ferritic Alloys
427
Figure 9.20 Graphite–cementite interface developed during dusting of iron at 6801C (a) FIB-milled section and (b) TEM bright field with SAD identifying nanoparticles as Fe3C. Reprinted from Ref. [62] with permission from Elsevier.
cementite decomposition by that mechanism is clearly not occurring in the iron dusting reaction depicted in Figures 9.17 and 9.18. Although the different gases react with the surface according to different mechanisms (see Section 9.6.3, Effects of temperature and gas composition on iron dusting), it also seems that the direction of carbon transport is different in the two sorts of experiment. The alternative mechanism of Fe3C particle production is mechanical disintegration resulting from volume expansion [67, 76]. Because Fe3C is a carbon diffuser [77, 78], the cementite layer grows inward and is consequently under compressive stress. Precipitation of graphite could occur at internal defects in a nucleation and growth process [67]. Such a process would be similar to the way carbon forms and grows at the rear of Fe3C particles (Figure 9.17). Growth of these precipitates could then disrupt the cementite surface. Examination of the C(gr)/Fe3C interface in Figure 9.20 shows that graphite is growing into the cementite layer, and that nanoparticles of Fe3C are detached from the bulk carbide. For these to exist, the carbon activity must be high enough to stabilize the phase. We therefore conclude that the graphite layer does not function as a barrier to the gas, and that aC at the coke–cementite interface is probably close to the value in the ambient gas. This conclusion is supported by the observation [79] that the surface cementite layer continues to thicken, and that the carbon content of the iron specimen increases as dusting proceeds. It is clear that carbon is diffusing through the cementite scale and into the iron, and that the description of Figure 9.18(b) applies. However, these experiments were of limited duration (up to ca. 40 h) and at a single temperature. Once the iron sample reaches a steady state of carbon supersaturation, the mechanism may well change [80] when an inward flux of carbon is no longer possible. Moreover, it is likely that the mechanism changes with gas composition and temperature. Zhang et al. [69, 81] have reported that at T ¼ 7001C, and low pCO values, the surface Fe3C scale decomposes to form a surface layer of ferrite. At still higher temperatures, no cementite layer is seen, and graphite deposits directly into the metal.
428
Chapter 9 Corrosion by Carbon
Figure 9.21 Fe–10Ge alloy after 10 h reaction in H2 =H2 O=CO (aC ¼ 2:9; pO2 ¼ 1023 atm) (a) FIB cross-section and (b) TEM cross-section with SAD identifying a-Fe. Reprinted from Ref. [62] with permission from Elsevier.
9.6.2 Iron dusting in the absence of cementite Given the important role played by cementite in the dusting of iron, it is reasonable to enquire whether dusting might be prevented if Fe3C formation were suppressed. Cementite can be destabilized with respect to graphite by alloying with silicon to raise the solute carbon activity. Unfortunately, silicon also oxidizes in the gases under discussion, as is discussed later. Germanium, however, forms a much less stable oxide, and by virtue of its chemical similarity to silicon, might be expected to suppress Fe3C formation. This is indeed the case [62], as shown in Figure 9.21, where graphite is seen to be growing directly into a ferritic Fe–Ge alloy, in the absence of any cementite. The nanoparticulate material near the disintegrating interface is also a-Fe(Ge), as are the particles found on coke filaments. Alloying with germanium suppresses Fe3C formation, but does not prevent metal dusting. Instead, dusting occurs more rapidly by the growth of graphite directly into the alloy. Metal particles are formed by disintegration of the bulk metal, as the graphite grows inwards. Again it is suggested that this is a consequence of the volume expansion accompanying nucleation and growth of graphite within the metal. This process is more rapid than the corresponding one involving Fe3C. It is noteworthy that the Fe–Ge/graphite interface morphology is similar to that developed between nickel and graphite (where no carbide forms) during dusting (see Section 9.7). However, dusting is much faster for the ferritic material. It is clear that suppression of Fe3C formation does not prevent dusting when this alternative mechanism is available.
9.6.3 Effects of temperature and gas composition on iron dusting As noted by Grabke [82], iron dusting and coking kinetics are very complex, and more detailed studies are needed to arrive at a comprehensive, self-consistent
9.6. Metal Dusting of Iron and Ferritic Alloys
429
Figure 9.22 Temperature effects on metal dusting for iron and low alloy steels left-hand side (LHS) in CO=H2 =H2 O [84] right-hand side (RHS) in COH2 [83]. With kind permission from Springer Science and Business Media.
picture. As seen in Figure 9.22, somewhat different temperature dependencies have been reported for different gas conditions. Grabke et al. [61] considered the temperature dependence at To5401C to reflect rate control by cementite decomposition, which they viewed as independent of gas composition. Ramanarayanan et al. [65, 83] identified two temperature regimes: To4501C where the coke was amorphous and the rate was controlled by physical disintegration of Fe3C, and 4501CoTo5701C where the chemical decomposition of Fe3C was thought to become important. The observed increase in rate with temperature was attribute to increased graphitization of the coke, providing a diffusion pathway for dissolved iron. The decline in dusting rates reported by Ramanarayanan et al. at TW5701C was attributed by them to a decrease in aC with increasing temperature. Grabke observed an increased dusting rate in the range 540–6201C, reporting it to vary with the product pCO pH2 [84], and concluded that carbon transfer from the gas was rate controlling. Part of the reason for this confusion is the way in which aC varies with temperature (Figure 9.1) and gas composition (Equations (9.10) and (9.11)) in CO/H2/H2O gas mixtures. The driving force for carbon precipitation, (aC1), is related to gas composition variables which themselves appear in kinetic expressions. Distinguishing the two effects can be difficult, and is impossible if the gas compositions are not carefully controlled. Thus the use of CO/H2O gases without H2O to buffer the composition means that aC is uncontrolled, and will vary with the extent of carbon deposition. As carbon deposition rates are rapid around 5501C, both aC and pCO can vary considerably in a nominal CO–H2 gas mixture. The dependence of both coking and dusting rates on the composition of CO/H2/H2O gases determined by Muller-Lorenz and Grabke [84] is shown in Figure 9.23. Similar results were found for iron dusting at 5501C by Chun et al. [65].
430
Chapter 9 Corrosion by Carbon
Figure 9.23 Dependence of coking and dusting rates on pCO in H2 =CO=H2 O mixtures [84]. Published with permission from Wiley-VCH.
In both cases it was concluded that the rate-determining step in the dusting process was reaction (9.7) leading to Rate ¼ k7 pCO pH2
(9.38)
with k7 a rate constant. However, this analysis neglects the effect of aC. Experiments [85] in which aC was maintained constant showed that keeping the product pCO pH2 constant but varying the individual partial pressures changed both coking and dusting rates. Obviously, the simple description of Equation (9.38) cannot be applied to either process. Considering the coking process first, it is seen that the Boudouard reaction (9.8) is likely to be important at high pCO values. Furthermore, when pH2 is high, it is likely that methanation (the reverse process in reaction (9.9)) will occur under catalysed conditions. Ignoring the reverse reactions in reactions (9.7) and (9.8), along with the forward process (9.9), we can write d DW C =A (9.39) ¼ k7 pCO pH2 þ k8 p2CO k9 p2H2 dt where the ki are rate constants. As seen in Figure 9.24, this expression is successful in describing coking rates with k7 ¼ 35.5, k8 ¼ 4.5 and k9 ¼ 5.6 mg cm2 atm2. We therefore conclude that coke deposition can be described in terms of gas–solid kinetics involving parallel reaction pathways.
9.6. Metal Dusting of Iron and Ferritic Alloys
431
9 8 7
r (mg/cm2h)
6 5 4 3 2 1 0 0
1
2
3 4 5 6 2 k1pCOpH2 + k2 pCO + k3 pH2 2
7
8
9
Figure 9.24 Variation of coking rates on iron at T ¼ 6501c according to Equation (9.39) [85].
More information is required on the variation of dusting kinetics with gas composition. The available data for dusting in CO/H2/H2O mixtures at 5001C [86] and 6501C [87] indicates the rate increases with aC. Data at 5501C [83] for wastage rates of iron exposed to CO/H2 mixtures reveal a maximum at pCO ¼ 0:5 atm ¼ pH2 . If the unavoidable water vapour impurity level was the same in all gases used, then aC ¼ K7 pCO pH2 =pH2 O also has its maximum at this composition.
9.6.4 Dusting of low alloy steels Dusting of 2¼Cr–1Mo and 1Cr–½Mo steels is seen in Figures 9.22 and 9.23 to be similar to pure iron in rate and dependence on temperature and gas composition. Reaction morphologies are also similar [82], and it may be concluded that mechanisms are the same. The reasons for the slightly faster dusting rates observed for 2¼Cr–1Mo steel have not been established. However, it is to be noted that in CO/H2/H2O gases, the pO2 values are high enough to oxidize the chromium. Although no Cr2O3 scales can form on such a dilute alloy, conversion of the steel surface to Fe3C may lead to encapsulation of chromium-rich oxide particles. These might act as nuclei for graphite precipitates, thereby accelerating the cementite disintegration. Addition of silicon to iron has two effects: a partial destabilization of Fe3C with respect to C(gr), and the promotion of SiO2 formation at the oxygen potentials of CO/H2/H2O gases. At low alloy levels, the SiO2 forms as a dendritic internal precipitate rather than an external scale (Figure 9.25). Thus the SiO2 provides little or no protection against carbon access to the metal. Cementite
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Chapter 9 Corrosion by Carbon
Internal silica
Cementite Graphite
Figure 9.25 6801C.
FIB image of Fe–3Si after dusting in CO=H2 =H2 O (aC ¼ 2:9; pO2 ¼ 1023 atm) at
layers formed by Fe–Si alloys are thinner than on iron, coking is faster and metal wastage is also more rapid [79]. The internal SiO2 precipitates are incorporated into the Fe3C scale as it grows into the alloy. These might act as graphite nucleation sites within the cementite, thereby accelerating its disintegration.
9.6.5 Dusting of ferritic chromium steels The behaviour of these alloys when exposed to CO/H2/H2O gas mixtures depends on whether a chromia scale is formed and retained. If the alloy chromium level is too low to form external Cr2O3, the steel will dust at essentially the same rate as a 2¼Cr–1Mo steel [87, 88]. If the steel forms a continuous, adherent chromia scale, resistance to dusting under isothermal conditions is very good, because the scale is an effective barrier to carbon entry. The factors determining the success or otherwise of a steel in resisting dusting are those governing its ability to quickly form a continuous Cr2O3 scale by diffusing chromium to the surface. The effect of temperature on DCr is clear from the studies of Grabke et al. [60]. Steels containing 17 and 26 Cr showed complete resistance to dusting at 6501C and 6001C, but underwent a slight extent of attack at 5501C. Thus the susceptibility to dusting increased as the temperature and DCr decreased. The effective value of DCr can be increased at the low temperatures involved here by creating a deformed and fine-grained alloy surface. This is done by surface
9.6. Metal Dusting of Iron and Ferritic Alloys
433
grinding, shot peening, etc., and has been shown [88] to lead to better dusting resistance. In the absence of such treatment (or after its effects have been annealed out) the ferritic nature of the alloy is itself important, because of the higher DCr value compared to austenitic materials. A comparison of the dusting performance of model ferritic and austenitic 25Cr alloys in Figure 9.26 illustrates this point. These alloys had been electropolished to remove any cold worked surface material, so that alloy chromium transport was via lattice diffusion. Alloys which successfully develop continuous, protective chromia scales are nonetheless subject to long term dusting attack. Under isothermal exposure conditions, growth stress accumulation in the scale leads ultimately to mechanical failure. A series of such events can exhaust the capacity of an alloy to regrow its protective scale, and metal dusting ensues [88, 89]. Discontinuous exposures combine the effects of accumulated growth stress and occasional thermal expansions and contractions. These have also been shown to produce
Figure 9.26 (a) Coke deposition and (b) metal wastage kinetics for electropolished 25Cr alloys at 6801C in CO=H2 =H2 O (aC ¼ 2:9; pO2 ¼ 1023 atm) [24]. With kind permission from Springer Science and Business Media.
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Chapter 9 Corrosion by Carbon
Figure 9.27 Onset of dusting: Fe–25Cr reacted at 6801C CO=H2 =H2 O (aC ¼ 2:9; pO2 ¼ 1023 atm) showing local internal carburization, surface cementite layer and its disintegration.
alloy depletion and eventual dusting [60, 82, 88, 90]. Short-term thermal cycling experiments induce the same failure mode, and are useful as accelerated corrosion tests [91]. In all cases, the chromia scale breaks down locally, allowing carbon to enter the chromium-depleted metal. Rapid inward diffusion of carbon leads to internal precipitation of chromium carbides, thereby preventing any subsequent rehealing of the scale. The depleted iron matrix forms a surface cementite layer [24, 92] which disintegrates, producing numerous cementite particles which catalyse further coke deposition [24]. This localized attack produces a pitted surface (Figure 9.27). However, as the reaction proceeds, more pits form and they widen and coalesce until the attack becomes general. If the alloy chromium level is high enough, dusting of ferritics can be prevented. An Fe–60Cr alloy survived 1,000 1 h cycles at 6801C, forming only Cr2O3 [24] which was impermeable to carbon. Furthermore, the chromia was catalytically inactive, and no coke deposited.
9.6.6 Dusting of FeAl and FeCrAl alloys Iron aluminides and FeCrAl alloys are able to develop alumina scales, and their ability to resist dusting is therefore of interest. The high diffusion coefficients characteristic of the ferritic FeCrAl materials (typically Fe–20Cr–5Al, Table 5.1) mean that they are able to reheal scales quickly, thereby preserving the surface barriers to carbon attack. Dusting of the intermetallic Fe3Al at 6501C in CO–H2–H2O was investigated by Strauss et al. [93], who reported extensive attack at localized pits. After addition of 2.2% Cr to the alloy, dusting was confined to the unpolished specimen edges. With 4.8% Cr and 0.15% Zr, pitting was completely suppressed, and only
9.7. Dusting of Nickel and Austenitic Alloys
435
a thin coke layer formed. Dusting was associated with formation of a surface layer of Fe3C. Further work on Fe–15Al and Fe–26Al by Schneider and Zhang [94, 95] showed that dusting was also associated with internal precipitation of the k-carbide, Fe3AlCx. Attack on Fe–15Al was general, but was reduced to localized pitting by alloying with 2.9% of Nb or Ta, and almost stopped by adding 2% of either V or Ti. Increases in temperature or alloy aluminium content led to reduced dusting rates. As pointed out by the authors, the observations are consistent with protection against dusting due to Al2O3 scale formation. However, at the relatively low temperature of 6501C, the binary intermetallic does not reliably form a continuous scale. Alloy additions of Cr, Nb, Ta, V and Ti all improve alumina scale formation. Nonetheless, once the scale is damaged, rapid carbon entry leads to internal carburization of the alloy and prevents subsequent alumina rehealing. The mechanism is thus very similar to that of attack on ferritic Fe–Cr alloys. The FeCrAl materials provide much better dusting resistance. Baker and Smith [90] reported that an oxide dispersion strengthened alloy, MA956 (Table 5.1), demonstrated very good dusting resistance at 6211C up to 9,000 h in a CO/H2/H2O gas which was oxidizing to aluminium. Good performance has also been reported [80, 91] for FeCrAl materials at 6501C in similar atmospheres. Internal precipitation of the k-carbide was observed after several thousand hours [80], and filamentary coke growth was catalysed by Fe3C particles [91] when the scale was damaged by repeated thermal cycling.
9.7. DUSTING OF NICKEL AND AUSTENITIC ALLOYS Metal dusting of nickel and austenitic alloys differs from the reaction of ferritic materials in that cementite is not formed, and the corresponding nickel carbide is unstable. An examination of the dusting behaviour of pure nickel provides a good basis for understanding the reaction of austenitic, heat-resisting alloys.
9.7.1 Metal dusting of nickel Exposure of nickel- to carbon-rich gases at oxygen potentials where the metal does not oxidize leads to catalysis of reactions (9.7)–(9.9), producing carbon. Hochman [56] and Schneider and Zhang [95] reported the rate of carbon uptake to be much slower than the corresponding process on iron. The kinetics are approximately linear [95, 96] after an induction period of length varying with temperature and gas composition. Metal consumption kinetics have not been measured directly. It is usually assumed that the carbon deposit contains an approximately constant nickel concentration (1–2 wt%), and on this basis linear dusting kinetics would be deduced. Chun et al. [98] measured metal surface recession after 7 h reaction in an unbuffered gas mixture of CO and H2 in the proportions 25:1, and found average rates to be of order 1 mm/year at temperatures above 6001C.
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Chapter 9 Corrosion by Carbon
Figure 9.28 Graphitization of nickel exposed to CO=H2 =H2 O (aC ¼ 19) for 100 h at 6501C. Reprinted from Ref. [97] with permission from Elsevier.
Reaction morphologies vary with ambient conditions, and the available information is incomplete. The 25:1 CO/H2 gas produced external attack, whereas at a CO to H2 ratio of 1:1, extensive internal graphitization also resulted. The appearance of both forms of attack on coarse-grained nickel exposed to a CO/H2/H2O gas is shown in Figure 9.28. Cold working the metal surface before reaction induces recrystallization of the near-surface region, and graphite formation at the multiple grain and subgrain boundaries results. It is clear that carbon dissolves in the nickel and diffuses inwards, supersaturating the metal until graphite precipitates nucleate and grow at favourable sites. Nava Paz and Grabke [58] reported earlier that CO/H2/H2O mixtures with low pCO led to internal graphitization, whereas high pCO mixtures induced surface deposition. Coke accumulates on the external nickel surface in three forms: a more-or-less uniform layer adjacent to the surface, clusters of approximately spherical particles and filaments (Figure 9.29). The carbon spheres contain nickel particles and the filaments carry nickel particles at their tips. Thus the presumed correlation between coke mass and metal consumption is seen to be reasonable. Nickel is catalytically active to all of reactions (9.7)–(9.9), and it was proposed long ago [72] that reactions such as CO þ H2 ¼ H2 O þ C
(9.40)
where C represents carbon dissolved in nickel, occur on the bare facets of the nickel particles. The carbon then diffuses rapidly through the particle and precipitates at the rear faces, causing elongation of the carbon filament. If the exposed nickel faces cannot dissolve carbon quickly enough, the particle is encapsulated with graphite, forming a roughly spherical particle like those in Figure 9.29. The accumulation of the outer, loose coke deposit is thereby
9.7. Dusting of Nickel and Austenitic Alloys
437
Figure 9.29 Coke developed on nickel exposed to CO=H2 =H2 O (aC ¼ 19) at 6501C: uniform layer, particle clusters and filaments.
explained. Of more interest, however, is the development of coke at the metal surface, and the way in which parent metal is ‘‘dusted’’ to form the catalytic nanoparticles. Zeng and Natesan [99] used Raman spectroscopy which is sensitive to the degree of carbon crystallinity, to show that the surface carbon layer is more graphitic than the outer coke. Grabke et al. [96, 100], Pippel et al. [64] and Chun et al. [98] all used TEM to examine the nickel–carbon interface. These authors agreed that the carbon is graphite, that the graphite basal planes are oriented approximately normal to the nickel surface when dusting occurred and that nickel is dissolved (1–2 wt%) in the graphite. The mechanism deduced from these observations was one of outward diffusion of solute nickel through the graphite, followed by precipitation of nickel particles in the outer regions of the graphite layer. The fundamental difficulty with this mechanism is essentially the same as was identified earlier in the iron dusting case. No driving force is apparent for mass transfer from bulk nickel to particulate metal, which would presumably be at a higher energy level as a result of its large specific surface area. A TEM image of the graphite layer and nickel concentrations analysed within it by EDAX [101] are shown in Figure 9.30. Little or no concentration gradient is apparent, suggesting either that no diffusion occurs or that DNi in graphite is extremely high. Examination of the microstructure in Figure 9.30 shows that in fact nickel nanoparticles are distributed throughout the graphite layers. Thus the surface layer is a two-phase, two component material in which isothermal diffusion could not occur if local equilibrium was in effect. It is nonetheless possible that a single-phase graphite–nickel solution might form under other reaction conditions and the nickel diffusion model could apply. In the example shown, it appears that mechanical disintegration of the metal is a consequence of the inward growth of graphite and the accompanying volume expansion. Such a process was in fact deduced from the original electron microscopy studies [64, 96, 98, 100], and the proposed diffusion of nickel through graphite is of secondary importance. The mechanism of graphite nucleation and growth is of fundamental importance to the dusting process. It is proposed [96, 98, 101] that the free
438
Chapter 9 Corrosion by Carbon
300 NiK
Intensity
250 200 150 100 50 0 0
0.5
1 1.5 Distance, μm
2
2.5
(a)
100nm
100nm (b)
Figure 9.30 (a) TEM bright field view and EDS line scan through uniform graphite layer on nickel and (b) bright and dark field images using (111) nickel reflection reveal particulate metal in graphite (CO=H2 =H2 O, aC ¼ 19, T ¼ 6801C). Reprinted from Ref. [101] with permission from Elsevier.
edges of graphite basal planes act as attachment sites for carbon atoms, permitting their extension into the metal (Figure 9.31a). The supply of carbon necessary for this process can only be maintained if direct gas access to the base metal continues throughout the reaction. Even when the surface is covered with graphite and coke, no effective barrier to the gas is formed. Most of the coke is obviously porous, and even the more dense graphite layer is extensively fissured. The factors controlling graphite formation on nickel have been investigated intensively because carbon fouling (coking) of industrial nickel catalysts is an important practical problem. Direct surface observation [103] using low-energy election diffraction (LEED) showed that a preferred epitaxial relationship developed between the graphite basal plane (0001) and Ni (111) faces. A computer simulation of this arrangement is shown in Figure 9.31b. Electron diffraction studies [104] confirmed that (111), (113) and (220) nickel faces were found at carbon filament–metal interfaces. The same epitaxies are observed in metal dusting studies.
439
9.7. Dusting of Nickel and Austenitic Alloys
Ni
C
(a)
(b)
Figure 9.31 (a) Schematic view of graphite growth into nickel. (b) Computer simulation of the epitaxial relationship between the graphite basal plane and a Ni (111) surface.
Examination by TEM of reacted nickel single crystal and polycrystalline surfaces [64, 98, 100] revealed that graphite basal planes developed parallel to nickel (111) and (110) surfaces, but at right angles to a (100) surface. In the short term, no dusting occurred at the (111) or (110) surfaces, but on the (100) surface graphite grew into the nickel, causing its disintegration. This pattern of behaviour is clearly consistent with the reaction model of Figure 9.31, which requires the graphite basal planes to be oriented at an angle to the surface. Of course, the description is somewhat oversimplified. Consider, for example a (111) surface which is in fact intersected by planes such as (111¯ ), providing favourable inward growth directions for graphite. These will be accessible at surface jogs, kinks, etc. and dusting does in fact ultimately commence on these surfaces [64, 98, 100]. Figure 9.32 shows graphite growing into the metal along nickel (111) and (113) planes. Penetration of graphite basal planes between adjacent planes of the nickel lattice destroys its structure. It has been suggested [99, 101] that the graphite nucleates within the metal interior, and this is self-evidently the case for internal graphitization (Figure 9.28). Such a process is analogous to the dissolution– precipitation mechanism producing carbon filaments from nickel nanoparticles. Some insight into the process can be gained from a consideration of alloying effects.
9.7.2 Dusting of nickel alloys in the absence of oxide scales The dusting of austenitic Ni–Fe alloys at 6501C in CO/H2/H2O gases such that no oxidation occurred was studied by Grabke et al. [106], who found that both coking and metal wastage rates increased monotonically with iron concentration. The changes in coking rate reflected a combination of changing catalytic activity
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Chapter 9 Corrosion by Carbon
Figure 9.32 Nickel facets at graphite–metal reaction front determined by SAD Reprinted from Ref. [101] with permission from Elsevier.
and dust particle size. Regardless of alloy iron content within the range 0–70%, the reaction morphologies were the same as for pure nickel. The dependence of dusting rate on alloy composition can be understood in part from the carbon permeability data of Figure 9.12. The higher permeability of iron-rich alloys would provide a greater flux to the graphite nucleation and growth sites, supporting more rapid graphitization and metal dusting. On this basis, however, pure nickel would be predicted to dust more rapidly than alloys with approximately 80% Ni, but in fact the metal dusted more slowly than the alloy. More information is required for high Ni/Fe ratios, which are typical of Inconel alloys (Table 5.1). Alloying copper with nickel has been found [105, 107] to decrease coking and dusting rates sharply (Figure 9.33). The coke deposit on alloys containing at least 10 wt% copper consisted solely of filaments. Thus metal wastage via the process leading to graphite particle clusters (Figure 9.29) was suppressed. Copper is known to be immune to dusting attack, but its effect on nickel alloy dusting was much greater than one of simple dilution. Similar results have been reported [108–110] for the effect of copper on catalytic coking by nickel. This can be understood [108, 110, 111] if the catalytically active sites consist of y nearneighbour atoms. Then the carbon deposition rate on an alloy, r, is described by r ¼ rNi ð1 N Cu Þy
(9.41)
9.7. Dusting of Nickel and Austenitic Alloys
441
Figure 9.33 Carbon uptake on Ni–Cu alloys at 6801C in CO=H2 =H2 O (aC ¼ 19). Continuous lines calculated from Equation (9.41) [105]. Published with permission from Wiley-VCH.
where rNi is the rate on pure nickel. The effect of copper can be described by this equation with y ¼ 18, as shown by the calculated lines in Figure 9.33. A catalytic site of 18 near-neighbour atoms is physically unrealistic if surface reactions of simple molecules (e.g. Equation (9.40)) are involved. However, if graphite nucleation is the process being catalysed, then a stable nucleus presumably requires at least one hexagonal carbon ring. As seen in Figure 9.31, it would require 7 near-neighbour nickel atoms on a free surface or 14 atoms on adjacent (111) planes for internal nucleation. We therefore conclude that the copper effect is consistent with internal graphite nucleation. Copper alloying also affects carbon solubility in the metal. The solubility is reported [112] to be reduced from a maximum of 0.18% in nickel to about 0.01% in Ni–90Cu. However, Mclellan and Chraska [113] showed that carbon solubility was unaffected by the presence of up to 40% copper. More information is required for carbon permeability, but on the basis of existing data, graphite nucleation appears to be more strongly affected.
9.7.3 Effects of temperature and gas composition on nickel dusting Average metal recession rates in a 50–50 mixture of CO–H2 were found [98] to increase with temperature to a maximum at about 8001C, and to remain constant at higher temperatures. The carbon activity in those experiments was uncontrolled, and interpretation of the high temperature results is therefore difficult. The low-temperature results were correlated with an observed increase in carbon graphitization with increasing temperature. Chun et al. [98] suggested that dusting was controlled by outward diffusion of nickel dissolved in graphite,
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Chapter 9 Corrosion by Carbon
and therefore accelerated with increased graphitization of the coke. However, it could also be argued that only graphite, and not amorphous carbon, was capable of growing into the metal, because graphite can develop a crystallographic orientation relationship with the metal. Increasing graphitization would therefore increase the extent of nickel disintegration. Carbon uptake rates in a gas mixture of H2–24CO–2H2O were found by Schneider et al. [96] to have a maximum at about 6251C, and decreased sharply at higher temperatures, reflecting the lower carbon activities reached at higher temperatures in a gas of fixed composition. Direct measurements of the dependence of metal consumption (i.e. dusting) rates on gas composition are lacking, but data are available for coking rates. At a fixed temperature of 6501C, carbon uptake rates vary with gas composition in a complex way. Experiments in which pCO and aC (as calculated from Equation (9.10)) were varied independently [97] showed that carbon uptake rates were not directly related to aC . Using instead an elementary kinetic description for reactions (9.7)–(9.9), one arrives at Equation (9.39). Figure 9.34 demonstrates the success of this description with k7 ¼ 0.73, k8 ¼ 0.06 and k9 ¼ 0.27 mg cm2 atm2 h1. This indicates that coke formation is controlled by the CO+H2 reaction (9.7) at moderate pCO levels and by the Boudouard reaction (9.8) at high pCO levels. The methanation process is important when pH2 is significant. It needs to be recognized that different dependencies are likely at different temperatures, and that the relationship between coking and dusting rates is likely also to be temperature dependent. More work is required to obtain a full understanding of the effects of environmental variables on nickel dusting.
r, experimental, mg/cm2h
0.2
0.15
0.1
0.05
0 0
0.05
0.1
0.15
0.2
r, calculated, mg/cm2h
Figure 9.34 Carbon uptake rates on nickel in CO/H2/H2O at 6501C plotted according to Equation (9.39). Reprinted from Ref. [97] with permission from Elsevier.
9.7. Dusting of Nickel and Austenitic Alloys
443
9.7.4 Dusting of austenitic alloys Grabke et al. [102, 106] found that the dusting of binary Fe–Ni alloys varied in reaction morphology and rate with nickel content. Essentially, low nickel content alloys behaved like pure iron, forming a surface layer of cementite, whereas high nickel alloys graphitized directly without forming carbide. The nickel level necessary to suppress cementite formation at 6501C was reported as 30% [106] and also [102] as 5–10%. The dusting of austenitic chromia-forming alloys is prevented for so long as the oxide scale acts as a barrier to carbon ingress [56]. The onset of dusting has been characterized by Grabke and co-workers [58, 60, 106] and the general features of the process are now clear. Selective oxidation of chromium produces a Cr2O3 scale and a chromium-depleted subsurface alloy region, until local scale damage allows gas access to the metal. If sufficient chromium remains, the Cr2O3 scale reheals; if not, other reactions follow. In the usual case, pO2 is too low for nickel or iron oxides to form and, instead, carbon enters the alloy, precipitating chromium carbides. At these low temperatures, DCr in the alloy is small, and the carbides are consequently very fine. Removal of chromium from the matrix renders future oxide healing of the surface impossible, and gas access to the chromium-depleted surface continues. The surface is now essentially an Fe–Ni alloy, and at high nickel levels it undergoes graphitization and disintegration in the same way as pure nickel. Thermal cycling dusting studies [24] on model Fe–xNi–25Cr alloys reveal considerable variation in metal wastage rate with nickel content (Figure 9.26). A 2.5Ni alloy is ferritic, and forms a surface layer of M3C, which disintegrates into cementite dust. Alloys with 5 and 10Ni have duplex a+g microstructures, in which the austenite is clearly carburized more rapidly than the ferrite. Dusting produces nanoparticles of M3C from the 5Ni alloys and both M3C and austenite from the 10Ni alloy. A 25Ni alloy is fully austenite and disintegrates to yield austenite dust. This shift from carbide to austenite particles with increasing nickel levels is the same as that seen for binary Fe–Ni alloys [102, 106], and reflects the mechanism of attack on chromium-depleted surfaces. The variation of dusting rate with Fe/Ni ratio shown in Figure 9.26 reflects mainly the difference in DCr accompanying the change from ferritic to austenitic structures. Because the alloy surfaces were electropolished and any cold-worked surface regions removed, chromium was available to the surface only via lattice diffusion. Thus rehealing was more effective, and frequency of dusting initiation less, in the alloy sequence a4ða þ gÞ4g. At still higher nickel levels, improved performance results from the lowering of alloy carbon permeability. A growing body of results on the dusting resistance of austenitic alloys is becoming available. It is generally agreed [60, 90, 106, 114] that higher nickel levels are beneficial, and that a minimum chromium level of about 25% is required [114, 115]. At these levels, scale breakdown allows formation of two internal carbide zones, usually spheroidal M7C3 near the surface and lamellar or Widmanstatten M23C6 at greater depths [24, 116]. Alloy additions of silicon and aluminium improve the ability of the scale system to exclude carbon
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Chapter 9 Corrosion by Carbon
[59, 90, 117–119]. Additions of carbide-forming metals (Mo, W, Nb) form stable carbides. Their ability to getter carbon allows unreacted chromium to reheal the surface scale, delaying the onset of dusting [119]. However, subsequent oxidation of these refractory metal carbides leads to volume expansion, and disruption of the protective scale [120]. It has been shown [121] that additions of copper improve the dusting resistance of 310 stainless steel and alloy 800, just as copper decreases the dusting of nickel itself. This effect is limited by the alloy solubility for copper, which increases with alloy nickel level. Szakalos and co-workers [25, 80, 122] have pointed out that the fine internal carbides formed after scale failure can be oxidized in situ, leading to disruption of the metal and contributing to the dusting process. This phenomenon is illustrated in Figure 6.38, and is in fact the ‘‘green rot’’ corrosion process [123], in which the large volume expansion accompanying carbide oxidation fractures the metal. Under dusting conditions, this could occur simultaneously with graphitization of the chromium-depleted surface metal. The two possible reactions for internal carbides near the surface are the oxidation process and simple dissolution, providing a chromium diffusion flux towards the surface. The competition between the two processes will depend on oxygen and carbon permeabilities, and DCr within the subsurface alloy region. Rates of carbon and oxygen dissolution into the region are likely to depend also on gas compositions.
9.8. PROTECTION BY OXIDE SCALING As noted earlier, industrial gas streams which cause carburization are almost always oxidizing to chromium, and therefore also to silicon and aluminium. Heat-resisting alloys used at temperatures up to about 1,0001C are usually chromia formers, and the protective nature of their scales is what preserves the alloys from carburization. Using radioactive 14C, Wolf and Grabke [124] showed that the solubility of carbon in Cr2O3 and Al2O3 at 1,0001C is below the detectability limit of 0.01 ppmm. Nonetheless, chromia scales grown on alloy surfaces can be permeable to carbon, presumably by transport through defects or along internal surfaces. Grabke et al. [125] showed that radiotracer carbon in a CO/CO2/H2/H2O gas mixture slowly permeated scales on preoxidized Fe–Cr alloys. Simultaneous internal carburization and external Cr2O3 growth have been observed [126] on Fe–28Cr exposed to CO/CO2 at 9001C. However, a Ni–28Cr alloy reacted in the same way formed no internal carbides, indicating a more gas tight scale. Cast heat resisting steels form scales consisting of mixed carbides and oxides, the proportion of oxide increasing with ambient pO2 . At high oxygen activities, the scale is mainly Cr2O3 with an outermost layer of manganese-rich spinel and, depending on alloy silicon levels, a more or less continuous SiO2 layer at the alloy–scale interface. For so long as they maintain their mechanical integrity, these scales completely block carbon access to the underlying alloys. The appearance of scales grown at 1,0001C, low pO2 values and aC ¼ 1 together with
9.8. Protection by Oxide Scaling
445
the corresponding diffusion paths mapped on the thermochemical diagram are shown in Figure 9.35. The scale grown at pO2 ¼ 1022 atm is a mixture of oxide (dark) and carbide (light) with a sublayer of SiO2 (black). The protectiveness of these scales depends on alloy silicon content, as shown in Figure 9.36, where a level of about 1.8 wt% is seen to reduce the carburization rate dramatically at 1,0501C. Kane [29] reported a value of 2 wt% to be required at 1,0931C. At pO2 ¼ 1024 atm, Cr2O3 is unstable, but SiO2 still forms. Exposure to these conditions [127] led to a scale of carbide over a thin silica layer at the alloy surface. This scale was not protective, and alloys carburized rapidly, even at silicon levels up to 2.4 wt%. We therefore conclude that conditions producing both SiO2 and Cr2O3 are necessary to provide a carbon resistant scale.
Figure 9.35 Scales grown on 25Cr–35Ni heat resisting steels at 1,0001C and aC ¼ 1 (a) pO2 ¼ 1022 atm, (b) pO2 ¼ 1024 atm [127] and (c) diffusion paths. With permission from the National Research Council of Canada.
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Chapter 9 Corrosion by Carbon
Figure 9.36 Dependence of carburization rate on alloy silicon content at 1,0501C, aC ¼ 1 and pO2 ¼ 3 1020 atm [128]. Published with permission from r NACE International 1982.
The location of the stability boundary between chromium carbide and oxide shown in Figure 9.35c is temperature dependent: 3Cr2 O3 þ 4C ¼ 2Cr3 C2 þ 92O2
(9.42)
DG ¼ 3; 192; 100 797:3T J mol1
(9.43)
In the presence of a coke deposit, aC ¼ 1, and the value of pO2 corresponding to the equilibrium (9.42) is calculated to be as shown in Figure 9.37. In a steamcracking reactor, the H2/H2O ratio is approximately unity, and the equilibrium pO2 values calculated for H2 þ 12O2 ¼ H2 O are seen to be much higher than the Cr3C2/Cr2O3 values, implying that the oxide is stable. However, as pointed out by Grabke et al. [6], the oxygen activity beneath a carbon deposit can be a great deal less. If the carbon deposit is gas tight, then the gas species will be CO and CO2, with the ratio p2CO =pCO2 set through the Boudouard equilibrium (9.8) with unit carbon activity. If the total pressure pCO þ pCO2 ¼ 1 atm the corresponding pO2 is found from the thermodynamics of reaction (9.2) to be low at high temperatures (Figure 9.37). If ~ 000 C, carbon will reduce the oxide and degrade the protective nature of T 41; the scale. Both Cr2O3 and Al2O3 scales provide effective barriers to carbon entry and metal dusting. However, such scales eventually fail by cracking or spallation. If sufficient chromium or aluminium remains at the alloy surface, then scale rehealing takes place. If not, carbon dissolves in the depleted alloy and diffuses inward, to precipitate carbides. At high carbon activities, metal dusting follows. The competition between outward metal diffusion to form a scale and inward
9.8. Protection by Oxide Scaling
1150
T (°C) 1050
1100
447
1000
-10
-12
log10pO2
H2/H2O -14
-16 Cr3C2/Cr2O3 C\CO\CO2
-18
-20 7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
104K/T
Figure 9.37 Thermodynamics of oxide to carbide conversion compared with CO=CO2 mixture at pT ¼ 1 atm in equilibrium with graphite, and with oxygen potentials in steam cracking furnaces.
carbon diffusion should in principle be described by an equation such as (9.15). Unfortunately, no rigorous test of this description is available. Qualitative support is provided by the finding [91] that several heat-resisting alloys can be ranked in their resistance to metal dusting during temperature cycling according ðsÞ to their N ðoÞ Cr DCr =N C DC values. The failure of oxide scales under creep conditions has been shown [7, 129] to lead to accelerated carburization at high creep rates. However, the strain rates necessary to prevent scale healing are so high [130] that this should not usually be a practical problem. A practical problem of another sort arises in the use of oxide scales for protection against carbon. Pre-oxidization procedures used to develop a chromia scale before service can also develop an outer scale layer of spinel, MCr2O4. If subsequent service conditions provide an oxygen potential below the spinel stability level, it is reduced leaving particles of metal, MCr2 O4 ¼ Cr2 O3 þ M þ 12O2
(9.44)
These particles act as catalytic sites, accelerating the onset of coking. This in turn can lead to scale disintegration and the commencement of dusting. Exposing austenitic chromia formers to alternately oxidizing and carburizing conditions has been shown [131] to lead to rapid scale failure, accelerated carburization and in some cases the commencement of dusting. To avoid this effect it is necessary to adjust the pre-oxidation conditions so that the oxides formed at that stage are stable during subsequent service.
448
Chapter 9 Corrosion by Carbon
Figure 9.38 Effect of sulfur on metal dusting. The hatched region represents the transition to an iron surface saturated with sulfur [134]. Published with permission from Wiley-VCH.
9.8.1 Protection by adsorbed sulfur The introduction of gaseous sulfur species such as H2S to industrial process steams is widely practiced in order to minimize carburization and metal dusting. Sulfur adsorbs on the metal surface, preventing carbon access [34, 132, 133]. Under these conditions, rehealing of damaged oxide scales is favoured over carbon penetration. The effect increases with pS2 , but the sulfur pressure must be kept below the value at which CrS can form. Adsorbed sulfur also provides protection against metal dusting, delaying the onset of the process and allowing more time for oxide rehealing to occur. Data assembled by Schneider et al. [134] for the effect on iron is shown in Figure 9.38. The H2S/H2 ratios required to yield protection increase with temperature because the sulfur adsorption process is strongly exothermic. In the case of pure iron, the sulfur adsorbs on cementite and prevents the nucleation of graphite.
9.8.2 Protection by coatings As is by now clear, long-term protection against metal dusting and carburization can only be achieved by forming a stable oxide scale which is capable of rapid rehealing. Coatings with high concentrations of scale forming elements can be used to provide this protection. Chemical vapour deposition [135–140] and flame spraying [141] have been used to produce carburization resistant coatings, and their utility under metal dusting conditions has also been tested [142].
9.9. Controlling Carbon Corrosion
449
Aluminium diffusion coatings were found to be protective for a series of ferritic metals (2.25–28Cr) and the austenitic alloy 800. However, long-term exposure led to pore development under the scale and cracking. Silicon diffusion coatings did not develop protective scales. A flame sprayed g-TiAl coating was successful on a ferritic material, but failed on alloy 800 as a result of thermal mismatch. This work showed that alumina scales provided better protection against carbon than did chromia.
9.9. CONTROLLING CARBON CORROSION Carburization reactions at aCp1 are well described by the classical theory of internal oxidation. Local equilibrium is achieved within the reacting alloy, solidstate diffusion of dissolved carbon controls the rate and parabolic kinetics result. Wagner’s diffusion theory provides good quantitative predictive capability, despite the approximate nature of some of its assumptions. Metal dusting reactions at aCW1 proceed according to complex mechanisms which are still not fully defined. Local equilibrium is not achieved within the gas or at the gas–solid interface. It is therefore necessary to consider both the thermodynamic state of the gas and the kinetics of the several parallel gas–solid reactions possible. This requires specification of the complete gas composition, including minority species, as well as temperature. Considerably more work is needed to define temperature and gas composition effects on dusting rates. Ferritic materials at moderate temperatures form Fe3C. This phase is either disintegrated by precipitation within it of graphite or, in other gases, decomposed to yield metallic iron. Unfortunately, the boundaries between the two regimes are still not defined. Austenitic materials form no carbide, and are disintegrated by precipitation and growth of graphite within the metal. A similar mechanism operates for ferritic materials when cementite formation is prevented by high temperatures or alloying. Protection against carburization and dusting requires the provision of a surface barrier between metal and gas, either an adsorbed sulfur layer or an oxide scale. The addition of low levels of sulfur-containing compounds to gas streams is widely practised in the operation of processes such as steam cracking and direct reduction of iron ore. The adventitious presence of sulfur in crude oil provides protection in the early stages of the refining process. However, gaseous sulfur is not always acceptable in process streams, as it can poison catalysts or contaminate the final products. Steam reforming is a catalysed process in which sulfur is unacceptable, and protection is achieved by providing a barrier oxide scale. Maintaining an effective oxide scale can be difficult under reducing conditions. The chromia plus silica scales formed by cast, heat resistant grades are successful at low carbon activities, but not at the higher activities encountered in cooler gases. In these situations, alumina scales are to be preferred. A variety of proprietary, aluminium-rich coatings is used to form the desired scales. Under some circumstances, FeCrAl alloys such as Kanthal are employed.
450
Chapter 9 Corrosion by Carbon
When attack by carbon does occur, it is catastrophically rapid. For this reason, protective measures must be employed, and their continued effectiveness monitored.
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CHAPT ER
10 Effects of Water Vapour on Oxidation
Contents
10.1. Introduction 10.2. Volatile Metal Hydroxide Formation 10.2.1 Chromia volatilization 10.2.2 Chromia volatilization in steam 10.2.3 Effects of chromia volatilization 10.2.4 Silica volatilization 10.2.5 Other oxides 10.3. Scale–Gas Interfacial Processes 10.4. Scale Transport Properties 10.4.1 Gas transport 10.4.2 Molecular transport 10.4.3 Molecular transport in chromia scales 10.4.4 Ionic transport 10.4.5 Relative importance of different water vapour effects on chromia scaling 10.5. Water Vapour Effects on Alumina Growth 10.6. Void Development in Growing Scales 10.7. Understanding and Controlling Water Vapour Effects References
455 458 459 462 463 466 468 468 472 472 475 480 484 487 488 489 490 492
10.1. INTRODUCTION In 1988, Kofstad [1] wrote, ‘‘It is well known that most technical steels oxidise faster in water vapour or in air or combustion gases containing water vapour than in dry oxygen. The reasons for this are poorly understood’’. At a subsequent Workshop on High Temperature Corrosion [2], it was concluded that understanding remained incomplete. Since then, considerable experimental effort has led to a better definition of the problem, and an improved level of understanding. However, there is still much to learn. As noted by Saunders and McCartney in 2006 [3], ‘‘It is well known that the oxidation rate of steels in steam is about an order of magnitude greater than in air or oxygen, but the mechanism responsible for this increased rate is still unclear’’.
455
456
Chapter 10 Effects of Water Vapour on Oxidation
The nature of the problem is illustrated in Figure 10.1, where the results of oxidizing a ferritic 9% Cr steel at 6501C in N2/O2 and N2/O2/H2O are compared. The dry gas produced an extremely thin (B50 nm) scale with a chromium-rich layer adjacent to the alloy, and protective behaviour was achieved. This was not the case in wet gas, where a porous, multiphase scale grew rapidly. The mechanisms whereby water vapour changes the phase constitution, microstructure and growth rate of the oxidation product are of both fundamental interest and practical importance. Water vapour is present in many gases of industrial importance. Atmospheric air contains water vapour at levels which vary with temperature and relative humidity. A temperature range of 18–281C corresponds to saturation values (i.e. at 100% relative humidity) of pH2 O ¼ 0:02 0:04 atm. As is seen later, these levels are sufficient to affect the oxidation rates of many alloys. Thus the results of laboratory experiments using uncontrolled atmospheric air are subject to these affects. Conversely, oxidation rates to be expected in, for example, air pre-heaters cannot be predicted from laboratory data obtained using dry air.
mounting
Ni-coating
oxide scale
steel
(a)
mounting
Ni-coating
hematite magnetite voids Fe3O4 + (Fe,Cr, Mn) 3O4
(b)
steel
Figure 10.1 Cross-section of P91 steel after 100 h exposure at 6501C to (a) N2-1% O2 and (b) N2-1% O2-2% H2O. Reprinted from [4] with permission from Elsevier.
10.1. Introduction
457
Water vapour is invariably a constituent of combustion gases, and can therefore affect corrosion in engines, direct fired furnaces and recuperators. It is also present in synthesis gas and coal gas, along with hydrogen. Similar mixtures are generated in fuel cell anode gas streams. Finally, pure steam is the working fluid in many power generating systems as well as being handled as a process stream in a diversity of chemical plants. The water molecule is very stable with respect to its dissociation H2 O ¼ H2 þ 12O2
(10.1)
as reflected by the free energy change DG1 ¼ 246; 440 54:8 T J mol1
(10.2)
Consequently, the value of pO2 in gases containing free molecular oxygen is essentially unchanged by reaction (10.1) if water vapour is added. In pure steam or inert gas–water vapour mixtures, the equilibrium value of pO2 is determined by the extent of H2O dissociation. In the case of pure steam, the dissociation of one mole yields x moles of H2 and x=2 moles of O2, with x to be calculated from the equilibrium expression. Using the method of Section 2.1, we find K21 ¼
x3 PT 2ð1 xÞ2 ð1 þ x=2Þ
(10.3)
where PT is the total pressure. Because K1 is small, x 1 and (10.3) is well approximated by 2 1=3 2K1 (10.4) x¼ PT pO2 ¼ xPT
(10.5)
Equilibrium oxygen partial pressures calculated in this way are seen in Figure 10.2 to be high enough to form Fe2O3 on iron at low temperatures. As expected, pO2 increases with temperature and total pressure. At high temperatures, hematite formation in steam is not possible, unless the pressure is large. If impurity amounts of O2(g) are present in the steam, then pO2 is set by the impurity level rather than H2O dissociation. However, it seems likely that any such impurities would be quickly scavenged by reaction with oxidizing metal, and the water dissociation equilibrium thereby restored. A final factor to be recognized in considering the reacting gas phase is hydrogen generation. In the case of pure steam, the oxidation process M þ H2 O ¼ MO þ H2
(10.6)
produces hydrogen. Depending on the mass transfer rates between the scale surface and steam phases, the local situation could be similar to that reached in synthesis gas or a laboratory H2/H2O mix. In the presence of free molecular oxygen, however, any hydrogen generated in this way is presumably oxidized rapidly to water vapour. Water vapour can, in principle, interact with an oxidizing metal in a number of ways. It can participate in surface reactions, thereby modifying the scale–gas
458
Chapter 10 Effects of Water Vapour on Oxidation
0
log10(po2/atm)
-5 -10
H2O(238atm) Fe2O3 /Fe3O4
-15
H2O(1atm)
FeO/Fe3O4
-20 Fe/FeO
-25 -30 8
9
10
11
12
13
104 K/T
Figure 10.2 Equilibrium oxygen partial pressures calculated for pure steam at indicated pressures compared with values required for oxide formation.
interface or even producing volatile hydrated species. It can interact with the scale interior, affecting its microstructure and properties, including its transport behaviour. These interactions include the possible dissolution of hydrogen in the oxide and the generation of lattice point defects. Finally, hydrogen generated by reaction (10.6) can dissolve in the metal itself.
10.2. VOLATILE METAL HYDROXIDE FORMATION Several metal oxides form volatile compounds by direct reaction with water vapour. Hydroxides and oxyhydroxides can be produced by hydration, e.g. FeOðsÞ þ H2 OðgÞ ¼ FeðOHÞ2 ðgÞ
(10.7)
MoO3 ðsÞ þ H2 OðgÞ ¼ MoO2 ðOHÞ2 ðgÞ
(10.8)
In addition, simultaneous oxidation and hydration sometimes occurs, e.g. 1 2Cr2 O3 ðsÞ
þ H2 OðgÞ þ 34O2 ðgÞ ¼ CrO2 ðOHÞ2 ðgÞ
(10.9)
Thermodynamic data for the more important reactions is summarized in Table 10.1, and a more extensive collection has been provided by Jacobson et al. [12]. Volatilization of a protective scale leads to accelerated consumption of the scale-forming element and its depletion in an alloy. In the usual case of an alloy exposed to a flowing gas, the rate at which a vapour species produced at low concentration at the oxide–gas interface transfers into the bulk of the gas is described by Equations (2.157) and (2.158). Assuming that none of the hydroxide is initially present in the gas, these two equations are combined to yield an
459
10.2. Volatile Metal Hydroxide Formation
Table 10.1
Standard free energies of metal hydroxide formation reactionsa DG ¼ A þ BT ðJÞ
Reaction
FeOðsÞ þ H2 OðgÞ ¼ FeðOHÞ2 ðgÞ Fe3 O4 ðsÞ þ 3H2 OðgÞ ¼ 3FeðOHÞ2 ðgÞ þ 12O2 ðgÞ Fe2 O3 ðsÞ þ 2H2 OðgÞ ¼ 2FeðOHÞ2 ðgÞ þ 12O2 ðgÞ NiOðsÞ þ H2 OðgÞ ¼ NiðOHÞ2 ðgÞ Cr2 O3 ðsÞ þ 2H2 OðgÞ þ 32O2 ðgÞ ¼ 2CrO2 ðOHÞ2 ðgÞ Al2 O3 ðsÞ þ 3H2 OðgÞ ¼ 2AlðOHÞ3 ðgÞ SiO2 ðsÞ þ 2H2 OðgÞ ¼ SiðOHÞ4 ðgÞ a
A
B
175,700 818,400 663,300 219,000 53,500 220,000 47,900
31.4 193 200 50.7 45.5 14.7 72.3
Ref.
[5] [6] [7] [6] [8] [9] [10–12]
For mole numbers of reactions as written.
expression for the molar flux 1=6 0:664 D4AB n 1=2 Ji ¼ pi RT L ng
(10.10)
Here pi is the hydroxide partial pressure at the scale surface, which is calculated on the supposition of scale–gas equilibrium, e.g. Equations (10.7)–(10.9). To assess the suitability of metal oxides for exposure to water vapour, it is necessary to establish at what temperatures the values of pi become high enough for volatilization to be significant.
10.2.1 Chromia volatilization The presence of water vapour has long been known [1, 13–15] to accelerate the degradation of chromia-forming alloys. More recently, it has been discovered that water vapour has adverse effects on such alloys at relatively low temperatures [16–18]. Asteman et al. [16, 19] investigated the reaction between O2/H2O gas mixtures and the Cr2O3 scale grown on 304L (Fe-18Cr-8Ni) stainless steel at 6001C. They showed that weight gain kinetics were accelerated by increasing pH2 O and the gas flow velocity. The faster oxidation was attributed to lower Cr/Fe ratios in the scales, and consequently more rapid diffusion. The change in Cr/Fe ratio was due to chromium volatilization, which was detected by analysing deposits condensed from the reaction gas downstream from the oxidized stainless steel. As seen in Figure 10.3, the Cr-O-H system contains a diversity of volatile species. Ebbinghaus [20] has reviewed the early thermodynamic data for this system. Using that data together with more recent results of Opila et al. [8] for CrO2(OH)2, the equilibrium partial pressures shown in Figure 10.3 were calculated for humid air (pO2 ¼ 0:21 atm, pH2 O ¼ 0:04 atm). It is clear that CrO2(OH)2 is the predominant vapour species at temperatures below about
460
Chapter 10 Effects of Water Vapour on Oxidation
0 -2
log 10(Pi /atm)
-4
CrO2(OH)
-6
CrO2(OH)2
-8 -10 CrO3 -12 -14 5
6
7
8
9
10
11
12
104 K/T
Figure 10.3 Temperature dependence of selected Cr-O-H species vapour pressures calculated for pO2 ¼ 0:21 atm, pH2 O ¼ 0:04 atm using thermodynamic data from Ebbinghaus [20] and Opila et al. [8].
Table 10.2
Mass transfer parameters for CrO2(OH)2 in air-10% H2O [21]
T (1C)
DAB ðcm2 s1 Þ
n ðcm2 s1 Þ
0:664 ðD4AB =nÞ1=6 ðcm sð1=2Þ Þ
650 700 800
0.870.1 0.970.1 1.070.1
1.077 1.169 1.380
0.5670.04 0.6070.05 0.6370.08
1,0001C. The rate at which this species evaporates into a flowing gas stream is now calculated. The reaction gas modelled here is air+10% H2O, an approximation to the water vapour content of a combustion gas. Calculation of the diffusion coefficient is performed using the Chapman–Enskog description [21] of the kinetic theory of gases, based on a simplified model of the gas as a binary N2/CrO2(OH)2 mixture. The calculation method is described in Section 2.9, Equations (2.157)–(2.169). Mass transfer parameters calculated [23] for PT ¼ 1 atm are shown in Table 10.2. The part of the mass transfer coefficient, km , which depends only on the gas state functions T; PT ; pi is seen to be relatively insensitive to temperature. The remaining term ðn=LÞ1=2 varies with experimental design. Oxidation results discussed here were obtained by Pint [24], using specimens of length L ¼ 18 mm, and an inlet (room temperature and pressure) volumetric flow rate of 0.85 L/min, corresponding to n ¼ 17, 18 and 20 mm/s at 650, 700 and 8001C, respectively. These values lead to the mass transfer coefficients shown in Table 10.3. Values of pCrO2 ðOHÞ2 for chromia in equilibrium with air + 10% H2O calculated from the reaction free energy for Equation (10.9) are also shown in the table, along with the resulting chromium loss rates predicted from Equation (10.10). The value of these
10.2. Volatile Metal Hydroxide Formation
Table 10.3
a
461
Chromium lossa as CrO2(OH)2 in air-10% H2O
T (1C)
km ðcm s1 Þ
pCrO2 ðOHÞ2 ðatmÞ
JCr ðg cm2 s1 Þ
650 700 800
0.5470.04 0.6070.05 0.6670.08
8.4 108 1.6 107 3.0 107
(3.170.2) 1011 (6.370.5) 1011 (1.270.1) 1010
Expressed as mass of metal.
6
Cr loss (mg/cm2)
5
4
Eqn (10.10)
3
2
1
0 0
1
2
3
4
5
6
10-3t /h
Figure 10.4 Comparison of measured chromium losses with values calculated for evaporation loss from alloy 709 exposed at 8001C to air+10% water vapour. Data from [22].
predictions is now assessed by performing a chromium mass balance for oxidized alloy foil. Foil specimens (ca. 100 mm thickness) of alloy 709 (Fe-25Ni-20Cr) oxidized in air — 10% H2O for up to 104 h at 650, 700 and 8001C [23, 24] grew scales of chromia containing low levels of iron and manganese. After lengthy exposures, large iron-rich nodules formed as the surface became depleted in chromium, and the reaction rate accelerated. Electron microprobe analysis of the entire thickness of reacted samples provided measurement of the residual chromium content. The amounts of chromium in the scales were calculated from their thicknesses, assuming that the oxide was pure Cr2O3. The sum of the amounts of chromium in the remaining foil and its scale was compared with the amount originally present in unreacted foil, and the deficit noted as a function of time. These values are compared in Figure 10.4 with chromium vaporization losses calculated from the flux value given in Table 10.3. The good agreement shows that the observed
462
Chapter 10 Effects of Water Vapour on Oxidation
chromium depletion can be completely accounted for by Cr2O3 scale formation and CrO2(OH)2 evaporation. Vaporization losses can also be investigated by considering scale thickening kinetics. The thickness increases as a result of solid-state diffusion and decreases by evaporation, leading [25] to the rate equation (1.36) dX kp ¼ kv dt X Thus X increases to a steady-state value, Xss , where dX=dt ¼ 0, and Xss ¼
kp kv
(10.11)
Scale thicknesses measured from polished cross-sections of oxidized alloy 709 are shown in Figure 10.5. Although scatter is considerable, the data appear to conform with Equation (1.36), with Xss ¼ 5 1 mm at 8001C. Evaluating kp as (2.070.1) 1014 cm2 s1 from early stage kinetics [22], it is found from Equation (10.11) that kv ¼ ð4 1Þ 1011 cm2 s1 , corresponding to an average evaporative flux of chromium, J Cr ¼ ð1:4 0:3Þ 1010 g cm2 s1 . This value is in good agreement with the mass transfer calculation result (Table 10.3) of J Cr ¼ ð1:2 0:1Þ 1010 g cm2 s1 .
10.2.2 Chromia volatilization in steam The performance of chromia scales in pure steam environments is relevant to the service conditions in supercritical and ultrasupercritical steam power plants. The oxygen potential in high purity steam is controlled by reaction (10.1), and therefore pO2 is given by Equations (10.4) and (10.5). The value of pCrO2 ðOHÞ2 is then found from the equilibrium expression for Equation (10.9) pCrO ðOHÞ2 K9 ¼ 3=42 (10.12) pO2 pH2 O 6
Scale Thickness (µm)
5 4 3 2 1 0 0
1000
2000
3000 4000 5000 Exposure Time (h)
6000
7000
Figure 10.5 Scale thickening kinetics for alloy 709 exposed at 8001C to air+10% H2O(g). Data from [22].
10.2. Volatile Metal Hydroxide Formation
463
log10(pCrO2(OH)2/atm)
-6 P = 240atm
-7
P = 140atm
-8 P = 17atm -9
-10 P = 1atm -11 0.90
Figure 10.6
0.95
1.00 104 K/T
1.05
1.10
Equilibrium CrO2(OH)2 partial pressures calculated for pure steam. Data from [22].
setting pH2 O ¼ PT , leading to the result pCrO2 ðOHÞ2 ¼ K9
K12 2
1=2
3=2
PT
(10.13)
which is seen to be strongly pressure dependent. Conventional boilers operate at maximum steam pressure of 120–150 atm in their superheaters. Supercritical boilers have superheater pressures of B240 atm. Equilibrium partial pressures for CrO2(OH)2 calculated for these conditions from Equation (10.13) are shown in Figure 10.6. The values are low as a result of the very low oxygen partial pressures in pure steam. Only at high total pressure does the CrO2(OH)2 partial pressure become significant. Calculation [22] of chromium volatilization rates shows that they are very low, except at very high total pressures. The calculation is, however, based on the Chapman–Enskog description, which depends on the assumption of ideal gas behaviours. It will not apply to the supercritical regime, and no prediction for chromia volatilization can be made on this basis.
10.2.3 Effects of chromia volatilization Increasing water vapour partial pressures are predicted from the preceding analysis to accelerate the rate of chromia volatilization for a given value of pO2 . In the case of O2/H2O gas mixtures PT ¼ pO2 þ pH2 O
(10.14)
and, at PT ¼ 1 atm, it follows from Equation (10.12) that pCrO2 ðOHÞ2 ¼ K9 ð1 pH2 O Þ3=4 pH2 O
(10.15)
464
Chapter 10 Effects of Water Vapour on Oxidation
The maximum value of pCrO2 ðOHÞ2 is found by setting the differential dpCrO2 ðOHÞ2 =dpH2 O ¼ 0, whereupon it is found that ð1 pH2 O Þ ¼ 34pH2 O
(10.16)
which has the solution pH2 O ¼ 0:57 atm. Thus the volatilization rate is predicted to increase with pH2 O up to a maximum at this value. Data to test this prediction are available only at low water vapour pressures. Jianian et al. [26] showed that the oxidation kinetics of binary Fe-Cr alloys in O2-H2O atmospheres (PT ¼ 1 atm, pH2 O up to 0.25 atm) were initially protective, before entering a breakaway stage. The time taken to reach breakaway decreased with increasing pH2 O (Figure 10.7), and increased with increasing alloy chromium level. In agreement with earlier results [27–30], breakaway was found to be associated with the progressive spread of iron-rich nodules until the previously protective Cr2O3 scale was destroyed and replaced with a porous, multilayered iron-rich scale. This behaviour is consistent with chromium depletion via volatilization, leading to iron enrichment in the scale. The rate of depletion increases with pH2 O , as discussed above. However, the time taken to reach a critical depletion level depends also on the size of the chromium reservoir available in the original alloy. The rate at which the initial chromia scale grows, kp , also varies with pH2 O . This affect is discussed in Section 10.4. There are situations where the rate of chromium volatilization is insignificant from the point of view of material durability, but unacceptable as a source of contamination. Consider semiconductor processing, where atmospheric pressure chemical vapour deposition (APCVD) can be used to deposit doped and undoped SiO2 onto silicon wafers at temperatures of about 400–6001C. Acceptable impurity metal deposition levels are very low, at about 1010 atom cm2. For this reason, ceramic hardware is often preferred, although alloys would offer practical advantages. Bailey [31] demonstrated that the
Figure 10.7 Oxidation kinetics for Fe-15Cr in O2/H2O mixtures at 9001C [26]. With kind permission from Springer Science and Business Media.
10.2. Volatile Metal Hydroxide Formation
465
chromia-forming IN601 (Ni-22Cr-17Fe-1.7Al) exposed to APCVD conditions evaporated CrO2(OH)2 at rates which exceeded acceptable limits for processed wafers. An alumina-forming alloy was found to provide satisfactory performance. Solid oxide fuel cells provide another example of chromium contamination at their operating temperatures of 750–9001C. A schematic view of a cell is shown in Figure 10.8. Zirconia is used as an oxygen ion electrolyte between a cathode exposed to air and an anode exposed to the fuel gas. The porous electrodes are electronically conducting perovskites, (La,Cr)MO3 where M is Co, Mn or Cr. These cells are stacked together to obtain usable power outputs. In the design depicted, the cells are planar and are separated by plates which provide structural support, electrical connection and gas stream separation. A practical materials solution is a chromia-forming alloy [32], because the resulting oxide scale has fairly good electronic conductivity. Unfortunately, however, it evaporates CrO2(OH)2 in humid air. Porous Cathode
Cr2O3
Porous ZrO2 Anode
Cr2O3
Fuel
Air
J O2-
Interconnect Alloy
Interconnect Alloy
Figure 10.8 Schematic section of solid oxide fuel cell with chromia-forming alloy interconnect plates.
466
Chapter 10 Effects of Water Vapour on Oxidation
Das et al. [33] and Quadakkers et al. [34] have demonstrated that exposure to air of normal humidity at 900–9501C leads to chromium transport from the chromium scale throughout the porous perovskite cathode. Reaction between the gaseous chromium species and the perovskite produces phases such as MnCr2O4, which increase the electrical resistivity of the cathode to an unacceptable level.
10.2.4 Silica volatilization The behaviour of silica in combustion environments is an important issue, because the silicon based ceramic composites (SiC, etc) are protected at high temperatures by a slow growing silica scale. The principal volatile species formed by interaction between silica and water vapour at temperatures around 1,2001C is Si(OH)4, but at temperatures above 1,4001C it is SiO(OH)2 [10–12]. Under strongly reducing conditions, however, the principal gas species is SiO, formed by the reactions [35, 36] SiO2 þ H2 ðgÞ ¼ SiOðgÞ þ H2 OðgÞ
(10.17)
SiO2 þ COðgÞ ¼ SiOðgÞ þ CO2 ðgÞ
(10.18)
Thus volatilization is possible in a wide range of gas atmospheres. Opila and Hann [37] showed that oxidation of SiC in flowing H2O/O2 gas mixtures led to weight uptake followed by weight loss (Figure 10.9). The kinetic data was analysed using the integrated form [25] of Equation (1.36) Z X dX ¼ t (10.19) kp kv X
Figure 10.9 Experimentally determined paralinear weight change kinetics for SiC reacted at 1,2001C in 50% H2O-50% O2. The smooth curve is the result of non-linear regression on Equations (10.21) and (10.22) [37]. Published with permission from the American Ceramic Society.
10.2. Volatile Metal Hydroxide Formation
which yields t¼
kp k2l
kl X kl X ln 1 kp kp
The analogous expression for weight uptake 0 a2 kw k DW 1 =A k0 DW 1 =A ln 1 l t¼ 0 2 l akw akw ðkl Þ
467
(10.20)
(10.21)
is summed with the expression for evaporative weight loss DW 2 =A ¼ bkl t
(10.22)
to obtain the net weight change. Here kw is the usual parabolic rate constant for diffusion-controlled weight uptake, k0l the linear rate constant for evaporative weight loss, a ¼ MW SiO2 =ðMW O2 MW c Þ and b ¼ MW SiC =MW SiO2 , where MW i is the molecular weight of the indicated species. Non-linear regression of kinetic data on Equations (10.21) and (10.22) is seen in Figure 10.9 to succeed. Estimates of k0l arrived at in this way were equal to rates measured for the volatilization of bulk silica. Furthermore, these rates were in agreement with evaporation rates calculated from Equation (10.10) for Si(OH)4 at temperatures of 1,200–1,4001C. The effects of different combustion conditions on silica volatilization have been examined by Smialek et al. [38–40]. Their results show that the reducing conditions produced by excess fuel lead to SiO volatilization, whereas the oxidizing, humid conditions resulting from combustion with excess air lead to Si(OH)4 vapour loss. In comparing results from laboratory reactors with those of high-pressure combustion, it is necessary to account for the effects of total pressure on the parameters in Equation (10.10). The diffusion coefficient DAB and the kinematic viscosity n are each inversely proportional to PT , leading to an overall pressure dependence of the evaporation rate ð1=2Þ
J i / pi PT
(10.23)
Applying equilibrium expressions for reactions (10.17) and SiO2 ðsÞ þ 2H2 OðgÞ ¼ SiðOHÞ4 ðgÞ
(10.24)
we find ð1=2Þ
(10.25)
3=2
(10.26)
J SiO / PT
J SiðOHÞ4 / PT
Thus increasing the total pressure of a particular gas mixture can alter the relative evaporation rates of SiO and Si(OH)4. This is observed in a comparison between SiC consumption in a laboratory reactor and high-pressure burner rig (Figure 10.10). Similar results have been found for Si3N4 [41, 42]. Opila [43] has provided maps of SiC consumption rates with gas velocity and pressure as ordinates. For typical combustion conditions, rapid recession rates (0.2–2 mm h1) are predicted for 1,200–1,4001C.
468
Chapter 10 Effects of Water Vapour on Oxidation
Figure 10.10 Calculated and measured rates of SiC consumption by volatilization during oxidation in fuel-rich combustion gas [30]. With kind permission from Springer Science and Business Media.
10.2.5 Other oxides The predominant aluminium hydrate vapour species is Al(OH)3 over the temperature range 1,100–1,9001C [9]. Its partial pressure is low, and vapourization rates have been measured [9] as 5 1011–5 1010 g(Al) cm2 s1 at temperatures of 1,250–1,5001C in O2 — 50% H2O flowing at 4.4 cm s1. Thus volatilization is unimportant for alumina-forming alloys at likely service temperatures of up to ca. 1,2001C. If alumina-based composites are used at higher temperatures in long-term applications, volatilization might play a role in limiting material lifetimes. Zirconia, hafnia and yttria all appear to be exceptionally stable in water vapour containing environments up to about 1,9001C [44–46], but directly measured thermodynamic data are lacking. The successful use of yttria-stabilized zirconia TBCs at surface temperatures exceeding 1,2001C confirms the stability of the oxides with respect to any hydrated species.
10.3. SCALE–GAS INTERFACIAL PROCESSES The oxygen uptake reaction at the scale–gas interface is close to equilibrium whenever scale growth kinetics are parabolic and diffusion is rate controlling. Thus the addition of H2O(g) to air or oxygen at a fixed pO2 value cannot increase the scaling rate by accelerating the scale–gas surface reaction. However, it could in principle decrease the rate if H2O adsorption occurred preferentially and if the reaction H2 OðadsÞ ¼ OXO þ H2 ðgÞ
(10.27)
469
10.3. Scale–Gas Interfacial Processes
were slow. There appear to be no instances of reaction in which scale growth in air or O2 plus H2O(g) is slower than in dry air or oxygen [1, 2]. However, if H2O(g) completely replaces oxygen, then the phase boundary reaction can become rate controlling if oxide diffusion is rapid. Turkdogan et al. [47] showed that the growth kinetics of Fe1dO scale on iron exposed at 850–1,1501C to H2/H2O mixtures were initially linear and subsequently parabolic. In the early stages of reaction the rate was controlled by an oxide–gas boundary reaction, formulated as H2 OðgÞ þ 2e ¼ H2 ðgÞ þ O¼
(10.28)
This is similar to Equation (3.133) for oxidation by CO2. A similar kinetic model based on a constant number of adsorption sites per unit area leads to a0o Rate ¼ kf yV pH2 O 1 00 (10.29) ao where, as before, yV is the fraction of surface sites vacant, and a0o and a00o are the oxygen activities at the metal–scale and scale–gas interfaces. Initial stage oxidation rates are seen in Figure 10.11 to vary with gas composition as predicted 20
dt
10
(
dn
)O×105 gatm O/cm2min
15
5
0
0.25
0.5
0.75
(1-1/a0∗)pH2o atm
Figure 10.11 Variation of initial linear kinetics for iron oxidation with gas composition according to Equation (10.29) [47]. Reprinted with permission from [47] Copyright (1965) American Chemical Society.
470
Chapter 10 Effects of Water Vapour on Oxidation
by Equation (10.29). As the scale thickens, diffusion becomes slower until it controls the rate, and the kinetics become parabolic. In fact, the reaction (10.28) is rather fast, and an initial period in which the boundary reaction controls the rate is only possible because diffusion in Fe1dO is very rapid. Diffusion in chromia and alumina scales is very much slower, and no period of rate control by a reaction such as Equation (10.28) has been reported. On the contrary, the growth of Cr2O3 scales is faster in H2O(g) than in O2, as is discussed in Section 10.4. Galerie et al. [48] have discussed the surface interaction between oxide scales and H2O(g) in terms of molecular dissociation as affected by the oxide chemistry. If the oxide microstructure and diffusion properties are unchanged by the water vapour, then the surface process becomes important. These authors propose a two-step dissociation process H2 OðgÞ þ S ¼ OHjS þ 12H2 ðgÞ
(10.30)
OHjS ¼ OjS þ 12H2 ðgÞ
(10.31)
represented here without considering charge transfer processes, and using S to denote a surface site. A consideration of bond energies in gaseous H2O leads to the conclusion that DH for reaction (10.30) is similar to that of O2(g) dissociation, but DH 31 is much larger. Assuming then that reaction (10.31) is slow and rate controlling, while reaction (10.30) is at equilibrium, we use the methods of Section 2.9 to find the general result Rate ¼
k28 K27 MpH2 O =pH2 1 þ K27 pH2 O =pH2
(10.32)
with M the surface concentration of adsorption sites. At low surface coverages this simplifies to Rate ¼ k28 K27 MpH2 O =pH2
(10.33)
and the overall rate clearly depends on both the rate constant k28 and the preequilibrium constant K27 . Galerie et al. [48] suggested that the adsorption constant K27 can be correlated with the enthalpy of oxide cation hydration. In this case the oxygen uptake rate given by Equation (10.30) is predicted to increase as the enthalpy of hydration becomes more negative. Estimates of hydration enthalpies are available from heats of solution and lattice energy calculations. As seen in Table 10.4, there is a small increase in DHhyd among transition metal cations from Cr3+ to Ni2+, and all have much lower enthalpy changes than that of Al3+. The kinetic data for oxide scaling shown in Table 10.4 reveals that NiO and FeO formed as compact scales in oxygen-free H2O(g) grow according to linear kinetics. Comparison with reaction in O2(g) (Figure 10.12) is consistent with the Galerie model of a slow surface process on these weakly hydrating oxides. On this basis it would be predicted that the process would be even slower on Cr2O3. However, diffusion in Cr2O3 is very much slower than in Fe3O4 or NiO, and remains rate controlling during reaction with H2O(g). The rate, however, is accelerated. Similarly, the
471
10.3. Scale–Gas Interfacial Processes
Table 10.4 Ion
Cation hydration energies (kJ mol1) at 298 K [49] and metal oxidation kinetics DH
Metal oxidation kinetics
Oxidation T (1C) H2O(g)
3+
Al Cr3+ Mn2+ Fe2+ Co2+ Ni2+ a
980 1,000
4,707 1,883 1,878 1,954 2,088 2,138
Ref.
O2(g)
kw ¼ 9 10
12a
kw ¼ 3 1013a kw ¼ 2 1012a
[50] [51]
550
linear
parabolic
[52]
800
linear
parabolic
[48]
Units: g2 cm4 s1.
6
weight gain mg/cm2
O2
T = 1100°C Oxidant pressure: 133 mbar
5 4 3 2
H 2O 1 0 0
5
10
15 Time (h) (a)
20
25
1.0 weight gain mg/cm2
O2
0.5
Ar+H2O
0
5
10
15
20
t/h (b)
Figure 10.12 Oxidation kinetics (a) nickel at 8001C [48] (published with permission from Trans Tech Publications Ltd.), (b) for iron at 5501C [52] (reprinted with permission from Elsevier).
472
Chapter 10 Effects of Water Vapour on Oxidation
surface reaction would be predicted to be rapid on the strongly hydrating Al2O3, and scaling kinetics would thereby be unaffected. Unfortunately, there appears to be no data for alumina growth in non-oxygenated steam. Data for Fe-21.5Cr5.5Al [50] shows that the addition of up to 0.31 atm of H2O(g) to dry oxygen leads to only a very small decrease in the value of kw . For many oxides, the surface effect discussed above is overwhelmed by the much greater changes in scale microstructure and/or diffusion properties brought about by water vapour. These more important effects are now considered.
10.4. SCALE TRANSPORT PROPERTIES In principle, water vapour can participate in the mass transfer processes within the scale in three different ways: as a gas species within cavities, cracks or voids, as a molecular species and by dissolving hydrogen into the oxide to form lattice species thereby affecting its point defect concentrations.
10.4.1 Gas transport Oxidation of low alloy steels and dilute Fe-Cr alloys is frequently observed to produce iron-rich scales containing closed pores and internal fissures. The extent to which scale integrity is lost can be large, as seen in Figure 10.1(b), but still these scales grow rapidly. Pfeil [53] noted that although oxygen anions might be immobile in the oxide lattice, gaseous oxygen can transport across pores and gaps, providing that the oxide dissociation pressure is sufficiently high. However, as seen in Section 2.9, the value of pO2 in equilibrium with FeO is far too low for the dissociation mechanism to provide a significant contribution to mass transfer [54]. The same conclusion is reached for magnetite scales formed in steam superheater conditions [4] and will obviously apply to more stable oxides such as Cr2O3 and chromium spinels. Fujii and Meussner [55, 56] observed that H2O(g) greatly accelerated the oxidation rate of dilute Fe-Cr alloys at 800–1,1001C, preventing the formation of a protective chromium-rich scale, promoting instead the growth of FeO plus spinel. Rahmel and Tobolski [57, 58] showed that the addition of H2O(g) to O2 slightly accelerated the rate of iron oxidation at 9501C. In both cases, the presence of H2O(g) caused the scales to develop considerable porosity, and vapour phase transport was considered to be important. Both sets of authors proposed that the presence of H2O(g) within the pore space would provide the necessary gaseous mass transport. If inward transport of H2O (or H2) through the scale and into the pore is relatively fast, then the partial pressure of H2O(g) in the cavity will approach that of the ambient gas. Oxygen transport is then effected by the reaction H2 OðgÞ ¼ H2 ðgÞ þ OXO þ V00Fe þ 2h
(10.34)
10.4. Scale Transport Properties
473
.
″ +2h →H2O H2+OOx +VFe
Oxide scale
H2O(g)
H2(g)
.
″ +2h H2O→H2+OOx +VFe
Steel
Figure 10.13 Schematic illustration of oxygen transport within a cavity supported by H2O(g). Based on [54–57].
proceeding in the forward direction on the side of a cavity nearest to the metal, and in the reverse direction at the outer surface of the cavity. These redox reactions are coupled with gas phase mass transfer, as shown in Figure 10.13. Fujii and Meussner [56] calculated that gas phase transport would provide sufficient oxygen flux to support the observed scaling rates at 1,1001C. The calculation is illustrated here for a lower temperature, where oxygen potentials are much reduced. At 6501C, the commercially important 9Cr ferritic steels form rapidly growing scales of porous magnetite plus spinel (Figure 10.1b) when exposed at 6501C to gases containing water vapour [4, 59, 60]. The existence range of Fe3O4 at 6501C corresponds to oxygen potentials of 1022–1013 atm, far too low to contribute significantly to mass transport in the cavities. However, if the value pH2 O ¼ 0:01 atm is adopted for the cavity interior, one calculates from the thermodynamics of Equation (10.1) that equilibrium pH2 values lie in the range 5 107 to 102 atm. According to Equation (2.155), these hydrogen pressures can support oxygen transfer rates of 5 107 to 102 mol cm2 s1. These rates are more than enough to support the observed rapid oxygen uptake rates of B109 mol cm2 s1 accompanying breakaway oxidation (Figure 10.14). The contribution of oxygen transport was confirmed by inert marker experiments. Rahmel and Tobolski [57] found platinum markers initially placed on their iron specimens to be located at the metal–scale interface after reaction with dry O2, but within the porous oxide after reaction with O2+H2O. Scales grown in Ar+H2O on iron and Fe-Cr alloys were found by Fujii and Meussner [55] to contain platinum markers at the interface between the outer FeO layer and the inner FeO+(Fe,Cr)3O4 layer. In both cases, inward scale growth beneath the marker was attributed to oxygen transport. The participation of H2O in gaseous mass transport within large scale voids thus appears to be firmly established for low alloy steels. The oxidation kinetics are approximately linear, after an initial period of parabolic kinetics. The linear rate constant for iron-rich scale growth on iron and Fe-Cr alloys exposed to
474
Chapter 10 Effects of Water Vapour on Oxidation
Figure 10.14 Breakaway (rapid) kinetics in isothermal oxidation of 9% Cr steel P91 in N2-1% O2-x% H2O at 6501C. Reprinted from [4] with permission from Elsevier.
Ar/H2O gases increased with pnH2 O , where n ¼ 0.5–0.9 [56]. However, the effect of pH2 O on scaling rates in O2-H2O gases is more complex, as seen in Figure 10.15. Both iron and the 9% Cr steel, P91 (Table 5.1), oxidize faster when H2O(g) is present, but the rate is insensitive to pH2 O beyond a certain level. In addition, a threshold value of pH2 O is required to accelerate the rate in Ar-O2-H2O mixtures, the threshold increasing with pO2 . This effect is the reason why P91 performs very well at the low pH2 O =pO2 ratios obtained in laboratory air, but fails at high pH2 O values. The existence of this effect requires explanation, as do the transport of H2 or H2O into the scale interior, and the way in which large voids form when water vapour is present. Before considering mechanisms of inward hydrogen transport, it is noted that water vapour induced acceleration of iron oxide scaling is not always accompanied by the development of porous oxide. Tuck et al. [61, 62] concluded that the purity of the iron was another factor involved. The permeability of FeO to hydrogen (or H2O) was demonstrated by Fujii and Meussner [56] in the experiment shown in Figure 10.16. A thin-walled thimble of Fe-5Cr was oxidized on its outside by Ar-10% H2O at 1,1001C, and the gas in the thimble analysed for hydrogen. A steady flow of hydrogen through the scale (and the alloy) was observed. The experiment does not reveal the chemical form of the mobile hydrogen species in the oxide, and Rahmel and Tobolski [57] speculated that hydrogen might pass through a wu¨stite scale as dissolved protons. Kofstad [1] suggested that it might migrate inwards as water molecules.
10.4. Scale Transport Properties
475
Figure 10.15 Dependence of oxidation behaviour on pH2 O in O2 bearing gases (a) pure Fe in O2/H2O at 9501C [56], (b) P91 steel in Ar/O2/H2O at 6501C. Reprinted with permission from Elsevier.
10.4.2 Molecular transport Experiments involving changing the reaction gas from wet to dry and vice versa are informative. As seen in Figure 10.17, switching from wet to dry gas after 24 h of breakaway oxidation leads to a rapid decrease in the scaling rate observed for the 9% Cr steel, P91 (Table 5.1). Examination of scale cross-sections after these two stages (Figure 10.18) reveals that the dry gas causes an increase in the amount of Fe2O3 at the expense of Fe3O4, and densification of the oxide. Thus
476
Chapter 10 Effects of Water Vapour on Oxidation
Figure 10.16 Schematic representation of hydrogen transfer experiment described by Fujii and Meussner [55].
Figure 10.17 Isothermal oxidation kinetics for P91 (a 9% Cr steel) at 6501C when gas alternated between N2-1% O2-4% H2O and N2-1% O2 every 24 h. Reprinted from [4] with permission from Elsevier.
10.4. Scale Transport Properties
477
Figure 10.18 Cross-section of scales grown on P91 after reaction stages shown in Figure 10.18: (a) 24 h, (b) 48 h. Reprinted from [4] with permission from Elsevier.
during the second stage of the experiment, oxygen enters the scale interior where it converts Fe3O4 to Fe2O3. The volume expansion accompanying this transformation, together with some additional oxide growth leads to much of the pore space being eliminated.
478
Chapter 10 Effects of Water Vapour on Oxidation
For this to occur, the scale originally grown in wet gas (Figure 10.18a) must be permeable to gas species. The outer Fe2O3 layer, despite its compact appearance, must allow inward gas species diffusion. Since, nevertheless, a large gradient in oxygen activity is maintained (as shown by the sequential distribution of oxide phases), this diffusion process must be much slower than gas phase transport. Molecular diffusion along internal surfaces, such as grain boundaries, would provide a suitable transport mechanism [4]. Commencing the experiment in dry rather than wet gas leads to very different results [4]. A protective scale of Fe2O3 on top of chromium-rich spinel grows in dry gas, and is not affected, at least for some days, by subsequent exposure to the wet gas. However, if the scale is cooled and reheated, the coefficient of thermal expansion difference between scale and metal leads to scale damage and subsequent rapid reaction in wet gas. Thus the Fe2O3 grown during isothermal exposure to dry gas is not subsequently permeable to H2O(g) in the time scale of the experiment. Unlike the scale grown in wet gas, the oxide grown in dry gas appears to be fully dense as long as no scale damage is introduced. Schutze et al. [65] also found breakaway of the initially formed protective scale on P91 to occur only in association with scale damage, as detected by acoustic emission analysis. Reaction of the P91 steel with an isotopically labelled gas mixture N2 1%16 O2 2%H2 18 O and subsequent analysis of isotope profiles in the scale leads to the results shown in Figure 1.17. It is found that 16O from molecular oxygen is always more abundant than 18O from H2O in the inner part of the scale. In the outer part of the scale, the two isotopes are present at approximately equal concentrations in a pre-breakaway scale, but 18O is enriched in this region after breakaway. These distributions confirm that when water vapour is present at a sufficient level, some of its oxygen content is incorporated into the scale interior, consistent with inward diffusion of a molecular species through the outer part of the scale. The different isotope distributions also show that molecular oxygen in the presence of water vapour does not react with (and thereby densify) the outer scale. Instead, reaction with H2O(g) is favoured in this region. The competition between O2 and H2O induced oxidation reactions is also evident in Figure 10.15(b), where the condition for breakaway oxidation can be approximated [4] as pH2 O =pO2 41
(10.35)
Hayashi and Narita [66] also proposed that the change from slow to rapid oxidation of Fe-5Al alloys at 8001C depends on the pH2 O =pO2 ratio. A simple qualitative interpretation of these findings is that a minimum pH2 O =pO2 ratio is required for sufficient H2O(g) to enter the scale and lead to breakaway oxidation. If molecular species enter the scale by adsorption on internal surface sites, S, we can write H2 OðgÞ þ S ¼ H2 OjS (10.36) O2 ðgÞ þ S ¼ O2 jS
(10.37)
10.4. Scale Transport Properties
479
where dissociative adsorption has been ignored. Treating the adsorption equilibria using the methods of Section 2.9, one finds ½H2 OjS ¼
½O2 jS ¼
MK36 pH2 O 1 þ K36 pH2 O þ K37 pO2
MK37 pO2 1 þ K36 pH2 O þ K37 pO2
(10.38)
(10.39)
with M the assumed constant concentration of surface sites. It follows immediately that ½H2 OjS K36 pH2 O ¼ ½O2 jS K37 pO2
(10.40)
This competitive adsorption process provides an explanation for the finding that higher pO2 values require higher pH2 O values to bring about breakaway oxidation, as expressed in Equation (10.35). When Equation (10.35) is satisfied, it is likely that adsorption of the polar H2O molecule predominates, and Equation (10.38) can be approximated by MK36 pH2 O ½H2 OS (10.41) 1 þ K36 pH2 O It is clear from this result that at sufficiently high pH2 O values, the surfaces saturate with H2O(ads), and the rate of reaction between this species and the scale would be independent of pH2 O . This would explain the insensitivity of breakaway rates to pH2 O (Figure 10.15). It should be noted, however, that K35 and K36 are temperature dependent, and the condition (10.35) is therefore expected to have different values for its right hand member at different temperatures. Thus relatively small additions of H2O(g) to air are sufficient at 9801C to induce rapid breakaway oxidation of Fe-13Cr and Fe-13Cr-2Al alloys [29]. The competitive adsorption process is also consistent with the isotope distribution experiments (Figure 1.17), which show that in the breakaway regime, oxygen from water vapour is the major species incorporated into the outer scale and molecular oxygen the major species taken up by the inner scale. The preferential adsorption of H2O(g) in the outer part of the scale largely excludes the O2 species from the surface and thereby reduces its uptake. Only deep within the scale, beyond the region in which most of the H2O(g) has been consumed, is O2 an effective reactant. In addition, the competitive adsorption process explains the ability of scales formed in breakaway inducing atmospheres to resist densification and retain their gas-permeability. Adsorbed H2O excludes O2 from the internal surfaces of the outer scale region, whilst itself reacting only relatively slowly. Only when H2O is removed from the gas phase, can O2 gain access to these surfaces. Finally, the adsorption model is consistent with the finding that dense, protective scales grown in dry oxygen are not subsequently permeated by H2O(g). In the absence of internal surfaces, adsorption and penetration of molecular H2O(g) is not possible.
480
Chapter 10 Effects of Water Vapour on Oxidation
Silica scales are usually amorphous, or glassy, and therefore contain no grain boundaries. Nonetheless, additions of water vapour to oxygen greatly accelerate the rate of silicon oxidation [63]. The activation energy is decreased, and becomes equal to that observed for the permeability of H2O in silica [64]. The effect is due to the silica network-modifying effect of the OH species.
10.4.3 Molecular transport in chromia scales Provided that the temperature and gas velocity are not too high, the term kv in Equation (1.36) is small, and the early stages of chromia scale growth in O2/H2O gases are close to parabolic in their kinetics. Despite the unimportance of the volatilization process at this stage, the presence of H2O(g) nonetheless affects significantly the short-term diffusion-controlled oxidation rate. Tveten and Hultquist [67–69] examined the effect of alloy impurity hydrogen on the oxidation of chromium-base alloys in pure oxygen and water vapour. The adhesion of scales grown in pure oxygen was very poor. Scales grown in H2O(g) were much more adherent, and grew more quickly. Quadakkers et al. [70] reported the similar finding that scales formed on chromium-base alloys in Ar/H2/H2O are more adherent than those grown in air. Michalik et al. [75] also found that oxide scale adherence on pure chromium depends on the oxygen and water vapour partial pressures of the reaction gas. Leaving discussion of the variation of kp with pO2 and pH2 O in H2/H2O atmospheres for the subsequent Section, we consider first the reasons for the differences between reaction in wet and dry atmospheres. Observations of chromia scale growth on NiCr alloys are of use in analysing this issue. Isothermal oxidation of Ni-25Cr at 1,0001C leads to the short-term parabolic rate constant values shown in Figure 10.19. Steady-state values of kw are higher for this alloy in Ar-4% H2-7% H2O than in Ar-20% O2. The addition of yttrium to the alloy decreases the rate in Ar/O2, but slightly increases the rate in Ar/H2/H2O. Scales formed on both NiCr and NiCrY in Ar/H2/H2O are considerably thicker and exhibit better adherence to their substrates than those grown in Ar/O2. Part of the explanation for these effects lies in the different diffusion mechanisms. Two-stage oxidation experiments using Ar/16O2 (or Ar/H2/H16 2 O) followed by Ar/18O2 (or Ar/H2/H18 2 O) lead to the isotope distributions shown in Figure 10.20. Normalized plots are used for the scale grown in Ar/O2 to compensate for the partial spallation which occurs on cooling. The profiles after Ar/O2 exposure show the well-known tracer distribution found for scales growing by cation diffusion [72–74]. Thus the oxygen in the outer scale is nearly exclusively 18O. Its concentration is seen to be approximately constant in the outer region, and then decrease rapidly to a low level in the inner region. After two-stage oxidation in Ar/H2/H2O, a substantial part of the 18O is again present in the outer part of the scale, but no region of constant concentration is found. Instead, the concentration decreases continuously as a function of sputter time and shows a minor enrichment at the scale–alloy interface. This distribution indicates that scale growth proceeds by inward oxygen transport. The same conclusion was reached by Hultquist et al. [69] for pure chromium oxidized in H2O(g).
10.4. Scale Transport Properties
481
Kp(t) (mg2/cm4*h)
1
0.1
NiCr
0.01
NiCrY 0.001 0
10
20
30
40 Time (h)
50
60
70
80
70
80
(a)
Kp(t) (mg2/cm4*h)
1
0.1
NiCrY
NiCr
0.01
0.001 0
10
20
30
40 Time (h) (b)
50
60
Figure 10.19 Instantaneous parabolic rate constant for Ni-25Cr and Ni-25Cr-0.1Y at 1,0001C, (a) in Ar-20% O2, (b) in Ar-4% H2-7% H2O. Reprinted from [71] with permission from Elsevier.
The Cr2O3 scale grown in Ar/O2 develops pores and voids at and near the oxide–alloy interface. Michalik et al. [75] proposed that this was due to condensation of vacancies left by outwardly diffusing metal. In contrast, the chromia scale grown in Ar/H2/H2O is compact and closely adherent to the substrate alloy. As shown earlier, water vapour can eliminate or at least decrease oxide porosity by providing rapid gas phase transport of oxygen within the pore space. Furthermore, inward oxygen transport leads to new oxide formation at the scale–metal interface, thereby reducing the probability of void nucleation and subsequent scale detachment. The
482
Chapter 10 Effects of Water Vapour on Oxidation
1
0.8
Isotope Ratios
O16/Ototal 0.6
O18/Ototal
0.4
0.2
0 0
1000
2000
3000
4000
Sputtering Time (s) (a) 100
Ni
Concentration (at.%)
80 Ototal 60 O16 Cr
40
20
O18
0 0
5000
10000
15000
Sputtering Time (s) (b)
Figure 10.20 Oxygen isotope profiles measured by SNMS after oxidation at 1,0501C of Ni-25Cr (a) first stage 0.5 h in Ar 20%16 O2 , second stage 2 h in Ar 20%18 O2 , (b) first stage 0.5 h in Ar 4%H2 2%H2 16 O, second stage 2 h in Ar 4%H2 2%H2 18 O. Reprinted from [71] with permission from Elsevier.
10.4. Scale Transport Properties
483
inward oxygen transport revealed by isotope profiling experiments in the case of Ar/H2/H2O reaction accounts satisfactorily for the observed decrease in scale porosity and improved scale adhesion, if the diffusing species contains both oxygen and hydrogen, either hydroxyl ions [48] or H2O(ads). As was discussed in Section 4.2, chromia scales grown in dry gases are permeable to nitrogen, but impermeable when the gas contains water vapour. This led to the suggestion that water vapour interacted with scale grain boundaries, affecting their ability to transmit molecular species. As seen in Figure 10.21, the oxide grain structures developed on Ni-25Cr are quite different in the presence and absence of water vapour. The scale formed in Ar/O2 has large, rather columnar grains, whereas the oxide grown in Ar/H2/H2O is extremely fine-grained, with some increase in grain size towards the alloy side. The much finer grain size provides a greater contribution to mass transport by inward grain boundary diffusion, thereby accounting for the faster scaling rate observed in this gas (Figure 10.19). The remaining question concerns the way in which H2O (or H2) alters the grain size. One possibility is that the presence of H2O(ads) at the oxide grain boundaries hinders their movement and thus grain growth. This would explain the extremely fine oxide grains formed in Ar/H2/H2O. One might, however, also argue the converse. The stronger contribution of inward scale growth might not be the result of the finer grain size: rather, the finer grain size could result from the modified scale growth process induced by Ar/H2/H2O gas. In the case of scales mainly growing by cation diffusion, the oxide grains at the free oxide surface can easily form and grow in size without any constraints, whereas during scale growth at the scale–oxide interface, nucleation of new grains might occur more easily than growth of existing grains. The available results do not allow a distinction to be drawn between the two possibilities. Nonetheless, it is clear that the effect of water vapour during oxidation in Ar/H2/H2O environments is Cr2O3
(a) (b)
NiO
Alloy Alloy
Cr2O3 Ni-Coating
Void
Figure 10.21 TEM bright field views of scale cross-sections developed on Ni-25Cr in 2.5 h at 1,0501C (a) in Ar/O2, (b) in Ar/H2/H2O. Reprinted from [71] with permission from Elsevier.
484
Chapter 10 Effects of Water Vapour on Oxidation
twofold: water molecules incorporated into the scale provide accelerated mass transport within voids whilst simultaneously promoting the formation of an inwardly growing, fine-grained oxide scale. The complex effects of yttrium additions (Figure 10.19) can now be understood. In the dry gas, yttrium addition has the expected effect of reducing the rate. As discussed in Section 7.5, yttrium and other reactive element metals segregate to oxide grain boundaries modifying their properties. Grain boundary cation diffusion is largely suppressed, and a slower rate of scale growth is supported by inward oxygen transport. However, scales formed on Ni-25Cr in Ar/H2/H2O grow mainly by inward diffusion, and the addition of yttrium cannot decrease the rate by lowering cation diffusion. The small increase in kw observed (Figure 19) for NiCrY is attributed to the internal oxidation of yttrium. It is seen that water vapour and alloy yttrium have qualitatively similar effects on chromia scale growth. In addition to the mass transport changes discussed above, both lead to oxide grain refinement ([76–78] and Figure 10.21). Furthermore, in both cases, grain size increases in the growth direction, i.e. towards the scale–metal interface. Water vapour is apparently a more effective grain refiner, leading to a higher value of Deff (Section 3.9) and somewhat more rapid scaling. The changes in mass transport mechanism brought about by both water vapour and alloy yttrium have the same result of improving scale adherence. Despite these benefits, water vapour is ultimately destructive in its promotion of chromium volatilization, which degrades the scale in the long term. The results reviewed here have led to the conclusion that both oxygen and hydrogen are transported inwards though growing scales of both chromium and iron-rich oxides. Direct evidence for the passage of hydrogen is provided by the experiment shown in Figure 10.16 for the scale on Fe-5Cr. The accumulation of hydrogen in an Fe-10Cr steel during oxidation in steam has been demonstrated by Nakai et al. [79], and in the chromia scale on a 430 stainless steel (Fe-16Cr0.5Mn) by Yamauchi et al. [80], using thermal desorption spectroscopy to analyse for hydrogen. Although the evidence for simultaneous hydrogen and oxygen transport is clear, it does not reveal the chemical form of the diffusing entity: H2O(ads), or OH ions. The possibility of hydrogen transport via ionic species is now considered.
10.4.4 Ionic transport Interactions between water vapour and ionic point defects have been studied in a number of oxides [1, 2], but attention is focused here on chromia scales. Not only are they important, but a significant amount of data is available. Unfortunately, because Cr2O3 is so closely stoichiometric, and its intrinsic defect concentrations so low, the defect behaviour is poorly defined. It seems (Section 3.9) that both metal excess and metal deficit behaviour are possible in appropriate oxygen potential ranges.
10.4. Scale Transport Properties
485
Consider first the principal point defect formation reactions involving cation vacancy and interstitial formation in Cr2O3 ¼ OXO þ 23V 000 Cr þ 2h
1 2O2 ðgÞ
::: 2CrXCr þ 3OXO ¼ 2C ri þ 6e0 þ 32O2 ðgÞ
(10.42) (10.43)
In the case of vacancy formation, the charge balance ½h ¼ 3½V 000 Cr
(10.44)
combined with the equilibrium expression for Equation (10.42) leads to 3=8 K42 3=16 ½V 000 ¼ pO2 (10.45) Cr 9 Wagner’s theory of diffusion control by lattice defects (Section 3.6) then leads to the scaling constant 3=16 3=16 kp ¼ const: p00O2 p0O2 (10.46) where p00O2 and p0O2 are the oxygen partial pressures at the scale–gas and scale– alloy interfaces, respectively. If, instead, the predominant defects are interstitials, the charge balance ::: ½e0 ¼ ½3C ri (10.47) leads to
2 kp ¼ const:4
1 p0O2
!3=16
!3=16 3 1 5 p00O2
(10.48)
Since p00O2 is usually much greater than p0O2 , both Equations (10.46) and (10.48) are easily simplified. If vacancies predominate, the rate is predicted to increase with 3=16 pO2 . If interstitials predominate, the rate is almost independent of pO2 . Comparisons [51, 71] of experimental data with these predictions show that they fail in both O2/H2O and H2/H2O atmospheres. However, Norby et al. [68, 81, 82] followed early work on other oxides (e.g. [1, 83–86]) in suggesting that hydrogen can be injected into the lattice as a proton: 1 2H2 OðgÞ
¼ Hi þ 14O2 ðgÞ þ e0
(10.49a)
or, equivalently, 1 2H2 ðgÞ
þ h ¼ Hi
(10.49b)
Combination of equilibrium expressions for Equations (10.42) and (10.49b) with the charge balance expression 3½V000 Cr ¼ ½h þ ½Hi
(10.50)
leads to the prediction that kp increases with pH2 at constant oxygen potential, and decreases with pH2 at constant pH2 O . However, the latter prediction is at
486
Chapter 10 Effects of Water Vapour on Oxidation
Table 10.5
Oxidation rate constants for pure Cr at 1,0001C [51]
Inlet gas
pO2 ðatmÞ
pH2 O ðatmÞ
kw ðg2 cm4 s2 Þ
Ar-4% Ar-4% Ar-4% Ar-8% Ar-8% Ar-4% Ar-4%
7.0 1016 2.8 1015 1.1 1014 2.8 1015 7.0 1016 0.04 0.04
0.02 0.04 0.08 0.08 0.04 0.04 0.08
2.0 1011 2.2 1011 7.0 1011 8.6 1011 6.7 1011 1.9 1011 2.0 1011
H2-2% H2O H2-4% H2O H2-8% H2O H2-8% H2O H2-4% H2O O2-4% H2O O2-8% H2O
variance with the results for pure chromium in H2/H2O atmospheres (Table 10.5) and this model cannot be used. Nonetheless, increasing pH2 O (and pH2 ), whilst maintaining pO2 constant, does increase the scaling rate (Table 10.5). If the hydrogen effect is modelled as a hydroxyl species formation þ OXO þ h ¼ OHO
(10.51)
3½V000 Cr ¼ ½OHO þ ½h
(10.52)
1 2H2
together with a charge balance
then the equilibrium expression for vacancy formation leads to 3=16
1=2
3=4 ½V000 Cr ¼ k1 pO2 ð1 þ k2 pH2 Þ
(10.53)
where k1 , k2 are constants, and the H2O(g) dissociation equilibrium has been used. Despite some successes, this model fails to account for the observed (Table 10.5) increase in rate with increasing pH2 at fixed pH2 O levels. Similarly, it can be shown [51] that a model based on hydrogen or water molecule penetration of an n-type scale leading to negative hydride formation 1 2H2 ðgÞ
þ e0 ¼ H0i
(10.54) ::: leads to an expression for ½C ri which correctly predicts the observed increase in rate with pH2 at fixed pH2 O . However, it fails to predict the observed rate dependence on pH2 O at fixed pH2 . It must be concluded that no single defect model explains the observed range of gas composition effects on chromium oxidation. However, a linear combina::: tion of mass transfer contributions by C ri and V 000 Cr together with a hydrogen dissolution equilibrium H2 þ OXO ¼ OHO þ H0i
(10.55)
does describe the gas compositional dependencies observed at low oxygen activities. The model contains many undetermined constants, and lacks quantitative value. However, it does show that an ionic transport model for chromia can only succeed if scale uptake of H2 or H2O is incorporated.
10.4. Scale Transport Properties
487
10.4.5 Relative importance of different water vapour effects on chromia scaling There is no single publication (or set of publications from the same laboratory) describing all the water vapour effects: volatilization, chromia scale microstructural change, alterations to the relative contributions of oxygen and metal diffusion and hydrogen doping. This makes for difficulty in assessing the relative magnitude of the different effects, because kinetic data for chromium oxidation vary so widely from one measurement to another (Figure 3.20). This variability is understandable. Because Cr2O3 has such a low intrinsic defect level, grain boundary diffusion predominates, and is therefore sensitive to oxide scale microstructure and the presence of dopants and boundary segregants. Minor variations in metal and gas purity, which lead to different oxide microstructures and dopant levels, are therefore of critical importance to the observed oxidation rates. Comparisons should therefore be restricted to results obtained with the same material and surface preparation. Several measurements of parabolic scaling rates for chromia growth in dry oxygen at 1,0001C shown in Table 10.6 illustrate the variability. It is expected, however, that volatilization from the scale surface would be largely independent of scale microstructure and doping level. Vaporization losses calculated from Equation (10.10) for CrO2(OH)2 formation in air-10% H2O(g) flowing at 2 cm s1 are shown in the Table as fractions of the scale thicknesses. It is seen that volatilization can be neglected for short-term laboratory experiments, even in the case of the remarkably slow scaling rates measured by Caplan and Cohen [52]. However, the changes made by water vapour to the microstructure and transport properties of growing chromia scales are important, even in the short term. The scaling rate for chromia growth on Ni-25Cr is five times higher in Ar/H2/H2O than in Ar/O2 at 1,0001C [71]. Pure chromium oxidizes 2–3 times faster in Ar/H2/H2O than in Ar-20% O2 [75]. This effect is clearly much more important than volatilization in these timeframes. The importance of hydrogen doping is difficult to assess. A large amount of experimental data has been collected for reaction in air, but the importance or otherwise of the low levels of H2O(g) has not been established. There is a need for comparative rate measurements for chromia growth in dry oxygen and dilute Table 10.6 Alloy
Cr Cr Cr Ni-25Cr a
Diffusion-controlled chromia scale growth and evaporationa at 1,0001C Gas
O2 Ar-1% O2 Ar-20% O2 Ar-20% O2
In air-10% H2O flowing at 2 cm s1.
kp (cm2 s1)
14
4 10 7 1012 5 1012 7 1013
Ref.
[52] [51] [75] [71]
Vaporization loss as fraction of diffusion term 24 h
100 h
0.1 0.007 0.008 0.02
0.15 0.01 0.02 0.04
488
Chapter 10 Effects of Water Vapour on Oxidation
mixtures of water vapour in oxygen. As seen in Table 10.5, doubling the value of pH2 O in Ar/O2/H2O gas mixtures produces only a 5% increase in rate at 1,0001C. However, any dopant effect might be near saturation at these levels, and the possibility remains open of more dramatic effects when water vapour is first added to an otherwise dry system.
10.5. WATER VAPOUR EFFECTS ON ALUMINA GROWTH Water vapour has been shown by Norby and Kofstad [87, 88] to affect the electrical conductivity of Al2O3 containing magnesium impurities. However, detailed observations of gas compositional effects on alumina scaling are sparse. In the case of alloys which are marginal with respect to selective alumina formation, water vapour does make a difference. Boggs [89] compared the oxidation of binary Fe-Al alloys in O2 and O2/H2O at 450–9001C. Scale growth was more rapid in the wet gas, because iron-rich oxide formation was favoured. Hayashi and Narita [90] compared the oxidation of Fe-5Al in N2-12.2H2O, O2-12.2H2O and N2-0.9O2-12.2H2O at 8001C. Internal aluminium-rich oxide precipitated, and multiple external scale layers developed in all gases. However, reaction was very slow in O2-12.2H2O as a result of FeAl2O4 developing as a single-phase layer. In N2-12.2H2O faster, but parabolic kinetics accompanied spinel formation as part of a two-phase FeAl2O4+FeO layer. In N2-0.9O2-12.2H2O much faster scale growth reflected the development of a porous iron-rich oxide over an FeAl2O4+FeO layer. Interestingly, changing the gas part way through an experiment brought about an instantaneous change in rate, indicating that the interior scale structure was accessible to the newly introduced gas. It seems likely that these results can be explained in part using a competitive adsorption model, as constructed for Fe-Cr in Section 10.4. Thus a high value of pO2 is sufficient to prevent scale degradation by H2O(g), but a small value is not. The new finding is that water vapour in the absence of O2 produces a slower oxidation rate than H2O(g) plus dilute oxygen. More information is required before these results can be fully understood. In the case of the alumina former, Kanthal A1 (Fe-21.5Cr-5.6Al), Buscail et al. [50] compared reactions with dry oxygen, O2-15H2O and O2-32H2O at 1,0001C. The presence of water vapour altered the rate at which transient alumina was converted to a-Al2O3, but had negligible effect on the steady-state rate of a-Al2O3 scale growth. Maris-Sada et al. [91] showed that the addition of water vapour (0.1–0.5 atm) to air accelerates the growth of the transient oxide mixture formed on PWA 1484 (Ni-5.6Al-6Cr-8.7Ta-10Co-2Mo-6W-3Re, Hf) at 1,1001C. Similar effects were reported for the model alloy Ni-8Cr-6Al. These changes were attributed to more rapid growth of NiO as a result of hydrogen doping H2 Oðor H2 þ 12O2 Þ ¼ OXO þ 2Hi þ V 00Ni
(10.56)
based on the earlier suggestion by Galerie et al. [48]. As is discussed in Chapter 11, water vapour can have a much more destructive effect on alumina scales by promoting their spallation.
10.6. Void Development in Growing Scales
489
10.6. VOID DEVELOPMENT IN GROWING SCALES It is clear that the presence of water vapour promotes the development of voids within iron oxide scales and the iron-rich oxides formed on dilute Fe-Cr and Fe-Al alloys. Analysis of mass transport mechanisms (Section 10.4) showed that H2O or H2 can reach these voids, and that gas phase mass transfer within them is rapid compared to overall scaling rates. The remaining question is as to the reason these voids develop so much more readily when water vapour is present. Void nucleation is generally thought to be due to vacancy condensation, either at the scale–metal interface [75] or within the scale [3]. Of course, such an event is impossible if the usual assumption of Wagner’s model, that the flux is constant or divergence-free, applies. Recognizing that pore formation corresponds to a divergence in the flux, Maruyama et al. [92, 93] have calculated elemental fluxes in the magnetite scales grown on pure iron in Ar/H2/H2O mixtures at 5501C. Applying the continuity condition to the magnetite concentration, CFe3 O4 , in the scale, they obtained @CFe3 O4 1 @J Fe 1 @J O ¼ ¼ (10.57) 3 @x 4 @x @t showing explicitly that a large oxygen diffusion contribution is required for a pore to form. The effective oxygen diffusion coefficient necessary to meet this requirement is found to exceed the measured [94, 95] value for Do in Fe3O4 by 4–5 orders of magnitude (Figure 10.22). However, if oxygen transport is effected by grain boundary migration and the operation of the H2/H2O couple within the voids (Figure 10.13), the discrepancy is accounted for.
Figure 10.22 Effective diffusion coefficients of iron and oxygen deduced from scale growth and pore development, compared with diffusion measurements [93]. Published with permission from Trans Tech Publications Ltd.
490
Chapter 10 Effects of Water Vapour on Oxidation
For a void to form within an oxide, both metal and oxygen must be transported. In the case of both FeO and Fe3O4 grown in dry atmospheres, oxygen anions lack mobility, and diffusion supported void growth is impossible. When hydrogen or water vapour can access the scale interior, however, oxygen mobility is effectively enhanced and voids grow. Direct measurement of the amount of gas contained within an iron oxide scale has been attempted by Anghel et al. [96]. Iron was oxidized at 9001C, cooled and exposed to air at room temperature for 100 h. The sample was then outgassed in a high vacuum chamber to which was attached a mass spectrometer. Analysis of the gas released from the scale showed the pH2 O =pN2 ratio to be 9:1, confirming the preferential uptake of water vapour. The total amount of gas released from the oxide was estimated as 104 mol cm3. However, the technique suffers from the disadvantage that damage to the oxide can be induced during cooling from reaction temperature. Pore development in Cr2O3 scales is qualitatively similar. As seen in Figure 3.1, scales grown in O2 show very little porosity, but scales grown in Ar/H2O and in H2/H2O develop pores (Figure 10.23). Pore volume fractions observed in Cr2O3 are much smaller than those seen in iron-rich oxide scales (Figure 10.1b). Although the presence of water vapour increases the extent of inward oxygen transport in both sorts of scale, fluxes in chromia are very much smaller than in the iron oxides. Any divergences in the chromia fluxes are therefore also smaller, and the rate of pore development is seen from Equation (10.57) to be consequently slower. Apparently different porosities formed in Ar/H2O and N2/H2/H2O are interesting. However, the experiments are not directly comparable because of the different oxygen activities (and chromium defect concentrations) and the observed [97] interactions between N2 and H2O transport through Cr2O3. Little is known about pore development in alumina scales grown under isothermal conditions. The formation of cavities at the scale–alloy interface during oxidation of b-NiAl (Section 5.8) is thought to be governed by the diffusion properties of the alloy and its impurity content. Information on any effects water vapour might have on this process is lacking.
10.7. UNDERSTANDING AND CONTROLLING WATER VAPOUR EFFECTS At the beginning of this Chapter we noted that the problem of water vapour accelerated corrosion and its mysterious nature had been pointed out decades ago. It is therefore reasonable to ask what progress has been made in developing a useful understanding of the processes involved. In brief, our ability to define acceptable limits to exposure conditions for particular oxides has improved greatly, and our knowledge of oxide–water vapour interaction mechanisms has expanded. However, our description of the effects is still largely qualitative, and provides guidelines rather than quantitative tools for alloy design.
10.7. Understanding and Controlling Water Vapour Effects
491
1 µm (a)
5 µm (b)
Figure 10.23 Chromia scales (a) grown in Ar/H2O at 9001C (courtesy of A. Galerie), (b) in N2/H2/H2O at 9001C.
Water vapour has a unique ability to accelerate volatilization of the important oxides Cr2O3 and SiO2, thereby shortening the lifetimes of materials which rely on protective scales of these oxides. Fortunately, good quality thermodynamic data have become available for these reactions. As seen in Section 10.2, this data can be combined with gaseous mass transfer calculations to provide accurate predictions of oxide loss rates as a function of ambient conditions. It is therefore possible to define regimes of temperature, total pressure, water vapour partial pressure and gas flow rate appropriate to desired loss rate limits. In principle, these rates can be combined with a diffusion calculation to predict depletion rates within an alloy component, and thereby arrive at lifetime estimates. Thus the present state of knowledge with regard to water vapour driven volatilization is satisfactory. Our understanding of water vapour effects involved in the development of porosity in iron-rich oxide scales has improved in that the requirement of
492
Chapter 10 Effects of Water Vapour on Oxidation
divergence in both metal and oxygen fluxes in the scale has been recognized. This requirement can only be met when the magnitude of the oxygen flux itself is much larger than can be supplied by relatively immobile lattice oxygen anions. As shown by isotope and other marker experiments, the required oxygen flux is generated when sufficient water vapour is present in the gas. The oxygen transport process involves simultaneous inwards transport of hydrogen, thereby explaining also how H2O(g) can be formed (and provide a gas phase mass transport mechanism) within closed voids inside the scale. It is clear that this undesirable outcome can be prevented only by excluding water vapour and its derivative species from the scale interior. A model of competitive oxygen and water vapour adsorption appears to be in qualitative agreement with the observed behaviour of iron-rich scales. It predicts that maintaining a sufficiently high pO2 =pH2 O ratio will prevent water vapour uptake. However, more information on just how the critical ratio depends on oxide chemistry, temperature and time is required. Chromia scales are more resistant to pore development in wet gases, as can be understood from the low fluxes and consequently low flux divergences in this oxide. The relatively small scale growth acceleration induced by water vapour does not support extensive pore growth. In this sense, alloying with chromium provides the same benefit in resisting both water vapour corrosion and dry oxidation. However, chromia is not completely resistant to water vapour induced pore development. The effects of water vapour on chromia scales are very similar to those of a reactive element metal (Section 7.5). Both segregate to oxide grain boundaries, where they have the effects of increasing oxygen transport relative to that of chromium and of refining the oxide grain structure. Both appear to improve scale–alloy adhesion. A further similarity exists at this stage: detailed information at a lattice species level is lacking for both water vapour and reactive element effects. It is to be noted that this has not prevented the exploitation of reactive element effects in alloy design. Much less information is available for the effects of water vapour on alumina scale performance, where the situation is complicated by interactions between water vapour and transient alumina phases. Finally, we have seen that water vapour often promotes the development of pores and voids in oxide scales. These defects obviously affect the mechanical integrity of the scale–alloy system, making scale exfoliation or spallation more likely. This problem is considered further in Chapter 11.
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CHAPT ER
11 Cyclic Oxidation
Contents
11.1. 11.2. 11.3. 11.4. 11.5.
Introduction Alloy Depletion and Scale Rehealing Spallation Models Combination of Spalling and Depletion Models Effects of Experimental Variables 11.5.1 Temperature cycle parameters 11.5.2 Continuous thermogravimetric analysis 11.5.3 Compositions of alloys and environment 11.6. Describing and Predicting Cyclic Oxidation References
497 502 506 514 517 517 520 521 527 530
11.1. INTRODUCTION Alloys used at high temperatures are subjected to duty cycles which vary widely among applications. These range from the rather short operating periods of propulsion engines through the weeks, months or even years of chemical process or power generation plant campaigns. In all cases, however, start up and shut down involve more-or-less rapid temperature changes, inducing stresses in the oxide scales which protect the alloys. If no stress relief mechanism is available, the thermally induced strain energy increases with scale thickness. Using the notation of Section 2.10, the resulting stored elastic energy per unit area of scale–alloy interface, W n , is written as W n ¼ ð1 np ÞEOX ðDT DaÞ2 X
(11.1)
assuming the oxide to be in the linear-elastic regime, and present as a thin layer on a much thicker substrate. It is assumed here that the scale is too thin to sustain a temperature gradient, and the stored energy represents thermal mismatch between oxide and metal, not thermal shock to the oxide. If the oxide thickens sufficiently, the strain energy stored in the oxide becomes greater than that required for interface fracture, and the scale, or part of it, spalls [1–4]. The critical stress value which will cause scale spallation depends on the details of the failure mechanism [5, 6], and will not be discussed here. Our concern is with the consequences of scale failure and the rate at which breakdown in corrosion protection is arrived at.
497
498
Chapter 11 Cyclic Oxidation
A common way of carrying out cyclic oxidation experiments is shown schematically in Figure 11.1a. Multiple alloy samples are inserted into a furnace and withdrawn again at pre-determined intervals using an electric motor drive and automatic timing device. Heating and cooling are quite rapid (Figure 11.1b), and relatively short cycles can be used. From time to time the experiment is
9
(a)
1000 900
Cycle 1
Cycle 2
Temperature (οC)
800 700 600 Cooling
Heating
500 400 300 200 100 0 0
(b)
10
20
30
40 50 60 Time (minutes)
70
80
90
100
Figure 11.1 (a) Experimental apparatus for cyclic oxidation and (b) observed temperature– time trajectories at specimen surfaces.
11.1. Introduction
499
Figure 11.2 Cyclic oxidation weight change data for b-Ni–50Al in dry air at 1,2001C.
interrupted and the samples withdrawn and weighed. Examples of weight change data accumulated in this way are shown in Figure 11.2. Since the measured weight changes are the net result of oxygen weight uptake due to scaling plus any internal oxidation, and weight losses due to metal oxide spallation, interpretation of results like these is not simple. However, the technique is economical and has become popular as a way of generating comparative alloy performance data under more-or-less realistic exposure conditions. One way of overcoming the interpretation problem is to capture spalled oxide and weigh it together with the sample. The resulting ‘‘gross mass gain’’ is shown plotted for some FeCrAl alloys in Figure 11.3, where it is compared with ‘‘net mass gains’’, i.e. the changes in weight of the reacted samples after loss of spalled oxide. Whilst the onset of spallation is clear in the case of PM2000 (alloy compositions in Table 5.1), it is obscured in the case of APM and JA13 by the continuing positive net mass gains. Separate measurement of spalled oxide makes the position clear, but the experiment presents practical difficulties. Spalled oxide is collected by holding reacting alloys inside inert, refractory crucibles. Because spallation can cause the violent ejection of oxide particles, the crucibles need to be fitted with lids. Such an arrangement impedes mass transfer between the specimen and gas flowing past the crucible, and is therefore not suited to the use of mixed gases. An alternative method for observing spallation directly is the use of continuous thermogravimetric analysis (CTGA). In the CTGA experiment, a microbalance is used to record weight changes during the entire process, cycle after cycle. Thus oxidation kinetics are observed directly during the high-temperature periods and abrupt weight losses corresponding to scale spallation are, at least in principle, observable.
500
Chapter 11 Cyclic Oxidation
(a)
(b)
Figure 11.3 Net mass gain and spalled oxide mass for FeCrAl alloys oxidized in air at 1,3001C [7]. Published with permission from IOM Communications.
The technique was reported by Pivin et al. [8], Christ et al. [9, 10] and Vangeli [11]. An example of the resulting data is shown in Figure 11.4. Because only one sample can be attached to the microbalance, the instrument is committed for hundreds or even thousands of hours, and the technique is expensive. Monceau et al. [12, 13] have described modifications to the technique designed to improve productivity by fitting multiple microbalances to a single, temperature-cycling apparatus.
11.1. Introduction
501
Figure 11.4 CTGA results obtained during (a) isothermal and (b) cyclic oxidation of 353 MA in air [11]. With permission from IOM Communications Ltd.
502
Chapter 11 Cyclic Oxidation
Partial or complete spallation means that the average scale thickness is decreased. Because scale growth is usually diffusion controlled, dðDW=AÞ k¯ w ¼ (11.2) dt DW=A and the rate of weight uptake, k¯ w averaged over multiple scale segments of different thickness, is consequently greater. The effect is illustrated in Figure 11.4, where the oxidation rate during high-temperature cycles is seen to be higher than rates observed during isothermal exposure for the same total time. Thus the value of k¯ w cannot be related to the isothermal kw value without knowledge of the spallation process. The practical result is that the alloy is consumed more rapidly. Cyclic oxidation testing is intended to provide information on alloy service lifetimes. The definition of lifetime, however, will depend on alloy functionality. If spallation leads to consequential and irreparable damage such as the loss of an adhering thermal barrier coating (Figure 1.6), then lifetime can be defined as the time to reach a certain fraction of surface area affected. In other cases, lifetime is usually defined as the time at which the alloy loses the capacity to ‘‘reheal’’ by reforming its protective oxide scale. Subsequent alloy degradation is rapid as a result of either fast oxidation of the alloy-based metal or attack on the unprotected alloy by secondary corrodents. The processes leading to the onset of this failure form the focus of the present chapter. We consider first the diffusion-controlled depletion of protective scaleforming metal within the alloy, and the way in which this is accelerated by spallation and rehealing. To make use of this analysis, it is then necessary to describe the kinetics of scale growth during repeated spallation. Models which have been developed for this purpose are then combined with the subsurface depletion description to arrive at lifetime predictions. Finally, the effects of experimental variables, in particular cycle duration and gas composition, on the results of cyclic oxidation exposures are reviewed. Attention is focused on alumina- and chromia-forming alloys.
11.2. ALLOY DEPLETION AND SCALE REHEALING The selective oxidation of chromium or aluminium removes metal from the alloy subsurface region. The resulting concentration profile for the reacting metal (B) is obtained by solving the diffusion equation (Fick’s Second Law) for that alloy component. In the steady state, where the scale–alloy interfacial concentration is time independent, Wagner’s analysis (Section 5.4) leads to the general solution given by N ðoÞ B N B;i ~ 1=2 ¼ Fðkc =2DÞ 1 N B;i
(5.25)
with 1
FðuÞ ¼ p2 uð1 erf uÞ exp ðu2 Þ
(5.26)
503
11.2. Alloy Depletion and Scale Rehealing
If the interface recession rate, kc as defined in Equation (1.28), is slow, as is the case for slow-growing chromia and alumina, the interfacial concentration (mole fraction) of reacting element B, N B;i , becomes N B;i ¼
N ðoÞ B f 1f
(11.3)
~ 1=2 with D ~ the where N ðoÞ B is the original alloy concentration of B, and f ¼ ðpkc =2DÞ alloy interdiffusion coefficient. Whittle [14] analyzed the conditions under which an alloy could reform its protective scale after a spallation event in which the entire scale was lost. This treatment ignored transient oxidation, applying Equation (11.3) to the first oxidation cycle, and enquired into the further depletion of B on the assumption that scale growth followed the same parabolic kinetics as in the first cycle. The model is shown schematically in Figure 11.5. A qualitative understanding of the situation can be arrived at from a consideration of the mass balance for B at the scale–alloy interface. After spallation at t ¼ tn , scale growth is assumed to recommence at the same rapid rate as at the beginning of the first cycle, causing the maximum rate of B withdrawal from the alloy. However, the chemical potential gradient of B at t ¼ tn is capable of delivering that element to the
(a)
(b) X (arbitary units)
t1 NB
t2
x
1 t/t*
(c)
2
(d)
t1 NB
NB,i
t2
x
1 t/t*
2
Figure 11.5 Whittle’s [14] cyclic oxidation model. (a) Depletion profiles during steady-state isothermal oxidation, t2 4t1 , (b) successive scale growth cycles for 100% spallation at t ¼ tn , (c) depletion profiles, t1 otn ot2 and (d) recovery of interfacial concentration after rehealing. With kind permission from Springer Science and Business Media.
504
Chapter 11 Cyclic Oxidation
interface only at the slow rate in effect at the end of the preceding cycle. The two possibilities are that BOn fails to reform, or that N B;i is further reduced to the point where the gradient in B is increased sufficiently to drive the required flux from the alloy to the interface. In the latter case, scale growth slows with time and the flux of B from the alloy allows the value of N B;i to increase. Eventually, if the cycle is long enough, steady-state conditions are restored. A quantitative description requires solution of Fick’s Second Law using as an initial condition the profile in N B;i at t ¼ tn , and a new formulation of the interfacial mass balance " #1=2 kc @N B (11.4) ¼D ð1 N B;i ðtÞÞ @x 2ðt tn Þ1=2 which replaces Equation (5.24). Because scale growth is assumed parabolic with ðt tn Þ, it is not parabolic with t, and a time-dependent interfacial concentration results. No exact analytical solution is possible. Instead, an approximate solution was found and verified by numerical analysis [15]. This led to an expression for the time dependence of N B;i for t4tn " 1=2 # f f ðoÞ ðoÞ 2 1 t NB f ð1 N B Þ sin N B;i ¼ (11.5) 1f 1f p tn The form of this result is illustrated in Figure 11.5d. The interfacial concentration is seen to drop instantaneously to a lower value, and then slowly recover. Depletion profiles before and after this spallation event are compared in Figure 11.5c. As time passes, N B;i increases until it reaches the steady-state value N SB;i . The depletion depth is then greater, as would also result from isothermal oxidation for a sufficiently long time (Figure 11.5a). The criterion used for protective scale formation was Wagner’s condition that sufficient flux of B is available to maintain exclusive BOn oxide scale growth. The minimum initial N ðoÞ B value, N B;min , is calculated for the first cycle from Equation (11.3) by setting N B;i o N IB;min ¼ f
(11.6)
where the superscript I indicates the value required to sustain scale growth during the first cycle. At any lower initial concentration, the interface concentration necessary to produce a sufficient flux of B in the alloy to sustain scale growth is less than zero, and exclusive BOn growth therefore ceases. Applying the same criterion after the first spallation event leads to the requirement that N B;min be large enough to keep N B;i 4o at t ¼ tn . From Equation (11.5) we find f ð1 N ðoÞ ð1 fÞ N B;i ðtn Þ ¼ N ðoÞ (11.7) B f B Þ 1f and it follows that the condition for N B;i ðtn Þ4o is 2 II N ðoÞ B N B;min ¼ 1 ð1 fÞ
(11.8)
where the superscript II signifies the value necessary to sustain exclusive B oxidation in a second cycle. Whittle extended the analysis to a third cycle by
11.2. Alloy Depletion and Scale Rehealing
505
using the criterion N B;i ðtn Þ f. Thus it was proposed that the interfacial concentration after the first spallation and rehealing event was not only greater than zero, as required to grow the second scale, but needed to be sufficient to grow a third scale when required. Application of this criterion to Equation (11.5) yields f f ðoÞ ðoÞ NB f ð1 N B Þ f (11.9) 1f 1f and hence 3 N III B;min 41 ð1 fÞ
(11.10)
Whittle also suggested that Equation (11.10) would provide an estimate of the required N B;min to reheal after further cycling. However, as pointed out by Nesbitt [16], this requires significant recovery in the value of N B;i between cycles, and this would not be available for regular cycles of period tn . Equation (11.5) predicts that N B;i recovers to approximately 50% of its former value in the time from tn to 2tn . Wahl [17] adopted a different approach in order to extend the analysis to greater numbers of cycles, assuming no recovery in N B;i at all. As a result, the value of the interfacial concentration decreases in a stepwise fashion with the decrease after each spallation event given by N B;iðbeforeÞ N B;iðafterÞ ¼ ð1 N B;iðafterÞ Þf
(11.11)
For an alloy to survive for n cycles, it needs a value of N B;iðafterÞ f for cycle ðn 1Þ. Using Equation (11.11) to count back through all n steps it is found that the required starting concentration N N B;min is given by n NN B;min ¼ 1 ð1 fÞ
(11.12)
Thus agreement was achieved with Whittle’s calculations for n ¼ 2 and 3. However, the assumed lack of recovery in interfacial concentration limits the ~ values. For applicability of the model to fast growing scales on alloys with low D slow-growing scales at high temperatures, the predicted maximum number of cycles an alloy can withstand is unrealistically small. Nesbitt [16] proposed a combination of the Whittle and Wahl models. As shown by Whittle’s Equation (11.5), the recovery in each regular cycle amounts to 50% of the value at the end of the previous cycle. Assuming that the decrease in N B;i immediately after each spallation is f, then the net decrease for each full cycle is f=2. Applying this to Wahl’s Equation (11.12) then yields the result 1f n f (11.13) ¼ 1 þ NN B;min 2 2 Unrealistically short lifetimes are still predicted for slow-growing scales. Despite their lack of success in predicting alloy lifetimes, these depletion models provide useful insight into the diffusion-supported depletion and recovery processes taking place beneath an alloy surface.
506
Chapter 11 Cyclic Oxidation
A11
O11
S11 A12
A22
O12
S11
S12
S22
A13
A23 33 A33
A33 O13 S13
S12 S33
S11 S23
S22 S33
Figure 11.6 Schematic representation of Smialek’s spalling model [18]. Dashed line shows original alloy surface. Subsequent alloy–scale interface represented as flat for simplicity.
The main reason why all of these models fail is because of their simplistic, and unduly pessimistic, assumption that all of the scale spalls at every cycle, and the alloy therefore needs to regrow a complete new scale. This amounts to a rather rapid average linear rate constant for alloy consumption, and is quite unrepresentative of practical alloys. As seen in Figure 5.24, spallation from even a susceptible material like undoped b-NiAl is incomplete. To deal with this reality, it is necessary to devise better spallation models.
11.3. SPALLATION MODELS One purpose of cyclic oxidation testing is to collect comparative alloy performance data relatively quickly, and use it to predict lifetimes which can be very lengthy under service conditions. To extrapolate from the accelerated laboratory test to operating performance, one needs a way of relating spallation and rehealing behaviour to experimental conditions. The spallation models attempt to provide a basis for the necessary relationships. Smialek [18] proposed a cyclic stepwise partial spallation model to account for the cyclic oxidation behaviour of undoped b-Ni–42Al (at.%) at 1,1001C. The basic assumptions are that spallation occurs only at the oxide–alloy interface, that a constant area fraction of all oxide segments still present spall during each cooling cycle, and that oxidation kinetics are parabolic. A schematic view of the reaction cross-section is shown in Figure 11.6, where the subscripts denote the
11.3. Spallation Models
507
following: m is the cycle number at which the oxide segment commenced growth, j the cycle number at which it spalled and n the total number of cycles so far. The surface area fractions of intact oxide are Amn , containing oxygen weights of Xmn per unit area. These contribute Omn ¼ Xmn Amn mass of oxygen per unit sample area, so that the total oxygen uptake on a sample after n cycles is n Wo X ¼ Omn (11.14) A m¼1 Shaded portions in the diagram represent parts of oxide which have spalled, and where consequently metal has been lost. The metal loss corresponding to each lost metal oxide segment is denoted Pj by Smj. The total loss per unit sample area sustained in cycle j is accordingly m¼1 Smj. The total loss accumulated by the nth cycle is therefore j
n X WM X ¼ Smj A j¼1 m¼1
(11.15)
The metal losses are related to the spalled oxide losses via Smj ¼ 1:125 Xmj Amj
(11.16)
where 1.125 is the ratio of metal to oxygen masses in Al2 O3 , and Xmj represents the mass of oxygen per unit area in spalled segments making up fractional areas Amj . The spallation model in Figure 11.6 represents a situation where the same fraction of the metal surface, ks , loses its oxide by spallation of each cycle. The remaining oxide (of varying thicknesses) covers a sample surface area fraction of (1 ks ). The fraction ks is termed the spallation constant or fraction. Different fractions of remnant oxide have differing histories. A1n ¼ ð1 ks Þn
m¼1
nðm1Þ
Amn ¼ ð1 ks Þ
ks
m2
ð11:17Þ
The thicknesses of these regions are determined by their existence time Dtðn m þ 1Þ, where D t is the duration of each cycle. Thus X2mn ¼ 2kw Dtðn m þ 1Þ and a combination of Equations (11.14), (11.17) and (11.18) leads to " # n X Wo 1=2 n 1=2 1m ¼ ð2kw DtÞ ð1 ks Þ 1 þ ks ðn m þ 1Þ ð1 ks Þ A m¼2 A similar accounting yields an estimate of the metal loss n pffi X WM ¼ 1:125 ð2kw DtÞ1=2 ks ið1 þ ðn iÞks Þð1 ks Þi1 A i¼1
(11.18)
(11.19)
(11.20)
and the net weight uptake is then DW W O W M ¼ A A A
(11.21)
508
ΔW/A
Chapter 11 Cyclic Oxidation
nmax
nc Cycles (n)
Figure 11.7 Net specimen weight changes predicted from Equations (11.19)–(11.21).
Although no closed form solutions were found, numerical computation showed that the model yielded a good approximation to the cyclic oxidation of several alloys, as we now discuss. An investigation [18] of the form of DW=A versus cycle number curves, and their dependence on the parameters kw , ks and Dt was fruitful. The general form of the curve predicted from Equations (11.19)–(11.21) is shown in Figure 11.7. It is seen to be of the same form as those observed experimentally (Figures 11.2, 11.3a and 11.11a). The initial increase in weight is due to the rapid scaling observed at short times, and as exposure time increases the parabolic scaling rate slows. However, if a constant fraction of the scale spalls at each cycle, the weight lost during each cycle increases with scale thickness and elapsed time. This causes the net weight change to become negative. Any resulting decrease in average scale thickness leads to an increase in scaling rate (Equation (11.2)), and a balance is struck between scale growth and scale loss. Spalled fragments contain metal as well as oxygen, and a steady-state net weight loss results. The aim of the spallation models is to describe the onset and subsequent rate of this metaldepleting process. The numbers of cycles required to reach the maximum weight gain nmax , and to reach the crossover between positive and negative net weight change, nc , were both found to depend on the quantity ð1 ks Þ=ks and nmax =nc was equal to 0.3. Comparison of the model with experimental data in Figure 11.8 [19] for NiCrAlZr subjected to 1 h cycles at 1,2001C shows a satisfactory fit over 2,000 cycles, during which the alloy continued to regrow alumina. The reason the alloy resisted depletion so well was the small amount of scale spalled at each cycle. Fitting the model to observed DW=A versus n curves yielded realistic
509
11.3. Spallation Models
3 Calculated 2
Observed
ΔW/A (mg cm-2)
1 0 0
500
1000
1500
2000
2500
3000
3500
-1 -2 -3 -4 -5 Number of cycles
Figure 11.8 Fit provided by model of Equations (11.18)–(11.21) for cyclic oxidation data for NiCrAlZr at 1,2001C [19]. Model uses isothermally measured kw and Q0 ¼ 104. Published with permission from r NACE International 1983.
Table 11.1
Application of spalling model of Smialek [18] to data for Ni–42Al at 1,1001C
Dt (h)
kw (mg2 cm4 h1)
ks
1 20 50
0.0026 0.0020 0.0036
0.0016 0.1225 0.1225
assessments of kw and the result ks 0:002. However, as seen in Table 11.1, the value of ks estimated for Ni–42Al by curve fitting increases substantially for longer cycle times. Direct measurement of ks by examination of spalled specimens showed that in fact ks varied widely, from 0.004 to 0.195. We therefore conclude that indeed ks 1, thereby accounting for the inapplicability of the early Whittle and Wahl models. However, it must also be concluded that the assumption of a constant ks value was incorrect. Further examination of the data showed that ks increased with average oxide thickness, as would be expected from Equation (11.1). The spalling model was subsequently developed further by Lowell et al. [19–21] to take account of this variation in ks . An empirical spalling constant, Qo , was used to relate the fraction of scale spalled to its average thickness (or weight per unit sample area, W r ) at the end of the preceding high-temperature cycle ks ¼ Qo W ar
(11.22)
510
Chapter 11 Cyclic Oxidation
Figure 11.9 Dependence of spall fraction on weight uptake for IN601 forming Cr2O3 at 1,1001C and TD–NiCrAl forming Al2O3 at 1,2001C [19]. Published with permission from r NACE International 1983.
The exponent a is an experimental constant, usually found to be close to unity. Examples of this relationship are shown in Figure 11.9. The weight of oxide spalled is in that case W s ¼ Qo W 2r
(11.23)
Because the amount spalled increases with oxide thickness, a pseudo steady state is reached in which the amount of oxide lost in each cycle is equal to the amount grown in the previous cycle (Figure 11.10). Under these conditions, the overall rate at which scale-forming metal is lost becomes linear. Thus the more-or-less linear rate of specimen weight loss in the later stages of thermal cycling exposure (e.g. Figure 11.3) is explained. The model has become known as Cyclic Oxidation Spalling Program (COSP) and is available as a computer program [22]. A variety of partial spall distributions is available within this program. The predictions of this model have been summarized by its authors [23]. For a given oxide, nmax / ðkw Dt Q2o Þ1=3
(11.24)
nc 3:3 nmax
(11.25)
DW kw Dt 1=3 / A max Qo
(11.26)
and the final linear mass loss rate dðW=AÞ kw Qo 1=3 / dt Dt final
(11.27)
511
11.3. Spallation Models
Figure 11.10 Predictions of the Lowell et al. [19–21] spalling model for time dependence of average scale thickness and rate of scale-forming metal consumption [16]. Reproduced by permission of The Electrochemical Society.
As seen in Figure 11.11, very good fits to net weight change data can be achieved with this model. However, although the effects of cycle frequency are well predicted for this chromia former, they are only approximately correct for the alumina former MA 956 (Y2O3 dispersed FeCrAlY) [23] and unsuccessful for Zr-doped NiAl [24]. Modifications to these spalling models have been suggested. Evans et al. [2, 25] have proposed that the quantity of spalled oxide be described by the empirical expression W s ¼ AW r þ BðW r DTÞ2 þ CðW 3r DT 4 Þ þ DðW 4r DT6 Þ or, more simply, by
ks ¼
W r DT2 b
(11.28)
m (11.29)
In these expressions, W r DT2 represents the elastic energy in the oxide resulting from rapid cooling (Equation (11.1)), b depends on the strength of the scale–metal interface, and m reflects the mechanical properties of the oxide. Similarly, Chan [26] proposed that W s / DT2 ðW r Þmþ1
(11.30)
512
Chapter 11 Cyclic Oxidation
Figure 11.11 Effect of cycle duration on cyclic weight changes for Ni–30Cr oxidized at 1,0501C [21]. With kind permission from Springer Science and Business Media.
Finally, the Smialek model of Figure 11.6 has been revisited by Poquillon and Monceau [27] who found a new solution for the amount of oxide grown in the nth cycle, 2 n1 pffi pffiffiffiffiffiffiffiffiffiffi X 1=2 4 DW o ðnÞ ¼ ð2kw DtÞ ks ð1 ks Þj1 j j1 j¼1
3 pffiffiffi pffiffiffiffiffiffiffiffiffiffiffi þ ð1 ks Þn1 n n 1 5
(11.31)
513
11.3. Spallation Models
Table 11.2 Application of spalling model of Poquillon and Monceau [27] to oxidation at 1,1501C in 1 h cycles Alloy (at. %)
nmax
nc
Experimental Calculated Experimental Calculated
Ni–45Al 9–115 Ni–47Al 37–69 Ni–51.2Al 41–55
23 64 74
9–115 166–240 147–198
73 221 249
106 kw ks (%) (mg2 cm4 s1)
2.5 3.7 1.6
0.48 0.54 1.55
where the index, j, defines the cycle in which spallation occurs. They showed analytically that in the limit as n becomes very large
(11.32) DW o ð1Þ ¼ ð2kw DtÞ1=2 ks Lið1=2Þ ðzÞ z Lið1=2Þ ðzÞ where z ¼ 1 ks and Lin ðzÞ is the polylogarithm function 1 j X z Lin ðzÞ ¼ jn j¼1
(11.33)
For ooks o1, Equation (11.33) converges to a limit, representing a constant oxidation weight gain per cycle. This, of course, represents a constant rate of metal loss, and is analogous to the COSP Equation (11.27). It depends in a straightforward way on kw and Dt, but in a complex way on ks , which appears in the Lin ðzÞ function. Poquillon and Monceau [27] tested the applicability of their spallation model to experimental weight change data for the cyclic oxidation of a series of alumina-forming alloys. To do this, they treated the rate constant kw and the spallation constant ks as adjustable parameters, minimizing the residual error between calculated and measured values n X
2 Errorðkw ; ks Þ ¼ DW i ðcalc:Þ DW i ðexp:Þ i¼1
over each set of n data points. Very good fits were obtained, and the results are summarized in Table 11.2 for binary Ni–Al alloys oxidized in 1 h cycles at 1,1501C. Reasonable agreement between measured and calculated values was found for both nmax and nc . In agreement with the COSP model, nc 3:3 nmax . Importantly, the values of kw and ks arrived at in minimizing the error in the fit were also consistent with the steady-state rates of weight loss observed in the long term. As we have seen, the spallation models appear to provide self-consistent descriptions of the major features of cyclic oxidation weight-change kinetics, in at least some cases. To predict the lifetime of an alloy (i.e. the exposure limit beyond which the alloy can no longer redevelop its protective scale) we need to relate spallation to the depletion in scale-forming metal.
514
Chapter 11 Cyclic Oxidation
11.4. COMBINATION OF SPALLING AND DEPLETION MODELS Nesbitt [16] used the spalling model of Equation (11.23) together with the computational approach of Equations (11.19)–(11.21) to calculate the rate at which scale-forming element is withdrawn from the alloy. For an oxygen uptake rate given by Equation (11.2), and an oxide of stoichiometry MOn, the corresponding rate of metal consumption is dðW M =AÞ mM kw ¼ dt 16n W o =A
(11.34)
This statement of metal flux out of the alloy surface can be used in the mass balance Equation (5.29) to provide a boundary condition for the alloy diffusion problem. Nesbitt applied this approach to the ternary Ni–Cr–Al system, using multicomponent diffusion equations of the form of Equation (2.115). To deal with the necessarily time-dependant values of N Al;i and N Cr;i , as well as the concentration dependence of the Dij , a finite difference calculation was employed. The description was applied to cyclic oxidation of Zr-doped Ni–Cr–Al alumina-forming alloys [28]. As seen in Figure 11.12, use of the fractional spallation model (Equations (11.23)–(11.27)) led to an estimate of
Figure 11.12 Aluminium consumption during cyclic oxidation of Ni–Cr–Al(Zr) at 1,2001C: points-measured; dashed line, Whittle and Wahl analysis; continuous lines, Nesbitt analysis [16]. Reproduced by permission of The Electrochemical Society.
11.4. Combination of Spalling and Depletion Models
515
Figure 11.13 Experimental (continuous curve) and predicted (dashed lines) alloy aluminium levels necessary for rehealing Al2O3 scales on Ni–Cr–Al+Zr over 200 1 h cycles at 1,2001C [16]. Reproduced by permission of The Electrochemical Society.
aluminium depletion which was much more realistic than the 100% spallation model of Whittle and Wahl. We conclude from this success that the COSP spallation model of Equations (11.23)–(11.27) combined with an accurate calculation of subsurface alloy depletion correctly describes the consumption of protective scale-forming metal in the early stages of reaction. Lifetime predictions for these alloys were only partially successful. The diffusion analysis was used to predict the value N Al;min required to survive 200 cycles of 1 h duration at 1,2001C before N Al;i was depleted to zero. As seen in Figure 11.13, reasonable agreement with experimental findings [29] was achieved for high N ðoÞ Cr values, but not for low chromium levels. This failure was attributed to the neglect of transient oxidation, the consequences of which would become more serious as aluminium depletion progressed with further cycling. The presence of chromium was thought to suppress the extent of transient oxidation, thereby rendering the model a more realistic description. Li and Gleeson [30] have carried out a somewhat similar analysis for the cyclic oxidation at 1,0001C of the chromia-forming alloy 800HT (a heat treated version of alloy 800 (Table 5.1)). The COSP treatment of spallation was used to obtain a value for the spalling constant Qo , and a finite difference technique employed to model the non-steady-state alloy diffusion process of depletion. However, this was simplified by treating the alloy as a quasi-binary, i.e. by setting Dij ðiajÞ ¼ 0. Diffusion coefficient values were estimated by applying the Boltzmann–Matano Equation (2.142) to a measured chromium concentration ~ for the range of concentrations involved. profile and calculating an average D This procedure was validated by comparing predicted and measured chromiumdepletion profiles at longer reaction times. Using an isothermal rate constant kw ¼ 6:3 1012 g2 cm4 s1 and a fit of experimental weight change data to the COSP model led to an estimate of Qo ¼ 0:008 for the 1-day cycles. Breakdown was observed after 18 cycles, at which point the value N Cr;i ¼ 0:073 was measured. Application of the combined
516
Chapter 11 Cyclic Oxidation
diffusion and COSP models led to the prediction that N Cr;i would be depleted to this level in 20 cycles, a very accurate forecast. However, the critical value of N Cr;i was measured rather than predicted. Furthermore, the extent of transient oxidation was high and the resulting spinel layer was observed on some occasions to spall, leaving the chromia layer more or less intact. The phenomenon of scale delamination at phase layer boundaries has been reported a number of times, and examples are shown in Figure 11.14. In the case of the Rene´ N5 superalloy (Table 5.1), the outer layer was made up of transient Ni-, Co- and Cr-rich oxide remnants, together with particles of Ta-rich oxide, and the inner layer was a-Al2Os. When this phenomenon is combined with
(a)
(b)
Spall ed area
Al2O3
NiAl2O4
NiO
Figure 11.14 Spallation of scale outer layers (a) on H2 annealed, Y-Free Rene´ N5 [31] with permission from IOM Communications Ltd, (b) on g=g 0 Ni–23Al.
11.5. Effects of Experimental Variables
517
occasional spallation of the inner, protective layer, the situation becomes very difficult to model. Alumina spallation from ferritic materials and the resulting depletion of aluminium have been modelled by Quadakkers et al., as described in Section 5.8. The situation is simplified in that case because alloy diffusion is very fast, and the depletion profiles in thin sheet materials are essentially flat. A complete analysis of alloy depletion accompanying spallation and rehealing requires an accurate description of diffusion in the subsurface alloy region. For the engineering alloys and coatings of interest, the necessary data are simply not available. Nonetheless, the models which have been developed provide a valuable predictive tool for the effect on material lifetime of varying the reaction conditions.
11.5. EFFECTS OF EXPERIMENTAL VARIABLES 11.5.1 Temperature cycle parameters Several parameters are irrelevant concepts in isothermal oxidation, but can be critical to the outcome of a cyclic oxidation experiment. These are the magnitude of the temperature change, DT, the heating and cooling rates and the cycle frequency or, equivalently, its duration. The magnitude of DT determines both the maximum stress (Equation (2.168)) and, through Equation (11.1), the maximum elastic strain energy available to fracture or spall the scale. The failure mechanism adopted by the scale depends on scale thickness [32], as does the available energy for a given DT. The net effect for a chromia-forming austenitic steel is shown in Figure 11.15. It is seen that the usual experiment, which involves cooling to room temperature, will provide sufficient thermal stress to spall oxides grown at high temperature. However, the slow oxidation rates characteristic of low temperatures mean that these scales can resist thermal cycling for very long periods. The thermally induced strain energy is only available to damage the scale if it is not dissipated by some other stress relief process. To a good approximation, this will be the case if the cooling rate is very fast. However, if it is slow, creep in the metal can reduce the stress. This effect is marked in FeCrAl materials which have low creep strength, and can accommodate thermal stress to the point where their alumina scales resist spallation up to large thicknesses [5, 33]. It can also be significant in materials like Haynes 214 (Ni–16Cr–3Fe–4.5Al–Y) which is a singlephase g alloy of modest creep strength above 9001C. If cooling to this temperature is slow enough, considerable stress can be relaxed by alloy creep [34]. The effects of cycling frequency have been examined many times. According to the spallation models, shorter and more frequent cycles lead to more frequent spallation events. As shown in Equation (11.24) this results in a smaller value of nmax Dt, which therefore increases with Dt 2=3 . As noted earlier, this prediction is borne out for Ni–30Cr and the alumina former MA 956, but not for Zr-doped NiAl. However, the more important factor is subsequent metal consumption.
518
Chapter 11 Cyclic Oxidation
0
Estimated Oxide Thickness, μm 2 3 4
1
800
5
6
Initial Temprature = 1123 K
Temperature Amplitude, -ΔT, K
700
600 wg (ΔT)2 = 6.0x 105 gm-2 K2 500
400
300
200 0
1.0
2.0
3.0
4.0 5.0 6.0 7.0 Gross Weight Gain, wg, g.m-2
8.0
9.0
10.0
Figure 11.15 Critical temperature drop necessary to spall chromia from a 20Cr–25Ni Nb-stabilized stainless steel [32]. Published with permission from Maney Publishing.
If, as is being assumed, the life of a material is determined by the rate of Cr or Al consumption during the final pseudo steady-state, then Equation (11.27) applies. This rate increases as Dt is decreased. Pint et al. [31] showed this to be qualitatively correct for the alumina formers FeCrAl, FeCrAlY, iron aluminides and undoped high-sulfur-content NiAl. Closer examination of the weight loss rates shown in Figure 11.16 for ‘‘NiAl-1’’ (Ni-50.2 at % Al, 27 ppma S) reveals average values of 4.7 mg2 cm2 h1 during 1 h cycling, and 1.2 mg cm2 h1 in 100 h cycling. The ratio between them is ca. 4:1, which compares well with the ratio predicted from Equation (11.27) of (100/1)1/3 ¼ 4.6:1. In the case of FeCrAl, the ratio of weight loss rates observed during 2 and 100 h cycles is 5.7:1, compared with a predicted ratio of 3.7:1. This remarkable level of agreement with the prediction of the COSP spallation model was not reproduced by another NiAl alloy ‘‘NiAl-2’’ (Ni-50.2 at % Al, 3 ppma S), which lost weight at essentially the same rate regardless of cycle duration. Unusual spalling behaviour of NiAl has also been reported by Smialek et al. [18, 23]. Wilber et al. [7] found little difference in the spalling behaviour of FeCrAl alloys cycled for 100 and 290 h. A reverse effect of cycle duration, i.e. more rapid weight loss in longer cycles, was reported by Smialek [18] for Ni-42Al, and by Pint et al. [31, 35] for platinum containing NiAl and a desulfurized version of the superalloy Rene´ N5 (Appendix A). This behaviour has been rationalized [18, 31] in terms of void enlargement at the scale–alloy interface during lengthy cycles. It is suggested that the development of much larger defects can lead to more extensive spallation, i.e. to
11.5. Effects of Experimental Variables
519
Figure 11.16 Specimen weight losses for undoped FeCrAl and NiAl for different cycle times at 1,2001C [31]. Published with permission from IOM Communications Ltd.
an increase in Qo . Experimental support is provided by the observations of Vialas et al. [36] who reported much larger spall fractions, ks , on NiPtAl after 6 300 h cycles than after 1,800 1 h cycles. Existing spallation models cannot easily deal with such a situation, and caution should be exercised in predicting cycle frequency effects. Finally, it should be noted that spallation-resistant materials such as Hf-doped NiAl show no change in oxidation kinetics with cycle duration, at least in the early stages. This is intuitively understandable as a simple consequence of the greater strain energy (and therefore scale thickness) required to damage the much stronger scale–alloy interface. The time taken to reach a critical scale thickness for the onset of spallation is then determined by accumulated time at temperature, rather than by periodic interruptions of the scale growth process. It is unfortunate that the currently available theory provides no generally applicable basis for predicting behaviour at a given cycle frequency from existing data acquired at another frequency. Current efforts [37–39] to devise a standard cyclic oxidation testing protocol are on this basis perhaps understandable. However, they will not resolve the difficulty, leaving the need to undertake additional testing programmes for new duty cycles. What is needed is an improved understanding of the way in which scale and interface mechanical properties, and defect sizes, evolve with time.
520
Chapter 11 Cyclic Oxidation
11.5.2 Continuous thermogravimetric analysis Observation of oxidation kinetics and individual spallation events via CTGA provides the opportunity to validate the assumptions of the spallation models. However, the direct observation of weight loss during spallation can be complicated by apparent weight changes due to buoyancy and convection effects. During cooling from T1 to T 2 , the gas density increases, leading to an apparent weight decrease, dW, found from Archimedes’ principle and the ideal gas equation to be MPT 1 1 dW ¼ (11.35) T1 T2 R Here M is the molar mass and PT the pressure of the gas, and it has been assumed that the microbalance counterweight experiences no temperature change. Although dW can be of the same order as spallation weight change, it is easily corrected for. Convection effects are much more difficult to quantify, and it is simpler to compare the recorded weight at the beginning of a high-temperature period with the weight at the end of the preceding one, as shown schematically in Figure 11.17. In the simplest case, heating and cooling are rapid, and the amount of oxidation occurring during the non-isothermal periods can be ignored. The total gross mass gain is obtained simply by summing the high-temperature oxygen uptake amounts, W o ; the spallation loss is the sum of the W s amounts, and the net mass gain is the difference between these sums. Because W s and the current net mass gain are available for each individual cycle, the spallation fraction ks can be tracked though the course of the experiment. These measurements can be refined by taking into account the small amount of oxidation
T
δwC W/A W/A δwh
WS
W0
T
t
Figure 11.17 CTGA data from thermal cycling, showing oxidation weight gain, buoyancy changes during cooling ðdwc Þ and heating ðdwh Þ and spallation weight loss ðW s Þ.
521
11.5. Effects of Experimental Variables
8
6
1,E-02
kp (mg2/cm4s)
Pn
4
1,E-03 2 1,E-04 0 1,E-05
-2 kp
1,E-06
Percentage of oxide scale weight spalled at each cycle (Pn) (%)
1,E-01
-4 0
10
20
30
40
50
Number of cycles Figure 11.18 Evolution of instantaneous parabolic weight gain constant and spallation constant for single crystal MC2 superalloy during 15 min high-temperature cycles. Reprinted from Ref. [40] with permission from Elsevier.
occurring during heating and cooling [40]. An example of the data obtainable in this way is shown in Figure 11.18 for a nickel-based, single crystal superalloy, MC2 (Table 1.2). It is seen that kw became approximately constant after 14 cycles. The spallation constant varied widely in the first 14 cycles, but then slowly increased with time over the course of this experiment, in agreement with Equation (11.22). Monceau et al. [27, 36, 40, 41] and Smialek [42] have used performance ‘‘maps’’, with spallation constant and parabolic scaling rate as axes, to compare the behaviour of different alloys and coatings. The example in Figure 11.19 shows data for various alumina formers cycled in air at 1,1501C. It shows that solute aluminium consumption by spallation increases in the order NiCoCrAlYoNiAloMC2. Also shown for comparison are isothermal oxidation rates for NiAl, superalloy MC2, NiCoCrAlYTa-coated superalloy and chromia formers.
11.5.3 Compositions of alloys and environment Cyclic oxidation experiments have been used to study the spallation behaviour of a wide variety of chromia and alumina formers. The effects of alloy compositional variables on spallation are reviewed in Section 7.5. Most research has been concerned with cyclic exposure to air or oxygen. However, hightemperature service environments frequently contain other constituents, and their effects are now considered. Water vapour is almost always present in high-temperature service environments. As seen in Chapter 10, it can affect the growth rates of many oxide scales.
522
Chapter 11 Cyclic Oxidation
1,E-02 Percentage of area spalled at each cycle (Pn) (%)
(1)
(2) Increasing performance
NiCoCrAlYTa/MC2
1,E-01 Cr203 zone (4)
NiAl
1,E+00
1,E+01 1,0E-04
MC2 This work
avg. MC2
1,0E-05
(3) 1,0E-06
1,0E-07
kp (mg2/cm4s)
Figure 11.19 Spallation–oxidation map for cyclic oxidation in air at 1,1501C of several alumina formers. Isothermal rate constants for NiAl (1), superalloy MC2 (2), NiCoCrAlYTa coated superalloy (3) and a range of chromia formers (4) shown for comparison. Reprinted from Ref. [40] with permission from Elsevier.
Of relevance here is its effect on the volatilization of chromia and its apparently very slight effect on isothermal alumina scaling. The cyclic oxidation of several chromia formers in air plus H2O(g) has been studied by Pint et al. [43–45], using lengthy cycles ðDt ¼ 100 hÞ and moderate temperatures. Spallation was not significant under these conditions, and alloy performance was determined by CrO2(OH)2 vaporization [46]. The situation is very different for alumina formers, because moisture can affect scale adhesion. Smialek has reported that exposure of oxidized samples to moisture after cooling produced increased spallation from the alumina formers NiAl [18], NiCrAl [47], PWA 1480 [48], Rene´ N5 [49] and PWA 1484 [23] (Table 1.2). Sigler [50] and Smith et al. [51] have also reported that water vapour promotes alumina spallation. Controlled atmosphere thermal cycling experiments confirm the damaging effect of water vapour. Janakiraman et al. [52] and Maris-Sida et al. [53] compared the cyclic oxidation performance of alumina-forming, nickelbased superalloys in dry and wet ðpH2 O ¼ 0:1 atmÞ air. Results in Figure 11.20 for two PWA alloys which contained 5–8 ppm S show the accelerated spallation resulting from the presence of water vapour. Similar results were obtained for CMSX-4, a CoCrAlY coating and an aluminide coating. Subsequent work on model Ni–Al alloys ðb; g=g 0 and gÞ [54] and on platinum and platinum–iridium modified g=g 0 alloys [55] has demonstrated the same effect. Materials which developed spallation-resistant alumina scales were not affected by the presence of water vapour. This is demonstrated by the behaviour of low sulfur and desulfurized PWA 1484 (Figure 11.21) and by Hf-doped b-NiAl
11.5. Effects of Experimental Variables
523
Figure 11.20 Effect of pH2 O ¼ 0:1 atm on alumina-forming superalloys exposed to 45 min oxidation cycles at 1,1001C [52]. With permission from IOM Communications Ltd.
(Figure 11.22). Examination confirmed that spallation was suppressed in these cases. However, acoustic emission signals during cooling of the low sulfur PWA 1484 alloy from reaction temperature indicated that oxide cracking did occur [52]. It was therefore concluded that water vapour was able to reach the alloy surface, even when spallation did not occur. The effect of sulfur content on nickel-based alumina-forming superalloys and on b-NiAl can be generalized as follows. In the absence of reactive elements, more than 3 ppmm S leads to scales which are poorly adherent and spallation prone. Lowering alloy sulfur levels to around 1 ppmm leads to a considerable improvement, but to realize the maximum scale adhesion, a level of p0.1 ppmm is required. Water vapour is known [56–59] to affect the fracture behaviour of oxides, including a-Al2O3. The polar water molecule is thought to attach to Al–O bonds at a crack tip, weakening those bonds and in effect reducing the fracture toughness of the oxide. Meier et al. [52, 53] propose that a similar phenomenon could occur at the alloy–alumina interface. When sulfur is present in the alloy, it segregates to the scale–metal interface, decreasing its toughness. Water vapour decreases the interfacial toughness even more, and oxide spallation is promoted. When sulfur is not present to weaken the interface, or when hafnium is added to strengthen the interface, the water vapour effect is prevented. Either the water molecules cannot access the interface (even though the oxide is cracked) or the
524
Chapter 11 Cyclic Oxidation
Figure 11.21 Appearance after cyclic oxidation of desulfurized PWA 1484 in (a) dry and (b) wet (pH2 O ¼ 0:1 atm) air, 45 min cycles at 1,1001C [52]. With permission from IOM Communications Ltd.
interfacial toughness is so high that any weakening caused by water is insufficient to cause spallation. Alloy breakdown can result from internal precipitation reactions as well as the more usually discussed external oxidation of alloy solvent metals. The development of internal oxidation during cyclic reaction has been reported several times [60–64]. The presence in the gas of secondary oxidants can exacerbate this situation if the other oxidant has a greater permeability in the alloy than oxygen. Both nitrogen and carbon have higher permeabilities than oxygen in austenite (Table 6.2), and are therefore potential threats to the longterm performance of heat-resistant steels and nickel-based alloys. The ability of an alloy to reform a protective oxide scale after spallation can be determined not simply by the depletion phenomena discussed in Sections 11.2 and 11.4, but by the competition between outward diffusion of scale-forming metal and inward diffusion of secondary oxidant. Internal precipitation of the scale-forming metal as nitride or carbide immobilizes it, effectively causing more severe depletion. As discussed in Chapter 9, carbon attacks heat-resisting alloys very rapidly, causing deep carburization and, in some atmospheres, metal dusting.
525
11.5. Effects of Experimental Variables
5 1wt% Hf, dry air
ΔW/A (mg/cm²)
4
1wt% Hf, air-12%H2O
3
2
1
0 0
200
400 600 number of 1-hr cycles
800
1000
Figure 11.22 Cyclic oxidation at 1,2001C (1 h cycles) of b-NiAl with Hf doping in dry and wet air (pH2 O ¼ 0:12 atm).
Cyclic exposure [65] of 304 stainless, Alloy 800 and 602CA (Table 9.1) to CO/CO2 atmospheres which are both oxidizing and carburizing to chromium lead to the reaction morphologies shown in Figure 11.23. The two chromia-forming alloys failed, suffering extensive internal precipitation. The reaction of 304 stainless was the more complex, forming multiple internal precipitation zones. Chromiumrich carbides precipitated deep within the alloy, and an internal oxidation front advanced into the alloy behind the carburization front as the in situ oxidation of internal carbide 2Cr7 C3 þ 21 O ¼ 7Cr2 O3 þ 6 C
(11.36)
continued. Subsequent spinel formation at the even higher oxygen potentials near the alloy surface Fe þCr2 O3 þ O ¼ FeCr2 O4
(11.37)
developed an additional internal precipitation zone (Section 6.9). The sequence of zones reflects the relative stabilities of the precipitates, and the faster diffusion of carbon. Alloy 602CA, which is a marginal alumina former, resisted carbon attack. As seen in Figure 11.23, very large oxide volume fractions resulted, causing significant expansion and disruption of the alloy surface. The magnitude of these effects can be estimated from precipitate species molar volumes on the assumption that all chromium is precipitated. Results are shown in Table 11.3. The mechanical stress associated with these large volume changes would have been exacerbated by thermal cycling, leading to the observed alloy disintegration. The role of carbon in producing this effect is critical. Such large quantities of internal oxide cannot normally form, an external scale developing instead.
526
Chapter 11 Cyclic Oxidation
(b) (a)
(c)
Figure 11.23 Heat-resisting alloys after exposure to CO/CO2 mixtures for 520 cycles at 7001C: (a) alloy 800, (b) 304 stainless and (c) 602 CA. Reprinted from Ref. [65] with permission from Elsevier. Table 11.3
Calculated effects of complete internal chromium precipitation in 304 stainless steel
Precipitate
fn
DV (%)
FeCr2O4 Cr2O3 Cr7C3 Cr23C6
0.45 0.32 0.21 0.20
40 21 3 3
Note: fn is precipitate volume fraction in internal reaction zone; DV is the resulting expansion of this zone.
It is the prior internal carburization resulting from thermal cycling-induced scale spallation which allows subsurface oxide formation via reactions (11.36) and (11.37). Thermal cycling in other oxidizing–carburizing environments can be used to accelerate protective scale failure, and the onset of metal dusting attack [66]. The permeability of nitrogen in austenite is not as high as that of carbon, but it is sufficient to accelerate internal attack of an alloy depleted by successive
11.6. Describing and Predicting Cyclic Oxidation
527
spallation–rehealing events. Thermal cycling in air can lead to the development of multizone internal precipitation regions beneath the surface, with nitrides located at greater depths than oxides [9, 67, 68]. This phenomenon may be more frequent than has been reported for air oxidation, because the nitrides can be difficult to distinguish metallographically from oxides (Figure 11.24). Internal precipitation kinetics are complex, as shown in Figure 11.24b, with initially parabolic behaviour followed by linear penetration. It has been suggested [60, 68] that the large internal precipitate volumes, coupled with cyclic thermal expansion and contraction lead to cracking and gas access to the alloy interior. Results obtained for cyclic corrosion in sulfur-bearing environments are complex. Laboratory hot corrosion tests (Section 8.8) often involve periodic addition of salt to sample surfaces. This is usually done at time intervals which are some multiples of Dt. Leyens et al. [69] have reported that the frequency (and rate) of salt addition is an important variable, the corrosion rate of NiCoCrAlY alloys increasing with less frequent but larger salt additions. Decomposition and evaporation of the sulfate salts is clearly involved, but the interaction between oxide spallation, corrosion and salt weight changes makes kinetic data difficult to interpret. As seen in Chapter 8, corrosion by reducing sulfidizing gases is particularly severe. The only practical way of protecting alloys against such gases is by forming oxide scales capable of surviving at low-oxygen activities. The ability of these alloy–scale systems to resist spallation and to reheal after damage is then of critical importance. Cyclic exposure experiments [70] have been used to explore the behaviour of ferritic and austenitic steels in sulfidizing–oxidizing gases at 6001C. Despite the relatively low temperature, thick scales were formed. However, the low temperature and slow rate of temperature change in the autoclave used in these experiments led to only small degrees of spallation. Weber and Schutze [71] subjected thermal spray coatings of Ni–48Al–1.5Cr (at. %), TiAl and TiSi2 on a low alloy steel and a ferritic 18Cr–1Al steel to cyclic exposure in Ar-5%H2-1%H2S at 7001C. Impurity amounts of H2O(g) made the gas oxidizing to aluminium and silicon, but borderline sulfidizing–oxidizing to titanium. The porous nature of spray deposited coatings makes them gas permeable. Although oxidation tends to fill the pore space, sulfides also form, and internal sulfidation of the substrate steels results. The presence of nickel was disadvantageous, and the TiAl and TiSi2 coatings provided better performance. The thermal cyclic performance of dense, aluminium-rich materials in sulfidizing gases might be interesting.
11.6. DESCRIBING AND PREDICTING CYCLIC OXIDATION Cyclic oxidation experiments combine high-temperature reaction with the mechanical effects of thermally induced stress on protective scales, providing a realistic simulation of high-temperature service. This is particularly so if controlled gas atmospheres are used to reproduce service conditions.
528
Chapter 11 Cyclic Oxidation
(a) Oxides
Nitrides
50 μm
(b)
Figure 11.24 Internal oxidation and nitridation of several a+b+g 3-phase Ni–Cr–Al alloys produced by thermal cycling in air at 1,1001C (260 1 h cycles): (a) reaction morphology in Ni–30Cr–20Al (fragmentary outer scale present but not visible) and (b) internal nitridation kinetics for different three-phase alloys.
11.6. Describing and Predicting Cyclic Oxidation
529
Modern alloys and coatings provide superior resistance to cyclic oxidation, and designing efficient laboratory test programmes is a challenge. One approach is simply to test for long times, two years or more [64, 72, 73], until depletion of the protective scale-forming metal leads to breakaway oxidation. It is obviously desirable to be able to accelerate the experiments, to reduce costs and speed the introduction of new materials. As we have seen, alloy degradation is accelerated by increasing temperature to speed the corrosion reaction, and by shortening the cycles to increase spalling frequency. However, this is useful only if a reliable method exists for extrapolating the laboratory test results to the service conditions of interest. For this very practical reason, we are interested in the use of modelling to arrive at an accurate description and a method of prediction for spallation-induced alloy depletion. The diffusion model for alloy depletion accompanying scale spallation and rehealing is well developed. Based on the interaction between the depletion process of selective oxidation and the replenishment process of alloy diffusion, ~ 1=2 . When combined it describes the balance in terms of the ratio f ¼ ðpkc =2DÞ with a realistic description of spallation extent, it can provide reasonable lifetime predictions. However, it succeeds only to the extent allowed by the accuracy and completeness of the data available for diffusion in the substrate alloy. In the case of Fe–Cr–Al alloys, which have very high diffusion coefficients at their typical operating temperatures, the depleted profile in N Al is adequately approximated as being flat in thin sections, and predictions of lifetimes can work well. However, diffusion in the commonly used austenitic heat-resisting alloys, in superalloys and in coating materials is slower, and varies in a complex way with composition. Available data is generally insufficient to justify calculations. However, this shortcoming can be overcome by the expedient of measuring average interdiffusion coefficients and the critical interface concentration, N B;i , of scale-forming metal required, at both the service and laboratory test temperatures. The spallation models examined in this chapter succeed in describing the general form of experimentally observed weight change kinetics. They also achieve quantitative success in relating the number of cycles required to reach the maximum weight uptake with the number at which the net weight change becomes negative and, most importantly, the ultimate constant rate of weight loss, and therefore depletion. With this degree of success, we might hope that the models would allow the all important prediction of the effects on lifetime of changing temperature and cycling frequency. Unfortunately, the empirical nature of models which treat spallation probability as an adjustable parameter permit no such thing. The essence of the problem is that spallation is treated as a random event, unrelated to experimental variables other than through Equation (11.1). It is therefore not possible to predict the effect of changing temperature on the spallation fraction (i.e. probability) without recourse to other, fracture mechanicsbased descriptions. These are numerous, reflecting the diversity of mechanisms available for the initiation and propagation of fast fracture in scale–substrate systems. It seems likely that the temperature effect on ks will be strongly dependent on the alloy–gas system involved, and more information is required.
530
Chapter 11 Cyclic Oxidation
Spallation-induced weight loss changes are predicted to change at a given temperature, and constant value of kw , with cycle frequency in a simple way. However, while the expected dependency of final weight loss rate on Dtð1=3Þ is found for a number of materials, for others it is not. One reason for this failure is the overly simplistic nature of the assumed oxidation morphology, that of a single-phase external scale. The real situation is much more complex. Remnant transient oxides (Section 5.7) form an outer layer which can spall, causing weight loss, but leaving the protective function of the underlying alumina or chromia unimpaired. As the concentration of the primary scale-forming metal is lowered, additional layers of spinel develop at the scale surface, altering the observed weight change rates. Finally, we note that depletion of an alloy often renders it susceptible to internal oxidation or attack by a secondary corrodent (Chapter 6), complicating still further the cyclic weight change behaviour. No model descriptions are available for the effect on cyclic weight change kinetics of these more complex reaction morphologies.
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CHAPT ER
12 Alloy Design
Contents
12.1. 12.2. 12.3. 12.4. 12.5.
Introduction Alloy Design for Resistance to Oxygen Design Against Oxide Scale Spallation Design for Resistance to Other Corrodents and Mixed Gases Future Research 12.5.1 Gas turbines 12.5.2 Electric power generation 12.5.3 Petrochemical and chemical process industries 12.5.4 Greenhouse gas emission control 12.6. Fundamental Research 12.6.1 Grain boundaries in oxide scales 12.6.2 Water vapour effects 12.6.3 Nucleation and growth phenomena 12.7. Conclusion References
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12.1. INTRODUCTION We have examined at some length the development of a theoretical basis for understanding and predicting the outcomes of high-temperature alloy corrosion reactions. On the one hand, thermodynamic analysis is aimed at predicting the identity of reaction products. On the other, diffusion analysis seeks to predict the rates of mass transfer in reaction product scales and the substrate alloy, thereby enabling calculation of overall corrosion rates and material lifetimes. In addition to exploring the intrinsically interesting nature of this complex problem, the theory aims to provide a rational basis for materials selection and design. In situations where measured data are lacking, the theory provides guidance for exploring the experimental space: the relationships between corrosion rate and alloy composition, oxidant activity, temperature, cycle frequency and so on. It is appropriate now to review the degree of success realized. A principal purpose of this examination is the identification of areas of inadequacy, where more work is required.
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12.2. ALLOY DESIGN FOR RESISTANCE TO OXYGEN Provided that exposure conditions are isothermal, the basic theory works rather well for steady-state conditions. Thermodynamic prediction of reaction product sequences is successful, even for complex multilayer scales and multiple internal oxidation zones. The Wagner theory for diffusion-controlled scale growth provides accurate predictive capability when the following conditions are met: (1) the scale layers are single phase; (2) diffusion is via the oxide lattice; (3) the scale behaves as a parallel-sided slab of structurally homogeneous material, and develops no pores, cracks or voids; (4) the integrity of the scale–alloy interface is maintained and (5) mass transfer processes in the ambient gas are rapid, and interfacial processes are close to equilibrium. These conditions are generally met in the oxidation of the common base metals, iron, cobalt and nickel, and for alloys which are mixtures of these metals. Quantitative success in predicting oxidation rates for these metals, and the effects thereon of oxygen partial pressure and temperature, rests on rather old research. Parabolic kinetics were reported by Tamman [1] in 1920 for steel, and by Pilling and Bedworth [2, 3] in 1922 and 1923 for heater alloys. The theory of point defects in crystal lattices was developed by Frenkel [4] and Schottky [5] in the 1920s, and Wagner’s model [6] for oxide scale growth supported by the diffusion of lattice defects dates from 1933. Despite that early success, a vast body of research into high-temperature oxidation has accumulated since that era. This reflects the unfortunate reality that Wagner’s theory does not apply to scales grown by alloys of practical interest. Oxides of iron, cobalt and to a lesser extent nickel grow too fast for them to be acceptable as protective scales. Alloys must be designed to form other slowgrowing oxides, most commonly Cr2O3 or Al2O3. The assumptions underlying Wagner’s model do not apply to chromia or alumina scales. Instead, it is transport of reactants along grain boundaries (and perhaps other microstructural defects) in these scales which controls their growth rates. If scale microstructures were always the same, it would be possible to modify the Wagner equations simply by using an appropriately adjusted ‘‘effective’’ diffusion coefficient. Of course, any such attempt is futile: grain size and shape vary with temperature, reaction time, surface preparation and both alloy and gas composition. The wide ranges of reported chromia (Figure 3.20) and alumina (Figures 7.6 and 7.24) scale growth rates are therefore understandable. Although the range of oxidation rates shown on the logarithmic scales of these figures is indeed large, it is in one sense unimportant. The ranges represent differences between very slow rates and even slower ones. The corresponding rates of alloy consumption are so slow as to be seldom of any concern in the case of structural components (although they can be in the case of alloy foils). Accordingly, our inability to predict the scaling rate is unimportant, provided that we are able to design alloys in ways that ensure the rapid formation of the
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desired slow-growing scale, and its continued stability. Here Wagner’s theories of alloy oxidation [7–9] are helpful in estimating the minimum alloy levels of chromium or aluminium, N B;min , necessary to sustain exclusive chromia or alumina growth and prevent internal oxidation. The difficulty of predicting scaling rate is avoided in Wagner’s treatment of the alloy diffusion process which delivers chromium or aluminium to the growing scale. Instead, a measured rate of metal consumption is compared with ~ is formed. Although the theory the alloy diffusion coefficient, and the ratio ðkc =DÞ is reasonably successful in predicting N B;min values for binary alloys (Section 5.4), it turns out that avoiding internal oxidation often requires higher values. Wagner’s treatment of this situation (Section 6.11) is based on a comparison of inward oxygen diffusion with outward metal diffusion, and generally succeeds in predicting N B;min for binary alloys. This success derives from the usual validity of the assumption that both oxygen and metal diffuse via the alloy lattice. The methodology can fail in cases where diffusion is accelerated by the existence of favourable pathways such as internal surfaces. Difficulties arise for alloys more complex than simple binaries, for which the necessary information on oxygen permeability and even metal diffusion coefficients is sparse. Because thermodynamic interactions between solute oxygen and oxide-forming metals are strong, deviations from ideal solution behaviour are large, and approximate calculations based on binary alloy data are of limited use. A very clear example is provided by the so called ‘‘third element effect’’ (Section 7.4) in which alloying with a third metal promotes formation of the primary protective oxide scale. Examples are chromium in Fe–Cr–Al and zinc in Cu–Zn–Al. Wagner’s theory [10] of secondary gettering is based on the supposition of transient oxidation of the third element to form a scale (of Cr2O3 or ZnO) which lowers the oxygen potential at the scale–alloy interface, thereby reducing greatly the alloy–oxygen permeability. Outward diffusion of the aluminium is then favoured, and a scale of alumina develops beneath the other oxide. However, tests of the theory using binary alloy diffusion data do not achieve quantitative success. The theory can fail completely for other systems such as Ni–Si–Al. In the absence of adequate data for oxygen solubility and diffusivity in ternary alloys, it is difficult to assess the value of Wagner’s gettering theory. The practical result is that our predictive capacity for the oxidation behaviour of the important M–Cr–Al alloys is very limited. Alloy design depends upon empirical knowledge gained by experimentation. An important function of any protective scale is preventing outward diffusion of alloy solvent metal, and formation of surface spinel layers. Existing knowledge of oxide-phase equilibria, including intersolubility levels, would be sufficient for the construction of diffusion paths if adequate diffusion data were available. Apart from the work of Lobnig et al. [11] on chromia, data are lacking. Again, alloy design or selection is based on empirical knowledge, often in the form of oxide maps. Despite the lack of important basic data for multicomponent diffusion and oxygen solubility, alloy designs for resisting attack by oxygen at high
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temperature are rather successful. Oxidation resistance at intermediate temperatures can be more difficult to achieve using the lower chromium levels favoured for such service. The reason is the slow alloy lattice diffusion in effect at lower temperatures. The solution is cold working of the alloy to introduce subsurface deformation and multiple pathways for accelerated diffusion (Section 5.10). More detailed information on the competitive nucleation and growth of surface oxides during the transient stages of reaction would be desirable. There are practical limits to the applicability of the alloy design approach we have discussed. An example is provided by nickel-based superalloys. Chromium additions to these alloys are deleterious to their creep strength at the levels required to ensure chromia scale formation and good hot corrosion resistance. The engineering solution is to provide a corrosion-resistant coating on an alloy with a composition optimized for strength. Another example is found in alumina-forming austenitic alloys. The relatively slow alloy diffusion process means that alumina scale formation can be achieved for reasonable NAl levels only at very high temperatures. For some of these alloys, a pre-oxidation anneal is required to establish alumina scales before they are placed in service. The need to perform this operation after fabrication limits the size of components in which these alloys can be used. Both examples, and there are many others, reflect the reality that alloy design has multiple purposes. Alloys must provide adequate mechanical properties at high temperature as well as being capable of survival in the service environment. Additional requirements such as weldability and thermal conductivity will arise for particular applications. The idea of separating the mechanical and oxidation resistance functions of a component, thereby resolving the conflicting property requirements, is not new. Just as structural steel is protected by paint, suitable substrate alloys provide high-temperature mechanical functionality, and coatings or other surface modifications provide oxidation resistance. A different sort of design limitation can arise when developing alloys to resist internal oxidation. An interesting example is provided by the unsuccessful attempt to develop niobium-based alloys for very high temperature applications. Although niobium has a very high melting point (2,4671C), it is unusable at high temperatures because it oxidizes rapidly and is embrittled by dissolution of oxygen and nitrogen. The strategy of alloying with aluminium has been investigated a number of times (see e.g. [12–16]) in an attempt to develop ultrahigh-temperature alloys. Forming alumina as a protective scale rather than internal precipitates is difficult because niobium has such a high permeability for oxygen. Solid solution alloys have a maximum aluminium content of about 12 atom% at 1,4001C and consequently oxidize internally. The intermetallic NbAl3 does form alumina scales. However, because it is closely stoichiometric, this intermetallic is transformed by aluminium depletion to Nb2Al. Because the diffusivity of the latter phase is low, it cannot for long sustain alumina scale growth, and the alloy fails. Further work aimed at improving the oxidation resistance of NbAl3 by adding chromium has led to multiphase alloys. An alternative approach based on titanium additions to increase the solubility and diffusivity of aluminium, and additions of chromium and vanadium to decrease
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the oxygen permeability led to an optimized alloy composition of 25.4Nb–29.1Ti– 2.8Cr–3.5V–39.2Al, in weight percent. In each case, the problem was solved only by making niobium a minor component. The goal of an oxidation resistant niobium-based alloy was not achieved. To summarize, our ability to design alloys to resist attack by oxygen is good, although the complexities of multiphase alloy oxidation need further attention [17, 18]. Where compositional limits are set by the need to achieve mechanical or other properties, they can be outflanked by the use of a suitable coating. However, formation of a protective oxide scale is a necessary but not a sufficient condition for design success. In addition, the design must prevent or cope with mechanical failure of the scale.
12.3. DESIGN AGAINST OXIDE SCALE SPALLATION Provision of surplus chromium or aluminium in an alloy can give it the ability to regrow the desired oxide scale when spallation exposes the partially depleted substrate to hot gas. Given knowledge of the spallation rate and accurate information on alloy diffusion, we can predict the number of regularly spaced spallation events required to exhaust an alloy’s capacity for rehealing [19, 20]. The problem ~ data for the multicomponent alloys of practical here is lack of reliable ðkc =DÞ interest. In consequence, alloys are assessed for their ability to resist spallation by subjecting them to cyclic oxidation and the stress cycles resulting from the difference in coefficient of thermal expansion between alloy and oxide [21]. Cyclic oxidation experiments appear to yield acceptably reproducible results and provide a means for ranking different alloys exposed to the same duty cycle. Difficulties can arise, however, in predicting the effects of changes in the key parameters, temperature and cycle length. These problems result from the empirical nature of the spallation models used in making these predictions. What is needed is a quantitative understanding of the ways in which temperature, scale thickness and gas composition change the mechanism of scale failure, its frequency and extent. Considerable research is being conducted into these questions, involving detailed consideration of the dynamic oxide–alloy interface, stress distribution and relaxation, the formation, interaction and growth of defects, etc. While we await a successful outcome to this work, alloy design proceeds in a semi-empirical way. The discovery that sulfur is deleterious to scale adhesion (Section 7.5) has led to the production of superalloys with ultralow (less than 1 ppm) sulfur levels [22]. While this approach is not economically viable for lower cost heat resisting alloys, the other major design strategy of alloying with reactive elements is in principle applicable to all chromia and alumina formers. Our understanding of the several ways in which reactive elements contribute to spallation-resistant scales seems reasonable, but it is qualitative. In designing an alloy or coating for spallation resistance, we need to know which reactive element (or combination of them) is best for a particular material, the minimum level required, and the optimal form (alloy solute or oxide dispersion) and
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distribution. Apart from thermodynamic information on solubility limits and the possible existence of reactive element intermetallics and mixed oxides, very little guidance is available. In this situation, designs are developed on the pragmatic basis of prior descriptive knowledge and new cyclic oxidation test programmes.
12.4. DESIGN FOR RESISTANCE TO OTHER CORRODENTS AND MIXED GASES The classical theory of oxidation applies equally well to sulfidation, carburization and nitridation. Thus the rapid growth of sulfide scales is predictable from the high diffusion coefficient values characteristic of many sulfides. Similarly, the extremely fast rates observed for internal carburization and nitridation are accounted for by the high permeabilities of many alloys for carbon and nitrogen. When the Wagner model is extended [23–25] to take account of the low stability precipitates and the resulting incomplete reaction of alloy solute metals, excellent quantitative agreement is attained (Section 6.6). Exploiting this success to design corrosion-resistant alloys is difficult in the case of sulfidation and apparently impossible in the case of carburization. Sulfidation-resistant alloy formulations have been developed to form stable, slow-growing sulfides. These materials contain large amounts of refractory metals in intermetallic phases, and are not practical alloys. They might, however, constitute useful coatings for service in reducing sulfidizing atmospheres. Alloying austenitics to prevent internal carburization in reducing environments appears not to be feasible (Section 9.4). The problem is similar to that of niobium noted earlier: oxidant permeability in the alloy matrix is simply too high. Furthermore, in reducing gases which are supersaturated with respect to carbon (aC W 1), metal-dusting attack on iron-, nickel- and cobalt-based alloys must be dealt with. Elucidation of the different dusting mechanisms has been hampered by the development of metastable states: Fe3C on ferritic alloys and carbon-supersaturated metal in the case of both ferritics and austenitics. The absence of diffusion and solubility data for the carbon-supersaturated metal renders quantitative calculation impossible. However, it now appears that nucleation and growth of graphite could be important in controlling the overall reaction rate [26, 27]. More work is required for a full understanding of the dusting reaction. However, a practical route to the design of carbon resistance is through alloy compositions which will form protective oxides capable of excluding carbon. Thermodynamic analysis succeeds in predicting the conditions necessary to favour oxide rather than carbide. Almost all process gases are oxidizing to alumina formers, and most are oxidizing to chromia formers. Kinetic analysis methods to determine N B;min values necessary to support external oxide growth rather than internal carburization have not yet been developed. However, design on the basis of preventing internal oxidation appears to succeed for initial isothermal exposure to carburizing–oxidizing gases.
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The success of this approach is limited by the fact that oxide scales are not impermeable to species such as CO. It also fails to deal with the competition between oxide scale rehealing and internal carburization which determines the outcome of temperature cycling during exposure to oxidizing–carburizing gases. Oxide scale formation can also provide protection against corrosion by sulfur (Sections 8.6 and 8.9). In this case, however, the success of thermodynamic analysis in predicting conditions leading to oxide rather than sulfide scales is much less certain (Section 4.6). Sulfur adsorption and enrichment on the scale surface leads to a local environment that differs from the bulk gas, and can stabilize chromium sulfide. To avoid this problem, it is necessary either to make the gas more oxidizing or to change the alloy to an alumina former. The greater stability of Al2O3 relative to the sulfide underlies the superior performance of these alloys. However, the service temperatures involved may make Al2O3 formation difficult for many materials. High-temperature pre-oxidation, or the use of aluminium-rich coatings or the selection of an Fe–Cr–Al–Y alloy are then the available solutions. Unfortunately, there is very little information available for the performance of engineering alloys under realistic, i.e. temperature cycling, sulfidizing–oxidizing conditions. Long-term cyclic corrosion experiments under controlled gas atmospheres are required. Analogous cyclic carburization–oxidation experiments have been carried out for a number of alloys, but far more information is desirable for a wider range of temperatures and gas compositions. Similarly, information is required for corrosion performance under imposed load conditions, so that the combined effects of surface attack and fatigue or creep can be examined.
12.5. FUTURE RESEARCH As has been said by a number of people, prediction is a difficult business, particularly when it concerns the future. In trying to identify possible future directions for research, it seems sensible to consider the factors motivating research groups and organizations as they make their choices. Closely related are the needs, choices and policies of the bodies that fund the research: private industry and government agencies. In a utilitarian age, research sponsors look to achieve value for their money rather than merely satisfying the curiosity of the researchers. While it is not difficult to identify high-temperature corrosion research which is at once fundamentally interesting and also of potential practical value, it nonetheless behoves researchers to consider closely the meaning of ‘‘value’’ to their sponsors. It is obviously associated with improving alloys and coatings so as to better provide the required mechanical performance at high temperatures in aggressive environments. The value of these improvements lies in the ability they confer on designers and operators to achieve desired process changes. This connection between materials technology and process design exists because so many processes already operate at or near the capability limits of the materials
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currently employed. Some desired process changes require significant advances in materials technology. An example is the desire to increase gas turbine inlet temperatures. Other changes can be accommodated by substituting already available, but more expensive, materials for those in current service. The research opportunity in such instances is to develop cheaper materials with the required capabilities. To proceed beyond these generalizations to the specification of particular research goals requires detailed analysis of each technology, and preferably some knowledge of the business plans of the organizations involved. Publicly available information of this sort is understandably scant. Nonetheless, it is possible to extrapolate from current research activities to the immediate future, and to consider what other activities might arise out of current government and societal pre-occupations. Finally, it is possible also to use the earlier parts of this chapter in an attempt to identify areas where advances in fundamental understanding might yield practical benefit.
12.5.1 Gas turbines An enormous research effort has been expended and continues still on the development of materials for service as hot stage components at ever higher inlet temperatures. Superalloy development is aimed at achieving high-temperature strength, and component design relies on coatings for corrosion resistance. Coating development aims at producing improved TBCs, including their underlying bondcoats. Current research pre-occupations include improved resistance to erosion and impact damage, and prevention of ceramic topcoat spallation. Spallation results from the combination of bondcoat oxidation and thermal cycling. Platinum-modified NiAl coatings progressively rumple, developing an undulating surface which ultimately induces cracks in the adjacent topcoat [28]. The cause of rumpling is the subject of dispute. In the case of MCrAlY bondcoats, abrupt delamination occurs at the TGO–bondcoat interface when imperfections penetrating the TGO form. The imperfection generation process is not fully understood. Lifetime predictions for TBCs are based on a critical TGO thickness [29]. However, the time and temperature dependence of the resulting predictions are the same as those of other diffusion-controlled compositional and microstructural changes occurring in the TBC system. A detailed mechanistic description allowing lifetime prediction awaits completion.
12.5.2 Electric power generation The total amount of electric power generated worldwide is increasing rapidly as Asia industrializes. This trend will presumably be continued in Africa. The majority of newly installed capacity is thermal, largely coal fired. An obvious consequence is a large increase in greenhouse gas emission, an issue considered in the next subsection. Technological change will result from the increasing use of
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supercritical and ultrasupercritical boilers throughout the world. The higher steam temperatures (6001C and perhaps even higher) mean that heat exchanger tubing operates at significantly higher temperatures than in conventional boilers, where the steam temperature is about 5401C. Improved corrosion resistance is being sought at minimal increase in materials cost. Laboratory testing of candidate steels has been conducted in heated air. Unfortunately, the encouraging results produced in that work have since been shown to be misleading. The introduction of water vapour to the reaction gas causes much more rapid oxidation of the intermediate chromium level steels involved. Clearly there is a need for testing under realistic conditions, including temperature cycling. Alternative technologies for the more efficient production of electric power from coal are under consideration. Most involve gasification, combustion of the resulting H2–CO mixture to drive a gas turbine, and utilization of the heat in raising steam that drives a conventional turbine. The efficiency of this ‘‘integrated gasification combined cycle’’ (IGCC) is attractive, as seen in Table 12.1, and is only slightly decreased by carbon capture. However, the technology presents some very significant materials challenges. These have contributed to the significant commissioning difficulties experienced with IGCC technologies (Figure 12.1). Gasifier designs vary, and are affected by coal quality. In many cases, the gasifier itself is a refractory-lined vessel, although weld overlays can also be used. Problems arise in the handling of the product gas. This can contain sulfur impurities and will be laden with dust. Cleaning the gas before its supply to a gas turbine is essential. In addition, extraction of heat from the gas will involve the use of heat exchangers. Metallic components of the gas-handling system must withstand reducing, strongly carburizing and perhaps sulfidizing gases. The performance of candidate alloys and coatings under realistically simulated conditions will need to be investigated experimentally. The possibility of underground coal gasification is being investigated. The in situ gasification of coal has the attraction of replacing a coal mine and a gasification plant, both of which are capital intensive. Conveying the product synthesis gas (H2 plus CO) from its underground source to surface facilities can be expected to involve a drop in temperature, and the risk of metal dusting. Table 12.1
a
Thermal efficiency (Z) of power generation from fossil fuelsa [30, 31]
Technology
Z (%)
Conventional coal fired Supercritical coal fired Ultrasupercritical coal fired Combined cycle gas fired IGCC
32–34 39–42 42–47 52–60 40–43
With no carbon capture.
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Figure 12.1 IGCC availability after commissioning of several demonstration units (excluding operation on back-up fuel).
The use of land-based gas turbines instead of coal-fired boilers for base load power generation reduces CO2 generation. However the very long operating periods will require high-performance coatings, reliable life expectancy prediction and on-line monitoring capabilities. Slow alloy-coating interdiffusion processes can, in the long term, degrade bondcoat performance. The current research efforts on more stable coatings [32] and diffusion barrier coating layers [33] seem likely to continue and expand.
12.5.3 Petrochemical and chemical process industries A diversity of high-temperature processes is used to produce many widely used commodities, such as materials (metals, cement, plastics), fertilizers and fuels. Expanding markets combined with limited resources will presumably continue to drive the search for improved process efficiencies. Process changes can also result from altered feedstocks, the development of new catalysts and the desire for increased profitability. The higher process temperatures used to enhance efficiency will test materials capabilities. Indeed, an American process equipment technology planning exercise [34] identified a key need as ‘‘fundamental models for corrosion behaviour of alloys’’. Very high temperature processes are usually carried out in refractory-lined vessels. The refractory lining is commonly cast (in the same way as concrete) onto the steel shell of the vessel, to which it is held by a large number of metal anchors. A common arrangement is illustrated in Figure 12.2. Because the refractory has some degree of porosity, the anchors are in contact with process gases. There is a
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Figure 12.2 Alloy anchors holding two-layered refractory lining (courtesy of Antec Engineering Pty. Ltd.).
large temperature drop across the refractory lining thickness. Consequently, the heat-resisting alloy chosen for the anchors must be able to resist corrosion over a range of temperatures up to a maximum somewhat below that of the refractory hot face. Increases in process temperatures can often be accommodated by the refractory, but are limited by the temperature capability and corrosion resistance of the anchors.
12.5.4 Greenhouse gas emission control Greenhouse gas abatement strategies based on emissions trading schemes or tax and regulation schemes are intended to provide powerful economic incentives for the introduction of technological change. The rate at which such schemes are introduced and spread internationally is difficult to predict. The first of these, the European Union emissions trading scheme, commenced in 2005 with a three-year trial. The second phase, from 2008 to 2013, introduces more realistic emission caps. Other countries are introducing or at least considering similar schemes. These schemes are aimed at reducing emissions of CO2, the principal greenhouse gas produced by industrialized economies. Technological changes which result are of two sorts: avoidance of CO2 production and modification of existing technologies to allow the capture and storage (sequestration) of CO2 emissions. The avoidance strategy replaces existing technologies, for example, wind power turbines replace coal-fired steam power turbines to generate electric power; nuclear replaces thermal power; solar energy is used to heat water; hydrogen fuel cells generate power. Biomass combustion to raise steam, and fermentation to produce ethanol are in a similar category. The concept is that the biomass would otherwise decompose, releasing at least some of its carbon content into the atmosphere
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anyway. Harnessing that carbon produces energy, at what is sometimes claimed to be no net carbon cost. To the extent that the biomass is existing waste, and to the degree that its decomposition products would enter the atmosphere rather than being retained in soil, this is correct. However, the effort involved in biomass collection and handling prior to combustion can vitiate the carbon economics of the operation. An exception is provided by bagasse, the waste remaining after sugar has been extracted from crushed cane. Combustion of bagasse to raise steam is a traditional practice, and improving its efficiency is desirable. Raising crops for the express purpose of providing biomass is also carbon neutral: CO2 removed from the atmosphere by photosynthesis is returned to it by combustion. Counting the carbon costs of fertilizing, raising, harvesting and transporting the crops, while allowing for the social costs and benefits of likely adverse effects on food crop prices but increased liquid fuel supplies, makes for an interesting exercise. The significance of biomass combustion from the corrosion point of view lies in the very different ash chemistries that result. Alkali metal contents can be high, and the possibility of molten deposits is increased. Modifications to coal or gas-fired power generating technologies range from those which increase efficiency (producing less CO2 per unit of power) to those which capture the CO2. The latter approach is made more feasible by burning the coal with oxygen rather than air, thereby avoiding the need to subsequently separate CO2 from nitrogen. Alternatively, coal is gasified to produce synthesis gas that is subsequently burnt. In both cases, the exhaust gas is CO2 plus water vapour. The need to handle this mixture at high temperatures could drive research into suitable materials, as very little has been published to date on the resulting corrosion.
12.6. FUNDAMENTAL RESEARCH The fundamentals of high-temperature corrosion science continue to provide a fertile area for research. One reason for this is undoubtedly the existence of technological needs, some of which are examined in Section 12.5. In addition, scientific research in this area is prompted by much the same factors as in any other field: new and puzzling observations, new techniques and new theories. Although no completely new theories of high-temperature oxidation have emerged in recent years, theories and models from other areas have been applied. The methods of fracture mechanics [35–37] have yielded a much improved understanding of scale spallation and cracking. The development of quantitative methods for predicting the probability of scale failure as a function simultaneously of scale thickness, and oxide microstructure, cycle frequency, heating and cooling rates and system chemistry, including gas-phase composition, remains to be achieved. The physical nature of the scale–metal interface is obviously important. Pieraggi and Rapp [38] have modelled the interface in terms of misfit
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dislocations. Further investigation, experimentally by TEM and atom probe microscopy, and theoretically via atomistic calculations, seems warranted. These approaches might improve our understanding of the interactions between sulfur, reactive elements and the metal–oxide interface. New characterization techniques have been applied to the dissection of oxidation mechanisms with considerable success. When EPMA was used to define metal distributions in alloy scales, the results assisted greatly in deducing mechanisms. Similar information on oxygen diffusion was obtained by using SIMS to probe isotope profiles. Subsequently developed techniques are providing information on the nanoscale necessary to understand grain boundary and other interface processes. The widespread adaption of FIB milling to produce TEM foil samples is likely to prove important. The ability to rapidly produce these foils from precisely located positions in reaction zones means that interfaces are easily captured for examination. The new atom probes are providing atomic resolution images for both conducting and non-conducting materials. Volumes of 106–107 atoms can be analysed in reasonable times. Application of this technique to the study of interfacial interactions among reactive element metals, alloy solvent metal, scale constituents and species derived from the gas phase would be of interest. EBSD now provides a rapid method for identifying the orientations of grains intersected by a polished surface. It is therefore suitable for application to traditional metallographic cross-sections, where it can identify preferred growth directions of corrosion products and any orientation relationships they may have with the parent alloy phases.
12.6.1 Grain boundaries in oxide scales As has been demonstrated conclusively, transport in chromia and alumina is predominantly a grain boundary process (Sections 7.2 and 7.3). What is now needed is a modelling capability, presumably based on an atomic-level description of the movement of individual species within the boundary, together with a detailed understanding of the segregation process. Because the boundaries are surfaces, they will be surrounded by narrow space-charge regions. Because transport occurs within the same narrow zones, space-charge effects cannot be ignored. Experimental measurement of grain boundary diffusion parameters has been applied by Atkinson [39] to the growth of NiO scales. Application to Cr2O3 and Al2O3 is more difficult because of the importance of impurity effects. As seen in Chapters 4, 7, 9 and 10, alloy solvent metal, reactive element metals and gas-phase constituents all segregate to grain boundaries. Interactions between these various species and with the oxide constituents need also to be modelled. The application of high-resolution microscopy techniques to grain boundaries dosed with different mixtures of segregant species seems likely to be rewarding. The permeability of oxide scales to gaseous species such as CO, SO2 and H2O is an important but poorly understood phenomenon (Sections 4.5 and 10.4). The nature of the transporting species (ionic or molecular) has not been determined,
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and reasons for their slower penetration of alumina are not well understood. High-temperature adsorption experiments in mixed-gas atmospheres might contribute to an understanding of the complex interaction effects reported.
12.6.2 Water vapour effects The multiple ways in which water vapour interacts with oxides have made an understanding of the overall situation elusive. The different behaviour of alloys in pure steam and in air–steam mixtures has further complicated the set of observations. Part of the difficulty in arriving at an understanding is the sensitivity of the oxidation result to small differences in exposure conditions. A review [40] of a comparative testing exercise, in which P92 alloy samples were exposed at 6001C and 6501C for 1,000 h in different laboratories revealed variations in scale thickness of 40–240 mm at 6501C. Some of the reasons were obvious, such as whether the steam was aerated or not. Additional changes were associated with steam pressure, flow rate, diluent argon levels and cooling procedures after the experiment. When chromia scales are formed, the presence of water vapour improves scale–alloy adhesion. In the case of alumina scales, spallation is promoted by the presence of water vapour. In addition, the presence of water vapour alters the rates at which transient alumina phases are transformed, thereby modifying the oxidation rate [41]. A systematic investigation of the interactive effects of water vapour and reactive element additions on the cyclic oxidation of different chromia and alumina formers is desirable.
12.6.3 Nucleation and growth phenomena The classical theories based on Wagner’s diffusion analyses all assume steadystate behaviour, and provide little guidance on how to achieve that desirable state. As already noted, forming the desired scale at intermediate temperatures ~ speeds formation of an oxide can be difficult. While we know that increasing D scale of the diffusing metal, we lack information on the surface nucleation and growth phenomena which must also be involved. Electron microscopy has been used to observe the initial formation of oxide islands on pure metal surfaces. Differential pumping of the microscope allows a small pressure of oxygen to be maintained around the specimen, while a high vacuum in the remainder of the column maintains a stable electron beam. Extension of the technique to alloys exposed to mixed gases is experimentally challenging, but might prove rewarding. The importance of nucleation and growth in the formation of internally precipitated oxide was first recognized and analyzed by Bohm and Kahlweit [42]. While that treatment was applicable only to very high stability precipitates, it showed clearly the difficulty of performing calculations in the absence of information on precipitate-matrix surface free energies and on oxidant activity coefficients. The same difficulties arise in treating the nucleation and growth of graphite, the essential feature of metal-dusting reactions.
References
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Currently, we have no ability to predict the rates of dusting reactions. There are qualitative indications that graphite nucleation, its growth and the diffusion of carbon to the nucleation or growth sites are all important, but a quantitative assessment of the contributions of these different processes to overall rate control is lacking.
12.7. CONCLUSION The deficiencies of the classical theory of oxidation have long been known and indeed were recognized by the original authors. In deliberately excluding from consideration the complexities of oxide microstructure and mixed-gas environments, Wagner was able to solve an otherwise intractable problem. Given that not even calculators, let alone computers, were available at the time, the decision to consider simple cases is seen to be eminently reasonable. Moreover, the treatment yielded considerable insight into the oxidation problem, one which continues to be of value. Modern approaches to alloy microstructure control through the modelling of phase transformation and grain growth kinetics are of interest in this context. Their application to the evolution of scale microstructure with time and temperature, and perhaps to initial transient oxidation will surely be explored. The complexities of corrosion in mixed gases are in need of resolution. After all, the gases encountered in practice are almost all of mixed composition. Work done to date has taught us how to avoid a number of deficiencies in experimental design. It has also shown us the necessity for using realistic reaction conditions and for being cautious in applying accelerated corrosion testing. Importantly, it has identified points of focus for future research. Mechanical scale failure continues to be an issue of great importance. Empirical research on optimizing the reactive element effect for particular alloys and coatings is complemented by theoretical and experimental research based on adhesion theory and a fracture mechanics approach. Research into high-temperature oxidation dates from 1920. Many quite difficult problems have been solved, but others await resolution. As in other fields of science and technology, past research provides a useful basis for future investigations.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.
G. Tamman, Z. Anorg. Chem., 111, 78 (1920). N.B. Pilling and R.E. Bedworth, Chem. Met. Eng., 27, 72 (1922). N.B. Pilling and R.E. Bedworth, J. Inst. Met., 29, 529 (1923). J. Frenkel, Z. Phys., 35, 652 (1926). W. Schottky and C. Wagner, Z. Phys. Chem., 11B, 163 (1930). C. Wagner, Z. Phys. Chem. B, 21, 25 (1933). C. Wagner, J. Electrochem. Soc., 99, 369 (1952). C. Wagner, Z. Elektrochem., 63, 772 (1959). C. Wagner, Corros. Sci., 8, 889 (1968).
548
Chapter 12 Alloy Design
10. C. Wagner, Corros. Sci., 5, 751 (1965). 11. R.E. Lobnig, H.P. Schmidt, K. Henneson and H.J. Grabke, Oxid. Met., 37, 81 (1992). 12. R.C. Svedberg, in Properties of High Temperature Alloys, eds. Z.A. Foroulis and F.S. Pettit, The Electrochemical Society, Pennington, NJ (1967), p. 331. 13. R.A. Perkins, K.T. Chiang and G.H. Meier, Scripta Metall., 22, 419 (1988). 14. J. Doychak and M.G. Hebsur, Oxid. Met., 36, 113 (1991). 15. V. Gauthier, C. Josse, J.P. Larpin and M. Vilasi, Oxid. Met., 54, 27 (2000). 16. S. Taniguchi, H. Tanaka and T. Maeda, Mater. Sci. Forum, 522–523, 625 (2006). 17. M.P. Brady, B. Gleeson and I.G. Wright, JOM, (January), 16 (2000). 18. D.J. Young and B. Gleeson, Corros. Sci., 44, 2345 (2002). 19. D.P. Whittle, Oxid. Met., 4, 171 (1972). 20. J.A. Nesbitt, J. Electrochem. Soc., 136, 1518 (1989). 21. J.L. Smialek and C.A. Barrett, in ASM Handbook, Materials Selection and Design, ASM International, Materials Park, OH (1997), Vol. 20, p. 589. 22. R.C. Reed, The Superalloys: Fundamentals and Applications, Cambridge University Press, Cambridge (2006). 23. J.S. Kirkaldy, Canad. Met. Q., 8, 35 (1969). 24. E.K. Ohriner and J.F. Morral, Scripta Metall., 13, 7 (1979). 25. M. Udyavar and D.J. Young, Corros. Sci., 42, 861 (2000). 26. J. Zhang and D.J. Young, ECS Trans., 3, 27 (2007). 27. D.J. Young, Mater. Sci. Forum, 522–523, 15 (2006). 28. A.G. Evans, D.R. Mumm, J.W. Hutchinson, G.H. Meier and F.S. Pettit, Prog. Mater. Res., 46, 505 (2001). 29. R.A. Miller, J. Amer. Ceram. Soc., 67, 517 (1984). 30. C. Henderson, International Energy Agency, http://www.iea.org/Textbase/publications/free_ new_Desc.asp?PUBS_ID ¼ 1978 31. E. Ikeda, A. Lowe, C. Spero and J. Stubington, Technical Performance of Electric Power Generation Systems, Cooperative Research Centre for Coal in Sustainable Development, Pullenvale, Queensland (2007). 32. T. Izumi, N. Mu, L. Zhang and B. Gleeson, Surf. Coat. Technol., 202, 628 (2007). 33. T. Narita, K.Z. Thosin, L. Fengqun, S. Hayashi, H. Murakami, B. Gleeson and D.J. Young, Mater. Corros., 56, 923–929 (2005). 34. Roadmap for Process Equipment Materials Technology (2003), http://www1.eere.energy.gov/ industry/imf/pdfs/mtiroadmap.pdf 35. H.E. Evans, Int. Mater. Rev., 40, 1 (1995). 36. M. Schu¨tze, Protective Oxide Scales and their Breakdown, Institute of Corrosion and Wiley, Chichester (1997). 37. J.A. Nychka, T. Xu, D.R. Clarke and A.G. Evans, Acta Mat., 52, 256 (2004). 38. B. Pieraggi and R.A. Rapp, J. Electrochem. Soc., 140, 2844 (1993). 39. A. Atkinson, Phil. Mag. B, 55, 637 (1987); Solid State Ionics, 28, 1377 (1988). 40. S. Osgerby and T. Fry, Measurement Good Practice Guide No. 74, National Physical Laboratory, Teddington (2005). 41. H. Goetlind, F. Liu, J.E. Svensson, M. Halvorsson and L.-G. Johansson, Oxid. Met., 67, 251 (2007). 42. G. Bohm and M. Kahlweit, Acta Met., 12, 641 (1964).
a
19.5 16 14 10 9.6 9.8 7.5 7.8 6.5 5 4.9 4.2 3 2 3.2
Waspaloy IN738 Rene´ 80 PWA 1480 SRR 99 Rene´ N4 Rene´ N5 MC2 CMSX-4 PWA 1484 TMS-82+ Rene´ N6 TMS-75 CMSX-10 TMS-138
Balance Ni.
Cr
Alloy
13.5 8.5 9.5 5 5 7.5 7.7 5.2 9 10 7.8 12.5 12 3 5.8
Co
3 3.4 3 5 12 4.2 6.2 5.0 5.6 5.6 5.3 5.8 6 5.7 5.9
Al
0.3 6 1.4 2.1 0.6 2 1.9 1.4 2 0.4 2.8
4.3 1.7 4
Mo
4 3 6 6.4 8.0 6 6 8.7 6 6 8 5.9
2.6
W
0.2
0.5
1.0
1.4 3.4 5 1.5 2.7 3.5
Ti
0.1
0.5
0.9
Nb
3 3 2.4 5.4 5 5.4 5.0
2.8
Re
12 0.9 4.8 7.1 5.8 6.5 8.7 6 7.2 6 7.2 5.6
1.7
Ta
Table A1 Precipitation strengthened nickel-based superalloy compositionsa (wt%)
0.1 0.1 0.1 0.15 0.1 0.15 0.1
0.15 0.15
Hf 0.1 0.1 0.03
Zr
2.0Ru
r2Fe
Other
APPENDIX
A
High Temperature Alloys
549
8–10.5 19–22 11 35 34–37 34–37 32 30–35 30–34 37 47 72 58–63 60–66 52 61 61 61 25 75 80
304 Stainless 310 Stainless 253MA 353MA 330 Stainless DS AC66 800 801 HR-120 45 TM 600 601 602CA 617 625 690 693 709 214 Nichrome
Balance Fe. Maximum.
b
a
Ni
Alloy
18–20 24–26 21 26 17–20 15–18 27 19–23 19–22 25 27 14–17 21–25 24–26 22 21 27 29 20 16 20
Cr
4.5
1–1.7 1.8–2.4 1.2 0.4 0.2 3.2
0.1
0.15 1.5 0.15–0.6
Al
0.1–0.2 0.3 0.17 0.24 0.38
0.15–0.6 0.75–1.5
0.15
Ti
0.05
0.1 0.1 0.05 0.08 0.15 0.1 0.25 0.07 0.02 0.02 0.01
0.08 0.04 0.09 0.05 0.08 0.15
Cb
Table A2 Wrought austenitic high-temperature alloy compositionsa (wt%)
0.5 0.1 0.1 0.1 0.5 0.2
1 1.5 1.7 1.5 0.75–1.5 1.5–2.5 0.2 1 1 0.6 2.7 0.5 0.5
Sib
0.5 0.1 0.2 0.1 1 0.5
1 1
0.5 1.5 1.5 0.7
2 2 0.6 1.7 2
Mnb
0.45Nb 1.5Mo, 0.2Nb, 0.16N 0.1Zr, 0.01Y
0.05–0.12Y, 0.01–0.1Zr 12.5Co, 9Mo 9Mo, 3.4(Nb+Ta), 0.3Co
Co-included in Ni specification
r3Co,2.5Mo, 2.5W, 0.7Nb, 0.2N
0.07Ce, 0.8Nb 0.8Cu
0.16N, 0.04Ce, 0.24Mo 0.13N, 0.05Ce
Other
550 Appendix A High Temperature Alloys
551
Appendix A High Temperature Alloys
Table A3
a
Ferritic alumina-forming alloy compositionsa (wt%)
Alloy
Cr
Si
Mn
Al
C
Kanthal A Kanthal AF Kawasaki R20 MA 956b PM2000b JA13
20.5–23.5 21 20 20 19 16
0.7
0.5
5.3 5.1 5.5 4.5 5.8 5.0
0.08
0.2
0.3
0.1
Other
0.01 0.01 0.01 0.03
0.08Ti, 0.06Zr 0.06La 0.5Ti, 0.5Y2O3 0.5Ti, 0.5Y2O3 0.3Y
Balance Fe. Mechanically alloyed.
b
Table A4
Oxide dispersion strengthened Inconel compositionsa (wt%)
Alloy
MA MA MA MA a
754 758 6000 760
Balance Ni.
Cr
Al
Ti
C
Y2O3
20 30 15 20
0.3 0.3 4.5 6.0
0.5 0.5 2.5
0.05 0.05 0.05 0.05
0.6 0.6 1.1 0.95
Mo
2 2
W
4 3.5
Other
1Fe 1Fe 2Ta
APPENDIX
B
Cation Diffusion Kinetics in Ionic Solids Contents
Thermodynamic Treatment Evaluation of Onsager Coefficients No oxygen potential gradient Oxygen potential gradient Chemical and tracer diffusion in ionic solids Reference
553 554 554 556 558 559
THERMODYNAMIC TREATMENT The description of Sections 2.5 and 2.6 is applied to the ternary solid solution (A,B)O in which cations A and B have the same valence. The anion sublattice is treated as immobile, and provides a solvent-fixed reference frame. For a p-type oxide, the species fluxes to be considered are those of the two cations, vacancies and positive holes. Because sites and charge are conserved, JA þ JB þ JV ¼ 0 ¼ JO
(B1)
2J V ¼ J h
(B2)
and the fluxes are clearly not independent. The entropy source expression n X T s_ ¼ J i rZi i¼1
leads to T s_ ¼ J AM rZðAM Þ þ J BM rZðBM Þ þ J V rZðVÞ þ J h rZðhÞ þ J OO rZðOO Þ
ðB3Þ
For clarity, the charges have been omitted from the point defect symbols. Application to Equation (B3) of the constraints in Equations (B1) and (B2) leads immediately to T s_ ¼ J AM r½ZðAM Þ ZðVÞ 2ZðhÞ þ J BM r½ZðBM Þ ZðVÞ 2ZðhÞ
ðB4Þ
553
554
Appendix B Cation Diffusion Kinetics in Ionic Solids
thereby identifying a set of relative building units (Section 3.4) whose potential gradients define the driving forces in a reduced set of flux equations J A ¼ L11 r½ZðAM Þ ZðVÞ 2ZðhÞ L12 r½ZðBM Þ ZðVÞ 2ZðhÞ J B ¼ L21 r½ZðAM Þ ZðVÞ 2ZðhÞ L22 r½ZðBM Þ ZðVÞ 2ZðhÞ
ðB5Þ
The defect reaction equilibria AðgÞ þ V 00M þ 2h ¼ AX M BðgÞ þ V 00M þ 2h ¼ BX M then allow simplification of Equation (B5) to J A ¼ L11 rmA L12 rmB
(B6)
J B ¼ L21 rmA L22 rmB
(B7)
Evaluation of the kinetic coefficients from absolute rate theory (Section 2.6) is now considered.
EVALUATION OF ONSAGER COEFFICIENTS No oxygen potential gradient Consider first the simple system in which no free carriers exist and consequently no net flux of vacancies is possible. Interchanges between nearest neighbours only are considered, and it is sufficient to examine two adjacent lattice planes normal to the diffusion direction, as shown in Figure B1. The site interchange mechanism automatically obeys the site conservation restraint. However, each interchange involves the movement of a vacancy, and must be balanced by a countercurrent vacancy movement. Because vacancy concentrations are low, the immediate return of the first vacancy to its former plane is the most likely mechanism. To contribute to diffusion, such a mechanism must involve the two
Figure B1 Site exchange model for diffusion in ternary oxide (A,B)O with fixed anion lattice. Vacancy indicated as V.
Evaluation of Onsager Coefficients
555
different cation species. The simplest microscopic mechanism which can fulfil these requirements is seen in Figure B1 to involve two successive steps. The net species flux from plane (1) to plane (2) in step (a) is found from Equation (2.110) to be ml2 nBn KBn aB an ðrZB rZn Þ RT
(B8)
ml2 nAn KAn aA an ðrZA rZn Þ RT
(B9)
J ðaÞ ¼ Similarly, it is found that J ðbÞ ¼
In addition, one can formulate an expression for the species flux as a single-step correlated transition from the initial to the final state of the mechanism, using an activated complex at equilibrium with each of these two states. Then for species B ð1Þ ð2Þ ð2Þ ð2Þ ð2Þ J 2 ¼ mln1 K1 ðað1Þ B an aA aA aB an Þ
(B10)
which after Taylor series expansion and retention of linear terms becomes J2 ¼
ml2 nI KI aA aB an ðrZA rZB Þ RT
(B11)
The quantity nI is found from the steady-state condition J 2 ¼ J ðaÞ ¼ J ðbÞ to be
nI ¼
K I aA K 1 aB þ nBn KBn nAn KAn
(B12) 1 (B13)
This expression is simplified by introducing the new variables m0i , which for Henrian solutions are strictly proportional to the species concentration m0i ¼ ai nin Kin
(B14)
Then Equation (B13) becomes nI ¼
nAn nBn m0A þ m0B
(B15)
Substitution of Equation (B15) together with the relationship KI ¼ KAn KBn
(B16)
into Equation (B11) yields J2 ¼
ml2 m0A m0B an ðrmA rmB Þ RT m0A þ m0B
(B17)
In the absence of free carriers, Equations (B1) and (B2) imply that J A ¼ J B , and the system is essentially a binary. Thus Equations (B6) and (B7) reduce to J B ¼ LAA ðrmB rmA Þ
(B18)
556
Appendix B Cation Diffusion Kinetics in Ionic Solids
Comparison of Equation (B17) with Equation (B18) yields LAA ¼
ml2 m0A m0B an RT m0A þ m0B
(B19)
Extension of this description to multicomponent systems is straightforward [1], and leads for a quaternary oxide (A,B,C,)O to the result J B ¼ ðfAB þ fBC ÞðrmB rmA Þ þ fBC ðrmC rmA Þ J C ¼ fBC ðrmB rmA Þ ðfAC þ fBC ÞðrmC rmA Þ
ðB20Þ
ðB21Þ
where fij ¼
0 0 ml2 mi mj an RT m0i þ m0j
(B22)
Thus LBB ¼ fAB þ fBC LBC ¼ LCB ¼ jBC LCC ¼ fAC þ fBC
(B23)
and the Onsager reciprocal relationships are explicit. The above treatment is applicable to a diffusion experiment conducted at uniform oxygen activity. Even when positive holes are present, their concentration and that of the cation vacancies are uniform as a result of the equilibrium 00 1 OX O þ V M þ 2h ¼ 2O2ðgÞ
We now consider the oxide scaling process, where an oxygen potential gradient exists, and both vacancies and positive holes will move.
Oxygen potential gradient Consider first a binary metal-deficit oxide M1dO containing divalent cation vacancies and positive holes as the only defects. An immobile anion sublattice is again taken to provide a solvent-fixed reference frame, and we examine only the cation sublattice in the microscopic kinetic model shown in Figure B2. Mechanism II is seen to obey both the zero net current constraint and the local charge neutrality condition through the correlated motion of matching numbers of vacancies and positive holes. Using the same procedures as above, we find the component fluxes due to this mechanism to be J IIV ¼ oA ðrmA 2rmh rmV Þ
(B24)
Evaluation of Onsager Coefficients
557
Figure B2 Site exchange models for diffusion of doubly charged vacancies and positive holes.
1 J IIA ¼ J IIh ¼ J IIV 2
(B25)
where oA ¼
m0A m0h ml2 0 RT mh þ 2m0A aV
(B26)
and m0h ¼ ah nh Kh
(B27)
and the relations mA ¼ ZA ;
mV þ 2mh ¼ ZV þ 2Zh
have been employed. Comparison reveals that LAA ¼ oA
(B28)
in this binary system. This description is extended to a ternary metal-deficit oxide (A,B)1dO in which cation vacancies and positive holes are the only defects. A microscopic kinetic model for the motion of the second cation is shown as mechanism III in Figure B2. By analogy with Equation (B24), J III V ¼ oB ðrmB 2rmh rmV Þ 1 III III J III B ¼ J h ¼ J V ; 2
J III A ¼0
(B29) (B30)
It is clear that mechanisms II and III produce no cross-effect between the cations. Nonetheless such an effect arises through the operation of mechanism I, which is
558
Appendix B Cation Diffusion Kinetics in Ionic Solids
also available to this oxide. Summation of component fluxes due to the operation of all three mechanisms leads to J A ¼ oA ðrmA rmV 2rmh Þ fAB ðrmA rmB Þ
(B31)
J B ¼ oB ðrmB 2rmh rmV Þ fAB ðrmB rmA Þ
(B32)
which can be rearranged to yield J A ¼ ðoA þ fAB ÞðrmA rmV 2rmh Þ þ fAB ðrmB rmV 2rmh Þ
ðB33Þ
J B ¼ fAB ðrmA rmV 2rmh Þ ðoB þ fAB ÞðrmB rmV 2rmh Þ
ðB34Þ
These are of the form of the phenomenological Equations (B5), and Onsager reciprocity is again seen to be explicit. The correlation between cation fluxes is seen to arise through site conservation, whereas the correlation between the net total cation flux and positive hole flux is due to electrostatic coupling.
Chemical and tracer diffusion in ionic solids The relationship between diffusion in a multicomponent solid and tracer diffusion in pure binary oxides is sought. The situation of counterdiffusing cations associated with an immobile sublattice is examined. A tracer diffusion experiment involves interchange of labelled and unlabelled cations in the absence of any oxygen potential gradient. No vacancy flux is generated, and J An ¼ LrðmAn mA Þ
(B35)
where denotes the tracer species. The coefficient is evaluated from Equation (B19), yielding J An ¼
ml2 m0A m0An an rðmAn mA Þ RT m0A þ m0An
(B36)
A tracer is an ideal solute, and Equation (B36) is rewritten as J An ¼
ml2 m0A m0An mA þ mAn an rmAn 0 0 RT mA þ mAn mA mAn
(B37)
with mi the molar concentration of the indicated component. Recalling the definition of m0i in Equation (B14), and setting nAV KAV ¼ nAn V KAn V we find from Equation (B37) that DAn ¼ l2 nAV KAV aV and a corresponding expression is found for DBn.
(B38)
Reference
559
For interdiffusion of two different cations A and B, we use Equation (B17) to evaluate the flux. Since the cations are of equal valence, rmA ¼ rmB and, for an ideal or Henrian solution (Section 2.3) Equation (B17) becomes JA ¼
ml2 m0A m0B mA þ mB an rmA RT m0A þ m0B mA mB
(B39)
Substituting for m0i from Equation (B14) and for Din from Equation (B38) we obtain DAn DBn JA ¼ ðmA þ mB ÞrmA (B40) mA DAn þ mB DBn whence ~ ¼ D
DAn DBn ðmA þ mB Þ mA DAn þ mB DBn
(B41)
This description can be extended to quaternary oxides (A,B,C)O [1]. It should be noted that the assumption of Henrian solution behaviour can be in serious error. An analogous relationship (2.135) was found for binary alloys to result from the differing intrinsic metal mobilities, which led to compensating bulk material flow. No such flow is possible in ionic solids if, as supposed, the anion sublattice is truly immobile. It is instead the electrostatic potential or field (developed by charge separation within the solid) that brings into balance the fluxes of charged species having different mobilities.
REFERENCE 1. J.S. Kirkaldy and D.J. Young, Diffusion in the Condensed State, Institute of Metals, London (1987).
APPENDIX
C
The Error Function Contents
The Error Function Reference
561 563
The error function is frequently encountered in solutions to the diffusion equations for infinite and semi-infinite media. It is defined by Z z 2 erfðzÞ ¼ pffiffiffi expðu2 Þdu p 0 with u a dimensionless, dummy variable. The function has the properties erfð0Þ ¼ 0 erfð1Þ ¼ 1 erfðzÞ ¼ erfðzÞ d 2 erfðzÞ ¼ pffiffiffi expðz2 Þ dz p For small z 1 2 X ð1Þn z2nþ1 erfðzÞ ¼ pffiffiffi p n¼0 ð2n þ 1Þn!
and for z W 1 erfðzÞ 1
1 expðz2 Þ X ð1Þn ½1 3 5 . . . ð2n 1Þ pffiffiffi 2n z2nþ1 p n¼0
The error function is available on spreadsheets. Its tabulated values (and those of its derivatives and integrals) are available in Ref. [1], and Table C1 lists some numerical values. The complementary error function defined by erfcðzÞ ¼ 1 erfðzÞ also appears in a number of solutions to the diffusion equations.
561
562
Table C1
Appendix C The Error Function
The error function
z
erf(z)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.2 2.4 2.6 2.8 3.0
0 0.056372 0.112463 0.167996 0.222703 0.276326 0.328627 0.379382 0.428392 0.475482 0.520500 0.563323 0.603856 0.642029 0.677801 0.711156 0.742101 0.770668 0.796908 0.820891 0.842701 0.880205 0.910314 0.934008 0.952285 0.966105 0.976348 0.983790 0.989091 0.992790 0.995322 0.998137 0.999311 0.999764 0.999925 0.999978
Reference
563
Solutions to the Fick Equations which take error function forms x Cðx; tÞ ¼ F erf pffiffiffiffiffiffi 2 Dt correspond to parabolic penetration kinetics. If a location of fixed composition, Cðx; tÞ ¼ C1 , such as a phase boundary, moves with time, it follows from the above solution that X erf pffiffiffiffiffiffi ¼ Constant 2 Dt with x ¼ X where C ¼ C1. Therefore
pffiffiffiffiffiffi X ¼ Constant 2 Dt
If the error function has the value 0.84, the well-known approximation X2 4Dt results.
REFERENCE 1. H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, Clarendon Press, Oxford (1959).
APPENDIX
D
Self-Diffusion Coefficients Contents
Tabulated Data References
565 566
Measured self-diffusion coefficients
Q D ¼ Do exp RT
for substitutional and interstitial solutes in binary alloys are summarized in Tables D1 and D2, respectively. Table D1
a
Self-diffusion coefficients in substitutional binary alloys
Solute–Solvent
Do (cm2 s1)
Q (kJ mol1)
Reference
Cr–Ni Al–Ni Cr–Fe (a) Cr–Fe (g) Al–Fea
1.1 1.0 8.2 0.25 0.27
272.6 260 250.8 263.9 188
[1] [2] [3] [4] [5]
Chemical (interdiffusion) coefficient.
Table D2
Self-diffusion coefficients for interstitial solutes
Solute–Solvent
Do (cm2 s1)
Q (kJ mol1)
Reference
O–Ni N–Ni C–Ni O–Fe(a) O–Fe(g) N–Fe(g) C–Fe(g) C–Fe(a)
0.049 0.42 0.15 0.037 5.75 0.70 0.33 0.033
164 135 138 98 168 166 147 87
[6] [7] [8] [9] [9] [10] [11] [12]
565
566
Appendix D Self-Diffusion Coefficients
REFERENCES 1. 2. 3. 4. 5. 6. 7.
8. 9. 10. 11. 12.
K. Monura, H. Suto and H. Oikaua, Nippon Kink. Gakk, 28, 188 (1964). W. Gust, H.B. Hintz, A. Lodding, H. Odelius and B. Predel, Phys. Stat. Sol., 64, 187 (1981). A.W. Bowen and G.M. Leak, Met. Trans., 1, 1695 (1970). P.J. Alberry and C.W. Haworth, Met. Sci., 8, 407 (1974). K. Hirano and A. Hishunima, J. Jpn. Inst. Met., 32, 516 (1968). J.W. Park and C.J. Altstetter, Met. Trans. A, 18A, 43 (1987). R.P. Ruby and D.L. Douglass, in High Temperature Corrosion of Advanced Materials and Protective Coatings, eds. Y. Saito, B. Onay and T. Maruyama, North-Holland, Amsterdam (1992), p. 133. S.K. Bose and H.J. Grabke, Z. Metallk., 69, 8 (1978). J.H. Swisher and E.T. Turkdogan, Trans. AIME, 239, 426 (1967). H.J. Grabke and E.M. Peterson, Scripta Met., 12, 1111 (1978). C. Wells, W. Betz and R.F. Mehl, Trans. AIME, 188, 553 (1950). R.P. Smith, Trans. AIME, 224, 105 (1962).
SUBJECT INDEX acidic dissolution, 388 acidic fluxing, 389–390 activation energies, 70–71, 110, 112, 116, 118–119, 122, 130–131, 321, 322, 480 for oxide scale growth, 83 active oxidation, 131 activity coefficient/gi, 43, 56, 205, 299, 405, 546 adsorbed sulphur/sulphur adsorption, 161, 162, 354, 448, 449 adsorption, 66–68, 349, 479 adsorption constant, 427 adsorption of H2O/H2O adsorption/water vapour adsorption, 468–472, 479, 492 Ag2O, 262, 302 alloy 800, 74, 444, 449, 515, 525–526, 528 alumina/Al2O3/aluminium oxide, 219–225, 316–325, 488 aluminium depletion, 515, 536 alumina forming alloys/alumina formers, 201, 220, 224, 243, 344, 347, 350, 355, 383, 468, 513, 514 alumina phase transformations, 219–226 aluminium/Al, 191, 222, 231, 237–241, 371–372, a-Al2O3, 219–243, 307, 318, 488, 523 g-Al2O3, 220, 224 d-Al2O3, 220 y-Al2O3, 220, 221, 222, 223, 224, 347 Al2S3 , 368, 371–372, 377, 382 AlxMo2S4/Al0.55 Mo2S4, 376 Al(OH)3, 468 ash, 544 basic dissolution/basic fluxing, 388, 390 boilers, 463, 540–542 Boltzmann-Matano analysis, 65 Bondcoat, 6, 8, 331, 540, 542 Boudouard reaction, 178, 400, 401, 430, 442 boundary layer, 69, 132 breakaway kinetics, 474 breakdown/breakaway oxidation, 238, 473, 475–480, 529 building units, 85, 89–91, 92, 95, 554 bursting, 178 b-NiAl, 191, 220, 222, 225, 227, 331, 332, 352, 371 b-Ni(Pt)Al, 334 carbide dissolution, 190, 233, 234 carbide oxidation, 267, 310, 444
carbide solubility product, 404, 405 carbon deposition, 178, 398, 400, 422, 423, 429, 440 carbon deposition/graphite precipitation, 178, 398, 400, 422, 423, 429, 440 carbon graphitization , 441 carbon nanotube, 424, 425 carbon permeability/carbon permeabilities, 296, 297, 354, 404, 416, 421, 440, 441, 443 carbon permeability of oxide, 354 carbon solubility, 174, 402, 405, 419, 421, 441 carbon steel, 1, 70, 128 carbon uptake, 435, 442 carburization constants/carburization rates, 408, 420, 421 catalysis/catalyse, 142, 155, 163, 400, 425, 435, 441, 449 cation hydration, 470 cellular M23C6, 413 cellular precipitation, 272, 284–290, 312 cellular reaction, 168 cementite decomposition/Fe3C decomposition, 423, 425, 426, 427, 429 cementite disintegration/Fe3C disintegration, 425, 431 cementite particles, 425, 434 Chapman-Enskog, 69, 460, 463 chemical diffusion coefficient, 62, 66 chemical potential, 30, 31, 43, 50, 52, 53, 55, 58, 84, 91, 92, 207, 333, 334, 503 chemical vapour deposition, 448, 464 chromia/Cr2O3/chromium oxide, 187–193, 326–330, 352–354, 459–466, 480–484, 487–488 Cr2O3 solubility/Cr2O3 solubilities, 274 chromia forming alloys/chromia formers, 187, 188, 200, 304, 345, 351, 391, 410, 421, 443, 459, 502, 525 chromium/Cr, 4–5, 147–150, 367–368, 372–373, 432–434, 412–415, 534–537 chromium carbide precipitation, 403, 405 chromium depletion, 194, 327, 349, 408, 462, 464 chromium volatilisation/chromium vapourisation, 459–462 coal, 140, 384, 399, 540–542, 543–544 coal gasification, 139–140, 362, 383, 399 coating, 5–8, 540, 542 Coble creep, 78 coefficient of thermal expansion, 478, 537
567
568
Subject Index
coking, 400, 422, 430, 432, 440, 442, 447 cold worked surface/cold working, 250, 353, 433, 436, 443, 536 combustion, 1–4 competitive adsorption, 67, 68, 174, 180, 479, 488 concentration profile/compositional profile, 115, 201, 207, 211, 214, 230, 235, 239, 333, 502, 515 continuous thermogravimetric analysis/ CTGA, 499, 520–521 copper-bearing steel, 235 copper-zinc/Cu-Zn, 62, 217, 219, 338, 535 corrosion rate constant, 17, 199 corrosion rate constant for Fe-4.4Al, 200 Fe-12Al, 200 Fe-28Cr, 200 Ni-10Al, 200 Ni-28Cr, 200 COSP/cyclic oxidation spalling program, 510 Cr-O-H vapour species, 460 cracking furnace/pyrolysis furnace, 9–10 creep, 9, 10, 74, 307, 399, 447, 517, 536, 539 critical precipitate volume fraction, 321 critical volume fraction of internal oxide, 302 cross effects, 53–54, 58–60, 63, 207, 266, 300 cyclic oxidation, 497–530 cycling frequency, 517, 529 carbides Fe3C, 402 Cr3C2, 402 Cr7C3, 402 Cr23C6, 402 M7C3, 406 Mo2FeC, 416 (CrMoFe)C, 416 SiC, 402 HfC, 343 Fe3AlCX, 435 Al4C3, 402 carburizing/carburization of chromium, 150, 285 Fe-25Cr, 254 Fe-20Ni-25Cr, 410 Fe-37.5Ni-25Cr, 252, 253 Fe-Cr, 408, 409 Fe-7.5Cr, 188 Fe-17Cr, 406 heat resisting steels, 304 Ni-Cr, 408 Fe-Ni-Cr, 407, 410 Ni-Nb, 408, 410 H101, 418 G4852, 418 G4868, 418 602CA, 418
Fe-45Ni-35Cr, 418 Fe-28Cr, 444 45Pa, 418 60 Ni alloys, 420 carburisation rates, 408, 410, 412, 414, 415, 416, 418, 419, 420, 421 cold-worked, 242, 443 Cu-Zn/copper-zinc, 62, 217, 219, 338, 535 cyclic oxidation of MA956, 240 Zr-doped NiAl, 511, 517 Zr-doped Ni-Cr-Al, 514 Rene´ N5, 521, 549 800HT, 515 Haynes 214, 517 Ni-30Cr, 517 FeCrAl, 499, 500 FeCrAlY, 518 Iron aluminide, 518 NiAl, 519, 522 Ni-42Al, 518 Rene´ N5B, 516, 518 NiPtAl, 519 cyclic oxidation in CO/CO2, 525–526 1¼Cr-1Mo steel, 189 CrO3(g) CrO2(OH)4, 459, 460–465, 487, 522 Co-Fe/Fe-Co, 212 (Co,Fe)O/CoO-FeO, 212 Cu2O, 111, 119, 217, 218, 300, 338 CrS/CrS1-d, 143, 170, 367, 448 Cr3S4, 179, 368, 374 Cr2S3, 362, 363 CoSO4-Na2SO4, 391 Co3O4, 98, 108, 110, 111 Cr2N/chromium nitride, 114, 253, 277, 284, 289 CoO/cobalt oxide, 99-101, 172 Cu-15Zn, 218 Darken-Hartley-Crank equation, 62 Decarburization, 189, 229, 233 po2 dependence/Po2 effects, 259, 274, 446, 447, 479 deformation, 8, 9, 71–72, 74, 226, 309, 341–342, 536 depletion, 51, 155 depletion profile , 202, 204, 349, 504, 515, 517 diffusion, 16–18 diffusion couple, 62, 63–66, 101, 334 diffusion in chromia/diffusion in Cr2O3, 470 diffusion path, 39 discontinuous precipitation, 285, 286, 287, 289, 413 dissociation mechanism, 125, 472 dissociation pressure, 35, 472 dissolution, 45–46, 230–235, 388, 398 dopants/doping, 114, 115, 222, 487
Subject Index
effective diffusion coefficient, 117, 339, 349, 534 efficiency, 5, 392, 398, 399, 541, 542, 544 EDAX/EDS, 22, 23, 222, 276, 423, 437 Ellingham diagram/Richardson diagram, 36, 37, 368 enrichment, 26, 190, 191, 295 EPMA, 23, 85, 200, 545, equilibrium constant, 32, 35, 48, 56, 87, 99, 109, 129, 160, 180 error function, 64, 198, 415, 561–563A, eutectic, 105, 186, 363, 365, 391 exclusive scale formation, 196 evaporation, 68, 119, 390, 462, 467, 527 excess functions, 45 Fick’s first law, 16, 102, 199 fracture toughness, 76, 523 frame of reference/frames of reference, 60, 203, 204 Frenkel defects, 87, 108 fuel cells, 465, 543 ferritic chromium steels, 432–434 FeCrAl/Fe-Cr-Al, 222, 224, 225, 382, 434–435, 449, 499, 517, 518 Fe-Cr, 46, 200, 205, 261 Fe-Ni, 46, 48, 212, 416 Fe-41Ni, 214, 379 Fe-Ni-Cr, 23, 330–331, 355, 403, 407, 410, 413, 415, 416 FeAl2O4, 222, 320, 323, 376, 488 FeCr2O4, 49, 51, 320, 326, 329, 526 FeS/Fe1-dS, 33, 41, 96, 362 (Fe,Mn)O, 211, 212 Fe-Mn, 211, 373, 374, 379 (Fe,Ni)S/(Fe,Ni)1-dS/FeS-NiS, 215 FeCrAl, 222, 224, 225, 332, 434–435, 449, 511, 518, 519 FeCrAlY, 511, 518 FeAl2S4, 371 Fe3C, 177, 402, 424 FexMo6S8-Z, 374, 376 FeSO4-Na2SO4, 391 FeS2, 105 Fe-Al-S, 371 FeNb2S4, 377 (Fe,Ni)1–dS, 214–215 fayalite flux divergence, 492 fossil fuel, 41, 139, 181, 361, 383, 398 fuel cell, 457, 465, 543 gas flow velocity, 459 gas permeability in chromia, 354 gas phase diffusion/gaseous diffusion, 15, 130, 156, 175 gas turbine, 5, 6, 384, 399, 540, 541, 542 Gibbs equation, 31, 90, 92, 207
569
Gibbs-Duhem equation, 43, 62, 91–92, 95, 209 grain boundary diffusion/boundary diffusion, 74, 116–122, 135, 199, 239, 286, 322, 343, 418, 483, 487, 545 grain boundary diffusion coefficient, 329 grain boundary diffusion in Cr2O3, 487 grain growth, 117, 119, 483, 547 graphite-nickel epitaxy, 439 graphite nucleation, 425, 432, 437, 440, 441, 547 gravimetric/thermogravimetric, 13, 17, 120, 499, 520–521 green rot, 296, 444 greenhouse gas, 6, 181, 540, 543–544 greenhouse gas/greenhouse gases, 6, 181, 540, 543–544 growth stress, 71, 124, 341, 343, 345, 433 gas mixtures H2/H2O, 31–34, 127 CO/CO2, 31–34, 127 O2/H2O, 459, 463 N2/CO/CO2, 163 CO/CO2/SO2, 140 CO/H2/H2O, 432 H2/H2S, 382 hafnium, 343, 523 heat resisting alloys, 236, 252, 276, 355, 363, 415–421, 444, 529 heat resisting alloy compositions, 187 heat resisting steels/heat-resisting steels, 10, 187, 195, 304, 330, 331, 354, 383, 419, 444 hematite/Fe2O3, 36, 38, 39, 101, 456, 457 Henry’s law, 45 Hertz-Langmuir-Knudsen equation, 68, 69 Hochman-Grabke model for dusting, 422 hot corrosion, 383–391, 527, 536 hot shortness, 191, 235 hydration enthalpies, 470 hydrocarbon, 9–10, 398, 400, 401 hydrocarbon cracking, 9–10, 400 hydrogen generation, 457 H218O, 266, 478, 482 H2S dissociation, 378, 380 H2O dissociation, 457 HP, 10, 399 HP Mod, 11 IN 601, 188 Incoloy, 187, 250 Inconel, 187, 188, 316, 440, 551 interaction coefficients, 299–300 interface stability, 229–230 interfacial concentration, 203, 205, 238, 241, 242, 305, 502, 503, 504, 505 interfacial oxygen diffusion, 271 intergranular attack/intergranular oxidation, 267, 307
570
Subject Index
intermetallic, 220, 331, 332, 334, 347, 354, 371, 377, 383, 434, 435, 536, 538 internal carbide distributions, 410 internal nitridation , 250, 276, 277, 284, 285, 286, 297, 298, 301, 304, 413 internal oxidation of silver alloys, 262 Ag-Cd, 282 Ag-Al, 307 Cu-0.72Al, 300 Cu-10.16Ni-0.76Al, 300 Cu-20.11Ni-0.79Al, 300 Cu-30.07Ni-0.80Al, 300 iron-chromium/Fe-Cr, 259 Fe-5Cr, 249 Fe-7.5Cr, 188 Fe-10Cr, 248 Fe-17Cr, 248 IN 617, 252 nickel-aluminium/Ni-Al, 259, 290 Ni-2.5Al, 254 Ni-3.5Cr-2.5Al, 255 Ag-In, 263, 302 Ni-Cr, 307 Cu-Si, 263 Fe-35Ni-27Cr, 272 Fe-20Ni-25Cr, 286 Ni-4Al, 308 304 stainless steel, 296 310 stainless steel, 295 Ni-Cr-Al, 307 Ni-15Fe-25Cr, 254 Ni-Al-Si, 307 Ni-25Cr-10Fe-2.5Al internal oxidation beneath scale, 305–306 intrinsic diffusion coefficient, 62 intrinsic disorder, 88, 89, 110, 381 iridium/Ir, 352, 522 iron/Fe, 35, 40, 101–107, 127–131, 150–151, 161, 421–434 iron dissolution in graphite/iron dissolved in graphite, 423–428 Fe-Ni/iron-nickel, 46, 48, 212, 330, 379, 412, 416, 443 isotope distribution(s), 479 isotopically labelled gas, 478 Kanthal, 74, 187, 222, 224, 225, 336, 449, 488, 551 Kellogg diagram, 42 kinetic theory of gases, 68, 69, 460 Kirkendall effect, 60–63 Kirkendall voids, 333 Kroger-Vink notation/Kroger and Vink, 84, 85 lattice particle, 55–58 lattice species, 84, 85, 89–91, 92, 93, 134, 472, 492
linear kinetics, 15–16, 70, 128, 158, 159, 161, 164, 170, 322, 325, 363, 470 logarithmic rate equation, 21, 410 MA 956, 511, 517, 551 magnetite/Fe3O4, 36–39, 42, 101, 160, 470, 472–473, 489 manganese/Mn, 142, 155, 179, 189, 350, 365–366, 373–374 manganese effects, 350 markers/inert markers, 61, 62, 63, 377, 473 mass balance at moving interface, 203, 504 mass transfer, 66-71, 128, 155, 203, 281, 460, mass transfer coefficient, 69, 460 mechanical stress, 25, 26, 71, 525 metal carbides, 402, 444 metal deficit oxide, 87, 91, 95, 108, 109, 112, 113, 114, 556, 557 metal excess oxide, 87, 109, 110, 114 metal dusting, 435–439, 440, 446–448, 449, 524, 526, 538, 546 metal hydroxide, 458–468 metal hydroxide formation, 458–468 metal recession, 17, 441 metal sulphate/sulphate, 41, 162, 163, 170, 384, 386, 392, 527 metal sulphide formation, 361, 362, 390 metastable alumina/transient alumina, 220, 222, 224 metastable sulphide, 159–163 microbalance, 13, 499, 500, 520 molar volume, 16, 17, 31, 61, 166, 168, 198, 257, 271, 278, 307, 308, 403, 404, 525 molecular diffusion, 173, 478 molten salt, 385-389, 390, 392 molybdenum, 62, 232, 366, 374–376, 380, 382, 390, 416, 418–419 multiple oxidants, 298, 311, 316 metal dusting of heat resisting steels, 10, 11, 75, 188, 189, 304, 330, 419, 444 Fe/iron, 421–431 Fe-10Ge, 428 2¼Cr-1Mo steel, 431, 432 1Cr-½Mo steel, 431 Fe-Si, 432 ferritic chromium steels, 432–434 Fe60Cr, 434 FeAl, 434–435 FeCrAl, 434–435 Fe3Al, 434 Fe-15Al, 435 Fe-25Cr, 434 low alloy steels, 431–432 MA956, 435 Ni/nickel, 435–439 Ni-Fe, 439–441
Subject Index
Ni-Cu, 441 Fe-Ni-25Cr, 443 310, 444 800, 444 multilayered scales, 122 M7C3, 406, 410, 411, 416, 417 M23C6, 233t, 252, 253, 406, 410–415 416, 418, 443 MCrAlY, 8, 540 MnO, 33, 142, 175, 206, 350 MnS, 142, 362, 363, 365, 366, 368, 373, 374, 381 MnCr2O4, 25, 320, 350, 466 MnS, 142, 362, 363, 365, 366, 368, 373, 374, 381 MoS27d/MoS2, 284, 362, 366, 368, 374 Nabarro-Herring creep, 74, 307, 309 NaCl structure, 107, 206 Nernst-Einstein relationship, 94 Nickel, 4, 97-98, 151-154, 316–322, 435–439, 439–441 nickel aluminide coating, 75, 385 nickel dissolution in graphite/nickel dissolved in graphite, 441 nickel oxide/NiO, 87, 172, 193, 196, 305, 340 nickel particles, 436, 437 nickel-base alloys/nickel base alloys, 10, 186, 316, 327, 339 niobium, 363, 366, 376, 377, 382, 419–420, 536, 537 nitrogen solubility, 277 nodules, 307, 324, 325, 354, 461, 464 non-steady-state, 101, 202–206, 219, 379, 515 nonstoichiometry, 90, 97, 365 nucleation, 219, 222, 227, 242, 243, 249, 250, 266, 277, 278–284, 287, 290, 301, 312, 441, 448, 481, 483, 489, 546–547 nitridation/nitriding of Cr/chromium, 143, 180 Ni-Cr-Ti, 301 Fe-Ni-Cr, 413 Fe-20Ni-25Cr, 285, 286, 414 Fe-15Ni-25Cr Ni-Al, 320, 322, 324, 325, 334, 336, 339, 352, 383, 513, 522 Ni-23Al, 192, 516 b-NiAl, 8, 191, 192, 220–228, 236, 316, 331–332, 341, 346, 351, 371, 383, 490, 506, 523, 525 b-NiAl+Zr, 220, 221 Ni-Cr, 60, 194, 196, 200, 201, 202, 259, 263, 264, 265, 267, 269, 284, 300, 303, 305, 306, 307, 309, 326-328, 329, 330, 354, 403–406, 410 Ni-Cr-Al, 59, 222, 236, 238, 297, 300, 301, 307, 334–336, 337–338, 340, 373, 514, 528 Ni-Cr-Al-Y/NiCrAlY, 334–336 NiO-CoO/CoO-NiO, 209, 210 Ni-Fe/Fe-Ni, 46, 212, 330, 352, 379, 410, 412, 416, 417, 439, 443 NiAl2O4, 290, 316, 318, 319, 320, 323, 334, 516
571
NiCr2O4, 193, 194, 320, 327 NiS/Ni1-dS, 206, 214, 377, 379, 380, 387 Ni7S6, 379, 380 Ni3S2, 152, 162–163, 177t, 362, 365, 377 NiO, 385, 387, 388, 459t, 470, 482, 488, 516, 545 NiAl2O4, 290, 316–320, 323, 334, 516 Nb2S3, 366 NbS2/Nb1+dS2, 366, 368, 377, 382 NiNb3S6, 377 Na2SO4, 384–388, 390–391 NiSO4-Na2SO4, 391 n-type, 87, 109, 115, 486 orientation relationship, 284, 287–289, 412, 413, 442, 545 oxidation map/oxidation maps/oxide map, 316, 317, 334, 335, 336, 337, 355, 522, 535 for Fe-Cr-Al, 337 for Ni-Al, 317 for Ni-Cr-Al, 335 oxidation rate constants, 100, 486 oxide grain refinement, 484 oxide solubilities in molten Na2SO4, 388 oxide solubility product, 388 oxygen solubility, 46, 230, 255, 259, 274, 299–302, 321, 355, 535 18 O tracer, 126 oxidation of Fe-24Cr, 353 HK40, 348 Cobalt, 98-101, 108, 110, 111 iron, 127 nickel, 97–98, 108, 177, 179 chromium, 201, 255, 292, 296, 329, 347, 443, 480, 502 copper, 111, 218 silicon, 111, 131–133 Fe-28Cr, 187–188, 194 Fe-5Cr, 444 Fe-7.5Cr, 188, 329 Ni-Cr, 269 Cu-Zn, 217 Cu-Ni, 219 Ni-Si, 231, 259 Co-Si, 231 Fe-Cu, 236 Ni-Cr-Al, 222, 297, 514 Fe-20Cr-5Al, 226, 239 Ni-20Cr, 241 1¼Cr-1Mo steel, 189 Fe-10Cr, 248 Fe-17Cr, 248 Incoloy 617/IN 617, 250 silver alloys, 262 JA 13, 499 APM, 499 PM 2000, 187, 499
572
Subject Index
Kanthal, 222, 330 PWA 1484, 8, 522, 523, 524, 549 Ni-8Cr-6Al, 488 NiCrY, 480 Ni-25Cr, 480 P91, 187, 474, 475, 476 9% Cr steel, 456, 474, 476 Ni-Al, 263, 305 Fe-Cr, 259, 274, 305 Cu-Si, 263 Fe-Al, 267, 303, 305, 323, 324, 488 Ni-5Cr, 266, 267 Ag-Cd, 282 Ag-In, 302, 303, 307 Co-Ti, 284 Cu-Al, 300 Cu-Ni-Al, 300 Ni-Si-Al, 293, 340 Fe-Si, 259, 305 Ag-Al, 307 Pd-Ag-Sn-In, 307 Ni-4Al, 289 Ni-3.5Cr-2.5Al, 253, 255 60HT, 311 Fe-Ni-Cr, 330–331 Ni-Pt-Al, 331–333 Ni-Cr-Al, 222, 297, 307, 334–337, 340, 514 Fe-Si-Al, 340 Ni-28Cr, 4, 349 Ni-28Cr-3Si, 349 Ni-20Cr-3Mn, 350 oxidation-carburization/oxidizing carburizing/carburization and oxidation of chromium, 143, 147–150, 447, 525 of Ni-3.9Cr, 295 of chromium-bearing alloys, 296 of 304 stainless steel, 296 oxide-sulphide scale/sulphide-oxide scale, 104, 147, 177, 180, 364, 365 manganese/Mn, 138, 350, 365–366, 373–374 mixed gas reaction/mixed gas reactions, 175, 181 palladium/Pd, 307, 352 parabolic-linear rate equation, 112 parabolic rate constants, 83, 104, 105, 156, 312 Al2O3 scale growth, 221, 225, 334, 338, 343, 344, 352, 488 iron/Fe, 83 cobalt/Co, 83 chromium/Cr, 83 nickel/Ni, 83 Fe-15Cr-0.5C, 232–234 M-Cr alloys, 328 Ni-25Cr, 481 Ni-25Cr-0.1Y, 481 b-NiAl+Zr, 221
pellet experiment, 124, 125 permeability/permeabilities, 259, 263, 264, 404 Permeability of Carbon, 296, 354, 404, 416, 417, 421, 440, 441 Nitrogen, 298, 299, 526, 535, 536 oxygen, 257, 258, 259, 260, 262, 263, 264, 267, 334, 537 phase boundary process/phase boundary reaction, 18, 112, 148, 160, 469 phase rule, 39, 41, 49 Pilling-Bedworth ratio, 15 platinum group metals, 352, 355, 391, 472, 481, 483, 490, 491, 542 pores/porous/porosity, 8, 15, 68, 69, 84, 124, 125, 126, 143, 170, 173, 327, 334, 472, 474, 481, 488, 490, 492, 527, 534 power generation, 140, 362, 398, 399, 540–542 precipitate growth, 253, 267, 278, 280, 281, 284, 288, 290, 312 precipitate nucleation, 249, 250, 255, 266, 278–284, 287, 301, 312 precipitate solubilities, 274 precipitate volume fraction, 275, 321, 415, 526 pre-oxidation/pre-oxidized, 167, 169, 170, 172, 173, 179, 180, 302, 329, 330, 382, 447, 536, 539 pre-oxidised chromium, 170, 173, 179 phase diagram Fe-O, 38, 85, 101 Fe-S, 105, 106 Fe-S-O, 150 Fe-Cr, 260 Fe-Cr-O, 49, 194, 195, 251 Fe-Al, 260 Fe-Si, 260, 261 Fe-Al-O, 322, 324 Fe-Cr-S, 367 Fe-Mo-S, 375 Fe-Ni-S, 380 Fe-Cr-C, 407 Ni-S, 85, 86 Ni-S-O, 151, 387 Ni-Cr-O, 193 Ni-Cr-Al, 238 Ni-Al-O, 319 Ni-Pt-Al, 331, 332 Ni-Cr-S, 370 Na-S-O, 386, 387 Cr-O-C, 147 Cr-O-N, 147 Ti-Al-O Pt-Ni, 196, 197, 199, 200, 235 PtO2, 332 PtAl, 351 p-type, 87, 89, 94, 553
Subject Index
point defects, 54-55, 84, 85–89, 90, 105, 363, 391, 458, 484, 534 pyrolysis tube, 9 reactive elements, 243, 344–347, 349, 350, 353, 355, 419-420, 484, 492, 523, 537, 545 rehealing, 325, 434, 435, 443, 446, 448, 502–506, 515, 527, 529, 537, 539 rehealing/scale rehealing, 325, 446, 502–506, 539 rejection, 235, 285 Rhines pack, 259, 264, 265, 265, 269, 300, 303, 323, 339 ridge/ridges, 222, 223 SAD/selected area diffraction pattern, 23, 284, 413 scale detachment, 124–126, 343–344 scaling rates in SO2, 143, 155 Schottky defects, 87 secondary oxidant / secondary corrodent, 352–354 selective oxidation, 197–206 self-diffusion, 60, 66, 97–98 self-diffusion coefficients for interstitial solutes, 565 self-diffusion coefficients for substitutional binary alloys, 66 Sievert’s equation, 46 silica/SiO2, 131 silica volatilization, 466–468 silicon, 111–112, 131–133, 235, 347–350, 419, 421, 449 silicon effects, 347–349 silver, 112 silver sulphide/Ag2S, 125 SIMS, 25–26 sinh rate equation, 21 solid solution oxides/solid solution scales, 206–216 solid solution sulphides, 172 solubility product / Ksp, 48 solute enrichment, 260 spallation, 74–76 spallation fraction, 520, 529 spallation model, 506–513 spallation-oxidation map, 522 spinel, 49–51, 320, 323, 326–327, 329, 330–331, 350, 353, 478, 488 spinel free energies of formation, 320 304 stainless steel, 296, 526 430 stainless steel, 484 stainless steel/stainless steels, 295, 296, 350, 369, 444, 459, 484, 518, 526 standard free energies of reaction, 32–33 steam, 457–458, 462–463, 541, 543–544, 546
573
steam oxygen partial pressure, 10, 34, 41, 84, 108–109, 114, 188, 194, 463 steam cracking, 398–399 steam reforming, 398–399, 449 steel, 1–4, 35, 47, 70, 129, 130, 189–190, 191, 296, 330–331, 350, 431–434, 459, 526 strain, 71 strain energy, 279, 497, 511, 517, 519 structural units, 84, 89–91 NiAs structure, 107, 363, 365 sulphate formation, 162–163 sulphidation rate, 364 sulphide eutectic temperatures, 363, 365 Sulphide formation free energies, 361–362, 363 sulphide nonstoichiometry, 365 sulphur dioxide/SO2, 13, 41, 156–159, 163–168, 140–142 sulphur effect, 342–343 sulphur permeability of oxide, 354, 545–546 sulphur segregation, 345 sulphur solubility, 172, 383 superalloy/superalloys, 6–8, 385, 391, 522, 523, 529, 536, 540 supercritical boilers, 463 superheater, 189 supersaturation, 278, 280–283 surface finish, 242 surface tension, 279 surface recession, 197, 435 surface process/surface reaction, 15 synthesis gas, 139, 399–401 sulphidation of Co-Nb, 377 Fe-Al, 371–372 Fe-Cr, 367–369, 371 Fe-25Cr, 374 Fe-Cr-Al/FeCrAl, 372–373 Fe-Mn, 374–375 Fe-25Mn, 374 Fe-Mn-Cr, 374 Fe-25Mn-10Cr, 374 Fe-Mn-Al, 374 Fe-Mo, 375–376 Fe-Mo-Al, 376 Fe-28Mo-32Mn, 375 Fe-41Ni, 379 Fe-18.5Cr-4.9Ni-2.7Mo stainless steel, 369 Fe-Nb, 376–377 Fe-Nb-Al, 377 Fe-30Nb-3Al, 376 Fe-Ni, 379–380 iron aluminides, 382–383 iron/Fe, 104–107, 365, 367, 371 manganese/Mn, 365–366, 373–374 b-NiAl, 371, 383 gu-Ni3Al, 383 nickel aluminides, 383
574
Subject Index
Ni-Cr-Al/NiCrAl, 373 Ni-Mo, 374, 376, 382 Ni-Mo-Al, 376 Ni-Nb, 376, 377 refractory metals, 366, 376–377 refractory metal alloys, 376–377 silver, 112, 124–125, 262–263, 307 TiAl, 377 sulphidation rate/ sulphidation rates Co, 363, 364, 365 Cr, 363, 364 Fe, 363, 364, 365, 376 Fe-Cr, 367–368, 369 Mn, 363, 364, 365–366 Mo, 363, 364 Ni, 363, 364, 365 Ta, 363, 364 W, 363, 364 sulphidising-oxidising/oxidisingsulphidising/sulphidation oxidation/ oxidation sulphidation of chromium/Cr, 150 of cobalt/Co, 159, 169–172 of iron/Fe, 150–151 of manganese/Mn, 155, 158, 175, 177, 179 of nickel/Ni, 151–154, 159 of 310 stainless steel, 295, 444 SiO (g), 112, 131 SO2, 545 Si(OH)4, 466–467 SiO(OH)2, 466 Si3N4 , 186, 467 surface finish, 242 temperature cycle parameters, 517–519 ternary interactions, 330–341 thermal barrier coating/TBC, 6, 391 thermal cycling/temperature cycling, 434, 435 thermal expansion, 73–74 thermal stress, 517 thermochemical diagrams, 147–148, 150, 180 thermodynamic forces, 52 thermogravimetric analysis, 17, 520–521 third element effect, 338–341 time dependent interfacial concentration, 504 titanium effects, 350–351 tracer coefficient/tracer diffusion coefficient, 100, 104, 107 transient alumina, 225, 336, 343 transient Cu2O, 219 transient reaction/transient oxidation, 217 transport in chromia, 480–484 tungsten, 18
g-TiAl, 225 TiS, 366, 377 TiS2, 366 Ti3S4, 377 ultrasupercritical boilers, 541 vacancy/vacancies, 54 vacancy condensation, 489 vacancy flux, 227, 558 vapourisation, 468 viscous flow, 131, 133 void development, 489–490 void formation/cavity formation, 192 void nucleation, 227 volatile metal hydroxide, 458–468 volatilisation, 18 V2O5, 384 Wagner model oxide scaling, 93–96 internal oxidation, 248, 257–258, 260, 263–266, 273–278, 280–282, 300, 301 selective oxidation of one alloy component, 196–202 solid solution oxide scales, 206–216 transition from internal to external oxidation, 301–305 simultaneous internal and external oxidatiothird element effect, 249 water vapour, 402 water vapour effects on alumina growth, 488 water vapour effects on chromia scaling, 487–488 water vapour effects on silica growth, 466–468 water vapour effects on iron oxidation, 461, 464, 469, 472–474, 484, 489–490 water vapour effects on cyclic oxidation, 521–524 water vapour in oxide scales, 456–490 whiskers, 133, 220, 379–380 wrinkle development/rumple development/ wrinkling/rumpling, 343 wu¨stite/FeO/Fe1-a¨O, 3 yttria-stabilised zirconia, 6, 468 yttrium, 484 g-TiAl, 225, 236–237, 377 gu-Ni3Al dissolution, 191–192 zirconia, 465, 468 zirconium, 222 ZnO/Zn1-dO, 119, 217–219, 338
