Abstract
The thermodynamic extremal principle is used for the treatment of the evolution of a binary system under the assumption that all phases in the system are nearly stoichiometric with no sources and sinks for vacancies in the bulk. The interfaces between the individual phases are assumed to act as ideal sources and sinks for vacancies, and to have an infinite mobility. Furthermore, it is assumed that several phases are nucleated in the contact plane of the diffusion couple at the beginning of the computer experiment. Then, it is shown that the number of newly nucleated phases determines the maximum number of polyfurcations (i.e., branching of a single configuration into several distinct configurations) of the initial contact (Kirkendall) plane. The model is demonstrated on a hypothetical binary system with four stoichiometric phases. The inverse problem, namely, the determination of the tracer diffusion coefficients in newly nucleated phases from the thicknesses of new phases and the positions of polyfurcated Kirkendall planes, is treated too.
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References
H. Nakajima, The Discovery and Acceptance of the Kirkendall Effect: The Result of a Short Research Career,JOM, 1997,6, p 15–19
A. Paul, M.J.H. van Dal, A.A. Kodentsov, and F.J.J. van Loo, The Kirkendall Effect in Multiphase Diffusion,Acta Mater., 2004,52, p 623–630
C. Wagner, The Evaluation of Data Obtained with Diffusion Couples of Binary Single-Phase and Multiphase Systems,Acta Metall., 1969,17, p 99–107
S.R. Shatynski, J.P. Hirth, and R.A. Rapp, A Theory of Multiphase Binary Diffusion,Acta Metall., 1976,24, p 1071–1078
D.S. Williams, R.A. Rapp, and J.P. Hirth, Multilayer Diffusional Growth in Silver-Zinc Alloys,Metall. Mater. Trans. A, 1981,12, p 639–652
G.X. Li and G.W. Powell, Theory of Reaction Diffusion in Binary Systems,Acta Metall., 1985,33, p 23–31
E. Metin, O.T. Inal, and A.D. Romig Jr., Solutions to Multiphase Diffusion in Binary Metal Interstitial Systems,Metall. Mater. Trans. A, 2005,36, p 1407–1415
M. Kajihara, Relationship Between Temperature Dependence of Interdiffusion and Kinetics of Reactive Diffusion in a Hypothetical Binary System,Mater. Sci. Eng., A, 2005,403, p 234–240
F.D. Fischer and N.K. Simha, Influence of Material Flux on the Jump Relations at a Singular Interface in a Multicomponent Solid,Acta Mech., 2004,171, p 213–223
M.J.H. van Dal, D.G.G.M. Huibers, A.A. Kodentsov, and F.J.J. van Loo, Formation of Co-Si Intermetallics in Bulk Diffusion Couples: Part I. Growth Kinetics and Mobilities of Species in the Silicide Phases,Intermetallics, 2001,9, p 409–421
M.J.H. van Dal, A.A. Kodentsov, and F.J.J. van Loo, Formation of Co-Si Intermetallics in Bulk Diffusion Couples: Part II. Manifestations of the Kirkendall Effect Accompanying Reactive Diffusion,Intermetallics, 2001,9, p 451–456
J. Svoboda, I. Turek, and F.D. Fischer, Application of the Thermodynamic Extremal Principle to Modeling of Thermodynamic Processes in Material Sciences,Philos. Mag., 2005,85, p 3699–3707
L. Onsager, Theories and Problems of Liquid Diffusion,Ann. N. Y. Acad. Sci., 1945,46, p 241–265
F.J.J. van Loo, Multiphase Diffusion in Binary and Ternary Solid-State Systems,Prog. Solid State Chem., 1990,20, p 47–99
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Svoboda, J., Gamsjäger, E., Fischer, F.D. et al. Modeling of kinetics of diffusive phase transformation in binary systems with multiple stoichiometric phases. JPED 27, 622–628 (2006). https://doi.org/10.1007/BF02736564
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DOI: https://doi.org/10.1007/BF02736564