Statistical theory of diffusion in concentrated alloys
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RDER, DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
Statistical Theory of Diffusion in Concentrated Alloys1 V. G. Vaksa,*, A. Yu. Stroeva, b, I. R. Pankratova, and A. D. Zabolotskiya, b a
b
National Research Center “Kurchatov Institute,” Moscow, 123182 Russia Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, 141700 Russia *email: [email protected] Received January 20, 2014
Abstract—The earliersuggested master equation approach is used to develop the statistical theory of steady state diffusion in concentrated substitution alloys considering fcc alloys with the nearestneighbor pairwise interactions as an example. General expressions for the Onsager coefficients in terms of microscopic inter atomic interactions and some statistical averages are presented. We discuss methods of calculations of these averages using various statistical approximations and various approximations for description of vacancy cor relations, with the full taking into account the vacancy–solute interactions. Our simplest statistical approxi mation, called the “kinetic meanfield approximation” (KMFA), corresponds to using the meanfield approximation for statistical averages and the paircluster approximation (PCA) for calculations of thermo dynamic parameters; for dilute alloys, the KMFA is exact. To describe vacancy correlation effects at any con centrations, we develop both the nearestneighborjump approximation and the secondshelljump approx imation. We also describe methods to take into account fluctuations in statistical averages using the PCA, and to describe nonpairwise vacancy–solute correlations using the triple vacancy–solute correlation model. For each of approximations and methods developed, we derive expressions for the Onsager coefficients at any composition of an alloy. For binary alloys, we also present expressions for the diffusion coefficients. The results obtained can provide a basis for microscopic calculations of diffusion coefficients at any composition of an alloy. DOI: 10.1134/S1063776114070103 1
1. INTRODUCTION The existing microscopic theories of diffusion in alloys based on the random walk theory and the “vacancy–solute association–dissociation” models (to be called “traditional” theories) have been devel oped only for dilute alloys [1–9]. For the concentrated alloys, diffusion is usually described using various phe nomenological approaches [10–12], and some authors believe that “the nature of concentration dependence” of diffusion coefficients “has never been fully explained and there does still not exist any ade quate theories for describing such a dependence” [11]. Even for a dilute binary alloy AB with a low solute frac tion cB 1, calculations of linear in cB terms in diffu sion coefficients (“enhancement factors”) for both chemical and tracer solute diffusion seem to be not performed, while existing calculations of tracer sol vent enhancement factors (which are used, in particu lar, to estimate the microscopic parameters important for dif
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