Statistical theory of diffusion in concentrated bcc and fcc alloys and concentration dependencies of diffusion coefficie
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OLIDS AND LIQUIDS
Statistical Theory of Diffusion in Concentrated bcc and fcc Alloys and Concentration Dependencies of Diffusion Coefficients in bcc Alloys FeCu, FeMn, FeNi, and FeCr1 V. G. Vaks, K. Yu. Khromova,b,*, I. R. Pankratova, and V. V. Popovc a National
Research Center “Kurchatov Institute,” Moscow, 123182 Russia Moscow Institute of Physics and Technology (State University), Moscow, 117303 Russia c Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620990 Russia * e-mail: [email protected] b
Received March 31, 2016
Abstract—The statistical theory of diffusion in concentrated bcc and fcc alloys with arbitrary pairwise interatomic interactions based on the master equation approach is developed. Vacancy–atom correlations are described using both the second-shell-jump and the nearest-neighbor-jump approximations which are shown to be usually sufficiently accurate. General expressions for Onsager coefficients in terms of microscopic interatomic interactions and some statistical averages are given. Both the analytical kinetic mean-field and the Monte Carlo methods for finding these averages are described. The theory developed is used to describe sharp concentration dependencies of diffusion coefficients in several iron-based alloy systems. For the bcc alloys FeCu, FeMn, and FeNi, we predict the notable increase of the iron self-diffusion coefficient with solute concentration c, up to several times, even though values of c possible for these alloys do not exceed some percent. For the bcc alloys FeCr at high temperatures T ≳ 1400 K, we show that the very strong and peculiar concentration dependencies of both tracer and chemical diffusion coefficients observed in these alloys can be naturally explained by the theory, without invoking exotic models discussed earlier. DOI: 10.1134/S1063776116070244
cussed below) have also been suggested [18, 19]. Kikuchi and coworkers used the Path Probability Method to describe diffusion in many different concentrated alloy systems [20–22]. However, only some simple models have been considered, and difficulties of generalizations to more consistent and general studies have been noted [22]. The recently-suggested master equation approach [23–30] opens opportunities for microscopic treatments of diffusion in alloys at any composition. This approach enables us to express all Onsager and diffusion coefficients via some statistical averages and microscopic interatomic interactions. These interactions can be calculated employing ab initio methods, while statistical averages can be evaluated using various methods of statistical physics. As the level of reliability of both ab initio calculations [3–5, 31, 32] and statistical methods [33–35] is steadily increasing, this approach seems to provide a basis for developments of microscopic theories of diffusion in alloys of any composition. First applications of the master equation approach to studies of diffusion in concentrated alloys have been made by Nastar with coworkers [24–26] (who call this a
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