A self-consistent mean field theory for diffusion in alloys

Abstract

Starting from a microscopic model of the atomic transport via vacancies and interstitials in alloys, a self-consistent mean field (SCMF) kinetic theory yields the phenomenological coefficients L_ij. In this theory, kinetic correlations are accounted for through a set of effective interactions within a non-equilibrium distribution function of the system. The introduction of a master equation describing the evolution with time of the distribution function and its moments leads to general self-consistent kinetic equations. The L_ij of a face centered cubic alloy are calculated using the kinetic equations of Nastar (M. Nastar, Philos. Mag., 2005, 85, 3767, ref. 1) derived from a microscopic broken bond model of the vacancy jump frequency. A first approximation leads to an analytical expression of the L_ij and a second approximation to a better agreement with the Monte Carlo simulations. A change of sign of the L_ij is studied as a function of the microscopic parameters of the jump frequency. The L_ij of a cubic centered alloy obtained for the complex diffusion mechanism of the dumbbell configuration of the interstitial (V. Barbe and M. Nastar, Philos. Mag., 2006, in press, ref. 2) are used to study the effect of an on-site rotation of the dumbbell on the transport.