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The Poisson equation is used to calculate the drift velocity in the two-dimensional diffusion couple. This approach is based on the bi-velocity (Darken) method which combines the Darken and Brenner concepts that the volume velocity is essential in defining the local material velocity in multicomponent mixture at non-equilibrium. As an example the arbitrary binary system is considered. It is shown that (1) the two dimensional calculations should be applied with the stochastization method and (2) the drift term in mass conservation law does not affect the calculations. [ABSTRACT FROM AUTHOR]

Abstract: An approach to the problem of interdiffusion in multicomponent–multiphase system is presented. It couples bi-velocity (Darken) method, in which the mass conservation and volume continuity laws are considered, with the phase field model and is a generalization of the model based on the diffusion equation implemented in Dictra. The proposed bi-velocity phase field method allows computing the kinetics of the process, diffusive mass transport in every phase, concentration profiles, diffusion paths, and Kirkendall effect. The example problem presented here is a fundamental problem concerning the reactive diffusion at high temperatures in Al–Cr–Ni ternary system. It is a starting point that will allow modeling the coating composition to reduce interdiffusion and stabilize a desired microstructure, i.e., to extend coating life time. [Copyright &y& Elsevier]