Darken’s phenomenological description of diffusion in binary systems was used to treat interdiffusion in multi-component mixtures. A mathematical model, for interdiffusion within a layer of finite thickness, was derived which allowed for a constant concentration and a variable diffusivity of the components. On the basis of the concept of a generalized solution, an exact expression was derived for the evolution of the component distribution. An asymptotic approximation to the exact expression was also considered. This could be easily applied to various initial conditions. Analytical results, and the complete algorithm for finding density profiles, were presented for the elementary case of interdiffusion in a 2-component mixture with constant diffusion coefficients. Experimental and theoretical results for a Cu-Ni solid solution were presented.

M.Danielewski, R.Filipek: Journal of Computational Chemistry, 1996, 17[13], 1497-507