INTERDIFFUSION IN MULTICOMPONENT SOLID-SOLUTIONS - THE MATHEMATICAL-MODEL FOR THIN-FILMS

A nonhomogeneous boundary value problem for interdiffusion in a solid multicomponent one-dimensional mixture showing constant concentration is analyzed. Darken's concept of separation of diffusional and drift flows is applied for the general case of diffusional transport in an r-component compound. The equations of local mass conservation, Darken's flux formula, the postulate of constant molar volume of the mixture, and the initial and boundary conditions form a self-consistent interdiffusion problem (the quantitative dynamical model). This problem is analyzed in open as well as closed systems and when the component diffusivities vary with composition. The variational form of the interdiffusion problem and the criterion of parabolicity are presented. Results of numerical simulation of interdiffusion in binary and ternary solid solutions of finite dimensions are presented. The development of the ''uphill diffusion'' concentration profile in the ternary alloy is displayed.