Unified description of interdiffusion in solids and liquids

This work presents a mathematical description of mass transport in multicomponent solution based on the Darken concept of drift velocity. The diffusion of components depends on the chemical potential gradient and on the stress that can be induced by diffusion and by boundary and initial conditions. The key postulate is cubic symmetry of a solid alloy, which implies a precise form for the stress tensor. In such a quasi-continuum, the energy, momentum, and mass transport are diffusion controlled, and the fluxes are given by the Nernst-Planck formulae. A modified form the Navier-Lame equation is postulated, and the resulting form of the continuity equation for energy is derived. It is shown that the Darken method is valid for multicomponent solid solutions as well as for liquids.