Substitutional diffusion in multicomponent solids with non-ideal sources and sinks for vacancies

Based on previous work by the authors the diffusion equations for a multicomponent solid are derived. Generation and annihilation of vacancies are described by an evolution law which is directly coupled with an eigenstrain rate. Manning’s correlation factor f is used in the kinetic factor for diffusion of vacancies. In addition to presentation of the diffusion equations, a rigorous treatment of the boundary conditions, assuming no or an ideal source and sink for vacancies at the surface, is presented. As an instructive example development of the site fractions of the components and the eigenstress state are demonstrated for a multicomponent chemically inhomogeneous layer on a substrate. Both the role of nonlinear terms and the correlation factor f in the diffusion equations are studied. Computational procedures to calculate to the proper boundary conditions are also outlined.