The role of Eshelby stress in composition-generated and stress-assisted diffusion

Abstract

The chemical potential used in interdiffusion analysis was derived by Li et al. in 1966 and by Larche and Cahn in 1982. It contains the trace of the stress tensor as the essential elasticity contribution to the configurational force conjugate to the material composition. As a result, the underlying diffusion equation is totally independent of any accompanying elastic field. In particular, when an alloy epifilm is annealed, the theory implies that the rather large lattice mismatch has no effect on the ensuing diffusion process. However, it is perhaps intuitively clear by now — almost 50 years since Eshelby published his first paper on energy momentum tensor in 1951 — that the trace of the (canonical) Eshelby stress tensor should be the total elasticity contribution to the desired configurational force. This conjecture is formally established in this paper for an n-component substitutional solid. Since the elastic energy is now a part of the chemical potential, the interplay between a composition-generated deformation and another elastic field may become important via the interaction energy. As an example, the effect of this interaction is calculated for the spinodal decomposition of a binary alloy solid/epifilm. The modification of the critical temperature is such that it is now a function of mismatch.