Interdiffusion in oxides (A,B)O (I): A numerical study of point-defect relaxation phenomena

We have investigated the role of point-defect relaxation in the course of ternary solid-state reactions, by numerical solution of the appropriate sets of coupled continuity equations using a finite-element code. The theoretical analysis of the flux equations and transport coefficients in the (A,B)O system, obeying Manning's random-alloy model at sufficiently high temperatures, is summarized. The results of one- and two-dimensional diffusion reveal the limited validity of both the classical Boltzmann transformation and the often-postulated assumption of local equilibrium. The crucial role of boundary conditions with regard to vacancy relaxation is emphasized. Two-dimensional calculations in particular demonstrate the inverse Kirkendall effect near crystal surfaces. In addition the stability of this nonlinear diffusion process in response to small fluctuations in composition is scrutinized. The study shows that strong transient oscillations of point defect concentrations occur but always vanish after comparatively short diffusion times.