Mathematical Treatment of Competitive Surface and Volume Diffusion Processes

Equations are derived for the surface diffusion of atoms into a half-plane (the boundary of which is kept at constant concentration) under conditions in which atoms are simultaneously being lost into the bulk via a volume diffusion mechanism. Two coupled boundary valued problems arise which are solved by treating the volume diffusion as a perturbation. Methods of evaluating the coefficient D8 of surface diffusion are discussed. The final surface concentration Ŝ resulting from the parasitic effect of volume diffusion contains three leakage terms. These terms have the effect of altering the time dependence of the concentration. This formulation is useful in interpreting surface diffusion data obtained in the high-temperature range.