COMBINED SURFACE AND GRAIN-BOUNDARY DIFFUSION

A mathematical analysis for the accumulation of tracer as diffused through a thin metallic slab by grain-boundary diffusion is presented. Boundary conditions on the side where the tracer is deposited consist of a small depletable source, and the grain-boundary concentration is enhanced by surface diffusion. Due to the mathematical difficulty associated with boundary conditions for combined grain-boundary and surface diffusion, two cases are studied: No accelerated surface diffusion and infinite surface diffusivity along with finite grain-boundary diffusivity. The difference between the accumulated tracer for the two cases is similar to the contribution from lattice diffusion only. Thus, for a relatively short diffusion time, grain-boundary diffusion analyses without surface diffusion complications are correct. © 1969 The American Institute of Physics.