Grain-boundary diffusion in thin films: I. The isolated grain boundary

Diffusion through grain boundaries in thin films is analyzed using a model with a single high-diffusivity plane perpendicular to the film. One surface of the film is maintained at unit concentration of the diffusing species, and a zero-flux boundary condition is applied at the other surface. It is shown that the region of the film where the diffusion species is supplied primarily by grain-boundary diffusion has a far smaller concentration gradient than that predicted by a similar model with semi-infinite geometry. As a result, calculations of grain-boundary diffusion coefficients in thin films based on the semi-infinite model may be in error by several orders of magnitude. Two methods for the analysis of thin-film diffusion data are described that should provide accurate values of grain-boundary diffusion coefficients.