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

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Abstract
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.