On the grain boundary diffusion theory of Fisher and Whipple

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Abstract
The theory of diffusion in grain boundaries was initiated by Fisher, using an idealized model in which a poorly diffusing half‐space (the crystal) is bisected by a thin well‐diffusing slab (the grain boundary), with a fixed concentration of diffusing material suddenly established at the free surface. In the present paper we first improve Fisher's result by removing one of his approximations. We then generalize Whipple's later exact solution to include anisotropicdiffusion in the crystal, and other changes; the generalized theory now contains both the original Whipple result and the improved Fisher result as special cases and displays individually the effects of the different assumptions.