A generalization of the Fisher model for grain boundary diffusion was suggested which took account of diffusion along short-circuit diffusion paths, such as dislocations, in the bulk of grains. Three different penetration modes were found for the B-regime of grain-boundary diffusion. At short times, the penetration depth of the element which diffused along the grain boundary was given by the Whipple solution to the Fisher model; but with pipe diffusion coefficients for the dislocation cores instead of volume diffusivities. At intermediate times, the penetration depth was a weak function of time. At long times, the penetration depth again increased with time according to the Whipple solution. However, the rate of this increase was much lower than in the initial time period.

Diffusion along Grain Boundaries in Crystals with Dislocations. L.Klinger, E.Rabkin: Interface Science, 1998, 6[3], 197-203. See also: Acta Materialia, 1999, 47[3], 725-34