An expansion of the Fisher model for concentration dependent grain boundary diffusion

In accounting for concentration dependent grain boundary diffusion, an extra term is derived and added to the boundary condition in Fisher's Model for atomic transport in fast diffusing boundaries under the condition of low diffusant concentration resulting in an expanded model. The validity of this is evaluated using an implicit finite difference model which shows that a minimum of around 0.5–0.6 order of magnitude difference between the minimum and maximum grain boundary diffusion values is necessary for a significant effect to be observed. This was investigated for a grain boundary diffusion coefficient that exponentially increased and decreased with concentration. Whereas effects on measured grain boundary diffusion coefficients are evaluated to be negligible, the concentration dependency of the grain boundary diffusion substantially affects the elemental distribution in the surrounding of the grain boundary. The latter directly influences grain boundary related metallurgical phenomena such as grain growth or phase transformations in nanocrystalline materials.