A model of grain boundary diffusion in polycrystals with evolving microstructure

We consider grain boundary diffusion in a polycrystal in which normal grain growth occurs simultaneously with diffusion. We assume that any point within the diffusion zone is swept a number of times by migrating grain boundaries, and develop a model which operates with the average concentrations of the diffusant in the planes parallel to diffusion front. We derive analytical expressions describing the diffusion profiles both for constant source and instantaneous source boundary conditions. Finally, we suggest a practical method for extracting the grain boundary diffusion coefficient from experimentally measured diffusion profiles. This method relies on microstructure characterization and requires the grain growth constant and grain growth exponent to be determined in the independent set of experiments.