Diffusion in polycrystalline materials was investigated by means of finite-element simulations for constant-source conditions. The grain boundaries were assumed to provide rapid diffusion paths. Emphasis was placed on situations that typically occurred in nanocrystals. That is, where the diffusion length was significant compared with the grain size, and the influence of boundaries that were parallel to the surface became important; in addition to the perpendicular ones. Also treated was the influence of blocking space-charge layers which sandwiched core pathways and thus channelled the grain-boundary diffusion.

Finite Element Simulation of Diffusion into Polycrystalline Materials. D.Gryaznov, J.Fleig, J.Maier: Solid State Sciences, 2008, 10[6], 754-60