Diffusion in 2 grain-boundary networks (parallel boundaries and square grains) was considered in order to analyze the effects of space-charge layers upon diffusion profiles. The space charge zones were supposed to be depleted of mobile charge carriers, leading to blocking of the transport of diffusing species. The finite element method was used to calculate numerically the concentration distribution and the corresponding integrated diffusion profiles. The accuracy of determination of the grain-boundary diffusivity from simulated profiles, by applying conventional equations, was estimated. Blocking space-charge layers led to a possible over-estimation of the grain-boundary diffusivity in the type-B kinetics regime. Moreover, they led to a significant shifting of kinetic regimes and extremely large diffusion times would have to be used in order to reduce errors when determining the grain-boundary diffusivity in the type-A regime.

Numerical Study of Grain Boundary Diffusion in Nanocrystalline Ionic Materials Including Blocking Space Charges. D.Gryaznov, J.Fleig, J.Maier: Solid State Ionics, 2006, 177[19-25], 1583-6