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D. Gryaznov, J. Fleig, J. Maier:
"Numerical study of grain boundary diffusion in nanocrystalline ionic materials including blocking space charges";
Solid State Ionics, 177 (2006), S. 1583 - 1586.

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

http://dx.doi.org/10.1016/j.ssi.2006.04.031

http://aleph.ub.tuwien.ac.at/F?base=tuw01&func=find-c&ccl_term=AC06587553