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I. Lubomirsky, J. Fleig, J. Maier:
"Modeling of space-charge effects in nanocrystalline ceramics: The influence of geometry";
Journal of Applied Physics, 92 (2002), S. 6819 - 6827.

The distribution of mobile charge carriers in the space-charge regions at grain boundaries of ceramic materials was modeled. Delocalization effects are neglected, i.e., we consider ionic defects or polarons. The calculations were performed for cubic-shaped grains of equal size. When considering the size dependence, the standard free chemical potentials of the defects rather than the specific grain-boundary charge density or the defects´ boundary concentration were set to be constant in accordance with the core space-charge model. Although specific edge and corner effects are neglected in the present analysis and hence the structural potentials are invariant along grain boundaries, the accumulation or depletion of charge carriers turns out to be inhomogeneous along the grain boundary and to be particularly pronounced near grain edges and grain corners if the grain size was smaller than four Debye lengths. Especially the accumulation near grain edges can have a strong influence on the effective conductivity (though being a purely geometric effect). The modeling also predicts that a contact of two grains that differ only in size, leads to a redistribution of mobile ions between grains, provided that either one or both grain sizes are smaller than the double width of space-charge layers. Such a charge transfer between the grains can be viewed as a "heterosize charging."

http://dx.doi.org/10.1063/1.1516836