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." (C) 2002 American Institute of
Physics