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J. Fleig, J. Maier:
"Finite-Element Calculations on the Impedance of Electroceramics with Highly Resistive Grain Boundaries: I, Laterally Inhomogeneous Grain Boundaries";
Journal of the American Ceramic Society, 82 (1999), 3485 - 3493.

Lateral inhomogeneities of grain boundaries caused by partially wetting grain-boundary phases or pores induced in the grain boundary give rise to current-constriction resistances close to grain-to-grain contacts. The present work presents a quantitative three-dimensional analysis of the resulting grain-boundary impedance. Numerical finite-element calculations of the impedance spectra of polycrystalline samples characterized by typical imperfect contact patterns are performed and analyzed. The validity of existing models is checked, and an interpolation formula for the grain-boundary resistance is given, using the fraction of contacted area and the number of contact spots per grain as parameters. The magnitude of the effects that can be expected in realistic ceramics is emphasized, as well as the question of the extent to which further conclusions on the grain-boundary mechanism can be drawn from the temperature, partial-pressure, bias, and grain-size dependence of the impedance spectra.

http://dx.doi.org/10.1111/j.1151-2916.1999.tb02270.x