Finite-element calculations on the impedance of electroceramics with highly resistive grain boundaries: I, laterally inhomogeneous grain boundaries

Lateral inhomogeneities of grain boundaries caused by partially wetting gra in-boundary phases or pores induced in the grain boundary give rise to curr ent-constriction resistances close to grain-to-grain contacts. The present work presents a quantitative three-dimensional analysis of the resulting gr ain-boundary impedance. Numerical finite-element calculations of the impeda nce spectra of polycrystalline samples characterized by typical imperfect c ontact 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 s pots per grain as parameters. The magnitude of the effects that can be expe cted in realistic ceramics is emphasized, as well as the question of the ex tent to which further conclusions on the grain-boundary mechanism can be dr awn from the temperature, partial-pressure, bias, and grain-size dependence of the impedance spectra.