The grain boundary impedance of random microstructures: numerical simulations and implications for the analysis of experimental data

The grain boundary impedance of polycrystalline materials is usually analyzed in terms of a simplified microstructure composed of cubic-shaped grains. In order to investigate the validity of such a “brick layer model”, impedance spectra of polycrystals with computer-generated microstructures (two-dimensional Voronoi diagrams) have been simulated. These calculations showed that the current density in polycrystals can be rather inhomogeneous and that the so-called grain boundary impedance depends on the bulk conductivity. Nevertheless, the corresponding grain boundary resistances, capacitances and relaxation frequencies are frequently close to the values expected from a brick layer model. The impact of these calculations on the analysis of grain boundary impedances caused by space charge depletion layers is discussed. It is shown in how far impedance parameters yield reliable space charge potentials. Measurements on polycrystalline SrTiO3 illustrate the suggested approach. In the quantitative analysis of these experiments, capacitances have been calculated from constant phase elements.