The impedance of ceramics with highly resistive grain boundaries: validity and limits of the brick layer model

Abstract

Impedance spectroscopy is an important tool to investigate the electrical properties of grain boundaries. For the analysis of the impedance spectra cubic grains, laterally homogeneous grain boundaries and identical properties of all grain boundaries are usually assumed (brick layer model). However, in real ceramics these assumptions are generally violated. Using the finite element method we calculated the impedance of several polycrystals exhibiting highly resistive grain boundaries with microstructures and grain boundary properties deviating from the simple brick layer model. Detours around highly resistive regions (e.g. due to high grain boundary density or enhanced grain boundary resistivity) can play an important role and lead to grain-boundary semicircles depending on bulk properties and even to additional semicircles. Conditions are discussed within which the brick layer model allows for a reasonable evaluation of the spectra.