Simulation of Electrical Properties of Grain Boundaries in Titanate Ceramics

Abstract

Using a numerical simulation method, the electrostatic properties of grain boundaries in titanate ceramics (SrTiO₃ and BaTiO₃) are calculated by the combination of a defect chemistry model and the general potential equation. Based on these results and a simple three-dimensional “brick-wall-model” of the ceramic microstructure, an equivalent network is developed for the ceramic body which consists of a great number of R C-branches. Using this network it is possible to calculate the frequency dependence of the complex impedance of the ceramic. The results of the impedance simulation can be compared to experimental results. This comparison yields information about the charge transport across and along the grain boundaries and about the influence of the temperature, the bulk dopant concentrations, and the donor- or acceptor-like grain boundary interface states on the electrical properties of the grain boundaries. By using the simulation technique one gets additional information to interpret and understand the experimental results and to model the physical and electrical behaviour of the grain boundaries which mainly determine the electrical characteristics of the ceramic.