Numerical simulation of the defect chemistry and electrostatics at grain boundaries in titanate ceramics

A computer program was developed to simulate the defect chemistry and the electrostatics for a single grain boundary in titanate ceramics by a one-dimensional scan perpendicular to the grain boundary interface. The fundamentals of the numerical treatment of the problem are (1) the calculation of all point defect concentrations by coupling the laws of mass action and the electroneutrality condition and (2) the solution of the one-dimensional discretized Poisson equation for the electrical potential φ by the Newton-algorithm for non-linear equation systems. It turned out to be beneficial to control the distances of the discrete calculation points on the spatial x-coordinate across the grain boundary region using a tunable transformation function. Based on these results, the profiles of the concentrations of all defect types and mobile charge carriers, the space charge density, the electrical field strength and the band bending are calculated respectively. As an example, the results for a grain boundary in an acceptor-doped SrTiO3 ceramic are outlined.