A computer program was developed for the simulation of the defect chemistry and electrostatics, for a single grain boundary in titanate ceramics, by means of a 1-dimensional scan perpendicular to the grain boundary interface. The fundamental features of the numerical treatment of the problem were the calculation of all point defect concentrations by coupling the laws of mass action to the electroneutrality condition, and the solution of the 1-dimensional discretized Poisson equation for the electrical potential by using the Newton algorithm for non-linear equation systems. It was found to be beneficial to control the distances of the discrete calculation points, in the spatial coordinate across the grain-boundary region, by using a tunable transformation function. On the basis of these results, the concentration profiles of all types of defect and mobile charge carrier, the space-charge density, the electrical field strength and the band-bending were calculated. As an example of the use of the technique, results were outlined for a grain boundary in acceptor-doped SrTiO3 ceramic.

R.Hagenbeck, L.Schneider-Stoermann, M.Vollmann, R.Waser: Materials Science and Engineering B, 1996, 39[3], 179-87