Point Defect Concentrations in Barium Titanate Revisited

An analytic link between the oxygen partial pressure and the concentrations of the point defects for given temperatures and A/B conditions is presented for perovskites. A clear distinction between three different conditions is made. These are the sintering conditions, an intermediate metastable state, and a low-temperature metastable state. The analytical solution for a metastable state resulting from nonequilibrated metal vacancies permits a more accurate and self-consistent approach to calculating the equilibrium constants from conductivity-P(O₂) data. One of the reasons for the higher accuracy is that there is no need to divide the existence regime into subregimes with different approximations to the electroneutrality equation (Brouwer approximation). An excellent fit of the experimental conductivity data to a single function with only two adjustable parameters over all conductivity-P(O₂) space is obtained. The relative importance of frozen-in metal vacancies and foreign acceptors is discussed for BaTiO₃.