Method for Calculating Ionic and Electronic Defect Concentrations in Proton Containing Perovskites

A general numerical method for calculation of concentrations of vacancies and ionic and electronic defects in solids in equilibrium with two gas pressures is presented. The method is applied to 5 at% B-site doped SrCeO3in equilibrium with oxygen and water vapor. The model includes protons and electronic defects, as well as cation vacancies on theAandBsites. The 10 concentrations in the model are determined uniquely by solving the linear and mass action law type equations in a rational sequence. No approximations or truncations of the equations are necessary. No information on the magnitude of the Schottky-equilibrium constant,Ks, controlling the population of cation vacancies is available. Limiting values ofKswere tested to illustrate suppression and enhancement of cation vacancy formation in perovskites. Deviations from Sieverts law are demonstrated. Deviation of theA/Bratio from unity has the same effect on the proton content as an increase of the dopant level.