A general numerical method was presented for calculating the concentrations of vacancies, and ionic or electronic defects, in solids which were in equilibrium with 2 gas pressures. The method was applied to 5at%B-site doped material which was in equilibrium with O and water vapor. The model included protons and electronic defects, as well as cation vacancies on the A and B sites. The 10 concentrations which were required by the model were uniquely determined by solving linear and mass-action law equations in a rational sequence. No approximations or truncations of the equations were necessary. No information concerning the magnitude of the Schottky equilibrium constant, which controlled the population of cation vacancies, was available. However, limiting values of the constant were used to illustrate the suppression and enhancement of cation vacancy formation in perovskites. Deviations from Sievert's law were demonstrated. It was noted that deviations from unity, of the A/B ratio, had the same effect upon the proton content as did an increase in the dopant level.

Method for Calculating Ionic and Electronic Defect Concentrations in Proton-Containing Perovskites. F.W.Poulsen: Journal of Solid State Chemistry, 1999, 143[1], 115-21