Comprehensive linkage of defect and phase equilibria through ferroelectric transition behavior in BaTiO₃-based dielectrics: Part 2. Defect modeling under low oxygen partial pressure conditions

Defect and phase equilibria have been investigated through the ferroelectric phase transition behavior of pure and equilibrated nonstoichiometric BaTiO₃ powders. The paraelectric-ferroelectric phase transition temperature (T_C-T) was found to vary systematically with materials fabricated with different Ba/Ti ratio (g^*) and under various oxygen partial pressure (Po₂) conditions.¹ The solubility regime, as determined through the T_C-T variation, decreased with decreasing.(Po₂) Determining the solubility limits and equilibrating the defect reactions at the solubility limits provide a direct approach to calculate the defect formation energies and provide data to test a new defect model for concurrent defect reactions of partial Schottky and reduction defects. A refined approach introduces a balanced equilibrium between the oxygen vacancy concentrations controlled by the partial Schottky and reduction reactions. In the limiting ambient cases the approach gives the expected results, and also fully explains the solubility trends under low Po₂'s. Universally, the theory supports all the experimental data over different temperatures and Po₂'s.