Comprehensive linkage of defect equilibrium and phase equilibria through ferroelectric transition behavior in BaTiO3-based dielectrics

Defect and phase equilibrium have been investigated via the paraelectric-ferroelectric phase transition temperature () behavior of pure and equilibrated non-stoichiometric BaTiO3 powder samples. Through fabricating the BaTiO3 materials under conditions to preserve the equilibrium conditions with respect to Ba/Ti ratio, annealing temperature (T), and oxygen partial pressure (Po2), systematic variations in the phase transition temperature can be noted with respect to Ba/Ti ratio, T, and Po2. From the data extracted we can determine the solubility limit at each condition. The solubility regime, as determined through the variation, decreased with decreasing. 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. The formation enthalpy and entropy for the partial Schottky defect reactions was evaluated to be 2.32±0.1 eV and 10.15 for the BaO partial Schottky defect, and 2.89±0.3 eV and 8.06 for TiO2 partial Schottky defects equilibrated under air annealing conditions. Under low Po2 conditions, 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 cases, and also fully explains the solubility trends under low Po2Ìs. Universally the theory supports all the experimental data over different temperatures and Po2Ìs.