Comprehensive linkage of defect and phase equilibria through ferroelectric transition behavior in BaTiO₃-based dielectrics: Part 1. Defect energies under ambient air conditions

Defect and phase equilibria have been investigated via the ferroelectric phase transition behavior of pure and equilibrated nonstoichiometric BaTiO ₃ powder samples. Through fabricating the BaTiO₃ materials under highly controlled conditions to preserve the equilibrium conditions with respect to Ba/Ti ratio, annealing temperature (T), and oxygen partial pressure (P_O2), systematic variations in the phase transition temperature can be noted with respect to Ba/Ti ratio and T. From the data extracted, we can then determine solubility limits. Equilibrating the defect reactions at the solubility limits provides a direct approach to identify and calculate the defect energetics. The phase transition temperature decreased with increasing concentration of the TiO₂ partial-Schottky defects (BaTi _1-δO_3-2δ) and the BaO partial-Schottky defects (Ba_1-δTiO_3-δ), and showed discontinuous changes in the two-phase region. The formation enthalpy and entropy for the partial-Schottky defect reactions was evaluated to be 2.32±0.1 eV and 10.15±0.7 k_B for the BaO partial-Schottky defect, and 2.89±0.1 eV and 8.0±1.5 k_B for the TiO₂ partial-Schottky defects equilibrated under air annealing conditions.