Charge-compensation in barium titanate

Different charge-compensation mechanisms of aliovalent dopants on the cation sublattice of BaTiO₃ are analyzed. It is argued that for most cases, more than one compensating defect should be considered. The partition between the various defects is a function of the degrees of freedom of the system, if equilibrium can be assumed. On cooling, the system is passed through two different metastable states. In the first one, the metal sublattice is frozen, and includes any metal vacancies that might be present. In the second one, the oxygen vacancies are also frozen into the anion sublattice and only electronic defects can compensate for the total ionic charge. (The aliovalent dopants are compensated in the metastable states by both frozen vacancies and electronic defects). The different options in terms of the overall A/B ratio, the oxygen partial pressure during the sintering and the dopant types and concentrations are outlined. Some important works on this subject are reviewed. The consequences of this model are discussed with examples of technological importance.