It was noted that the close-packed structure of perovskites excluded native or foreign interstitials from the bulk. Interstitial protons were regarded as being OHO▪; in terms of the Kröger-Vink notation. Antisites were also unlikely due to size, charge and coordination number mismatches. The only possible point defects were therefore substitutional atoms and vacancies. The kinetic limitations of these species, and the results in terms of grain boundary engineering, were considered here. A clear distinction was drawn between 3 different conditions. At very high temperatures, it was assumed that all of the relevant defects were mobile and could equilibrate; at least locally. Their concentrations were therefore all functions of the degrees of freedom of the system. At lower temperatures, the cation sub-lattice was frozen. The concentrations of metal vacancies and substitutional cations were then constant and, from a local electrical neutrality point of view, a new parameter became important. This was the concentration of frozen charge. The concentrations of electronic defects and O vacancies in this metastable state were functions of temperature, O partial pressure and frozen charge. The normalized concentration of frozen metal vacancies was calculated as a function of the non-stoichiometry parameter and the doping factor: the ratio of the electron concentration in a given state to that in a reference state. At around room temperature, the anion sub-lattice was also frozen and only electrons and holes exhibited significant transport properties.

Kinetic Considerations in the Formation of Electrical Active Grain Boundaries in Barium Titanate and Similar Perovskites. Y.Tsur: Interface Science, 2001, 9[3-4], 163-7