Kinetic considerations in the formation of electrical active grain boundaries in barium titanate and similar perovskites

Grain boundaries in ceramic barium titanate and related materials can be engineered in order to obtain desired transport behavior. Our ability to do so is closely related to kinetic limitations during the preparation. The close-packed structure of perovskites excludes native or foreign interstitials in the bulk. (Interstitial protons are regarded as OH(O)(<)bullet>, using the Kroger-Vink notation). Antisites are also unlikely due to size, charge and coordination number mismatch. The possible point defects are, therefore, substitutionals and vacancies. The kinetic limitations of these species, and the results in terms of grain boundary engineering, are considered in this contribution. A clear distinction between three different conditions is made. At very high temperatures, it is assumed that all the relevant defects are mobile and can equilibrate, at least locally. Hence, their concentrations are all functions of the degrees of freedom of the system. At lower temperatures, the cation sublattice is frozen. Therefore, the concentrations of metal vacancies and substitutional cations are constants and, from local electrical neutrality point of view, a new parameter becomes important: the concentration of frozen charge. The concentrations of electronic defects and oxygen vacancies in this metastable state are functions of temperature, oxygen partial pressure and frozen charge. The normalized concentration of frozen metal vacancies is calculated as a function of the doping factor, f (defined as the ratio between the electron concentration at a given state and at a reference state), and a nonstoichiometry parameter. Around room temperature, the anion sublattice is also frozen, and only electrons and holes exhibit significant transport properties.