A density functional study of vacancy formation in grain boundaries of undoped α-alumina

Recent oxygen permeation experiments with α-alumina have shown that the two major diffusing species at the grain boundaries, i.e. oxygen and aluminum vacancies, switch over in terms of their dominance depending on the oxygen partial pressure at high temperatures (the so-called p-n transition). In order to investigate this transition behavior the formation energies of charged oxygen and aluminum vacancies at Al₂O₃ grain boundaries were evaluated using density functional theory. The electronic structures affecting the carrier concentrations are assessed for three types of grain boundaries. The ratios of the grain boundary band gaps relative to the bulk value lie in the range of 0.6-0.85 depending on the degree of grain boundary misorientation. From the formation energies we find that, at band gaps around 60% compared to the bulk value, the dominant vacancy alters depending on the pressure, consistent with the oxygen permeation experiments. Our results suggest that the band bap narrowing occurring at grain boundaries enhances the creation of oxygen vacancies and conduction electrons, facilitating the observed transition.