Various approaches, including Hartree-Fock  ab initio  cluster calculations, semi-empirical intermediate neglect of differential overlap calculations, and atom-atom potentials, were used to model the spatial and electronic structures and migration mechanisms of intrinsic defects (self-trapped holes, defect-trapped holes, O vacancies, Al vacancies) and impurities (Co, Fe, Mg, Mn, and Ti ions). The atomic structures of all of the hole centers were found to be similar to those of VK centers in alkali halides (2-site model). Their formation was energetically favored. The energy which was required for 60 hole re-orientation within the basic O triangles was found to be similar to both the energy for hops between such triangles and the experimental activation energy for self-trapped hole migration (0.7eV). A novel mechanism for hole polaron motion in ionic solids was proposed on the basis of quantum-chemical cluster calculations. The role of clustering in the solution of impurities was shown to be pivotal. Finally, 5 types of O vacancy hop were simulated. In several cases, the activation energy was considerably decreased when the hopping ion was allowed to deviate from a straight path. Theoretical considerations predicted the lowest activation energy to be 1.85eV. This was in excellent agreement with the value that was observed experimentally below 1550C. Theoretical predictions of the Arrhenius energy for diffusion at high temperatures were also in excellent agreement with experimental data for temperatures above 1590C.

P.W.M.Jacobs, E.A.Kotomin: Journal of the American Ceramic Society, 1994, 77[10], 2505-8