Theory of point defects and vacancy motion in corundum crystals

The energies of formation of Schottky and Frenkel defects in corundum (α-Al₂O₃) have been calculated and also the activation energies for cation and anion vacancy hopping using the method of atom-atom potentials as formulated in the Mott-Littleton strategy and implemented in the CASCADE computer code. Special attention has been paid to the ability of the two-body potentials used to describe the crystal structure and properties and the need to allow for the energy change associated with the relaxation of basis strains. Several mechanisms of oxygen vacancy hopping were also simulated by means of the quantum chemical INDO method which takes into account the covalent contribution of chemical bonding in corundum. These calculations show insignificant increase in the effective charge of the hopping O atom in its saddle point, which justifies the use of atom-atom potentials in this context, The INDO activation energies for vacancy hops reveal the same trend as obtained in CASCADE calculations: where they disagree indicates a failure to optimize ionic displacements completely in the INDO calculation. In agreement with CASCADE calculations these migration energies are much lower when the hopping ion is allowed to deviate from a straight path (typically by 0.3-0.4 Å). Both kinds of calculations predict the activation energy for vacancy hopping between basic structural O triangles to be the factor limiting oxygen migration.