The behavior of a single O vacancy in α-phase material was studied by means of super-cell total-energy calculations, using a first-principles method that was based upon density-functional theory. The super-cell model, with 120 atoms in an hexagonal lattice, was sufficiently large to give realistic results for an isolated single vacancy, . Self-consistent calculations were performed for each assumed lattice relaxation configuration which involved nearest-neighbor Al atoms and next-nearest neighbor O atoms of the vacancy site. The total-energy data which were obtained were used to construct an energy hypersurface. A theoretical zero-temperature vacancy formation energy of 5.83eV was deduced. The results revealed a large relaxation of Al atoms, away from the vacancy site, by about 16% of the original Al- distance. There was a similarly large relaxation of O atoms away from the vacancy site by about 8% of the original O- distance. The relaxation of the neighboring Al atoms exhibited a much weaker energy dependence than did the O atoms. The O vacancy introduced a deep and doubly-occupied defect level, or an F-center in the gap, and 3 unoccupied defect levels near to the conduction band edge. The positions of the latter were sensitive to the degree of relaxation. The defect-state wave-functions were not so localized, but extended up to the boundary of the super-cell. Defect-induced levels were also found in the valence-band region below the O 2s and the O 2p bands. The case of a singly occupied defect level (an F+ center) was also investigated. This was done by reducing the total number of electrons in the super-cell, and the background positive charge by one electron, in self-consistent electronic structure calculations. Optical transitions between occupied and excited states of the F and F+ centers were also investigated and were found to be anisotropic; in agreement with optical data.

Y.N.Xu, Z.Q.Gu, X.F.Zhong, W.Y.Ching: Physical Review B, 1997, 56[12], 7277-84