Based on the most recently determined noncubic structure for $\gamma {\text{-Al}}_2{\text{O}}_3$ by Menendez-Proupin and Gutierrez, a comprehensive list of physical properties is investigated theoretically. These include lattice dynamics and phonon spectra, elastic constants and bulk structural parameters, electronic structure and interatomic bonding, optical properties, and x-ray absorption near-edge structure (XANES) spectra. Compared to similar calculations of $\alpha {\text{-Al}}_2{\text{O}}_3$, we find a smaller lowest zone-center vibrational mode at $97.6{\text{cm}}^{-1}$, a lower heat capacity, a smaller bulk modulus, and a much larger thermal-expansion coefficient. The threefold bonded O ions introduce highly localized vibrational modes near $751{\text{cm}}^{-1}$. The calculated thermal Grüneisen parameter indicates a strong anharmonicity in $\gamma {\text{-Al}}_2{\text{O}}_3$. The elastic tensor and the elastic wave velocities are also evaluated showing the longitudinal wave to be nearly isotropic. For the electronic structure, we find that $\gamma {\text{-Al}}_2{\text{O}}_3$ has a smaller band gap but a refractive index similar to $\alpha {\text{-Al}}_2{\text{O}}_3$. Highly localized states at the top of the valence band originating from threefold bonded O in the more covalently bonded ${\text{AlO}}_4$ tetrahedra are identified. The calculated Mulliken effective charges and bond order values indicate that the structural model for $\gamma {\text{-Al}}_2{\text{O}}_3$ has a high degree of disorder. The octahedral unit $\left({\text{AlO}}_6\right)$ is a stronger polyhedron than the tetrahedral unit $\left({\text{AlO}}_4\right)$ although the latter has stronger Al–O bonds. The calculated $\text{Al-}K$, $\text{Al-}{L}_3$, and $\text{O-}K$ edges for Al and O in $\gamma {\text{-Al}}_2{\text{O}}_3$ show strong dependence on their local coordination and environments. These results are in good agreement with available experimental data but the effect of the $\gamma {\text{-Al}}_2{\text{O}}_3$ samples’ porosity should be properly assessed. It is argued that the traditional view that stoichiometric $\gamma {\text{-Al}}_2{\text{O}}_3$ is a defective spinel with cation vacancies (or its variations) should be modified. $\gamma {\text{-Al}}_2{\text{O}}_3$ is better described as an amorphous networklike structure such that the ratio of tetrahedrally coordinated Al to octahedrally coordinated Al is close to 0.6; and the O ions are bonded to Al in either a threefold or fourfold configurations in about equal proportion.

• Received 24 April 2008

DOI:https://doi.org/10.1103/PhysRevB.78.014106