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Atomistic simulation methods based on pair-wise interatomic potentials and energy minimization have been applied to elucidate the energetics of cation vacancies and the incorporation of 13 trivalent M 31 cations (Cr 31 , Ga 31 , Fe 31 , Lu 31 , Yb 31 , Er 31 , Y 31 , Tb 31 , Gd 31 , Eu 31 , Sm 31 , Nd 31 , La 31 ) in c-Al 2 O 3 . Calculations have been carried out using Al 64 O 96 defect spinel supercells containing eight aluminum vacancies. The lowest energy configurations correspond to a random distribution of tetrahedral and octahedral vacancies. The energy gain in comparison with exclusive tetrahedral or octahedral vacancies is rather small (0.03 and 0.09 eV/Al 2 O 3 , respectively). Unit cell volume, density, and lattice properties of optimized structures are in good agreement with the experimental values or the results of high-quality density functional theory calculations. The trends observed for the solution energy of the M 2 O 3 oxides in the supercell with minimum energy indicate the preferential incorporation of the foreign ions at the tetrahedral site and an increase of the solubility of M 2 O 3 in the defect spinel in comparison with a-Al 2 O 3 . Configurations with the lowest energy have negative solution energies and, consequently, incorporation of trivalent ions can improve the thermodynamic stability of c-Al 2 O 3 in comparison with a-Al 2 O 3 and increase the c-a transition temperature. D. Johnson-contributing editor

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