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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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Static-lattice atomistic calculations have been used to study the solution energy for the incorporation of 13 foreign cations at 3 different lattice positions of 12 synthetic garnets. Trends have been obtained as a function of the ionic radius of the dopant cation, and the predictions about site preference have been compared with both literature and experimental data. The preferred substitution site is mainly determined by the ionic size and has been correctly predicted in all cases. Moreover, the energy difference between the preferred substitution site and the next favored site is relatively small in several cases, and hence the foreign ions can be inserted at two different positions by using the correct stoichiometry. A remarkably different behavior has been encountered for Al garnets, due to the smaller size of the unit cell. In particular, some cations, such as Fe3+ and Ga3+, can be inserted at the dodecahedral position usually occupied by the rare-earth ion. Despite the limitations of the static-lattice approach, the results of the present simulations help in the understanding of the defect chemistry of garnets, which is strongly responsible for the physicochemical properties (such as luminescence and ferrimagnetism) that make garnets interesting for technological applications. Such results lead to the possibility of tuning the optical and luminescence properties of garnets by the formation of different types of solid solutions.

The self-propagating high-temperature reaction in nickel−aluminum powder mixtures has been investigated by computer simulated experiments using a monodimensional model. The model describes the overall reaction mechanism considering several elemental steps such as melting of the reactant Al, diffusion-controlled dissolution of solid nickel into the molten pool, (possible) melting of the Ni reactant, precipitation and melting of the compound, and precipitation of the eutectic mixture of Al + AlNi. Melting of pure aluminum and nickel and eutectic crystallization are considered in terms of thermal balance only, whereas an explicit diffusion controlled kinetic for the dissolution of nickel in molten aluminum was accounted for. The results show that the reaction propagates under almost steady conditions with constant wave velocity and peak temperature, close to experimentally reported values, when suitable values for the thermal conductivity of the green compact were set.

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