Geometry Optimization and Ground‐State Properties of Complex Ceramic Oxides

The crystal structures of the several complex oxides including MgAl 2 O 4 , α‐Al 2 O 3 , θ‐Al 2 O 3 , r ‐Al 2 O 3 , Y 2 O 3 , Y 3 Al 5 O 12 , and YAlO 3 are fully optimized by means of first‐principles total energy calculations with relaxation of all internal parameters. This is achieved by the implementation of a simple scheme based on the finite difference method for the energy gradient. In most cases, the predicted lattice constants are within 0.5% of the experimental values. The bulk moduli and the pressure coefficients for these crystals are calculated from fitting the energy vs volume data to the equation of state. Because all of the internal parameters of the crystal are optimized at different volumes, the calculated ground‐state properties are found to be in excellent agreement with measured data. For the polymorphs of the Al 2 O 3 system, comparison to other existing calculations are made and discussed.