High-precision, all-electron, full-potential calculation of the equation of state and elastic constants of corundum

Abstract

The all-electron, full-potential linear combinations of Gaussian type orbitals–fitting function technique has been used to perform high-precision total-energy calculations on α-alumina (corundum). The calculations yield zero-pressure lattice parameters that are in 0.3% agreement with experiment and symmetry-preserving elastic constants that agree with experiment to within 5%. The bulk modulus and pressure derivatives of the lattice parameters are also in good agreement with existing data. The calculated energies have been used to generate an analytical equation of state (EOS) for corundum that should be valid up to at least 250 GPa. The fitted EOS agrees with room temperature diamond anvil cell data up to 175 GPa to within the known limitations of the experimental data. The c/a ratio, band gap, and tetragonal shear modulus have been determined for pressures up to 250 GPa. The c/a ratio varies by less than 3% over the entire pressure range. For pressures above 150 GPa, the band gap changes from direct to indirect and the tetragonal shear modulus softens. The linear pressure coefficient of the band gap is estimated to be 5.1 meV/kbar at zero pressure.