Transferable model for the atomistic simulation of ${\mathrm{Al}}_2$${\mathrm{O}}_3$

We calculate the energies of different solid phases of ${\mathrm{Al}}_2$${\mathrm{O}}_3$ using a shell model, a compressible ion model, and a compressible ion model which includes both dipole and quadrupolar polarizability of the ${\mathrm{O}}^{2\mathrm{-}}$ ions. Compressible oxygen ions are found to stabilize the corundum structure with respect to the θ form of alumina. The observed corundum structure is nevertheless unstable with respect to the bixbyite structure until quadrupolar polarizability of the oxygen is also included. Entropy differences are estimated with a lattice dynamics calculation and are found to make an insignificant contribution to stabilizing the corundum. We also calculate the relative energies of the corundum and bixbyite structures using the ab initio pseudopotential method, within the local-density approximation for exchange and correlation. The resulting self-consistent electron density shows graphically how the quadrupolar distortions around the oxygen develop as the basis is made more complete (the plane-wave cutoff is increased from 500 to 700 eV), which at the same time brings the energy of the corundum structure below that of the bixbyite structure. © 1996 The American Physical Society.