The α-alumina(0001)surface: relaxations and dynamics from shell model and density functional theory

We have investigated the dynamics and harmonic free energy of the (0001) surface of α-Al2O3 with both semi-empirical and ab initio techniques. The shell models provide a convenient way to to simulate the more expensive ab initio methods and to check some of their technical limitations, in particular the quality of the vibrational Brillouin zone sampling and the harmonic approximation. We have used the supercell approach to compute the frequencies of normal modes at special k-points, which allows the free energy to be calculated at different temperatures. From the corresponding phonon eigenvectors we evaluate the mean square displacements of Al and O ions. The surface phonons are particularly sensitive to the modelling technique. The ab initio surface modes are more localized and of higher amplitude, but they are not anharmonic enough to account for the discrepancy observed between the measured and calculated inward relaxation of the surface aluminium atoms.