Lattice dynamics of corundum

The short-range force constants and the contribution of the potential energy to the elastic constants have been calculated from explicit expressions for the elastic constants and for the optical frequencies. The large elastic constants of corundum are attributable to the contribution of the large short-range stretching forces. The frequencies of the phonon spectrum and the contribution of the potential energy to the frequencies have also been calculated based on a rigid-ion and polarizable-ion model. The effective charge of an oxygen ion is found to be ?0.955e. The electronic polarizability of an aluminium and oxygen ion is found to be 0.05 and 1.36 ų, respectively.