LATTICE-DYNAMICS OF ALPHA-QUARTZ .2. THEORY

The recently determined phonon dispersion curves of alpha-quartz have been analysed with various polarizable-ion, bond-charge and shell mode ls, the shell models giving a very satisfactory account of the dispers ion curves as well as of the scattering intensities. Due to the use of interatomic potentials the number of free model parameters can be kep t small. Investigating the dielectric constants in the framework of th e developed shell models yields an ionic charge of about -2e for the o xygen ion, indicating a strongly ionic crystal. The polarizability of the O2- pseudo-ion in quartz should be close to 1.8 angstrom3. The phy sical significance of the obtained potentials has been tested by study ing the equilibrium conditions. It turns out that additional valence f orces of the Keating type improve the fulfillment of the equilibrium c onditions, but that it is not possible to satisfy them completely.