Interatomic forces and lattice dynamics of α-quartz

Abstract

The axially symmetric force-constant model of Elcombe (1966-7) for alpha -quartz is developed to take account of (i) forces between SiO4 tetrahedra and (ii) rotational invariance. For a non-ionic model without rotational invariance, stiffening the Si-O-Si angles with an Si-Si interaction leads to rather better agreement with experimental phonon frequencies and much better agreement with elastic constants. However, subsequent imposition of the conditions for rotational invariance reduces some of the calculated frequencies, especially that of the lowest acoustic mode at the A-point on the Brillouin zone boundary; this indicates that further weak intertetrahedral forces are required. Ionic (rigid-ion) models are also investigated, but give little improvement. The observed variation with temperature of certain phonon frequencies as the alpha - beta transition is approached can be qualitatively explained by the change in lattice geometry.