Ab initio studies of phonon softening and high-pressure phase transitions of $\ensuremath{\alpha}$-quartz $\mathrm{Si}{\mathrm{O}}_{2}$

Ab initio studies of phonon softening and high-pressure phase transitions of $α$ -quartz $Si O_{2}$

N. Choudhury and S. L. Chaplot

Phys. Rev. B 73, 094304 – Published 22 March 2006

Abstract

Density functional perturbation theory calculations of $α -$ quartz using extended norm conserving pseudopotentials have been used to study the elastic properties and phonon dispersion relations along various high symmetry directions as a function of bulk, uniaxial, and nonhydrostatic pressure. The computed equation of state, elastic constants, and phonon frequencies are found to be in good agreement with the available experimental data. A zone boundary ( $1 ∕ 3$ , $1 ∕ 3$ , 0) K-point phonon mode becomes soft for pressures above $P = 32 GPa$ . Around the same pressure, studies of the Born stability criteria reveal that the structure is mechanically unstable. The phonon and elastic softening are related to the high pressure phase transitions and amorphization of quartz, and these studies suggest that the mean transition pressure is lowered under nonhydrostatic conditions. The application of uniaxial pressure results in a post-quartz crystalline monoclinic $C 2$ structural transition in the vicinity of the K-point instability. This structure, intermediate between quartz and stishovite has two-thirds of the silicon atoms in octahedral coordination while the remaining silicon atoms remain tetrahedrally coordinated. This monoclinic $C 2$ polymorph of silica, which is found to be metastable under ambient conditions, is possibly one of the several competing dense forms of silica containing octahedrally coordinated silicon. The possible role of high pressure ferroelastic phases in causing pressure induced amorphization in silica are discussed.