  Density functional perturbation theory calculations of alpha-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 non-hydrostatic pressure. The
computed equation of state, elastic constants and phonon frequencies are found
to be in good agreement with 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
non-hydrostatic conditions. Application of uniaxial pressure, results in a
post-quartz crystalline monoclinic C2 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 novel
monoclinic C2 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.
