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<i>Ab initio</i>studies of phonon softening and high-pressure phase transitions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>-quartz<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Si</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>

<i>Ab initio</i>studies of phonon softening and high-pressure phase transitions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>-quartz<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Si</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>

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 …