The effect of temperature and anisotropic pressure on the phase transitions in $\alpha$-cristobalite

The role of temperature and anisotropy of the pressure tensor in the pressure--induced transformations of $\alpha$-cristobalite is investigated by means of first principle molecular dynamics combined with an improved version of the metadynamics algorithm for the study of solid-solid phase transitions\footnote{R.~Marto\v{n}\'{a}k, D. Donadio, A. R. Oganov and M. Parrinello, Nat. Mat. \textbf{5}, 623 (2006).} We reproduce for the first time the transition to $\alpha-$PbO$_2$ as found in experiments\footnote{L.~S. Dubrovinsky {\it et al.} Chem. Phys. Lett. \textbf{333}, 264 (2001).} and we observe that the transition paths are qualitatively different and yield different products whether the applied pressure is hydrostatic or not. While in hydrostatic conditions $\alpha-$PbO$_2$ or stishovite is obtained depending on the temperature and initial conditions, more complicated pathways with several metastable structures are followed upon non-hydrostatic compression and post-stishovite phases are obtained. Based of our simulations, we predict the metastability of a new class of high pressure polymorphs of silica obtained by non-hydrostatic compression.