Quantum Monte Carlo computations of phase stability, equations of state, and elasticity of high-pressure silica

Absence of diagonal force constants in cubic Coulomb crystals

The quasi-harmonic model proposes that a crystal can be modelled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss’s law shows that the ion–ion potential for a cubic Coulomb system can have no diagonal harmonic contribution and so cannot necessarily be modelled by springs. We investigate the repercussions of this observation by examining three illustrative regimes: the bare ionic, density tight-binding and density nearly-free electron models. For the bare ionic model, we demonstrate the zero elements in the force constants matrix and explain this phenomenon as a natural consequence of Poisson’s law. In the density tight-binding model, we confirm that the inclusion of localized electrons stabilizes all major crystal structures at harmonic order and we construct a phase diagram of preferred structures with respect to core and valence electron radii. In the density nearly-free electron model, we verify that the inclusion of delocalized electrons, in the form of a background jellium, is enough to counterbalance the diagonal force constants matrix from the ion–ion potential in all cases and we show that a first-order perturbation to the jellium does not have a destabilizing effect. We discuss our results in connection to Wigner crystals in condensed matter, Yukawa crystals in plasma physics, as well as the elemental solids.

A molecular dynamics study of ambient and high pressure phases of silica: structure and enthalpy variation with molar volume

Extensive molecular dynamics studies of 13 different silica polymorphs are reported in the isothermal-isobaric ensemble with the Parrinello-Rahman variable shape simulation cell. The van Beest-Kramer-van Santen (BKS) potential is shown to predict lattice parameters for most phases within 2%-3% accuracy, as well as the relative stabilities of different polymorphs in agreement with experiment. Enthalpies of high-density polymorphs - CaCl2-type, α-PbO2-type, and pyrite-type - for which no experimental data are available as yet, are predicted here. Further, the calculated enthalpies exhibit two distinct regimes as a function of molar volume-for low and medium-density polymorphs, it is almost independent of volume, while for high-pressure phases a steep dependence is seen. A detailed analysis indicates that the increased short-range contributions to enthalpy in the high-density phases arise not only from an increased coordination number of silicon but also shorter Si-O bond lengths. Our results indicate that amorphous phases of silica exhibit better optimization of short-range interactions than crystalline phases at the same density while the magnitude of Coulombic contributions is lower in the amorphous phase.

Prediction of a hexagonal SiO2 phase affecting stabilities of MgSiO3 and CaSiO3 at multimegabar pressures

Ultrahigh-pressure phase relationship of SiO(2) silica in multimegabar pressure condition is still quite unclear. Here, we report a theoretical prediction on a previously uncharacterized stable structure of silica with an unexpected hexagonal Fe(2)P-type form. This phase, more stable than the cotunnite-type structure, a previously postulated postpyrite phase, was discovered to stabilize at 640 GPa through a careful structure search by means of ab initio density functional computations over various structure models. This is the first evidential result of the pressure-induced phase transition to the Fe(2)P-type structure among all dioxide compounds. The crystal structure consists of closely packed, fairly regular SiO(9) tricapped trigonal prisms with a significantly compact lattice. Additional investigation further elucidates large effects of this phase change in SiO(2) on the stability of MgSiO(3) and CaSiO(3) at multimegabar pressures. A postperovskite phase of MgSiO(3) breaks down at 1.04 TPa along an assumed adiabat of super-Earths and yields Fe(2)P-type SiO(2) and CsCl (B2)-type MgO. CaSiO(3) perovskite, on the other hand, directly dissociates into SiO(2) and metallic CaO, skipping a postperovskite polymorph. Predicted ultrahigh-pressure and temperature phase diagrams of SiO(2), MgSiO(3), and CaSiO(3) indicate that the Fe(2)P-type SiO(2) could be one of the dominant components in the deep mantles of terrestrial exoplanets and the cores of gas giants.