Thermodynamics of Mg$_2$SiO$_4$ liquid from first principles molecular dynamics simulations

As the main medium through which planetary differentiation occurs, silicate liquids have a central role in the study of the Earth. We determine the structural and thermodynamic properties of Mg$_2$SiO$_4$ liquid using first principles molecular dynamics in the framework of density functional theory and the local density approximation (LDA). Calculations, performed in the canonical ensemble with a Nose thermostat, span a range of pressures (0 - 150 GPa) and temperatures (3000 - 6000 K). Simulations are performed over 3000 time steps (femto seconds), yielding the total energy and average pressure from which the equation of state, heat capacity and Gruneisen parameter are determined. Preliminary results show that, in addition to the increase in Si coordination with pressure, about one third of the O atoms are not bound to Si at low pressure, a fraction which vanishes with increased Si coordination.