Free energy models for ice VII and liquid water derived from pressure, entropy, and heat capacity relations

We present equations of state relevant to conditions encountered in ramp and multiple-shock compression experiments of water. These experiments compress water from ambient conditions to pressures as high as about 14 GPa and temperatures of up to several hundreds of Kelvin. Water may freeze into ice VII during this process. Although there are several studies on the thermodynamic properties of ice VII, an accurate and analytic free energy model from which all other properties may be derived in a thermodynamically consistent manner has not been previously determined. We have developed such a free energy model for ice VII that is calibrated with pressure-volume-temperature measurements and melt curve data. Furthermore, we show that liquid water in the pressure and temperature range of interest is well-represented by a simple Mie-Grüneisen equation of state. Our liquid water and ice VII equations of state are validated by comparing to sound speed and Hugoniot data. Although they are targeted towards ramp and multiple-shock compression experiments, we demonstrate that our equations of state also behave reasonably well at pressures and temperatures that lie somewhat beyond those found in the experiments.