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We present a 5-phase equation of state for elemental carbon which addresses a wide range of density and temperature conditions: 3g/cc < ρ < 20g/cc, 0 K < T < ∞. The phases considered are diamond, BC8, simple cubic, simple hexagonal, and the liquid/plasma state. The solid phase free energies are constrained by density functional theory (DFT) calculations. Vibrational contributions to the free energy of each solid phase are treated within the quasiharmonic framework. The liquid free energy model is constrained by fitting to a combination of DFT molecular dynamics performed over the range 10 000 K < T < 100 000 K, and path integral quantum Monte Carlo calculations for T > 100 000 K (both for ρ between 3 and 12 g/cc, with select higher-ρ DFT calculations as well). The liquid free energy model includes an atom-in-jellium approach to account for the effects of ionization due to temperature and pressure in the plasma state, and an ion-thermal model which includes the approach to the ideal gas limit. The precise manner in which the ideal gas limit is reached is greatly constrained by both the highest-temperature DFT data and the path integral data, forcing us to discard an ion-thermal model we had used previously in favor of a new one. Predictions are made for the principal Hugoniot and the room-temperature isotherm, and comparisons are made to recent experimental results.

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The properties of hydrogen-helium mixtures at Mbar pressures and intermediate temperatures (4000 to 10000 K) are calculated with first-principles molecular dynamics simulations. We determine the equation of state as a function of density, temperature, and composition and, using thermodynamic integration, we estimate the Gibbs free energy of mixing, thereby determining the temperature, at a given pressure, when helium becomes insoluble in dense metallic hydrogen. These results are directly relevant to models of the interior structure and evolution of Jovian planets. We find that the temperatures for the demixing of helium and hydrogen are sufficiently high to cross the planetary adiabat of Saturn at pressures Ϸ5 Mbar; helium is partially miscible throughout a significant portion of the interior of Saturn, and to a lesser extent in Jupiter.ab initio molecular dynamics ͉ high pressure ͉ planetary interiors T he two lightest elements, hydrogen and helium, are fascinating to physicists. Ubiquitous in the universe, their abundance ratio provide stringent checks on cosmological nucleosynthesis theories and the global distribution of hydrogen in the observable universe provides clues to the origin and large scale structures of galaxies. They are the essential elements of stars and giant planets. Yet, despite the seeming simplicity of their electronic structure, there are many unanswered questions about their fundamental properties, especially at high pressures. One such question is under what conditions are these elements miscible. The answer will have a crucial impact on our understanding of the evolution and the structure of the giant planets in our solar system and beyond.Jupiter and Saturn, the simplest among the Jovian planets, are generally believed to have been formed approximately at the same time as the sun, although certain direct observations (such as Saturn's excess luminosity) appear to contradict this planetary formation theory. In addition to being mostly made of hydrogen and helium, a characteristic of Jovian planets is that they radiate more energy than they take in from the sun. Various models of their evolution and structure have been developed (1-4) to describe a relation between the age, volume, and mass of the planet and its luminosity. The current luminosity of Jupiter is well described with an evolution model for a convective homogeneous planet radiating energy left over from its formation 4.55 billion years ago. However, a similar model seriously underes-

[1] The most energetic planetary collisions attain shock pressures that result in abundant melting and vaporization. Accurate predictions of the extent of melting and vaporization require knowledge of vast regions of the phase diagrams of the constituent materials. To reach the liquid-vapor phase boundary of silica, we conducted uniaxial shock-and-release experiments, where quartz was shocked to a state sufficient to initiate vaporization upon isentropic decompression (hundreds of GPa). The apparent temperature of the decompressing fluid was measured with a streaked optical pyrometer, and the bulk density was inferred by stagnation onto a standard window. To interpret the observed post-shock temperatures, we developed a model for the apparent temperature of a material isentropically decompressing through the liquid-vapor coexistence region. Using published thermodynamic data, we revised the liquid-vapor boundary for silica and calculated the entropy on the quartz Hugoniot. The silica post-shock temperature measurements, up to entropies beyond the critical point, are in excellent qualitative agreement with the predictions from the decompressing two-phase mixture model. Shock-and-release experiments provide an accurate measurement of the temperature on the phase boundary for entropies below the critical point, with increasing uncertainties near and above the critical point entropy. Our new criteria for shock-induced vaporization of quartz are much lower than previous estimates, primarily because of the revised entropy on the Hugoniot. As the thermodynamics of other silicates are expected to be similar to quartz, vaporization is a significant process during high-velocity planetary collisions.Citation: Kraus, R. G., et al. (2012), Shock vaporization of silica and the thermodynamics of planetary impact events,