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  1. Anharmonicity and Phase Diagram of Magnesium Oxide in the Megabar Regime

    With density functional molecular dynamics simulations, we computed the phase diagram of MgO from 50 to 2000 GPa up to 20000 K. Via thermodynamic integration (TDI), we derive the Gibbs free energies of the B1, B2, and liquid phases and determine their phase boundaries. With TDI and a pseudo-quasi-harmonic approach, we show that anharmonic effects are important and stabilize the B1 phase in particular. As a result, the B1-B2 transition boundary in the pressure-temperature plane exhibits a steep slope. We predict the B1-B2-liquid triple point to occur at approximately T= 10000 K and P = 370 GPa, which is highermore » in pressure than was inferred with quasi-harmonic methods alone. We predict the principal shock Hugoniot curve to enter the B2 phase stability domain but only over a very small range of parameters. Here, this may render it difficult to observe this phase with shock experiments because of kinetic effects.« less
  2. Equation of state of hot, dense magnesium derived with first-principles computer simulations

    Using two first-principles computer simulation techniques, path integral Monte Carlo and density functional theory molecular dynamics, we derive the equation of state of magnesium in the regime of warm dense matter, with densities ranging from 0.43 to 86.11 g cm–3 and temperatures from 20,000 K to 5×108 K. These conditions are relevant for the interiors of giant planets and stars as well as for shock compression measurements and inertial confinement fusion experiments. Here, we study ionization mechanisms and the electronic structure of magnesium as a function of density and temperature. We show that the L shell electrons, 2s and 2pmore » energy bands, merge at high densities. This results in gradual ionization of the L-shell with increasing density and temperature. In this regard, Mg differs from MgO, which is also reflected in the shape of its principal shock Hugoniot curve. For Mg, we predict a single broad pressure-temperature region, where the shock compression ratio is approximately 4.9. Mg thus differs from Si and Al plasmas that exhibit two well-separated compression maxima on the Hugoniot curve for L and K shell ionizations. Finally, we study multiple shocks and effects of preheat and precompression.« less
  3. Path integral Monte Carlo and density functional molecular dynamics simulations of warm dense MgSiO 3

    In order to provide a comprehensive theoretical description of MgSiO3 at extreme conditions, we combine results from path integral Monte Carlo and density functional molecular dynamics simulations and generate a consistent equation of state for this material. We consider a wide range of temperature and density conditions from 104 to 108 K and from 0.321 to 64.2 g/cm-3 (0.1- to 20-fold the ambient density). We study how the L and K shell electrons are ionized with increasing temperature and pressure. We derive the shock Hugoniot curve and compare with experimental results. Our Hugoniot curve is in good agreement with themore » experiments, and we predict a broad compression maximum that is dominated by the K shell ionization of all three nuclei while the peak compression ratio of 4.70 is obtained when the Si and Mg nuclei are ionized. To conclude, we analyze the heat capacity and structural properties of the liquid.« less
  4. Magnesium oxide at extreme temperatures and pressures studied with first-principles simulations

    We combine two first-principles computer simulation techniques, path integral Monte Carlo and density functional theory molecular dynamics, to determine the equation of state of magnesium oxide in the regime of warm dense matter, with densities ranging from 0.35 to 71 g cm-3 and temperatures ranging from 10 000 K to 5 × 108 K. These conditions are relevant for the interiors of giant planets and stars as well as for shock wave compression measurements and inertial confinement fusion experiments. We study the electronic structure of MgO and the ionization mechanisms as a function of density and temperature. We show thatmore » the L-shell orbitals of magnesium and oxygen hybridize at high density. This results in a gradual ionization of the L-shell with increasing density and temperature. In this regard, MgO behaves differently from pure oxygen, which is reflected in the shape of the MgO principal shock Hugoniot curve. The curve of oxygen shows two compression maxima, while that of MgO shows only one. We predict a maximum compression ratio of 4.66 to occur for a temperature of 6.73 × 107 K. Lastly, we research how multiple shocks and ramp waves can be used to cover a large range of densities and temperatures.« less
  5. Electrical conductivity and magnetic dynamos in magma oceans of Super-Earths

    Super-Earths are extremely common among the numerous exoplanets that have been discovered. The high pressures and temperatures in their interiors are likely to lead to long-lived magma oceans. If their electrical conductivity is sufficiently high, the mantles of Super-Earth would generate their own magnetic fields. With ab initio simulations, we show that upon melting, the behavior of typical mantle silicates changes from semi-conducting to semi-metallic. The electrical conductivity increases and the optical properties are substantially modified. Melting could thus be detected with high-precision reflectivity measurements during the short time scales of shock experiments. We estimate the electrical conductivity of mantlemore » silicates to be of the order of 100 Ω-1 cm-1, which implies that a magnetic dynamo process would develop in the magma oceans of Super-Earths if their convective velocities have typical values of 1 mm/s or higher. We predict exoplanets with rotation periods longer than 2 days to have multipolar magnetic fields.« less
  6. Path integral Monte Carlo simulations of dense carbon-hydrogen plasmas

    Carbon-hydrogen plasmas and hydrocarbon materials are of broad interest to laser shock experimentalists, high energy density physicists, and astrophysicists. Accurate equations of state (EOSs) of hydrocarbons are valuable for various studies from inertial confinement fusion to planetary science. By combining path integral Monte Carlo (PIMC) results at high temperatures and density functional theory molecular dynamics results at lower temperatures, we compute the EOSs for hydrocarbons from simulations performed at 1473 separate (ρ, T)-points distributed over a range of compositions. These methods accurately treat electronic excitation effects with neither adjustable parameter nor experimental input. PIMC is also an accurate simulation methodmore » that is capable of treating many-body interaction and nuclear quantum effects at finite temperatures. These methods therefore provide a benchmark-quality EOS that surpasses that of semi-empirical and Thomas-Fermi-based methods in the warm dense matter regime. By comparing our first-principles EOS to the LEOS 5112 model for CH, we validate the specific heat assumptions in this model but suggest that the Grüneisen parameter is too large at low temperatures. Based on our first-principles EOSs, we predict the principal Hugoniot curve of polystyrene to be 2%-5% softer at maximum shock compression than that predicted by orbital-free density functional theory and SESAME 7593. By investigating the atomic structure and chemical bonding of hydrocarbons, we show a drastic decrease in the lifetime of chemical bonds in the pressure interval from 0.4 to 4 megabar. We find the assumption of linear mixing to be valid for describing the EOS and the shock Hugoniot curve of hydrocarbons in the regime of partially ionized atomic liquids. We make predictions of the shock compression of glow-discharge polymers and investigate the effects of oxygen content and C:H ratio on its Hugoniot curve. In conclusion, our full suite of first-principles simulation results may be used to benchmark future theoretical investigations pertaining to hydrocarbon EOSs and should be helpful in guiding the design of future experiments on hydrocarbons in the gigabar regime.« less
  7. Properties of hydrogen, helium, and silicon dioxide mixtures in giant planet interiors

    Recent observations of Jupiter and Saturn provided by spacecraft missions, such as Juno and Cassini, compel us to revise and improve our models of giant planet interiors. Even though hydrogen and helium are by far the dominant species in these planets, heavy elements can play a significant role in the structure and evolution of the planet.
  8. Equation of state and shock compression of warm dense sodium—A first-principles study

    As one of the simple alkali metals, sodium has been of fundamental interest for shock physics experiments, but knowledge of its equation of state (EOS) in hot, dense regimes is not well known. By combining path integral Monte Carlo (PIMC) results for partially ionized states at high temperatures and density functional theory molecular dynamics (DFT-MD) results at lower temperatures, we have constructed a coherent equation of state for sodium over a wide density-temperature range of 1.93-11.60 g/cm3 and 103–1.29×108 K. We find that a localized, Hartree-Fock nodal structure in PIMC yields pressures and internal energies that are consistent with DFT-MDmore » at intermediate temperatures of 2×106 K. Since PIMC and DFT-MD provide a first-principles treatment of electron shell and excitation effects, we are able to identify two compression maxima in the shock Hugoniot curve corresponding to K-shell and L-shell ionization. Our Hugoniot curves provide a benchmark for widely used EOS models: SESAME, LEOS, and Purgatorio. Due to the low ambient density, sodium has an unusually high first compression maximum along the shock Hugoniot curve. At beyond 107 K, we show that the radiation effect leads to very high compression along the Hugoniot curve, surpassing relativistic corrections, and observe an increasing deviation of the shock and particle velocities from a linear relation. Here, we also compute the temperature-density dependence of thermal and pressure ionization processes.« less
  9. First-principles equation of state and electronic properties of warm dense oxygen

    In this paper, we perform all-electron path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of oxygen. Our simulations cover a wide density-temperature range of 1–100 g cm-3 and 104–109 K. By combining results from PIMC and DFT-MD, we are able to compute pressures and internal energies from first-principles at all temperatures and provide a coherent equation of state. We compare our first-principles calculations with analytic equations of state, which tend to agree for temperatures above 8 × 106 K. Pair-correlation functions and the electronic density of states reveal anmore » evolving plasma structure and ionization process that is driven by temperature and density. As we increase the density at constant temperature, we find that the ionization fraction of the 1s state decreases while the other electronic states move towards the continuum. The computed shock Hugoniot curves show an increase in compression as the first and second shells are ionized.« less

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