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.

We develop an all-electron path integral Monte Carlo method with free-particle nodes for warm dense matter and apply it to water and carbon plasmas. We thereby extend path integral Monte Carlo studies beyond hydrogen and helium to elements with core electrons. Path integral Monte Carlo results for pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics calculations at temperatures of (2.5-7.5)×10(5) K, and both methods together form a coherent equation of state over a density-temperature range of 3-12 g/cm(3) and 10(4)-10(9) K.

We extend the applicability range of fermionic path integral Monte Carlo simulations to heavier elements and lower temperatures by introducing various localized nodal surfaces. Hartree-Fock nodes yield the most accurate prediction for pressure and internal energy that we combine with the results from density functional molecular dynamics simulations to obtain a consistent equation of state for hot, dense silicon under plasma conditions and in the regime of warm dense matter (2.3−18.6 g cm −3 , 5.0 × 10 5 − 1.3 × 10 8 K). The shock Hugoniot curve is derived and the structure of the fluid is characterized with various pair correlation functions.

Silicon undergoes a phase transition from the semiconducting diamond phase to the metallic ␤-Sn phase under pressure. We use quantum Monte Carlo calculations to predict the transformation pressure and compare the results to density-functional calculations employing the local-density approximation, the generalizedgradient approximations PBE, PW91, WC, AM05, PBEsol, and the hybrid functional HSE06 for the exchangecorrelation functional. Diffusion Monte Carlo predicts a transition pressure of 14.0Ϯ 1.0 GPa slightly above the experimentally observed transition pressure range of 11.3-12.6 GPa. The HSE06 hybrid functional predicts a transition pressure of 12.4 GPa in excellent agreement with experiments. Exchange-correlation functionals using the local-density approximation and generalized-gradient approximations result in transition pressures ranging from 3.5 to 10.0 GPa, well below the experimental values. The transition pressure is sensitive to stress anisotropy. Anisotropy in the stress along any of the cubic axes of the diamond phase of silicon lowers the equilibrium transition pressure and may explain the discrepancy between the various experimental values as well as the small overestimate of the quantum Monte Carlo transition pressure.

We perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of aluminum. Our equation of state (EOS) simulations cover a wide density-temperature range of 0.1-32.4gcm^{-3} and 10^{4}-10^{8} K. Since PIMC and DFT-MD accurately treat effects of the atomic shell structure, we find two compression maxima along the principal Hugoniot curve attributed to K-shell and L-shell ionization. The results provide a benchmark for widely used EOS tables, such as SESAME, QEOS, and models based on Thomas-Fermi and average-atom techniques. A subsequent multishock analysis provides a quantitative assessment for how much heating occurs relative to an isentrope in multishock experiments. Finally, we compute heat capacity, pair-correlation functions, the electronic density of states, and 〈Z〉 to reveal the evolution of the plasma structure and ionization behavior.

No abstract

Quantitative, nanometer-scale spatial resolution electron energy-loss spectroscopy (EELS) was used to map the composition of coherent islands grown by molecular-beam epitaxy of pure Ge onto Si(100). The Ge concentration XGe decreased, and the Ge/Si interface became more diffuse as the growth temperature increased from 400 to 700 °C. Integrated island volumes measured by atomic force microscopy (AFM) increased linearly with Ge coverage θGe, with slopes greater than 1. This result confirmed that island growth is faster than the Ge deposition rate due to Si interdiffusion. The linearity of the island volume versus θGe curves implied that XGe was independent of island size. XGe measured by EELS and AFM agree well with each other and correctly predicted the minimum dome size observed at each growth temperature.

All-electron path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) simulations provide a consistent, first-principles investigation of warm dense neon plasmas in the density-temperature range of 1-15 g cm −3 and 10 4-10 8 K. At high temperatures, DFT-MD becomes intractable because of too many partially occupied bands, while at lower temperatures, PIMC is intractable because of the free-particle approximation of fermion nodes. In combination, PIMC and DFT-MD pressures and internal energies provide a coherent equation of state with a region of overlap in which the two methods cross-validate each other. Pair-correlation functions at various temperatures and densities provide details of the plasma structure and the temperature-driven ionization process. The electronic density of states of neon shows that a gap persists for the highest density-temperature conditions studied here with DFT-MD. Finally, the computed shock Hugoniot curves show an increase in compression as the first and second shells are ionized.