First-principles equation of state and shock compression predictions of warm dense hydrocarbons

Mixture of hydrogen and methane under planetary interior conditions

We employ first-principles molecular dynamics simulations to provide equation-of-state data, pair distribution functions (PDFs), diffusion coefficients, and band gaps of a mixture of hydrogen and methane under planetary interior conditions as relevant for Uranus, Neptune, and similar icy exoplanets. We test the linear mixing approximation, which is fulfilled within a few percent for the chosen P-T conditions. Evaluation of the PDFs reveals that methane molecules dissociate into carbon clusters and free hydrogen atoms at temperatures greater than 3000 K. At high temperatures, the clusters are found to be short-lived. Furthermore, we calculate the electrical conductivity from which we derive the non-metal-to-metal transition region of the mixture. We also calculate the electrical conductivity along the P-T profile of Uranus [N. Nettelmann et al., Planet. Space Sci., 2013, 77, 143-151] and observe the transition of the mixture from a molecular to an atomic fluid as a function of the radius of the planet. The density and temperature ranges chosen in our study can be achieved using dynamic shock compression experiments and seek to aid such future experiments. Our work also provides a relevant data set for a better understanding of the interior, evolution, luminosity, and magnetic field of the ice giants in our solar system and beyond.

First-principles equation of state of CHON resin for inertial confinement fusion applications

A wide-range (0 to 1044.0 g/cm^{3} and 0 to 10^{9} K) equation-of-state (EOS) table for a CH_{1.72}O_{0.37}N_{0.086} quaternary compound has been constructed based on density-functional theory (DFT) molecular-dynamics (MD) calculations using a combination of Kohn-Sham DFT MD, orbital-free DFT MD, and numerical extrapolation. The first-principles EOS data are compared with predictions of simple models, including the fully ionized ideal gas and the Fermi-degenerate electron gas models, to chart their temperature-density conditions of applicability. The shock Hugoniot, thermodynamic properties, and bulk sound velocities are predicted based on the EOS table and compared to those of C-H compounds. The Hugoniot results show the maximum compression ratio of the C-H-O-N resin is larger than that of CH polystyrene due to the existence of oxygen and nitrogen; while the other properties are similar between CHON and CH. Radiation hydrodynamic simulations have been performed using the table for inertial confinement fusion targets with a CHON ablator and compared with a similar design with CH. The simulations show CHON outperforms CH as the ablator for laser-direct-drive target designs.

First-principles equation of state database for warm dense matter computation

We put together a first-principles equation of state (FPEOS) database for matter at extreme conditions by combining results from path integral Monte Carlo and density functional molecular dynamics simulations of the elements H, He, B, C, N, O, Ne, Na, Mg, Al, and Si as well as the compounds LiF, B_{4}C, BN, CH_{4}, CH_{2}, C_{2}H_{3}, CH, C_{2}H, MgO, and MgSiO_{3}. For all these materials, we provide the pressure and internal energy over a density-temperature range from ∼0.5 to 50 g cm^{-3} and from ∼10^{4} to 10^{9} K, which are based on ∼5000 different first-principles simulations. We compute isobars, adiabats, and shock Hugoniot curves in the regime of L- and K-shell ionization. Invoking the linear mixing approximation, we study the properties of mixtures at high density and temperature. We derive the Hugoniot curves for water and alumina as well as for carbon-oxygen, helium-neon, and CH-silicon mixtures. We predict the maximal shock compression ratios of H_{2}O, H_{2}O_{2}, Al_{2}O_{3}, CO, and CO_{2} to be 4.61, 4.64, 4.64, 4.89, and 4.83, respectively. Finally we use the FPEOS database to determine the points of maximum shock compression for all available binary mixtures. We identify mixtures that reach higher shock compression ratios than their end members. We discuss trends common to all mixtures in pressure-temperature and particle-shock velocity spaces. In the Supplemental Material, we provide all FPEOS tables as well as computer codes for interpolation, Hugoniot calculations, and plots of various thermodynamic functions.

Benchmarking boron carbide equation of state using computation and experiment

Boron carbide (B_{4}C) is of both fundamental scientific and practical interest due to its structural complexity and how it changes upon compression, as well as its many industrial uses and potential for use in inertial confinement fusion (ICF) and high-energy density physics experiments. We report the results of a comprehensive computational study of the equation of state (EOS) of B_{4}C in the liquid, warm dense matter, and plasma phases. Our calculations are cross-validated by comparisons with Hugoniot measurements up to 61 megabar from planar shock experiments performed at the National Ignition Facility (NIF). Our computational methods include path integral Monte Carlo, activity expansion, as well as all-electron Green's function Korringa-Kohn-Rostoker and molecular dynamics that are both based on density functional theory. We calculate the pressure-internal energy EOS of B_{4}C over a broad range of temperatures (∼6×10^{3}-5×10^{8} K) and densities (0.025-50 g/cm^{3}). We assess that the largest discrepancies between theoretical predictions are ≲5% near the compression maximum at 1-2×10^{6} K. This is the warm-dense state in which the K shell significantly ionizes and has posed grand challenges to theory and experiment. By comparing with different EOS models, we find a Purgatorio model (LEOS 2122) that agrees with our calculations. The maximum discrepancies in pressure between our first-principles predictions and LEOS 2122 are ∼18% and occur at temperatures between 6×10^{3}-2×10^{5} K, which we believe originate from differences in the ion thermal term and the cold curve that are modeled in LEOS 2122 in comparison with our first-principles calculations. To account for potential differences in the ion thermal term, we have developed three new equation-of-state models that are consistent with theoretical calculations and experiment. We apply these new models to 1D hydrodynamic simulations of a polar direct-drive NIF implosion, demonstrating that these new models are now available for future ICF design studies.

Species Separation and Hydrogen Streaming upon Shock Release from Polystyrene under Inertial Confinement Fusion Conditions

Shock release from inertial confinement fusion (ICF) shells poses a great challenge to single-fluid hydrodynamic equations, especially for describing materials composed of different ion species. This has been evidenced by a recent experiment [Haberberger et al., Phys. Rev. Lett. 123, 235001 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.235001], in which low-density plasmas (10^{19} to 10^{20}  cm^{-3}) are measured to move far ahead of what radiation-hydrodynamic simulations predict. To understand such experimental observations, we have performed large-scale nonequilibrium molecular-dynamics simulations of shock release in polystyrene (CH) at experimental conditions. These simulations revealed that upon shock releasing from the back surface of a CH foil, hydrogen can stream out of the bulk of the foil due to its mass being lighter than carbon. This released hydrogen, exhibiting a much broader velocity distribution than carbon, forms low-density plasmas moving in nearly constant velocities ahead of the in-flight shell, which is in quantitative agreement with the experimental measurements. Such kinetic effect of species separation is currently missing in single-fluid radiation-hydrodynamics codes for ICF simulations.

High Pressure Hydrocarbons Revisited: From van der Waals Compounds to Diamond

Methane and other hydrocarbons are major components of the mantle regions of icy planets. Several recent computational studies have investigated the high-pressure behaviour of specific hydrocarbons. To develop a global picture of hydrocarbon stability, to identify relevant decomposition reactions, and probe eventual formation of diamond, a complete study of all hydrocarbons is needed. Using density functional theory calculations we survey here all known C-H crystal structures augmented by targeted crystal structure searches to build hydrocarbon phase diagrams in the ground state and at elevated temperatures. We find that an updated pressure-temperature phase diagram for methane is dominated at intermediate pressures by CH 4 :H 2 van der Waals inclusion compounds. We discuss the P-T phase diagram for CH and CH 2 (i.e., polystyrene and polyethylene) to illustrate that diamond formation conditions are strongly composition dependent. Finally, crystal structure searches uncover a new CH 4 (H 2 ) 2 van der Waals compound, the most hydrogen-rich hydrocarbon, stable between 170 and 220 GPa.

Ionization potential depression and Pauli blocking in degenerate plasmas at extreme densities

New facilities explore warm dense matter (WDM) at conditions with extreme densities (exceeding ten times condensed matter densities) so that electrons are degenerate even at temperatures of 10-100 eV. Whereas in the nondegenerate region correlation effects such as Debye screening are relevant for the ionization potential depression (IPD), new effects have to be considered in degenerate plasmas. In addition to the Fock shift of the self-energies, the bound-state Pauli blocking becomes important with increasing density. Standard approaches to IPD such as Stewart-Pyatt and widely used opacity tables (e.g., OPAL) do not contain Pauli blocking effects for bound states. The consideration of degeneracy effects leads to a reduction of the ionization potential and to a higher degree of ionization. As an example, we present calculations for the ionization degree of carbon plasmas at T = 100 eV and extreme densities up to 40 g/cm^{3}, which are relevant to experiments that are currently scheduled at the National Ignition Facility.

Theoretical and experimental investigation of the equation of state of boron plasmas

We report a theoretical equation of state (EOS) table for boron across a wide range of temperatures (5.1×10^{4}-5.2×10^{8} K) and densities (0.25-49 g/cm^{3}) and experimental shock Hugoniot data at unprecedented high pressures (5608±118 GPa). The calculations are performed with first-principles methods combining path-integral Monte Carlo (PIMC) at high temperatures and density-functional-theory molecular-dynamics (DFT-MD) methods at lower temperatures. PIMC and DFT-MD cross-validate each other by providing coherent EOS (difference <1.5 Hartree/boron in energy and <5% in pressure) at 5.1×10^{5} K. The Hugoniot measurement is conducted at the National Ignition Facility using a planar shock platform. The pressure-density relation found in our shock experiment is on top of the shock Hugoniot profile predicted with our first-principles EOS and a semiempirical EOS table (LEOS 50). We investigate the self-diffusivity and the effect of thermal and pressure-driven ionization on the EOS and shock compression behavior in high-pressure and -temperature conditions. We also study the sensitivity of a polar direct-drive exploding pusher platform to pressure variations based on applying pressure multipliers to LEOS 50 and by utilizing a new EOS model based on our ab initio simulations via one-dimensional radiation-hydrodynamic calculations. The results are valuable for future theoretical and experimental studies and engineering design in high-energy density research.

Absolute Equation-of-State Measurement for Polystyrene from 25 to 60 Mbar Using a Spherically Converging Shock Wave

We have developed an experimental platform for the National Ignition Facility that uses spherically converging shock waves for absolute equation-of-state (EOS) measurements along the principal Hugoniot. In this Letter, we present one indirect-drive implosion experiment with a polystyrene sample that employs radiographic compression measurements over a range of shock pressures reaching up to 60 Mbar (6 TPa). This significantly exceeds previously published results obtained on the Nova laser [R. Cauble et al., Phys. Rev. Lett. 80, 1248 (1998)PRLTAO0031-900710.1103/PhysRevLett.80.1248] at a strongly improved precision, allowing us to discriminate between different EOS models. We find excellent agreement with Kohn-Sham density-functional-theory-based molecular dynamics simulations.

Path integral Monte Carlo simulations of warm dense aluminum

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.