First-principles Equation Of State Research Articles

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,andMgSiO_{3}. For all these materials, we provide the pressure and internal energy over a density-temperature range from ∼0.5 to 50 gcm^{-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,andCO_{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.

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.

A review on ab initio studies of static, transport, and optical properties of polystyrene under extreme conditions for inertial confinement fusion applications

Polystyrene (CH), commonly known as “plastic,” has been one of the widely used ablator materials for capsule designs in inertial confinement fusion (ICF). Knowing its precise properties under high-energy-density conditions is crucial to understanding and designing ICF implosions through radiation–hydrodynamic simulations. For this purpose, systematic ab initio studies on the static, transport, and optical properties of CH, in a wide range of density and temperature conditions (ρ = 0.1 to 100 g/cm3 and T = 103 to 4 × 106 K), have been conducted using quantum molecular dynamics (QMD) simulations based on the density functional theory. We have built several wide-ranging, self-consistent material-properties tables for CH, such as the first-principles equation of state, the QMD-based thermal conductivity (κQMD) and ionization, and the first-principles opacity table. This paper is devoted to providing a review on (1) what results were obtained from these systematic ab initio studies; (2) how these self-consistent results were compared with both traditional plasma-physics models and available experiments; and (3) how these first-principles–based properties of polystyrene affect the predictions of ICF target performance, through both 1-D and 2-D radiation–hydrodynamic simulations. In the warm dense regime, our ab initio results, which can significantly differ from predictions of traditional plasma-physics models, compared favorably with experiments. When incorporated into hydrocodes for ICF simulations, these first-principles material properties of CH have produced significant differences over traditional models in predicting 1-D/2-D target performance of ICF implosions on OMEGA and direct-drive–ignition designs for the National Ignition Facility. Finally, we will discuss the implications of these studies on the current small-margin ICF target designs using a CH ablator.

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

We use path integral Monte Carlo and density functional molecular dynamics to construct a coherent set of equations of state (EOS) for a series of hydrocarbon materials with various C:H ratios (2:1, 1:1, 2:3, 1:2, and 1:4) over the range of 0.07-22.4gcm^{-3} and 6.7×10^{3}-1.29×10^{8}K. The shock Hugoniot curve derived for each material displays a single compression maximum corresponding to K-shell ionization. For C:H = 1:1, the compression maximum occurs at 4.7-fold of the initial density and we show radiation effects significantly increase the shock compression ratio above 2 Gbar, surpassing relativistic effects. The single-peaked structure of the Hugoniot curves contrasts with previous work on higher-Z plasmas, which exhibit a two-peak structure corresponding to both K- and L-shell ionization. Analysis of the electronic density of states reveals that the change in Hugoniot structure is due to merging of the L-shell eigenstates in carbon, while they remain distinct for higher-Z elements. Finally, we show that the isobaric-isothermal linear mixing rule for carbon and hydrogen EOS is a reasonable approximation with errors better than 1% for stellar-core conditions.

First-principles equation-of-state table of silicon and its effects on high-energy-density plasma simulations

Using density-functional theory-based molecular-dynamics simulations, we have investigated the equation of state for silicon in a wide range of plasma density and temperature conditions of ρ=0.001-500g/cm^{3} and T=2000-10^{8}K. With these calculations, we have established a first-principles equation-of-state (FPEOS) table of silicon for high-energy-density (HED) plasma simulations. When compared with the widely used SESAME-EOS model (Table3810), we find that the FPEOS-predicted Hugoniot is ∼20% softer; for off-Hugoniot plasma conditions, the pressure and internal energy in FPEOS are lower than those of SESAME EOS for temperatures above T ≈ 1-10 eV (depending on density), while the former becomes higher in the low-T regime. The pressure difference between FPEOS and SESAME 3810 can reach to ∼50%, especially in the warm-dense-matter regime. Implementing the FPEOS table of silicon into our hydrocodes, we have studied its effects on Si-target implosions. When compared with the one-dimensional radiation-hydrodynamics simulation using the SESAME 3810 EOS model, the FPEOS simulation showed that (1) the shock speed in silicon is ∼10% slower; (2) the peak density of an in-flight Si shell during implosion is ∼20% higher than the SESAME 3810 simulation; (3) the maximum density reached in the FPEOS simulation is ∼40% higher at the peak compression; and (4) the final areal density and neutron yield are, respectively, ∼30% and ∼70% higher predicted by FPEOS versus the traditional simulation using SESAME 3810. All of these features can be attributed to the larger compressibility of silicon predicted by FPEOS. These results indicate that an accurate EOS table, like the FPEOS presented here, could be essential for the precise design of targets for HED experiments.

First-principles studies on the equation of state, thermal conductivity, and opacity of deuterium-tritium (DT) and polystyrene (CH) for inertial confinement fusion applications

Using first-principles (FP) methods, we have performed ab initio compute for the equation of state (EOS), thermal conductivity, and opacity of deuterium-tritium (DT) in a wide range of densities and temperatures for inertial confinement fusion (ICF) applications. These systematic investigations have recently been expanded to accurately compute the plasma properties of CH ablators under extreme conditions. In particular, the first-principles EOS and thermal-conductivity tables of CH are self-consistently built from such FP calculations, which are benchmarked by experimental measurements. When compared with the traditional models used for these plasma properties in hydrocodes, significant differences have been identified in the warm dense plasma regime. When these FP-calculated properties of DT and CH were used in our hydrodynamic simulations of ICF implosions, we found that the target performance in terms of neutron yield and energy gain can vary by a factor of 2 to 3, relative to traditional model simulations.

First-principles equation of state and electronic properties of warm dense oxygen.

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 10(4)-10(9) 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 × 10(6) K. Pair-correlation functions and the electronic density of states reveal an 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. Finally, the computed shock Hugoniot curves show an increase in compression as the first and second shells are ionized.

First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions

Obtaining an accurate equation of state (EOS) of polystyrene (CH) is crucial to reliably design inertial confinement fusion (ICF) capsules using CH/CH-based ablators. With first-principles calculations, we have investigated the extended EOS of CH over a wide range of plasma conditions (ρ=0.1to100g/cm(3) and T=1000 to 4,000,000 K). When compared with the widely used SESAME-EOS table, the first-principles equation of state (FPEOS) of CH has shown significant differences in the low-temperature regime, in which strong coupling and electron degeneracy play an essential role in determining plasma properties. Hydrodynamic simulations of cryogenic target implosions on OMEGA using the FPEOS table of CH have predicted ∼30% decrease in neutron yield in comparison with the usual SESAME simulations. This is attributed to the ∼5% reduction in implosion velocity that is caused by the ∼10% lower mass ablation rate of CH predicted by FPEOS. Simulations using CH-FPEOS show better agreement with measurements of Hugoniot temperature and scattered light from ICF implosions.

First-principles equation of state and phase stability of niobium pentoxide

Niobium pentoxide is a polymorphic wide-gap semiconductor with good dielectric properties that make it an important material in technological applications. In spite of its significance, there are not theoretical studies of its phase stability and polymorphism. We have investigated the energetics and phase stability of several phases of Nb2O5 under pressure. The equation of state, the isothermal bulk moduli and the equilibrium crystal structures have been calculated from first-principles density functional theory for pressures up to 100kbar. The equation of state reveals that the stable crystalline structure at zero pressure is the H phase, then, a crystallographic phase transition takes place at 0.24kbar to the B phase. Additionally, it is shown that in the pressure range studied the B phase remains as the sole high-pressure stable phase.

First-principles equation-of-state table of deuterium for inertial confinement fusion applications

Understanding and designing inertial confinement fusion (ICF) implosions through radiation-hydrodynamics simulations rely on the accurate knowledge of the equation of state (EOS) of the deuterium and tritium fuels. To minimize the drive energy for ignition, the imploding shell of DT fuel must be kept as cold as possible. Such low-adiabat ICF implosions can access to coupled and degenerate plasma conditions, in which the analytical or chemical EOS models become inaccurate. Using the path-integral Monte Carlo (PIMC) simulations we have derived a first-principles EOS (FPEOS) table of deuterium that covers typical ICF fuel conditions at densities ranging from 0.002 to 1596 g/cm3 and temperatures of 1.35 eV to 5.5 keV. We report the internal energy and the pressure, and discuss the structure of the plasma in terms of pair-correlation functions. When compared with the widely used SESAME table and the revised Kerley03 table, discrepancies in the internal energy and in the pressure are identified for moderately coupled and degenerate plasma conditions. In contrast to the SESAME table, the revised Kerley03 table is in better agreement with our FPEOS results over a wide range of densities and temperatures. Although subtle differences still exist for lower temperatures (T < 10 eV) and moderate densities (1 to 10 g/cc), hydrodynamics simulations of cryogenic ICF implosions using the FPEOS table and the Kerley03 table have resulted in similar results for the peak density, areal density ({\rho}R), and neutron yield, which are significantly different from the SESAME simulations.

Strong Coupling and Degeneracy Effects in Inertial Confinement Fusion Implosions

Accurate knowledge about the equation of state (EOS) of deuterium is critical to inertial confinement fusion (ICF). Low-adiabat ICF implosions routinely access strongly coupled and degenerate plasma conditions. Using the path integral Monte Carlo method, we have derived a first-principles EOS (FPEOS) table of deuterium. It is the first ab initio EOS table which completely covers typical ICF implosion trajectory in the density and temperature ranges of ρ=0.002-1596 g/cm3 and T=1.35 eV-5.5 keV. Discrepancies in internal energy and pressure have been found in strongly coupled and degenerate regimes with respect to SESAME EOS. Hydrodynamics simulations of cryogenic ICF implosions using the FPEOS table have indicated significant differences in peak density, areal density (ρR), and neutron yield relative to SESAME simulations.

Ab Initio Equation of State of the Organic Molecular Crystal: β-Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine

We apply a simple strategy for calculating from first principles a thermodynamically complete equation of state for molecular crystals using readily available quantum chemistry techniques. The strategy involves a combination of separate methods for the temperature-independent mechanical compression and the thermal vibrational contributions to the free energy. A first principles equation of state for beta-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (beta-HMX) has been calculated for temperatures between 0 and 400 K and for specific volumes from 0.42 to 0.55 cm(3)/g, corresponding to relative volumes from 0.8 to 1.03. The calculated 300 K isotherm agrees very well with the experimentally measured pressure-volume relation. We also discuss thermodynamic properties of the material such as the volumetric thermal expansion coefficient, the Gruneisen parameter, and the specific heat (1.0 kJ/kg/K at 300 K and atmospheric pressure). The developed computational approach exhibits a reliable predictive power and is easily transferable to other molecular materials.

A Massive Core in Jupiter Predicted from First-Principles Simulations

Hydrogen-helium mixtures at conditions of Jupiter's interior are studied with first-principles computer simulations. The resulting equation of state (EOS) implies that Jupiter possesses a central core of 14-18 Earth masses of heavier elements, a result that supports core accretion as standard model for the formation of hydrogen-rich giant planets. Our nominal model has about 2 Earth masses of planetary ices in the H-He-rich mantle, a result that is, within modeling errors, consistent with abundances measured by the 1995 Galileo Entry Probe mission (equivalent to about 5 Earth masses of planetary ices when extrapolated to the mantle), suggesting that the composition found by the probe may be representative of the entire planet. Interior models derived from this first-principles EOS do not give a match to Jupiter's gravity moment J4 unless one invokes interior differential rotation, implying that jovian interior dynamics has an observable effect on the measured gravity field.

First-principles equations of state and elastic properties of seven metals

We present a systematic comparison of first-principles zero-temperature equations of state and elastic constants of seven metals (aluminum, titanium, copper, tantalum, tungsten, platinum, and gold) with the most recent diamond-anvil-cell (DAC) experimental data, for pressures up to 150 GPa. Our calculations were performed within density functional theory, testing both the local density approximation (LDA) and the generalized gradient approximation (GGA) to the exchange-correlation term, and using several types of pseudopotentials. The obtained pressure-volume relationships show good agreement with DAC data: the difference between ab initio pressure and experiment is at most 5 GPa at 100--150 GPa except for Au and Pt. The equilibrium volumes ${V}_{0}$ and bulk moduli ${K}_{0}$ are determined within 1.5% and 6% of DAC data respectively. Experimental results are better reproduced with GGA for Al, Ti, Cu, Ta and W, but with LDA for Pt and Au, in agreement with previous theoretical studies. The predicted elastic constants are within 10% of experiment. For tantalum we have also calculated phonon spectra under pressure. They are in excellent agreement with experimental data: especially they accurately reproduced the inflexion on the longitudinal branch in the $\ensuremath{\Gamma}$-H direction, which is typical of the VB column (V, Nb, Ta).

Erratum: First-principles equation of state and phase stability for the Ni-Al system under high pressures [Phys. Rev. B70, 094203 (2004)

Received 21 February 2005DOI:https://doi.org/10.1103/PhysRevB.71.139903©2005 American Physical Society

First-Principles Equation of State for an Energetic Intermetallic Mixture

AbstractThe thermodynamically complete equation of state P=P(ρ,T) for a intermetallic mixture of nickel and aluminum is obtained via first principle calculations for pressures up to 300GPa and temperatures up to 1000K. The calculations for the static-lattice EOS are carried out in the framework of the density functional theory (DFT), using generalized gradient approximations and ultrasoft psuedopotentials. The phonon modes are calculated by using the density functional perturbation theory (DFPT). First, the EOS for each species is obtained based on ab initio prediction of the electron ground state and thermal excitations. Then, the mixture theories are utilized to obtain the EOS for the mixture. Two mixture theories are proposed, which correspond to the two limiting cases. The nature of the real mixture is intermediate to those of the two idealized mixtures and hence can be modeled as a weighted combination of the two cases. The Comparisons of the EOS for nickel and aluminum obtained from existing shock Hugoniot data show good agreement with the theoretical results.

The evolution of multicomponent systems at high pressures: VI. The thermodynamic stability of the hydrogen-carbon system: the genesis of hydrocarbons and the origin of petroleum.

The spontaneous genesis of hydrocarbons that comprise natural petroleum have been analyzed by chemical thermodynamic-stability theory. The constraints imposed on chemical evolution by the second law of thermodynamics are briefly reviewed, and the effective prohibition of transformation, in the regime of temperatures and pressures characteristic of the near-surface crust of the Earth, of biological molecules into hydrocarbon molecules heavier than methane is recognized. For the theoretical analysis of this phenomenon, a general, first-principles equation of state has been developed by extending scaled particle theory and by using the technique of the factored partition function of the simplified perturbed hard-chain theory. The chemical potentials and the respective thermodynamic Affinity have been calculated for typical components of the H-C system over a range of pressures between 1 and 100 kbar (1 kbar = 100 MPa) and at temperatures consistent with those of the depths of the Earth at such pressures. The theoretical analyses establish that the normal alkanes, the homologous hydrocarbon group of lowest chemical potential, evolve only at pressures greater than approximately 30 kbar, excepting only the lightest, methane. The pressure of 30 kbar corresponds to depths of approximately 100 km. For experimental verification of the predictions of the theoretical analysis, a special high-pressure apparatus has been designed that permits investigations at pressures to 50 kbar and temperatures to 1,500 degrees C and also allows rapid cooling while maintaining high pressures. The high-pressure genesis of petroleum hydrocarbons has been demonstrated using only the reagents solid iron oxide, FeO, and marble, CaCO3, 99.9% pure and wet with triple-distilled water.

First-principles equations of state for Al, Cu, Mo, and Pb to ultrahigh pressures

Using accurate electronic-structure, interatomic-potential, and statistical methods, first-principles theoretical equations of state (EOSs) have been developed for the prototype metals Al, Cu, Mo, ...