Multiphase equation of state for carbon addressing high pressures and temperatures

Benedict, Lorin X.; Driver, Kevin P.; Hamel, Sébastien; Militzer, Burkhard; Qi, Tingting; Correa, Alfredo A.; Saúl, Andrés; Schwegler, Eric

doi:10.1103/physrevb.89.224109

Cited by 153 publications

(191 citation statements)

References 80 publications

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“…To test the validity of the linear mixing approximation at higher temperatures, relevant for stellar cores, we performed additional PIMC and DFT-MD simulations for pure H and C and combined them with EOS tables from Refs. [68,73]. Our results in Figs.…”

Section: Figsupporting

confidence: 69%

“…Similar to the PIMC simulations of hydrogen [57,58,[64][65][66][67][68][69][70], helium [59,71], H-He mixtures [72], carbon [60,73], nitrogen [74], oxygen [75], neon [76], and water [60], we employ a free-particle nodal structure. We enforce fermion nodes at a small imaginary time interval of 1/8192 Hartree −1 (Ha −1 ) while pair density matrices [77,78] are evaluated in larger step of 1/1024 Ha −1 [67].…”

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confidence: 99%

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

et al. 2017

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We use path integral Monte Carlo and density functional molecular dynamics to construct a coherent set of equation of state 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 − 22.4 g cm −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 EOSs is a reasonable approximation with errors better than 1% for stellar-core conditions.Introduction. Hydrocarbon ablator materials are of primary importance for laser-driven shock experiments, such as those central to the study of inertial confinement fusion (ICF) [1][2][3] and the measurement of high energy density states relevant to giant planets [4] and stellar objects [5]. Accurate knowledge of the equation of state (EOS) of the hydrocarbon ablator is essential for optimizing experimental designs to achieve desired density and temperature states in a target. Consequently, a number of planar-driven shock wave experiments have been performed on hydrocarbon materials, including polystyrene (CH) [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], glow-discharge polymer (GDP) [24][25][26][27][28], and foams [29][30][31][32], to measure the EOS. The highest pressure achieved among these experiments is 40 Mbar [14,15], which is yet not high enough to probe the effects of Kshell ionization on the shock Hugoniot curve. Since the first X-ray scattering results on CH at above 0.1 Gbar (1 Gbar=100 TPa) [33], ongoing, spherically-converging shock experiments using the Gbar platform at the National Ignition Facility (NIF) [34][35][36][37][38] and the OMEGA laser [39] will extend measurements of the shock Hugoniot curve of polystyrene to pressures above 0.35 Gbar and into the K-shell ionization regime [40].

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

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“…While previous EOS for aluminum have been constructed [6][7][8] , none provide the high pressure solid phases, or have had access to the broad range of high accuracy simulations we have performed to constrain particularly the liquid state. However, several recent EOS have been constructed for different materials which are both multiphase and inclusive of the warm dense matter regime, and have also highly relied on simulation data [9][10][11] .…”

Section: Introductionmentioning

confidence: 99%

Multiphase aluminum equations of state via density functional theory

2016

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We have performed density functional theory (DFT) based calculations for aluminum in extreme conditions of both pressure and temperature, up to 5 times compressed ambient density and over 1 000 000 K in temperature. In order to cover such a domain, DFT methods including phonon calculations, quantum molecular dynamics, and orbital-free DFT are employed. The results are then used to construct a SESAME equation of state for the aluminum 1100 alloy, encompassing the fcc, hcp and bcc solid phases as well as the liquid regime. We provide extensive comparison with experiment and based on this we also provide a slightly modified equation of state for the aluminum 6061 alloy.

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“…Recently, we have been developing PIMC for simulating heavier elements [46][47][48][52][53][54][55][56][57][58] , which is efficient at high temperatures, and can be used to complement DFT-MD calculations that are efficient at comparatively low temperatures. Combined data from PIMC and DFT-MD provide a coherent EOS over a wide density-temperature range that spans the condensed matter, WDM, and plasma regimes.…”

Section: Introductionmentioning

confidence: 99%

Equation of state and shock compression of warm dense sodium—A first-principles study

Zhang

Driver

Soubiran

et al. 2017

The Journal of Chemical Physics

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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 [B. Militzer and K. P. Driver, Phys. Rev. Lett. 115, 176403 (2015)] 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 densitytemperature range of 1.93 − 11.60 g/cm 3 and 10 3 − 1.29 × 10 8 K. We find that a localized, Hartree-Fock nodal structure in PIMC yields pressures and internal energies that are consistent with DFT-MD at intermediate temperatures of 2×10 6 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 10 7 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. We also compute the temperature-density dependence of thermal and pressure ionization processes.

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Multiphase equation of state for carbon addressing high pressures and temperatures

Cited by 153 publications

References 80 publications

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

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

Multiphase aluminum equations of state via density functional theory

Equation of state and shock compression of warm dense sodium—A first-principles study

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