Path Integral Monte Carlo Calculation of the Deuterium Hugoniot

Militzer, Burkhard; Ceperley, David M.

doi:10.1103/physrevlett.85.1890

Cited by 264 publications

(309 citation statements)

References 16 publications

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“…Therefore, PIMC becomes increasingly efficient at higher temperatures as paths become shorter and more classical in nature. However, application of PIMC to study real materials other than hydrogen 45,52,[63][64][65][66][67][68][69] , helium 53,70 , hydrogen-helium mixtures 71 , and one-component plasmas 72,73 , is difficult because of the complex fermion sign problem, nonlocal pseudopotentials, and complex nodal structures 74 . The sign problem in fermionic PIMC simulations is usually addressed with the fixed-node approximation 74 that restricts paths to positive regions of a trial density matrix, ρ T (R, R t ; t) > 0.…”

Section: Simulation Methodsmentioning

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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Section: Simulation Methodsmentioning

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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“…In order to minimize finite-size errors, the total energy was converged to better than 0.2% for a 24 atom cubic cell. Though this may seem like a small number of atoms, we stress that the number of atoms/cell needed to accurately compute energy and pressure decreases rapidly for condensed systems as T is increased into the plasma regime [14,34,51].…”

Section: B Pimc Calculationsmentioning

confidence: 99%

“…Fermionic PIMC simulations have been applied to study hydrogen [31][32][33][34][35][36][37][38][39], helium [40,41], hydrogen-helium mixtures [42], and one-component plasmas [43,44], and most recently to simulate carbon and water plasmas [14]. In PIMC simulations, electrons and nuclei are treated equally as Feynman paths in a stochastic framework for solving the full, finite-temperature, quantum many-body problem.…”

Section: B Pimc Calculationsmentioning

confidence: 99%

Multiphase equation of state for carbon addressing high pressures and temperatures

et al. 2014

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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.

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“…Typically the EOS is pieced together from different analytically known limits, experimental data, and computer simulation results. However, the high compressions seen in the predictions of chemical models were not confirmed by first principles simulation techniques such as density functional molecular dynamics [6] and PIMC [7]. Both results are in relatively good agreement with each other, predicting a lower compressibility and a Hugoniot curve close to that of the Sesame model.…”

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confidence: 83%

Path integral calculation of shock Hugoniot curves of precompressed liquid deuterium

Militzer¹

2003

J. Phys. A: Math. Gen.

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Abstract. Path integral Monte Carlo simulations have been used to study deuterium at high pressure and temperature. The equation of state has been derived in the temperature and density region of 10 000 ≤ T ≤ 1 000 000 K and 0.6 ≤ ρ ≤ 2.5 g cm −3 . A series of shock Hugoniot curves is computed for different initial compressions in order to compare with current and future shock wave experiments using liquid deuterium samples precompressed in diamond anvil cells. The equation of state of dense deuterium has been the topic of intense discussions since Nova laser shock wave experiments [1] measured the Hugoniot curve up to megabar pressures in 1997 and predicted an unexpectedly high compressibility. Four years later, Knudson et al. measured a significantly smaller compressibility using magnetically driven flyer plates [2]. This controversy continues to initiate new efforts to determine the EOS in different regions of the high temperature phase diagram. In a new approach to reach higher densities, G.W. Collins and P. Cellier use a diamond anvil cell (DAC) to precompress samples of liquid deuterium and then launch laser shock into them. The focus of this article is to use path integral Monte Carlo (PIMC) results to determine Hugoniot curves for precompressed samples in order to make a prediction for comparison with current and future experiments.The two series of shock wave experiments using the Nova laser [1, 3] reached pressures of up to 340 GPa and predicted a 50% higher compressibility than previously estimated. The results provided the first experimental data in a regime of extreme pressure and temperature, in which our understanding had so far been primarily based on analytical models and computer simulations. The experimental findings suggested that standard EOS models such as Sesame [4] were too stiff, predicting a maximum compression of about 4-fold the initial density. Instead the measured EOS was found to be closer to softer models like [5] that predicts a maximum compression ratio of about 6. Such a difference in the EOS of dense hydrogen and deuterium would have significant consequences for our understanding of Jovian planets, brown dwarfs, and low mass stars as well as for the design of the inertial confinement fusion strategies. § militzer@llnl.gov

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Path Integral Monte Carlo Calculation of the Deuterium Hugoniot

Cited by 264 publications

References 16 publications

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

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

Multiphase equation of state for carbon addressing high pressures and temperatures

Path integral calculation of shock Hugoniot curves of precompressed liquid deuterium

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