Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements

Militzer, Burkhard; Driver, Kevin P.

doi:10.1103/physrevlett.115.176403

Cited by 89 publications

(89 citation statements)

References 62 publications

(84 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In recent work 47 , we show that the applicability range of PIMC simulations can extend to lower temperatures when a number of n s atomic orbitals at each ion I are added to the FP nodes,…”

Section: Simulation Methodsmentioning

confidence: 99%

“…Similar to the PIMC simulations of Si 47 and recently of Na at one density 58 , we treat the nuclei classically because of the high temperatures considered here. Electronic Coulomb interactions are introduced via pair density matrices 77 .…”

Section: Simulation Methodsmentioning

confidence: 99%

“…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%

“…Development of rigorous, first-principles frameworks, such as path integral Monte Carlo (PIMC) [45][46][47] or density functional theory molecular dynamics (DFT-MD) [48][49][50][51] , for computing the EOS and behavior of materials in extreme pressure and temperature conditions is needed as Gbar-range shock experiments are emerging and data need to be interpreted. 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.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…In recent work 47 , we show that the applicability range of PIMC simulations can extend to lower temperatures when a number of n s atomic orbitals at each ion I are added to the FP nodes,…”

Section: Simulation Methodsmentioning

confidence: 99%

Section: Simulation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…Early developmental work established the accuracy of the method for fully-ionized hydrogen [57,58] and helium [59] plasmas using free-particle nodes. In recent works, we have further developed free-particle [60] and localized [61] nodal structures, which has allowed us to compute first-principles EOSs across a wide range of density-temperature regimes for heavier, first-and second-row, elements.…”

mentioning

confidence: 99%

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

et al. 2017

Self Cite

View full text Add to dashboard Cite

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].

show abstract

Understanding Jupiter's interior

et al. 2016

Self Cite

View full text Add to dashboard Cite

This article provides an overview of how models of giant planet interiors are constructed. We review measurements from past space missions that provided constraints for the interior structure of Jupiter. We discuss typical three‐layer interior models that consist of a dense central core and an inner metallic and an outer molecular hydrogen‐helium layer. These models rely heavily on experiments, analytical theory, and first‐principles computer simulations of hydrogen and helium to understand their behavior up to the extreme pressures ∼10 Mbar and temperatures ∼10,000 K. We review the various equations of state used in Jupiter models and compare them with shock wave experiments. We discuss the possibility that helium rain, core erosion, and double diffusive convection have affected the structure and evolution of giant planets. In July 2016 the Juno spacecraft entered orbit around Jupiter, promising high‐precision measurements of the gravitational field that will allow us to test our understanding of gas giant interiors better than ever before.

show abstract

Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements

Cited by 89 publications

References 62 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

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

Understanding Jupiter's interior

Contact Info

Product

Resources

About