First-principles prediction of the softening of the silicon shock Hugoniot curve

Hu, S. X.; Militzer, B.; Collins, L. A.; Driver, K. P.; Kress, J. D.

doi:10.1103/PhysRevB.94.094109

Title: First-principles prediction of the softening of the silicon shock Hugoniot curve

Journal Article · Thu Sep 15 00:00:00 EDT 2016 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.94.094109· OSTI ID:1328774

Hu, S. X. ^[1]; Militzer, B. ^[2]; Collins, L. A. ^[3]; Driver, K. P. ^[2]; Kress, J. D. ^[3]

Univ. of Rochester, Rochester, NY (United States)
Univ. of California, Berkeley, CA (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Here, whock compression of silicon (Si) under extremely high pressures (>100 Mbar) was investigated by using two first-principles methods of orbital-free molecular dynamics (OFMD) and path integral Monte Carlo (PIMC). While pressures from the two methods agree very well, PIMC predicts a second compression maximum because of 1s electron ionization that is absent in OFMD calculations since Thomas–Fermi-based theories lack inner shell structure. The Kohn–Sham density functional theory is used to calculate the equation of state (EOS) of warm dense silicon for low-pressure loadings (P < 100 Mbar). Combining these first-principles EOS results, the principal Hugoniot curve of silicon for pressures varying from 0.80 Mbar to above ~10 Gbar was derived. We find that silicon is ~20% or more softer than what was predicted by EOS models based on the chemical picture of matter. Existing experimental data (P ≈ 1–2 Mbar) seem to indicate this softening behavior of Si, which calls for future strong-shock experiments (P > 10 Mbar) to benchmark our results.

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Research Organization:: Univ. of Rochester, NY (United States). Lab. for Laser Energetics

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0001944; AC52-06NA25396; SC0010517

OSTI ID:: 1328774

Alternate ID(s):: OSTI ID: 1324863

Journal Information:: Physical Review B, Vol. 94, Issue 9; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 37 works

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References (72)

Axial Yield Strengths and Two Successive Phase Transition Stresses for Crystalline Silicon Gust, W. H.; Royce, E. B. Journal of Applied Physics, Vol. 42, Issue 5 https://doi.org/10.1063/1.1660465	journal	April 1971
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
Benchmarking density functionals for hydrogen-helium mixtures with quantum Monte Carlo: Energetics, pressures, and forces Clay, Raymond C.; Holzmann, Markus; Ceperley, David M. Physical Review B, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevB.93.035121	journal	January 2016
The chemistry of silicon in hot molecular cores Mackay, D. D. S. Monthly Notices of the Royal Astronomical Society, Vol. 274, Issue 3 https://doi.org/10.1093/mnras/274.3.694	journal	June 1995
Dynamical and optical properties of warm dense hydrogen Collins, L. A.; Bickham, S. R.; Kress, J. D. Physical Review B, Vol. 63, Issue 18 https://doi.org/10.1103/PhysRevB.63.184110	journal	April 2001
Molecular dynamics simulations of shock-compressed single-crystal silicon Mogni, Gabriele; Higginbotham, Andrew; Gaál-Nagy, Katalin Physical Review B, Vol. 89, Issue 6 https://doi.org/10.1103/PhysRevB.89.064104	journal	February 2014
Thermodynamics of hot dense H-plasmas: path integral Monte Carlo simulations and analytical approximations Filinov, V. S.; Bonitz, M.; Ebeling, W. Plasma Physics and Controlled Fusion, Vol. 43, Issue 6 https://doi.org/10.1088/0741-3335/43/6/301	journal	May 2001
First-principles equation of state and electronic properties of warm dense oxygen Driver, K. P.; Soubiran, F.; Zhang, Shuai The Journal of Chemical Physics, Vol. 143, Issue 16 https://doi.org/10.1063/1.4934348	journal	October 2015
Properties and computation of the Coulomb pair density matrix Pollock, E. L. Computer Physics Communications, Vol. 52, Issue 1 https://doi.org/10.1016/0010-4655(88)90171-3	journal	December 1988
Equation of State of the Hydrogen Plasma by Path Integral Monte Carlo Simulation Pierleoni, C.; Ceperley, D. M.; Bernu, B. Physical Review Letters, Vol. 73, Issue 16 https://doi.org/10.1103/PhysRevLett.73.2145	journal	October 1994
Improving the hot-spot pressure and demonstrating ignition hydrodynamic equivalence in cryogenic deuterium–tritium implosions on OMEGA Goncharov, V. N.; Sangster, T. C.; Betti, R. Physics of Plasmas, Vol. 21, Issue 5 https://doi.org/10.1063/1.4876618	journal	May 2014
Reduction of Shear Strength and Phase-Transition in Shock-Loaded Silicon Goto, Tsuneaki; Sato, Toshiyuki; Syono, Yasuhiko Japanese Journal of Applied Physics, Vol. 21, Issue Part 2, No. 6 https://doi.org/10.1143/JJAP.21.L369	journal	June 1982
Very-high-temperature molecular dynamics Lambert, Flavien; Clérouin, Jean; Zérah, Gilles Physical Review E, Vol. 73, Issue 1 https://doi.org/10.1103/PhysRevE.73.016403	journal	January 2006
Path Integral Monte Carlo Calculation of the Deuterium Hugoniot Militzer, B.; Ceperley, D. M. Physical Review Letters, Vol. 85, Issue 9 https://doi.org/10.1103/PhysRevLett.85.1890	journal	August 2000
$Ab$ $initio$ calculation of the shock Hugoniot of bulk silicon Strickson, Oliver; Artacho, Emilio Physical Review B, Vol. 93, Issue 9 https://doi.org/10.1103/PhysRevB.93.094107	journal	March 2016
Experimental reduction of laser imprinting and Rayleigh–Taylor growth in spherically compressed, medium-Z-doped plastic targets Fiksel, G.; Hu, S. X.; Goncharov, V. A. Physics of Plasmas, Vol. 19, Issue 6 https://doi.org/10.1063/1.4729732	journal	June 2012
First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions Hu, S. X.; Collins, L. A.; Goncharov, V. N. Physical Review E, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevE.92.043104	journal	October 2015
Dense hydrogen plasma: Comparison between models Clérouin, J. G.; Bernard, S. Physical Review E, Vol. 56, Issue 3 https://doi.org/10.1103/PhysRevE.56.3534	journal	September 1997
Ab initiomolecular dynamics for liquid metals Kresse, G.; Hafner, J. Physical Review B, Vol. 47, Issue 1, p. 558-561 https://doi.org/10.1103/PhysRevB.47.558	journal	January 1993
Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements Militzer, Burkhard; Driver, Kevin P. Physical Review Letters, Vol. 115, Issue 17 https://doi.org/10.1103/PhysRevLett.115.176403	journal	October 2015
Computation of the high temperature Coulomb density matrix in periodic boundary conditions Militzer, B. Computer Physics Communications, Vol. 204 https://doi.org/10.1016/j.cpc.2016.03.011	journal	July 2016
Shock compression of Fe-Ni-Si system to 280 GPa: Implications for the composition of the Earth's outer core: Sekine, et al.: Shock compression of Fe-Ni-Si system Zhang, Youjun; Sekine, Toshimori; He, Hongliang Geophysical Research Letters, Vol. 41, Issue 13 https://doi.org/10.1002/2014GL060670	journal	July 2014
Multiphase equation of state for carbon addressing high pressures and temperatures Benedict, Lorin X.; Driver, Kevin P.; Hamel, Sebastien Physical Review B, Vol. 89, Issue 22 https://doi.org/10.1103/PhysRevB.89.224109	journal	June 2014
Progress on LMJ targets for ignition Cherfils-Clérouin, C.; Boniface, C.; Bonnefille, M. Journal of Physics: Conference Series, Vol. 244, Issue 2 https://doi.org/10.1088/1742-6596/244/2/022009	journal	August 2010
Direct verification of mixing rules in the hot and dense regime Lambert, F.; Clérouin, J.; Danel, J. -F. Physical Review E, Vol. 77, Issue 2 https://doi.org/10.1103/PhysRevE.77.026402	journal	February 2008
Electron-ion equilibration in a strongly coupled plasma Ng, A.; Celliers, P.; Xu, G. Physical Review E, Vol. 52, Issue 4 https://doi.org/10.1103/PhysRevE.52.4299	journal	October 1995
Average atom transport properties for pure and mixed species in the hot and warm dense matter regimes Starrett, C. E.; Clérouin, J.; Recoules, V. Physics of Plasmas, Vol. 19, Issue 10 https://doi.org/10.1063/1.4764937	journal	October 2012
On the transport coefficients of hydrogen in the inertial confinement fusion regime Lambert, Flavien; Recoules, Vanina; Decoster, Alain Physics of Plasmas, Vol. 18, Issue 5 https://doi.org/10.1063/1.3574902	journal	May 2011
First-principles simulations and shock Hugoniot calculations of warm dense neon Driver, K. P.; Militzer, B. Physical Review B, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevB.91.045103	journal	January 2015
First-principles equation of state calculations of warm dense nitrogen Driver, K. P.; Militzer, B. Physical Review B, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevB.93.064101	journal	February 2016
Density-functional calculations of the liquid deuterium Hugoniot, reshock, and reverberation timing Desjarlais, Michael P. Physical Review B, Vol. 68, Issue 6 https://doi.org/10.1103/PhysRevB.68.064204	journal	August 2003
Outstanding questions in electron-ion energy relaxation, lattice stability, and dielectric function of warm dense matter Ng, Andrew International Journal of Quantum Chemistry, Vol. 112, Issue 1 https://doi.org/10.1002/qua.23197	journal	September 2011
Shock Response and Phase Transitions of MgO at Planetary Impact Conditions Root, Seth; Shulenburger, Luke; Lemke, Raymond W. Physical Review Letters, Vol. 115, Issue 19 https://doi.org/10.1103/PhysRevLett.115.198501	journal	November 2015
Silicon chemistry in interstellar clouds Langer, William D.; Glassgold, A. E. The Astrophysical Journal, Vol. 352 https://doi.org/10.1086/168519	journal	March 1990
A new quotidian equation of state (QEOS) for hot dense matter More, R. M.; Warren, K. H.; Young, D. A. Physics of Fluids, Vol. 31, Issue 10 https://doi.org/10.1063/1.866963	journal	January 1988
Gradient correction to the statistical electronic free energy at nonzero temperatures: Application to equation-of-state calculations Perrot, F. Physical Review A, Vol. 20, Issue 2 https://doi.org/10.1103/PhysRevA.20.586	journal	August 1979
All-Electron Path Integral Monte Carlo Simulations of Warm Dense Matter: Application to Water and Carbon Plasmas Driver, K. P.; Militzer, B. Physical Review Letters, Vol. 108, Issue 11 https://doi.org/10.1103/PhysRevLett.108.115502	journal	March 2012
The experimental plan for cryogenic layered target implosions on the National Ignition Facility—The inertial confinement approach to fusion Edwards, M. J.; Lindl, J. D.; Spears, B. K. Physics of Plasmas, Vol. 18, Issue 5 https://doi.org/10.1063/1.3592173	journal	May 2011
Thermal equilibration in a shock wave Celliers, P.; Ng, A.; Xu, G. Physical Review Letters, Vol. 68, Issue 15 https://doi.org/10.1103/PhysRevLett.68.2305	journal	April 1992
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/PhysRevB.54.11169	journal	October 1996
Molecular dynamics simulation of Coulomb explosion, melting and shock wave creation in silicon after an ionization pulse Li, Zhongyu; Chen, Di; Wang, Jing Journal of Applied Physics, Vol. 115, Issue 14 https://doi.org/10.1063/1.4869795	journal	April 2014
Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium Kresse, G.; Hafner, J. Physical Review B, Vol. 49, Issue 20, p. 14251-14269 https://doi.org/10.1103/PhysRevB.49.14251	journal	May 1994
Inhomogeneous Electron Gas Hohenberg, P.; Kohn, W. Physical Review, Vol. 136, Issue 3B, p. B864-B871 https://doi.org/10.1103/PhysRev.136.B864	journal	November 1964
Quantum molecular dynamics simulations of hot, dense hydrogen Collins, L.; Kwon, I.; Kress, J. Physical Review E, Vol. 52, Issue 6 https://doi.org/10.1103/PhysRevE.52.6202	journal	December 1995
Strong Coupling and Degeneracy Effects in Inertial Confinement Fusion Implosions Hu, S. X.; Militzer, B.; Goncharov, V. N. Physical Review Letters, Vol. 104, Issue 23 https://doi.org/10.1103/PhysRevLett.104.235003	journal	June 2010
Combining Kohn-Sham and orbital-free density-functional theory for Hugoniot calculations to extreme pressures Sheppard, Daniel; Kress, Joel D.; Crockett, Scott Physical Review E, Vol. 90, Issue 6 https://doi.org/10.1103/PhysRevE.90.063314	journal	December 2014
Plastic Deformation in Silicon Crystal Induced by Heat-Assisted Laser Shock Peening Cheng, Gary J.; Cai, M.; Pirzada, Daniel Journal of Manufacturing Science and Engineering, Vol. 130, Issue 1 https://doi.org/10.1115/1.2815343	journal	February 2008
First-principles equations of state for simulations of shock waves in silicon Swift, D. C.; Ackland, G. J.; Hauer, A. Physical Review B, Vol. 64, Issue 21 https://doi.org/10.1103/PhysRevB.64.214107	journal	November 2001
Variational density matrix method for warm, condensed matter: Application to dense hydrogen Militzer, Burkhard; Pollock, E. L. Physical Review E, Vol. 61, Issue 4 https://doi.org/10.1103/PhysRevE.61.3470	journal	April 2000
Direct-drive inertial confinement fusion: A review Craxton, R. S.; Anderson, K. S.; Boehly, T. R. Physics of Plasmas, Vol. 22, Issue 11 https://doi.org/10.1063/1.4934714	journal	November 2015
Path integrals in the theory of condensed helium Ceperley, D. M. Reviews of Modern Physics, Vol. 67, Issue 2 https://doi.org/10.1103/RevModPhys.67.279	journal	April 1995
Simulations of dense atomic hydrogen in the Wigner crystal phase Militzer, Burkhard; Graham, Rebekah L. Journal of Physics and Chemistry of Solids, Vol. 67, Issue 9-10 https://doi.org/10.1016/j.jpcs.2006.05.015	journal	September 2006
First Principles Calculations of Shock Compressed Fluid Helium Militzer, B. Physical Review Letters, Vol. 97, Issue 17 https://doi.org/10.1103/PhysRevLett.97.175501	journal	October 2006
Quantum molecular dynamics simulations of transport properties in liquid and dense-plasma plutonium Kress, J. D.; Cohen, James S.; Kilcrease, D. P. Physical Review E, Vol. 83, Issue 2 https://doi.org/10.1103/PhysRevE.83.026404	journal	February 2011
Thermal Properties of the Inhomogeneous Electron Gas Mermin, N. David Physical Review, Vol. 137, Issue 5A https://doi.org/10.1103/PhysRev.137.A1441	journal	March 1965
First-principles equation-of-state table of deuterium for inertial confinement fusion applications Hu, S. X.; Militzer, B.; Goncharov, V. N. Physical Review B, Vol. 84, Issue 22 https://doi.org/10.1103/PhysRevB.84.224109	journal	December 2011
A generic model for the ionic contribution to the equation of state Johnson, J. D. High Pressure Research, Vol. 6, Issue 5 https://doi.org/10.1080/08957959108203212	journal	December 1991
Germanium multiphase equation of state Crockett, S. D.; Lorenzi-Venneri, G. De; Kress, J. D. Journal of Physics: Conference Series, Vol. 500, Issue 3 https://doi.org/10.1088/1742-6596/500/3/032006	journal	May 2014
Mitigating Laser Imprint in Direct-Drive Inertial Confinement Fusion Implosions with High- $Z$ Dopants Hu, S. X.; Fiksel, G.; Goncharov, V. N. Physical Review Letters, Vol. 108, Issue 19 https://doi.org/10.1103/PhysRevLett.108.195003	journal	May 2012
Reflectivity and Optical Brightness of Laser-Induced Shocks in Silicon Löwer, Th.; Kondrashov, V. N.; Basko, M. Physical Review Letters, Vol. 80, Issue 18 https://doi.org/10.1103/PhysRevLett.80.4000	journal	May 1998
Anomalous Elastic Response of Silicon to Uniaxial Shock Compression on Nanosecond Time Scales Loveridge-Smith, A.; Allen, A.; Belak, J. Physical Review Letters, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevLett.86.2349	journal	March 2001
The Chemistry of Silicon in Hot Molecular Cores Mackay, D. D. S. Circumstellar Matter 1994 https://doi.org/10.1007/978-94-011-0147-9_117	book	January 1995
Ab initio calculation of the shock Hugoniot of bulk silicon Strickson, O.; Artacho, Emilio Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.11119	text	January 2016
Anomalous Elastic Response of Silicon to Uniaxial Shock Compression on Nanosecond Time Scales Allen, A.; Belak, J.; Boehly, T. The American Physical Society https://doi.org/10.17877/de290r-16258	text	January 2001
The chemistry of silicon in hot molecular cores Mackay, D. D. S. Astrophysics and Space Science, Vol. 224, Issue 1-2 https://doi.org/10.1007/bf00667928	journal	February 1995
Shock Response and Phase Transitions of MgO at Planetary Impact Conditions Root, Seth; Shulenburger, Luke; Lemke, Raymond W. arXiv https://doi.org/10.48550/arxiv.1502.00009	text	January 2015
Ab initio calculation of the shock Hugoniot of bulk silicon Strickson, Oliver; Artacho, Emilio arXiv https://doi.org/10.48550/arxiv.1507.01751	text	January 2015
Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements Militzer, Burkhard; Driver, Kevin P. arXiv https://doi.org/10.48550/arxiv.1510.07278	text	January 2015
First-Principles Equation of State and Electronic Properties of Warm Dense Oxygen Driver, K. P.; Soubiran, F.; Zhang, Shuai arXiv https://doi.org/10.48550/arxiv.1601.05782	text	January 2016
Simulations of Dense Atomic Hydrogen in the Wigner Crystal Phase Militzer, Burkhard; Graham, Rebekah L. arXiv https://doi.org/10.48550/arxiv.cond-mat/0506463	text	January 2005
First Principles Calculations of Shock Compressed Fluid Helium Militzer, B. arXiv https://doi.org/10.48550/arxiv.cond-mat/0609640	text	January 2006
Variational Density Matrix Method for Warm Condensed Matter and Application to Dense Hydrogen Militzer, Burkhard; Pollock, E. L. arXiv https://doi.org/10.48550/arxiv.physics/9910009	text	January 1999

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