First-principles equation-of-state table of beryllium based on density-functional theory calculations

Ding, Y. H.; Hu, S. X.

doi:10.1063/1.4984780

First-principles equation-of-state table of beryllium based on density-functional theory calculations

Journal Article · Tue Jun 06 04:00:00 EDT 2017 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4984780· OSTI ID:1361691

Ding, Y. H. ^[1]; Hu, S. X. ^[2]

Univ. of Rochester, NY (United States). Lab. for Laser Energetics. Dept. of Mechanical Engineering; Laboratory for Laser Energetics, University of Rochester
Univ. of Rochester, NY (United States). Lab. for Laser Energetics

Beryllium has been considered a superior ablator material for inertial confinement fusion (ICF) target designs. An accurate equation-of-state (EOS) of beryllium under extreme conditions is essential for reliable ICF designs. Based on density-functional theory (DFT) calculations, we have established a wide-range beryllium EOS table of density ρ = 0.001 to 500 g/cm³ and temperature T = 2000 to 10⁸ K. Our first-principle equation-of-state (FPEOS) table is in better agreement with the widely used SESAME EOS table (SESAME 2023) than the average-atom INFERNO and Purgatorio models. For the principal Hugoniot, our FPEOS prediction shows ~10% stiffer than the last two models in the maximum compression. Although the existing experimental data (only up to 17 Mbar) cannot distinguish these EOS models, we anticipate that high-pressure experiments at the maximum compression region should differentiate our FPEOS from INFERNO and Purgatorio models. Comparisons between FPEOS and SESAME EOS for off-Hugoniot conditions show that the differences in the pressure and internal energy are within ~20%. By implementing the FPEOS table into the 1-D radiation–hydrodynamic code LILAC, we studied in this paper the EOS effects on beryllium-shell–target implosions. Finally, the FPEOS simulation predicts higher neutron yield (~15%) compared to the simulation using the SESAME 2023 EOS table.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Rochester, NY (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); Univ. of Rochester (United States); New York State Energy Research and Development Authority (United States)

Grant/Contract Number:: NA0001944

OSTI ID:: 1361691

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 6 Vol. 24; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (63)

Purgatorio—a new implementation of the Inferno algorithm Wilson, B.; Sonnad, V.; Sterne, P. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 99, Issue 1-3 https://doi.org/10.1016/j.jqsrt.2005.05.053	journal	May 2006
Beryllium 10 concentrations in the Greenland Ice Sheet Project 2 ice core from 3-40 ka Finkel, R. C.; Nishiizumi, K. Journal of Geophysical Research: Oceans, Vol. 102, Issue C12 https://doi.org/10.1029/97JC01282	journal	November 1997
Inertial-confinement fusion with lasers Betti, R.; Hurricane, O. A. Nature Physics, Vol. 12, Issue 5 https://doi.org/10.1038/nphys3736	journal	May 2016
Overview of materials technologies for space nuclear power and propulsion Zinkle, S. J.; Ott, L. J.; Ingersoll, D. T. SPACE TECHNOLOGY AND APPLICATIONS INTERNATIONAL FORUM- STAIF 2002, AIP Conference Proceedings https://doi.org/10.1063/1.1449838	conference	January 2002
Performance of direct-drive cryogenic targets on OMEGA Goncharov, V. N.; Sangster, T. C.; Radha, P. B. Physics of Plasmas, Vol. 15, Issue 5 https://doi.org/10.1063/1.2856551	journal	May 2008
Shock compression of molybdenum to 2.0 TPa by means of a nuclear explosion Ragan III, C. E.; Silbert, M. G.; Diven, B. C. Journal of Applied Physics, Vol. 48, Issue 7 https://doi.org/10.1063/1.324094	journal	July 1977
Equation of state of beryllium at shock pressures of 0.4–1.1 TPa (4–11 Mbar) Nellis, W. J.; Moriarty, J. A.; Mitchell, A. C. Journal of Applied Physics, Vol. 82, Issue 5 https://doi.org/10.1063/1.366029	journal	September 1997
Crossed-beam energy transfer in direct-drive implosions Igumenshchev, I. V.; Seka, W.; Edgell, D. H. Physics of Plasmas, Vol. 19, Issue 5, Article No. 056314 https://doi.org/10.1063/1.4718594	journal	May 2012
Mitigation of cross-beam energy transfer: Implication of two-state focal zooming on OMEGA Froula, D. H.; Kessler, T. J.; Igumenshchev, I. V. Physics of Plasmas, Vol. 20, Issue 8 https://doi.org/10.1063/1.4818427	journal	August 2013
Optimized beryllium target design for indirectly driven inertial confinement fusion experiments on the National Ignition Facility Simakov, Andrei N.; Wilson, Douglas C.; Yi, Sunghwan A. Physics of Plasmas, Vol. 21, Issue 2 https://doi.org/10.1063/1.4864331	journal	February 2014
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
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
First-principles investigations on ionization and thermal conductivity of polystyrene for inertial confinement fusion applications Hu, S. X.; Collins, L. A.; Goncharov, V. N. Physics of Plasmas, Vol. 23, Issue 4 https://doi.org/10.1063/1.4945753	journal	April 2016
Fast temperature relaxation model in dense plasmas Faussurier, Gérald; Blancard, Christophe Physics of Plasmas, Vol. 24, Issue 1 https://doi.org/10.1063/1.4973225	journal	January 2017
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
Ignition target design and robustness studies for the National Ignition Facility Krauser, William J.; Hoffman, Nelson M.; Wilson, Douglas C. Physics of Plasmas, Vol. 3, Issue 5 https://doi.org/10.1063/1.872006	journal	May 1996
Absolute measurements of the equations of state of low-Z materials in the multi-Mbar regime using laser-driven shocks Cauble, R.; Da Silva, L. B.; Perry, T. S. Physics of Plasmas, Vol. 4, Issue 5 https://doi.org/10.1063/1.872362	journal	May 1997
The development and advantages of beryllium capsules for the National Ignition Facility Wilson, Douglas C.; Bradley, Paul A.; Hoffman, Nelson M. Physics of Plasmas, Vol. 5, Issue 5 https://doi.org/10.1063/1.872865	journal	May 1998
Review of indirect-drive ignition design options for the National Ignition Facility Dittrich, T. R.; Haan, S. W.; Marinak, M. M. Physics of Plasmas, Vol. 6, Issue 5 https://doi.org/10.1063/1.873467	journal	May 1999
Introduction to Beryllium: Uses, Regulatory History, and Disease Kolanz, Marc E. Applied Occupational and Environmental Hygiene, Vol. 16, Issue 5 https://doi.org/10.1080/10473220119088	journal	May 2001
Progress towards polar-drive ignition for the NIF McCrory, R. L.; Betti, R.; Boehly, T. R. Nuclear Fusion, Vol. 53, Issue 11 https://doi.org/10.1088/0029-5515/53/11/113021	journal	September 2013
Beryllium ignition target design for indirect drive NIF experiments Simakov, A. N.; Wilson, D. C.; Yi, S. A. Journal of Physics: Conference Series, Vol. 688 https://doi.org/10.1088/1742-6596/688/1/012110	journal	March 2016
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
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/PhysRev.140.A1133	journal	November 1965
Ultrahigh-pressure shock-wave experiments Ragan, Charles E. Physical Review A, Vol. 21, Issue 2 https://doi.org/10.1103/PhysRevA.21.458	journal	February 1980
Shock compression measurements at 1 to 7 TPa Ragan, Charles E. Physical Review A, Vol. 25, Issue 6 https://doi.org/10.1103/PhysRevA.25.3360	journal	June 1982
New Potential Function for Atomic and Solid-State Calculations Liberman, David A. Physical Review B, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevB.2.244	journal	July 1970
Self-consistent field model for condensed matter Liberman, David A. Physical Review B, Vol. 20, Issue 12 https://doi.org/10.1103/PhysRevB.20.4981	journal	December 1979
Self-interaction correction to density-functional approximations for many-electron systems Perdew, J. P.; Zunger, Alex Physical Review B, Vol. 23, Issue 10, p. 5048-5079 https://doi.org/10.1103/PhysRevB.23.5048	journal	May 1981
Atoms embedded in an electron gas: Immersion energies Puska, M. J.; Nieminen, R. M.; Manninen, M. Physical Review B, Vol. 24, Issue 6 https://doi.org/10.1103/PhysRevB.24.3037	journal	September 1981
Atomic vibrations in a self-consistent-field atom-in-jellium model of condensed matter Liberman, David A.; Bennett, Bard I. Physical Review B, Vol. 42, Issue 4 https://doi.org/10.1103/PhysRevB.42.2475	journal	August 1990
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
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
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
From ultrasoft pseudopotentials to the projector augmented-wave method Kresse, G.; Joubert, D. Physical Review B, Vol. 59, Issue 3, p. 1758-1775 https://doi.org/10.1103/PhysRevB.59.1758	journal	January 1999
Raman scattering intensities in α-quartz: A first-principles investigation Umari, P.; Pasquarello, Alfredo; Dal Corso, Andrea Physical Review B, Vol. 63, Issue 9 https://doi.org/10.1103/PhysRevB.63.094305	journal	February 2001
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
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
Thermophysical properties of warm dense hydrogen using quantum molecular dynamics simulations Holst, Bastian; Redmer, Ronald; Desjarlais, Michael P. Physical Review B, Vol. 77, Issue 18 https://doi.org/10.1103/PhysRevB.77.184201	journal	May 2008
Calculations of high-pressure properties of beryllium: Construction of a multiphase equation of state Benedict, Lorin X.; Ogitsu, Tadashi; Trave, Andrea Physical Review B, Vol. 79, Issue 6 https://doi.org/10.1103/PhysRevB.79.064106	journal	February 2009
Temperature and density dependence of XANES spectra in warm dense aluminum plasmas Recoules, V.; Mazevet, S. Physical Review B, Vol. 80, Issue 6 https://doi.org/10.1103/PhysRevB.80.064110	journal	August 2009
Multiphase equation of state of hydrogen from ab initio calculations in the range 0.2 to 5 g/cc up to 10 eV Caillabet, L.; Mazevet, S.; Loubeyre, P. Physical Review B, Vol. 83, Issue 9 https://doi.org/10.1103/PhysRevB.83.094101	journal	March 2011
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
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
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
First-principles prediction of the softening of the silicon shock Hugoniot curve Hu, S. X.; Militzer, B.; Collins, L. A. Physical Review B, Vol. 94, Issue 9 https://doi.org/10.1103/PhysRevB.94.094109	journal	September 2016
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
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
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
Equations of state and transport properties of warm dense beryllium: A quantum molecular dynamics study Wang, Cong; Long, Yao; Tian, Ming-Feng Physical Review E, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevE.87.043105	journal	April 2013
Properties of warm dense polystyrene plasmas along the principal Hugoniot Hu, S. X.; Boehly, T. R.; Collins, L. A. Physical Review E, Vol. 89, Issue 6 https://doi.org/10.1103/PhysRevE.89.063104	journal	June 2014
First-principles opacity table of warm dense deuterium for inertial-confinement-fusion applications Hu, S. X.; Collins, L. A.; Goncharov, V. N. Physical Review E, Vol. 90, Issue 3 https://doi.org/10.1103/PhysRevE.90.033111	journal	September 2014
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
Experimental and ab initio investigations of microscopic properties of laser-shocked Ge-doped ablator Huser, G.; Recoules, V.; Ozaki, N. Physical Review E, Vol. 92, Issue 6 https://doi.org/10.1103/PhysRevE.92.063108	journal	December 2015
First-principles equation-of-state table of silicon and its effects on high-energy-density plasma simulations Hu, S. X.; Gao, R.; Ding, Y. Physical Review E, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevE.95.043210	journal	April 2017
Ab Initio Determination of Thermal Conductivity of Dense Hydrogen Plasmas Recoules, Vanina; Lambert, Flavien; Decoster, Alain Physical Review Letters, Vol. 102, Issue 7 https://doi.org/10.1103/PhysRevLett.102.075002	journal	February 2009
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
Molecular-Atomic Transition along the Deuterium Hugoniot Curve with Coupled Electron-Ion Monte Carlo Simulations Tubman, Norm M.; Liberatore, Elisa; Pierleoni, Carlo Physical Review Letters, Vol. 115, Issue 4 https://doi.org/10.1103/PhysRevLett.115.045301	journal	July 2015
Low Fuel Convergence Path to Direct-Drive Fusion Ignition Molvig, Kim; Schmitt, Mark J.; Albright, B. J. Physical Review Letters, Vol. 116, Issue 25 https://doi.org/10.1103/PhysRevLett.116.255003	journal	June 2016
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
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
Absolute Equation-of-State Data in the 10–40 Mbar (1–4 TPa) Regime Cauble, R.; Perry, T. S.; Bach, D. R. Physical Review Letters, Vol. 80, Issue 6 https://doi.org/10.1103/PhysRevLett.80.1248	journal	February 1998
Beryllium metal matrix composites for aerospace and commercial applications Parsonage, T. Materials Science and Technology, Vol. 16, Issue 7-8 https://doi.org/10.1179/026708300101508522	journal	July 2000

Cited By (7)

A review on ab initio studies of static, transport, and optical properties of polystyrene under extreme conditions for inertial confinement fusion applications Collins, L. A.; Boehly, T. R.; Ding, Y. H. Physics of Plasmas, Vol. 25, Issue 5 https://doi.org/10.1063/1.5017970	journal	May 2018
Beryllium capsule implosions at a case-to-capsule ratio of 3.7 on the National Ignition Facility Zylstra, A. B.; Yi, S. A.; MacLaren, S. Physics of Plasmas, Vol. 25, Issue 10 https://doi.org/10.1063/1.5041285	journal	October 2018
Mitigating laser-imprint effects in direct-drive inertial confinement fusion implosions with an above-critical-density foam layer Hu, S. X.; Theobald, W.; Radha, P. B. Physics of Plasmas, Vol. 25, Issue 8 https://doi.org/10.1063/1.5044609	journal	August 2018
Structure and dynamics of warm dense aluminum: a molecular dynamics study with density functional theory and deep potential Liu, Qianrui; Lu, Denghui; Chen, Mohan Journal of Physics: Condensed Matter, Vol. 32, Issue 14 https://doi.org/10.1088/1361-648x/ab5890	journal	January 2020
Direct-drive double-shell implosion: A platform for burning-plasma physics studies Hu, S. X.; Epstein, R.; Theobald, W. Physical Review E, Vol. 100, Issue 6 https://doi.org/10.1103/physreve.100.063204	journal	December 2019
Atom-in-jellium equations of state in the high-energy-density regime Swift, Damian C.; Lockard, Thomas; Kraus, Richard G. Physical Review E, Vol. 99, Issue 6 https://doi.org/10.1103/physreve.99.063210	journal	June 2019
Atom-in-jellium equations of state in the high energy density regime Swift, Damian C.; Lockard, Thomas; Kraus, Richard G. arXiv https://doi.org/10.48550/arxiv.1903.00163	text	January 2019

Similar Records

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

Journal Article · Fri Apr 21 00:00:00 EDT 2017 · Physical Review E · OSTI ID:1355166

Properties of warm dense polystyrene plasmas along the principal Hugoniot

Journal Article · Mon Jun 30 00:00:00 EDT 2014 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics · OSTI ID:1140284

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

Journal Article · Wed Oct 14 00:00:00 EDT 2015 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics · OSTI ID:1223806

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Beryllium
Computer modeling
Equations of state
Inertial confinement
Plasma temperature

First-principles equation-of-state table of beryllium based on density-functional theory calculations

Citation Formats

References (63)

Cited By (7)

Similar Records

Related Subjects