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

## Abstract

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/cm ^{3} and temperature T = 2000 to 10 ^{8} 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 SESAMEmore »

- Authors:

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

- Publication Date:

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

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

- OSTI Identifier:
- 1361691

- Grant/Contract Number:
- NA0001944

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 6; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

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

### Citation Formats

```
Ding, Y. H., and Hu, S. X.
```*First-principles equation-of-state table of beryllium based on density-functional theory calculations*. United States: N. p., 2017.
Web. doi:10.1063/1.4984780.

```
Ding, Y. H., & Hu, S. X.
```*First-principles equation-of-state table of beryllium based on density-functional theory calculations*. United States. doi:10.1063/1.4984780.

```
Ding, Y. H., and Hu, S. X. Tue .
"First-principles equation-of-state table of beryllium based on density-functional theory calculations". United States. doi:10.1063/1.4984780. https://www.osti.gov/servlets/purl/1361691.
```

```
@article{osti_1361691,
```

title = {First-principles equation-of-state table of beryllium based on density-functional theory calculations},

author = {Ding, Y. H. and Hu, S. X.},

abstractNote = {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.},

doi = {10.1063/1.4984780},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 6,

volume = 24,

place = {United States},

year = {2017},

month = {6}

}

Works referenced in this record:

##
Generalized Gradient Approximation Made Simple

journal, October 1996

- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868

##
From ultrasoft pseudopotentials to the projector augmented-wave method

journal, January 1999

- Kresse, G.; Joubert, D.
- Physical Review B, Vol. 59, Issue 3, p. 1758-1775

##
*Ab initio*molecular dynamics for liquid metals

journal, January 1993

- Kresse, G.; Hafner, J.
- Physical Review B, Vol. 47, Issue 1, p. 558-561

##
Self-Consistent Equations Including Exchange and Correlation Effects

journal, November 1965

- Kohn, W.; Sham, L. J.
- Physical Review, Vol. 140, Issue 4A, p. A1133-A1138

##
Crossed-beam energy transfer in direct-drive implosions

journal, May 2012

- Igumenshchev, I. V.; Seka, W.; Edgell, D. H.
- Physics of Plasmas, Vol. 19, Issue 5, Article No. 056314

##
Efficient iterative schemes for *ab initio* total-energy calculations using a plane-wave basis set

journal, October 1996

- Kresse, G.; Furthmüller, J.
- Physical Review B, Vol. 54, Issue 16, p. 11169-11186

##
*Ab initio* molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium

journal, May 1994

- Kresse, G.; Hafner, J.
- Physical Review B, Vol. 49, Issue 20, p. 14251-14269