Development of a multiphase equation of state for gallium with experiments and ab initio free-energy calculations

Wu, Christine J.; Myint, Philip C.; Bonev, Stanimir A.; Prisbrey, Carrie J.

doi:10.1116/6.0004516

Development of a multiphase equation of state for gallium with experiments and ab initio free-energy calculations

Journal Article · Thu May 29 00:00:00 EDT 2025 · Journal of Vacuum Science & Technology A

DOI:https://doi.org/10.1116/6.0004516· OSTI ID:2587417

^[1]; ^[1]; Bonev, Stanimir A. ^[1]; ^[1]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Here, we present a five-phase equation of state (EOS) for elemental gallium (Ga) that is developed using both experimental data and new theoretical predictions. Four experimentally observed solid phases (Ga-I, Ga-II, Ga-III, and Ga-IV) and one liquid phase are included. To improve our understanding of the thermal behavior of Ga and its phase boundaries under compression, we have performed ab initio density functional theory (DFT) free-energy calculations for the Ga-III and liquid phases, which enables us to determine the melt temperature to be 2214 ± 100 K at 110 GPa, extending significantly beyond the existing experimental melt data, which are limited to 25 GPa. In order to best describe the electron-thermal contribution, which dominates the liquid free energy at high temperatures, we have carried out averaged-atom-in-jellium DFT calculations to cover the entire temperature and density range of the EOS. The resulting multiphase Ga EOS is able to accurately reproduce a diverse variety of data, including known phase boundaries, the principal Hugoniot, low-pressure liquid isobars, and diamond-anvil-cell isotherm measurements at high pressures. It agrees more closely with key experimentally measured properties than other Ga EOS models targeted for high-pressure applications.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

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

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2587417

Report Number(s):: LLNL--JRNL-2002940

Journal Information:: Journal of Vacuum Science & Technology A, Journal Name: Journal of Vacuum Science & Technology A Journal Issue: 4 Vol. 43; ISSN 0734-2101; ISSN 1520-8559

Publisher:: American Vacuum SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (56)

Shock adiabatic curves of metals: New data, statistical analysis, and general laws Al'tshuler, L. V.; Bakanova, A. A.; Dudoladov, I. P. Journal of Applied Mechanics and Technical Physics, Vol. 22, Issue 2 https://doi.org/10.1007/BF00907938	journal	January 1981
X-ray diffraction measurements for expanded liquid gallium Tamura, Kozaburo; Hosokawa, Shinya Journal of Non-Crystalline Solids, Vol. 156-158 https://doi.org/10.1016/0022-3093(93)90039-Z	journal	May 1993
Fusion curves and polymorphic transitions of the group III elements—Aluminum, gallium, indium and thallium—At high pressures Jayaraman, A.; Klement, W.; Newton, R. C. Journal of Physics and Chemistry of Solids, Vol. 24, Issue 1 https://doi.org/10.1016/0022-3697(63)90036-2	journal	January 1963
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set Kresse, G.; Furthmüller, J. Computational Materials Science, Vol. 6, Issue 1, p. 15-50 https://doi.org/10.1016/0927-0256(96)00008-0	journal	July 1996
Temperature-dependent structure evolution in liquid gallium Xiong, L. H.; Wang, X. D.; Yu, Q. Acta Materialia, Vol. 128 https://doi.org/10.1016/j.actamat.2017.02.038	journal	April 2017
Equation of state, occupation probabilities and conductivities in the average atom Purgatorio code Sterne, P. A.; Hansen, S. B.; Wilson, B. G. High Energy Density Physics, Vol. 3, Issue 1-2 https://doi.org/10.1016/j.hedp.2007.02.037	journal	May 2007
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
Development of a Multiphase Beryllium Equation of State and Physics-based Variations Wu, Christine J.; Myint, Philip C.; Pask, John E. The Journal of Physical Chemistry A, Vol. 125, Issue 7 https://doi.org/10.1021/acs.jpca.0c09809	journal	February 2021
Ab initio phase diagram and nucleation of gallium Niu, Haiyang; Bonati, Luigi; Piaggi, Pablo M. Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-16372-9	journal	May 2020
Local structure of liquid gallium under pressure Li, Renfeng; Wang, Luhong; Li, Liangliang Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-05985-8	journal	July 2017
A Gallium Multiphase Equation of State Crockett, Scott D.; Greeff, Carl W.; Elert, Mark SHOCK COMPRESSION OF CONDENSED MATTER 2009: Proceedings of the American Physical Society Topical Group on Shock Compression of Condensed Matter, AIP Conference Proceedings https://doi.org/10.1063/1.3295016	conference	January 2009
A new global equation of state model for hot, dense matter Young, David A.; Corey, Ellen M. Journal of Applied Physics, Vol. 78, Issue 6 https://doi.org/10.1063/1.359955	journal	September 1995
Crystal structures of Ga(II) and Ga(III) Bosio, Louis The Journal of Chemical Physics, Vol. 68, Issue 3 https://doi.org/10.1063/1.435841	journal	February 1978
Study of liquid gallium at high pressure using synchrotron x-ray Yu, Tony; Chen, Jiuhua; Ehm, Lars Journal of Applied Physics, Vol. 111, Issue 11 https://doi.org/10.1063/1.4726256	journal	June 2012
Study of liquid gallium as a function of pressure and temperature using synchrotron x-ray microtomography and x-ray diffraction Li, Renfeng; Li, Liangliang; Yu, Tony Applied Physics Letters, Vol. 105, Issue 4 https://doi.org/10.1063/1.4891572	journal	July 2014
Anomalous properties and the liquid-liquid phase transition in gallium Li, Renzhong; Sun, Gang; Xu, Limei The Journal of Chemical Physics, Vol. 145, Issue 5 https://doi.org/10.1063/1.4959891	journal	August 2016
Equation of state for a chemically dissociative, polyatomic system: Carbon dioxide Wu, Christine J.; Young, David A.; Sterne, Philip A. The Journal of Chemical Physics, Vol. 151, Issue 22 https://doi.org/10.1063/1.5128127	journal	December 2019
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
Electronic Structure and Compressibility of Metals at high Pressures Al'tshuler, L. V.; Bakanova, A. A. Soviet Physics Uspekhi, Vol. 11, Issue 5 https://doi.org/10.1070/pu1969v011n05abeh003741	journal	May 1969
Interpreting dynamic-compression experiments to uncover the time dependence of freezing: Application to gallium Belof, Jonathan L.; Brown, Justin L.; Myint, Philip C. Proceedings of the National Academy of Sciences, Vol. 122, Issue 20 https://doi.org/10.1073/pnas.2424703122	journal	May 2025
Equations of state for Cu, Ag, and Au and problems with shock wave reduced isotherms Holzapfel, Wilfried B. High Pressure Research, Vol. 30, Issue 3 https://doi.org/10.1080/08957959.2010.494845	journal	September 2010
Pressure-volume relations for Zn, Cd, Ga, In and TI at room temperature to 30 GPa and above Schulte, O.; Nikolaenko, A.; Holzapfel, W. B. High Pressure Research, Vol. 6, Issue 3 https://doi.org/10.1080/08957959108203207	journal	April 1991
Equations of state for solids under strong compression Holzapfel, W. B. High Pressure Research, Vol. 16, Issue 2 https://doi.org/10.1080/08957959808200283	journal	October 1998
Physics of solids under strong compression Holzapfel, W. B. Reports on Progress in Physics, Vol. 59, Issue 1 https://doi.org/10.1088/0034-4885/59/1/002	journal	January 1996
Universal features of the equation of state of solids Vinet, P.; Rose, J. H.; Ferrante, J. Journal of Physics: Condensed Matter, Vol. 1, Issue 11 https://doi.org/10.1088/0953-8984/1/11/002	journal	March 1989
Dynamics of monatomic liquids Chisolm, Eric D.; Wallace, Duane C. Journal of Physics: Condensed Matter, Vol. 13, Issue 37 https://doi.org/10.1088/0953-8984/13/37/201	journal	August 2001
Thermodynamic properties of liquid gallium from picosecond acoustic velocity measurements Ayrinhac, S.; Gauthier, M.; Le Marchand, G. Journal of Physics: Condensed Matter, Vol. 27, Issue 27 https://doi.org/10.1088/0953-8984/27/27/275103	journal	June 2015
The density and coefficient of expansion of liquid gallium over a wide range of temperature Hoather, W. H. Proceedings of the Physical Society, Vol. 48, Issue 5 https://doi.org/10.1088/0959-5309/48/5/303	journal	September 1936
Wide-ranged multiphase equation of state for iron and model variations addressing uncertainties in high-pressure melting Wu, Christine J.; Benedict, Lorin X.; Myint, Philip C. Physical Review B, Vol. 108, Issue 1 https://doi.org/10.1103/PhysRevB.108.014102	journal	July 2023
Fluid-phase helium: Shock-compression experiments, quantum molecular dynamics simulations, and development of an equation of state Myint, Philip C.; Root, Seth; Wu, Christine J. Physical Review B, Vol. 108, Issue 13 https://doi.org/10.1103/PhysRevB.108.134202	journal	October 2023
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 calculations of structural and electronic properties of gallium solid-state phases Bernasconi, M.; Chiarotti, Guido L.; Tosatti, E. Physical Review B, Vol. 52, Issue 14 https://doi.org/10.1103/PhysRevB.52.9988	journal	October 1995
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
Effect of pressure on the atomic volume of Ga and Tl up to 68 GPa Schulte, Olaf; Holzapfel, Wilfried B. Physical Review B, Vol. 55, Issue 13 https://doi.org/10.1103/PhysRevB.55.8122	journal	April 1997
High-pressure bct-fcc phase transition in Ga Kenichi, Takemura; Kazuaki, Kobayashi; Masao, Arai Physical Review B, Vol. 58, Issue 5 https://doi.org/10.1103/PhysRevB.58.2482	journal	August 1998
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
High-pressure and high-temperature x-ray absorption study of liquid and solid gallium Comez, Lucia; Di Cicco, Andrea; Itié, Jean Paul Physical Review B, Vol. 65, Issue 1 https://doi.org/10.1103/PhysRevB.65.014114	journal	December 2001
Modeling of compound semiconductors: Analytical bond-order potential for Ga, As, and GaAs Albe, Karsten; Nordlund, Kai; Nord, Janne Physical Review B, Vol. 66, Issue 3 https://doi.org/10.1103/PhysRevB.66.035205	journal	July 2002
Liquid gallium in confined droplets under high-temperature and high-pressure conditions Poloni, R.; De Panfilis, S.; Di Cicco, A. Physical Review B, Vol. 71, Issue 18 https://doi.org/10.1103/PhysRevB.71.184111	journal	May 2005
Possible liquid-liquid transition of gallium confined in opal Tien, Cheng; Charnaya, Elena V.; Wang, Wenya Physical Review B, Vol. 74, Issue 2 https://doi.org/10.1103/PhysRevB.74.024116	journal	July 2006
First-principles study of the connection between structure and electronic properties of gallium Voloshina, Elena; Rosciszewski, Krzysztof; Paulus, Beate Physical Review B, Vol. 79, Issue 4 https://doi.org/10.1103/PhysRevB.79.045113	journal	January 2009
Assessing the performance of recent density functionals for bulk solids Csonka, Gábor I.; Perdew, John P.; Ruzsinszky, Adrienn Physical Review B, Vol. 79, Issue 15 https://doi.org/10.1103/PhysRevB.79.155107	journal	April 2009
Structural and thermodynamic properties of liquid Na-Li and Ca-Li alloys at high pressure Teweldeberhan, A. M.; Bonev, S. A. Physical Review B, Vol. 83, Issue 13 https://doi.org/10.1103/PhysRevB.83.134120	journal	April 2011
Raising the superconducting T c of gallium: In situ characterization of the transformation of α -Ga into β -Ga Campanini, D.; Diao, Z.; Rydh, A. Physical Review B, Vol. 97, Issue 18 https://doi.org/10.1103/PhysRevB.97.184517	journal	May 2018
Statistical mechanics model for the transit free energy of monatomic liquids Wallace, Duane C.; Chisolm, Eric D.; Bock, N. Physical Review E, Vol. 81, Issue 4 https://doi.org/10.1103/PhysRevE.81.041201	journal	April 2010
Structural Ordering in Liquid Gallium under Extreme Conditions Drewitt, James W. E.; Turci, Francesco; Heinen, Benedict J. Physical Review Letters, Vol. 124, Issue 14 https://doi.org/10.1103/PhysRevLett.124.145501	journal	April 2020
Scaling Law for the Onset of Solidification at Extreme Undercooling Myint, Philip C.; Sterbentz, Dane M.; Brown, Justin L. Physical Review Letters, Vol. 131, Issue 10 https://doi.org/10.1103/PhysRevLett.131.106101	journal	September 2023
Ground State of the Electron Gas by a Stochastic Method Ceperley, D. M.; Alder, B. J. Physical Review Letters, Vol. 45, Issue 7, p. 566-569 https://doi.org/10.1103/PhysRevLett.45.566	journal	August 1980
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
Liquid-Liquid Phase Transition in Elemental Carbon: A First-Principles Investigation Wu, Christine J.; Glosli, James N.; Galli, Giulia Physical Review Letters, Vol. 89, Issue 13 https://doi.org/10.1103/PhysRevLett.89.135701	journal	September 2002
Structural Complexity in Gallium under High Pressure: Relation to Alkali Elements Degtyareva, O.; McMahon, M. I.; Allan, D. R. Physical Review Letters, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevLett.93.205502	journal	November 2004
Apparently Complex High-Pressure Phase of Gallium as a Simple Modulated Structure Perez-Mato, J. M.; Elcoro, Luis; Aroyo, Mois I. Physical Review Letters, Vol. 97, Issue 11 https://doi.org/10.1103/PhysRevLett.97.115501	journal	September 2006
Structure cristalline du gallium β Bosio, L.; Defrain, A.; Curien, H. Acta Crystallographica Section B Structural Crystallography and Crystal Chemistry, Vol. 25, Issue 5 https://doi.org/10.1107/S0567740869003360	journal	May 1969
Structure cristalline de Ga γ Bosio, L.; Curien, H.; Dupont, M. Acta Crystallographica Section B Structural Crystallography and Crystal Chemistry, Vol. 28, Issue 6 https://doi.org/10.1107/S0567740872005357	journal	June 1972
Structure cristalline de Gaδ Bosio, L.; Curien, H.; Dupont, M. Acta Crystallographica Section B Structural Crystallography and Crystal Chemistry, Vol. 29, Issue 2 https://doi.org/10.1107/S0567740873002530	journal	February 1973
Elastic properties of crystalline and liquid gallium at high pressures Lyapin, A. G.; Gromnitskaya, E. L.; Yagafarov, O. F. Journal of Experimental and Theoretical Physics, Vol. 107, Issue 5 https://doi.org/10.1134/S1063776108110125	journal	November 2008

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