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Roy AJ, Bergermann A, Bethkenhagen M, Redmer R. Mixture of hydrogen and methane under planetary interior conditions. Phys Chem Chem Phys 2024; 26:14374-14383. [PMID: 38712595 DOI: 10.1039/d4cp00058g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/08/2024]
Abstract
We employ first-principles molecular dynamics simulations to provide equation-of-state data, pair distribution functions (PDFs), diffusion coefficients, and band gaps of a mixture of hydrogen and methane under planetary interior conditions as relevant for Uranus, Neptune, and similar icy exoplanets. We test the linear mixing approximation, which is fulfilled within a few percent for the chosen P-T conditions. Evaluation of the PDFs reveals that methane molecules dissociate into carbon clusters and free hydrogen atoms at temperatures greater than 3000 K. At high temperatures, the clusters are found to be short-lived. Furthermore, we calculate the electrical conductivity from which we derive the non-metal-to-metal transition region of the mixture. We also calculate the electrical conductivity along the P-T profile of Uranus [N. Nettelmann et al., Planet. Space Sci., 2013, 77, 143-151] and observe the transition of the mixture from a molecular to an atomic fluid as a function of the radius of the planet. The density and temperature ranges chosen in our study can be achieved using dynamic shock compression experiments and seek to aid such future experiments. Our work also provides a relevant data set for a better understanding of the interior, evolution, luminosity, and magnetic field of the ice giants in our solar system and beyond.
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Affiliation(s)
- Argha Jyoti Roy
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - Armin Bergermann
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - Mandy Bethkenhagen
- LULI, CNRS, CEA, Sorbonne Université, École Polytechnique - Institut Polytechnique de Paris, 91128 Palaiseau, France.
| | - Ronald Redmer
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
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Militzer B, González-Cataldo F, Zhang S, Driver KP, Soubiran F. First-principles equation of state database for warm dense matter computation. Phys Rev E 2021; 103:013203. [PMID: 33601631 DOI: 10.1103/physreve.103.013203] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Accepted: 12/11/2020] [Indexed: 06/12/2023]
Abstract
We put together a first-principles equation of state (FPEOS) database for matter at extreme conditions by combining results from path integral Monte Carlo and density functional molecular dynamics simulations of the elements H, He, B, C, N, O, Ne, Na, Mg, Al, and Si as well as the compounds LiF, B_{4}C, BN, CH_{4}, CH_{2}, C_{2}H_{3}, CH, C_{2}H, MgO, and MgSiO_{3}. For all these materials, we provide the pressure and internal energy over a density-temperature range from ∼0.5 to 50 g cm^{-3} and from ∼10^{4} to 10^{9} K, which are based on ∼5000 different first-principles simulations. We compute isobars, adiabats, and shock Hugoniot curves in the regime of L- and K-shell ionization. Invoking the linear mixing approximation, we study the properties of mixtures at high density and temperature. We derive the Hugoniot curves for water and alumina as well as for carbon-oxygen, helium-neon, and CH-silicon mixtures. We predict the maximal shock compression ratios of H_{2}O, H_{2}O_{2}, Al_{2}O_{3}, CO, and CO_{2} to be 4.61, 4.64, 4.64, 4.89, and 4.83, respectively. Finally we use the FPEOS database to determine the points of maximum shock compression for all available binary mixtures. We identify mixtures that reach higher shock compression ratios than their end members. We discuss trends common to all mixtures in pressure-temperature and particle-shock velocity spaces. In the Supplemental Material, we provide all FPEOS tables as well as computer codes for interpolation, Hugoniot calculations, and plots of various thermodynamic functions.
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Affiliation(s)
- Burkhard Militzer
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
- Department of Astronomy, University of California, Berkeley, California 94720, USA
| | - Felipe González-Cataldo
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
| | - Shuai Zhang
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA
| | - Kevin P Driver
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - François Soubiran
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
- CEA DAM-DIF, 91297 Arpajon, France
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Militzer B, González-Cataldo F, Zhang S, Whitley HD, Swift DC, Millot M. Nonideal mixing effects in warm dense matter studied with first-principles computer simulations. J Chem Phys 2020; 153:184101. [DOI: 10.1063/5.0023232] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Burkhard Militzer
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
- Department of Astronomy, University of California, Berkeley, California 94720, USA
| | - Felipe González-Cataldo
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
| | - Shuai Zhang
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA
| | - Heather D. Whitley
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Damian C. Swift
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Marius Millot
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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Soubiran F, Militzer B. Anharmonicity and Phase Diagram of Magnesium Oxide in the Megabar Regime. PHYSICAL REVIEW LETTERS 2020; 125:175701. [PMID: 33156661 DOI: 10.1103/physrevlett.125.175701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2018] [Revised: 06/15/2020] [Accepted: 09/17/2020] [Indexed: 06/11/2023]
Abstract
With density functional molecular dynamics simulations, we computed the phase diagram of MgO from 50 to 2000 GPa up to 20 000 K. Via thermodynamic integration (TDI), we derive the Gibbs free energies of the B1, B2, and liquid phases and determine their phase boundaries. With TDI and a pseudo-quasi-harmonic approach, we show that anharmonic effects are important and stabilize the B1 phase in particular. As a result, the B1-B2 transition boundary in the pressure-temperature plane exhibits a steep slope. We predict the B1-B2-liquid triple point to occur at approximately T=10000 K and P=370 GPa, which is higher in pressure than was inferred with quasiharmonic methods alone. We predict the principal shock Hugoniot curve to enter the B2 phase stability domain but only over a very small range of parameters. This may render it difficult to observe this phase with shock experiments because of kinetic effects.
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Affiliation(s)
- François Soubiran
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
- École Normale Supérieure de Lyon, Université Lyon 1, Laboratoire de Géologie de Lyon, CNRS UMR 5276, 69364 Lyon Cedex 07, France
- CEA DAM-DIF, 91297 Arpajon, France
| | - Burkhard Militzer
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
- Department of Astronomy, University of California, Berkeley, California 94720, USA
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Models of Saturn's Interior Constructed with an Accelerated Concentric Maclaurin Spheroid Method. ACTA ACUST UNITED AC 2019. [DOI: 10.3847/1538-4357/ab23f0] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Schöttler M, Redmer R. Ab Initio Calculation of the Miscibility Diagram for Hydrogen-Helium Mixtures. PHYSICAL REVIEW LETTERS 2018; 120:115703. [PMID: 29601747 DOI: 10.1103/physrevlett.120.115703] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2017] [Indexed: 06/08/2023]
Abstract
We use finite-temperature density functional theory coupled to classical molecular dynamics simulation to calculate the miscibility gap of hydrogen-helium mixtures. The van der Waals density functional (vdW-DF) theory is used, which leads to lower demixing temperatures compared to computations using the Perdew-Burke-Ernzerhof functional. Our calculations suggest that current Jupiter models are most likely too hot to allow demixing in the interior. A Jupiter isentrope based on our vdW-DF data is presented. Our demixing phase diagram still predicts phase separation in Saturn, but in a significantly reduced fraction of its volume.
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Affiliation(s)
- Manuel Schöttler
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - Ronald Redmer
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
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Zhang S, Driver KP, Soubiran F, Militzer B. First-principles equation of state and shock compression predictions of warm dense hydrocarbons. Phys Rev E 2017; 96:013204. [PMID: 29347225 DOI: 10.1103/physreve.96.013204] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2017] [Indexed: 06/07/2023]
Abstract
We use path integral Monte Carlo and density functional molecular dynamics to construct a coherent set of equations of state (EOS) 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 0.07-22.4gcm^{-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 EOS is a reasonable approximation with errors better than 1% for stellar-core conditions.
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Affiliation(s)
- Shuai Zhang
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
| | - Kevin P Driver
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
| | - François Soubiran
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
| | - Burkhard Militzer
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA and Department of Astronomy, University of California, Berkeley, California 94720, USA
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