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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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2
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Kovačević T, González-Cataldo F, Stewart ST, Militzer B. Miscibility of rock and ice in the interiors of water worlds. Sci Rep 2022; 12:13055. [PMID: 35906271 PMCID: PMC9338078 DOI: 10.1038/s41598-022-16816-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Accepted: 07/15/2022] [Indexed: 11/17/2022] Open
Abstract
Super-Earths and sub-Neptunes are the most common planet types in our galaxy. A subset of these planets is predicted to be water worlds, bodies that are rich in water and poor in hydrogen gas. The interior structures of water worlds have been assumed to consist of water surrounding a rocky mantle and iron core. In small planets, water and rock form distinct layers with limited incorporation of water into silicate phases, but these materials may interact differently during the growth and evolution of water worlds due to greater interior pressures and temperatures. Here, we use density functional molecular dynamics (DFT-MD) simulations to study the miscibility and interactions of enstatite (MgSiO3), a major end-member silicate phase, and water (H2O) at extreme conditions in water world interiors. We explore pressures ranging from 30 to 120 GPa and temperatures from 500 to 8000 K. Our results demonstrate that enstatite and water are miscible in all proportions if the temperature exceeds the melting point of MgSiO3. Furthermore, we performed smoothed particle hydrodynamics simulations to demonstrate that the conditions necessary for rock-water miscibility are reached during giant impacts between water-rich bodies of 0.7–4.7 Earth masses. Our simulations lead to water worlds that include a mixed layer of rock and water.
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Affiliation(s)
- Tanja Kovačević
- Department of Earth and Planetary Science, University of California, Berkeley, CA, 94720, USA.
| | - Felipe González-Cataldo
- Department of Earth and Planetary Science, University of California, Berkeley, CA, 94720, USA
| | - Sarah T Stewart
- Department of Earth and Planetary Sciences, University of California, Davis, CA, 95616, USA
| | - Burkhard Militzer
- Department of Earth and Planetary Science, University of California, Berkeley, CA, 94720, USA.,Department of Astronomy, University of California, Berkeley, CA, 94720, USA
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3
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Bergermann A, French M, Redmer R. Gibbs-ensemble Monte Carlo simulation of H 2-H 2O mixtures. Phys Chem Chem Phys 2021; 23:12637-12643. [PMID: 34037010 DOI: 10.1039/d1cp00515d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The miscibility gap in hydrogen-water mixtures is investigated by conducting Gibbs-ensemble Monte Carlo simulations with analytical two-body interaction potentials between the molecular species. We calculate several demixing curves at pressures below 150 kbar and temperatures of 1000 K ≤T≤ 2000 K. Despite the approximations introduced by the two-body interaction potentials, our results predict a large miscibility gap in hydrogen-water mixtures at similar conditions as found in experiments. Our findings are in contrast to those from ab initio simulations and provide a renewed indication that hydrogen-water immiscibility regions may have a significant impact on the structure and evolution of ice giant planets like Uranus and Neptune.
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Affiliation(s)
- Armin Bergermann
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany.
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4
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Li Z, Winisdoerffer C, Soubiran F, Caracas R. Ab initio Gibbs ensemble Monte Carlo simulations of the liquid-vapor equilibrium and the critical point of sodium. Phys Chem Chem Phys 2021; 23:311-319. [PMID: 33347522 DOI: 10.1039/d0cp04158k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The ab initio (ai) Gibbs ensemble (GE) Monte Carlo (MC) method coupled with Kohn-Sham density functional theory is successful in predicting the liquid-vapour equilibrium of insulating systems. Here we show that the aiGEMC method can be used to study also metallic systems, where the excited electronic states play an important role and cannot be neglected. For this we include the electronic free energy in the formulation of the effective energy of the system to be used in the acceptance criteria for the MC moves. The application of this aiGEMC method to sodium yields a good agreement with available experimental data on the liquid-vapour equilibrium densities. We predict a critical point for sodium at 2338 ± 108 K and 0.24 ± 0.03 g cm-3. The liquid structure stemming from aiGEMC simulations is very similar to the one from ab initio molecular dynamics. Since this method can determine phase transition without computing the Gibbs free energy, it may offer a new possibility to study other materials with a reasonable computational cost.
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Affiliation(s)
- Zhi Li
- CNRS, École Normale Supérieure de Lyon, Laboratoire de Géologie de Lyon LGLTPE UMR 5276, 46 allée d'Italie, Lyon 69364, France.
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Helled R, Fortney JJ. The interiors of Uranus and Neptune: current understanding and open questions. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190474. [PMID: 33161856 DOI: 10.1098/rsta.2019.0474] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
Uranus and Neptune form a distinct class of planets in our Solar System. Given this fact, and ubiquity of similar-mass planets in other planetary systems, it is essential to understand their interior structure and composition. However, there are more open questions regarding these planets than answers. In this review, we concentrate on the things we do not know about the interiors of Uranus and Neptune with a focus on why the planets may be different, rather than the same. We next summarize the knowledge about the planets' internal structure and evolution. Finally, we identify the topics that should be investigated further on the theoretical front as well as required observations from space missions. This article is part of a discussion meeting issue 'Future exploration of ice giant systems'.
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Affiliation(s)
- Ravit Helled
- Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zurich, Zurich, Switzerland
| | - Jonathan J Fortney
- Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA
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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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Stability of H 3O at extreme conditions and implications for the magnetic fields of Uranus and Neptune. Proc Natl Acad Sci U S A 2020; 117:5638-5643. [PMID: 32127483 DOI: 10.1073/pnas.1921811117] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The anomalous nondipolar and nonaxisymmetric magnetic fields of Uranus and Neptune have long challenged conventional views of planetary dynamos. A thin-shell dynamo conjecture captures the observed phenomena but leaves unexplained the fundamental material basis and underlying mechanism. Here we report extensive quantum-mechanical calculations of polymorphism in the hydrogen-oxygen system at the pressures and temperatures of the deep interiors of these ice giant planets (to >600 GPa and 7,000 K). The results reveal the surprising stability of solid and fluid trihydrogen oxide (H3O) at these extreme conditions. Fluid H3O is metallic and calculated to be stable near the cores of Uranus and Neptune. As a convecting fluid, the material could give rise to the magnetic field consistent with the thin-shell dynamo model proposed for these planets. H3O could also be a major component in both solid and superionic forms in other (e.g., nonconvecting) layers. The results thus provide a materials basis for understanding the enigmatic magnetic-field anomalies and other aspects of the interiors of Uranus and Neptune. These findings have direct implications for the internal structure, composition, and dynamos of related exoplanets.
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Zeng L, Jacobsen SB, Sasselov DD, Petaev MI, Vanderburg A, Lopez-Morales M, Perez-Mercader J, Mattsson TR, Li G, Heising MZ, Bonomo AS, Damasso M, Berger TA, Cao H, Levi A, Wordsworth RD. Growth model interpretation of planet size distribution. Proc Natl Acad Sci U S A 2019; 116:9723-9728. [PMID: 31036661 PMCID: PMC6525489 DOI: 10.1073/pnas.1812905116] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The radii and orbital periods of 4,000+ confirmed/candidate exoplanets have been precisely measured by the Kepler mission. The radii show a bimodal distribution, with two peaks corresponding to smaller planets (likely rocky) and larger intermediate-size planets, respectively. While only the masses of the planets orbiting the brightest stars can be determined by ground-based spectroscopic observations, these observations allow calculation of their average densities placing constraints on the bulk compositions and internal structures. However, an important question about the composition of planets ranging from 2 to 4 Earth radii (R⊕) still remains. They may either have a rocky core enveloped in a H2-He gaseous envelope (gas dwarfs) or contain a significant amount of multicomponent, H2O-dominated ices/fluids (water worlds). Planets in the mass range of 10-15 M⊕, if half-ice and half-rock by mass, have radii of 2.5 R⊕, which exactly match the second peak of the exoplanet radius bimodal distribution. Any planet in the 2- to 4-R⊕ range requires a gas envelope of at most a few mass percentage points, regardless of the core composition. To resolve the ambiguity of internal compositions, we use a growth model and conduct Monte Carlo simulations to demonstrate that many intermediate-size planets are "water worlds."
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Affiliation(s)
- Li Zeng
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138;
- Center for Astrophysics | Harvard & Smithsonian, Department of Astronomy, Harvard University, MA 02138
| | - Stein B Jacobsen
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138
| | - Dimitar D Sasselov
- Center for Astrophysics | Harvard & Smithsonian, Department of Astronomy, Harvard University, MA 02138
| | - Michail I Petaev
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138
- Center for Astrophysics | Harvard & Smithsonian, Department of Astronomy, Harvard University, MA 02138
| | - Andrew Vanderburg
- Department of Astronomy, The University of Texas at Austin, Austin, TX 78712
| | - Mercedes Lopez-Morales
- Center for Astrophysics | Harvard & Smithsonian, Department of Astronomy, Harvard University, MA 02138
| | - Juan Perez-Mercader
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138
| | - Thomas R Mattsson
- High Energy Density Physics Theory Department, Sandia National Laboratories, Albuquerque, NM 87185
| | - Gongjie Li
- School of Physics, Georgia Institute of Technology, Atlanta, GA 30313
| | - Matthew Z Heising
- Center for Astrophysics | Harvard & Smithsonian, Department of Astronomy, Harvard University, MA 02138
| | - Aldo S Bonomo
- Istituto Nazionale di Astrofisica-Osservatorio Astrofisico di Torino, 10025 Pino Torinese, Italy
| | - Mario Damasso
- Istituto Nazionale di Astrofisica-Osservatorio Astrofisico di Torino, 10025 Pino Torinese, Italy
| | - Travis A Berger
- Institute for Astronomy, University of Hawaii, Honolulu, HI 96822
| | - Hao Cao
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138
| | - Amit Levi
- Center for Astrophysics | Harvard & Smithsonian, Department of Astronomy, Harvard University, MA 02138
| | - Robin D Wordsworth
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138
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11
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12
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Zhang S, Militzer B, Benedict LX, Soubiran F, Sterne PA, Driver KP. Path integral Monte Carlo simulations of dense carbon-hydrogen plasmas. J Chem Phys 2018; 148:102318. [DOI: 10.1063/1.5001208] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Shuai Zhang
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - 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
| | - Lorin X. Benedict
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - François Soubiran
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
| | - Philip A. Sterne
- Lawrence Livermore National Laboratory, Livermore, California 94550, 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
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14
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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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