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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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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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Zhang S, Marshall MC, Yang LH, Sterne PA, Militzer B, Däne M, Gaffney JA, Shamp A, Ogitsu T, Caspersen K, Lazicki AE, Erskine D, London RA, Celliers PM, Nilsen J, Whitley HD. Benchmarking boron carbide equation of state using computation and experiment. Phys Rev E 2020; 102:053203. [PMID: 33327061 DOI: 10.1103/physreve.102.053203] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2020] [Accepted: 10/08/2020] [Indexed: 11/07/2022]
Abstract
Boron carbide (B_{4}C) is of both fundamental scientific and practical interest due to its structural complexity and how it changes upon compression, as well as its many industrial uses and potential for use in inertial confinement fusion (ICF) and high-energy density physics experiments. We report the results of a comprehensive computational study of the equation of state (EOS) of B_{4}C in the liquid, warm dense matter, and plasma phases. Our calculations are cross-validated by comparisons with Hugoniot measurements up to 61 megabar from planar shock experiments performed at the National Ignition Facility (NIF). Our computational methods include path integral Monte Carlo, activity expansion, as well as all-electron Green's function Korringa-Kohn-Rostoker and molecular dynamics that are both based on density functional theory. We calculate the pressure-internal energy EOS of B_{4}C over a broad range of temperatures (∼6×10^{3}-5×10^{8} K) and densities (0.025-50 g/cm^{3}). We assess that the largest discrepancies between theoretical predictions are ≲5% near the compression maximum at 1-2×10^{6} K. This is the warm-dense state in which the K shell significantly ionizes and has posed grand challenges to theory and experiment. By comparing with different EOS models, we find a Purgatorio model (LEOS 2122) that agrees with our calculations. The maximum discrepancies in pressure between our first-principles predictions and LEOS 2122 are ∼18% and occur at temperatures between 6×10^{3}-2×10^{5} K, which we believe originate from differences in the ion thermal term and the cold curve that are modeled in LEOS 2122 in comparison with our first-principles calculations. To account for potential differences in the ion thermal term, we have developed three new equation-of-state models that are consistent with theoretical calculations and experiment. We apply these new models to 1D hydrodynamic simulations of a polar direct-drive NIF implosion, demonstrating that these new models are now available for future ICF design studies.
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Affiliation(s)
- Shuai Zhang
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA.,Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA
| | | | - Lin H Yang
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Philip A Sterne
- 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
| | - Markus Däne
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - James A Gaffney
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Andrew Shamp
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Tadashi Ogitsu
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Kyle Caspersen
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Amy E Lazicki
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - David Erskine
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Richard A London
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Peter M Celliers
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Joseph Nilsen
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Heather D Whitley
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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