1
|
Tkalčić H, Belonoshko AB, Muir JB, Mattesini M, Moresi L, Waszek L. Imaging the top of the Earth's inner core: a present-day flow model. Sci Rep 2024; 14:8999. [PMID: 38637675 PMCID: PMC11026418 DOI: 10.1038/s41598-024-59520-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2023] [Accepted: 04/11/2024] [Indexed: 04/20/2024] Open
Abstract
Despite considerable progress in seismology, mineral physics, geodynamics, paleomagnetism, and mathematical geophysics, Earth's inner core structure and evolution remain enigmatic. One of the most significant issues is its thermal history and the current thermal state. Several hypotheses involving a thermally-convecting inner core have been proposed: a simple, high-viscosity, translational mode, or a classical, lower-viscosity, plume-style convection. Here, we use state-of-the-art seismic imaging to probe the outermost shell of the inner core for its isotropic compressional speed and compare it with recently developed attenuation maps. The pattern emerging in the resulting tomograms is interpreted with recent data on the viscosity of iron as the inner core surface manifestation of a thermally-driven flow, with a positive correlation among compressional speed and attenuation and temperature. Although the outer-core convection controls the heat flux across the inner core boundary, the internally driven inner-core convection is a plausible model that explains a range of observations for the inner core, including distinct anisotropy in the innermost inner core.
Collapse
Affiliation(s)
- Hrvoje Tkalčić
- Research School of Earth Sciences, The Australian National University, Canberra, ACT, 2601, Australia.
| | - Anatoly B Belonoshko
- School of Earth Sciences and Engineering, Nanjing University, Nanjing, 210093, China
| | - Jack B Muir
- Department of Earth Sciences, University of Oxford, Oxford, OX1 3AN, UK
| | - Maurizio Mattesini
- Department of Earth's Physics and Astrophysics, Complutense University of Madrid, Madrid, Spain
- Facultad de Ciencias Físicas, Instituto de Geociencias (UCM-CSIC), Madrid, Spain
| | - Louis Moresi
- Research School of Earth Sciences, The Australian National University, Canberra, ACT, 2601, Australia
| | - Lauren Waszek
- Physical Sciences, James Cook University, Townsville, QLD, 4810, Australia
- Department of Physics, New Mexico State University, Las Cruces, NM, 88003, Australia
| |
Collapse
|
2
|
Demyanov GS, Fokin VB, Knyazev DV, Minakov DV, Paramonov MA, Levashov PR. How to read optical properties of matter via the Kubo-Greenwood approach. Phys Rev E 2023; 108:L053301. [PMID: 38115528 DOI: 10.1103/physreve.108.l053301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Accepted: 11/03/2023] [Indexed: 12/21/2023]
Abstract
Substances with a complex electronic structure exhibit non-Drude optical properties that are challenging to interpret experimentally and theoretically. In our recent paper [Phys. Rev. E 105, 035307 (2022)2470-004510.1103/PhysRevE.105.035307], we offered a computational method based on the continuous Kubo-Greenwood formula, which expresses dynamic conductivity as an integral over the electron spectrum. In this Letter, we propose a methodology to analyze the complex conductivity using liquid Zr as an example to explain its nontrivial behavior. To achieve this, we apply the continuous Kubo-Greenwood formula and extend it to include the imaginary part of the complex conductivity into the analysis. Our method is suitable for a wide range of substances, providing an opportunity to explain optical properties from ab initio calculations of any difficulty.
Collapse
Affiliation(s)
- G S Demyanov
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - V B Fokin
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - D V Knyazev
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - D V Minakov
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - M A Paramonov
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia
| | - P R Levashov
- Joint Institute for High Temperatures, Izhorskaya 13 Building 2, Moscow 125412, Russia
- Moscow Institute of Physics and Technology, Institutskiy Pereulok 9, Dolgoprudny, Moscow Region 141701, Russia
| |
Collapse
|
3
|
Ohta K, Suehiro S, Kawaguchi SI, Okuda Y, Wakamatsu T, Hirose K, Ohishi Y, Kodama M, Hirai S, Azuma S. Measuring the Electrical Resistivity of Liquid Iron to 1.4 Mbar. PHYSICAL REVIEW LETTERS 2023; 130:266301. [PMID: 37450814 DOI: 10.1103/physrevlett.130.266301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Accepted: 05/04/2023] [Indexed: 07/18/2023]
Abstract
We determined the electrical resistivity of liquid Fe to 135 GPa and 6680 K using a four-probe method in a diamond-anvil cell combined with two novel techniques: (i) enclosing a molten Fe in a sapphire capsule, and (ii) millisecond time-resolved simultaneous measurements of the resistance, x-ray diffraction, and temperature of instantaneously melted Fe. Our results show the minimal temperature dependence of the resistivity of liquid Fe and its anomalous resistivity decrease around 50 GPa, likely associated with a gradual magnetic transition, both in agreement with previous ab initio calculations.
Collapse
Affiliation(s)
- Kenji Ohta
- Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo 152-8551, Japan
| | - Sho Suehiro
- Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo 152-8551, Japan
| | - Saori I Kawaguchi
- Japan Synchrotron Radiation Research Institute, SPring-8, Hyogo 679-5198, Japan
| | - Yoshiyuki Okuda
- Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo 152-8551, Japan
- Department of Earth and Planetary Science, The University of Tokyo, Tokyo 113-0033, Japan
| | - Tatsuya Wakamatsu
- Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo 152-8551, Japan
| | - Kei Hirose
- Department of Earth and Planetary Science, The University of Tokyo, Tokyo 113-0033, Japan
- Earth-Life Science Institute, Tokyo Institute of Technology, Tokyo 152-8550, Japan
| | - Yasuo Ohishi
- Japan Synchrotron Radiation Research Institute, SPring-8, Hyogo 679-5198, Japan
| | - Manabu Kodama
- Department of Mechanical Engineering, Tokyo Institute of Technology, Tokyo 152-8551, Japan
| | - Shuichiro Hirai
- Department of Mechanical Engineering, Tokyo Institute of Technology, Tokyo 152-8551, Japan
| | - Shintaro Azuma
- Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo 152-8551, Japan
| |
Collapse
|
4
|
Jang BG, He Y, Shim JH, Mao HK, Kim DY. Oxygen-Driven Enhancement of the Electron Correlation in Hexagonal Iron at Earth's Inner Core Conditions. J Phys Chem Lett 2023; 14:3884-3890. [PMID: 37071052 PMCID: PMC10150722 DOI: 10.1021/acs.jpclett.3c00500] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2023] [Accepted: 04/11/2023] [Indexed: 05/03/2023]
Abstract
Earth's inner core (IC) consists of mainly iron with some light elements. Understanding its structure and related physical properties has been elusive as a result of its required extremely high pressure and temperature conditions. The phase of iron, elastic anisotropy, and density-velocity deficit at the IC have long been questions of great interest. Here, we find that the electron correlation effect is enhanced by oxygen and modifies several important features, including the stability of iron oxides. Oxygen atoms energetically stabilize hexagonal-structured iron at IC conditions and induce elastic anisotropy. Electrical resistivity is much enhanced in comparison to pure hexagonal close-packed (hcp) iron as a result of the enhanced electron correlation effect, supporting the conventional thermal convection model. Moreover, our calculated seismic velocity shows a quantitative match with geologically observed preliminary reference Earth model (PREM) data. We suggest that oxygen is the essential light element to understand and model Earth's IC.
Collapse
Affiliation(s)
- Bo Gyu Jang
- Center
for High Pressure Science and Technology Advanced Research (HPSTAR), Shanghai 201203, People’s Republic of China
- Korea
Institute for Advanced Study, Seoul 02455, Korea
| | - Yu He
- Center
for High Pressure Science and Technology Advanced Research (HPSTAR), Shanghai 201203, People’s Republic of China
- Key
Laboratory of High-Temperature and High-Pressure Study of the Earth’s
Interior, Institute of Geochemistry, Chinese
Academy of Sciences, Guiyang, Guizhou 550081, People’s Republic of China
| | - Ji Hoon Shim
- Department
of Chemistry, Pohang University of Science
and Technology, Pohang 37673, Korea
- Division
of Advanced Materials Science, Pohang University
of Science and Technology, Pohang 37673, Korea
| | - Ho-kwang Mao
- Center
for High Pressure Science and Technology Advanced Research (HPSTAR), Shanghai 201203, People’s Republic of China
| | - Duck Young Kim
- Center
for High Pressure Science and Technology Advanced Research (HPSTAR), Shanghai 201203, People’s Republic of China
- Shanghai
Key Laboratory of Material Frontiers Research in Extreme Environments
(MFree), Shanghai Advanced Research in Physical
Sciences (SHARPS), Pudong, Shanghai 201203, P.R. China
| |
Collapse
|
5
|
Gendron F, Cliche N, Amadon B. Role of pressure on electronic, magnetic and structural properties at iron's Curie temperature: a DFT + DMFT study. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:464003. [PMID: 36067782 DOI: 10.1088/1361-648x/ac8fd0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 09/06/2022] [Indexed: 06/15/2023]
Abstract
We use the combination of density functional theory and dynamical mean-field theory to compute the Curie temperature of the iron body-centered cubicαphase and probe its pressure dependence. Our calculations reveal thatTCshows a decrease which is very weak over a domain of pressures that is much larger than the stability domain of theαphase. This is consistent with the experimental results. We highlight the importance of the Hund's couplingJnot only on the electronic and magnetic properties but also on the structural properties. Lastly, we analyze the electronic and magnetic properties under pressure and discuss the evolution of magnetic moments in both phases in relation to the change of Curie temperature.
Collapse
Affiliation(s)
- F Gendron
- CEA, DAM, DIF, F-91297 Arpajon, France
- Université Paris-Saclay, CEA, Laboratoire Matière en Conditions Extrêmes, 91680 Bruyères-le-Châtel, France
| | - N Cliche
- CEA, DAM, DIF, F-91297 Arpajon, France
| | - B Amadon
- CEA, DAM, DIF, F-91297 Arpajon, France
- Université Paris-Saclay, CEA, Laboratoire Matière en Conditions Extrêmes, 91680 Bruyères-le-Châtel, France
| |
Collapse
|
6
|
French M, Röpke G, Schörner M, Bethkenhagen M, Desjarlais MP, Redmer R. Electronic transport coefficients from density functional theory across the plasma plane. Phys Rev E 2022; 105:065204. [PMID: 35854489 DOI: 10.1103/physreve.105.065204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2022] [Accepted: 05/18/2022] [Indexed: 06/15/2023]
Abstract
We investigate the thermopower and Lorenz number of hydrogen with Kohn-Sham density functional theory (DFT) across the plasma plane toward the near-classical limit, i.e., weakly degenerate and weakly coupled states. Our results are in concordance with certain limiting values for the Lorentz plasma, a model system which only considers electron-ion scattering. Thereby, we clearly show that the widely used method of calculating transport properties via the Kubo-Greenwood (KG) formalism does not capture electron-electron scattering processes. Our discussion also addresses the inadequateness of assuming a Drude-like frequency behavior for the conductivity of nondegenerate plasmas by revisiting the relaxation time approximation within kinetic theory.
Collapse
Affiliation(s)
- Martin French
- Universität Rostock, Institut für Physik, Albert-Einstein-Str. 23-24, D-18059 Rostock, Germany
| | - Gerd Röpke
- Universität Rostock, Institut für Physik, Albert-Einstein-Str. 23-24, D-18059 Rostock, Germany
| | - Maximilian Schörner
- Universität Rostock, Institut für Physik, Albert-Einstein-Str. 23-24, D-18059 Rostock, Germany
| | - Mandy Bethkenhagen
- Universität Rostock, Institut für Physik, Albert-Einstein-Str. 23-24, D-18059 Rostock, Germany
- École Normale Supérieure de Lyon, Université Lyon 1, Laboratoire de Géologie de Lyon, CNRS UMR 5276, 69364 Lyon Cedex 07, France
| | | | - Ronald Redmer
- Universität Rostock, Institut für Physik, Albert-Einstein-Str. 23-24, D-18059 Rostock, Germany
| |
Collapse
|
7
|
Thermal conductivity of Fe-Si alloys and thermal stratification in Earth's core. Proc Natl Acad Sci U S A 2022; 119:2119001119. [PMID: 34969863 PMCID: PMC8740763 DOI: 10.1073/pnas.2119001119] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/16/2021] [Indexed: 11/18/2022] Open
Abstract
Light elements in Earth's core play a key role in driving convection and influencing geodynamics, both of which are crucial to the geodynamo. However, the thermal transport properties of iron alloys at high-pressure and -temperature conditions remain uncertain. Here we investigate the transport properties of solid hexagonal close-packed and liquid Fe-Si alloys with 4.3 and 9.0 wt % Si at high pressure and temperature using laser-heated diamond anvil cell experiments and first-principles molecular dynamics and dynamical mean field theory calculations. In contrast to the case of Fe, Si impurity scattering gradually dominates the total scattering in Fe-Si alloys with increasing Si concentration, leading to temperature independence of the resistivity and less electron-electron contribution to the conductivity in Fe-9Si. Our results show a thermal conductivity of ∼100 to 110 W⋅m-1⋅K-1 for liquid Fe-9Si near the topmost outer core. If Earth's core consists of a large amount of silicon (e.g., > 4.3 wt %) with such a high thermal conductivity, a subadiabatic heat flow across the core-mantle boundary is likely, leaving a 400- to 500-km-deep thermally stratified layer below the core-mantle boundary, and challenges proposed thermal convection in Fe-Si liquid outer core.
Collapse
|