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Generalization of the Unified Analytic Melt-Shear Model to Multi-Phase Materials: Molybdenum as an Example. CRYSTALS 2019. [DOI: 10.3390/cryst9020086] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The unified analytic melt-shear model that we introduced a decade ago is generalized to multi-phase materials. A new scheme for calculating the values of the model parameters for both the cold ( T = 0 ) shear modulus ( G ) and the melting temperature at all densities ( ρ ) is developed. The generalized melt-shear model is applied to molybdenum, a multi-phase material with a body-centered cubic (bcc) structure at low ρ which loses its dynamical stability with increasing pressure (P) and is therefore replaced by another (dynamically stable) solid structure at high ρ . One of the candidates for the high- ρ structure of Mo is face-centered cubic (fcc). The model is compared to (i) our ab initio results on the cold shear modulus of both bcc-Mo and fcc-Mo as a function of ρ , and (ii) the available theoretical results on the melting of bcc-Mo and our own quantum molecular dynamics (QMD) simulations of one melting point of fcc-Mo. Our generalized model of G ( ρ , T ) is used to calculate the shear modulus of bcc-Mo along its principal Hugoniot. It predicts that G of bcc-Mo increases with P up to ∼240 GPa and then decreases at higher P. This behavior is intrinsic to bcc-Mo and does not require the introduction of another solid phase such as Phase II suggested by Errandonea et al. Generalized melt-shear models for Ta and W also predict an increase in G followed by a decrease along the principal Hugoniot, hence this behavior may be typical for transition metals with ambient bcc structure that dynamically destabilize at high P. Thus, we concur with the conclusion reached in several recent papers (Nguyen et al., Zhang et al., Wang et al.) that no solid-solid phase transition can be definitively inferred on the basis of sound velocity data from shock experiments on Mo. Finally, our QMD simulations support the validity of the phase diagram of Mo suggested by Zeng et al.
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Zhang Y, Sekine T, He H, Yu Y, Liu F, Zhang M. Experimental constraints on light elements in the Earth's outer core. Sci Rep 2016; 6:22473. [PMID: 26932596 PMCID: PMC4773879 DOI: 10.1038/srep22473] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2015] [Accepted: 02/16/2016] [Indexed: 11/09/2022] Open
Abstract
Earth's outer core is liquid and dominantly composed of iron and nickel (~5-10 wt%). Its density, however, is ~8% lower than that of liquid iron, and requires the presence of a significant amount of light element(s). A good way to specify the light element(s) is a direct comparison of density and sound velocity measurements between seismological data and those of possible candidate compositions at the core conditions. We report the sound velocity measurements of a model core composition in the Fe-Ni-Si system at the outer core conditions by shock-wave experiments. Combining with the previous studies, we found that the best estimate for the outer core's light elements is ~6 wt% Si, ~2 wt% S, and possible ~1-2.5 wt% O. This composition satisfies the requirements imposed by seismology, geochemistry, and some models of the early core formation. This finding may help us to further constrain the thermal structure of the Earth and the models of Earth's core formation.
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Affiliation(s)
- Youjun Zhang
- Department of Earth and Planetary Systems Science, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima 739-8526, Japan
| | - Toshimori Sekine
- Department of Earth and Planetary Systems Science, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima 739-8526, Japan
| | - Hongliang He
- National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, PO Box 919-111, Mianyang 621900, China
| | - Yin Yu
- National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, PO Box 919-111, Mianyang 621900, China
| | - Fusheng Liu
- College of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, China
| | - Mingjian Zhang
- College of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, China
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Akin MC, Nguyen JH. Practical uncertainty reduction and quantification in shock physics measurements. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2015; 86:043903. [PMID: 25933867 DOI: 10.1063/1.4917555] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2014] [Accepted: 04/02/2015] [Indexed: 06/04/2023]
Abstract
We report the development of a simple error analysis sampling method for identifying intersections and inflection points to reduce total uncertainty in experimental data. This technique was used to reduce uncertainties in sound speed measurements by 80% over conventional methods. Here, we focused on its impact on a previously published set of Mo sound speed data and possible implications for phase transition and geophysical studies. However, this technique's application can be extended to a wide range of experimental data.
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Affiliation(s)
- M C Akin
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - J H Nguyen
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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Hidden carbon in Earth's inner core revealed by shear softening in dense Fe7C3. Proc Natl Acad Sci U S A 2014; 111:17755-8. [PMID: 25453077 DOI: 10.1073/pnas.1411154111] [Citation(s) in RCA: 81] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Earth's inner core is known to consist of crystalline iron alloyed with a small amount of nickel and lighter elements, but the shear wave (S wave) travels through the inner core at about half the speed expected for most iron-rich alloys under relevant pressures. The anomalously low S-wave velocity (vS) has been attributed to the presence of liquid, hence questioning the solidity of the inner core. Here we report new experimental data up to core pressures on iron carbide Fe7C3, a candidate component of the inner core, showing that its sound velocities dropped significantly near the end of a pressure-induced spin-pairing transition, which took place gradually between 10 GPa and 53 GPa. Following the transition, the sound velocities increased with density at an exceptionally low rate. Extrapolating the data to the inner core pressure and accounting for the temperature effect, we found that low-spin Fe7C3 can reproduce the observed vS of the inner core, thus eliminating the need to invoke partial melting or a postulated large temperature effect. The model of a carbon-rich inner core may be consistent with existing constraints on the Earth's carbon budget and would imply that as much as two thirds of the planet's carbon is hidden in its center sphere.
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Aspherical Structure of the Mantle, Tectonic Plate Motions, Nonhydrostatic Geoid, and Topography of the Core-Mantle Boundary. ACTA ACUST UNITED AC 2013. [DOI: 10.1029/gm072p0135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Pari G, Peltier WR. The heat flow constraint on mantle tomography-based convection models: Towards a geodynamically self-consistent inference of mantle viscosity. ACTA ACUST UNITED AC 2012. [DOI: 10.1029/95jb01078] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Duffy TS, Ahrens TJ. Compressional sound velocity, equation of state, and constitutive response of shock-compressed magnesium oxide. ACTA ACUST UNITED AC 2012. [DOI: 10.1029/94jb02065] [Citation(s) in RCA: 92] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Mackrodt WC, Williamson EA, Williams D, Allan NL. A first-principles Hartree-Fock description of MnO at high pressures. ACTA ACUST UNITED AC 2009. [DOI: 10.1080/13642819808206405] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- W. C. Mackrodt
- a School of Chemistry, University of St Andrews , St Andrews Fife, KY16 9ST, Scotland
| | - E.-A. Williamson
- a School of Chemistry, University of St Andrews , St Andrews Fife, KY16 9ST, Scotland
| | - D. Williams
- a School of Chemistry, University of St Andrews , St Andrews Fife, KY16 9ST, Scotland
| | - N. L. Allan
- b School of Chemistry, University of Bristol , Cantock's Close, Bristol , BS8 ITS , England
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Duffy TS. Some recent advances in understanding the mineralogy of Earth's deep mantle. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2008; 366:4273-4293. [PMID: 18826921 DOI: 10.1098/rsta.2008.0172] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Understanding planetary structure and evolution requires a detailed knowledge of the properties of geological materials under the conditions of deep planetary interiors. Experiments under the extreme pressure-temperature conditions of the deep mantle are challenging, and many fundamental properties remain poorly constrained or are inferred only through uncertain extrapolations from lower pressure-temperature states. Nevertheless, the last several years have witnessed a number of new developments in this area, and a broad overview of the current understanding of the Earth's lower mantle is presented here. Some recent experimental and theoretical advances related to the lowermost mantle are highlighted. Measurements of the equation of state and deformation behaviour of (Mg,Fe)SiO3 in the CaIrO3-type (post-perovskite) structure yield insights into the nature of the core-mantle boundary region. Theoretical studies of the behaviour of MgSiO3 liquids under high pressure-temperature conditions provide constraints on melt volumes, diffusivities and viscosities that are relevant to understanding both the early Earth (e.g. deep magma oceans) and seismic structure observed in the present Earth (e.g. ultra-low-velocity zones).
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Affiliation(s)
- Thomas S Duffy
- Department of Geosciences, Princeton University, Princeton, NJ 08544, USA.
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Bovolo CI. The physical and chemical composition of the lower mantle. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2005; 363:2811-35. [PMID: 16286292 DOI: 10.1098/rsta.2005.1675] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
This article reviews some of the recent advances made within the field of mineral physics. In order to link the observed seismic and density structures of the lower mantle with a particular mineral composition, knowledge of the thermodynamic properties of the candidate materials is required. Determining which compositional model best matches the observed data is difficult because of the wide variety of possible mineral structures and compositions. State-of-the-art experimental and analytical techniques have pushed forward our knowledge of mineral physics, yet certain properties, such as the elastic properties of lower mantle minerals at high pressures and temperatures, are difficult to determine experimentally and remain elusive. Fortunately, computational techniques are now sufficiently advanced to enable the prediction of these properties in a self-consistent manner, but more results are required.A fundamental question is whether or not the upper and lower mantles are mixing. Traditional models that involve chemically separate upper and lower mantles cannot yet be ruled out despite recent conflicting seismological evidence showing that subducting slabs penetrate deep into the lower mantle and that chemically distinct layers are, therefore, unlikely.Recent seismic tomography studies giving three-dimensional models of the seismic wave velocities in the Earth also base their interpretations on the thermodynamic properties of minerals. These studies reveal heterogeneous velocity and density anomalies in the lower mantle, which are difficult to reconcile with mineral physics data.
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Affiliation(s)
- C Isabella Bovolo
- University of Newcastle upon Tyne School of Civil Engineering & Geosciences Newcastle upon Tyne NE1 7RU, UK.
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Adler JF. A high-pressure X-ray diffraction study of iron nitrides: Implications for Earth's core. ACTA ACUST UNITED AC 2005. [DOI: 10.1029/2004jb003103] [Citation(s) in RCA: 61] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Merkel S, Wenk HR, Shu J, Shen G, Gillet P, Mao HK, Hemley RJ. Deformation of polycrystalline MgO at pressures of the lower mantle. ACTA ACUST UNITED AC 2002. [DOI: 10.1029/2001jb000920] [Citation(s) in RCA: 182] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Sébastien Merkel
- Laboratoire des sciences de la Terre; École normale supérieure de Lyon; Lyon France
- Geophysical Laboratory; Carnegie Institution of Washington; Washington District of Columbia USA
| | - Hans Rudolf Wenk
- Department of Earth and Planetary Science; University of California; Berkeley California USA
| | - Jinfu Shu
- Geophysical Laboratory; Carnegie Institution of Washington; Washington District of Columbia USA
| | - Guoyin Shen
- Consortium for Advanced Radiation Sources; University of Chicago and Advanced Photon Source, Argonne National Laboratory; Argonne Illinois USA
| | - Philippe Gillet
- Laboratoire des sciences de la Terre; École normale supérieure de Lyon; Lyon France
| | - Ho-kwang Mao
- Geophysical Laboratory; Carnegie Institution of Washington; Washington District of Columbia USA
| | - Russell J. Hemley
- Geophysical Laboratory; Carnegie Institution of Washington; Washington District of Columbia USA
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Affiliation(s)
- V. S. Solomatov
- Department of Physics; New Mexico State University; Las Cruces New Mexico USA
| | - L.-N. Moresi
- Australian Geodynamics Cooperative Research Centre; CSIRO Exploration and Mining; Nedlands Western Australia Australia
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Elasticity of mantle minerals (experimental studies). ACTA ACUST UNITED AC 2000. [DOI: 10.1029/gm117p0181] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Koper KD, Wiens DA, Dorman L, Hildebrand J, Webb S. Constraints on the origin of slab and mantle wedge anomalies in Tonga from the ratio ofStoPvelocities. ACTA ACUST UNITED AC 1999. [DOI: 10.1029/1999jb900130] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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Wysession ME, Lay T, Revenaugh J, Williams Q, Garnero EJ, Jeanloz R, Kellogg LH. The D″ discontinuity and its implications. THE CORE‐MANTLE BOUNDARY REGION 1998. [DOI: 10.1029/gd028p0273] [Citation(s) in RCA: 149] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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Pari G, Peltier WR. The free-air gravity constraint on subcontinental mantle dynamics. ACTA ACUST UNITED AC 1996. [DOI: 10.1029/96jb02099] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Affiliation(s)
- Quentin Williams
- Earth Sciences Board and Institute of Tectonics, University of California, Santa Cruz, CA 95064, USA
| | - Edward J. Garnero
- Earth Sciences Board and Institute of Tectonics, University of California, Santa Cruz, CA 95064, USA
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Seismic constraints on mantle flow and topography of the 660-km discontinuity: evidence for whole-mantle convection. Nature 1993. [DOI: 10.1038/365506a0] [Citation(s) in RCA: 55] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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