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Gharakhanyan V, Wirth LJ, Garrido Torres JA, Eisenberg E, Wang T, Trinkle DR, Chatterjee S, Urban A. Discovering melting temperature prediction models of inorganic solids by combining supervised and unsupervised learning. J Chem Phys 2024; 160:204112. [PMID: 38804486 DOI: 10.1063/5.0207033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2024] [Accepted: 04/29/2024] [Indexed: 05/29/2024] Open
Abstract
The melting temperature is important for materials design because of its relationship with thermal stability, synthesis, and processing conditions. Current empirical and computational melting point estimation techniques are limited in scope, computational feasibility, or interpretability. We report the development of a machine learning methodology for predicting melting temperatures of binary ionic solid materials. We evaluated different machine-learning models trained on a dataset of the melting points of 476 non-metallic crystalline binary compounds using materials embeddings constructed from elemental properties and density-functional theory calculations as model inputs. A direct supervised-learning approach yields a mean absolute error of around 180 K but suffers from low interpretability. We find that the fidelity of predictions can further be improved by introducing an additional unsupervised-learning step that first classifies the materials before the melting-point regression. Not only does this two-step model exhibit improved accuracy, but the approach also provides a level of interpretability with insights into feature importance and different types of melting that depend on the specific atomic bonding inside a material. Motivated by this finding, we used a symbolic learning approach to find interpretable physical models for the melting temperature, which recovered the best-performing features from both prior models and provided additional interpretability.
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Affiliation(s)
- Vahe Gharakhanyan
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA
- Columbia Electrochemical Energy Center, Columbia University, New York, New York 10027, USA
| | - Luke J Wirth
- Department of Materials Science and Engineering, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Jose A Garrido Torres
- Department of Chemical Engineering, Columbia University, New York, New York 10027, USA
| | - Ethan Eisenberg
- Department of Chemical Engineering, Columbia University, New York, New York 10027, USA
| | - Ting Wang
- Department of Chemical Engineering, Columbia University, New York, New York 10027, USA
| | - Dallas R Trinkle
- Department of Materials Science and Engineering, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA
| | | | - Alexander Urban
- Columbia Electrochemical Energy Center, Columbia University, New York, New York 10027, USA
- Department of Chemical Engineering, Columbia University, New York, New York 10027, USA
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de With G. Melting Is Well-Known, but Is It Also Well-Understood? Chem Rev 2023; 123:13713-13795. [PMID: 37963286 PMCID: PMC10722469 DOI: 10.1021/acs.chemrev.3c00489] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Revised: 10/11/2023] [Accepted: 10/12/2023] [Indexed: 11/16/2023]
Abstract
Contrary to continuous phase transitions, where renormalization group theory provides a general framework, for discontinuous phase transitions such a framework seems to be absent. Although the thermodynamics of the latter type of transitions is well-known and requires input from two phases, for melting a variety of one-phase theories and models based on solids has been proposed, as a generally accepted theory for liquids is (yet) missing. Each theory or model deals with a specific mechanism using typically one of the various defects (vacancies, interstitials, dislocations, interstitialcies) present in solids. Furthermore, recognizing that surfaces are often present, one distinguishes between mechanical or bulk melting and thermodynamic or surface-mediated melting. After providing the necessary preliminaries, we discuss both types of melting in relation to the various defects. Thereafter we deal with the effect of pressure on the melting process, followed by a discussion along the line of type of materials. Subsequently, some other aspects and approaches are dealt with. An attempt to put melting in perspective concludes this review.
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Affiliation(s)
- Gijsbertus de With
- Laboratory of Physical Chemistry, Eindhoven University of Technology, Het Kranenveld 14, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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Sharma S, Pasricha R, Weston J, Blanton T, Jagannathan R. Synthesis of Self-Assembled Single Atomic Layer Gold Crystals-Goldene. ACS APPLIED MATERIALS & INTERFACES 2022; 14:54992-55003. [PMID: 36453468 PMCID: PMC9756290 DOI: 10.1021/acsami.2c19743] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Accepted: 11/18/2022] [Indexed: 06/17/2023]
Abstract
We report, for the first time, a technique to synthesize free-standing, one-atom thick 2D gold crystals (namely, goldene) and self-assembled 2D periodic arrays of goldene. High-resolution transmission electron microscopy (HRTEM) imaging of goldene revealed herringbone and honeycomb lattices, which are primarily gold surface features due to its reconstruction. Imaging of these surface-only features by a nonsurface characterization technique such as HRTEM is an unequivocal proof of the absence of three-dimensionality in goldene. Atomic force microscopy confirmed 1-2 Å thickness of goldene. High-resolution X-ray photoelectron spectroscopy (HR-XPS), selective area electron diffraction, and energy-dispersive X-ray spectroscopy confirmed the chemical identity of goldene. We discovered the phenomenon of electric field-induced self-assembly of goldene supracrystals with a herringbone structure and developed an electric field printing (e-print) technique for goldene arrays. Goldene showed a semiconductor response with a knee voltage of ∼3.2 V, and I/V spectroscopy revealed periodic room temperature Coulomb blockade oscillations. These observations are consistent with the theoretical calculations reported in the literature predicting enhanced Coulombic interactions between gold valence electrons and the nucleus in stable 2D gold. Goldene exhibited multiple, intense, and well-resolved optical absorption peaks and several fine bands across the UV-vis region, and we calculated its optical band gap to be 3.59 eV. Magnetic force microscopy measurements of goldene periodic arrays showed a ∼5 mV peak amplitude confirming its ferromagnetism. Optical and magnetic properties of goldene are consistent with those reported in the literature for 2D planar gold clusters with less than 12 atoms.
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Affiliation(s)
- Sudhir
Kumar Sharma
- Engineering
Division, New York University Abu Dhabi, Abu Dhabi 129188, United Arab Emirates
| | - Renu Pasricha
- Core
Technology Platform, New York University
Abu Dhabi, Abu Dhabi 129188, United Arab Emirates
| | - James Weston
- Core
Technology Platform, New York University
Abu Dhabi, Abu Dhabi 129188, United Arab Emirates
| | - Thomas Blanton
- International
Centre for Diffraction Data, 12 Campus Boulevard, Newtown
Square, Pennsylvania 19073, United States
| | - Ramesh Jagannathan
- Engineering
Division, New York University Abu Dhabi, Abu Dhabi 129188, United Arab Emirates
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Wu J, González-Cataldo F, Soubiran F, Militzer B. The phase diagrams of beryllium and magnesium oxide at megabar pressures. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:144003. [PMID: 35026747 DOI: 10.1088/1361-648x/ac4b2a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Accepted: 01/13/2022] [Indexed: 06/14/2023]
Abstract
We performab initiosimulations of beryllium (Be) and magnesium oxide (MgO) at megabar pressures and compare their structural and thermodynamic properties. We make a detailed comparison of our two recently derived phase diagrams of Be (Wuet al2021Phys. Rev.B104014103) and MgO (Soubiran and Militzer 2020Phys. Rev. Lett.125175701) using the thermodynamic integration technique, as they exhibit striking similarities regarding their shape. We explore whether the Lindemann criterion can explain the melting temperatures of these materials through the calculation of the Debye temperature at high pressure. From our free energy calculations, we find that the melting line of both materials is well represented by the Simon-Glazel fitTm(P) =T0(1 +P/a)1/c, whereT0= 1564 K,a= 15.8037 GPa andc= 2.4154 for Be, whileT0= 3010 K,a= 10.5797 GPa andc= 2.8683 for the MgO in the B1. For the B2 phase, we use the valuesa= 26.1163 GPa andc= 2.2426. Both materials exhibit negative Clapeyron slopes on the boundaries between the two solid phases that are strongly affected by anharmonic effects, which also influence the location of the solid-solid-liquid triple point. We find that the quasi-harmonic approximation underestimates the stability range of the low-pressure phases, namely hcp for Be and B1 for MgO. We also compute the phonon dispersion relations at low and high pressure for each of the phases of these materials, and also explore how the phonon density of states is modified by temperature. Finally, we derive secondary shock Hugoniot curves in addition to the principal Hugoniot curve for both materials, and study their offsets in pressure between solid and liquid branches.
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Affiliation(s)
- Jizhou Wu
- Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, United States of America
| | - Felipe González-Cataldo
- Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, United States of America
| | | | - Burkhard Militzer
- Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, United States of America
- Department of Astronomy, University of California, Berkeley, CA 94720, United States of America
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A Review of the Melting Curves of Transition Metals at High Pressures Using Static Compression Techniques. CRYSTALS 2021. [DOI: 10.3390/cryst11040416] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
The accurate determination of melting curves for transition metals is an intense topic within high pressure research, both because of the technical challenges included as well as the controversial data obtained from various experiments. This review presents the main static techniques that are used for melting studies, with a strong focus on the diamond anvil cell; it also explores the state of the art of melting detection methods and analyzes the major reasons for discrepancies in the determination of the melting curves of transition metals. The physics of the melting transition is also discussed.
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On the influence of the electron dose rate on the HRTEM image contrast. Ultramicroscopy 2017; 176:37-45. [DOI: 10.1016/j.ultramic.2016.11.016] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2016] [Revised: 11/16/2016] [Accepted: 11/18/2016] [Indexed: 10/20/2022]
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Smirnov NA. Ab initio calculations of the elastic and thermodynamic properties of gold under pressure. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:105402. [PMID: 28075332 DOI: 10.1088/1361-648x/aa58ca] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The paper presents first-principles FP-LMTO calculations on the relative stability of fcc, bcc, hcp and dhcp gold under pressure. They were done in local density approximation (LDA), as well as in generalized gradient approximation (GGA) with and without spin-orbit interaction. Phonon spectra for the considered gold structures were obtained from LDA calculations within linear response theory and the contribution of lattice vibrations to the free energy of the system was determined in quasiharmonic approximation. Our thorough adjustment of FP-LMTO internal parameters (linearization and tail energies, the MT-sphere radius) helped us to obtain results that agree well with the available experimental phase relation Dubrovinsky et al (2007 Phys. Rev. Lett. 98 045503) between fcc and hcp structures of gold under pressure. The calculations suggest that gold compressed at room temperature successively undergoes the following structural changes: [Formula: see text]. The paper also presents the calculated elastic constants of fcc, bcc and hcp Au, the principal Hugoniot and the melting curve. Calculated results were used to construct the PT-diagram which describes the relative stability of the gold structures under study up to 500 GPa.
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Affiliation(s)
- N A Smirnov
- Russian Federal Nuclear Center-Institute of Technical Physics, 456770, Snezhinsk, Russia
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Stixrude L. Melting in super-earths. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2014; 372:20130076. [PMID: 24664915 DOI: 10.1098/rsta.2013.0076] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We examine the possible extent of melting in rock-iron super-earths, focusing on those in the habitable zone. We consider the energetics of accretion and core formation, the timescale of cooling and its dependence on viscosity and partial melting, thermal regulation via the temperature dependence of viscosity, and the melting curves of rock and iron components at the ultra-high pressures characteristic of super-earths. We find that the efficiency of kinetic energy deposition during accretion increases with planetary mass; considering the likely role of giant impacts and core formation, we find that super-earths probably complete their accretionary phase in an entirely molten state. Considerations of thermal regulation lead us to propose model temperature profiles of super-earths that are controlled by silicate melting. We estimate melting curves of iron and rock components up to the extreme pressures characteristic of super-earth interiors based on existing experimental and ab initio results and scaling laws. We construct super-earth thermal models by solving the equations of mass conservation and hydrostatic equilibrium, together with equations of state of rock and iron components. We set the potential temperature at the core-mantle boundary and at the surface to the local silicate melting temperature. We find that ancient (∼4 Gyr) super-earths may be partially molten at the top and bottom of their mantles, and that mantle convection is sufficiently vigorous to sustain dynamo action over the whole range of super-earth masses.
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Affiliation(s)
- Lars Stixrude
- Department of Earth Sciences, University College London, , Gower St, London WC1E 6BT, UK
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Brown JM, McQueen RG. Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa. ACTA ACUST UNITED AC 2012. [DOI: 10.1029/jb091ib07p07485] [Citation(s) in RCA: 593] [Impact Index Per Article: 49.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Brown JM, Ahrens TJ, Shampine DL. Hugoniot data for pyrrhotite and the Earth's core. ACTA ACUST UNITED AC 2012. [DOI: 10.1029/jb089ib07p06041] [Citation(s) in RCA: 118] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Heinz DL, Jeanloz R. Measurement of the melting curve of Mg0.9Fe0.1SiO3at lower mantle conditions and its geophysical implications. ACTA ACUST UNITED AC 2012. [DOI: 10.1029/jb092ib11p11437] [Citation(s) in RCA: 160] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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12
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Batsanov SS. The dynamic criteria of melting-crystallization. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A 2009. [DOI: 10.1134/s0036024409110053] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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An Q, Zheng L, Fu R, Ni S, Luo SN. Solid–liquid transitions of sodium chloride at high pressures. J Chem Phys 2006; 125:154510. [PMID: 17059275 DOI: 10.1063/1.2357737] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate solid-liquid transitions in NaCl at high pressures using molecular dynamics simulations, including the melting curve and superheating/supercooling as well as solid-solid and liquid-liquid transitions. The first-order B1-B2 (NaCl-CsCl type) transition in solid is observed at high pressures besides continuous liquid structure transitions, which are largely analogous to the B1-B2 transition in solid. The equilibrium melting temperatures (T(m)) up to megabar pressure are obtained from the solid-liquid coexistence technique and the superheating-supercooling hysteresis method. Lindemann's vibrational and Born's mechanical instabilities are found upon melting. The Lindemann frequency is calculated from the vibrational density of states. The Lindemann parameter (fractional root-mean-squared displacement) increases with pressure and approaches a constant asymptotically, similar to the Lennard-Jones system. However, the Lindemann melting relation holds for both B1 and B2 phases to high accuracy as for the Lennard-Jonesium. The B1 and B2 NaCl solids can be superheated by 0.18T(m) and 0.24T(m), and the NaCl liquid, supercooled by 0.22T(m) and 0.32T(m), respectively, at heating or cooling rates of 1 K/s and 1 K/ps. The amount of maximum superheating or supercooling and its weak pressure dependence observed for NaCl are in accord with experiments on alkali halides and with simulations on the Lennard-Jones system and Al.
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Affiliation(s)
- Qi An
- School of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui 230026, PRC
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Nunomura S, Samsonov D, Zhdanov S, Morfill G. Self-diffusion in a liquid complex plasma. PHYSICAL REVIEW LETTERS 2006; 96:015003. [PMID: 16486468 DOI: 10.1103/physrevlett.96.015003] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2005] [Indexed: 05/06/2023]
Abstract
Self-diffusion has been experimentally studied in a two-dimensional underdamped liquid complex (dusty) plasma. It was found that the self-diffusion coefficient D increases linearly with the temperature T: D/omega(E)a2 = (0.019 +/- 0.007)(T/T(m) - 1), where T(m), omega(E), and a are the melting temperature, the Einstein frequency, and the mean particle separation, respectively. No superdiffusion was observed, whereas a subdiffusion occurred at temperatures close to melting.
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Affiliation(s)
- S Nunomura
- Max-Planck-Institut für Extraterrestrische Physik, D-85740 Garching, Germany
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Luo SN, Strachan A, Swift DC. Vibrational density of states and Lindemann melting law. J Chem Phys 2005; 122:194709. [PMID: 16161608 DOI: 10.1063/1.1902948] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We examine the Lindemann melting law at different pressures using the vibrational density of states (DOS), equilibrium melting curve, and Lindemann parameter delta(L) (fractional root-mean-squared displacement, rmsd, at equilibrium melting) calculated independently from molecular dynamics simulations of the Lennard-Jones system. The DOS is obtained using spectra analysis of atomic velocities and accounts for anharmonicity. The increase of delta(L) with pressure is non-negligible: delta(L) is about 0.116 and 0.145 at ambient and extreme pressures, respectively. If the component of rmsd normal to a reflecting plane as in the Debye-Waller-factor-type measurements using x rays is adopted for delta(L), these values are about 0.067 (+/-0.002) and 0.084 (+/-0.003), and are comparable with experimental and calculated values for face-centered-cubic elements. We find that the Lindemann relation holds accurately at ambient and high pressures. The non-negligible pressure dependence of delta(L) suggests that caution should be exerted in applying the Lindemann law to obtaining the high pressure melting curve anchored at ambient pressure.
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Affiliation(s)
- Sheng-Nian Luo
- P-24 Plasma Physics, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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The three-dimensional phase diagram of iron. ACTA ACUST UNITED AC 2003. [DOI: 10.1029/gd031p0083] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/09/2023]
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17
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Cohen RE, Gong Z. Melting and melt structure of MgO at high pressures. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:12301-12311. [PMID: 9975388 DOI: 10.1103/physrevb.50.12301] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Godwal BK, Meade C, Jeanloz R, Garcia A, Liu AY, Cohen ML. Ultrahigh-Pressure Melting of Lead: A Multidisciplinary Study. Science 1990; 248:462-5. [PMID: 17815595 DOI: 10.1126/science.248.4954.462] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Measurements of the melting temperature of lead, carried out to pressures of 1 megabar (10(11) pascal) and temperatures near 4000 kelvin by means of a laser-heated diamond cell, are in excellent agreement with the results of previous shock-wave experiments. The data are analyzed by means of first principles quantum mechanical calculations, and the agreement documents the reliability of current experimental and theoretical techniques for studies of melting at ultrahigh pressures. These studies have potentially wide-ranging applications, from planetary science to condensed matter physics.
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Anderson OL. The high-pressure triple points of iron and their effects on the heat flow from the Earth's core. ACTA ACUST UNITED AC 1990. [DOI: 10.1029/jb095ib13p21697] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Stixrude L, Bukowinski MST. Fundamental thermodynamic relations and silicate melting with implications for the constitution ofD″. ACTA ACUST UNITED AC 1990. [DOI: 10.1029/jb095ib12p19311] [Citation(s) in RCA: 105] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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LaViolette RA, Stillinger FH. Multidimensional geometric aspects of the solid–liquid transition in simple substances. J Chem Phys 1985. [DOI: 10.1063/1.449826] [Citation(s) in RCA: 118] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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