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Zhang Y, Wang Y, Huang Y, Wang J, Liang Z, Hao L, Gao Z, Li J, Wu Q, Zhang H, Liu Y, Sun J, Lin JF. Collective motion in hcp-Fe at Earth's inner core conditions. Proc Natl Acad Sci U S A 2023; 120:e2309952120. [PMID: 37782810 PMCID: PMC10576103 DOI: 10.1073/pnas.2309952120] [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: 06/14/2023] [Accepted: 08/15/2023] [Indexed: 10/04/2023] Open
Abstract
Earth's inner core is predominantly composed of solid iron (Fe) and displays intriguing properties such as strong shear softening and an ultrahigh Poisson's ratio. Insofar, physical mechanisms to explain these features coherently remain highly debated. Here, we have studied longitudinal and shear wave velocities of hcp-Fe (hexagonal close-packed iron) at relevant pressure-temperature conditions of the inner core using in situ shock experiments and machine learning molecular dynamics (MLMD) simulations. Our results demonstrate that the shear wave velocity of hcp-Fe along the Hugoniot in the premelting condition, defined as T/Tm (Tm: melting temperature of iron) above 0.96, is significantly reduced by ~30%, while Poisson's ratio jumps to approximately 0.44. MLMD simulations at 230 to 330 GPa indicate that collective motion with fast diffusive atomic migration occurs in premelting hcp-Fe primarily along [100] or [010] crystallographic direction, contributing to its elastic softening and enhanced Poisson's ratio. Our study reveals that hcp-Fe atoms can diffusively migrate to neighboring positions, forming open-loop and close-loop clusters in the inner core conditions. Hcp-Fe with collective motion at the inner core conditions is thus not an ideal solid previously believed. The premelting hcp-Fe with collective motion behaves like an extremely soft solid with an ultralow shear modulus and an ultrahigh Poisson's ratio that are consistent with seismic observations of the region. Our findings indicate that premelting hcp-Fe with fast diffusive motion represents the underlying physical mechanism to help explain the unique seismic and geodynamic features of the inner core.
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Affiliation(s)
- Youjun Zhang
- Institute of Atomic and Molecular Physics, Sichuan University, Chengdu610065, China
- International Center for Planetary Science, College of Earth Sciences, Chengdu University of Technology, Chengdu610059, China
| | - Yong Wang
- National Laboratory of Solid State Microstructures, School of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing210093, China
| | - Yuqian Huang
- Institute of Atomic and Molecular Physics, Sichuan University, Chengdu610065, China
| | - Junjie Wang
- National Laboratory of Solid State Microstructures, School of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing210093, China
| | - Zhixin Liang
- National Laboratory of Solid State Microstructures, School of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing210093, China
| | - Long Hao
- National Key Laboratory for Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang621900, China
| | - Zhipeng Gao
- National Key Laboratory for Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang621900, China
| | - Jun Li
- National Key Laboratory for Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang621900, China
| | - Qiang Wu
- National Key Laboratory for Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang621900, China
| | - Hong Zhang
- College of Physics, Sichuan University, Chengdu610065, China
| | - Yun Liu
- International Center for Planetary Science, College of Earth Sciences, Chengdu University of Technology, Chengdu610059, China
| | - Jian Sun
- National Laboratory of Solid State Microstructures, School of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing210093, China
| | - Jung-Fu Lin
- Department of Earth and Planetary Sciences, Jackson School of Geosciences, The University of Texas at Austin, Austin, TX78712
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Myint PC, Sterbentz DM, Brown JL, Stoltzfus BS, Delplanque JPR, Belof JL. Scaling Law for the Onset of Solidification at Extreme Undercooling. PHYSICAL REVIEW LETTERS 2023; 131:106101. [PMID: 37739355 DOI: 10.1103/physrevlett.131.106101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2022] [Revised: 04/20/2023] [Accepted: 07/17/2023] [Indexed: 09/24/2023]
Abstract
Quasi-isentropic compression enables one to study the solidification of metastable liquid states that are inaccessible through other experimental means. The onset of this nonequilibrium solidification is known to depend on the compression rate and material-specific factors, but this complex interdependence has not been well characterized. In this study, we use a combination of experiments, theory, and computational simulations to derive a general scaling law that quantifies this dependence. One of its applications is a novel means to elucidate melt temperatures at high pressures.
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Affiliation(s)
- Philip C Myint
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Dane M Sterbentz
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
- Department of Mechanical & Aerospace Engineering, University of California, Davis, California 95616, USA
| | - Justin L Brown
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | | | - Jean-Pierre R Delplanque
- Department of Mechanical & Aerospace Engineering, University of California, Davis, California 95616, USA
| | - Jonathan L Belof
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
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3
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Wang X, Zhang J, Sethian J. High precision control of laser energy for laser-matter interaction studies. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2023; 94:073003. [PMID: 37449893 DOI: 10.1063/5.0149115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2023] [Accepted: 07/01/2023] [Indexed: 07/18/2023]
Abstract
Precise, highly reproducible control of the laser energy is required for high confidence laser-matter interaction research such as in dynamic compression science and high energy density physics. The energy must be adjustable without affecting the pulse shape (time varying intensity) or beam smoothness. We have developed a convenient two-stage energy tuning method for a nominal 100 J, 351 nm (UV) laser. The energy is adjusted in 10 J (10%) increments by operating the laser at full energy and inserting a beam splitter in the laser output. As the splitter is located after the final frequency tripling optics, the UV pulse shape is unchanged. The energy is varied by substituting a splitter of different reflectivity. For finer 3 J (3%) increments, the infrared pulse is attenuated inside the laser before the final amplifier. This requires modest tuning to preserve the pulse shape. The demonstrated variation in shot-to-shot reproducibility is less than +/-2.5 J (5% of the full energy), irrespective of the laser output energy. These approaches can be adapted to most ∼100 J class lasers. We describe these techniques and show two examples where they have elucidated the underlying physics in laser shock compression experiments. One used only the beam splitters to establish the pressure for melting in iron. The other combined both techniques to finely increment the peak stress (∼2 GPa steps) in germanium to precisely determine the onset and completion of melting-including the melting kinetics. These unambiguous results would not be possible without the developments described here.
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Affiliation(s)
- Xiaoming Wang
- Dynamic Compression Sector, Institute for Shock Physics, Washington State University, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Jun Zhang
- Dynamic Compression Sector, Institute for Shock Physics, Washington State University, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - John Sethian
- Dynamic Compression Sector, Institute for Shock Physics, Washington State University, Argonne National Laboratory, Lemont, Illinois 60439, USA
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4
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Renganathan P, Sharma SM, Turneaure SJ, Gupta YM. Real-time (nanoseconds) determination of liquid phase growth during shock-induced melting. SCIENCE ADVANCES 2023; 9:eade5745. [PMID: 36827368 PMCID: PMC9956119 DOI: 10.1126/sciadv.ade5745] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/24/2022] [Accepted: 01/20/2023] [Indexed: 06/18/2023]
Abstract
Melting of solids is a fundamental natural phenomenon whose pressure dependence has been of interest for nearly a century. However, the temporal evolution of the molten phase under pressure has eluded measurements because of experimental challenges. By using the shock front as a fiducial, we investigated the time-dependent growth of the molten phase in shock-compressed germanium. In situ x-ray diffraction measurements at different times (1 to 6 nanoseconds) behind the shock front quantified the real-time growth of the liquid phase at several peak stresses. These results show that the characteristic time for melting in shock-compressed germanium decreases from ~7.2 nanoseconds at 35 gigapascals to less than 1 nanosecond at 42 gigapascals. Our melting kinetics results suggest the need to consider heterogeneous nucleation as a mechanism for shock-induced melting and provide an approach to measuring melting kinetics in shock-compressed solids.
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Affiliation(s)
- Pritha Renganathan
- Institute for Shock Physics, Washington State University, Pullman, WA 99164, USA
| | - Surinder M. Sharma
- Institute for Shock Physics, Washington State University, Pullman, WA 99164, USA
| | - Stefan J. Turneaure
- Institute for Shock Physics, Washington State University, Pullman, WA 99164, USA
| | - Yogendra M. Gupta
- Institute for Shock Physics, Washington State University, Pullman, WA 99164, USA
- Department of Physics and Astronomy, Washington State University, Pullman, WA 99164, USA
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Ghosh M, Zhang S, Hu L, Hu SX. Cooperative diffusion in body-centered cubic iron in Earth and super-Earths' inner core conditions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:154002. [PMID: 36753774 DOI: 10.1088/1361-648x/acba71] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 02/08/2023] [Indexed: 06/18/2023]
Abstract
The physical chemistry of iron at the inner-core conditions is key to understanding the evolution and habitability of Earth and super-Earth planets. Based on full first-principles simulations, we report cooperative diffusion along the longitudinally fast⟨111⟩directions of body-centered cubic (bcc) iron in temperature ranges of up to 2000-4000 K below melting and pressures of ∼300-4000 GPa. The diffusion is due to the low energy barrier in the corresponding direction and is accompanied by mechanical and dynamical stability, as well as strong elastic anisotropy of bcc iron. These findings provide a possible explanation for seismological signatures of the Earth's inner core, particularly the positive correlation between P wave velocity and attenuation. The diffusion can also change the detailed mechanism of core convection by increasing the diffusivity and electrical conductivity and lowering the viscosity. The results need to be considered in future geophysical and planetary models and should motivate future studies of materials under extreme conditions.
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Affiliation(s)
- Maitrayee Ghosh
- Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14623, United States of America
- Department of Chemistry, University of Rochester, Rochester, NY 14611, United States of America
| | - Shuai Zhang
- Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14623, United States of America
| | - Lianming Hu
- Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14623, United States of America
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14611, United States of America
| | - S X Hu
- Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14623, United States of America
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14611, United States of America
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Duwal S, McCoy CA, Dolan Iii DH, Melton CA, Knudson MD, Root S, Hacking R, Farfan B, Johnson C, Alexander CS, Seagle CT. Samarium: from a distorted-fcc phase to melting under dynamic compression using in-situ x-ray diffraction. Sci Rep 2022; 12:16777. [PMID: 36202947 PMCID: PMC9537147 DOI: 10.1038/s41598-022-21332-y] [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: 04/08/2022] [Accepted: 09/26/2022] [Indexed: 11/16/2022] Open
Abstract
Lattice and electronic structure interactions for f-electrons are fundamental challenges for lanthanide equation of state development. Difficulties in first-principles calculations, such as density functional theory (DFT), emphasize the need for well-characterized experimental data. Here, we measure in-situ x-ray diffraction of shocked samarium (Sm) and temperature along the Hugoniot for the first time, providing direct evidence for phase transitions. We report direct evidence of a distorted fcc (dfcc) phase at 23 GPa. Shocked samarium melts from the dfcc phase starting at 33 GPa (1333 K), with complete melt at 40 GPa (1468 K). Previous work indicated shock melt at 27 GPa (1200 K), underscoring the significance of x-ray measurements for detecting phase transitions. Interestingly, our observed melting is in sharp contrast with the melting reported by a diamond anvil cell study. These experimental data can tightly constrain first principles calculations and serve as key touchstones for equation of state modeling.
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Affiliation(s)
- Sakun Duwal
- Sandia National Laboratories, Albuquerque, NM, 87125, USA.
| | - Chad A McCoy
- Sandia National Laboratories, Albuquerque, NM, 87125, USA
| | | | - Cody A Melton
- Sandia National Laboratories, Albuquerque, NM, 87125, USA
| | | | - Seth Root
- Sandia National Laboratories, Albuquerque, NM, 87125, USA
| | - Richard Hacking
- Mission Support and Test Services, Albuquerque Operations, Albuquerque, NM, 87125, USA
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Abstract
Iron crystallization in super-Earth interiors plays a key role in their habitability.
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Affiliation(s)
- Youjun Zhang
- Institute of Atomic and Molecular Physics, Sichuan University, Chengdu, China.,International Center for Planetary Science, College of Earth Sciences, Chengdu University of Technology, Chengdu, China
| | - Jung-Fu Lin
- Department of Geological Sciences, Jackson School of Geosciences, The University of Texas at Austin, Austin, TX, USA
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Kraus RG, Hemley RJ, Ali SJ, Belof JL, Benedict LX, Bernier J, Braun D, Cohen RE, Collins GW, Coppari F, Desjarlais MP, Fratanduono D, Hamel S, Krygier A, Lazicki A, Mcnaney J, Millot M, Myint PC, Newman MG, Rygg JR, Sterbentz DM, Stewart ST, Stixrude L, Swift DC, Wehrenberg C, Eggert JH. Measuring the melting curve of iron at super-Earth core conditions. Science 2022; 375:202-205. [PMID: 35025665 DOI: 10.1126/science.abm1472] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
The discovery of more than 4500 extrasolar planets has created a need for modeling their interior structure and dynamics. Given the prominence of iron in planetary interiors, we require accurate and precise physical properties at extreme pressure and temperature. A first-order property of iron is its melting point, which is still debated for the conditions of Earth’s interior. We used high-energy lasers at the National Ignition Facility and in situ x-ray diffraction to determine the melting point of iron up to 1000 gigapascals, three times the pressure of Earth’s inner core. We used this melting curve to determine the length of dynamo action during core solidification to the hexagonal close-packed (hcp) structure. We find that terrestrial exoplanets with four to six times Earth’s mass have the longest dynamos, which provide important shielding against cosmic radiation.
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Affiliation(s)
- Richard G Kraus
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Russell J Hemley
- Departments of Physics, Chemistry, and Earth and Environmental Sciences, University of Illinois at Chicago, Chicago, IL 60607, USA
| | - Suzanne J Ali
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Jonathan L Belof
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Lorin X Benedict
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Joel Bernier
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Dave Braun
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - R E Cohen
- Earth and Planets Laboratory, Carnegie Institution for Science, Washington, DC 20015, USA
| | - Gilbert W Collins
- Department of Mechanical Engineering, Department of Physics and Astronomy, and Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14627, USA
| | - Federica Coppari
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | | | | | - Sebastien Hamel
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Andy Krygier
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Amy Lazicki
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - James Mcnaney
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Marius Millot
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Philip C Myint
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Matthew G Newman
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
| | - James R Rygg
- Department of Mechanical Engineering, Department of Physics and Astronomy, and Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14627, USA
| | - Dane M Sterbentz
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Sarah T Stewart
- Department of Earth and Planetary Sciences, University of California Davis, Davis, CA 95616, USA
| | - Lars Stixrude
- Department of Earth, Planetary, and Space Sciences, University of California Los Angeles, Los Angeles, CA 90095, USA
| | - Damian C Swift
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Chris Wehrenberg
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Jon H Eggert
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
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10
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McMahon MI. Probing extreme states of matter using ultra-intense x-ray radiation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:043001. [PMID: 33725673 DOI: 10.1088/1361-648x/abef26] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2020] [Accepted: 03/16/2021] [Indexed: 06/12/2023]
Abstract
Extreme states of matter, that is, matter at extremes of density (pressure) and temperature, can be created in the laboratory either statically or dynamically. In the former, the pressure-temperature state can be maintained for relatively long periods of time, but the sample volume is necessarily extremely small. When the extreme states are generated dynamically, the sample volumes can be larger, but the pressure-temperature conditions are maintained for only short periods of time (ps toμs). In either case, structural information can be obtained from the extreme states by the use of x-ray scattering techniques, but the x-ray beam must be extremely intense in order to obtain sufficient signal from the extremely-small or short-lived sample. In this article I describe the use of x-ray diffraction at synchrotrons and XFELs to investigate how crystal structures evolve as a function of density and temperature. After a brief historical introduction, I describe the developments made at the Synchrotron Radiation Source in the 1990s which enabled the almost routine determination of crystal structure at high pressures, while also revealing that the structural behaviour of materials was much more complex than previously believed. I will then describe how these techniques are used at the current generation of synchrotron and XFEL sources, and then discuss how they might develop further in the future at the next generation of x-ray lightsources.
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Affiliation(s)
- M I McMahon
- SUPA, School of Physics and Astronomy, and Centre for Science at Extreme Conditions, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
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Myint PC, Benedict LX, Wu CJ, Belof JL. Minimization of Gibbs Energy in High-Pressure Multiphase, Multicomponent Mixtures through Particle Swarm Optimization. ACS OMEGA 2021; 6:13341-13364. [PMID: 34056482 PMCID: PMC8158846 DOI: 10.1021/acsomega.1c01300] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2021] [Accepted: 04/19/2021] [Indexed: 05/11/2023]
Abstract
We present a global optimization method to construct phase boundaries in multicomponent mixtures by minimizing the Gibbs energy. The minimization method is, in essence, an extension of the Maxwell construction procedure that is used in single-component systems. For a given temperature, pressure, and overall mixture composition, it reveals the mole fractions of the thermodynamically stable phases and the composition of these phases. Our approach is based on particle swarm optimization (PSO), which is a gradient-free, stochastic method. It is not reliant on good initial guesses for the phase fractions and compositions, which is an important requirement for the high-pressure applications considered in this study because data on phase boundaries at high pressures tend to be extremely limited. One practical use of this method is to create equation-of-state tables needed by continuum-scale, multiphysics codes that are ubiquitous in high-pressure science. Currently, there does not exist a method to generate such tables that rigorously account for changes in phase boundaries due to mixing. We have done extensive testing to demonstrate that PSO can reliably determine the Gibbs energy minimum and can capture nontrivial features like eutectic and peritectic temperatures to produce coherent phase diagrams. As part of our testing, we have developed a PSO-based Helmholtz-energy minimization procedure that we have used to cross-check the results of the Gibbs energy minimization. We conclude with a critique of our approach and provide suggestions for future work, including a PSO-based entropy-maximization method that would enable the aforementioned continuum codes to perform on-the-fly, phase-equilibria calculations of multicomponent mixtures.
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Affiliation(s)
- Philip C. Myint
- Physics
Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, United States
| | - Lorin X. Benedict
- Physics
Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, United States
| | - Christine J. Wu
- Physics
Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, United States
| | - Jonathan L. Belof
- Materials
Science Division, Lawrence Livermore National
Laboratory, 7000 East
Avenue, Livermore, California 94550, United States
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