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Cao Y, Yang M, Du Q, Chiang FK, Zhang Y, Chen SW, Ke Y, Lou H, Zhang F, Wu Y, Wang H, Jiang S, Zhang X, Zeng Q, Liu X, Lu Z. Continuous polyamorphic transition in high-entropy metallic glass. Nat Commun 2024; 15:6702. [PMID: 39112483 PMCID: PMC11306636 DOI: 10.1038/s41467-024-51080-8] [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: 03/27/2024] [Accepted: 07/29/2024] [Indexed: 08/10/2024] Open
Abstract
Polyamorphic transition (PT) is a compelling and pivotal physical phenomenon in the field of glass and materials science. Understanding this transition is of scientific and technological significance, as it offers an important pathway for effectively tuning the structure and property of glasses. In contrast to the PT observed in conventional metallic glasses (MGs), which typically exhibit a pronounced first-order nature, herein we report a continuous PT (CPT) without first-order characteristics in high-entropy MGs (HEMGs) upon heating. This CPT behavior is featured by the continuous structural evolution at the atomic level and an increasing chemical concentration gradient with temperature, but no abrupt reduction in volume and energy. The continuous transformation is associated with the absence of local favorable structures and chemical heterogeneity caused by the high configurational entropy, which limits the distance and frequency of atomic diffusion. As a result of the CPT, numerous glass states can be generated, which provides an opportunity to understand the nature, atomic packing, formability, and properties of MGs. Moreover, this discovery highlights the implication of configurational entropy in exploring polyamorphic glasses with an identical composition but highly tunable structures and properties.
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Affiliation(s)
- Yihuan Cao
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, China
- Institute of Materials Intelligent Technology, Liaoning Academy of Materials, Shenyang, China
| | - Ming Yang
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, China
| | - Qing Du
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, China
| | - Fu-Kuo Chiang
- National Institute of Clean-and-Low-Carbon Energy, Shenhua NICE, Beijing, China
| | - Yingjie Zhang
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, China
| | - Shi-Wei Chen
- National Synchrotron Radiation Research Center Hsinchu, Hsinchu, Taiwan, China
| | - Yubin Ke
- China Spallation Neutron Source, Dongguan, Guangdong, China
| | - Hongbo Lou
- Center for High Pressure Science and Technology Advanced Research, Shanghai, China
- Shanghai Key Laboratory of Material Frontiers Research in Extreme Environments (MFree), Shanghai Advanced Research in Physical Sciences (SHARPS), Shanghai, China
| | - Fei Zhang
- Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China
| | - Yuan Wu
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, China
- Institute of Materials Intelligent Technology, Liaoning Academy of Materials, Shenyang, China
| | - Hui Wang
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, China
| | - Suihe Jiang
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, China
| | - Xiaobin Zhang
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, China
| | - Qiaoshi Zeng
- Center for High Pressure Science and Technology Advanced Research, Shanghai, China
- Shanghai Key Laboratory of Material Frontiers Research in Extreme Environments (MFree), Shanghai Advanced Research in Physical Sciences (SHARPS), Shanghai, China
| | - Xiongjun Liu
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, China.
- Institute of Materials Intelligent Technology, Liaoning Academy of Materials, Shenyang, China.
| | - Zhaoping Lu
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, China.
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Yongyong W, Panpan Z, Qing L, Gong L. Structural evolution of heavy rare Earth-based metal glass under high pressure. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 33:035405. [PMID: 33022658 DOI: 10.1088/1361-648x/abbea4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2020] [Accepted: 10/06/2020] [Indexed: 06/11/2023]
Abstract
The structural evolution of Er55Al25Co20metallic glasses (MGs) at high pressure was studied through x-ray diffraction with synchrotron radiation. The compression ratio, differential structure factor, pair distribution functiong(r), and relative resistance as functions of pressure were analyzed and discussed. A reversible polyamorphic transition with a clear hysteresis was detected in the Er55Al25Co20MGs. The irreversible annihilation of free volume and voids led to a densification of the specimens. Electronic resistance measurements demonstrated that the transition was strongly correlated with the electronic structural evolution. The results provide a new insight into understanding the mechanisms of polyamorphism in MGs.
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Affiliation(s)
- Wang Yongyong
- College of Physics, Henan Normal University, Xinxiang 453007, People's Republic of China
- Henan Key Laboratory of Photovoltaic Materials, Xinxiang 453007, People's Republic of China
| | - Zhang Panpan
- College of Physics, Henan Normal University, Xinxiang 453007, People's Republic of China
- Henan Key Laboratory of Photovoltaic Materials, Xinxiang 453007, People's Republic of China
| | - Li Qing
- School of Chemistry and Chemical Engineering, Henan Normal University, Xinxiang 453007, People's Republic of China
| | - Li Gong
- State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, People's Republic of China
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Abstract
Metallic glasses are expected to have quite tunable structures in their configuration space, without the strict constraints of a well-defined crystalline symmetry and large energy barriers separating different states in crystals. However, effectively modulating the structure of metallic glasses is rather difficult. Here, using complementary in situ synchrotron x-ray techniques, we reveal thermal-driven structural ordering in a Ce65Al10Co25 metallic glass, and a reverse disordering process via a pressure-induced rejuvenation between two states with distinct structural order characteristics. Studies on other metallic glass samples with different compositions also show similar phenomena. Our findings demonstrate the feasibility of two-way structural tuning states in terms of their dramatic ordering and disordering far beyond the nearest-neighbor shells with the combination of temperature and pressure, extending accessible states of metallic glasses to unexplored configuration spaces.
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Chen H, Li D, Zhao Y, Qu B, Zhou R, Zhang B. Structural origin of the high glass-forming ability of Ce 70Ga 10Cu 20 alloys. Phys Chem Chem Phys 2019; 21:4209-4214. [PMID: 30742160 DOI: 10.1039/c8cp07478j] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The CeGaCu amorphous alloy has a good glass-forming ability and many special properties. However, its structure at the atomic scale is unclear. We systematically investigated the structure evolution of Ce70GaxCu30-x (x = 6, 10, 13) glass formation melts by ab initio molecular dynamics (AIMD) simulations. Based on the trajectories from the simulations, the pair-correlation function, coordination numbers, chemical short-range order, Voronoi polyhedra and electronic structures were discussed. Our results show that the concentration of Ga- and Cu-centered icosahedral (-like) clusters in Ce70Ga10Cu20 melts are larger than those in Ce70Ga6Cu24 and Ce70Ga13Cu17 melts. Furthermore, electronic analysis showed that the hybridization between Ga 4p and Cu 3d (Ce 5d) orbitals is strong and that of Cu 3d orbitals and Ga 4p orbitals was strengthened in Ce70Ga10Cu20 melts, which means that the interactions between Ga and Cu atoms nearby were enhanced in the Ce70Ga10Cu20 melts. The stability of the Ga- or Cu-centered icosahedral clusters increased accordingly, which favored their glass-forming ability. Our investigation helps people obtain an increased understanding of the glass-forming ability from the viewpoint of chemical interactions for metallic glasses.
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Affiliation(s)
- Heng Chen
- Institute of Amorphous Matter Science, School of Materials Science and Engineering, Hefei University of Technology, Hefei, Anhui 230009, China.
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Eremenko VV, Sirenko VA, Baran A, Čižmár E, Feher A. Spin-glass polyamorphism induced by a magnetic field in LaMnO 3 single crystal. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:205801. [PMID: 29629878 DOI: 10.1088/1361-648x/aabc9d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We present experimental evidence of field-driven transition in spin-glass state, similar to pressure-induced transition between amorphous phases in structural and metallic glasses, attributed to the polyamorphism phenomena. Cusp in temperature dependences of ac magnetic susceptibility of weakly disordered LaMnO3 single crystal is registered below the temperature of magnetic ordering. Frequency dependence of the cusp temperature proves its spin-glass origin. The transition induced by a magnetic field in spin-glass state, is manifested by peculiarity in dependence of cusp temperature on applied magnetic field. Field dependent maximum of heat capacity is observed in the same magnetic field and temperature range.
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Affiliation(s)
- V V Eremenko
- B. Verkin Institute for Low Temperature Physics and Engineering NASU, Kharkov 61103, Ukraine
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Pressure-induced structural change in liquid GaIn eutectic alloy. Sci Rep 2017; 7:1139. [PMID: 28442718 PMCID: PMC5430730 DOI: 10.1038/s41598-017-01233-1] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2017] [Accepted: 03/28/2017] [Indexed: 11/09/2022] Open
Abstract
Synchrotron x-ray diffraction reveals a pressure induced crystallization at about 3.4 GPa and a polymorphic transition near 10.3 GPa when compressed a liquid GaIn eutectic alloy up to ~13 GPa at room temperature in a diamond anvil cell. Upon decompression, the high pressure crystalline phase remains almost unchanged until it transforms to the liquid state at around 2.3 GPa. The ab initio molecular dynamics calculations can reproduce the low pressure crystallization and give some hints on the understanding of the transition between the liquid and the crystalline phase on the atomic level. The calculated pair correlation function g(r) shows a non-uniform contraction reflected by the different compressibility between the short (1st shell) and the intermediate (2nd to 4th shells). It is concluded that the pressure-induced liquid-crystalline phase transformation likely arises from the changes in local atomic packing of the nearest neighbors as well as electronic structures at the transition pressure.
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Elastic Anomaly and Polyamorphic Transition in (La, Ce)-based Bulk Metallic Glass under Pressure. Sci Rep 2017; 7:724. [PMID: 28389659 PMCID: PMC5429654 DOI: 10.1038/s41598-017-00737-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2017] [Accepted: 03/09/2017] [Indexed: 11/09/2022] Open
Abstract
Pressure-induced polyamorphism in Ce-based metallic glass has attracted significant interest in condensed matter physics. In this paper, we discover that in association with the polyamorphism of La32Ce32Al16Ni5Cu15 bulk metallic glass, the acoustic velocities, measured up to 12.3 GPa using ultrasonic interferometry, exhibit velocity minima at 1.8 GPa for P wave and 3.2 GPa for S wave. The low and high density amorphous states are distinguished by their distinct pressure derivatives of the bulk and shear moduli. The elasticity, permanent densification, and polyamorphic transition are interpreted by the topological rearrangement of solute-centered clusters in medium-range order (MRO) mediated by the 4f electron delocalization of Ce under pressure. The precisely measured acoustic wave travel times which were used to derive the velocities and densities provided unprecedented data to document the evolution of the bulk and shear elastic moduli associated with a polyamorphic transition in La32Ce32Al16Ni5Cu15 bulk metallic glass and can shed new light on the mechanisms of polyamorphism and structural evolution in metallic glasses under pressure.
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Abstract
Metallic glass (MG) is an important new category of materials, but very few rigorous laws are currently known for defining its "disordered" structure. Recently we found that under compression, the volume (V) of an MG changes precisely to the 2.5 power of its principal diffraction peak position (1/q1). In the present study, we find that this 2.5 power law holds even through the first-order polyamorphic transition of a Ce68Al10Cu20Co2 MG. This transition is, in effect, the equivalent of a continuous "composition" change of 4f-localized "big Ce" to 4f-itinerant "small Ce," indicating the 2.5 power law is general for tuning with composition. The exactness and universality imply that the 2.5 power law may be a general rule defining the structure of MGs.
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Wu M, Tse JS, Wang S, Wang C, Jiang J. Origin of pressure-induced crystallization of Ce75Al25 metallic glass. Nat Commun 2015; 6:6493. [DOI: 10.1038/ncomms7493] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2014] [Accepted: 02/03/2015] [Indexed: 11/09/2022] Open
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Luo Q, Garbarino G, Sun B, Fan D, Zhang Y, Wang Z, Sun Y, Jiao J, Li X, Li P, Mattern N, Eckert J, Shen J. Hierarchical densification and negative thermal expansion in Ce-based metallic glass under high pressure. Nat Commun 2015; 6:5703. [PMID: 25641091 DOI: 10.1038/ncomms6703] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2013] [Accepted: 10/29/2014] [Indexed: 11/09/2022] Open
Abstract
The polyamorphsim in amorphous materials is one of the most fascinating topics in condensed matter physics. In amorphous metals, the nature of polyamorphic transformation is poorly understood. Here we investigate the structural evolution of a Ce-based metallic glass (MG) with pressure at room temperature (RT) and near the glass transition temperature by synchrotron X-ray diffraction, uncovering novel behaviours. The MG shows hierarchical densification processes at both temperatures, arising from the hierarchy of interatomic interactions. In contrast with a continuous and smooth process for the low- to medium-density amorphous state transformation at RT, a relatively abrupt and discontinuous transformation around 5.5 GPa is observed at 390 K, suggesting a possible weak first-order nature. Furthermore, both positive and abnormal-negative thermal expansion behaviours on medium-range order are observed in different pressure windows, which could be related to the low-energy vibrational motions and relaxation of the weakly linked solute-centred clusters.
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Affiliation(s)
- Qiang Luo
- School of Materials Science and Engineering, Tongji University, Shanghai 201804, P.R. China
| | - Gaston Garbarino
- European Synchrotron Radiation Facility (ESRF), BP22, 6 rue Jules Horowitz, 38043 Grenoble, France
| | - Baoan Sun
- IFW Dresden, Institute for Complex Materials, Helmholtzstr. 20, D-01069 Dresden, Germany
| | - Dawei Fan
- 1] Key Laboratory of High-temperature and High-pressure Study of the Earth's Interior, Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550002, China [2] Center for High Pressure Science and Technology Advanced Research (HPSTAR), Changchun 130012, China
| | - Yue Zhang
- Ames Laboratory-USDOE, Iowa State University, Ames, Iowa 50011, USA
| | - Zhi Wang
- IFW Dresden, Institute for Complex Materials, Helmholtzstr. 20, D-01069 Dresden, Germany
| | - Yajuan Sun
- School of Materials Science and Engineering, Tongji University, Shanghai 201804, P.R. China
| | - Jin Jiao
- School of Materials Science and Engineering, Tongji University, Shanghai 201804, P.R. China
| | - Xiaodong Li
- Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
| | - Pengshan Li
- Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
| | - Norbert Mattern
- IFW Dresden, Institute for Complex Materials, Helmholtzstr. 20, D-01069 Dresden, Germany
| | - Jürgen Eckert
- 1] IFW Dresden, Institute for Complex Materials, Helmholtzstr. 20, D-01069 Dresden, Germany [2] TU Dresden, Institute of Materials Science, D-01062 Dresden, Germany
| | - Jun Shen
- School of Materials Science and Engineering, Tongji University, Shanghai 201804, P.R. China
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11
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Xiong LH, Yoo H, Lou HB, Wang XD, Cao QP, Zhang DX, Jiang JZ, Xie HL, Xiao TQ, Jeon S, Lee GW. Evolution of atomic structure in Al75Cu25 liquid from experimental and ab initio molecular dynamics simulation studies. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:035102. [PMID: 25524926 DOI: 10.1088/0953-8984/27/3/035102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
X-ray diffraction and electrostatic levitation measurements, together with the ab initio molecular dynamics simulation of liquid Al(75)Cu(25) alloy have been performed from 800 to 1600 K. Experimental and ab initio molecular dynamics simulation results match well with each other. No abnormal changes were experimentally detected in the specific heat capacity over total hemispheric emissivity and density curves in the studied temperature range for a bulk liquid Al(75)Cu(25) alloy measured by the electrostatic levitation technique. The structure factors gained by the ab initio molecular dynamics simulation precisely coincide with the experimental data. The atomic structure analyzed by the Honeycutt-Andersen index and Voronoi tessellation methods shows that icosahedral-like atomic clusters prevail in the liquid Al(75)Cu(25) alloy and the atomic clusters evolve continuously. All results obtained here suggest that no liquid-liquid transition appears in the bulk liquid Al(75)Cu(25) alloy in the studied temperature range.
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Affiliation(s)
- L H Xiong
- International Center for New-Structured Materials (ICNSM), Laboratory of New-Structured Materials, State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou 310027, People's Republic of China. Department of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, People's Republic of China
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12
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Rault J. A universal modified van der Waals equation of state. Part I: Polymer and mineral glass formers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:113. [PMID: 25403833 DOI: 10.1140/epje/i2014-14113-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2014] [Revised: 06/06/2014] [Accepted: 09/17/2014] [Indexed: 06/04/2023]
Abstract
PVT data of glass formers (minerals and polymers) published in the literature are re-analyzed. All the polymer glass formers (PS, PVAc, PVME, PMMA, POMS, PBMA, PVC, PE, PP, PMPS, PMTS, PPG) present two main properties which have never been noted: a) the isobars P(V) have a fan structure characterized by the two parameters T* and V*; b) the isotherms verify the principle of temperature-pressure superposition for P < P*. From these properties we show that the Equation Of State (EOS) can be put on a modified van der Waals form (VW-EOS), (V - V*) = (V0 - V*)P*/(P + P*). The characteristic pressure P* and the covolume V* are T and P independent. In polymer glass formers P* and V* have same values in the α (melt) and β (glass) domains. The characteristic temperatures T* deduced from the Fan Structure of the Isobar (FSIb) above and below T(g) are different. The characteristic temperature T*(α) of the melt state is found near the Vogel temperature T0 for linear polymers and more than 100 K below T0 for atactic polymers (with pendent groups). This difference in atactic polymers (and in some low molecular weight compounds) is explained by the importance of the β motions due to the pendent groups. The independence of T0 on P is discussed. A modified VFT equation (analogous to the compensation law and Meyer-Neldel rule) giving the relaxation time τ of the α motions as a function of P and T is proposed. The fan structure of the isotherm logτ versus P is explained. It is shown that organic non-polymeric liquids (C6H12, C6H14, DHIQ, OTP, Glycerol, Salol, PDE, DGEBA), mineral glass (SiO2, Se, GeSe4, GeSe2, GeO2, As2O3 and two metallic glasses (LaCe and CaAl alloys) verify this VW-EOS with similar accuracy. The relation P* = B 0/γ B among the characteristic pressure P*, the zero-pressure modulus B0 and the Slatter-Grüneisen anharmonicity parameter γ(B0 deduced from the VW-EOS, is observed in all the glass formers.
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Affiliation(s)
- Jacques Rault
- Laboratoire de Physique des Solides, Université de Paris-Sud, 91405, Orsay, France,
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Cadien A, Hu QY, Meng Y, Cheng YQ, Chen MW, Shu JF, Mao HK, Sheng HW. First-order liquid-liquid phase transition in cerium. PHYSICAL REVIEW LETTERS 2013; 110:125503. [PMID: 25166820 DOI: 10.1103/physrevlett.110.125503] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2012] [Indexed: 06/03/2023]
Abstract
We report the first experimental observation of a liquid-liquid phase transition in the monatomic liquid metal cerium, by means of in situ high-pressure high-temperature x-ray diffraction experiments. At 13 GPa, upon increasing temperature from 1550 to 1900 K high-density liquid transforms to a low-density liquid, with a density difference of 14%. Theoretic models based on ab initio calculations are built to investigate the observed phase behavior of the liquids at various pressures. The results suggest that the transition primarily originates from the delocalization of f electrons and is deemed to be of the first order that terminates at a critical point.
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Affiliation(s)
- A Cadien
- School of Physics, Astronomy and Computational Sciences, George Mason University, Fairfax, Virginia 22030, USA
| | - Q Y Hu
- School of Physics, Astronomy and Computational Sciences, George Mason University, Fairfax, Virginia 22030, USA
| | - Y Meng
- High Pressure Collaborative Access Team, Geophysical Laboratory, Carnegie Institution of Washington, Argonne, Illinois 60439, USA
| | - Y Q Cheng
- Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - M W Chen
- WPI Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
| | - J F Shu
- Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015, USA
| | - H K Mao
- High Pressure Collaborative Access Team, Geophysical Laboratory, Carnegie Institution of Washington, Argonne, Illinois 60439, USA and Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015, USA
| | - H W Sheng
- School of Physics, Astronomy and Computational Sciences, George Mason University, Fairfax, Virginia 22030, USA and Center for Computational Materials Science, George Mason University, Fairfax, Virginia 22030, USA
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