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Scaling of Phase Diagram and Critical Point Parameters in Liquid-Vapour Phase Transition of Metallic Fluids. CONDENSED MATTER 2021. [DOI: 10.3390/condmat6010006] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The first objective of this paper is to investigate the scaling behavior of liquid-vapor phase transition in FCC and BCCmetals starting from the zero-temperature four-parameter formula for cohesive energy. The effective potentials between the atoms in the solid are determined while using lattice inversion techniques as a function of scaling variables in the four-parameter formula. These potentials are split into repulsive and attractive parts, as per the Weeks–Chandler–Anderson prescription, and used in the coupling-parameter expansion for solving the Ornstein–Zernike equation that was supplemented with an accurate closure. Thermodynamic quantities obtained via the correlation functions are used in order to obtain critical point parameters and liquid-vapor phase diagrams. Their dependence on the scaling variables in the cohesive energy formula are also determined. An equally important second objective of the paper is to revisit coupling parameter expansion for solving the Ornstein–Zernike equation. The Newton–Armijo non-linear solver and Krylov-space based linear solvers are employed in this regard. These methods generate a robust algorithm that can be used to span the entire fluid region, except very low temperatures. The accuracy of the method is established by comparing the phase diagrams with those that were obtained via computer simulation. The avoidance of the ’no-solution-region’ of the Ornstein-Zernike equation in coupling-parameter expansion is also discussed. Details of the method and complete algorithm provided here would make this technique more accessible to researchers investigating the thermodynamic properties of one component fluids.
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Schmidt KM, Vasquez VR. A generalized method for the inversion of cohesive energy curves from isotropic and anisotropic lattice expansions. Phys Chem Chem Phys 2015; 17:23423-37. [PMID: 26291033 DOI: 10.1039/c5cp03792a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Cohesive energy curves contain important information about energetics of atomic interactions in crystalline materials, and these are more often obtained using ab initio methods such as density functional theory. Decomposing these curves into the different interatomic contributions is of great value to evaluate and characterize the energetics of specific types of atom-atom interactions. In this work, we present and discuss a generalized method for the inversion of cohesive energy curves of crystalline materials for pairwise interatomic potentials extraction using detailed geometrical descriptions of the atomic interactions to construct a list of atomic displacements and degeneracies, which is modified using a Gaussian elimination process to isolate the pairwise interactions. The proposed method provides a more general framework for cohesive energy inversions that is robust and accurate for systems well-described by pairwise potential interactions. Results show very good reproduction of cohesive energies with the same or better accuracy than current approaches with the advantage that the method has broader applications.
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Affiliation(s)
- Kevin M Schmidt
- Chemical and Materials Engineering Department, University of Nevada-Reno, Reno, NV 89557, USA.
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Yuan XJ, Chen NX, Shen J, Hu W. Embedded-atom-method interatomic potentials from lattice inversion. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:375503. [PMID: 21403199 DOI: 10.1088/0953-8984/22/37/375503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The present work develops a physically reliable procedure for building the embedded-atom-method (EAM) interatomic potentials for the metals with fcc, bcc and hcp structures. This is mainly based on Chen-Möbius lattice inversion (Chen et al 1997 Phys. Rev. E 55 R5) and first-principles calculations. Following Baskes (Baskes et al 2007 Phys. Rev. B 75 094113), this new version of the EAM eliminates all of the prior arbitrary choices in the determination of the atomic electron density and pair potential functions. Parameterizing the universal form deduced from the calculations within the density-functional scheme for homogeneous electron gas as the embedding function, the new-type EAM potentials for Cu, Fe and Ti metals have successfully been constructed by considering interatomic interactions up to the fifth neighbor, the third neighbor and the seventh neighbor, respectively. The predictions of elastic constants, structural energy difference, vacancy formation energy and migration energy, activation energy of vacancy diffusion, latent heat of melting and relative volume change on melting all satisfactorily agree with the experimental results available or first-principles calculations. The predicted surface energies for low-index crystal faces and the melting point are in agreement with the experimental data to the same extent as those calculated by other EAM-type potentials such as the FBD-EAM, 2NN MEAM and MS-EAM. In addition, the order among the predicted low-index surface energies is also consistent with the experimental information.
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Affiliation(s)
- Xiao-Jian Yuan
- Institute for Applied Physics, University of Science and Technology Beijing, Beijing, People's Republic of China.
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Site preference and vibrational properties of R3T4+xAl12−x (R=Y, Ce, Gd, U, Th; T=Fe, Ru). J SOLID STATE CHEM 2010. [DOI: 10.1016/j.jssc.2009.12.022] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Argon AS, Shi LT. Analysis of plastic flow in an amorphous soap bubble raft by the use of an inter-bubble potential. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/01418618208239919] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Shi LT, Argon AS. The potential and force law between different-size bubbles in soap bubble rafts. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/01418618208239918] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Esposito E, Carlsson AE, Ling DD, Ehrenreich H, Gelatt CD. First-principles calculations of the theoretical tensile strength of copper. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/01418618008236140] [Citation(s) in RCA: 64] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Guo J, Shen J, Chen N. Prediction of the lowest-energy structures of actinide-series metal clusters using Möbius inversion pair potentials. Chem Phys 2006. [DOI: 10.1016/j.chemphys.2005.10.030] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Han X, Zhang Y, Xu H. First-principles pair potentials across the metal-ceramic interface. J Comput Chem 2004; 25:968-73. [PMID: 15027108 DOI: 10.1002/jcc.20024] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Systematic approaches are presented to invert the first-principle binding energy to obtain the pair potentials across the metal/ceramic interfaces. The conformation characteristics of two virtual interface models suitable for the inversion are summarized: (1) the positions of one kind of ceramic ions stay unchanged, but those of the other change; or, (2) there is no change in the relative positions of the ceramic ions to the metal atoms but the positions of two kinds of ceramic ions are all exchanged each other. As an example, we derive the pair potentials of Ni-Zr(4+) and Ni-O(2-) across the Ni/ZrO(2) interface with this method, which exhibit comparable accuracy to the first-principle results. This provides direct evidence that the interfacial potentials obtained from this method can reasonably describe the general features of bondings across the metal-ceramic interface. The limitation of this method is also discussed.
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Affiliation(s)
- Xiaoping Han
- School of Materials Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, People's Republic of China
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Wen T, Ming D, Dai X, Dai J, Evenson WE. Type of inversion problem in physics: an inverse emissivity problem. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:045601. [PMID: 11308905 DOI: 10.1103/physreve.63.045601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2000] [Indexed: 05/23/2023]
Abstract
Inversion problems have recently drawn vast amounts of attention from the physics community due to their potential widespread applications. In this Rapid Communication, a different type of inversion problem in physics is proposed: an inverse emissivity problem, which aims to determine the emissivity g(nu) by measuring only the total radiated power J(T). Like other inverse problems, this one has potential for important practical applications. An exact solution is obtained for the proposed inverse problem. A unique existence theorem and techniques for eliminating divergences are also presented. A universal function set (UFS) suggested for numerical calculations is shown to be very useful in a numerical example. The UFS makes this inversion method practical and convenient for realistic calculations.
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Affiliation(s)
- T Wen
- Group of Quantum Statistics & Method of Theoretical Physics and Surface Physics Laboratory, Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
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Dagens L. Effective interatomic potentials in strong-scattering open shell metals: application to bonding force in d-band metals. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0305-4608/16/11/011] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Ming D, Wen T, Dai J, Dai X, Evenson WE. Exact solution of the specific-heat-phonon spectrum inversion from the Mobius inverse formula. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:R3019-22. [PMID: 11088868 DOI: 10.1103/physreve.62.r3019] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2000] [Indexed: 11/06/2022]
Abstract
The application of the Mobius inversion formula to the specific-heat-phonon spectrum inversion problem (SPI) initially appeared promising [N.X. Chen, Phys. Rev. Lett. 64, 1193 (1990); J. Maddox, Nature (London) 344, 377 (1990)]. However, no one has previously been able to obtain the exact Debye spectrum with the correct cut-off factor and frequency dependence from the Mobius formula. The main difficulty arises from the fact that the Mobius function &mgr;(n) is not completely known for large n in practice. In this paper, some exact solutions of SPI are obtained by using the Mobius inversion formula, most importantly the Debye spectrum as a special case, and the problem of the unknown Mobius function &mgr;(n) for large n is avoided. It is shown that the Mobius inversion formula can be useful for exact solutions to spectral inversion problems.
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Affiliation(s)
- D Ming
- Group of Quantum Statistics and Methods of Theoretical Physics, Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
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Bazant MZ, Kaxiras E. Modeling of Covalent Bonding in Solids by Inversion of Cohesive Energy Curves. PHYSICAL REVIEW LETTERS 1996; 77:4370-4373. [PMID: 10062521 DOI: 10.1103/physrevlett.77.4370] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Xie Q, Chen N. Matrix-inversion method: Applications to Möbius inversion adn deconvolution. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:6055-6065. [PMID: 9964122 DOI: 10.1103/physreve.52.6055] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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March NH, Tosi MP, Klein DJ. Coordination-dependent equations of state and pair potentials for cold metal crystals. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:9115-9116. [PMID: 9979937 DOI: 10.1103/physrevb.52.9115] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Xie Q, Chen N. Recovery of an N-body potential from a universal cohesion equation. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:15856-15860. [PMID: 9978563 DOI: 10.1103/physrevb.51.15856] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Chen N, Ren G. Carlsson-Gelatt-Ehrenreich technique and the Möbius inversion theorem. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:8177-8180. [PMID: 10000643 DOI: 10.1103/physrevb.45.8177] [Citation(s) in RCA: 55] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Cheng H, Ellis DE. Electronic structure, binding energies, and interaction potentials of transition metal clusters. J Chem Phys 1991. [DOI: 10.1063/1.459745] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Moriarty JA. Density-functional formulation of the generalized pseudopotential theory. III. Transition-metal interatomic potentials. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 38:3199-3231. [PMID: 9946660 DOI: 10.1103/physrevb.38.3199] [Citation(s) in RCA: 94] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Banerjea A, Smith JR. Origins of the universal binding-energy relation. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 37:6632-6645. [PMID: 9943929 DOI: 10.1103/physrevb.37.6632] [Citation(s) in RCA: 70] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Rebonato R, Welch DO, Hatcher RD, Bilello JC. A modification of the Finnis-Sinclair potentials for highly deformed and defective transition metals. ACTA ACUST UNITED AC 1987. [DOI: 10.1080/01418618708214375] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Biswas R, Hamann DR. Interatomic potentials for silicon structural energies. PHYSICAL REVIEW LETTERS 1985; 55:2001-2004. [PMID: 10031984 DOI: 10.1103/physrevlett.55.2001] [Citation(s) in RCA: 125] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Moriarty JA. First-principles interatomic potentials in transition metals. PHYSICAL REVIEW LETTERS 1985; 55:1502-1505. [PMID: 10031840 DOI: 10.1103/physrevlett.55.1502] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Ferrante J, Smith J, Rose J. Universal Binding Energy Relations in Metallic Adhesion. MICROSCOPIC ASPECTS OF ADHESION AND LUBRICATION, PROCEEDINGS OF THE 34TH INTERNATIONAL MEETING OF THE SOCIÉTÉ DE CHIMIE PHYSIQUE 1981. [DOI: 10.1016/s0167-8922(08)70869-1] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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