A self-contained algorithm for determination of solid-liquid equilibria in an alloy system

Yang, L.; Sun, Y.; Ye, Z.; Zhang, F.; Mendelev, M. I.; Wang, C. Z.; Ho, K. M.

doi:10.1016/j.commatsci.2018.04.028

A self-contained algorithm for determination of solid-liquid equilibria in an alloy system

Journal Article · Fri Apr 20 00:00:00 EDT 2018 · Computational Materials Science

DOI:https://doi.org/10.1016/j.commatsci.2018.04.028· OSTI ID:1459538

Yang, L. ^[1]; Sun, Y. ^[2]; Ye, Z. ^[2]; Zhang, F. ^[2]; Mendelev, M. I. ^[2]; Wang, C. Z. ^[1]; Ho, K. M. ^[3]

Ames Lab. and Iowa State Univ., Ames, IA (United States). Dept. of Physics
Ames Lab., Ames, IA (United States)
Ames Lab. and Iowa State Univ., Ames, IA (United States). Dept. of Physics; Univ. of Science and Technology of China, Hefei (China). Hefei National Lab. for Physical Sciences at the Microscale. Dept. of Physics

In this paper, we describe a self-contained procedure to evaluate the free energy of liquid and solid phases of an alloy system. The free energy of a single-element solid phase is calculated with thermodynamic integration using the Einstein crystal as the reference system. Then, free energy difference between the solid and liquid phases is calculated by Gibbs-Duhem integration. The central part of our method is the construction of a reversible alchemical path connecting a pure liquid and a liquid alloy to calculate the mixing enthalpy and entropy. We have applied the method to calculate the free energy of solid and liquid phases in the Al-Sm system. Finally, the driving force for fcc-Al nucleation in Al-Sm liquid and the melting curve for fcc-Al and Al₃Sm are also calculated.

View Accepted Manuscript (DOE)

Research Organization:: Ames Lab. and Iowa State Univ., Ames, IA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); Ames Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC02-07CH11358

OSTI ID:: 1459538

Report Number(s):: IS--J 9689; PII: S0927025618302696

Journal Information:: Computational Materials Science, Journal Name: Computational Materials Science Vol. 150; ISSN 0927-0256

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (38)

Contribution to the study of the alloys and intermetallic compounds of aluminium with the rare-earth metals Saccone, A.; Cacciamani, G.; Macciò, D. Intermetallics, Vol. 6, Issue 3 https://doi.org/10.1016/s0966-9795(97)00066-6	journal	January 1998
Ensemble variance in free energy calculations by thermodynamic integration: Theory, optimal ?Alchemical? path, and practical solutions Blondel, Arnaud Journal of Computational Chemistry, Vol. 25, Issue 7 https://doi.org/10.1002/jcc.20025	journal	January 2004
THE weighted histogram analysis method for free-energy calculations on biomolecules. I. The method Kumar, Shankar; Rosenberg, John M.; Bouzida, Djamal Journal of Computational Chemistry, Vol. 13, Issue 8 https://doi.org/10.1002/jcc.540130812	journal	October 1992
Fast Parallel Algorithms for Short-Range Molecular Dynamics Plimpton, Steve Journal of Computational Physics, Vol. 117, Issue 1 https://doi.org/10.1006/jcph.1995.1039	journal	March 1995
Efficient estimation of free energy differences from Monte Carlo data Bennett, Charles H. Journal of Computational Physics, Vol. 22, Issue 2 https://doi.org/10.1016/0021-9991(76)90078-4	journal	October 1976
Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling Torrie, G. M.; Valleau, J. P. Journal of Computational Physics, Vol. 23, Issue 2 https://doi.org/10.1016/0021-9991(77)90121-8	journal	February 1977
Amorphous, nanoquasicrystalline and nanocrystalline alloys in Al-based systems Inoue, Akihisa Progress in Materials Science, Vol. 43, Issue 5 https://doi.org/10.1016/S0079-6425(98)00005-X	journal	December 1998
Phase selection in Al–TM–RE alloys: nanocrystalline Al versus intermetallics Rizzi, P.; Baricco, M.; Borace, S. Materials Science and Engineering: A, Vol. 304-306 https://doi.org/10.1016/S0921-5093(00)01537-9	journal	May 2001
Contribution to the study of the alloys and intermetallic compounds of aluminium with the rare-earth metals Saccone, A.; Cacciamani, G.; Macciò, D. Intermetallics, Vol. 6, Issue 3 https://doi.org/10.1016/S0966-9795(97)00066-6	journal	January 1998
Eutectic-to-metallic glass transition in the Al–Sm system Wang, N.; Kalay, Y. E.; Trivedi, R. Acta Materialia, Vol. 59, Issue 17 https://doi.org/10.1016/j.actamat.2011.07.015	journal	October 2011
Implementing molecular dynamics on hybrid high performance computers – short range forces Brown, W. Michael; Wang, Peng; Plimpton, Steven J. Computer Physics Communications, Vol. 182, Issue 4 https://doi.org/10.1016/j.cpc.2010.12.021	journal	April 2011
On the role of Sm in solidification of Al-Sm metallic glasses Bokas, G. B.; Zhao, L.; Perepezko, J. H. Scripta Materialia, Vol. 124 https://doi.org/10.1016/j.scriptamat.2016.06.045	journal	November 2016
Toward Fast and Accurate Binding Affinity Prediction with pmemdGTI: An Efficient Implementation of GPU-Accelerated Thermodynamic Integration Lee, Tai-Sung; Hu, Yuan; Sherborne, Brad Journal of Chemical Theory and Computation, Vol. 13, Issue 7 https://doi.org/10.1021/acs.jctc.7b00102	journal	June 2017
Calculation of Partition Functions and Free Energies of a Binary Mixture Using the Energy Partitioning Method: Application to Carbon Dioxide and Methane Do, Hainam; Hirst, Jonathan D.; Wheatley, Richard J. The Journal of Physical Chemistry B, Vol. 116, Issue 15 https://doi.org/10.1021/jp212168f	journal	April 2012
Appropriate methods to combine forward and reverse free-energy perturbation averages Lu, Nandou; Singh, Jayant K.; Kofke, David A. The Journal of Chemical Physics, Vol. 118, Issue 7 https://doi.org/10.1063/1.1537241	journal	February 2003
Constrained fluid λ-integration: Constructing a reversible thermodynamic path between the solid and liquid state Grochola, Gregory The Journal of Chemical Physics, Vol. 120, Issue 5 https://doi.org/10.1063/1.1637575	journal	February 2004
Some Topics in the Theory of Fluids Widom, B. The Journal of Chemical Physics, Vol. 39, Issue 11 https://doi.org/10.1063/1.1734110	journal	December 1963
High‐Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases Zwanzig, Robert W. The Journal of Chemical Physics, Vol. 22, Issue 8 https://doi.org/10.1063/1.1740409	journal	August 1954
Statistical Mechanics of Fluid Mixtures Kirkwood, John G. The Journal of Chemical Physics, Vol. 3, Issue 5 https://doi.org/10.1063/1.1749657	journal	May 1935
Toward a robust and general molecular simulation method for computing solid-liquid coexistence Eike, David M.; Brennecke, Joan F.; Maginn, Edward J. The Journal of Chemical Physics, Vol. 122, Issue 1 https://doi.org/10.1063/1.1823371	journal	January 2005
Gibbs free-energy estimates from direct path-sampling computations Adjanor, G.; Athènes, M. The Journal of Chemical Physics, Vol. 123, Issue 23 https://doi.org/10.1063/1.2137698	journal	December 2005
Atomistic simulation of solid-liquid coexistence for molecular systems: Application to triazole and benzene Eike, David M.; Maginn, Edward J. The Journal of Chemical Physics, Vol. 124, Issue 16 https://doi.org/10.1063/1.2188400	journal	April 2006
Thermodynamic modelling of glasses at atomistic scale Adjanor, Gilles; Athènes, Manuel; Avilov, Anatoly S. ELECTRON MICROSCOPY AND MULTISCALE MODELING- EMMM-2007: An International Conference, AIP Conference Proceedings https://doi.org/10.1063/1.2918104	conference	January 2008
Waste-recycling Monte Carlo with optimal estimates: Application to free energy calculations in alloys Adjanor, Gilles; Athènes, Manuel; Rodgers, Jocelyn M. The Journal of Chemical Physics, Vol. 135, Issue 4 https://doi.org/10.1063/1.3610423	journal	July 2011
New Monte Carlo method to compute the free energy of arbitrary solids. Application to the fcc and hcp phases of hard spheres Frenkel, Daan; Ladd, Anthony J. C. The Journal of Chemical Physics, Vol. 81, Issue 7 https://doi.org/10.1063/1.448024	journal	October 1984
Multiconfiguration thermodynamic integration Straatsma, T. P.; McCammon, J. A. The Journal of Chemical Physics, Vol. 95, Issue 2 https://doi.org/10.1063/1.461148	journal	July 1991
Nosé–Hoover chains: The canonical ensemble via continuous dynamics Martyna, Glenn J.; Klein, Michael L.; Tuckerman, Mark The Journal of Chemical Physics, Vol. 97, Issue 4 https://doi.org/10.1063/1.463940	journal	August 1992
Discovery of a metastable Al20Sm4 phase Ye, Z.; Zhang, F.; Sun, Y. Applied Physics Letters, Vol. 106, Issue 10 https://doi.org/10.1063/1.4914399	journal	March 2015
Solid-liquid interface free energies of pure bcc metals and B2 phases Wilson, S. R.; Gunawardana, K. G. S. H.; Mendelev, M. I. The Journal of Chemical Physics, Vol. 142, Issue 13 https://doi.org/10.1063/1.4916741	journal	April 2015
A simple empirical N -body potential for transition metals Finnis, M. W.; Sinclair, J. E. Philosophical Magazine A, Vol. 50, Issue 1 https://doi.org/10.1080/01418618408244210	journal	July 1984
A New Version of the Insertion Particle Method for Determining the Chemical Potential by Monte Carlo Simulation Nezbeda, Ivo; Kolafa, Jiří Molecular Simulation, Vol. 5, Issue 6 https://doi.org/10.1080/08927029108022424	journal	February 1991
Development of interatomic potentials appropriate for simulation of devitrification of Al ₉₀ Sm ₁₀ alloy Mendelev, M. I.; Zhang, F.; Ye, Z. Modelling and Simulation in Materials Science and Engineering, Vol. 23, Issue 4 https://doi.org/10.1088/0965-0393/23/4/045013	journal	April 2015
Canonical dynamics: Equilibrium phase-space distributions Hoover, William G. Physical Review A, Vol. 31, Issue 3 https://doi.org/10.1103/PhysRevA.31.1695	journal	March 1985
Phonons in aluminum at high temperatures studied by inelastic neutron scattering Kresch, M.; Lucas, M.; Delaire, O. Physical Review B, Vol. 77, Issue 2 https://doi.org/10.1103/PhysRevB.77.024301	journal	January 2008
Einstein crystal as a reference system in free energy estimation using adiabatic switching de Koning, M.; Antonelli, A. Physical Review E, Vol. 53, Issue 1 https://doi.org/10.1103/PhysRevE.53.465	journal	January 1996
Theoretical calculation of the melting curve of Cu-Zr binary alloys Gunawardana, K. G. S. H.; Wilson, S. R.; Mendelev, M. I. Physical Review E, Vol. 90, Issue 5 https://doi.org/10.1103/PhysRevE.90.052403	journal	November 2014
Direct dynamical calculation of entropy and free energy by adiabatic switching Watanabe, Masakatsu; Reinhardt, William P. Physical Review Letters, Vol. 65, Issue 26 https://doi.org/10.1103/PhysRevLett.65.3301	journal	December 1990
Free energy landscape from path-sampling: application to the structural transition in LJ38 Adjanor, G.; Athènes, M.; Calvo, F. The European Physical Journal B, Vol. 53, Issue 1 https://doi.org/10.1140/epjb/e2006-00353-0	journal	September 2006

Cited By (2)

Effects of dopants on the glass forming ability in Al-based metallic alloy Sun, Yang; Zhang, Feng; Yang, Lin Physical Review Materials, Vol. 3, Issue 2 https://doi.org/10.1103/physrevmaterials.3.023404	journal	February 2019
Effects of Dopants on the Glass Forming Ability in Al-Based Metallic Alloy Ph. D., Yang Sun,; Zhang, Feng; Yang, Lin SSRN Electronic Journal https://doi.org/10.2139/ssrn.3289659	journal	January 2018

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36 MATERIALS SCIENCE
97 MATHEMATICS AND COMPUTING
alchemical path
free energy calculations
solid-liquid equilibria
thermodynamics integration

A self-contained algorithm for determination of solid-liquid equilibria in an alloy system

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References (38)

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