Improvements to the two-phase sandwich method for calculating the melting points of pure metals
Rybacki Kamil *, Winczewski Szymon, Pleechystyy Valeriy, Rybicki Jarosław
Gdańsk University of Technology
Faculty of Applied Physics and Mathematics
Narutowicza 11/12, Gdańsk, Poland
*E-mail: kamil.rybacki@pg.edu.pl
Received:
Received: 02 June 2019; revised: 23 June 2019; accepted: 25 June 2019; published online: 30 June 2019
DOI: 10.12921/cmst.2019.0000018
Abstract:
The thermophysical properties of metal alloys are often investigated via molecular dynamics (MD) simulations. An exact and reliable estimation of the thermophysical parameters from the MD data requires a properly and carefully elaborated methodology. In this paper, an improved two-phase sandwich method for the determination of the metal melting temperature is proposed, based on the solid-liquid equilibrium theory. The new method was successfully implemented using the LAMMPS software and the C++11 Standard Libraries and then applied to aluminum and copper systems. The results show that the proposed procedure allows more precise calculations of the melting temperature than the widely used onephase boundary methods.
Key words:
References:
[1] Y. Kaushik, A review on use of aluminium alloys in aircraft components, i-manager’s Journal on Material Science 3, 33–38 (2015).
[2] S. Ferraris, L.M. Volpone, Aluminium alloys in third millennium shipbuilding: Materials, technologies, perspectives, The Fifth International Forum on Aluminum Ships, 1–11 (2005).
[3] J. Hirsch, Recent development in aluminium for automotive applications, Transactions of Nonferrous Metals Society of China 24, 1995–2002 (2014).
[4] Y. Hiwatari, E. Stoll, T. Schneider, Molecular-dynamics investigation of solid-liquid coexistence, J. Chem. Phys. 68(8), 3401–3404 (1978).
[5] S. Toxvaerd, E. Praestgaard, Molecular dynamics calculation of the liquid structure up to a solid surface, J. Chem. Phys. 67(11), 5291–5295 (1977).
[6] Y.J. Lv, M. Chen, Thermophysical properties of undercooled alloys: An overview of the molecular simulation approaches, International Journal of Molecular Sciences 12(1), 278–316 (2011).
[7] X. Liu, X. Wen, R. Hoffmann, Surface activation of transition metal nanoparticles for heterogeneous catalysis: What we can learn from molecular dynamics, ACS Catalysis 8(4), 3365–3375 (2018).
[8] C.F. Sanz-Navarro, P.O. Åstrand, D. Chen, M. Rønning, A.C.T. van Duin, W.A. Goddard, Molecular dynamics simulations of metal clusters supported on fishbone carbon nanofibers, J. Phys. Chem. C 114(8), 3522–3530 (2010).
[9] M. Matsumiya, K. Seo, A Molecular Dynamics Simulation of the Transport Properties of Molten (La 1/3,K)Cl, Zeittschrift für Naturforschung A 60, 187–192 (2005).
[10] M.E. Trybula, Structure and transport properties of the liquid Al 80 Cu 20 alloy – A molecular dynamics study, Computational Materials Science 122 (2016).
[11] J. Rybicki, J. Dziedzic, S. Winczewski, Structure and properties of liquid Al–Cu alloys: Empirical potentials compared, Computational Materials Science 114, 219–232 (2016).
[12] F.R. Eshelman, J.F. Smith, Single-crystal elastic constants of Al2Cu, Journal of Applied Physics 49(6), 3284–3288 (1978).
[13] S.N. Luo, A. Strachan, D.C. Swift, Nonequilibrium melting and crystallization of a model Lennard-Jones system, J. Chem. Phys. 120, 11640 (2004).
[14] S.N. Luo, T.J. Ahrens, Superheating systematics of crystalline solids, Applied Physics Letters 82(12), 1836–1838 (2003).
[15] W. Zhang, Y. Peng, Z. Liu, Molecular dynamics simulations of the melting curve of NiAl alloy under pressure, AIP Advances 4, 057110 (2014).
[16] A. Stukowski, Structure identification methods for atomistic simulations of crystalline materials, Modelling and Simulation in Materials Science and Engineering 20 (2012).
[17] P.M. Larsen, S. Schmidt, J. Schiøtz, N. Ummen, T. Kraska, Common neighbour analysis for binary atomic systems Recent citations Common neighbour analysis for binary atomic systems, Modelling Simul. Mater. Sci. Eng 15, 319–334 (2007).
[18] P.J. Steinhardt, D.R. Nelson, M. Ronchetti, Icosahedral bond orientational order in supercooled liquids, Phys. Rev. Lett. 47, 1297–1300 (1981).
[19] S. Winczewski, J. Dziedzic, J. Rybicki, A highly-efficient technique for evaluating bond orientational order parameters, Computer Physics Communications 198, 128–138 (2016).
[20] S. Yoo, X.C. Zeng, J.R. Morris, The melting lines of model silicon calculated from coexisting solid–liquid phases, J. Chem. Phys. 120(123), 1654–1656 (2004).
[21] J.R. Morris, X. Song, The Melting Lines of Model Systems Calculated from Coexistence Simulations, Chemical Physics 116 (2002).
[22] S. Maćkowiak, S. Pieprzyk, A.C. Brańka, D.M. Heyes, A Nosé-Hoover Thermostat Adapted to a Slab Geometry, CMST 23(3), 211–218 (2017).
[23] Y. Zhang, E.J. Maginn, A comparison of methods for melting point calculation using molecular dynamics simulations, J. Chem. Phys. 136 (2012).
[24] S. Plimpton, Fast Parallel Algorithms for Short-range Molecular Dynamics, J. Comput. Phys. 117(1), 1–19 (1995).
[25] A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO – the open visualization tool, Modelling and Simulation in Materials Science and Engineering 18(1) (2010).
[26] F. Apostol, Y. Mishin, Interatomic potential for the Al-Cu system, Phys. Rev. B 83, 054116 (2011).
[27] Y. Mishin, M.J. Mehl, D.A. Papaconstantopoulos, A.F. Voter, J.D. Kress, Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations, Phys. Rev. B 63 (2001).
[28] X.W. Zhou, D.K. Ward, M.E. Foster, An analytical bondorder potential for the aluminum copper binary system, Journal of Alloys and Compounds 680, 752–767 (2016).
[29] G.A. DeWijs, G. Kresse, M.J. Gillan, First-order phase transitions by first-principles free energy calculations: The melting of Al, Phys. Rev. Lett. 74, 1823–1826 (1995).
[30] D.R. Lide, CRC Handbook of Chemistry and Physics, American Chemical Society, Boca Raton, 87th ed. (2006).
[31] L.F. Zhu, B. Grabowski, J. Neugebauer, Efficient approach to compute melting properties fully from ab initio with application to Cu, Phys. Rev. B 96 (2017).
[32] H. Brand, D.P. Dobson, L.V. Cadlo, I.G.Wood, Melting curve of copper measured to 16 GPa using a multi-anvil press, High Pressure Research 26(3), 185–191 (2006).
The thermophysical properties of metal alloys are often investigated via molecular dynamics (MD) simulations. An exact and reliable estimation of the thermophysical parameters from the MD data requires a properly and carefully elaborated methodology. In this paper, an improved two-phase sandwich method for the determination of the metal melting temperature is proposed, based on the solid-liquid equilibrium theory. The new method was successfully implemented using the LAMMPS software and the C++11 Standard Libraries and then applied to aluminum and copper systems. The results show that the proposed procedure allows more precise calculations of the melting temperature than the widely used onephase boundary methods.
Key words:
References:
[1] Y. Kaushik, A review on use of aluminium alloys in aircraft components, i-manager’s Journal on Material Science 3, 33–38 (2015).
[2] S. Ferraris, L.M. Volpone, Aluminium alloys in third millennium shipbuilding: Materials, technologies, perspectives, The Fifth International Forum on Aluminum Ships, 1–11 (2005).
[3] J. Hirsch, Recent development in aluminium for automotive applications, Transactions of Nonferrous Metals Society of China 24, 1995–2002 (2014).
[4] Y. Hiwatari, E. Stoll, T. Schneider, Molecular-dynamics investigation of solid-liquid coexistence, J. Chem. Phys. 68(8), 3401–3404 (1978).
[5] S. Toxvaerd, E. Praestgaard, Molecular dynamics calculation of the liquid structure up to a solid surface, J. Chem. Phys. 67(11), 5291–5295 (1977).
[6] Y.J. Lv, M. Chen, Thermophysical properties of undercooled alloys: An overview of the molecular simulation approaches, International Journal of Molecular Sciences 12(1), 278–316 (2011).
[7] X. Liu, X. Wen, R. Hoffmann, Surface activation of transition metal nanoparticles for heterogeneous catalysis: What we can learn from molecular dynamics, ACS Catalysis 8(4), 3365–3375 (2018).
[8] C.F. Sanz-Navarro, P.O. Åstrand, D. Chen, M. Rønning, A.C.T. van Duin, W.A. Goddard, Molecular dynamics simulations of metal clusters supported on fishbone carbon nanofibers, J. Phys. Chem. C 114(8), 3522–3530 (2010).
[9] M. Matsumiya, K. Seo, A Molecular Dynamics Simulation of the Transport Properties of Molten (La 1/3,K)Cl, Zeittschrift für Naturforschung A 60, 187–192 (2005).
[10] M.E. Trybula, Structure and transport properties of the liquid Al 80 Cu 20 alloy – A molecular dynamics study, Computational Materials Science 122 (2016).
[11] J. Rybicki, J. Dziedzic, S. Winczewski, Structure and properties of liquid Al–Cu alloys: Empirical potentials compared, Computational Materials Science 114, 219–232 (2016).
[12] F.R. Eshelman, J.F. Smith, Single-crystal elastic constants of Al2Cu, Journal of Applied Physics 49(6), 3284–3288 (1978).
[13] S.N. Luo, A. Strachan, D.C. Swift, Nonequilibrium melting and crystallization of a model Lennard-Jones system, J. Chem. Phys. 120, 11640 (2004).
[14] S.N. Luo, T.J. Ahrens, Superheating systematics of crystalline solids, Applied Physics Letters 82(12), 1836–1838 (2003).
[15] W. Zhang, Y. Peng, Z. Liu, Molecular dynamics simulations of the melting curve of NiAl alloy under pressure, AIP Advances 4, 057110 (2014).
[16] A. Stukowski, Structure identification methods for atomistic simulations of crystalline materials, Modelling and Simulation in Materials Science and Engineering 20 (2012).
[17] P.M. Larsen, S. Schmidt, J. Schiøtz, N. Ummen, T. Kraska, Common neighbour analysis for binary atomic systems Recent citations Common neighbour analysis for binary atomic systems, Modelling Simul. Mater. Sci. Eng 15, 319–334 (2007).
[18] P.J. Steinhardt, D.R. Nelson, M. Ronchetti, Icosahedral bond orientational order in supercooled liquids, Phys. Rev. Lett. 47, 1297–1300 (1981).
[19] S. Winczewski, J. Dziedzic, J. Rybicki, A highly-efficient technique for evaluating bond orientational order parameters, Computer Physics Communications 198, 128–138 (2016).
[20] S. Yoo, X.C. Zeng, J.R. Morris, The melting lines of model silicon calculated from coexisting solid–liquid phases, J. Chem. Phys. 120(123), 1654–1656 (2004).
[21] J.R. Morris, X. Song, The Melting Lines of Model Systems Calculated from Coexistence Simulations, Chemical Physics 116 (2002).
[22] S. Maćkowiak, S. Pieprzyk, A.C. Brańka, D.M. Heyes, A Nosé-Hoover Thermostat Adapted to a Slab Geometry, CMST 23(3), 211–218 (2017).
[23] Y. Zhang, E.J. Maginn, A comparison of methods for melting point calculation using molecular dynamics simulations, J. Chem. Phys. 136 (2012).
[24] S. Plimpton, Fast Parallel Algorithms for Short-range Molecular Dynamics, J. Comput. Phys. 117(1), 1–19 (1995).
[25] A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO – the open visualization tool, Modelling and Simulation in Materials Science and Engineering 18(1) (2010).
[26] F. Apostol, Y. Mishin, Interatomic potential for the Al-Cu system, Phys. Rev. B 83, 054116 (2011).
[27] Y. Mishin, M.J. Mehl, D.A. Papaconstantopoulos, A.F. Voter, J.D. Kress, Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations, Phys. Rev. B 63 (2001).
[28] X.W. Zhou, D.K. Ward, M.E. Foster, An analytical bondorder potential for the aluminum copper binary system, Journal of Alloys and Compounds 680, 752–767 (2016).
[29] G.A. DeWijs, G. Kresse, M.J. Gillan, First-order phase transitions by first-principles free energy calculations: The melting of Al, Phys. Rev. Lett. 74, 1823–1826 (1995).
[30] D.R. Lide, CRC Handbook of Chemistry and Physics, American Chemical Society, Boca Raton, 87th ed. (2006).
[31] L.F. Zhu, B. Grabowski, J. Neugebauer, Efficient approach to compute melting properties fully from ab initio with application to Cu, Phys. Rev. B 96 (2017).
[32] H. Brand, D.P. Dobson, L.V. Cadlo, I.G.Wood, Melting curve of copper measured to 16 GPa using a multi-anvil press, High Pressure Research 26(3), 185–191 (2006).
