Abstract
Context
Gallium, renowned for its notably low melting point and unique property of becoming liquid at room temperature, is a valuable constituent in phase change materials. In this study, we investigate the solid–liquid phase transition of gallium using the modified embedded atom method (MEAM) potential. It addresses the technique to compute the free energy difference between the solid and liquid without using a reference state. We examine various thermodynamic and dynamic properties, including density, specific heat capacity, diffusivity, and radial distribution functions. We compute the coexistence temperature of the solid–liquid phase transitions of gallium from free energy analysis. This information is crucial for understanding the behavior of the material under different pressure conditions and can be valuable for various applications, such as materials processing and high-pressure studies. The analysis, findings, and insights of the present work will be of great significance to the broad scientific and engineering communities in the field of phase transformation of materials.
Methods
A series of molecular dynamics(MD) simulations were conducted using the LAMMPS software packages. The gallium atoms are modeled using the modified embedded atom method (MEAM) potential. To accurately predict the solid–liquid phase transitions of gallium, we calculated free energy by employing the “constrained λ integration” method, coupled with multiple histogram reweighting (MHR). The solid–liquid coexistence line is determined through the Gibbs–Duhem integration technique.
Similar content being viewed by others
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
Jara DAC, Fontana Michelon M, Antonelli A, De Koning M (2009) Theoretical evidence for a first-order liquid-liquid phase transition in gallium. J Chem Phys 130. https://doi.org/10.1063/1.3154424
Ge H, Li J (2013) Keeping smartphones cool with gallium phase change material. J Heat Transfer 135:1–5. https://doi.org/10.1115/1.4023392
Mingear J, Farrell Z, Hartl D, Tabor C (2021) Gallium-indium nanoparticles as phase change material additives for tunable thermal fluids. Nanoscale 13:730–738. https://doi.org/10.1039/d0nr06526a
Saha SK (2022) Dynamics of phase change of gallium under magnetic field and thermocapillary effects under variable gravity conditions. Therm Sci Eng Prog 29:101234. https://doi.org/10.1016/j.tsep.2022.101234
Lin Y, Genzer J, Dickey MD (2020) Attributes, fabrication, and applications of gallium-based liquid metal particles. Adv Sci 7. https://doi.org/10.1002/advs.202000192
Peng H, Guo W, Li M, Feng S (2021) Melting behavior and heat transfer performance of gallium for spacecraft thermal energy storage application. Energy 228:120575. https://doi.org/10.1016/j.energy.2021.120575
Khoshmanesh K, Tang SY, Zhu JY et al (2017) Liquid metal enabled microfluidics. Lab Chip 17:974–993. https://doi.org/10.1039/c7lc00046d
Agarwal G, Kazior T, Kenny T, Weinstein D (2017) Modeling and analysis for thermal management in gallium nitride HEMTs using microfluidic cooling. J Electron Packag Trans ASME 139:1–11. https://doi.org/10.1115/1.4035064
Xie W, Allioux FM, Ou JZ et al (2021) Gallium-based liquid metal particles for therapeutics. Trends Biotechnol 39:624–640. https://doi.org/10.1016/j.tibtech.2020.10.005
Abdelhamid HN, Mathew AP (2022) Cellulose–metal organic frameworks (CelloMOFs) hybrid materials and their multifaceted applications: a review. Coord Chem Rev 451:214263. https://doi.org/10.1016/j.ccr.2021.214263
Li R, Sun G, Xu L (2016) Anomalous properties and the liquid-liquid phase transition in gallium. J Chem Phys 145. https://doi.org/10.1063/1.4959891
Ravelo R, Baskes M (1997) Equilibrium and thermodynamic properties of grey, white, and liquid tin. Phys Rev Lett 79:2482–2485. https://doi.org/10.1103/PhysRevLett.79.2482
Baskes MI (2000) Atomistic model of plutonium. Phys Rev B - Condens Matter Mater Phys 62:15532–15537. https://doi.org/10.1103/PhysRevB.62.15532
Daw MS, Baskes MI (1983) Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals. Phys Rev Lett 50:1285–1288. https://doi.org/10.1103/PhysRevLett.50.1285
Foiles SM, Baskes MI, Daw MS (1986) Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys Rev B 33:7983–7991. https://doi.org/10.1103/PhysRevB.33.7983
Baskes MI (1992) Modified embedded-atom potentials for cubic materials and impurities. Phys Rev B 46:2727–2742. https://doi.org/10.1103/PhysRevB.46.2727
Baskes MI (1987) Application of the embedded-atom method to covalent materials: a semiempirical potential for silicon. Phys Rev Lett 59:2666–2669. https://doi.org/10.1103/PhysRevLett.59.2666
Baskes MI, Nelson JS, Wright AF (1989) Semiempirical modified embedded-atom potentials for silicon and germanium. Phys Rev B 40:6085–6100. https://doi.org/10.1103/PhysRevB.40.6085
Cajahuaringa S, De Koning M, Antonelli A (2012) Dynamics near a liquid-liquid phase transition in a non-tetrahedral liquid: the case of gallium. J Chem Phys 136. https://doi.org/10.1063/1.3684550
Sweatman MB, Quirke N (2004) Simulating fluid-solid equilibrium with the Gibbs ensemble. Mol Simul 30:23–28. https://doi.org/10.1080/08927020310001626238
Chen B, Siepmann JI, Klein ML (2001) Direct Gibbs ensemble Monte Carlo simulations for solid-vapor phase equilibria: applications to Lennard-Jonesium and carbon dioxide. J Phys Chem B 105:9840–9848. https://doi.org/10.1021/jp011950p
Wang S, Zhang G, Liu H, Song H (2013) Modified Z method to calculate melting curve by molecular dynamics. J Chem Phys 138. https://doi.org/10.1063/1.4798225
Morris JR, Wang CZ, Ho KM, Chan CT (1994) Melting line of aluminum from simulations of coexisting phases. Phys Rev B 49:3109–3115. https://doi.org/10.1103/PhysRevB.49.3109
Wilding NB, Bruce AD (2000) Freezing by monte carlo phase switch. Phys Rev Lett 85:5138–5141. https://doi.org/10.1103/PhysRevLett.85.5138
Wilding NB (2002) A new simulation approach to the freezing transition. Comput Phys Commun 146:99–106. https://doi.org/10.1016/S0010-4655(02)00440-X
Eike DM, Brennecke JF, Maginn EJ (2005) Toward a robust and general molecular simulation method for computing solid-liquid coexistence. J Chem Phys 122:1–12. https://doi.org/10.1063/1.1823371
Das CK, Singh JK (2013) Effect of confinement on the solid-liquid coexistence of Lennard-Jones Fluid. J Chem Phys 139:1–14. https://doi.org/10.1063/1.4827397
Hoover WG, Ree FH (1967) The melting transition and calculate the 47:4837
Frenkel D, Ladd AJC (1984) New Monte Carlo method to compute the free energy of arbitrary solids. Application to the fcc and hcp phases of hard spheres. J Chem Phys 81:3188–3193. https://doi.org/10.1063/1.448024
Grochola G (2004) Constrained fluid λ-integration: constructing a reversible thermodynamic path between the solid and liquid state. J Chem Phys 120:2122–2126. https://doi.org/10.1063/1.1637575
Das CK, Singh JK (2014) Oscillatory melting temperature of stockmayer fluid in slit pores. J Phys Chem C 118:20848–20857. https://doi.org/10.1021/jp503044v
Das CK, Singh JK (2014) Melting transition of Lennard-Jones fluid in cylindrical pores. J Chem Phys 140. https://doi.org/10.1063/1.4876077
Sinha VK, Metya AK, Das CK (2024) Estimation of solid-liquid coexistence curve for coarse-grained water models through reliable free energy method. Fluid Phase Equilib 577:113985. https://doi.org/10.1016/j.fluid.2023.113985
Thompson AP, Aktulga HM, Berger R et al (2022) LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput Phys Commun 271:108171. https://doi.org/10.1016/j.cpc.2021.108171
Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J coputational Phys 117:1–19
Baskes MI, Chen SP, Cherne FJ (2002) Atomistic model of gallium. Phys Rev B - Condens Matter Mater Phys 66:1–9. https://doi.org/10.1103/PhysRevB.66.104107
Nosé S (1984) A molecular dynamics method for simulations in the canonical ensemble. Mol Phys 52:255–268. https://doi.org/10.1080/00268978400101201
Nosé S (1984) A unified formulation of the constant temperature molecular dynamics methods. J Chem Phys 81:511–519. https://doi.org/10.1063/1.447334
Kofke DA (1993) Direct evaluation of phase coexistence by molecular simulation via integration along the saturation line. J Chem Phys 98:4149–4162. https://doi.org/10.1063/1.465023
Di Cicco A (1998) Phase transitions in confined gallium droplets. Phys Rev Lett 81:2942–2945. https://doi.org/10.1103/PhysRevLett.81.2942
Niu H, Bonati L, Piaggi PM, Parrinello M (2020) Ab initio phase diagram and nucleation of gallium. Nat Commun 11:1–9. https://doi.org/10.1038/s41467-020-16372-9
Ferrenberg AM, Swendsen RH (1988) New Monte Carlo technique for studying phase transitions. Phys Rev Lett 61:2635–2638. https://doi.org/10.4324/9780203216446-20
Bosio L (1978) Crystal structures of Ga(II) and Ga(III). J Chem Phys 68:1221–1223
Acknowledgements
We acknowledge the National Institute of Technology Raurkela for providing a computational facility to perform the present work.
Author information
Authors and Affiliations
Contributions
The manuscript was written through the contributions of all authors. All authors have approved the final version of the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Debnath, A., Das, C.K. Theoretical investigation on the solid–liquid phase transition of gallium through free energy analysis. J Mol Model 30, 111 (2024). https://doi.org/10.1007/s00894-024-05909-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00894-024-05909-0