Atomistic simulations of thermodynamic properties with nuclear quantum effects of liquid gallium from first principles

Abstract

Determining thermodynamic properties in disordered systems remains a formidable challenge because of the difficulty in incorporating nuclear quantum effects into large-scale and nonperiodic atomic simulations. In this study, we employ a machine learning deep potential model in conjunction with the quantum thermal bath method, enabling machine learning molecular dynamics to simulate thermodynamic quantities of liquid materials with satisfactory accuracy without significantly increasing computational costs. Using this approach, we accurately calculate the variations in various thermodynamic quantities of liquid metal gallium at temperatures ranging from zero to room temperature. The calculated thermodynamic properties accurately capture the solid-liquid phase transition behavior of gallium, whereas classical molecular dynamics methods fail to reproduce realistic results. Through this approach, we offer a potential method for accurately calculating the thermodynamic properties of liquids and other disordered systems.

Keywords

liquid metals / machine learning / molecular dynamics / nuclear quantum effects / thermodynamic properties

References

[1] Massobrio C, Du J, Bernasconi M, Salmon PS, et al. Molecular dynamics simulations of disordered materials. Vol 215. Springer; 2015.

[2] Kittel C, McEuen P, McEuen P. Introduction to solid state physics. Vol 8. Wiley; 1996.

[3] Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comput Phys. 1995; 117(1): 1-19.

[4] Greywall DS. Specific heat of normal liquid ³He. Phys Rev B. 1983; 27(5): 2747-2766.

[5] Ceperley DM. Path integrals in the theory of condensed helium. Rev Mod Phys. 1995; 67(2): 279-355.

[6] Marx D, Parrinello M. Ab initio path-integral molecular dynamics. Z Phys B Condens Matter. 1994; 95(2): 143-144.

[7] Marx D, Parrinello M. Ab initio path integral molecular dynamics: basic ideas. J Chem Phys. 1996; 104(11): 4077-4082.

[8] Miller WH. Quantum dynamics of complex molecular systems. Proc Natl Acad Sci. 2005; 102(19): 6660-6664.

[9] Becker CA, Tavazza F, Trautt ZT, Macedo RAB. Considerations for choosing and using force fields and interatomic potentials in materials science and engineering. Curr Opin Solid State Mater Sci. 2013; 17(6): 277-283.

[10] Gunsteren WF, Mark AE. Validation of molecular dynamics simulation. J Chem Phys. 1998; 108(15): 6109-6116.

[11] Zhang L, Wang H, Car R, Weinan E. Phase diagram of a deep potential water model. Phys Rev Lett. 2021; 126(23):236001.

[12] Sosso GC, Chen J, Cox SJ, et al. Crystal nucleation in liquids: open questions and future challenges in molecular dynamics simulations. Chem Rev. 2016; 116(12): 7078-7116.

[13] Niu H, Bonati L, Piaggi PM, Parrinello M. Ab initio phase diagram and nucleation of gallium. Nat Commun. 2020; 11(1):2654.

[14] Wu H, He R, Lu Y, Zhong Z. Large-scale atomistic simulation of quantum effects in SrTiO₃ from first principles. Phys Rev B. 2022; 106(22):224102.

[15] Qin X, Wu H, Shi G, Zhang C, Jiang P, Zhong Z. Zero-point quantum diffusion of protons in the hydrogen-rich superconductor LaH₁₀ from first principles. Phys Rev B. 2023; 108(6):064102.

[16] Zhang L, Han J, Wang H, Saidi W, Car R, E W. End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems. In: edited by S Bengio, H Wallach, H Larochelle, K Grauman, N Cesa-Bianchi, R Garnett, Advances in Neural Information Processing Systems 31Curran Associates. Inc.; 2018.

[17] Zhang L, Han J, Wang H, Car R, Weinan E. Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics. Phys Rev Lett. 2018; 120(14):143001.

[18] Dammak H, Chalopin Y, Laroche M, Hayoun M, Greffet JJ. Quantum thermal bath for molecular dynamics simulation. Phys Rev Lett. 2009; 103(19):190601.

[19] Callen HB, Welton TA. Irreversibility and generalized noise. Phys Rev. 1951; 83(1): 34-40.

[20] Sostman HE. Melting point of gallium as a temperature calibration standard. Rev Sci Instrum. 1977; 48(2): 127-130.

[21] Lin Y, Genzer J, Dickey MD. Attributes, fabrication, and applications of gallium-based liquid metal particles. Adv Sci. 2020; 7(12):2000192.

[22] Song H, Kim T, Kang S, Jin H, Lee K, Yoon HJ. Ga-Based liquid metal micro/nanoparticles: recent advances and applications. Small. 2020; 16(12):1903391.

[23] Tang SY, Tabor C, Kalantar-Zadeh K, Dickey MD. Gallium liquid metal: the devil’s elixir. Annu Rev Mater Res. 2021; 51(1): 381-408.

[24] Zhang Y, Wang H, Chen W, et al. DP-GEN: a concurrent learning platform for the generation of reliable deep learning based potential energy models. Comput Phys Commun. 2020; 253:107206.

[25] Zhang L, Lin DY, Wang H, Car R, E W. Active learning of uniformly accurate interatomic potentials for materials simulation. Phys Rev Mater. 2019; 3(2):023804.

[26] Perdew JP, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett. 1997; 78(7):1396.

[27] Barrat JL, Rodney D. Portable implementation of a quantum thermal bath for molecular dynamics simulations. J Stat Phys. 2011; 144(3): 679-689.

[28] Dammak H, Hayoun M, Chalopin Y, Greffet JJ. Dammak et al. Reply:. Phys Rev Lett. 2011; 107(19):198902.

[29] Barrett C, Spooner F. Lattice constants of gallium at 297 K. Nature. 1965; 207(5004):1382.

[30] Petit J, Nachtrieb NH. Self-diffusion in liquid gallium. J Chem Phys. 1956; 24(5): 1027-1028.

[31] Kumar VB, Porat Z, Gedanken A. DSC measurements of the thermal properties of gallium particles in the micron and sub-micron sizes, obtained by sonication of molten gallium. J Therm Anal Calorim. 2015; 119(3): 1587-1592.

[32] He H, Fei GT, Cui P, et al. Relation between size and phase structure of gallium: differential scanning calorimeter experiments. Phys Rev B. 2005; 72(7):073310.

[33] Adams Jr. GB, Johnston HL, Kerr EC. The heat capacity of gallium from 15 to 320 K. The heat of fusion at the melting point. J Am Chem Soc. 1952; 74(19): 4784-4787.

RIGHTS & PERMISSIONS

2025 The Author(s). Materials Genome Engineering Advances published by Wiley-VCH GmbH on behalf of University of Science and Technology Beijing.