Temperature-Dependent Structural, Thermodynamic, and Phonon Properties of Lithium Fluoride from a Neuro-Evolution Machine-Learning Potential
DOI:
https://doi.org/10.15377/2409-5826.2025.12.7Keywords:
Lithium fluoride (LiF), Phonon anharmonicity, Neuro-evolution potential (NEP), Thermal conductivity and expansion, High-temperature molecular dynamics, Machine-learning interatomic potentialAbstract
Accurate prediction of structural and thermodynamic properties at finite temperature is a prerequisite for deploying ionic-crystal LiF in solid-state electrolytes and molten-salt coolants. To simultaneously boost predictive accuracy and accessible simulation scale, we have developed a neuro-evolution potential (NEP) machine-learning model for LiF. The potential exhibits outstanding fidelity and stability when describing high-temperature structures and thermodynamics. Force-field molecular dynamics driven by this NEP yields a thermal-expansion coefficient and lattice thermal conductivity in excellent agreement with experiments. LiF displays remarkable dynamical stability at elevated temperature, a conclusion corroborated by its elastic constants and phonon dispersion relations. A pronounced frequency resonance between Li and F motions appears at high temperature, underscoring strong phonon anharmonicity. This work delivers a rigorously validated and transferable potential for LiF, providing both a research framework and a data foundation for future investigations of its behaviour at electrolyte interfaces, in high-temperature solid solutions and under other extreme thermodynamic conditions.
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References
[1] Boehler R, Ross M, Boercker DB. Melting of LiF and NaCl to 1 Mbar: Systematics of ionic solids at extreme conditions. Phys Rev Lett. 1997; 78: 4589. https://doi.org/10.1103/physrevlett.78.4589 DOI: https://doi.org/10.1103/PhysRevLett.78.4589
[2] Roessler DM, Walker WC. Optical constants of magnesium oxide and lithium fluoride in the far ultraviolet. J Opt Soc Am. 1967; 57: 835–6. https://doi.org/10.1364/JOSA.57.000835 DOI: https://doi.org/10.1364/JOSA.57.000835
[3] Briscoe CV, Squire CF. Elastic constants of LiF from 4.2K to 300K by ultrasonic methods. Phys Rev. 1957; 106: 1175. https://doi.org/10.1103/PhysRev.106.1175 DOI: https://doi.org/10.1103/PhysRev.106.1175
[4] Miller RA, Smith CS. Pressure derivatives of the elastic constants of LiF and NaF. J Phys Chem Solids. 2014; 25: 1279-92. https://doi.org/10.1016/0022-3697(64)90043-5 DOI: https://doi.org/10.1016/0022-3697(64)90043-5
[5] Thacher PD. Effect of boundaries and isotopes on the thermal conductivity of LiF. Phys Rev. 1967; 156: 975. https://doi.org/10.1103/PhysRev.156.975 DOI: https://doi.org/10.1103/PhysRev.156.975
[6] Barkusky F, Path C, Mann K, Feigl T, Kaiser N. Formation and direct writing of color centers in LiF using a laser-induced extreme ultraviolet plasma in combination with a Schwarzschild objective. Rev Sci Instrum. 2005; 76: 10. https://doi.org/10.1063/1.2072147 DOI: https://doi.org/10.1063/1.2072147
[7] Rigg PA, Knudson MD, Scharff RJ, Hixson RS. Determining the refractive index of shocked [100] lithium fluoride to the limit of transmissibility. Appl Phys. 2014; 116: 10. https://doi.org/10.1063/1.4890714 DOI: https://doi.org/10.1063/1.4890714
[8] Sun X, Liu Z, Quan W, Song T, Khenata R. High-pressure and high-temperature physical properties of LiF studied by density functional theory calculations and molecular dynamics simulations. J Phys Chem Solids. 2018; 116: 209-15. https://doi.org/10.1016/j.jpcs.2018.01.037 DOI: https://doi.org/10.1016/j.jpcs.2018.01.037
[9] Modak P, Modak B. Insight into enhanced thermoluminescence property of (Mg, Cu, Ag)-Doped LiF: A DFT study. J Lumin. 2021; 117779. https://doi.org/10.1016/j.jlumin.2020.117779 DOI: https://doi.org/10.1016/j.jlumin.2020.117779
[10] Singh BK, Roy MK, Menon VJ, Sood KC. Effects of dispersion, correction term, and isotopes on the thermal conductivity of LiF crystal. Phys Rev B. 2003; 67: 014302. https://doi.org/10.1103/PhysRevB.67.014302 DOI: https://doi.org/10.1103/PhysRevB.67.014302
[11] Chruszcz-Lipska K, Szostak E, Zborowski KK, Knapik E. Study of the structure and infrared spectra of LiF, LiCl and LiBr using density functional theory (DFT). Materials. 2023; 16: 5353. https://doi.org/10.3390/ma16155353 DOI: https://doi.org/10.3390/ma16155353
[12] Wang J, Deng M, Chen Y, Liu X, Ke W, Li D, et al. Structural, elastic, electronic and optical properties of lithium halides (LiF, LiCl, LiBr, and LiI): First-principle calculations. Mater Chem Phys. 2020; 244: 122733. https://doi.org/10.1016/j.matchemphys.2020.122733 DOI: https://doi.org/10.1016/j.matchemphys.2020.122733
[13] Liang T, Chen W, Hu C, Chen X, Chen Q. Lattice dynamics and thermal conductivity of lithium fluoride via first-principles calculations. Solid State Commun. 2018; 272: 28-32. https://doi.org/10.1016/j.ssc.2018.01.004 DOI: https://doi.org/10.1016/j.ssc.2018.01.004
[14] Liu J, Dubrovinsky L, Ballaran TB, Crichton W. Equation of state and thermal expansivity of LiF and NaF. High Pressure Res. 2007; 27: 483-9. https://doi.org/10.1080/08957950701684690 DOI: https://doi.org/10.1080/08957950701684690
[15] Heyl V, Beeler B. An ab initio molecular dynamics study of varied compositions of the LiF-NaF-KF molten salt. J Nucl Mater. 2023; 585: 154641. https://doi.org/10.1016/j.jnucmat.2023.154641 DOI: https://doi.org/10.1016/j.jnucmat.2023.154641
[16] Behler J, Parrinello M. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys Rev Lett. 2007; 98: 146401. https://doi.org/10.1103/PhysRevLett.98.146401 DOI: https://doi.org/10.1103/PhysRevLett.98.146401
[17] Lam ST, Li Q, Ballinger R, Forsberg C, Li J, et al. Modeling LiF and FLiBe molten salts with robust neural network interatomic potential. ACS Appl Mater Interfaces. 2021; 13: 24582-92. https://doi.org/10.1021/acsami.1c00604 DOI: https://doi.org/10.1021/acsami.1c00604
[18] Fan Z, Zeng Z, Zhang C, Wang Y, Song K, Dong H, et al. Neuroevolution machine learning potentials: Combining high accuracy and low cost in atomistic simulations and application to heat transport. Phys Rev B. 2021; 104: 104309. https://doi.org/10.1103/PhysRevB.104.104309 DOI: https://doi.org/10.1103/PhysRevB.104.104309
[19] Rodriguez A, Lam S, Hu M. Thermodynamic and transport properties of LiF and FLiBe molten salts with deep learning potentials. ACS Appl Mater Interfaces. 2021; 13: 55367-79. https://doi.org/10.1021/acsami.1c17942 DOI: https://doi.org/10.1021/acsami.1c17942
[20] Xu B, Bai L, Xu S, Wu Q. Observing nucleation and crystallization of rock salt LiF from molten state through molecular dynamics simulations with refined machine-learned force field. J Chem Phys. 2025; 162: 23. https://doi.org/10.1063/5.0276535 DOI: https://doi.org/10.1063/5.0276535
[21] Wang Y, Fan Z, Qian P, Caro MA, Ala-Nissila T, et al. Quantum-corrected thickness-dependent thermal conductivity in amorphous silicon predicted by machine learning molecular dynamics simulations. Phys Rev B. 2023; 107: 054303. https://doi.org/10.1103/PhysRevB.107.054303 DOI: https://doi.org/10.1103/PhysRevB.107.054303
[22] Li S, Fan D, Wang J, Chen W, Song H, Lu Y. Lattice thermal conductivity of solid LiF based on machine learning force fields and the Green–Kubo approach. J Appl Phys. 2024; 135: 17. https://doi.org/10.1063/5.0200038 DOI: https://doi.org/10.1063/5.0200038
[23] Xu K, Liang T, Xu N, Ying P, Chen S, Wei N, et al. NEP-MB-pol: A unified machine-learned framework for fast and accurate prediction of water’s thermodynamic and transport properties. npj Comput Mater. 2025; 11: 279. https://doi.org/10.1038/s41524-025-01777-1 DOI: https://doi.org/10.1038/s41524-025-01777-1
[24] Li G, Lv Y, Zhang L, Jiang K, Zhang L, Liu Y, et al. Machine learning-driven exploration of composition- and temperature-dependent transport and thermodynamic properties in LiF-NaF-KF molten salts for nuclear applications. J Phys Chem. B. 2025; 27: 483-9. https://doi.org/10.1021/acs.jpcb.5c03444 DOI: https://doi.org/10.1021/acs.jpcb.5c03444
[25] Ying P, Qian C, Zhao R, Wang Y, Xu K, Ding F, et al. Advances in modeling complex materials: The rise of neuroevolution potentials. Chem Phys Rev. 2025; 6: 1. https://doi.org/10.1063/5.0259061 DOI: https://doi.org/10.1063/5.0259061
[26] Kong Q, Shibuta Y. High-precision prediction of thermal conductivity of metals by molecular dynamics simulation in combination with machine learning approach. Mater. Trans. 2023; 64: 1241-9. https://doi.org/10.2320/matertrans.MT-M2022204 DOI: https://doi.org/10.2320/matertrans.MT-M2022204
[27] Jones RE, Ward DK. Estimates of crystalline LiF thermal conductivity at high temperature and pressure by a Green-Kubo method. Phys Rev B. 2016; 94: 014309. https://doi.org/10.1103/PhysRevB.94.014309 DOI: https://doi.org/10.1103/PhysRevB.94.014309
[28] Ishii Y, Sato K, Salanne M, Madden PA, Ohtori N. Thermal conductivity of molten alkali metal fluorides (LiF, NaF, KF) and their mixtures. J Phys Chem B. 2014; 118: 3385-91. https://doi.org/10.1021/jp411781n DOI: https://doi.org/10.1021/jp411781n
[29] Fan Z, Wang Y, Ying P, Song K, Wang J, Wang Y, et al. GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations. Chem Phys. 2022; 157: 11. https://doi.org/10.1063/5.0106617 DOI: https://doi.org/10.1063/5.0106617
[30] Blochl PE. Projector augmented-wave method. Phys Rev B. 1994; 50: 17953. https://doi.org/10.1103/PhysRevB.50.17953 DOI: https://doi.org/10.1103/PhysRevB.50.17953
[31] Kresse G, Furthmuller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B. 1996; 54: 11169. https://doi.org/10.1103/PhysRevB.54.11169 DOI: https://doi.org/10.1103/PhysRevB.54.11169
[32] Perdew JD, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett. 1996; 77: 3865. https://doi.org/10.1103/PhysRevLett.77.3865 DOI: https://doi.org/10.1103/PhysRevLett.77.3865
[33] Monkhorst HJ, Pack JD. Special points for Brillouin-zone integrations. Phys Rev B. 1976; 13: 5188. https://doi.org/10.1103/PhysRevB.13.5188 DOI: https://doi.org/10.1103/PhysRevB.13.5188
[34] Togo A, Chaput L, Tanaka I, Hug G. First-principles phonon calculations of thermal expansion in Ti3SiC2, Ti3AlC2, and Ti3GeC2. Phys Rev B. 2010; 81: 174301. https://doi.org/10.1103/PhysRevB.81.174301 DOI: https://doi.org/10.1103/PhysRevB.81.174301
[35] Nose S. A unified formulation of the constant temperature molecular dynamics methods. J Chem Phys. 1984; 81: 511-19. https://doi.org/10.1063/1.447334 DOI: https://doi.org/10.1063/1.447334
[36] Hoover WG. Canonical dynamics: Equilibrium phase-space distributions. Phys Rev A. 1985; 31: 1695. https://doi.org/10.1103/PhysRevA.31.1695 DOI: https://doi.org/10.1103/PhysRevA.31.1695
[37] Green M. Markoff random processes and the statistical mechanics of time-dependent phenomena. J Chem Phys. 1952; 20: 1281-95. https://doi.org/10.1063/1.1740082 DOI: https://doi.org/10.1063/1.1700722
[38] Green M. Markoff random processes and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids. J Chem Phys. 1954; 22: 398-413. https://doi.org/10.1063/1.1740082 DOI: https://doi.org/10.1063/1.1740082
[39] Kubo R. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J Phys Soc Jpn. 1957; 12: 570-86. https://doi.org/10.1143/JPSJ.12.570 DOI: https://doi.org/10.1143/JPSJ.12.570
[40] Kubo R, Yokota M, Nakajima S. Statistical-mechanical theory of irreversible processes. II. Response to thermal disturbance. J Phys Soc Jpn. 1957; 12: 1203-11. https://doi.org/10.1143/JPSJ.12.1203s DOI: https://doi.org/10.1143/JPSJ.12.1203
[41] McGaughey AJH, Kaviany M. Phonon transport in molecular dynamics simulations: formulation and thermal conductivity prediction. Adv Heat Transf. 2006; 39: 169-255. https://doi.org/10.1016/S0065-2717(06)39002-8 DOI: https://doi.org/10.1016/S0065-2717(06)39002-8
[42] Fan Z, Pereira LFC, Hirvonen PM, Ervasti MM, Elder KR, Donadio D, et al. Thermal conductivity decomposition in two-dimensional materials: Application to graphene. Phys Rev B. 2017; 95: 144309. https://doi.org/10.1103/PhysRevB.95.144309 DOI: https://doi.org/10.1103/PhysRevB.95.144309
[43] Hutchison CA, Johnston HL. Determination of crystal densities by the temperature of flotation method. Density and lattice constant of lithium fluoride. J Am Chem Soc. 1940; 62: 3165-8. https://doi.org/10.1021/ja01868a075 DOI: https://doi.org/10.1021/ja01868a075
[44] Jones LEA. High-temperature behaviour of the elastic moduli of LiF and NaF: Comparison with MgO and CaO. Phys Earth Planet Inter 1976; 13: 105-18. https://doi.org/10.1016/0031-9201(76)90075-3 DOI: https://doi.org/10.1016/0031-9201(76)90075-3
[45] Haussühl S. Thermo-elastische Konstanten der Alkalihalogenide vom NaCl-typ. Z. Angew Phys. 1960; 159: 2. https://doi.org/10.1007/bf01338349 DOI: https://doi.org/10.1007/BF01338349
[46] Pathak P, Vasavada N. Thermal expansion of LiF by X-ray diffraction and the temperature variation of its frequency spectrum. Acta Crystallogr A. 1972; 28: 30-3. https://doi.org/10.1107/S0567739472000063 DOI: https://doi.org/10.1107/S0567739472000063
[47] Voigt W. Lehrbuch der Kristallphysik (mit Ausschluss der Kristalloptik). B. G. Teubner. 1910; 34.
[48] Reuss A. Berechnung der fließgrenze von mischkristallen auf grund der plastizitätsbedingung für einkristalle. ZAMM-Z. Angew Math Mech. 1929; 9: 49. DOI: https://doi.org/10.1002/zamm.19290090104
[49] Hill R. The elastic behaviour of a crystalline aggregate. Proc Phys Soc A. 1952; 65: 349. https://doi.org/10.1088/0370-1298/65/5/307 DOI: https://doi.org/10.1088/0370-1298/65/5/307
[50] Lu Y, Wang BT, Li RW, Shi HL, Zhang P. Structural, electronic, mechanical, and thermodynamic properties of UN2: Systematic density functional calculations. J Nucl Mater. 2011; 410: 46-51. https://doi.org/10.1016/j.jnucmat.2010.12.308 DOI: https://doi.org/10.1016/j.jnucmat.2010.12.308
[51] Mouhat F, Coudert FX. Necessary and sufficient elastic stability conditions in various crystal systems. Phys Rev B. 2014; 90: 224104. https://doi.org/10.1103/PhysRevB.90.224104 DOI: https://doi.org/10.1103/PhysRevB.90.224104
[52] Petrov AV, Tsypkina NS, Seleznev VE. The behaviour of lattice thermal conductivity of crystals at high temperatures. High Temp.-High Press. 1976; 8: 537-43.
[53] Andersson S, Backstrom G. Thermal conductivity and heat capacity of single-crystal LiF and CaF2 under hydrostatic pressure. J Phys C Solid State Phys. 1987; 20: 5951. https://doi.org/10.1088/0022-3719/20/35/011 DOI: https://doi.org/10.1088/0022-3719/20/35/011
[54] Elhadj S, Matthews MJ, Yang ST, Cooke DJ, Stolken JS, Vignes RM, et al. Determination of the intrinsic temperature dependent thermal conductivity from analysis of surface temperature of laser irradiated materials. Appl Phys Lett. 2010; 96: 071110. https://doi.org/10.1063/1.3291665 DOI: https://doi.org/10.1063/1.3291665
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