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  • Letter
  • Open Access

Generalized approach for rapid entropy calculation of liquids and solids

Qi-Jun Hong1,* and Zi-Kui Liu2

  • *Contact author: qijun.hong@asu.edu
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Phys. Rev. Research 7, L012030 – Published 7 February, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L012030

Abstract

We build a comprehensive methodology for the fast computation of entropy across both solid and liquid phases. The proposed method utilizes a single trajectory of molecular dynamics (MD) to facilitate the calculation of entropy, which is composed of three components. The electronic entropy is determined through the temporal average acquired from density functional theory MD simulations. The vibrational entropy, typically the predominant contributor to the total entropy, even within the liquid state, is evaluated by computing the phonon density of states via the velocity autocorrelation function. The most arduous component to quantify, the configurational entropy, is assessed by probability analysis of the local structural arrangement and atomic distribution. We illustrate, through a variety of examples, that this method is both a versatile and valid technique for characterizing the thermodynamic states of both solids and liquids. Furthermore, this method is employed to expedite the calculation of melting temperatures, demonstrating its practical utility in computational thermodynamics.

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References (39)

  1. B. Widom, Some topics in the theory of fluids, J. Chem. Phys. 39, 2808 (1963).
  2. B. Widom, Potential-distribution theory and the statistical mechanics of fluids, J. Phys. Chem. 86, 869 (1982).
  3. Q. J. Hong and A. van de Walle, Direct first-principles chemical potential calculations of liquids, J. Chem. Phys. 137, 094114 (2012).
  4. H. S. Green, The Molecular Theory of Fluids (North-Holland, Amsterdam, The Netherlands, 1952).
  5. D. C. Wallace, On the role of density fluctuations in the entropy of a fluid, J. Chem. Phys. 87, 2282 (1987).
  6. M. Widom and M. Gao, First principles calculation of the entropy of liquid aluminum, Entropy 21, 131 (2019).
  7. S. T. Lin, M. Blanco, and W. A. Goddard, The two-phase model for calculating thermodynamic properties of liquids from molecular dynamics: Validation for the phase diagram of Lennard-Jones fluids, J. Chem. Phys. 119, 11792 (2003).
  8. A. van de Walle and G. Ceder, The effect of lattice vibrations on substitutional alloy thermodynamics, Rev. Mod. Phys. 74, 11 (2002).
  9. Z.-K. Liu, Y. Wang, and S.-L. Shang, Zentropy theory for positive and negative thermal expansion, J. Phase Equilib. Diffus. 43, 598 (2022).
  10. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L012030 for detailed derivations and computational results.
  11. P. Perrot, A to Z of Thermodynamics (Oxford University Press, Oxford, 1998).
  12. J. W. Gibbs, Elementary Principles in Statistical Mechanics (Dover, New York, 1960).
  13. J. von Neumann, Thermodynamics of quantum mechanical ensembles, in Proceedings of the Society of Sciences in Göttingen, Mathematical-Physical Class (1927), pp. 273–291.
  14. C.E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27, 379 (1948).
  15. D. Frenkel and B. Smit, Understanding Molecular Simulation, 2nd ed. (Academic Press, Inc., San Diego, 2001).
  16. NIST chemistry webbook, https://webbook.nist.gov/chemistry/.
  17. Q.-J. Hong and A. van de Walle, A user guide for SLUSCHI: Solid and liquid in ultra small coexistence with hovering interfaces, CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 52, 88 (2016).
  18. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  19. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  20. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  21. G. P. Francis and M. C. Payne, Finite basis set corrections to total energy pseudopotential calculations, J. Phys.: Condens. Matter 2, 4395 (1990).
  22. S. Nosé, A molecular dynamics method for simulations in the canonical ensemble, Mol. Phys. 52, 255 (1984).
  23. S. Nosé, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys. 81, 511 (1984).
  24. W. G. Hoover, Canonical dynamics: Equilibrium phase-space distributions, Phys. Rev. A 31, 1695 (1985).
  25. G. J. Martyna and M. L. Klein, Nose-Hoover chains: The canonical ensemble via continuous dynamics, J. Chem. Phys. 97, 2635 (1992).
  26. Q.-J. Hong and A. van de Walle, Solid-liquid coexistence in small systems: A statistical method to calculate melting temperatures, J. Chem. Phys. 139, 094114 (2013).
  27. R. C. Garvie, R. H. Hannink, and R. T. Pascoe, Ceramic steel? Nature (London) 258, 703 (1975).
  28. O. Fabrichnaya, M. Zinkevich, and F. Aldinger, Thermodynamic modelling in the ZrO2−La2O3−Y2O3−Al2O3 system, Int. J. Mater. Res. 98, 838 (2007).
  29. M. Kilo, C. Argirusis, G. Borchardt, and R. A. Jackson, Oxygen diffusion in yttria stabilised zirconia-experimental results and molecular dynamics calculations, Phys. Chem. Chem. Phys. 5, 2219 (2003).
  30. C. Wang, M. Zinkevich, and F. Aldinger, The zirconia-hafnia system: DTA measurements and thermodynamic calculations, J. Am. Ceram. Soc. 89, 3751 (2006).
  31. Q. J. Hong, S. V. Ushakov, D. Kapush, C. J. Benmore, R. J. K. Weber, A. van de Walle, and A. Navrotsky, Combined computational and experimental investigation of high temperature thermodynamics and structure of cubic ZrO2 and HfO2, Sci. Rep. 8, 14962 (2018).
  32. Q.-J. Hong and A. van de Walle, Prediction of the material with highest known melting point from ab initio molecular dynamics calculations, Phys. Rev. B 92, 020104(R) (2015).
  33. H. Xie, N. Liu, Q. Zhang, H. Zhong, L. Guo, X. Zhao, D. Li, S. Liu, Z. Huang, A. D. Lele, A. H. Brozena, X. Wang, K. Song, S. Chen, Y. Yao, M. Chi, W. Xiong, J. Rao, M. Zhao, M. N. Shneider et al., A stable atmospheric-pressure plasma for extreme-temperature synthesis, Nature (London) 623, 964 (2023).
  34. B. C. Wyatt, S. K. Nemani, G. E. Hilmas, E. J. Opila, and B. Anasori, Ultra-high temperature ceramics for extreme environments, Nat. Rev. Mater. 9, 773 (2023).
  35. V. S. Buinevich, A. A. Nepapushev, D. O. Moskovskikh, G. V. Trusov, K. V. Kuskov, S. G. Vadchenko, A. S. Rogachev, and A. S. Mukasyan, Fabrication of ultra-high-temperature nonstoichiometric hafnium carbonitride via combustion synthesis and spark plasma sintering, Ceram. Int. 46, 16068 (2020).
  36. Q.-J. Hong, Methods for melting temperature calculation, Ph.D. thesis, California Institute of Technonology, 2015.
  37. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys. 21, 1087 (1953).
  38. W. Petry, A. Heiming, J. Trampenau, M. Alba, C. Herzig, H.R. Schober, and G. Vogl, Phonon dispersion of the bcc phase of group-IV metals. I. bcc titanium, Phys. Rev. B 43, 10933 (1991).
  39. S. Kadkhodaei, Q.-J. Hong, and A. van de Walle, Free energy calculation of mechanically unstable but dynamically stabilized bcc titanium, Phys. Rev. B 95, 064101 (2017).

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Phys. Rev. Research 7, L012030– Published 7 February, 2025
  • Received 5 April 2024
  • Revised 19 June 2024
  • Accepted 12 January 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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