Skip to main content
Log in

Temperature dependent Grüneisen parameter

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

Grüneisen parameter is one of the most valuable quantities in thermodynamics, which links the material properties of bulk modulus, heat capacity at constant volume, thermal expansion coefficient, and volume together. A new thermodynamic model of temperature-dependent potential energy is proposed here to investigate the temperature dependent Grüneisen parameter of bulk material. The newly developed thermodynamic model leads to temperature dependent analytical solutions of Grüneisen parameter and other thermo-mechanical properties including the Grüneisen equation of state. Molecular dynamics simulations are conducted on single crystalline Ni, Cu, and Au bulk crystals and the simulation results verify the newly developed thermodynamic model and quantitively evaluate the theoretically derived physical quantities. In addition, the Debye model is also employed in the study of temperature dependent Grüneisen parameter and the results also verify the theoretical approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Debye P. Zur theorie der spezifischen wärmen. Ann Phys, 1912, 344: 789–839

    Article  MATH  Google Scholar 

  2. Moruzzi V L, Janak J F, Schwarz K. Calculated thermal properties of metals. Phys Rev B, 1988, 37: 790–799

    Article  Google Scholar 

  3. Jankovský O, Sofer Z, Vítek J, et al. Structure, oxygen non-stoichiometry and thermal properties of (Bi0.4Sr0.6)Sr2CoO5-δ. Thermo-Chim Acta, 2015, 600: 89–94

    Article  Google Scholar 

  4. Fultz B. Vibrational thermodynamics of materials. Prog Mater Sci, 2010, 55: 247–352

    Article  Google Scholar 

  5. Gillet P, Richet P, Guyot F, et al. High-temperature thermodynamic properties of forsterite. J Geophys Res, 1991, 96: 11805–11816

    Article  Google Scholar 

  6. Narasimhan S, De Gironcoli S. Ab initio calculation of the thermal properties of Cu: Performance of the LDA and GGA. Phys Rev B, 2002, 65: 064302

    Article  Google Scholar 

  7. Skelton J M, Parker S C, Togo A, et al. Thermal physics of the lead chalcogenides PbS, PbSe, and PbTe from first principles. Phys Rev B, 2014, 89: 205203

    Article  Google Scholar 

  8. Huang L F, Zeng Z. Lattice dynamics and disorder-induced contraction in functionalized graphene. J Appl Phys, 2013, 113: 083524

    Article  Google Scholar 

  9. Souadkia M, Bennecer B, Kalarasse F. Elastic, vibrational and thermodynamic properties of based group IV semiconductors and GeC under pressure. J Phys Chem Solids, 2013, 74: 1615–1625

    Article  Google Scholar 

  10. Hellman O, Steneteg P, Abrikosov I A, et al. Temperature dependent effective potential method for accurate free energy calculations of solids. Phys Rev B, 2013, 87: 104111

    Article  Google Scholar 

  11. Errea I, Calandra M, Mauri F. First-principles theory of anharmonicity and the inverse isotope effect in superconducting palladium-hydride compounds. Phys Rev Lett, 2013, 111: 177002

    Article  Google Scholar 

  12. Hooton D J. A new treatment of anharmonicity in lattice thermodynamics: I. London Edinburgh Dublin Philos Mag J Sci, 1955, 46: 422–432

    Article  MathSciNet  MATH  Google Scholar 

  13. Lavrentiev M Y, Drautz R, Nguyen-Manh D, et al. Monte Carlo study of thermodynamic properties and clustering in the bcc Fe-Cr system. Phys Rev B, 2007, 75: 014208

    Article  Google Scholar 

  14. Karimi M, Stapay G, Kaplan T, et al. Temperature dependence of the elastic constants of Ni: Reliability of EAM in predicting thermal properties. Modell Simul Mater Sci Eng, 1997, 5: 337

    Article  Google Scholar 

  15. Zhou X Y, Huang B L, Zhang T Y. Size- and temperature-dependent Young’s modulus and size-dependent thermal expansion coefficient of thin films. Phys Chem Chem Phys, 2016, 18: 21508–21517

    Article  Google Scholar 

  16. Yang X, Zhai P, Liu L, et al. Thermodynamic and mechanical properties of crystalline CoSb3: A molecular dynamics simulation study. J Appl Phys, 2011, 109: 123517

    Article  Google Scholar 

  17. Cai C L, Chen Q F, Cui S X, et al. The Grüneisen parameter of NaCl at high pressures and temperatures: A molecular dynamics study. Chin Phys Lett, 2005, 22: 514–516

    Article  Google Scholar 

  18. Lagache M, Ungerer P, Boutin A, et al. Prediction of thermodynamic derivative properties of fluids by Monte Carlo simulation. Phys Chem Chem Phys, 2001, 3: 4333–4339

    Article  Google Scholar 

  19. van Duin A C T, Dasgupta S, Lorant F, et al. ReaxFF: Areactive force field for hydrocarbons. J Phys Chem A, 2001, 105: 9396–9409

    Article  Google Scholar 

  20. Stillinger F H, Weber T A. Computer simulation of local order in condensed phases of silicon. Phys Rev B, 1985, 31: 5262–5271

    Article  Google Scholar 

  21. Patterson J D, Bailey B C. Solid-State Physics: Introduction to the Theory. Berlin: Springer, 2007

    Google Scholar 

  22. Kittel C. Introduction to Solid State Physics. New York: Wiley, 1976

    MATH  Google Scholar 

  23. Cohen R E, Gülseren O. Thermal equation of state of tantalum. Phys Rev B, 2001, 63: 224101

    Article  Google Scholar 

  24. Born M, Huang K. Dynamical Theory of Crystal Lattices. Oxford: Clarendon Press, 1954

    MATH  Google Scholar 

  25. Barron T H K. Grüneisen parameters for the equation of state of solids. Ann Phys, 1957, 1: 77–90

    Article  Google Scholar 

  26. Eliezer S, Ghatak A K, Hora H. Fundamentals of Equations of State. Singapore: World Scientific, 2002

    Book  MATH  Google Scholar 

  27. Decker D L. High-pressure equation of state for NaCl, KCl, and CsCl. J Appl Phys, 1971, 42: 3239–3244

    Article  Google Scholar 

  28. Hanfland M, Beister H, Syassen K. Graphite under pressure: Equation of state and first-order Raman modes. Phys Rev B, 1989, 39: 12598–12603

    Article  Google Scholar 

  29. Birch F. Equation of state and thermodynamic parameters of NaCl to 300 kbar in the high-temperature domain. J Geophys Res-Solid Earth, 1986, 91: 4949–4954

    Article  Google Scholar 

  30. Bukowinski M S T. A theoretical equation of state for the inner core. Phys Earth Planet Inter, 1977, 14: 333–344

    Article  Google Scholar 

  31. Wachtman J B, Tefft W E, Lam D G, et al. Exponential temperature dependence of Young’s modulus for several oxides. Phys Rev, 1961, 122: 1754–1759

    Article  Google Scholar 

  32. Varshni Y P. Temperature dependence of the elastic constants. Phys Rev B, 1970, 2: 3952–3958

    Article  Google Scholar 

  33. Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comput Phys, 1995, 117: 1–19

    Article  MATH  Google Scholar 

  34. Foiles S M, Baskes M I, Daw M S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys Rev B, 1986, 33: 7983–7991

    Article  Google Scholar 

  35. Nosé S. A molecular dynamics method for simulations in the canonical ensemble. Mol Phys, 1984, 52: 255–268

    Article  Google Scholar 

  36. Martyna G J, Tobias D J, Klein M L. Constant pressure molecular dynamics algorithms. J Chem Phys, 1994, 101: 4177–4189

    Article  Google Scholar 

  37. Parrinello M, Rahman A. Polymorphic transitions in single crystals: A new molecular dynamics method. J Appl Phys, 1981, 52: 7182–7190

    Article  Google Scholar 

  38. Shinoda W, Shiga M, Mikami M. Rapid estimation of elastic constants by molecular dynamics simulation under constant stress. Phys Rev B, 2004, 69: 134103

    Article  Google Scholar 

  39. Thompson A P, Plimpton S J, Mattson W. General formulation of pressure and stress tensor for arbitrary many-body interaction potentials under periodic boundary conditions. J Chem Phys, 2009, 131: 154107

    Article  Google Scholar 

  40. Kresse G, Hafner J. Ab initio molecular dynamics for liquid metals. Phys Rev B, 1993, 47: 558–561

    Article  Google Scholar 

  41. Kresse G, Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B, 1996, 54: 11169–11186

    Article  Google Scholar 

  42. Blöchl P E. Projector augmented-wave method. Phys Rev B, 1994, 50: 17953–17979

    Article  Google Scholar 

  43. Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett, 1996, 77: 3865–3868

    Article  Google Scholar 

  44. Monkhorst H J, Pack J D. Special points for Brillouin-zone integrations. Phys Rev B, 1976, 13: 5188–5192

    Article  MathSciNet  Google Scholar 

  45. Callister Jr W D, Rethwisch D G. Fundamentals of Materials Science and Engineering: An Integrated Approach. Hoboken: John Wiley & Sons, 2012

    Google Scholar 

  46. Kang M H, Tatar R C, Mele E J, et al. Real-space formulation of the mixed-basis pseudopotential method: Bulk structural properties of elemental copper. Phys Rev B, 1987, 35: 5457–5472

    Article  Google Scholar 

  47. Kong L T. Phonon dispersion measured directly from molecular dynamics simulations. Comput Phys Commun, 2011, 182: 2201–2207

    Article  Google Scholar 

  48. Çağin T, Dereli G, Uludoğan M, et al. Thermal and mechanical properties of some fcc transition metals. Phys Rev B, 1999, 59: 3468–3473

    Article  Google Scholar 

  49. Hasegawa M, Young W H. Gruneisen parameters for simple metals. J Phys F-Met Phys, 1980, 10: 225–234

    Article  Google Scholar 

  50. Gauster W B. Low-temperature Grüneisen parameters for silicon and aluminum. Phys Rev B, 1971, 4: 1288–1296

    Article  Google Scholar 

  51. Singh R N, Arafin S, George A K. Temperature-dependent thermoelastic properties of s-, p- and d-block liquid metals. Phys B-Condensed Matter, 2007, 387: 344–351

    Article  Google Scholar 

  52. Boehler R, Ramakrishnan J. Experimental results on the pressure dependence of the Grüneisen parameter: A review. J Geophys Res, 1980, 85: 6996–7002

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Tao Xu or TongYi Zhang.

Additional information

This work was supported by the National Key R&D Program of China (Grant No. 2017YFB0701604), and the National Natural Science Foundation of China (Grant Nos. 11672168 & 11802169).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, X., Sun, S., Xu, T. et al. Temperature dependent Grüneisen parameter. Sci. China Technol. Sci. 62, 1565–1576 (2019). https://doi.org/10.1007/s11431-019-9526-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-019-9526-3

Keywords

Navigation