Thermodynamic properties of rhodium at high temperature and pressure by using mean field potential approach

  • Priyank Kumar
  • Nisarg K. Bhatt
  • Pulastya R. Vyas
  • Vinod B. Gohel
Regular Article


The thermophysical properties of rhodium are studied up to melting temperature by incorporating anharmonic effects due to lattice ions and thermally excited electrons. In order to account anharmonic effects due to lattice vibrations, we have employed mean field potential (MFP) approach and for thermally excited electrons Mermin functional. The local form of the pseudopotential with only one effective adjustable parameter r c is used to construct MFP and hence vibrational free energy due to ions – F ion . We have studied equation of state at 300 K and further, to access the applicability of present conjunction scheme, we have also estimated shock-Hugoniot and temperature along principle Hugoniot. We have carried out the study of temperature variation of several thermophysical properties like thermal expansion (β P ), enthalpy (E H ), specific heats at constant pressure and volume (C P and C V ), specific heats due to lattice ions and thermally excited electrons (C V ion and C V el, isothermal and adiabatic bulk moduli (B T and B s ) and thermodynamic Gruneisen parameter (γ th ) in order to examine the inclusion of anharmonic effects in the present study. The computed results are compared with available experimental results measured by using different methods and previously obtained theoretical results using different theoretical philosophy. Our computed results are in good agreement with experimental findings and for some physical quantities better or comparable with other theoretical results. We conclude that local form of the pseudopotential used accounts s-p-d hybridization properly and found to be transferable at extreme environment without changing the values of the parameter. Thus, even the behavior of transition metals having complexity in electronic structure can be well understood with local pseudopotential without any modification in the potential at extreme environment. Looking to the success of present scheme (MFP + pseudopotential) we would like to extend it further for the study of liquid state properties as well as thermophysical properties of d and f block metals.


Solid State and Materials 


  1. 1.
    Y. Wang, L. Li, Phys. Rev. B 62, 196 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    Y. Wang, Phys. Rev. B 61, 863 (2000)Google Scholar
  3. 3.
    Yi Wang, Sun Yun-Feng, Chin. Phys. Lett. 18, 864 (2001)ADSGoogle Scholar
  4. 4.
    Y. Wang, Z.K. Liu, L.Q. Chen, L. Burakovsky, D.L. Preston, W. Luo, B. Johansson, R. Ahuja, Phys. Rev. B 71, 054110 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    Y. Wang, Z.K. Liu, L.Q. Chen, J. Appl. Phys. 100, 023533 (2006)ADSCrossRefGoogle Scholar
  6. 6.
    M.I. Katsnelson, I.I. Naumov, A.V. Trefilov, M.N. Khlopkin, K.Yu. Khromov, Philos. Mag. B 75, 389 (1997)ADSCrossRefGoogle Scholar
  7. 7.
    M.I. Katsnelson, M. Sigalas, A.V. Trefilov, K.Yu. Khromov, Philos. Mag. B 75, 407 (1997)ADSCrossRefGoogle Scholar
  8. 8.
    M.I. Katsnelson, A.V. Trefilov, M.N. Khlopkin, K.Yu. Khromov, Philos. Mag. B 81, 1893 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    M.I. Katsnelson, A.F. Maksyutov, A.V. Trefilov, Phys. Lett. A 295, 50 (2002)ADSCrossRefGoogle Scholar
  10. 10.
    N.K. Bhatt, P.R. Vyas, V.B. Gohel, A.R. Jani, Eur. Phys. J. B 58, 61 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    N.K. Bhatt, P.R. Vyas, A.R. Jani, Philos. Mag. 90, 1599 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    S. Ahmed, M. Zafar, M. Shakil, M.A. Choudhary, Condens. Matter Phys. 18, 23601 (2015)CrossRefGoogle Scholar
  13. 13.
    V.L. Moruzzi, J.F. Janak, K. Schwarz, Phys. Rev. B 37, 790 (1988)ADSCrossRefGoogle Scholar
  14. 14.
    R.C. Shukla, Phys. Rev. B 22, 5997 (1980)ADSCrossRefGoogle Scholar
  15. 15.
    R.C. Shukla, Phys. Rev. B 23, 3087 (1981)ADSCrossRefGoogle Scholar
  16. 16.
    R.A. McDonald, W.M. MacDonald, Phys. Rev. B 24, 1715 (1981)ADSCrossRefGoogle Scholar
  17. 17.
    V.V. Hung, K.M. Jindo, J. Phys. Soc. Jpn 99, 2067 (2000)ADSCrossRefGoogle Scholar
  18. 18.
    D. Alfe, M.J. Gillan, G.D. Price, Phys. Rev. B 65, 165118 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    O.Y. Kontsevoi, Y.N. Gornostyrev, A.J. Freeman, J. Miner. Metals Mater. Soc. 57, 43 (2005)CrossRefGoogle Scholar
  20. 20.
    C. Cazorla, D. Alfe, M.J. Gillan, Phys. Rev. B 85, 064113 (2012)ADSCrossRefGoogle Scholar
  21. 21.
    C. Cazorla, M.J. Gillan, S. Taioli, D. Alfe, J. Chem. Phys. 126, 194502 (2007)ADSCrossRefGoogle Scholar
  22. 22.
    L. Li, Y. Wang, Phys. Rev. B 63, 245108 (2001)ADSCrossRefGoogle Scholar
  23. 23.
    Y. Wang, D.Q. Chen, X.W. Zhang, Phys. Rev. Lett. 84, 3220 (2000)ADSCrossRefGoogle Scholar
  24. 24.
    Y. Wang, R. Ahuja, B. Johansson, Phys. Rev. B 65, 014104 (2001)ADSCrossRefGoogle Scholar
  25. 25.
    N.K. Bhatt, P.R. Vyas, A.R. Jani, V.B. Gohel, Int. J. Mod. Phys. B 19, 999 (2005)ADSCrossRefGoogle Scholar
  26. 26.
    G.L. Krasko, Z.A. Gurskii, Zh. ETF. Pis. Red. 9, 596 (1969)ADSGoogle Scholar
  27. 27.
    S.M. Osman, S.M. Mujibur Rahman, Mod. Phys. Lett. B 9, 553 (1995)ADSCrossRefGoogle Scholar
  28. 28.
    J. Hubbard, Proc. Roy. Soc. A 243, 336 (1957)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    L.J. Sham, Proc. Roy. Soc. A 283, 33 (1965)ADSCrossRefGoogle Scholar
  30. 30.
    J.A. Moriarty, Phys. Rev. B 6, 4445 (1972)ADSCrossRefGoogle Scholar
  31. 31.
    J.F. Wax, R. Albaki, J.L. Bretonnet, Phys. Rev. B 62, 14818 (2000)ADSCrossRefGoogle Scholar
  32. 32.
    C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1996)Google Scholar
  33. 33.
    Jinwoo Park, Byung Deok Yu, Suklyun Hong, Curr. Appl. Phys. 15, 885 (2015)ADSCrossRefGoogle Scholar
  34. 34.
    B.K. Godwal, S.K. Sikka, R. Chidambaram, Pramana J. Phys. 29, 93 (1987)ADSCrossRefGoogle Scholar
  35. 35.
    Y.S. Touloukian, R.K. Kirby, R.E. Taylor, P.D. Desai, Thermal Expansion, Metallic Elements and alloys, in Thermophysical Properties of Matter (Plenum, New York, 1975), Vol. 12Google Scholar
  36. 36.
    J.W. Arblaster, Platinum Metals Rev. 41, 184 (1997)Google Scholar
  37. 37.
    F.R. Caldwell, Thermocouple Materials (National Bureau of Standards Monograph 40, Washington 25, D.C., 1962)Google Scholar
  38. 38.
    B. Barter, A.S. Darling, Platinum Metals Rev. 4, 138 (1960)Google Scholar
  39. 39.
    M.H. Rice, R.G. McQueen, J.H. Walsh, Solid State Phys. 6, 1 (1958)Google Scholar
  40. 40.
    C. Cazorla, D. Alfe, M.J. Gillan, Phys. Rev. B 77, 224103 (2008)ADSCrossRefGoogle Scholar
  41. 41.
    C. Cazorla, D. Alfe, M.J. Gillan, Comput. Mater. Sci. 50, 2732 (2011)CrossRefGoogle Scholar
  42. 42.
    R.A. Robie, B.S. Hemingway, J.R. Fisher, Thermodynamic Properties of Minerals and Related Substances at 298.15 K and 1 Bar (105 Pascals) Pressure and at Higher Temperatures (U.S. Geological Survey Bulletin 1452) (United States Government Printing Office, Washington, 1978)Google Scholar
  43. 43.
    T. Cagin, G. Dereli, M. Uludogan, M. Tomak, Phys. Rev. B 59, 3468 (1999)ADSCrossRefGoogle Scholar
  44. 44.
    N.D. Mermin, Phys. Rev. 137, 1441 (1965)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Raj Pal Singh, Asian J. Adv. Basic Sci. 2, 116 (2014)Google Scholar
  46. 46.
    R. Sahara, H. Mizuseki, Y. Kawazoe, K. Ohno, J. Korean Phys. Soc. 52, 1259 (2008)ADSCrossRefGoogle Scholar
  47. 47.
    K.A. Gschneidner, in Solid State Physics Advances in Research and Applications, edited by F. Seitz, D. Turnball (Academic Press, New York, 1964), Vol. 16, p. 412Google Scholar
  48. 48.
    C.V. Pandya, P.R. Vyas, T.C. Pandya, V.B. Gohel, Bull. Mater. Sci. 25, 63 (2002)CrossRefGoogle Scholar
  49. 49.
    S.P. Marsh, LASL Shock Hugoniot Data (S. P. University of California Press, Berkeley, 1980)Google Scholar
  50. 50.
    C. Fiolhais, J.P. Perdew, S.Q. Armster, J.M. MacLaren, Phys. Rev. B 51, 14001 (1995)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Priyank Kumar
    • 1
  • Nisarg K. Bhatt
    • 2
  • Pulastya R. Vyas
    • 3
  • Vinod B. Gohel
    • 3
  1. 1.Department of ScienceGovernment PolytechnicGandhinagarIndia
  2. 2.Department of PhysicsSardar Patel UniversityVallabh VidyanagarIndia
  3. 3.Department of PhysicsSchool of Science, Gujarat UniversityAhmedabadIndia

Personalised recommendations