Thermophysical Properties of Cerium and Ytterbium via Local Pseudopotential with Mean Field Potential Approach at Extreme Environment

  • Priyank KumarEmail author
  • N. K. Bhatt
  • P. R. Vyas
  • V. B. Gohel


In the present communication, the ion motional contribution (\(\hbox {F}_{\mathrm{ion}}\)) to the total Helmholtz free energy has been accounted for by using mean field potential (MFP) approximation. The MFP is constructed using the local pseudopotential for divalent ytterbium and trivalent cerium. Further, MFP is used to evaluate static as well as temperature-dependent thermodynamic properties of these metals up to their melting temperature. Computed results are compared with experimental findings as well as results obtained by applying other theoretical methods. Present conjunction scheme with its computational simplicity, physical transparency and transferability of local pseudopotential explains the role of pressure-induced interband transfer of electrons which is crucial in the determination of thermodynamic properties of complex metals like lanthanides.


Lanthanides Mean field potential Pseudopotential Thermophysical properties 



Authors are thankful for computational facilities developed using financial assistance provided by Department of Sciences and Technology (DST), New Delhi, through the DST-FIST (Level 1) project (SR/FST/PST-001/2006). Authors are also thankful to Dr. Rajesh Iyer (Head, Department of Physics, St. Xavier’s College, Ahmedabad, Gujarat, India), Mr. K. H. Talati (Lecturer in English, Government Polytechnic, Gandhinagar, Gujarat, India) and Mrs. N. V. Chauhan (Lecturer in English, Government Polytechnic, Gandhinagar, Gujarat, India) for their careful observation and making suggestions and corrections to improve the language and readability of the manuscript.


  1. 1.
    H. Kurzen, L. Bovigny, C. Bulloni, C. Daul, Chem. Phys. Lett. 574, 129 (2013)ADSCrossRefGoogle Scholar
  2. 2.
    B. Johansson, A. Rosengren, Phys. Rev. B 11, 1367 (1975)ADSCrossRefGoogle Scholar
  3. 3.
    W.A. Grosshans, W.B. Holzapfel, Phys. Rev. B 45, 5171 (1992)ADSCrossRefGoogle Scholar
  4. 4.
    L.L. Sun, J.I. Guang Fu, C. Xiang-Rong, G. Qing-Quan, Chin. Phys. Lett. 26, 017101 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    Y.Y. Boguslavskii, V.A. Goncharova, G.G. ll’ina, JETP 80, 248 (1995)ADSGoogle Scholar
  6. 6.
    K. Takemura, K. Syassen, J. Phys. F Met. Phys. 15, 543 (1985)ADSCrossRefGoogle Scholar
  7. 7.
    W.A. Grosshans, W.B. Holzapfel, J. Phys. C8, 141 (1984)Google Scholar
  8. 8.
    J.M. Konings Rudy, O. Benes, J. Phys. Chem. Ref. Data 39, 043102-1 (2010)ADSGoogle Scholar
  9. 9.
    J.F. Herbst, J.W. Wikins, Phys. Rev. B 29, 5992 (1984)ADSCrossRefGoogle Scholar
  10. 10.
    W.H. Zachariasen, F.H. Ellinger, Acta Cryst. A33, 155 (1977)CrossRefGoogle Scholar
  11. 11.
    J.S. Olsen, L. Gerward, U. Benedict, J.P. Itie, Physica B 133, 129 (1985)CrossRefGoogle Scholar
  12. 12.
    J.W. Ward, J. Less Common Met. 93, 279 (1983)CrossRefGoogle Scholar
  13. 13.
    S.U. Devi, A.K. Singh, Bull. Mater. Sci. 6, 395 (1984)CrossRefGoogle Scholar
  14. 14.
    J. Bieder, B. Amadon, Phys. Rev. B 89, 195132 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    Y. Wang, L.G. Hector Jr., H. Zhang, S.L. Shang, L.Q. Chen, Z.K. Liu, Phys. Rev. B 78, 104113 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    Y. Wang, Phys. Rev. B 61, 863 (2000)Google Scholar
  17. 17.
    B. Johansson, W. Luo, S. Li, R. Ahuja, Sci. Rep. 4, 6398 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    M. Casadei, X. Ren, P. Rinke, A. Rubio, M. Scheffler, Phys. Rev. B 93, 075153 (2016)ADSCrossRefGoogle Scholar
  19. 19.
    C.E. Hu, Z.Y. Zeng, L. Zhang, X.R. Chen, L.C. Cai, Physica B 406, 669 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    P. Strange, A. Svane, W.M. Temmerman, Z. Szotek, H. Winter, Nature 399, 756 (1999)ADSCrossRefGoogle Scholar
  21. 21.
    K.E. Spear, S. Visco, E.J. Wuchina, E.D. Wachman, The Electrochemical Society Interface, vol. 15 (2006), p. 48.
  22. 22.
    S.L. Chaplot, R. Mittal, N. Choudhury, Thermophysical Properties of Solids: Experiment and Modeling (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2010)CrossRefGoogle Scholar
  23. 23.
    N. Dubrovinskaia, L. Dubrovinsky, Advances in High Pressure Technology for Geophysical Applications (Elsevier, Amsterdam, 2005)Google Scholar
  24. 24.
    N.K. Bhatt, P.R. Vyas, A.R. Jani, V.B. Gohel, J. Phys. Chem. Solids 66, 797 (2005)ADSCrossRefGoogle Scholar
  25. 25.
    N.K. Bhatt, A.R. Jani, P.R. Vyas, V.B. Gohel, Physica B 357, 259 (2005)ADSCrossRefGoogle Scholar
  26. 26.
    N.K. Bhatt, P.R. Vyas, A.R. Jani, Philos. Mag. 90, 1599 (2010)ADSCrossRefGoogle Scholar
  27. 27.
    Y. Wang, L. Li, Phys. Rev. B 62, 196 (2000)ADSCrossRefGoogle Scholar
  28. 28.
    G.L. Krasko, Z.A. Gurskii, ZhETF Pis. Red. 9, 596 (1969)ADSGoogle Scholar
  29. 29.
    S.M. Osman, S.M. Mujibur Rahman, Mod. Phys. Lett. B 9, 553 (1995)ADSCrossRefGoogle Scholar
  30. 30.
    A.M. Bratkovskii, V.G. Vaks, A.V. Trefilov, Sov. Phys. JETP 59, 1245 (1984)Google Scholar
  31. 31.
    J.A. Moriarty, Phys. Rev. B 8, 1338 (1973)ADSCrossRefGoogle Scholar
  32. 32.
    X. Sha, R.E. Cohen, Phys. Rev. B. 73, 104303 (2006)ADSCrossRefGoogle Scholar
  33. 33.
    J. Hubbard, Proc. Roy. Soc. A243, 336 (1958)ADSGoogle Scholar
  34. 34.
    L.J. Sham, Proc. Roy. Soc. A283, 33 (1965)ADSGoogle Scholar
  35. 35.
    A. Rosengren, I. Ebbsjo, B. Johansson, Phys. Rev. B 12, 1337 (1975)ADSCrossRefGoogle Scholar
  36. 36.
    J.F. Wax, R. Albaki, J.L. Bretonnet, Phys. Rev. B 62, 14818 (2000)ADSCrossRefGoogle Scholar
  37. 37.
    J.A. Moriarty, Phys. Rev. B 6, 4445 (1972)ADSCrossRefGoogle Scholar
  38. 38.
    C. Kittel, Introduction to Solid State Physics, 8th edn. (Wiley, New York, 1996)zbMATHGoogle Scholar
  39. 39.
  40. 40.
    Y.S. Touloukian, R.K. Kirby, R.E. Taylor, P.D. Desai, Thermophysical Properties of Matter: Thermal Expansion, Metallic Elements and alloys, vol. 12 (Plenum, New York, 1975), pp. 53, 382Google Scholar
  41. 41.
    K.A. Gschneidner, Solid State Phys. 16, 275 (1964)CrossRefGoogle Scholar
  42. 42.
    Y. Wang, Z.K. Liu, L.Q. Chen, J. Appl. Phys. 100, 023533 (2006)ADSCrossRefGoogle Scholar
  43. 43.
    Y. Wang, R. Ahuja, M.C. Qian, B. Johansson, J. Phys. Condens. Matter 14, L695 (2002)ADSCrossRefGoogle Scholar
  44. 44.
    Y. Wang, R. Ahuja, O. Eriksson, B. Johansson, C. Grimvall, J. Phys. Condens. Matter 14, L453 (2002)ADSCrossRefGoogle Scholar
  45. 45.
    C. Cazorla, D. Errandonea, E. Sola, Phys. Rev. B 80, 064105 (2009)ADSCrossRefGoogle Scholar
  46. 46.
    C. Cazorla, J. Iniguez, Phys. Rev. B 88, 214430 (2013)ADSCrossRefGoogle Scholar
  47. 47.
    C. Cazorla, J. Boronat, Phys. Rev. B 91, 024103 (2015)ADSCrossRefGoogle Scholar
  48. 48.
    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) p. 44–115Google Scholar
  49. 49.
    R.A. MacDonald, W.M. MacDonald, Phys. Rev. B 24, 1715 (1981)ADSCrossRefGoogle Scholar
  50. 50.
    H.K. Rai, S.P. Shukla, A.K. Mishra, A.K. Pandey, J. Chem. Pharm. Res. 2, 343 (2010)Google Scholar
  51. 51.
    L. Burakovsky, C.W. Greeff, D.L. Preston, Phys. Rev. B 67, 094107–1 (2003)ADSCrossRefGoogle Scholar
  52. 52.
    L. Burakovsky, D.L. Preston, Y. Wang, Solid State Commun. 132, 151 (2004)Google Scholar
  53. 53.
    C. Bhattacharya, S.V.G. Menon, J. Appl. Phys. 105, 064907–1 (2009)ADSCrossRefGoogle Scholar
  54. 54.
    C. Cazorla, D. Alfe, M.J. Gillan, Phys. Rev. B 85, 064113 (2012)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Priyank Kumar
    • 1
    Email author
  • N. K. Bhatt
    • 2
  • P. R. Vyas
    • 3
  • V. B. Gohel
    • 3
  1. 1.Department of ScienceGovernment PolytechnicGandhinagarIndia
  2. 2.Department of PhysicsM. K. Bhavanagar UniversityBhavanagarIndia
  3. 3.Department of Physics, School of ScienceGujarat UniversityAhmedabadIndia

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