, Volume 42, Issue 5, pp 387–394 | Cite as

The elastic moduli, the volume contribution and the Cauchy ratio ford andf shell metals

  • N Singh
  • B S Yadav


The elastic constants of nine transition metals and four rare-earths and actinides are calculated using the ion-ion interaction defined by us recently. The volume contribution to elastic moduli is calculated by exploiting the density dependence of the screening function. The calculated volume contribution to bulk modulus is found to vary between 17.1% and 62.4% for a number of metals, which is quite significant and play an important role for describing quantitatively the violation of the Cauchy ratio for these metals.


Elastic constants Cauchy ratio bulk modulus 




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    G Jaccuci and R Taylor,J. Phys. F11, 787 (1981)CrossRefADSGoogle Scholar
  2. [2]
    M S Duesbery and R Taylor,J. Phys. F7, 47 (1977)CrossRefADSGoogle Scholar
  3. [3]
    M S Duesbery, G Jaccuci and R Taylor,J. Phys. F9, 413 (1979)CrossRefADSGoogle Scholar
  4. [4]
    D G Pettifor and M A Ward,Solid State Commun. 49, 291 (1984)CrossRefADSGoogle Scholar
  5. [4a]
    M A Ward,Ph.D. Thesis, Imperial College, London, England, (1985)Google Scholar
  6. [5]
    D G Pettifor,Phys. Scr. 11, 26 (1982)CrossRefGoogle Scholar
  7. [6]
    J Lindhard,Kgl. Danske Mat. Fys. Medd. (Denmark)28, 8 (1954)MathSciNetGoogle Scholar
  8. [7]
    J Hafner and V Heine,J. Phys. F16, 1429 (1986)CrossRefADSGoogle Scholar
  9. [8]
    J Friedel,Philos. Mag. 43, 153 (1952)MATHGoogle Scholar
  10. [9]
    R A Johnson,Phys. Rev. B6, 2094 (1972)ADSGoogle Scholar
  11. [10]
    M Finnis,J. Phys. F4, 1645 (1974)CrossRefADSGoogle Scholar
  12. [11]
    A B Walker and R Taylor,J. Phys. F2, 9481 (1990);2, 9501 (1990)Google Scholar
  13. [12]
    M S Daw and M I Baskes,Phys. Rev. B29, 6443 (1984)ADSGoogle Scholar
  14. [13]
    S M Foiles, M I Baskes and M S Daw,Phys. Rev. B33, 7983 (1986)ADSGoogle Scholar
  15. [14]
    J K Norskov and N D Lang,Phys. Rev. B22, 2131 (1980)ADSGoogle Scholar
  16. [15]
    K W Jacobsen, J K Norskov and M J Puska,Phys. Rev. B35, 7423 (1987)ADSGoogle Scholar
  17. [16]
    M S Daw, inAtomistic simulation of materials: Beyond pair potentials Edited by V Vitek and D J Srolovitz (Plenum, New York, 1989) p. 181Google Scholar
  18. [17]
    M W Finnis and J E Sinclair,Philos. Mag. A50, 45 (1984)Google Scholar
  19. [18]
    G J Ackland, M W Finnis and V Vitek,J. Phys. F18, L153 (1988)Google Scholar
  20. [19]
    F Ercolessi, S Tosatti and M Parrinello,Phys. Rev. Lett. 57, 719 (1986)CrossRefADSGoogle Scholar
  21. [20]
    M Born and K Huang,Dynamical theory of crystal lattices (Clarendon, Oxford, 1954)MATHGoogle Scholar
  22. [21]
    H J P van Midden and A G B M Sasse,Phys. Rev. B46, 6020 (1992)ADSGoogle Scholar
  23. [22]
    D C Wallace,Thermodynamics of Crystals (Wiley, New York, 1972)Google Scholar
  24. [23]
    J M Martin,J. Phys. C8, 2837 (1975);C8, 2858 (1975)ADSGoogle Scholar
  25. [24]
    J M Wills and W A Harrison,Phys. Rev. B28, 4363 (1983)ADSGoogle Scholar
  26. [25]
    W A Harrison,Phys. Rev. B28, 550 (1983)ADSGoogle Scholar
  27. [26]
    U Walzer,Phys. Status Solidi B125, 55 (1984)CrossRefGoogle Scholar
  28. [27]
    Per Soderlind, Olle Erikssen, J M Wills and A M Boring,Phys. Rev. B48, 5844 (1993)ADSGoogle Scholar
  29. [28]
    Per Soderlind, Olle Eriksson, J M Wills and A M Boring,Phys. Rev. B48, 9306 (1993)ADSGoogle Scholar
  30. [29]
    N Singh and B S Yadav,Physica B192, 205 (1993)ADSGoogle Scholar
  31. [30]
    V Heine and I V Abarenkov,Philos. Mag. 9, 451 (1964)CrossRefGoogle Scholar
  32. [31]
    N W Ashcroft,Phys. Lett. 23, 48 (1966)CrossRefADSGoogle Scholar
  33. [32]
    S Ichimaru and K Utsumi,Phys. Rev. B24, 7385 (1981)ADSGoogle Scholar
  34. [33]
    S H Taole and H R Glyde,Can. J. Phys. 57, 1870 (1979)Google Scholar
  35. [34]
    R Evans, inElectrons in disordered metals and metallic surfaces Edited by P Phariseau, B L Györffy and L Scheire (Plenum, New York, 1979)Google Scholar
  36. [35]
    D Pines,Elementary excitations in solids (Benjamin, Amsterdam, 1963)Google Scholar
  37. [36]
    N Singh and S P Singh,Phys. Rev. B42, 1652 (1990)ADSGoogle Scholar
  38. [37]
    K Takanaka and R Yamamoto,Phys. Status. Solidi B84, 813 (1977)CrossRefGoogle Scholar
  39. [38]
    W B Pearson,A Handbook of lattice spacings and structure of metals and alloys (Pergamon, New York, 1958)Google Scholar
  40. [39]
    C Kittel,Introduction to solid state physics, 5th ed. (Wiley, New York, 1976)Google Scholar
  41. [40]
    C R C Handbook of chemistry and physics Edited by R C Weast and M J Astle, 61st ed. (Chemical Rubber Company, Florida, 1980)Google Scholar
  42. [41]
    G Simmons and H Wang,Single crystal elastic constants and calculated aggregate properties: A Handbook (MIT, Press, Cambridge, 1971)Google Scholar
  43. [42]
    D I Bolef and J de Klerk,Phys. Rev. 129, 1063 (1963)CrossRefADSGoogle Scholar
  44. [43]
    H B Huntigton, inSolid State Physics Edited by F Seitz and D Turnbull (Academic, New York, 1958) Vol. 7Google Scholar
  45. [44]
    C Stassis, C K Loong and J Zarestky,Phys. Rev. B26, 5426 (1982)ADSGoogle Scholar
  46. [45]
    C Stassis, T Gould, O D Macmasters, K A Gschneider Jr and R M Nicklow,Phys. Rev. B19, 5746 (1979)ADSGoogle Scholar
  47. [46]
    C Stassis, C K Loong, C Theisen and R M Nicklow,Phys. Rev. B26, 4106 (1982)ADSGoogle Scholar
  48. [47]
    G D Barrera and A Batana,Phys. Rev. B47, 8588 (1993)ADSGoogle Scholar
  49. [48]
    R F Wallis, A A Maradudin, V Bortolani, A G Equiluz, A A Quong, A Franchini and G Santoro,Phys. Rev. B48, 6043 (1993)ADSGoogle Scholar

Copyright information

© the Indian Academy of Sciences 1994

Authors and Affiliations

  • N Singh
    • 1
  • B S Yadav
    • 1
  1. 1.Department of PhysicsM.D. UniversityRohtakIndia

Personalised recommendations