Advertisement

Liquid Alkali Metals and Alkali-Based Alloys as Electron-Ion Plasmas

  • M. P. Tosi
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 81)

Abstract

The article reviews the theory of thermodynamic and structural properties of liquid alkali metals and alkali-based alloys, within the framework of linear screening theory for the electron-ion interactions.

Keywords

Radial Distribution Function Phonon Dispersion Curve Partial Structure Factor Liquid Alkali Metal Density Response Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Bohm and T. Staver, Phys. Rev. 84, 836 (1951); see also D. Pines, ‘Elementary Excitations in Solids’ ( Benjamin, New York 1964 ).ADSCrossRefGoogle Scholar
  2. 2.
    T. Toya, J. Res. Inst. Catalysis, Hokkaido Univ. 6, 161 and 183 (1958).Google Scholar
  3. 3.
    N. W. Ashcroft and D.C. Langreth, Phys. Rev. 155, 682 (1967); D.C. Wallace, Phys. Rev. 182, 778 (1969).CrossRefGoogle Scholar
  4. 4.
    See e.g. R. H. Fowler, J. Chem. Phys. 59, 3435 (1973); A. Rahman, Phys. Rev. Lett. 32, 52 (1974) and Phys. Rev. A9, 1667 (1974); M. Parrinello and A. Rahman, Phys. Rev. Lett. 45, 1196 (1980).ADSCrossRefGoogle Scholar
  5. 5.
    For a review see M. Baus and J.P. Hansen, Phys. Repts 59, 1 (1980).MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    D. L. Price, K. S. Singwi and M. P. Tosi, Phys. Rev. B2, 2983 (1970).ADSCrossRefGoogle Scholar
  7. 7.
    N. W. Ashcroft, J. Phys. C1, 232 (1968).ADSGoogle Scholar
  8. 8.
    T. E. Faber, in ‘Physics of Modern Materials’, vol. II, p. 645 ( IAEA, Vienna 1980 ).Google Scholar
  9. 9.
    This condition for the electron gas is known as the ‘compressibility sum rule’: see D. Pines and P. Nozières, ‘The Theory of Quantum Liquids’ (Benjamin, New York 1966). It states that the inverse screening length ke in the electronic dielectric function must agree with the value calculated from the ground state energy Eg through the expression ke2 = 4πρ2e2Ke where Ke is the electron gas compressibility, determined by the second derivative of Eg with respect to the electron density.Google Scholar
  10. 10.
    E. G. Brovman and Yu. Kagan, Z. Eksp. Teor. Fiz. 52, 557 (1967) and 57, 1329 (1969) [English translations: Sov. Phys. JETP, 25, 365 (1967) and 30, 721 (1970)]; C. Pethick, Phys. Rev. B2, 1789 (1970).Google Scholar
  11. 11.
    F. Postogna and M. P. Tosi, N. Cimento 55B, 399 (1980).ADSCrossRefGoogle Scholar
  12. 12.
    See e.g. N.H. March and M.P. Tosi, ‘Atomic Dynamics in Liquids’ ( Macmillan, London 1976 ).Google Scholar
  13. 13.
    S. Galam and J.P. Hansen, Phys. Rev. A14, 816 (1976); F. Postogna and M.P. Tosi, ref.ll. Strictly speaking, S(k) in (3.5) describes the diffraction pattern from interference between waves scatterd by pairs of ions and does not fully describe the X-ray diffraction pattern, which also contains interference terms involving the conduction electrons; see P. A. Egelstaff, N.H. March and N.C. McGill, Cand. J. Phys. 52, 1651 (1974).ADSCrossRefGoogle Scholar
  14. 14.
    D.K. Chaturvedi, M. Rovere, G. Senatore and M.P. Tosi, Physica (in the press). A preliminary report has been given by D. K. Chaturvedi, G. Senatore and M. P. Tosi, Lett. N. Cimento 30, 47 (1981).ADSCrossRefGoogle Scholar
  15. 15.
    P. Vieillefosse and J. P. Hansen, Phys. Rev. A12,1106 (1975); H. E. De Witt, Phys. Rev. A14, 1290 (1976); J. P. Hansen, G. M. Torrie and P. Vieillefosse, Phys. Rev. A16, 2153 (1977). The relation between ki2 and the free energy of the OCP is analogous to the ‘compressibility sum rule’ for the electron gas mentioned in ref. 9 above, namely ki2 = 4πρiz2 e2Ki where Ki is the isothermal compressibility of the OCP. Notice that the OCP appropriate to alkali metals near freezing is in a strong coupling regime, where ki2 takes strongly negative values.ADSCrossRefGoogle Scholar
  16. 16.
    M. Watabe and M. Hasegawa, in ‘The Properties of Liquid Metals’, p.133 (edited by S. Takeuchi; Francis and Taylor, London 1973); J. Chihara, ibid., p.137.Google Scholar
  17. 17.
    D. L. Price, Phys. Rev. A4, 358 (1971).ADSCrossRefGoogle Scholar
  18. 18.
    S. G. Brush, H. L. Sahlin and E. Teller, J. Chem. Phys. 45, 2102 (1966); J. P. Hansen, Phys. Rev. A8, 3096 (1973); S. Galam and J. P. Hansen, ref. 13.ADSCrossRefGoogle Scholar
  19. 19.
    M.J. Gillan, J. Phys. C7, L1 (1974)Google Scholar
  20. 20.
    The Debye-Hückel approximation for the classical plasma, when applied at all values of r, corresponds to the RPA for the degenerate electron gas. It assumes for So (k) the form of eqn.(3.8) at all values of k, with ki2 replaced by kD2.Google Scholar
  21. 21.
    D. K. Chaturvedi, G. Senatore and M. P. Tosi, N. Cimento 62B, 375 (1981).ADSCrossRefGoogle Scholar
  22. 22.
    A close similarity between the structure factor of the OCP and those of liquid alkali metals in the region of the main peak and beyond was first noticed by H. Minoo, C. Deutsch and J. P. Hansen, J. Phys. Lettres, 38, L191 (1977).Google Scholar
  23. 23.
    For the freezing of the OCP see J. P. Hansen, ref.18; W.L. Slattery, G. D. Doolen and H. E. De Witt, Phys. Rev. A21, 2087 (1980). A. Ferraz and N. H. March, Solid State Commun. 36, 977 (1980) have proposed a freezing criterion for the alkali metals in accord with the viewpoint expressed here.CrossRefGoogle Scholar
  24. 24.
    M. J. Huijben and W. van der Lugt, in ‘Liquid Metals, 1976’, p.141 (Conference Series No. 30, The Institute of Physics, Bristol 1977 ).Google Scholar
  25. 25.
    A.J. Greenfield, J. Wellendorf and N. Wiser, Phys. Rev. A4, 1607 (1971).ADSCrossRefGoogle Scholar
  26. 26.
    R. Block, J. B. Suck, W. Freyland, F. Hensel and W. Gläser, in ‘Liquid Metals, 1976’, p.126 (Conference Series No. 30, The Institute of Physics, Bristol 1977 ).Google Scholar
  27. 27.
    G. Senatore and M.P. Tosi, Phys. Chem. Liquids (in the press). The optimized random-phase approximation was introduced for argon-like liquids by H. C. Andersen, D. Chandler and J. D. Weeks, J. Chem. Phys. 56, 3812 (1972).CrossRefGoogle Scholar
  28. 28.
    J. G. Kirkwood and F. Buff, J. Chem. Phys. 19, 774 (1951).MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    S. P. McAlister and R. Turner, J. Phys. F2, L51 (1972).ADSCrossRefGoogle Scholar
  30. 30.
    A. B. Bhatia, W. H. Hargrove and N. H. March, J. Phys. C6, 621 (1973).ADSGoogle Scholar
  31. 31.
    N. H. March, M.P. Tosi and A. B. Bhatia, J. Phys. C6, L59 (1973).ADSGoogle Scholar
  32. 32.
    J. Baur, K. Maschke and A. Baldereschi, to be published.Google Scholar
  33. 33.
    A. R. Miedema, F. R. de Boer and P. F. de Châtel, J. Phys. F3, 1558 (1973); A. R. Miedema, P. F. de Châtel and F. R. de Boer, Physica 100B, 1 (1980).ADSGoogle Scholar
  34. 34.
    M. P. Iniguez and J. A. Alonso, to be published.Google Scholar
  35. 35.
    J. A. Alonso and N. H. March, Phys. Chem. Liquids (in the press).Google Scholar
  36. 36.
    B. P. Alblas and W. van der Lugt, J. Phys. F10, 531 (1980).ADSCrossRefGoogle Scholar
  37. 37.
    For general reviews see M. A. Bredig, in ‘Molten Salt Chemistry’, p.367 (edited by M. Blander; Interscience, New York 1964); J. D. Corbett, in ‘Fused Salts’, p.341 (edited by B. Sundheim; McGraw-Hill, New York 1964 ).Google Scholar
  38. 38.
    G. P. Flynn, Phys. Rev. B9, 1984 (1974).ADSCrossRefGoogle Scholar
  39. 39.
    H. R. Bronstein, A.S. Dworkin and M.A. Bredig, J. Chem. Phys. 37, 677 (1962) and other references given therein.ADSCrossRefGoogle Scholar
  40. 40.
    G. Senatore, M. P. Tosi and P. V. Giaquinta, Physica (in the press).Google Scholar
  41. 41.
    I. Katz and S. A. Rice, J. Amer. Chem. Soc. 94, 4874 (1972); see also P. J. Durham and D. A. Greenwood, Phil. Mag. 33, 427 (1976).Google Scholar
  42. 42.
    N. H. Nachtrieb, Adv. Chem. Phys. 31, 465 (1975) and references given therein.CrossRefGoogle Scholar
  43. 43.
    G, Senatore, M. Parrinello and M. P. Tosi, Phil. Mag. B41, 595 (1980).CrossRefGoogle Scholar
  44. 44.
    J. F. Jal, Thèse présentée devant l’Université Claude Bernard - Lyon I (July 1981).Google Scholar
  45. 45.
    F. Hensel, Adv. Phys. 28, 555 (1979) and references given therein.ADSCrossRefGoogle Scholar
  46. 46.
    R. Dupree, D. J. Kirby, W. Freyland and W. W. Warren Jr, Phys. Rev. Lett. 45, 130 (1980).ADSCrossRefGoogle Scholar
  47. 47.
    W. Martin, W. Freyland, P. Lamparter and S. Steeb, Phys. Chem. Liquids 10 49, 61 and 77 (1980).Google Scholar
  48. 48.
    R. Evans and M. M. Telo da Gama, Phil. Mag. 41, 351 (1980).CrossRefGoogle Scholar
  49. 49.
    R. K. Sharma, G. Senatore and M. P. Tosi, to be published.Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • M. P. Tosi
    • 1
    • 2
  1. 1.GNSM-CNR, Instituto di Fisica Teorica dell ’UniversitàTriesteItaly
  2. 2.International Centre for Theoretical PhysicsTriesteItaly

Personalised recommendations