Advertisement

Pair Potentials in Metals and Alloys: Order, Stability, and Dynamics

  • J. Hafner
Part of the Physics of Solids and Liquids book series (PSLI)

Abstract

A full understanding of the physics of metallic bonding, including the energy, structure, and dynamics of perfect crystals, of defects such as substitutional impurities, vacancies, etc., of liquids and liquid mixtures, and finally of metastable phases such as glasses, requires the solution of the Schrödinger equation for 1023 electrons, all interacting with one another and with the positive ions. For a perfect crystal, Bloch’s theorem allows us to solve the equation only in one unit cell, and the electron—electron interaction problem may be greatly simplified by introducing the local-density approximation assuming that the exchange correlation potential is determined by the local electron density.

Keywords

Amorphous Alloy Volume Energy Pair Potential Pair Correlation Function Dynamic Structure Factor 
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.
    For a detailed discussion of the Born-Oppenheimer approximation see, e.g., G. V. Chester, Adv. Phys. 10, 357 (1961).CrossRefGoogle Scholar
  2. 2.
    W. Kohn and L. Sham, Phys. Rev. A 140 1133 (1965); for a discussion of the connection between the local density approximation and pseudopotential perturbation theory, see Hafner“ and Hafner and Eschrig.”Google Scholar
  3. 3.
    The first to invent the pseudopotential technique appears to be H. Hellmann, Acta Physico-Chimica URSS 1, 913 (1935); 4, 225 (1936).Google Scholar
  4. 4.
    V. Heine, D. Weaire, and M. H. Cohen, in: Solid State Physics, Vol. 24, Academic Press, New York (1971).Google Scholar
  5. 5.
    For a general review see E. G. Brovman and Yu. M. Kagan, in: Dynamical Properties of Solids (A. A. Maradudin and G. K. Horton, eds.), Vol. 1, North-Holland, Amsterdam (1974).Google Scholar
  6. 6.
    The second-order expansion was first given by M. H. Cohen, Phys. Rev. 130, 1301 (1963), an explicit form of the third-order expansion has been presented by P. Lloyd and C. A. Sholl, J. Phys. C 1, 1620 (1968), and an approximate form of the fourth-order term has been given by J. Hammerberg and N. W. Ashcroft, Phys. Rev. B 9, 409 (1974).CrossRefGoogle Scholar
  7. 7.
    M. W. Finnis, J. Phys. F 4, 1465 (1974).Google Scholar
  8. 8.
    D. Pines and Ph. Nozières, Elementary Excitations in Solids, Benjamin, New York (1962).Google Scholar
  9. 9.
    J. C. Kimball, Phys. Rev. A 7, 1648 (1973).CrossRefGoogle Scholar
  10. 10.
    D. J. W. Geldart and R. Taylor, Can J. Phys. 48, 167 (1970).CrossRefGoogle Scholar
  11. 11.
    P. Vashishta and K. S. Singwi, Phys. Rev. B 6, 875 (1972).CrossRefGoogle Scholar
  12. 12.
    S. Ichimaru and K. Utsumi, Phys. Rev. B 24, 7385. S. Ichimaru, Rev. Mod. Phys. 54, 1017 (1982).CrossRefGoogle Scholar
  13. 13.
    J. M. Luttinger and J. C. Ward, Phys. Rev. 118, 1417 (1960).CrossRefGoogle Scholar
  14. 14.
    G. Solt, Phys. Rev. B 18, 720 (1978).CrossRefGoogle Scholar
  15. 15.
    J. Hafner and V. Heine, J. Phys. F 13, 2479 (1983).CrossRefGoogle Scholar
  16. 16.
    D. Pettifor, Physica Scripta T1, 26 (1982).CrossRefGoogle Scholar
  17. 17.
    W. A. Harrison, Pseudopotentials in the Theory of Metals, Benjamin, New York (1966).Google Scholar
  18. 18.
    M. H. Cohen and V. Heine, Phys. Rev. 122, 1821 (1961).CrossRefGoogle Scholar
  19. 19.
    J. Hafner, J. Phys. B 22, 351 (1975); 24, 41 (1976), J. Hafner and H. Eschrig, Phys. Status Solidi B 72, 179 (1976).Google Scholar
  20. 20.
    I. V. Abarenkov and V. Heine, Phil. Mag. 12, 529 (1965).CrossRefGoogle Scholar
  21. 21.
    L. Dagens, M. Rasolt, and R. Taylor, Phys. Rev. B 11, 2726 (1975). M. Rasolt and R. Taylor, Phys. Rev. B 11, 2717 (1975).CrossRefGoogle Scholar
  22. 22.
    D. R. Hamann, M. Schlüter, and C. Chiang, Phys. Rev. Lett. 43 1494 (1979). G. B. Bachelet, D. R. Hamann, and M. Schlüter, Phys. Rev. B 26 4199 (1982).Google Scholar
  23. 23.
    N. W. Ashcroft, Phys. Rev. Lett. 23, 48 (1966).Google Scholar
  24. 24.
    J. Hafner, J. Phys. F 6, 1243 (1976).CrossRefGoogle Scholar
  25. 25.
    N. Q. Lam, N. van Doan, L. Dagens, and Y. Adda, J. Phys. F 11, 2231 (1981).CrossRefGoogle Scholar
  26. 26.
    P. Beauchamp, R. Taylor, and V. Vitek, J. Phys. F 4, 2017 (1975).CrossRefGoogle Scholar
  27. 27.
    G. Grimvall, in: Ab Initio Calculations of Phonon Dispersion Relations ( J. T. Devreese, ed.), Plenum Press, New York (1982).Google Scholar
  28. 28.
    D. Pettifor, in: Atomistics of Fracture, Proc. NATO—ASI, Corsica (1981).Google Scholar
  29. 29.
    J. Hafner and G. Punz, J. Phys. F 13, 1393 (1983).CrossRefGoogle Scholar
  30. 30.
    C. L. Leung, J. Phys. F 9, 179 (1979).CrossRefGoogle Scholar
  31. 31.
    J. Hafner, Phys. Rev. B 15, 617 (1977); 19, 5094 (1979).Google Scholar
  32. 32.
    J. Hafner, Phys. Rev. B 21, 406 (1980).CrossRefGoogle Scholar
  33. 33.
    A. Blandin, in: Phase Stability in Metals and Alloys ( P. S. Rudman, J. Stringer, and R. I. Jaffee, eds.), McGraw-Hill Book Co., New York (1967).Google Scholar
  34. 34.
    W. H. Young, in: Liquid Metals 76 (R. Evans and D. A. Greenwood, eds.), p. 1, The Institute of Physics, Bristol (1977).Google Scholar
  35. 35.
    J. Hafner, Phys. Rev. A 16, 351 (1977).CrossRefGoogle Scholar
  36. 36.
    H. C. Andersen, D. Chandler, and J. D. Weeks, Adv. Chem. Phys. 34, 105 (1976).CrossRefGoogle Scholar
  37. 37.
    H. C. Andersen and D. Chandler, J. Chem. Phys. 53, 547 (1970); ibid. 57, 1918 (1972).Google Scholar
  38. 38.
    M. Ross, Phys. Rev. B 21, 3140 (1980).CrossRefGoogle Scholar
  39. 39.
    G. Kahl and J. Hafner, Phys. Chem. Liq. 12, 109 (1982).CrossRefGoogle Scholar
  40. 40.
    G. Kahl and J. Hafner, Phys. Rev. A 29, 3310 (1984).CrossRefGoogle Scholar
  41. 41.
    C. Regnault, J. P. Badiali, and M. Dupont, J. Phys. C 8, 603 (1980); Phys. Lett. A 74, 245 (1979).CrossRefGoogle Scholar
  42. 42.
    J. Hafner and G. Kahl, J. Phys. F 14, 2259 (1984).CrossRefGoogle Scholar
  43. 43.
    G. Jacucci and R. Taylor, J. Phys. F 11, 787 (1981).CrossRefGoogle Scholar
  44. 44.
    J. Hafner and F. Sommer, CALPHAD 1, 351 (1977).CrossRefGoogle Scholar
  45. 45.
    P. Chieux and H. Ruppersberg, J. Physique (Paris), 41, C8–145 (1980).Google Scholar
  46. 46.
    J. Hafner, in: Liquid Metals 76 (R. Evans and D. A. Greenwood, eds.), p. 107, The Institute of Physics, Bristol (1977).Google Scholar
  47. 47.
    R. Evans, A. Copestake, H. Ruppersberg, and W. Schirmacher, J. Phys. F 13, 1993 (1983); J. Hafner, A. Pasturel, and P. Hicter, J. Phys. F 14, 1137 (1984); ibid 14, 2279 (1984).Google Scholar
  48. 48.
    W. Ostwald, Z. Phys. Chem. 22, 289 (1897).Google Scholar
  49. 49.
    J. Hafner, in: Nuclear Methods in the Investigation of Metallic Glasses (U. Gonser, ed.), At. Energy Rev., Suppl. 1, 27 (1981).Google Scholar
  50. 50.
    J. Hafner, J. Phys. C 16, 5773 (1983).CrossRefGoogle Scholar
  51. 51.
    J. Hafner and L. von Heimendahl, Phys. Rev. Lett. 42, 386 (1979).CrossRefGoogle Scholar
  52. 52.
    J. Hafner, Phys. Rev. B 26, 678 (1983).CrossRefGoogle Scholar
  53. 53.
    J. Hafner, Phys. Rev. B 28, 1734 (1983).CrossRefGoogle Scholar
  54. 54.
    P. Häussler, W. H. Müller, and F. Baumann, Z. Phys. B 35, 67 (1979). P. Häussler and F. Baumann, Z. Phys. B 49, 303 (1983).Google Scholar
  55. 55.
    U. Mizutani, in: Proc. 4th Int. Conf. On Rapidly Quenched Metals ( T. Masumoto and K. Suzuki, eds.), p. 1279, The Japan Institute of Metals, Sendai (1982).Google Scholar
  56. 56.
    T. Mizoguchi, H. Narumi, N. Akutsu, N. Watanabe, N. Shiotani and M. Ito, J. Non-Cryst. Solids 61+62, 285 (1984).Google Scholar
  57. 57.
    E. Nassif, P. Lamparter, W. Speri, and S. Steeb, Z. Naturforsch., 38a, 142 (1983).Google Scholar
  58. 58.
    J. Hafner, in: Ab Initio Calculations of Phonon Dispersion Relations (J. T. Devreese, ed.), p. 151, Plenum Press, New York (1982).Google Scholar
  59. 59.
    J. Hafner, J. Phys. C 14, L287 (1981).CrossRefGoogle Scholar
  60. 60.
    J. B. Suck, H. Rudin, H. J. Güntherodt, and H. Beck, J. Phys. C 14, 2305 (1981); J. Phys. F 11, 1375 (1981); Phys. Rev. Lett. 50, 49 (1983).CrossRefGoogle Scholar
  61. 61.
    J. B. Suck and H. Rudin, in: Glassy Metals II (J. J. Güntherodt and H. Beck, eds.), Topics in Applied Physics, Vol. 53, Springer-Verlag, Berlin-Heidelberg (1983), p. 217.Google Scholar
  62. 62.
    D. G. Pettifor and M. A. Ward, Sol. State Comm. 49, 291 (1984).CrossRefGoogle Scholar
  63. 63.
    J. Hafner and V. Heine, J. Phys. F,in press.Google Scholar
  64. 64.
    J. Hafner and G. Punz, Phys. Rev. B 30, 7336 (1984).CrossRefGoogle Scholar
  65. 65.
    G. Punz and J. Hafner, Z. Phys. B,in press.Google Scholar
  66. 66.
    T. Ohba, Y. Kitano, and Y. Komura, Acta Cryst. C 40, 1 (1984).CrossRefGoogle Scholar
  67. 67.
    J. Hafner, J. Phys. F,in press.Google Scholar
  68. 68.
    N. E. Christensen, Phys. Rev. B, in press.Google Scholar
  69. 69.
    J. Hafner and W. Weber, Sol. State Comm.,in press.Google Scholar
  70. 70.
    G. Jacucci, M. Ronchetti, and W. Schirmacher, in Neutron Physics Today and Tomorrow (Oxford, 1984 ).Google Scholar
  71. 71.
    A. Pasturel and J. Hafner, Phys. Rev. B,in press.Google Scholar
  72. 72.
    G. Kahl and J. Hafner, J. Phys. F,in press.Google Scholar
  73. 73.
    J. Hafner, in Amorphous Metals and Nonequilibrium Processing, ed. by M. von Allmen (Les Editions de physique, Paris 1984 ), p. 219.Google Scholar
  74. 74.
    J. Hafner, Proc. 5th Internat. Conference on Rapidly Quenched Metals,Würzburg 1984, J. Noncryst. Sol. 69 (in press).Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • J. Hafner
    • 1
    • 2
  1. 1.Institut für Theoretische PhysikTechnische Universität WienWienAustria
  2. 2.Laboratoire de Thermodynamique et Physico-Chimie MétallurgiquesDomaine UniversitaireSaint Martin d’HèresFrance

Personalised recommendations