Interatomic Forces and Phonon Dispersion Curves

  • Peter Brüesch
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 34)

Abstract

Phonon dispersion curves ω(\(\vec q\)) can be measured by inelastic neutron scattering techniques; this important method will be discussed in [1.35]. The curves determined by experiments are mainly of interest because they provide chance of testing various models of interatomic forces. The forces between the atoms are governed by the electronic structure of the atoms involved, and in simple cases it is possible to derive force constants from “first principles” which are based on the electronic wave functions [4.1–5]. With the exception of some qualitative remarks about metals, we shall not discuss these microscopic models here but consider only certain phenomenological models for the interatomic forces. A good model should contain only a few, but physically meaningful, parameters.

Keywords

Entropy Graphite Argon Helium GaAs 

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References

  1. 4.1
    M.T. Yin, M.L. Cohen: Phys. Rev. Lett. 45, 1004 (1980)CrossRefADSGoogle Scholar
  2. 4.2
    P.E. Van Camp, V.E. Van Doren, J.T. Devreese: Phys. Rev. Lett. 42, 1224 (1979)CrossRefADSGoogle Scholar
  3. 4.3
    A. Baldereschi, K. Maschke: In Lattice Dynamics, ed. by M. Balkanski (Flammerion, Paris 1978) p.36; ibid. S.K. Sinha, p.7; ibid R. Zeyher, p.17Google Scholar
  4. 4.4
    H. Wendel, R.M. Martin: Phys. Rev. B19, 5251 (1979)ADSGoogle Scholar
  5. 4.5
    S.G. Louie, M.L. Cohen: Phys. Rev. B17, 3174 (1978)ADSGoogle Scholar
  6. 4.6
    J. Grindlay, R. Howard: In Lattice Dynamics, ed. by R.F. Wallis (Pergamon, New York 1965 ) p. 129Google Scholar
  7. 4.7
    Y. Fujii, N.A. Lurie, R. Pynn, G. Shirane: Phys. Rev. B10, 3647 (1974)ADSGoogle Scholar
  8. 4.8
    E.W. Kellermann: Phil. Trans. Roy. Soc. London A238, 513 (1940)Google Scholar
  9. 4.9
    A.A. Maradudin, E.W. Montroll, G.H. Weiss, I.P. Ipatova: p.200 of [3.20]Google Scholar
  10. 4.10
    W. Cochran: Crit. Rev. Solid State Sci. 2, 1 (1971)CrossRefGoogle Scholar
  11. 4.11
    W. Cochran, R.A. Cowley: Encyclopedia of Physics25/2a (Springer, Berlin, Heidelberg, New York 1967 ) p. 83Google Scholar
  12. 4.12
    B.G. Dick, Jr., A.W. Overhauser: Phys. Rev. 112, 90 (1958)Google Scholar
  13. 4.13
    W. Cochran: Phys. Rev. Lett. 2, 495 (1959)CrossRefADSGoogle Scholar
  14. 4.14
    W. Cochran. Phonons in Perfect Lattices and in Lattices with Point Imperfections, ed. by R.W.H. Stevenson (Oliver and Boyd, Edinburgh, London 1966 ) p. 64Google Scholar
  15. 4.15
    S.K. Sinha: Crit. Rev. Solid State Sci. (USA) 3, No. 3, 273 (1973)Google Scholar
  16. 4.16
    U. Schröder: Solid State Commun. 4, 347 (1966)CrossRefADSGoogle Scholar
  17. 4.17
    W. Weber: Phys. Rev. Lett. 33, 371 (1974)CrossRefADSGoogle Scholar
  18. W. Weber: Phys. Rev. 15, 4789 (1977)CrossRefADSGoogle Scholar
  19. 4.18
    K.C. Rustagi, W. Weber: Solid State Commun. 18, 673 (1976)Google Scholar
  20. 4.19
    E.B. Wilson, Jr., J.C. Decius, P.C. Cross: Molecular Vibrations(McGraw-Hill, New York, Toronto, London 1955 )Google Scholar
  21. 4.20
    G. Herzberg: Molecular Spectra and Molecular Structure: II. Infrared and Raman Spectra of Polyatomic Molecules(Van Nostrand, Princeton, NJ, New York 1945 )Google Scholar
  22. 4.21
    H.L. McMurry, A.W. Soibrig, J.K. Boyter, C. Noble: J. Phys. Chem. Solids 28, 2359 (1967)CrossRefADSGoogle Scholar
  23. 4.22
    J.C. Decius, R.M. Hexter: Molecular Vibrations in Crystals(McGraw-Hill, New York, London 1977 )Google Scholar
  24. 4.23
    G. Venkataraman, C. Sahni: Rev. Mod. Phys. 42, 409 (1970)CrossRefADSGoogle Scholar
  25. 4.24
    F. London, R. Eisenshitz: Z. Phys. 60, 491 (1930)CrossRefADSGoogle Scholar
  26. 4.25
    H. Margenau: Rev. Mod. Phys. 11, 1 (1939)CrossRefMATHADSGoogle Scholar
  27. 4.26
    Data from D.N. Batchelder, D.L. Losee, R.O. Simmons: Phys. Rev. 162, 767 (1967)CrossRefADSGoogle Scholar
  28. M.L. Klein, G.K. Horton, J.L. Feldmann: Phys. Rev. 184, 968 (1969)CrossRefADSGoogle Scholar
  29. E.R. Dobbs, G.O. Jones: Rep. Prog. Phys. 20, 516 (1957)Google Scholar
  30. 4.27
    N. Bernardes: Phys. Rev. 112, 1534 (1958)CrossRefADSGoogle Scholar
  31. 4.28
    J.S. Brown, G.K. Horton: Phys. Rev. Lett. 18, 647 (1967)CrossRefADSGoogle Scholar
  32. 4.29
    N.S. Gillis, N.R. Werthamer: Phys. Rev. 165, 951 (1968)CrossRefADSGoogle Scholar
  33. 4.30
    M.V. Bobetic, J.A. Barber: Phys. Rev. B2, 4169 (1970)ADSGoogle Scholar
  34. 4.31
    N.E. Massa, S.S. Mitra, J.F. Vetelino: Phys. Stat. Sol. (b) 94, 387 (1979)Google Scholar
  35. 4.32
    P.P. Ewald: Ann. Phys. (Lpz.) (4) 64, 253 (1921)CrossRefMATHGoogle Scholar
  36. 4.33
    W. Cochran: [4.6, p.75]Google Scholar
  37. 4.34
    C. Kittel: [3.1, Chap.12]Google Scholar
  38. 4.35
    C. Kittel: [3.1, Chap.3]Google Scholar
  39. 4.36
    M. Born, K. Huang: Dynamical Theory of Crystal Lattices(Oxford Univ. Press, London, New York 1954 ) p. 299MATHGoogle Scholar
  40. 4.37
    T.H.K. Barron: Phys. Rev. 123, 1995 (1961)CrossRefMATHADSGoogle Scholar
  41. A.A. Maradudin, G.H. Weiss: Phys. Rev. 123, 1968 (1961)CrossRefMATHADSMathSciNetGoogle Scholar
  42. 4.38
    A.A. Maradudin, E.W. Montroll, G.H. Weiss, I.P. Ipatova: [4.9,225]Google Scholar
  43. 4.39
    A.D.B. Woods, B.N. Brokhouse, R.A. Cowley, W. Cochran: Phys. Rev. 131, 1025 (1963)CrossRefADSGoogle Scholar
  44. R.A. Cowley, W. Cochran, B.N. Brockhouse, A.D.B. Woods: Phys. Rev. 131, 1030 (1963)CrossRefADSGoogle Scholar
  45. 4.40
    B. Szigeti: Proc. Roy. Soc. A204, 51 (1950)ADSGoogle Scholar
  46. 4.41
    M. Hass, B.W. Henvis: J. Phys. Chem. Solids 23, 1099 (1962)CrossRefADSGoogle Scholar
  47. W. Cochran: Nature 191, 60 (1961)CrossRefADSGoogle Scholar
  48. 4.42
    R.J. Nemanich, G. Lucovsky: Solid State Commun. 23, 117 (1977)Google Scholar
  49. 4.43
    R.H. Lyddane, R.G. Sachs, E. Teller: Phys. Rev. 59, 673 (1941)CrossRefMATHADSGoogle Scholar
  50. 4.44
    W. Cochran: Z. Kristallogr. 112, 465 (1959)CrossRefGoogle Scholar
  51. 4.45
    W. Cochran, R.A. Cowley: J. Phys. Chem. Solids 23, 447 (1962)CrossRefADSGoogle Scholar
  52. 4.46
    A.N. Basu, S. Sengupta: Phys. Status Solidi 29, 367 (1968)Google Scholar
  53. 4.47
    J.R. Hardy: Phil. Mag. 4, 1278 (1959)CrossRefADSGoogle Scholar
  54. J.R. Hardy: Phil. Mag. 5, 859 (1960)CrossRefADSGoogle Scholar
  55. J.R. Hardy: Phil. Mag. 6, 27 (1961)CrossRefADSGoogle Scholar
  56. 4.48
    J.R. Hardy: Phil. Mag. 7, 315 (1962)CrossRefMATHADSGoogle Scholar
  57. H.J.L. van der Valk, C. Haas: Phys. Stat. Sol. (b) 80, 321 (1977)Google Scholar
  58. A. Frey, R. Zeyher: Solid State Commun. 28, 435 (1978)Google Scholar
  59. 4.49
    G. Benedek, A. Frey: Phys. Rev. B21, 2482 (1980)ADSGoogle Scholar
  60. 4.50
    J.P. Walter, M.L. Cohen: Phys. Rev. B2, 1821 (1970)ADSGoogle Scholar
  61. 4.51
    J.C. Phillips: Covalent Bonding in Crystals, Molecules and Polymers(Univ. of Chicago Press, Chicago, London 1969); Bonds and Bands in Semiconductors(Academic Press, New York, London 1973 )Google Scholar
  62. 4.52
    R.M. Martin: Phys. Rev. 186, 871 (1969)CrossRefADSGoogle Scholar
  63. 4.53
    F.A. Johnson: Proc. Roy. Soc. London A339, 73 (1974)Google Scholar
  64. 4.54
    F.A. Johnson, K. Moore: Proc. Roy. Soc. London A339, 85 (1974)ADSGoogle Scholar
  65. 4.55
    R.G. Parr, R.F. Borkman: J. Chem. Phys. 49, 1055 (1968)CrossRefADSGoogle Scholar
  66. 4.56
    R.G. Parr, J.E. Brown: J. Chem. Phys. 49, 4849 (1968)CrossRefADSGoogle Scholar
  67. 4.57
    V.V. Walatka, Jr., M.M. Labes, J.H. Perlstein: Phys. Rev. Lett. 31, 1139 (1973)CrossRefADSGoogle Scholar
  68. 4.58
    M.A. Nusimovici, J.L. Birman: Phys. Rev. 156, 925 (1967)CrossRefADSGoogle Scholar
  69. 4.59
    L.A. Feldkamp, D.K. Steinmann, N. Vagelatos, J.S. King, G. Venkataraman: J. Phys. Chem. Solids 32, 1573 (1971)CrossRefADSGoogle Scholar
  70. 4.60
    H.C. Teh, B.N. Brockhouse: Phys. Rev. B3, 2733 (1971)ADSGoogle Scholar
  71. 4.61
    H. Jex: Solid State Commun. 9, 2057 (1971)CrossRefADSGoogle Scholar
  72. 4.62
    G.L. Squires: Inelastic Scattering of Neutrons in Solids and Liquids( International Atomic Energy Agency, Vienna 1963 )Google Scholar
  73. 4.63
    B.N. Brockhouse, T. Arase, G. Caglioti, K.R. Rao, A.D.B. Woods: Phys. Rev. 128, 1099 (1962)CrossRefADSGoogle Scholar
  74. 4.64
    W. Kohn: Phys. Rev. Lett. 2, 393 (1959)CrossRefADSGoogle Scholar
  75. 4.65
    C.B. Clark: Phys. Rev. 109, 1133 (1958)CrossRefMATHADSGoogle Scholar
  76. 4.66
    N.W. Ashcroft, N.D. Mermin: Solid State Physics (Holt, Rinehart, Winston 1976) Chaps.1,26Google Scholar
  77. 4.67
    W. Cochran: [4.14,Chap.2]Google Scholar
  78. 4.68
    J. Bardeen: Phys. Rev. 52, 688 (1937)CrossRefADSGoogle Scholar
  79. 4.69
    N.W. Ashcroft, N.D. Mermin: [4.66, Chap.17]Google Scholar
  80. 4.70
    D. Bohm, T. Stayer: Phys. Rev. 84, 836 (1950)CrossRefADSGoogle Scholar
  81. 4.71
    W.A. Harrison: In Phonons in Perfect Lattices and in Lattices with Point Imperfections, ed. by R.W.H. Stevenson (Oliver and Boyd, Edinburgh, London 1966 ) p. 73Google Scholar
  82. 4.72
    [2.11,p.278]Google Scholar
  83. 4.73
    A.P.P. Nicholson, D.J. Bacon: J. Phys. C (Solid State Phys.) 10, 2295 (1977)CrossRefADSGoogle Scholar
  84. 4.74
    R. Nicklov, N. Wakabayashi, H.G. Smith: Phys. Rev. B5, 4951 (1972)ADSGoogle Scholar
  85. 4.75
    J.C. Bowman, J.A. Krumhansl: J. Phys. Chem. Solids 6, 367 (1958)CrossRefADSGoogle Scholar
  86. 4.76
    K. Komatsu: J. Phys. Soc. Jpn. 10, 346 (1955)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Peter Brüesch
    • 1
    • 2
  1. 1.Brown Boveri Research CenterBaden-DättwilGermany
  2. 2.Ecole Polytechnique Fédéral de LausanneLausanneSwitzerland

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