Advertisement

Phonon Dispersion Relations

Part of the The IBM Research Symposia Series book series (IRSS)

Abstract

The understanding of the basic properties of phonons has been increased very much during the last decade mainly due to inelastic neutron scattering. Successful models have been developed which allow a satisfactory description of simple insulators and metals with a few parameters.1 Difficulties arise with crystals of highly polarizable ions and such of low symmetry. In addition, the explanation of the model parameters on a microscopic basis2 is still to a large extent an open problem. This holds even more for phonon-determined crystal properties like infra-red absorption etc. There exist at the present time strong efforts to explain all these effects by rigorous quantum-mechanical treatments.

Keywords

Shell Model Ionic Crystal Solid State Phys Inelastic Neutron Scattering Dynamical Matrix 
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. 1a.
    A.A. Maradudin, E.W. Montroll and G.H. Weiss, Solid State Phys. Suppl. 3, 1963Google Scholar
  2. 1b.
    W. Cochran and R.A. Cowley, Handbuch der Physik XXV/2a, S9, 1967Google Scholar
  3. 1c.
    W. Ludwig, Springer Tracts in Mod.Phys. 43, 1967Google Scholar
  4. 1d.
    W. Cochran, Critical Reviews in Solid State Sciences 2, 1 (1971)CrossRefGoogle Scholar
  5. 4e.
    S.K. Joshi and A.K. Rajagopal, Solid State Phys. 22, 159 (1969)CrossRefGoogle Scholar
  6. 2.
    A condensed review has been given by L.J. Sham in: The Simon Frazer Univ.Lect. 2, 143 (1969)Google Scholar
  7. 3.
    M. Born and K. Huang, Dynamical Theory of Crystal Lattices, 1954Google Scholar
  8. 4.
    E.G. Brovman and Yu.Kagan, JETP 52, 557 (1957)Google Scholar
  9. 5.
    D. Sherrington, to be publishedGoogle Scholar
  10. 6.
    P.E. Choquard, The Anharmonic Crystal, New York 1967 see also the paper in this sympos. by R.A. CowleyGoogle Scholar
  11. 7.
    B. Leigh, B. Szigeti and V.Tewary, Proc. Roy. Soc., A320, 505 (1971)ADSGoogle Scholar
  12. 8.
    E.W. Kellermann, Phil. Trans. Roy. Soc. A238, 513 (1940)ADSMATHCrossRefGoogle Scholar
  13. 9.
    B.G. Dick and A.W. Overhauser, Phys. Rev. 112, 90 (1958)ADSCrossRefGoogle Scholar
  14. 10.
    R.A. Cowley, W. Cochran, B.N. Brockhouse and A.D.B. Woods, Phys. Rev. 131, 1030 (1963)ADSCrossRefGoogle Scholar
  15. 11.
    J.G. Traylor, H.G. Smith, R.M. Nicklow and M.K. Wilkinson, Phys. Rev. B 3, 3457 (1971)ADSCrossRefGoogle Scholar
  16. 12.
    M. Lax, Lattice Dynamics, Pergamon Press, Oxford, 179, (1965)Google Scholar
  17. 13.
    U. Schröder, Solid State Commun. 4, 347 (1966) V. Nüsslein and U. Schröder, phys. stat. sol. 21, 309 (1967)CrossRefGoogle Scholar
  18. 14.
    U. Schröder, private communication; G. Mahler and P. Engelhardt, phys. stat. sol. (b) 45, 543 (1971)Google Scholar
  19. 15.
    J.R. Hardy, Phil. Mag. 4, 1278 (1959)ADSCrossRefGoogle Scholar
  20. 16.
    M.J.L. Sangster, G. Peckham, and D.H. Saunderson, J. Phys. C. (Solid State Phys.) 3, 1026 (1970)ADSCrossRefGoogle Scholar
  21. 17.
    J.S. Melvin, J.D. Pirie, and T. Smith, Phys. Rev., 175, 1082 (1968)ADSCrossRefGoogle Scholar
  22. 17a.
    S.O. Lundquist, Ark. Fysik, 6, 25 (1952), 9, 435 (1955), and 12, 263 (1957)Google Scholar
  23. 18.
    P.O. Löwdin, Thesis, Uppsala 1948; Adv. Phys. 5, 1 (1956)Google Scholar
  24. 19.
    K. Fischer, H. Bilz and W. Weber, to be publishedGoogle Scholar
  25. 20.
    R.H. Lyddane, R.G. Sachs, and E. Teller, Phys. Rev. 59, 673 (1941)ADSMATHCrossRefGoogle Scholar
  26. 21.
    For a discussion see B. Szigeti, Enrico Fermi Summerschool, VARENNA, 1971Google Scholar
  27. 22.
    B. Szigeti, Trans. Faraday Soc., 45, 155 (1949); Proc. Roy. Soc., A204, 51 (1950)MATHCrossRefGoogle Scholar
  28. 23.
    B.G. Dick, Phys. Rev. 129, 1583 (1962)ADSCrossRefGoogle Scholar
  29. 24.
    B. Gliss, R. Zeyher and H. Bilz, phys. stat, sol. 44, 747 (1971)ADSCrossRefGoogle Scholar
  30. 25.
    R. Zeyher, phys. stat. sol., to be publishedGoogle Scholar
  31. 26.
    M.P. Verma and R.K. Singh, phys. stat. sol. 33, 769 (1969) R.K. Singh and M.O. Verma, phys stat sol. 36, 335 (1969) and 38, 851 (1970)Google Scholar
  32. 27.
    P.R. Vijayaraghavan, R. M. Nicklow, H.G. Smith and M.K. Wilkinson, Phys. Ree. B 40, 4819 (1970)ADSCrossRefGoogle Scholar
  33. 28.
    G. Raunio and S. Rolandson, phys. stat. sol. 40, 749 (1970)ADSCrossRefGoogle Scholar
  34. 29.
    J.C. Phillips, Rev. Mod. Phys. 42, 317 (1970)ADSCrossRefGoogle Scholar
  35. 30.
    G. Dolling, R.A. Cowley, C. Schittenhelm, and I.M. Thorson, Phys. Rev., 147, 577, 1966ADSCrossRefGoogle Scholar
  36. 31.
    W. Kress, to be published in phys stat sol. (b), 49 (1972)Google Scholar
  37. 32.
    R. Martin, Phys. Bev. Lett. 21, 536 (1968)ADSCrossRefGoogle Scholar
  38. 33.
    A.W. Solbrig, Jr., J. Phys. Chem. Solids 32, 1761 (1971)ADSCrossRefGoogle Scholar
  39. 34.
    R. Brout,Phys. Rev. 113, 43 (1958)Google Scholar
  40. 35.
    S.K. Sinha, R.P. Gupta and D.L. Price, Phys. Rev. Lett. 26, 1324 (1971)ADSCrossRefGoogle Scholar
  41. 36.
    H.G. Smith and W. Gläser, Phys. Rev. Letters 25, 1611 (1970)ADSCrossRefGoogle Scholar
  42. 37.
    W. Weber, H. Bilz and U. Schröder, to be publishedGoogle Scholar
  43. 38.
    H. Jex, phys. stat. sol. (b), 45, 343 (1971)ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1972

Authors and Affiliations

  • H. Bilz
    • 1
  1. 1.Physik-DepartmentTechnische Universität MünchenGarching b. MünchenGermany

Personalised recommendations