Advertisement

Computational Aspects of Anharmonic Lattice Dynamics

  • T. R. Koehler
Conference paper
Part of the The IBM Research Symposia Series book series (IRSS)

Abstract

One major subfield of lattice dynamics is concerned with the evaluation of the physical properties of a defectless or ideal crystal for which the adiabatic approximation should be valid. In this approximation one assumes that the solid is well modeled by a collection of atoms which interact through an interatomic potential and that electronic effects, except as they contribute to the potential, are negligible. This approximation is appropriate for insulating crystals and should be especially good for the solid isotopes of helium, commonly called the quantum crystals, and the rare gas solids. In practice, it is also found to work even for the lattice dynamics of metals.

Keywords

Brillouin Zone Lattice Dynamic Computational Aspect Adiabatic Approximation Solid Helium 
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.
    HA treats effects caused by changes of the lattice constant as perturbations whereas QHA uses a different set of bare quantities at each lattice constant. Since the latter approach only requires the change of one data element in a computer program, we see little need to consider the former approach at all. Thus, in Section III what could be called SCQHA is called SCHA.Google Scholar
  2. 2.
    M. Born and K. Huang, Dynamical Theory of Crystal Lattices. (Oxford University Press, London, 1954 ).Google Scholar
  3. 3.
    A. A. Maradudin, E. W. Montroll and G. H. Weiss, Solid State Physics (ed. by F. Seitz and D. Turnbull) (Academic Press, New York, 1963 ), Suppl. 3.Google Scholar
  4. 4.
    A. A. Maradudin, P. A. Flinn and R. A. Coldwell-Horsfull, Ann. Phys. (N.Y.) 15, 337 (1961).ADSMATHCrossRefGoogle Scholar
  5. 5.
    R. A. Cowley, Advan. Phys. 12, 421 (1963).ADSCrossRefGoogle Scholar
  6. 6.
    N. R. Werthamer, Phys. Rev. A2, 2050 (1970).ADSCrossRefGoogle Scholar
  7. 7.
    R. A. Cowley, Rept. Progr. Phys. 31, 123 (1968).ADSCrossRefGoogle Scholar
  8. 8.
    M. L. Klein, G. K. Horton and J. L. Feldman, Phys. Rev. 184, 968 (1969).ADSCrossRefGoogle Scholar
  9. 9.
    W.J.L. Buyers and R. A. Cowley, Phys. Rev. 180, 755 (1969).ADSCrossRefGoogle Scholar
  10. 10.
    T. Högberg and R. Sandström, Phys. Stat. Solidi 33, 169 (1969); T. R. Koehler, N. S. Gillis and D. C. Wallace, Phys. Rev. B1, 4521 (1970); and T. R. Koehler and N. S. Gillis, Phys. Rev. B3, 3568 (1971).Google Scholar
  11. 11.
    M. Born, Fest. d. Akad. Wiss. Gottingen (1951). A translation of this article has been issued as Bell Laboratories TR.70-14.Google Scholar
  12. 12.
    D. J. Hooton, Phil. Mag. 46, 422 and 433 (1955).Google Scholar
  13. 13.
    The appropriate references can be found in Ref. 14 and 15. Of these two, Ref. 14 has the simplest exposition of the theory.Google Scholar
  14. 14.
    N. R. Werthamer, Am. J. Phys. 37, 763 (1969).ADSCrossRefGoogle Scholar
  15. 15.
    N. R. Werthamer, Phys. Rev. B1, 572 (1970).ADSCrossRefGoogle Scholar
  16. 16.
    N. S. Gillis, N. R. Werthamer and T. R. Koehler, Phys. Rev. 165, 951 (1968).ADSCrossRefGoogle Scholar
  17. 17.
    T. R. Koehler, Phys. Rev. 165, 942 (1968).ADSCrossRefGoogle Scholar
  18. 18.
    T. R. Koehler, Phys. Rev. 144, 789 (1966).ADSCrossRefGoogle Scholar
  19. 19.
    T. R. Koehler, Phys. Rev. Letters 17, 589 (1966).ADSCrossRefGoogle Scholar
  20. 20.
    M. L. Klein, V. V. Goldman and G. K. Horton, J. Phys. Chem. Solids 31, 2441 (1970). References to other calculations by these authors may be found in this reference.Google Scholar
  21. 21.
    T. R. Koehler, unpublished.Google Scholar
  22. 22.
    F. W. de Wette and B.R.A. Nijboer, Phys. Letters 18, 19 (1965).Google Scholar
  23. 23.
    T. R. Koehler and N. R. Werthamer, Phys. Rev. A2074 (1971); and P. Gillissen and W. Biem, Z. Phys. 242, 250 (1971).CrossRefGoogle Scholar
  24. 24.
    T. R. Koehler and N. R. Werthamer, to be published.Google Scholar
  25. 25.
    H. R. Glyde and F. C. Khanna, to be published.Google Scholar
  26. 26.
    B. H. Brandow, Phys. Rev. A4, 422 (1971).ADSGoogle Scholar
  27. 27.
    R. A. Guyer in Solid State Physics, Vol. 23 (ed. by F. Seitz D. Turnball and H. Ehrenreich) (Academic Press, New York, 1969 ).Google Scholar
  28. 28.
    N. S. Gillis and T. R. Koehler, Phys. Rev. to be published.Google Scholar
  29. 29.
    T. R. Koehler and R. L. Gray, Bull. Am. Phys. Soc. 16, 439 (1971).Google Scholar
  30. 30.
    R. C. Shukla and E. R. Cowley, Phys. Rev. B3, 4055 (1971).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1972

Authors and Affiliations

  • T. R. Koehler
    • 1
  1. 1.IBM Research LaboratorySan JoseUSA

Personalised recommendations