AB initio study of phonon spectra of solids

  • P. E. Van Camp
  • V. E. Van Doren
  • J. T. Devreese
II. Theoretical Approaches for Ordered Systems
Part of the Lecture Notes in Physics book series (LNP, volume 113)


In the dielectric screening approach, the phonon frequencies of a covalent crystal are calculated with the aid of the polarizability matrix. Instead of a direct summation over the conduction bands, the integrand of this matrix is expanded in a continued fraction. As a first approximation the second coefficient in the series, which is the ratio of the first to the zeroth moment, is treated as a constant and the higher moments are neglected. This method gives a description of the lattice dynamics based solely on the occupied one-electron states with the elimination of the unoccupied states.


Ground State Energy Phonon Dispersion Dynamical Matrix Reciprocal Lattice Vector Electron Charge Density 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Born, K. Huang, “Dynamical Theory of Crystal Lattices” (Oxford University Press, Oxford (1954))Google Scholar
  2. [2]
    P. Hohenberg, W. Kohn, Phys. Rev., 136, B864 (1964)Google Scholar
  3. [3]
    L.J. Sham, in “Dynamical Properties of Solids”, eds. G.K. Horton and A.A. Maradudin (North Holland, Amsterdam (1974)), vol. 1, p. 301Google Scholar
  4. [3a]
    F.A. Johnson, Proc. Roy. Soc., A310, 79 (1969); A310, 89 (1969); A310, 101 (1969)Google Scholar
  5. [4]
    H. Ehrenreich, M.H. Cohen, Phys. Rev., 115, 786 (1959)Google Scholar
  6. [5]
    R.G. Gordon, Journ. Math. Phys., 9, 655 (1968)Google Scholar
  7. [6]
    P.E. Van Camp, V.E. Van Doren, J.T. Devreese, Inst. Phys. Conf. Ser., 43, 685 (1979)Google Scholar
  8. [6a]
    P.E. Van Camp, V.E. Van Doren, J.T. Devreese, Phys. Rev. Lett., 42, 1224 (1979)Google Scholar
  9. [7]
    K. Shinco, I. Ohkoshi, Journ. Phys. Soc. Jap., 42, 1423 (1977)Google Scholar
  10. [8]
    M.L. Cohen, T.K. Bergstresser, Phys. Rev., 141, 789 (1966)Google Scholar
  11. [9]
    G. Dolling, in “Symposium on Inelastic Scattering of Neutrons in Solids and Liquids” (IAEA, Vienna, Austria, 1963), vol.2, p. 37Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • P. E. Van Camp
    • 1
  • V. E. Van Doren
    • 1
  • J. T. Devreese
    • 1
    • 2
  1. 1.Rijksuniversitair Centrum AntwerpenAntwerpenBelgium
  2. 2.Universitaire Instelling AntwerpenWilrijkBelgium

Personalised recommendations