Advertisement

Quantum theory of Lattice Vibrations

  • R. Orbach
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 8)

Abstract

The quantum mechanical theory of lattice vibrations in solids is reviewed and summarized. The formalism is developed first in the classical manner, and the various symmetries of the normal mode eigenvalues are discussed. The transition to the quantum mechanical formalism is done by introducing operator forms for the appropriate physical (observable) quantities. As an extension of the quantum mechanical formalism, the thermodynamic properties of the lattice vibrations (entropy, free energy, etc.) are investigated. An extensive treatment of critical points in the phonon density of states is given; this includes a discussion of the so-called Van Hove singularities, and a cataloguing of the types of singularities involved. Finally, the lattice vibrational equation of state is formulated, and the effects of the boundary conditions on the frequency distribution are discussed.

Keywords

Saddle Point Quantum Theory Brillouin Zone Lattice Vibration Reciprocal Lattice 
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.
    E. W. Montroll, J. Chem. Phys. 11, 48l (1943).CrossRefGoogle Scholar
  2. 2.
    L. Van Hove, Phys. Rev. 84, 1189 (1953).CrossRefGoogle Scholar
  3. 3.
    G. H. Wannier, Elements of Solid State Theory, Cambridge University Press, London, 1959, p. 73.zbMATHGoogle Scholar
  4. 4.
    J. C. Phillips, Phys. Rev. 104, 1263 (1956);MathSciNetADSCrossRefGoogle Scholar
  5. 4a.
    J. C. Phillips, Phys. Rev. 105, 1933 (1957).ADSCrossRefGoogle Scholar
  6. 5.
    M. Arenstein, R.D. Hatcher and J. Neuberger, Phys. Rev. 131, 2087 (1963).ADSCrossRefGoogle Scholar
  7. 6.
    R. E. Peierls, Proc. National Institute of Science of India 20, 121 (1954).Google Scholar
  8. 7.
    For effects of finite size, see M. Hass, Phys. Rev. Lett. 13, 429 (1974).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1975

Authors and Affiliations

  • R. Orbach
    • 1
  1. 1.Department of PhysicsTel Aviv UniversityRamat Aviv, Tel AvivIsrael

Personalised recommendations