Soviet Physics Journal

, Volume 22, Issue 11, pp 1196–1199 | Cite as

Use of natural coordinates in calculating particle oscillations in a crystal lattice

  • I. V. Rigina
  • A. A. Zaitsev
  • R. I. Podgaetskaya


On the basis of the classical theory of crystal-lattice oscillation and the theory of molecular oscillation, the problem of writing equations of motion for crystal-lattice oscillation, using the change in bond length and angles between bonds as the coordinates, is considered. General methods of taking into account translational symmetry in the force-constant and kinematic-coefficient matrices are determined, and the problem of eliminating unwanted coordinates is considered. Oscillations in a plane quadratic lattice are used to illustrate the method.


Bond Length Crystal Lattice Classical Theory Translational Symmetry Quadratic Lattice 


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Literature cited

  1. 1.
    L. A. Gribov, Theory of ER Polymer Spectra [in Russian], Nauka, Moscow (1977).Google Scholar
  2. 2.
    M. Born and Khuan Kun', Dynamic Crystal-Lattice Theory [Russian translation], IL, Moscow (1958).Google Scholar
  3. 3.
    M. V. Vol'kenshtein, M. A. El'yashevich, L. A. Gribov, and B. I. Stepanov, Molecular Oscillations [in Russian], Nauka, Moscow (1972).Google Scholar
  4. 4.
    L. S. Mayants, Theory and Calculation of Molecular Oscillation [in Russian], Izd. Akad. Nauk SSSR, Moscow (1960).Google Scholar
  5. 5.
    T. Shimanouchi, M. Tsuboi, and T. Migazawa, J. Chem. Phys.,35, 1597 (1961).Google Scholar
  6. 6.
    I. N. Godnev and I. V. Orlova, Opt. Spektrosk.,6, 583 (1959).Google Scholar
  7. 7.
    I. V. Rigina and I. N. Godnev, Opt. Spektrosk.,8, 171 (1960).Google Scholar
  8. 8.
    I. N. Godnev, A. A. Zaitsev, and L. V. Rigina, Opt. Spektrosk.,19, 874 (1965).Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • I. V. Rigina
    • 1
  • A. A. Zaitsev
    • 1
  • R. I. Podgaetskaya
    • 1
  1. 1.Siberian Technological InstituteUSSR

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