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Current issue   Ukr. J. Phys. 2015, Vol. 60, N 6, p.528-537
https://doi.org/10.15407/ujpe60.06.0528   Paper

Stupka A.A.

Oles Honchar National University of Dnipropetrovsk (72, Gagarin Ave., Dnipropetrovsk 49050, Ukraine; e-mail: antonstupka@mail.ru)

Long-Wave Optical Vibrations in Diatomic Ionic Crystals

Section: Solid matter
Language: English

Abstract: Long-wave phonon-polaritons and longitudinal optical phonons have been considered as eigenwaves of the electromagnetic field in ionic crystals with two atoms per unit cell. The Kun Huang model is used to describe the sublattices of point charges vibrating with the frequency ω0. The dispersion laws for optical vibrations in crystals are generalized, by considering the thermal motion of charges. An additional longitudinal phonon with the frequency 2ω0 and two upper phonon-polaritons are found in the second-order approximation with respect to the ratio between the standard deviation and the wavelength.

Key words: ionic crystal, electromagnetic field; long-wave vibrations, phonon-polaritons, longitudinal optical phonons, harmonics.


  1. V.A. Volodin and V.A. Sachkov, Zh. Eksp. Teor. Fiz. 143, 100 (2013).
  2. V. Conti Nibali, G. D'Angelo, and M. Tarek, Phys. Rev. E 89, 050301(R) (2014).
  3. Xue-jin Zhang, Ran-qi Zhu, Jun Zhao, Yan-feng Chen, and Yong-yuan Zhu, Phys. Rev. B 69, 085118 (2004). CrossRef
  4. S.-O. Katterwe, H. Motzkau, A. Rydh, and V.M. Krasnov, Phys. Rev. B 83, 100510(R) (2011).
  5. E.A. Vinogradov, B.N. Mavrin, N.N. Novikova, and V.A. Yakovlev, Usp. Fiz. Nauk 179, 313 (2009). CrossRef
  6. K. Huang, Proc. Roy. Soc. A 208, 352 (1951). CrossRef
  7. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, 1958).
  8. A.F. Alexandrov, L.S. Bogdankevich, and A.A. Rukhadze, Principles of Plasma Electrodynamics (Springer, Berlin, 1984). CrossRef
  9. A.A. Stupka, Ukr. Fiz. Zh. 59, 793 (2014).
  10. B. Szigeti, Trans. Faraday Soc. 45, 155 (1949). CrossRef
  11. L.D. Landau and E.M. Lifshitz, Mechanics (Butterworth Heinemann, Oxford, 2001).
  12. A.S. Davydov, Solid State Theory (Academic Press, New York, 1980).
  13. A.I. Akhiezer and S.V. Peletminsky, Methods of Statistical Physics (Pergamon Press, New York, 1981).
  14. A. Sokolovsky and A. Stupka, in Proceedings of the 12-th International Conference on Mathematical Methods of Electromagnetic Theory (MMET'12) (Odesa, 2008), p. 262.
  15. A.G. Sitenko, Electromagnetic Fluctuations in Plasma (Academic Press, New York, 1967).
  16. Yu.L. Klimontovich, The Kinetic Theory of Electromagnetic Processes (Springer, Berlin. 1983).
  17. I.B. Bernstein, Phys. Rev. 109, 10 (1958). CrossRef
  18. R.A. Lyddane, R.G. Sachs, and E. Teller, Phys. Rev. 59, 673 (1941). CrossRef
  19. Ch. Kittel, Introduction to Solid State Physics (Wiley, New York, 1995).
  20. A.A. Stupka, Ukr. Fiz. Zh. 58, 865 (2013).
  21. R. Fitzpatrick, Introduction to Plasma Physics: A graduate level course [http://plasma.fisica.unimi.it/matplasmi/dispense_Fitz.pdf].
  22. E.M. Lifshitz and L.P. Pitaevskii, Physical Kinetics (Pergamon Press, London, 1979).