Geodesic
Long-waves principle and phonon spectra of cubic crystal lattices
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 1 (2009), pp. 97-104 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the article the authors obtain and solve a system of equations, describing vibrations of the monoatomic body-centered and face-centered cubic lattices during the force interaction possessing van der Waals nature. They demonstrate that the system allows implement of the long waves principle according to which the equations of crystal lattice vibrations are to resolve themselves into the equations of elastic deformation wave propagation in a crystal as in the continuous medium. The comparison of the received and classical equations allows to show the force constants of the dynamical model in terms of elastic constants of a given substance, and to calculate the phonon spectra of some body-centered and face-centered cubic lattices crystals.
Keywords: dynamic model, crystal lattice, elastic constants, dispersion curves, phonon spectrum.
Mots-clés : dipole, dispersion relations 
@article{VYURM_2009_1_a16,
     author = {V. E. Kholodovsky and I. O. Machikhina},
     title = {Long-waves principle and phonon spectra of cubic crystal lattices},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {97--104},
     year = {2009},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2009_1_a16/}
}
TY  - JOUR
AU  - V. E. Kholodovsky
AU  - I. O. Machikhina
TI  - Long-waves principle and phonon spectra of cubic crystal lattices
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
PY  - 2009
SP  - 97
EP  - 104
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VYURM_2009_1_a16/
LA  - ru
ID  - VYURM_2009_1_a16
ER  - 
%0 Journal Article
%A V. E. Kholodovsky
%A I. O. Machikhina
%T Long-waves principle and phonon spectra of cubic crystal lattices
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
%D 2009
%P 97-104
%N 1
%U http://geodesic.mathdoc.fr/item/VYURM_2009_1_a16/
%G ru
%F VYURM_2009_1_a16
V. E. Kholodovsky; I. O. Machikhina. Long-waves principle and phonon spectra of cubic crystal lattices. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 1 (2009), pp. 97-104. http://geodesic.mathdoc.fr/item/VYURM_2009_1_a16/

[1] V. E. Kholodovskii, I. O. Machikhina, E. A. Kulchenkov, “Dispersionnye sootnosheniya dlya kubicheskikh kristallicheskikh reshetok v modeli dipol-dipolnykh vzaimodeistvii”, Vestnik YuUrGU. Seriya «Matematika, fizika, khimiya», 10(143):12 (2009), 92–99

[2] V. E. Kholodovskii, I. O. Sergeeva, “Potok energii i sila reaktsii na izluchenie podvizhnogo dipolya”, Vestnik BGU. Seriya «Estestvennye i tochnye nauki», 4(273):12 (2005), 266–268

[3] M. Born, K. Khuan, Dinamicheskaya teoriya kristallicheskikh reshetok, Inostr. literatura, M., 1958, 488 pp.

[4] Ch. Kittel, Vvedenie v fiziku tverdogo tela, Nauka, M., 1978, 792 pp.

[5] G. V. Samsonov (red.), Svoistva elementov, Spravochnik, v. 1, Fizicheskie svoistva, Metallurgiya, M., 1976, 600 pp.