Sound Vibrations in Ionic Crystal Taking Electric Field Correlations into Account

Authors

  • A. A. Stupka Oles Honchar Dnipropetrovsk National University

DOI:

https://doi.org/10.15407/ujpe58.12.1156

Keywords:

sound vibrations, electric field correlation, Euler equation

Abstract

Small vibrations in a solid insulator in the presence of a self-consistent electric field with the first strength moment at the equilibrium equal to zero and the second one different from zero have been considered. A new variable, the second moment of electric field strength, was introduced into the Euler equation, and a temporal equation for this variable was derived on the basis of Maxwell equations in the hydrodynamic approximation. A wave equation was obtained, and its solutions – two transverse and one longitudinal sound vibration branches – are found. The transverse sound velocity is calculated; the results obtained correspond to those calculated using the shear modulus to an accuracy of about 10%.

References

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A.A. Stupka, Magnetohydrodynamics 46, No. 2, 137 (2010).

L.D. Landau and E.M. Lifshitz, Fluid Mechanics (Pergamon Press, Oxford, 1993).

N.W. Ashcroft and N.D. Mermin, Solid State Physics (Saunders College, Philadelphia, PA, 1976).

I.N. Frantsevich, F.F. Voronov, and S.A. Bakuta, Elastic Constants and Elastic Moduli of Metals and Nonmetals (Naukova Dumka, Kiev, 1982) (in Russian).

Published

2018-10-11

How to Cite

Stupka, A. A. (2018). Sound Vibrations in Ionic Crystal Taking Electric Field Correlations into Account. Ukrainian Journal of Physics, 58(12), 1156. https://doi.org/10.15407/ujpe58.12.1156

Issue

Section

Solid matter