Local vibrational modes in crystal lattices with a simply connected region of the quasi-continuous phonon spectrum

A. V. Kotlyar*, S. B. Feodosyev

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

It is shown that the use of the mode classification adopted in the Jacobi matrix method and which is the most natural one for describing localized states leads to extremely rapid convergence of the Green functions for frequencies lying outside the quasi-continuum band of the crystal. This has made it possible to obtain rather general analytical expressions for the conditions of formation and the characteristics of local modes due to the presence of light impurity atoms in crystal lattices having a simply connected region of the quasi-continuous phonon spectrum. The accuracy with which the frequencies and intensities of the local modes are determined using these expressions is illustrated for examples of light substitutional impurities (isotopic and weakly coupled) and close-packed structures (fcc and hcp) and also isolated pairs of isotopic impurities in an fcc crystal lattice. In particular, the results permit simple and extremely accurate evaluation of the parameters of the host lattice and defect from the known values of the local frequencies.

Original languageEnglish
Pages (from-to)256-269
Number of pages14
JournalLow Temperature Physics
Volume32
Issue number3
DOIs
Publication statusPublished - 7 Jul 2006

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crystal lattices
vibration mode
Jacobi matrix method
impurities
Green's functions
continuums
evaluation
defects
crystals
atoms

Bibliographical note

Copyright © 2006 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Low Temperature Physics 32, 256 (2006) and may be found at https://doi.org/10.1063/1.2178484

Cite this

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abstract = "It is shown that the use of the mode classification adopted in the Jacobi matrix method and which is the most natural one for describing localized states leads to extremely rapid convergence of the Green functions for frequencies lying outside the quasi-continuum band of the crystal. This has made it possible to obtain rather general analytical expressions for the conditions of formation and the characteristics of local modes due to the presence of light impurity atoms in crystal lattices having a simply connected region of the quasi-continuous phonon spectrum. The accuracy with which the frequencies and intensities of the local modes are determined using these expressions is illustrated for examples of light substitutional impurities (isotopic and weakly coupled) and close-packed structures (fcc and hcp) and also isolated pairs of isotopic impurities in an fcc crystal lattice. In particular, the results permit simple and extremely accurate evaluation of the parameters of the host lattice and defect from the known values of the local frequencies.",
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Local vibrational modes in crystal lattices with a simply connected region of the quasi-continuous phonon spectrum. / Kotlyar, A. V.; Feodosyev, S. B.

In: Low Temperature Physics, Vol. 32, No. 3, 07.07.2006, p. 256-269.

Research output: Contribution to journalArticle

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