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The Spectral Distribution of Acoustical Phonons in a Plate
Author(s) -
Iosilevskii Ya. A.
Publication year - 1974
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220640203
Subject(s) - isotropy , phonon , mean free path , function (biology) , distribution (mathematics) , physics , distribution function , expression (computer science) , surface (topology) , path (computing) , simple (philosophy) , stress (linguistics) , mathematical analysis , condensed matter physics , computational physics , molecular physics , optics , geometry , mathematics , quantum mechanics , scattering , philosophy , linguistics , epistemology , evolutionary biology , computer science , biology , programming language
Abstract A general expression is obtained for the spectral density, g(ω 2 ), of acoustical phonon states in the elastically isotropic plate of arbitrary thickness, d, with stress‐free boundaries using the Green‐function method. The cases are analysed where the phonon mean free path, l ph , is much larger and conversely much less than d. It is shown that the surface contribution to the thermodynamical values is additive at T ≫ πħc/kd (c is a characteristic velocity of sound) while the exact function g(02) is not additive for l ph ≫ d. In this case a simple analytical expression is found for the effective distribution which allows to calculate the surface contribution to the thermodynamical characteristics of the sample of arbitrary configuration.