Damping of Phonons by Metal Particles Embedded in an Insulating Matrix
The energy spectrum of electrons confined to small region in space becomes discrete due to the quantum-size effect. The problem associated with the observation of such features has been receiving considerable attention using submicron metal particles, particularly from light scattering, magnetic susceptibility, and specific heat. In this paper we point out that such characteristics can be observed through the damping of phonons by metal particles embedded in an insulating matrix. The mean-level spacing ̄δ depends on the size of particles. For example, ̄δ can be estimated to be about 1K for 100A metal particles using the relation ̄δ = 4Ef/3N, where N and Ef are the number of electrons and the Fermi energy of metal particle; i.e., N ∿ 10 and Ef ∿ 104 K for a particle with diameter 100A. It should be emphasized here that the level spacings are distributed for an assembly of metal particles owing to different shapes and impurities. The physical quantities must be averaged by the distribution function P(δ) which should be determined by the random matrix theory. It will be shown in this paper that the remarkable property of energy spectrum of metal particles; i.e., quantum-size effect, can be observable through the frequency and the temperature dependence of the attenuation and the velocity dispersion of phonons. Hereafter a system of units is used in which kB = <Inline>1</Inline> = 1.
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