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The direct proportionality relation between the boson peak maximum in glasses, ω b , and the IoffeRegel crossover frequency for phonons, ω d , is established. For several investigated materials ω b = (1.5 ± 0.1)ω d . At the frequency ω d the mean free path of the phonons l becomes equal to their wavelength because of strong resonant scattering on quasilocal harmonic oscillators. Above this frequency phonons cease to exist. We prove that the established correlation between ω b and ω d holds in the general case and is a direct consequence of bilinear coupling of quasilocal oscillators with the strain field.61. 43.Fs, 63.50+x, 78.30.Ly The properties of harmonic vibrational excitations in disordered media and glasses become now a very active topic of scientific research [1]. Contrary to the quite well established behavior of electrons in disordered conductors there is no consensus at all regarding the harmonic vibrations in ordinary glasses. The most common and challenging of their signatures is the so-called boson peak observed in numerous experiments in the low-frequency Raman and inelastic neutron scattering. The physical origin of the peak is however still a matter of great debates. The common view is that the solution of this problem is a corner-stone for our veritable understanding of glassy vibrational dynamics.The main discussion in the literature involves now the question whether the harmonic vibrations responsible for the boson peak are propagating plane waves (phonon like) [2] or localized because of disorder [3]. The third possibility, which we share in this paper, is that they are neither propagating waves nor localized but have a diffusive nature [4].For the solution of this crucial question quite powerful and expensive experimental techniques are now in use. First of all these are Raman experiments themselves. But since visible light due to energy and momentum conservation laws does not interact properly with sound-like excitations, one has to use two other possibilities, namely inelastic X-ray and neutron scattering.The main difficulty in the inelastic X-ray scattering experiments is the very high incident photon energy (≃ 20 KeV), and its relatively small change, of the order of 10 −7 . As a result, the "X-ray boson peak" is superimposed on the steep wings of strong elastic line in the forward direction. Therefore, a serious problem arises to correctly resolve it and answer the crucial question whether it changes with the momentum transfer.This difficulty explains why recently two independent groups using the same experimental setup but different fitting procedures have arrived to completely opposite conclusions about the propagating character of the excitations in vitreous SiO 2 at the boson peak range [2,3]. The situation with inelastic neutron Brillouin scattering (for small momentum transfer) is not much better.To solve this problem from our point of view it is necessary to separate the Brillouin (phonon) lines of the boson peak (as in the usual light scattering experiments). Then increasing...

Semiconducting crystalline materials that are poor conductors of heat are important as thermoelectric materials and for technological applications involving thermal management.

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