Do high-frequency acoustic vibrations propagate in structurally disordered solids?

Glasses exhibit well known and apparently universal anomalies in their thermal properties. Their excess specific heat poses the question of the nature of the modes that contribute to the density of vibrational states and to the plateau in their thermal conductivity of the propagation of acoustic phonons. The vibrational modes involved in both anomalies must have frequencies well above 100 GHz, reaching into the terahertz range. This is a difficult region for direct spectroscopic observation of acoustic excitations. New small-angle inelastic neutron and inelastic X-ray scattering spectroscopies now give access to the structure factor S(Q, ω) in this region. Recent results on vitreous silica are discussed in the light of other well established spectroscopic information. We show in some detail that an elementary model, which consists in fitting inelastic spectra simply with a damped harmonic oscillator response, gives the impression that a mode continues to exist at frequencies ω above the strong phonon-scattering cross-over. It shows then, over some range of ω, an apparently constant velocity and a damping proportional to Q 2 . Our present understanding, instead, is that the boson peak observed in S(Q, ω) relates to this strong scattering of the phonons by the structural disorder. The latter produces a cross-over from plane waves to non-propagating excitations which agrees with all the available information.