Temperature and frequency dependence of the sound velocity in vitreous silica due to scattering off localized modes

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Abstract
The behavior of the sound velocity in vitreous silica is investigated in a range of temperatures around that of the plateau in the thermal conductivity. Localized vibrational modes play an important role in thermal transport and inelastic phonon scattering in this temperature regime. A model based on the idea of a crossover from phonon to fracton vibrational dynamics at frequencies of the order of the plateau temperature has been developed, and is used to calculate the expected temperature and frequency dependence of the velocity of sound. The result can be expressed in terms of experimentally measurable quantities, and contains no arbitrary parameters. Good agreement is obtained with available experimental data.