Thermal conductivity and terahertz vibrational dynamics of vitreous silica

The dynamic structure factor of vitreous silica is measured at terahertz frequencies by inelastic scattering of x rays (IXS) and neutrons (INS). The IXS experiment is performed at exchanged wave vectors q between 4 and 15 nm^{−1} and at temperatures above and below the glass transition. The neutron time-of-flight technique is used as a high-resolution probe in a comparable q region. The data analysis confirms the presence of two inelastic features in the IXS spectra in the entire explored wave-vector range. The lower-frequency component is nondispersive and is observed by both IXS and INS around the boson peak frequency. The higher-frequency one, associated with the longitudinal-acoustic-like branch, is marked by a positive dispersion, confirming the results of a previous study [Ruzicka et al., Phys. Rev. B 69, 100201 (2004)]. As q increases, the vibrational modes of the disordered structure progressively lose their plane-wave character; for q around that of the first sharp diffraction peak, the dynamic structure factor converges to an effective density of vibrational states. The contribution of the terahertz vibrations to the thermal conductivity of vitreous silica is then evaluated by means of a Kubo-type formula for the diffusivity in disordered systems. The acousticlike modes that persist at terahertz frequencies represent a heat conduction channel which accounts for only a fraction, although relevant, of the thermal conductivity. The failure of this approach to fully describe the conductivity data is attributed to the nondiagonal elements of the heat current operator that are not experimentally accessible.