Anelastic and Dielectric Relaxation of Excess Vibrational Modes in Silica

Anelastic and dielectric measurements of fused-silica and soda-silica glasses have been made at low temperatures. The results indicate the presence of distinct relaxation processes at ∼11 and ∼35°K. It is suggested that these relaxations are due to vibrational modes in excess of the usual Debye spectrum. The existence of these additional modes, or "Einstein modes," has already been deduced from low-temperature specific-heat measurements. A simple theoretical treatment of a charged harmonic oscillator coupled to the strain through a Grüneisen constant shows that anelastic and dielectric relaxations are expected from an excess mode of this kind. Very general considerations of the interactions between the "Einstein oscillator" and the bulk phonons suggest that the relaxation time $\tau$ describing the approach to equilibrium of the perturbed oscillator is of the form $\tau ={\tau }_0{e}^{\frac{Q}{\mathrm{kT}}}$. This expression is found to be in good agreement with the experimental observations. For the 11°K relaxation $Q=0.0140\mathrm{}\pm 0.0008$ eV, while for the 35°K relaxation $Q=0.053\mathrm{}\pm 0.007$eV.