Crossover in the vibrational density of states of silica aerogels studied by high-resolution neutron spectroscopy

Abstract

Applying the backscattering technique, neutron scattering measurements of the vibrational density of states of silica aerogels have been extended down into the GHz range; in that regime, the wavelength of the phonons reaches the size of the largest inhomogeneities within the aerogels. The resemblance of the observed behavior to a phonon to fracton crossover is discussed. Using a simple model for the density of states, the crossover frequencies ${\omega }_{\mathrm{co}}$ and empirical scaling exponents for the density of states above ${\omega }_{\mathrm{co}}$ are determined for three base-catalyzed silica aerogels of different mass density. In contrast to theoretical predictions no indication for a hump in the crossover region has been found.