CROSSOVER IN THE VIBRATIONAL DENSITY OF STATES OF SILICA AEROGELS STUDIED BY HIGH-RESOLUTION NEUTRON SPECTROSCOPY

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 co and empirical scaling exponents for the density of states above 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. © 1990 The American Physical Society.