Measurement of the phonon-fracton crossover in the density of states of silica aerogels

The density of vibrational states in a fractal silica aerogel of Hausdorff dimension D≃2.4 has been determined using spin-echo neutron spectroscopy. A smooth phonon-fracton crossover is found with a fracton spectral dimension of {Mathematical expression}. This direct measurement of {Mathematical expression} near crossover agrees with a previous finding based on scaling Brillouin-spectroscopy results obtained with several samples. We also show that protons adsorbed in the gel vibrate with substantially higher amplitude than the silica matrix. © 1990 Springer-Verlag.