Observation of fractons in silica aerogels

The first lineshape analysis of fracton spectra is reported. We find that the phonon-fracton crossover is characterized by smooth plane-wave dispersion and loss curves. Scattering in the fracton regime peaks slightly above the crossover frequency. A fully self-consistent analysis of many samples reveals that their elastic correlation lengths are about five times their density correlation lengths, and gives a fracton dimension d = 1.3 ± 0.1. © 1988 IOP Publishing Ltd.