Ultrasound Propagation in Sintered Metal Powder: Evidence for a Crossover from Phonons to Fractons

Abstract

Ultrasonic experiments performed on a three-dimensional percolating system made from sintered copper powder show a rapid increase in the attenuation, corresponding to a sudden decrease in the localization length for vibrations, at wavelengths approaching the percolation correlation length. The data support recent theoretical predictions of a crossover from extended phonon excitations to localized fracton excitations at a length scale below which the structure has the self-similarity of a fractal system.