Acoustic and thermal transport properties of hard carbon formed from ${\mathrm{C}}_{60}$ fullerene

We report on extended investigation of the thermal transport and acoustical properties on hard carbon samples obtained by pressurization of ${\mathrm{C}}_{60}$ fullerene. Structural investigations performed by different techniques on the same samples indicate a very inhomogeneous structure at different scales, based on fractal-like amorphous clusters on the micrometer to submillimeter scale, which act as strong acoustic scatterers, and scarce microcrystallites on the nanometer scale. Ultrasonic experiments show a rapid increase in the attenuation with frequency, corresponding to a decrease in the localization length for vibrations. The data give evidence for a crossover from extended phonon excitations to localized fracton excitations. The thermal conductivity is characterized by a monotonous increase versus temperature, power law $T^{1.4},$ for T ranging from 0.1 to 10 K, without any well-defined plateau, and a strictly linear-in-T variation between 20 and 300 K. The latter has to be related to the linear-in-T decrease of the sound velocity between 4 and 100 K, both linear regimes being characteristic of disordered or generally aperiodic structures, which can be analyzed by the “phonon-fracton hopping” model developed for fractal and amorphous structures.