We report on extended investigation of the thermal transport and acoustical properties on hard carbon samples obtained by pressurization of C60 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 submillimetre 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 300K. 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 analysed by the phonon-fracton hopping model developed for fractal and amorphous structures.
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