Density of states of elastic waves in a strongly scattering porous "mesoglass"

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Hildebrand, William Kurt
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The density of states of elastic waves in a porous amorphous “mesoglass” has been measured in the strong-scattering regime. Samples were constructed by sintering glass beads percolated on a random lattice. This structure was investigated via x-ray tomography, and fractal behaviour was observed with fractal dimension D = 2.6. Using sufficiently small samples, the individual modes of vibration could be resolved and counted in the Fourier transform of each transmitted ultrasonic pulse. A statistical treatment of the data, designed to account for the possibility of missing modes, was developed, yielding a robust method for measuring the density of states. In the strong-scattering regime, the data are in good agreement with a simple model based on mode conservation, though the density of states significantly exceeds the predictions of the Debye approximation at low frequencies. At intermediate frequencies, an average density of states of 47.1 ± 0.3 MHz⁻¹ mm⁻³ was found, with a frequency dependence of f^(0.01 ± 0.04).
condensed matter, mesoglass, fractal, density of states, amorphous, percolation, acoustic, phonon