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Phonon Density of States and Thermodynamic Behavior in Highly Amorphous Media

We calculate the phonon density of states (DOS) for strongly amorphous materials with a short-ranged interatomic potential. Exponentially decaying and abruptly truncated interatomic potentials are examined. Thermally excited mean square deviations from equilibrium are calculated with rapid increases noted as the average number of neighbors is reduced. The Inverse Participation Ratio (IPR) is used to characterize the phonon states and identify localized phonon modes as the bonding range (and hence the average number of neighbors per atom) is diminished. For the truncated potential, the characteristics of the IPR histogram change qualitatively below $n_{\mathrm{neigh}}$ with the appearance of localized phonon modes below $n_{\mathrm{neigh}} = 6.0$.