Vibrational densities of states and network rigidity in chalcogenide glasses

Vibrational spectra have been measured by neutron scattering for a series of Se-Ge and Se-As-Ge glasses, spanning a wide range in composition and, consequently, in network connectivity. Low-frequency ‘‘floppy’’ modes arising from underconstrained atomic configurations have been observed, in qualitative agreement with recent theories of the dynamics of network glasses. The number of floppy modes was found to depend only on the average coordination number 〈r〉. There is some indication of a rigidity percolation threshold at 〈r〉≊2.4, but the effect in the vibrational densities of states is not dramatic. The wave-vector dependence of the scattering at low vibrational energies (≊2 meV) is acoustic-phonon-like. Specific heats C calculated from the measured densities of states show a strongly composition-dependent bump in C/${\mathit{T}}^3$ near 4 K, in accord with experiment.