Dihedral-angle-averaged Bethe lattice for vibrations in glasses

An exact solution is found for a Bethe-lattice model of the vibrations in ${\mathrm{AX}}_2$ glasses when the dihedral angle is assumed to be completely random and is averaged throughout the lattice. The vibrational density of states agrees very well with that calculated by Bell and co-workers for a large ball-and-stick model, and is much simpler to compute. The Raman, infrared, and inelastic neutron scattering spectra are calculated for vitreous ${\mathrm{SiO}}_2$ and ${\mathrm{GeO}}_2$, which show satisfactory agreement with the main features of the experimental spectra.