T3specific-heat anomaly in network solids

A large $T^3$ specific-heat anomaly associated with a vibrational mode near 40 ${\mathrm{cm}}^{\mathrm{-}1}$ is found in cristobalite and vitreous silica, but not in quartz or g-${\mathrm{B}}_2$ ${\mathrm{O}}_3$. A material-specific structural model is proposed for this anomaly. The model also explains the 40- and 80-${\mathrm{cm}}^{\mathrm{-}1}$ modes observed by neutron scattering in cristobalite and g-${\mathrm{SiO}}_2$ as well as the absence of dispersion in the hypersonic transverse sound velocity. Specific relations with recently observed anomalies in the 775-${\mathrm{cm}}^{\mathrm{-}1}$ Raman band of mixed alkali silicates are suggested and specific experiments designed to test phase separation at the elemental molecular level (true spinodal decomposition) are proposed.