Elastic properties of a network model of glasses

A standard model of glasses is shown to exhibit unexpected and remarkably simple elastic properties. For a sequence of networks of decreasing degree or coordination z, the number of zero-frequency vibrational modes (also called ‘‘degrees of freedom’’) increases as ${\mathit{e}}^{\mathrm{-}\mathit{z}/\mathrm{\zeta }}$. A simple statistical model is given which illuminates this behavior. In addition, the elastic constant ${\mathit{c}}_{44}$ decreases as (z-${\mathit{z}}_0$${)}^{\nu }$; in certain cases other elastic constants also exhibit this behavior. These simple functional relationships appear to hold accurately for all z>${\mathit{z}}_0$, where ${\mathit{z}}_0$ is the critical average degree at which the elastic constants vanish.