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 e-z/zeta. A simple statistical model is given which illuminates this behavior. In addition, the elastic constant c44 decreases as (z-z0)nu; in certain cases other elastic constants also exhibit this behavior. These simple functional relationships appear to hold accurately for all z > z0, where z0 is the critical average degree at which the elastic constants vanish.