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Elastic properties of a network model of glasses

1992; American Physical Society; Volume: 68; Issue: 14 Linguagem: Inglês

10.1103/physrevlett.68.2172

1092-0145

Deborah S. Franzblau, J. Tersoff,

Topological and Geometric Data Analysis

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 ${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathit{z}/\mathrm{\ensuremath{\zeta}}}$. A simple statistical model is given which illuminates this behavior. In addition, the elastic constant ${\mathit{c}}_{44}$ decreases as (z-${\mathit{z}}_{0}$${)}^{\ensuremath{\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.