Glass-forming tendency, percolation of rigidity, and onefold-coordinated atoms in covalent networks

A three-dimensional covalent network of N atoms possessing a fraction (${\mathit{n}}_{\mathit{r}}$/N) of r-fold-coordinated atoms will, in general, display percolation of rigidity at an average coordination number 〈r〉=2.4-0.4(${\mathit{n}}_1$/N), where ${\mathit{n}}_1$/N represents the fraction of onefold-coordinated atoms. As an example, we show how these ideas can elucidate the glass-forming region in the Ge-S-I ternary system.