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

A three-dimensional covalent network of N atoms possessing a fraction (nᵣ/N) of r-fold-coordinated atoms will, in general, display percolation of rigidity at an average coordination number 〈r〉=2.4-0.4(n₁/N), where n₁/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.