The count of Lagrangian bonding constraints $n_c\left(y\right)$ in ternary ${\mathrm{Ge}}_{25}{\mathrm{S}}_{75-y}{\mathrm{I}}_y$ glasses $(0<y<\mathrm{}0.30\mathrm{})$ is established from the molecular structure using Raman scattering and first-principles cluster calculations. The results show that $n_c\left(y\right)$ decreases to 3 as y increases close to $y_c=0.162\mathrm{}\left(3\right)$, where a sharply defined global minimum in the nonreversing heat flow, $\Delta H_{\mathrm{nr}}\left(y\right)$ near $T_g$, is observed in scanning calorimetry. Here we have a rigidity transition induced by I dangling ends, with its sharpness resulting from the absence of self-organization in the random network.

• Received 29 March 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.185503