Direct Evidence for Stiffness Threshold in Chalcogenide Glasses

Raman scattering in ${\mathrm{Ge}}_{x}{X}_{1\ensuremath{-}x}$ glasses, $X\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{S}$ or Se, reveals that the frequency of ${A}_{1}$ modes of corner-sharing $\mathrm{Ge}({X}_{1/2}{)}_{4}$ tetrahedra displays a discontinuous jump between $x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.225$ and $x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.230$, which coincides with a minimum in the nonreversing heat flow at the glass transition ${T}_{g}$ established from modulated differential scanning calorimetry. These results constitute direct evidence for a stiffness threshold at a mean coordination $〈r{〉}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2.46(1)$, which is well described by mean-field constraint counting procedures.