Rigidity transitions and molecular structure of ${\mathrm{As}}_x{\mathrm{Se}}_{1-x}$ glasses

T-modulated differential scanning calorimetry measurements on bulk ${\mathrm{As}}_x{\mathrm{Se}}_{1-x}$ glasses show that the glass transition temperature $T_g\mathrm{}\left(x\right)\mathrm{}$ variation at $x<\mathrm{}0.12\mathrm{}$ is linear with a slope ${\mathrm{dT}}_g/dx=4.1\mathrm{}°\mathrm{C}/\mathrm{at}.\%\mathrm{As},$ and the nonreversing heat flow, $\Delta H_{\mathrm{nr}}\mathrm{}\left(x\right)\mathrm{}$ almost vanishes in the 0.291(1)<x<0.37(1) composition range. These thermal results analyzed by agglomeration theory and constraint theory suggest that in addition to $\mathrm{As}({\mathrm{Se}}_{1/2}{)}_3$ units, quasitetrahedral ${\mathrm{S}\mathrm{e}=\mathrm{A}\mathrm{s}(\mathrm{S}\mathrm{e}}_{1/2}{)}_3$ units also serve to crosslink ${\mathrm{Se}}_q$ chains at $x<\mathrm{}\frac{2}{5}.$ The results also suggest that rigidity onsets at $r_c\mathrm{}\left(1\right)=2.29\mathrm{}\left(1\right)\mathrm{}$ and the transition to the stressed rigid phase occurs at $r_c\mathrm{}\left(2\right)=2.37\mathrm{}\left(1\right),$ below the chemical threshold at $r_{\mathrm{ct}}=2.40\mathrm{}$ (or $x=\frac{2}{5}).\mathrm{}$