Average energy gaps in the binary glass-alloy systems: ${\mathrm{Ge}}_{1-x}{\mathrm{Se}}_x$ and ${\mathrm{As}}_{1-x}{\mathrm{Se}}_x$

New results are presented for the composition dependence of the optical-frequency dielectric constant in the glass-forming regimes of the binary alloy systems, ${\mathrm{Ge}}_{1-x}{\mathrm{Se}}_x$ and ${\mathrm{As}}_{1-x}{\mathrm{Se}}_x$. Local extrema are found at the compound compositions, Ge${\mathrm{Se}}_2$ and ${\mathrm{As}}_2$ ${\mathrm{Se}}_3$, leading in turn to extrema in the calculated values of an average energy gap, ${\overline{E}}_g$. The average gaps are compared with minimum gaps determined from optical absorption and are shown to display similar behavior as a function of alloy composition in the vicinity of the compounds. By assuming that the pressure derivative of the average gap $\left(\frac{1}{{\overline{E}}_g}\right){\left(\frac{d{\overline{E}}_g}{\mathrm{dP}}\right)}_T$ is approximately equal to that measured for the minimum gap, we can explain the large and positive pressure derivatives of the refractive index for the chalcogenide amorphous semiconductors without the necessity of invoking large local-field corrections as had been previously proposed.