Band gap of (In$_{2}$S$_3$)$_{x}$(AgIn$_{5}$S$_8$)$_{1-x}$ single-crystal alloys

In$_{2}$S$_{3}$, AgIn$_{5}$S$_{8}$, and (In$_{2}$S$_3$)$_{x}$(AgIn$_{5}$S$_8$)$_{1-x}$-alloy single crystals are grown by the Bridgman method. The composition and structure of the crystals are determined. It is established that both the initial compounds and their alloys crystalize with the formation of the cubic spinel structure. The unit-cell parameters of the single crystals are calculated, and the dependences of these parameters on the alloy composition are constructed. It is shown that, in the system, Vegard's law is satisfied. The transmittance spectra of the crystals in the region of the fundamental absorption edge are studied at room temperature, and the band gap $(E_g)$ is determined. It is shown that $E_g$ varies with the composition parameter $x$, with some deviation from a linear dependence.