On the band gap in (In$_2$S$_3$)$_x$(CuIn$_5$S$_8$)$_{1-x}$ alloy single crystals

For In$_2$S$_3$, CuIn$_5$S$_8$ and (In$_2$S$_3$)$_x$(CuIn$_5$S$_8$)$_{1-x}$ alloy single crystals grown by the Bridgman method (vertical variant), the transmittance spectra in the region of the fundamental absorption-band edge are studied at 80 and 295 K. From the spectra, the band gaps of the In$_2$S$_3$ and CuIn$_5$S$_8$ compounds and the alloys based on them are determined, and the dependences of the band gap on the composition parameter $x$ of the alloys are established. It is shown that, at 80 and 295 K, the band gap nonlinearly varies with x and the variation is described by a quadratic function.