Crystal structure and band gap of (MnIn$_{2}$S$_{4}$)$_{1-x}$ $\cdot$ (AgIn$_{5}$S$_{8}$)$_{x}$ alloys

The (MnIn$_{2}$S$_{4}$)$_{1-x}$ $\cdot$ (AgIn$_{5}$S$_{8}$)$_{x}$ alloy single crystals are grown for the first time by the Bridgman method in the entire range of component concentrations. The composition of the single crystals and their crystal structure are determined. It is shown that the alloy crystallizes in the cubic spinel structure. The unit-cell parameter of the single crystals $(a)$ is calculated, and its dependence on the composition parameter $(x)$ is determined. It is established that the parameter a linearly varies with $x$. From the transmittance spectra in the region of the fundamental absorption edge, the band gap $(E_g)$ of the MnIn$_{2}$S$_{4}$ and AgIn$_{5}$S$_{8}$ compounds and (MnIn$_{2}$S$_{4}$)$_{1-x}$ $\cdot$ (AgIn$_{5}$S$_{8}$)$_{x}$ alloys is determined, and the dependence of $E_g$ on the parameter $x$ is constructed. It is found that the band gap $E_g$ nonlinearly varies with $x$ and has a maximum at $x$ = 0.6.