On the band gap and thermal expansion of MnIn$_{5.0}$S$_{8.5}$ single crystals

MnIn$_{5.0}$S$_{8.5}$ single crystals are grown by the Bridgman method. The width and length of the crystals are $\sim$ 14 and $\sim$ 40 mm, respectively. The composition, structure and unit-cell parameter of the crystals are established. From the transmittance spectra recorded in the temperature range 20–300 K, the band gap $E_g$ and its temperature dependence $E_g(T)$ are determined. The dependence $E_g(T)$ is adequately described by the corresponding theoretical expression. The specific expansion $(\Delta l/l_0)$ versus temperature is measured, and the coefficient of linear thermal expansion $(\alpha_L)$ is determined. From the data on $\alpha_L$, the Debye temperature $(\Theta_D)$ and the rms dynamic atomic displacements $(\sqrt{\bar{u}^2})$ are calculated. It is established that the Debye temperature $\Theta_D$ decreases with increasing temperature, whereas the rms atomic displacements increase.