Argentite-acanthite transformation in silver sulfide as a disorder-order transition

An alternative model has been proposed for the phase transition from cubic argentite $\beta$-Ag$_2$S to monoclinic acanthite $\alpha$-Ag$_2$S in silver sulfide as a disorder-order transition. It has been shown that, as the temperature decreases below the transition temperature $T_{\mathrm{trans}}$, $\mathrm{S}$ atoms equiprobably occupying the sites of the body centered cubic (bcc) nonmetal sublattice of argentite are concentrated at four sites of the monoclinic nonmetal sublattice, whereas the other sites remain vacant. A disorder-order transition channel including three superstructure vectors of $\mathbf{k}_9$ and $\mathbf{k}_4$ stars has been determined. The distribution function of sulfur atoms in monoclinic acanthite $\alpha$-Ag$_2$S has been calculated. It has been shown that displacements of sulfur atoms distort the bcc nonmetal sublattice of argentite, forming a monoclinic lattice, where silver atoms are spaced by quite large distances and occupy their crystallographic positions with a probability of $1$. The region of allowed values of the long-range order parameters $\eta_9$ and $\eta_4$ for the model monoclinic ordered phase $\alpha$-Ag$_2$S has been determined.