Phase transition in Ag$_2$S and the relative position of atomic planes of the $\alpha$-Ag$_2$S and $\beta$-Ag$_2$S phases

The relative position of atomic planes of low-temperature monoclinic acanthite $\alpha$-Ag$_2$S and high-temperature bcc argentite $\beta$-Ag$_2$S has been determined from X-ray and electron microscopy data. A reversible $\beta$-Ag$_2$S–$\alpha$-Ag$_2$S phase transition is due to the distortion of the bcc S sublattice in the structure of argentite $\beta$-Ag$_2$S to the monoclinic sublattice of acanthite $\alpha$-Ag$_2$S. Distances between Ag atoms in cubic argentite are too small for the sites of the metal sublattice to be completely filled with Ag atoms. For this reason, the filling probabilities of sites of the metal sublattice is less than $0.1$. Silver atoms in acanthite are at fairly large distances from each other because of monoclinic distortion and fill their positions with a probability close to $1$. The relative orientations of the atomic planes of acanthite and argentite have been determined taking into account the displacements S and Ag atoms.