Elastic properties of Ag$_{2}$S and ZnS nanocrystalline cubic sulfides

The structure of Ag$_{2}$S and ZnS heteronanostructures is considered taking into account the anisotropy of the elastic properties of Ag$_{2}$S and ZnS sulfides. It is shown that a large amount of cubic zinc sulfide stabilizes the cubic structure of $\beta$-Ag$_{2}$S argentite at 300 K during the deposition of Ag$_{2}$S and ZnS heteronanostructures from colloidal solutions. The elastic stiffness constants $c_{11}$, $c_{12}$, and $c_{44}$ of cubic argentite $\beta$-Ag$_{2}$S and sphalerite ZnS are estimated at a temperature of 300 K. Physically possible variants of the arrangement of silver atoms at fixed crystallographic positions of cubic argentite are determined. It is shown that the energetically most favorable is the formation of $\beta$-Ag$_{2}$S heterostructures, in which the interface is formed by the ($hk$ 0) plane of ZnS sphalerite and the ($hk$ 0.5) plane of $\beta$-Ag$_{2}$S argentite. Calculation of the universal criterion for the anisotropy of the elastic properties of cubic argentite $\beta$-Ag$_{2}$S and sphalerite ZnS showed that the studied silver and zinc sulfides are elastically anisotropic.