Velocities of longitudinal and transverse elastic vibrations in superionic silver sulfide

It has been shown that the heat capacity of argentite $\beta$-Ag$_2$S, which is nanocrystalline superionic silver sulfide, includes an additional positive contribution caused by the existence of the lower and upper bounds of the phonon spectrum because of a small size of particles. The estimate of this contribution from experimental data on the difference of the heat capacities of nano- and coarse-crystalline argentite $\beta$-Ag$_2$S, in the region of its existence 470–850 K makes it possible to determine for the first time the velocities of propagation of longitudinal and transverse elastic oscillations $c_l$ and $c_t$ and the elastic rigidity constants $c_{11}$, $c_{12}$, and $c_{44}$. It has been found that an increase in the temperature results in a decrease in the elastic characteristics of argentite. The directions of the crystal lattice of argentite corresponding to the maximum and minimum elastic moduli have been determined.