The effects of doping of lead sulfide by silver on the lattice and optical properties of solid solutions Pb$_{1-x}$Ag$_{x}$S

Single-phase cubic Pb$_{1-x}$Ag$_{x}$S limited solid solutions based on PbS with a metal sublattice doped with Ag are produced. The maximal relative content of Ag in the Pb$_{1-x}$Ag$_{x}$S solid solutions reaches up to $x$ = 0.15. The thermal expansion of semiconductor Pb$_{1-x}$Ag$_{x}$S solid solutions is first measured by the dilatometry technique in the temperature range from 295 to 580 K. The replacement of Pb atoms by Ag atoms in Pb$_{1-x}$Ag$_{x}$S results in a decrease in the coefficient of thermal expansion, which is due to a change in the anharmonicity of atomic vibrations and a slight increase in the elastic properties. For single-crystal PbS particles and Pb$_{1-x}$Ag$_{x}$S solid solutions, the spatial distributions of the modulus of elasticity $E$, the Poisson ratio $\mu$, and the linear compressibility $\beta$ in relation to the $(hkl)$ direction are determined. The reflectance spectra of synthesized PbS, Ag$_2$S, and Pb$_{1-x}$Ag$_{x}$S powders are recorded, and it is shown that the replacement of Pb by Ag in PbS is accompanied by an increase in the band gap.