Temperature dependence of the lattice parameters of Cu$_{2-x}$Se (0.03 $\le x\le$ 0.23) powders fabricated by mechanochemical synthesis

The Cu$_{2-x}$Se (0.03 $\le x\le$ 0.23) powders fabricated by mechanochemical synthesis have been studied by X-ray diffraction. The in situ study has been carried out for the temperature dependences of the lattice parameters, the structures, and the phase compositions of the powders in the temperature range 25–350$^{\circ}$C. The powder compositions are shown to differ from the charge compositions and are shifted to lower copper concentrations. The estimation of peak half-widths of the cubic $\beta$ phase indicates an increase in the structure imperfection after the phase transition from the $\alpha$ phase to the $\beta$ phase of Cu$_{2-x}$Se at 140$^{\circ}$C. It is shown that the superpositions of the subtraction solutions (copper vacancies) and interstitials solutions (copper atoms in interstitial sites), whose proportion is changed as a function of temperature and the deviation from stoichiometry, are in the thermodynamic equilibrium in the copper selenide solid solution at room temperature. The change in the slope of the dependence of the lattice parameter of the powder Cu$_{2-x}$Se samples on the composition (0.03 $\le x \le$ 0.23) in the temperature range 25–350$^{\circ}$C enables the suggestion that interstitial copper atom concentration increases with temperature and deviation from stoichiometry.