Thermal conductivity of Cu$_2$Se taking into account the influence of mobile copper ions

The temperature dependence of the thermal conductivity of nanostructured samples of copper selenide prepared by mechanochemical synthesis from initial pure components in a planetary ball mill followed by spark plasma sintering has been studied. The thermal conductivity of nanostructured samples was measured in the temperature range 410–860 K. At 410–780 K, the thermal lattice conductivity $\kappa_{\operatorname{ph}}$ varies insignificantly in the range 0.35–0.37 W/(m K). At a higher temperature $T>$ 780 K, $\kappa_{\operatorname{ph}}$ decreases to 0.19 W/(m K). To analyze the influence of mobile copper ions on the thermal conductivity of the lattice, molecular-dynamic calculations were performed using a classical interatomic potential obtained from ab initio calculations for the cubic $\beta$-Cu$_2$Se modification. The simulation results demonstrate a high mobility of copper ions, and the calculated temperature dependence of the lattice thermal conductivity agrees with the experiment to 780 K. At a temperature $T>$ 780 K, $\kappa_{\operatorname{ph}}$ deviates from the calculation results, and this deviation is most pronounced in the nanostructured material. As a result, at the maximum measurement temperature, the lattice thermal conductivity decreased to $\sim$0.19 W/(m K), which agrees with available data for nanostructured Cu$_2$Se samples produced by various methods.