Phase transition of tetragonal copper sulfide Cu2S at low temperatures

Abstract

The low-temperature behavior of tetragonal copper sulfide, ${\mathrm{Cu}}_{2}\mathrm{S}$, was investigated by powder and single-crystal x-ray diffraction, calorimetry, electrical resistance measurements, and ambient temperature optical absorption spectroscopy. The experiments were complemented by density-functional-theory-based calculations. High-quality, polycrystalline samples and single crystals of tetragonal copper sulfide were synthesized at 5 GPa and 700 K in a large volume multianvil press. Tetragonal ${\mathrm{Cu}}_{2}\mathrm{S}$ undergoes a temperature-induced phase transition to an orthorhombic structure at around 202 K with a hysteresis of $\ifmmode\pm\else\textpm\fi{}21$ K, an enthalpy of reaction of 1.3(2) $\mathrm{kJ}\phantom{\rule{0.16em}{0ex}}{\mathrm{mol}}^{\ensuremath{-}1}$, and an entropy of reaction of 6.5(2) $\mathrm{J}\phantom{\rule{0.16em}{0ex}}{\mathrm{mol}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$. The temperature dependence of the heat capacity at the transition temperature indicates that the transition from the tetragonal to the low-temperature polymorph is not a single process. The structure of the low-temperature polymorph at 100 K was solved in space group $Pna{2}_{1}$. The structure is based on a slightly distorted cubic close packing of sulfur with copper in threefold coordination similar to the structure of tetragonal copper sulfide. The electrical resistance changes several orders of magnitude at the transition following the temperature hysteresis. The activation energy of the conductivity for the tetragonal phase and the low-temperature polymorph are 0.15(2) and 0.22(1) eV, respectively. The direct band gap of the tetragonal polymorph is found to be 1.04(2) eV with the absorption spectrum following Urbach's law. The activation energies and the band gaps of both phases are discussed with respect to the results of the calculated electronic band structures.