From Rattling to Incipient Ionic Conductivity: Neutron Scattering Studies of Tetrahedrite

The thermoelectric performance of tetrahedrites, which are minerals composed predominantly of environmentally-friendly and abundant copper and sulfur, is currently attracting considerable interest. Tetrahedrites, which are <i>p-</i>type materials with low lattice thermal conductivities, crystallise in a collapsed sodalite structure in which corner-sharing CuS₄ tetrahedra form cages. Each cage contains an octahedral cluster formed by six trigonal-planar copper cations.<br/>We have exploited a range of neutron scattering techniques to investigate the origin of low thermal conductivity in tetrahedrite, Cu₁₂Sb₄S₁₃, which has been previously attributed to the rattling vibrations of the trigonal-planar copper ions and has also been linked to a phonon instability arising from a low-temperature phase transition. Analysis of neutron and synchrotron X-ray diffraction data collected on tetrahedrite shows that copper rattling is a direct consequence of a tetragonal-to-cubic phase transition at 90 K, which results in a sharp increase, by approximately 200%, of the atomic displacement parameters of the trigonal-planar copper cations. This phase transition occurs because of the orbital degeneracy of the highest occupied 3<i>d</i> cluster orbitals of the copper clusters found inside the sodalite cages. In the high-temperature cubic phase, the trigonal-planar copper cations form regular octahedral Cu₆⁷⁺ clusters, which are electronically degenerate. Below 90 K, tetrahedrite contains pentameric Cu₅⁷⁺ clusters. The Jahn-Teller electronic instability which leads to the formation of “molecular-like” Cu₅⁷⁺ clusters, suppresses copper rattling vibrations due to the strengthening of direct copper-copper interactions.<br/>At temperatures above 200 K, quasielastic neutron scattering (QENS) measurements on tetrahedrite, Cu₁₂Sb₄S₁₃, and copper-rich tetrahedrite, Cu₁₄Sb₄S₁₃, combined with molecular dynamics simulations, reveal that copper ion diffusion occurs. However, although the copper ions are mobile between 200 and 400 K, they are largely trapped inside the sodalite cages. Analysis of inelastic neutron scattering (INS) data reveals the presence of a low-energy optical mode at 3-4 meV, which can be attributed to the intra-cage diffusion of the trigonal-planar copper ions. This low-energy optical mode, which softens on cooling revealing strong anharmonicity, is capable of strongly scattering the heat-carrying acoustic phonons, and hence lowers the lattice thermal conductivity.