Low-temperature heat capacity and localized vibrational modes in natural and synthetic tetrahedrites

The heat capacity of natural (Cu12−x (Fe, Zn, Ag)x(Sb, As)4S13) and synthetic (Cu12−xZnxSb4S13 with x = 0, 1, 2) tetrahedrite compounds was measured between 2 K and 380 K. It was found that the temperature dependence of the heat capacity can be described using a Debye term and three Einstein oscillators with characteristic temperatures that correspond to energies of ∼1.0 meV, ∼2.8 meV, and ∼8.4 meV. The existence of localized vibrational modes, which are assigned to the displacements of the trigonally coordinated Cu atoms in the structure, is discussed in the context of anharmonicity and its effect on the low lattice thermal conductivity exhibited by these compounds.