Low-temperature heat capacity and localized vibrational modes in natural and synthetic tetrahedrites
The heat capacity of natural (Cu{sub 12−x} (Fe, Zn, Ag){sub x}(Sb, As){sub 4}S{sub 13}) and synthetic (Cu{sub 12−x}Zn{sub x}Sb{sub 4}S{sub 13} 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.