A note on the bonding,optical spectrum and composition of tetrahedrite

Tetrahedrites of composition (Cu, Ag)₁₀(Cu₂, Fe, Zn)₂(Sb, As)₄S₁₃ or Cu₁₂Sb_14/3S₁₃ have 208 valence electrons per unit cell and are expected to be semiconductors. The bands are full in these cases, whereas compositions towards the classical formula Cu₁₂Sb₄S₁₃ (204 valence electrons per unit cell) have only partially filled bands and are therefore expected to be metallic. These predictions are supported by new optical absorption spectra of tetrahedrites with 205 and 208 valence electrons per unit cell. The gap between valence and conduction bands of the semiconductor is about 1.7 (±0.2) eV. A further prediction based on a nearly-free electron model is that 208 valence electrons per unit cell represent a compositional limit for tetrahedrites, and that the stability increases as compositions approach this limit. Existing data indicate an exponential increase in the number of occurrences as the limit is approached.