Bonding relationships in some ternary and quarternary phosphide and tetrahedrite structures: (Ag₆M₄P₁₂)M₆', Cu12+xSb₄S₁₃and Cu14-xSb₄S₁₃, Ln₆Ni₆P₁₇

Electronic structure calculations are reported for three different, but structurally related, types of ternary or quaternary compounds that can be classified as derivatives of tetrahedral structures. The compounds (Ag 6 M 4 P 12 )M 6 ' (M=Ge, Sn; M'=Ge, Si) are calculated to have semiconducting properties, with forbidden energy gaps of about 0.7-0.9 eV. It is shown that structurally there materials contain Ag 6 octahedral clusters trapped in, and rather weakly coupled to, a closed network of covalent bonds. Among the tetrahedrite and tennantite family, compounds with chemical formulae such as Cu 14 Sb 4 S 13 or Cu 10 Zn 2 Sb 4 S 13 would have closed-shell valence bands with semiconducting gaps of around 1 eV. The complications associated with nonstoichiometry and phase separation into copper-rich and copper-poor phases are discussed. Finally, the authors consider bonding in the isotypic rare-earth polyphosphides Ln 6 Ni 6 P 17 (Ln=La, Ce, Pr).