Electronic structures of M21S8 (M = Nb, Zr) and (M,M')21S8 (M, M' = Hf, Ti; Nb, Ta) phases and reasons for variations in the metal site occupations.

Abstract

The electronic structures of binary M21S8 (M = Nb, Zr) and isostructural ternary (M,M')21S8 (M, M' = Hf, Ti; Nb, Ta) phases have been studied by means of extended Hückel tight-binding band structure calculations. For the valence electron concentration in the binary group 5 metal phase Nb21S8, metal-metal bonding is optimized whereas, in the isostructural group 4 metal phase Zr21S8, metal-metal bonding levels exist above the Fermi level. However, the electronic structure analysis suggests a stable structure for M21S8 phases with group 4 metals and that (M,M')21S8 phases with mixed group 4 and group 5 metals, even if not yet reported, could well exist. In the ternary phase Nb6.9Ta14.1S8, a linear relationship exists between the magnitude of the metal-metal bonding capacity (as expressed by the total metal-metal Mulliken overlap population) of each crystallographically independent metal site and the occupation of the site with the heavier metal (i.e., the element with the greater bonding capability). The situation is quite more complex in Hf7.5Ti13.5S8, where the metal-metal bonding capacity of each site, differences in electronegativity between Ti and Hf, and site volume arguments must be taken into account to understand the metal site occupation.