Frequency of filler vibrations in CoSb₃ skutterudites: A mechanical interpretation

A mechanical interpretation of the frequency trend observed in Ca-, Sr-, and Ba-filled CoSb₃ skutterudites is presented. Relevant vibrational frequencies computed at the zone center are presented for fully filled, half-filled, and unfilled systems. The frequency of the filler vibrations increases as the mass of the filler atom increases, which is a counterintuitive trend that is difficult to explain within the classical "rattler" concept. As an alternative theory, we propose the interpretation of the filler vibrations as modified Sb ring vibrations instead. The energetically degenerate Sb ring vibrations in unfilled CoSb₃ split into two separate groups of vibrations through the mechanical interaction introduced by fillers, and one of the group forms the filler vibrations. A one-dimensional mass-spring model is also presented for illustrative purposes. The frequency trend of the ab initio phonons at the zone center is reproduced by the model, substantiating our interpretation. The result suggests that engineering pnictogens in skutterudites may have significant impacts on the properties of filler vibrations.