Which phonons contribute most to negative thermal expansion in ScF<b>3</b>?

Abstract

Using calculations of the phonon distribution in ScF3 across the whole of reciprocal space, we show that the important phonons for the negative thermal expansion in this material are those associated with the rigid unit modes (RUMs) and associated quasi-RUMs. We discuss the role of the bond-bending flexibility within the ScF6 octahedra, and how this enables other phonons to make an additional but ultimately much weaker contribution to negative thermal expansion. These results inform recent discussions on the role of correlated atomic motions in giving rise to negative thermal expansion in ScF3.