The role of rigid unit modes in negative thermal expansion

The rigid unit mode (RUM) model provides a valuable computational method to investigate correlations of transverse thermal motions of atoms important in negative thermal expansion (NTE) materials. We report here detailed RUM calculations of ten framework oxide structures that have been studied for their negative (or ultra low) thermal expansion properties. The results negate any simple and direct correlation between presence or absence of RUMs in a structure and its NTE property. All the structures considered can be viewed as networks of polyhedral connected by corners only. All evidence supports the importance the transverse motion of the atoms at the corners, but NTE does not correlate well with the presence RUMs for the polyhedra.