Quantitative understanding of negative thermal expansion in scandium trifluoride from neutron total scattering measurements

Negative thermal expansion (NTE)-the phenomenon where some materials shrink rather than expand when heated-is both intriguing and useful but remains poorly understood. Current understanding hinges on the role of specific vibrational modes, but in fact thermal expansion is a weighted sum of contributions from every possible mode. Here we overcome this difficulty by deriving a real-space model of atomic motion in the prototypical NTE material scandium trifluoride, ScF3, from total neutron scattering data. We show that NTE in this material depends not only on rigid unit modes-the vibrations in which the scandium coordination octahedra remain undistorted-but also on modes that distort these octahedra. Furthermore, in contrast with previous predictions, we show that the quasiharmonic approximation coupled with renormalization through anharmonic interactions describes this behavior well. Our results point the way towards a new understanding of how NTE is manifested in real materials.