Abstract
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 renormalisation through anharmonic interactions describes this behaviour well. Our results point the way towards a new understanding of how NTE is manifested in real materials.
Highlights
Almost all materials expand when heated, but some shrink instead
We present here an experimentally-based atomic-scale analysis of negative thermal expansion (NTE) in the prototypical material ScF3 [14,15,16], obtained from neutron total scattering measurements analyzed using the reverse Monte Carlo (RMC) method
The POLARIS instrument can measure down to a wavelength of 0.1 Å [42], which gives a maximum energy transfer far in excess of the upper limit of 85 meV required from the density functional theory (DFT) phonon calculations on ScF3 [16], and the experiments and subsequent analysis capture the full range of phonon excitations
Summary
Almost all materials expand when heated, but some shrink instead. This phenomenon of negative thermal expansion (NTE) [1,2,3,4] is of fundamental interest from a structural and thermodynamic point of view, and commercially important [5,6,7], for instance in preparing substrates resistant to thermal shock. The energy cost of polyhedral distortions may reduce the effect of such tension-effect vibrations In view of this discussion, there is currently no physical understanding of why our subject material, ScF3, shows NTE, whereas almost every cubic perovskite material has positive thermal expansion, even though they all have the same basic network structure [13]. We present here an experimentally-based atomic-scale analysis of NTE in the prototypical material ScF3 [14,15,16], obtained from neutron total scattering measurements analyzed using the reverse Monte Carlo (RMC) method. This approach is used to refine configurations of atoms so that both their long-range and their local structure are consistent with experimental data. Total scattering data analyzed using the reverse Monte Carlo method is the only way to obtain information about these issues from experiment
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