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

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, ScF 3 , 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.

Soft mode anisotropy in negative thermal expansion material ReO$_3$

“…The difference in flexibility with respect to distortions of the O-Re-O (F-Sc-F) bond angle is smaller than that for distortions of the Re-O-Re (Sc-F-Sc) linkage. However, molecular dynamics simulations have shown that the sign of the coefficient of thermal expansion is more sensitive to changes in the force constant governing the former 24 . Another difference of note is that the trends in the X-M -X bond angle for ReO 3 and ScF 3 are opposed.…”

“…Compared to typical ABX 3 perovskites, which also exhibit rigid rotations of the octahedral units, ReO 3 and ScF 3 both have a vacant A-site, allowing larger tilt angles 19 . Recent analysis of the local structure of ScF 3 23,24 demonstrated that flexibility of the octahedra themselves, i.e., distortions of the intraoctrahedral F-Sc-F bond angles away from 90 • , is a key contributor to the NTE. In perovskites, pure RUMs are restricted to the line M-R in reciprocal space, which in principle gives their mode Grüneisen parameters a vanishingly small contribution towards the mean Grüneisen parameter.…”

“…Molecular dynamics simulations of an ReO 3 -like structural model have also shown a decreasing magnitude of NTE for increasing anion interaction strengths 26 . In particular, the sign of the coefficient of thermal expansion in ScF 3 has been shown to be highly sensitive to changes in the force constant governing flexing of the F−Sc−F right angle 24 . We investigate this hypothesis by using a symmetrymotivated approach to analyze neutron pair distribution function (PDF) data collected on ReO 3 across its entire temperature range of stability.…”

“…The data points shown in red are from the longer collections which were used for total scattering measurements. (b) Plots of the PDF peak position ratios indicated in the legend.Peak positions for ScF3 were extracted from atomistic configurations generated using the reverse Monte Carlo method on neutron PDF data24 and OriginLab was used to fit the peaks for ReO3. The error bars for ReO3 correspond to the uncertainties from the peak fitting algorithm.…”

Symmetry-adapted pair distribution function analysis (SAPA): a novel approach to evaluating lattice dynamics and local distortions from total scattering data

“…A low energy cost for scissoringtype deformations of the octahedra would increase the proportion of quasi-RUMs, modes of mixed RUM and octahedral deformation character, with negative Grü neisen parameters. Both of these possibilities are analysed further in our (Bird et al, 2020) and others' recent work (Dove, 2019;Dove et al, 2020).…”