Anharmonicity and scissoring modes in the negative thermal expansion materials ScF3 and CaZrF6

Abstract

We use a symmetry-motivated approach to analysing X-ray pair distribution functions to study the mechanism of negative thermal expansion in two ReO3-like compounds; ScF3 and CaZrF6. Both average and local structure suggest that it is the flexibility of M-F-M linkages (M = Ca, Zr, Sc) due to dynamic rigid and semi-rigid "scissoring" modes that facilitates the observed NTE behaviour. The amplitudes of these dynamic distortions are greater for CaZrF6 than for ScF3, which corresponds well with the larger magnitude of the thermal expansion reported in the literature for the former. We show that this flexbility is enhanced in CaZrF6 due to the rock-salt ordering mixing the characters of two of these scissoring modes. Additionally, we show that in ScF3 anharmonic coupling between the modes responsible for the structural flexibility and the rigid unit modes contributes to the unusually high NTE behaviour in this material.

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

“…While this model of uncorrelated Sc-F motion is appealing as an intuitive interpretation of the tension effect, it is completely inconsistent with our knowledge of the phonon dispersion curves by both ab initio calculation [16,32,33] and inelastic x-ray scattering measurements [33]. A recent paper based on new x-ray total scattering measurements [29] supports the interpretation presented here, based on an earlier preprint of this paper, over the model of uncorrelated F-atom motions proposed in Ref. [26].…”

“…We collected total neutron scattering data from a powder sample of scandium trifluoride, measuring both the Bragg scattering-sensitive to the long-range order-and the diffuse scattering. Although several previous pair distribution function studies of ScF 3 have used x-rays [15,[27][28][29], for our analysis neutron radiation was a more appropriate choice, for three reasons. First, the accessible range of scattering vector Q, and hence the resolution of the pair distribution function derived from it, is much greater: we were able to measure up to a maximum value of Q max = 50 Å −1 , while with x rays the maximum achievable value of Q with a short-wavelength silver anode is 22.5 Å −1 and is usually practically up to around 30 Å −1 with synchrotron radiation measurements.…”

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

“…The first quantitative measurements using this technique were made in the 1930s, when experiments were performed on liquid mercury (Debye & Menke, 1930) and sodium (Tarasov & Warren, 1936). Since this early work, the technique has seen a wide range of uses, such as comparing crystalline and amorphous structures of the same materials (Biscoe & Warren, 1938;Hultgren et al, 1935;Warren et al, 1936;Peterson et al, 2013), modelling crystalline disorder (Keen et al, 2005;Senn et al, 2016), and studying the dynamics of more ordered materials (Bird et al, 2020;Conterio et al, 2008;Goodwin et al, 2009). The focus of this work is to present a novel approach for the latter.…”

“…This method does not aim to produce a dispersion curve from diffraction data; the goal is to determine which of the symmetry-adapted distortion modes are most responsible for local deviations from a parent or average structure. The method has been used successfully to study order-disorder-type phase transitions in BaTiO 3 (Senn et al, 2016) and the dynamic distortions responsible for the large magnitude of negative thermal expansion in ScF 3 and CaZrF 6 (Bird et al, 2020). The process itself is similar to one presented by Kerman et al (2012) to determine the average structure of a distorted material, although the primary aim of the SAPA method is to determine how the local structure deviates from the average.…”

Low-temperature luminescence of ScF3 single crystals under excitation by VUV synchrotron radiation

“…ScF 3 demonstrates strong negative thermal expansion (NTE) [2], which is more pronounced than that of most known NTE materials. Therefore, intensive studies of the NTE phenomenon in ScF 3 by means of both experimental and theoretical approaches have been reported during recent years [3][4][5][6]. Nevertheless, optical and luminescence properties of ScF 3 are poorly studied so far.…”