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

## TL;DR

This study uses neutron scattering data to develop a real-space model of atomic motions in scandium trifluoride, revealing that negative thermal expansion arises from both rigid and distorted vibrational modes, and that quasiharmonic approximation effectively describes this behavior.

## Contribution

The paper introduces a real-space atomic motion model for NTE in ScF3, highlighting the roles of both rigid and distorted modes, and demonstrates the effectiveness of quasiharmonic approximation with anharmonic corrections.

## Key findings

- NTE in ScF3 depends on both rigid and distorted vibrational modes.
- Quasiharmonic approximation with anharmonic renormalization describes NTE well.
- A new real-space model of atomic motion in NTE materials is proposed.

## 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.