---
abstract: 'A simulation study of negative thermal expansion in Y$_2$W$_3$O$_{12}$ was carried out using calculations of phonon dispersion curves through the application of density functional perturbation theory. The mode eigenvectors were mapped onto flexibility models and results compared with calculations of the mode Grüneisen parameters. It was found that many lower-frequency phonons contribute to negative thermal expansion in Y$_2$W$_3$O$_{12}$, all of which can be described in terms of rotations of effectively rigid WO$_4$ tetrahedra and Y–O rods. The results are strikingly different from previous phonon studies of higher-symmetry materials that show negative thermal expansion.'
address:
- '$^1$ School of Physics and Astronomy *and* Materials Research Institute, Queen Mary University of London, Mile End Road, London, E1 4NS, United Kingdom.'
- '$^2$ CrystalMaker Software Ltd, Centre for Innovation & Enterprise, Oxford University Begbroke Science Park, Woodstock Road, Begbroke, Oxfordshire, OX5 1PF, United Kingdom.'
- '$^3$ Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EQ, United Kingdom.'
author:
- 'Leila H N Rimmer$^{1,2,3}$ and Martin T Dove$^{1,3}$'
title: 'Simulation study of negative thermal expansion in yttrium tungstate Y$_2$W$_3$O$_{12}$'
---

Introduction
============

Atomic-scale origin of negative thermal expansion
-------------------------------------------------

As has been highlighted in several recent reviews [@Barrera_2005_review; @Romao_2013_NTEReview; 