material as they typically undergo NTE along one or two axes coupled with PTE along the remaining axis or axes [@Sleight_1995_Endeavour_NTE]. Furthermore, Y$_2$W$_3$O$_{12}$ has some of the largest coefficients of NTE of the entire **A**$_2$**M**$_3$O$_{12}$ family; its average linear expansion coefficient has been measured as $-7.0$ MK$^{-1}$ [@Forster_Sleight_1999_IntJInorgMat_Y2W3O12NTEExpt], which equates to a volumetric coefficient of thermal expansion of $\alpha_{\mathrm{V}}\approx-21$ MK$^{-1}$.

Y$_2$W$_3$O$_{12}$ is an NTE material of particular interest to us because, if thought of as a series of rigid YO$_6$ and WO$_4$ coordination polyhedra, then the crystal structure would be too over-constrained to support RUMs (this is discussed further in \[maxwell\_counting\]). The existence of NTE in this material therefore suggests a degree of flexibility of either or both of the YO$_6$ octahedra and WO$_4$ tetrahedra, and it is important to understand how this flexibility generates a tension effect of sufficient strength to generate NTE.

Analysis of neutron diffraction data [@Forster_Sleight_1999_IntJInorgMat_Y2W3O12NTEExpt] suggests that NTE in Y$_2$W$_3$O$_{12}$ may be driven by transverse vibrations of oxygens within the Y–O–W linkages, as per the tension effect. However, this prediction has yet to be confirmed through analysis of the vibrational spectrum. No experimental study of the phonon spectrum of Y$_2$W$_3$O$_{12}$ has yet been published but 