mode matching is described in \[draw\] and \[flexibility\_models\].

Results
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![(a) Low energy dispersion curves and densities of states for Y$_2$W$_3$O$_{12}$. The notation of Bradley and Cracknell [@Bradley_Cracknell_1972_CrystalBZSymmetryBook] is used to denote special Brillouin zone points ($\Gamma \equiv [0,0,0]$, $\mathrm{X} \equiv [\frac{1}{2},0,0]$, $\mathrm{Y} \equiv [0,\frac{1}{2},0]$, $\mathrm{Z} \equiv [0,0,\frac{1}{2}]$). (b) Shows the same data shaded according to the value of $\gamma_{\mathbf{k},i}$ of each mode at each wave vector. The colour scale ranges from red ($\gamma_{\mathbf{k},i}\le-9$) to white ($\gamma_{\mathbf{k},i}=0$) through to blue ($\gamma_{\mathbf{k},i}\ge+9$). Bins that make up the density of states are shaded according to the average $\gamma_{\mathbf{k},i}$ for each bin using the same colour scale.[]{data-label="Y2W3O12Phonons1"}](figure_2.pdf){width="70.00000%"}

Phonon dispersion and mode Grüneisen parameters in Y$_2$W$_3$O$_{12}$ {#ntephononsiny2w3o12section}
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a shows the calculated phonon dispersion curves and density of states of Y$_2$W$_3$O$_{12}$ in the 0–12 THz frequency range. As can be seen, Y$_2$W$_3$O$_{12}$ dispersion curves are relatively complex due to many mode crossings and the existence of multiple phonons within a tight frequency range. Nevertheless, it can be seen that the density of states is a continuous function up to about 8 THz, with a gap before another band of phonons in the range 9–11.5 THz. Not shown in the diagram is a further tight 