greyscale shading for this model in . It is consistent with the analysis of \[maxwell\_counting\], which shows that adding the additional Y…W distance constraint greatly reduces the flexibility of this model from 48 to exactly zero excess degrees of freedom. In short, a model with rigid WO$_4$ tetrahedra is unable to support motions in which the Y…W distance is conserved.

### Rigid YO$_6$ octahedra and W–O bonds

It is seen from \[maxwell\_counting\] that a flexibility model consisting of rigid YO$_6$ octahedra and W–O rods has 36 excess degrees of freedom, which is fewer than for the rigid WO$_4$ tetrahedron/Y–O rod model discussed above. Accordingly, shows that the overall match between this flexibility model and the *ab initio* dispersion curves is lower than for the rigid WO$_4$/Y–O model. Once again, a significant amount of eigenvector mixing is also apparent.

The strength of the match between this model and the *ab initio* phonons is greatest for the lowest frequency NTE phonons in the 0–2 THz range. In general, the match is weaker than that found for the rigid WO$_4$ tetrahedra/Y–O rod model and, aside from the acoustic phonons at the $\Gamma$ point, a perfect match is never achieved. There is one exception 