It has been suggested that in ZrW$_2$O$_8$, a similar material to Y$_2$W$_3$O$_{12}$ (in that both are frameworks of corner-linked tetrahedral and polyhedral groups of atoms), the NTE phonons may exhibit strong correlations between the motions of adjacent metal sites, with the W–O–Zr bond angles remain undistorted [@Cao_etal_2002_PRL_ZrW2O8NTEFrustratedModes; @Cao_etal_2003_PRB_ZrW2O8NTEXAFS; @Figueiredo_Perottoni_2007_DFTZrW2O8BondStiffness]. In order to investigate the possibility of a similar correlation between Y and W atoms in Y$_2$W$_3$O$_{12}$, additional flexibility models were constructed such that Y…W correlations could be taken into account via one of

1.  No Y…W bond

2.  Rigid Y…W rod

In total this yielded eight different Y$_2$W$_3$O$_{12}$ flexibility models. However, the two models containing both rigid WO$_4$ tetrahedra and rigid YO$_6$ octahedra are over-constrained (see \[maxwell\_counting\] and [@Hammonds_octahedra]) and are, therefore, not discussed here (although models were constructed and tested to confirm this was actually the case).

The six remaining flexibility models were constructed as a set of simple force field models within the GULP lattice simulation program [@GULP_2003]. Simple bond stretching and bond angle bending forces were added to each model as discussed in \[flexibility\_models\], using the ambient pressure structure calculated by CASTEP at 0 GPa.

In order to compare the eigenvectors of the *ab initio* simulation with 