In our previous work on Si clathrates we found a strong correlation between the group velocities and the number of atoms n a in the primitive cell, and a secondary correlation with crystal symmetry (spacegroup). Based on this, we would expect the κ/τ CRTA to vary in the order BTO (rhombohedral, n a = 5) > STO (tetragonal, n a = 10) > CTO (orthorhombic, n a = 20). CTO and STO follow this trend, with κ/τ CRTA = 4 and 10.7 at 1000 K, whereas for BTO κ/τ CRTA = 3.9 which is comparable to but slightly lower than CTO. This is consistent with the phonon dispersions in Fig. , which show a notably shallower dispersion for BTO, particularly in the low-frequency acoustic modes. The much larger κ/τ CRTA of STO compared to CTO, despite the larger mass m A of the A-site, suggests that this cannot be attributed to Ba having the largest m A . One explanation is that accommodating the larger Ba cation places a strain on the TiO 6 octahedral framework, which may be reflected in the larger volume per formula unit of BTO compared to the similar volumes of CTO and STO (c.f. Table ). Another is that the off-centering of the B-site Ti 4+ cation in the R3m structure has a larger impact on the chemical bonding in the TiO 6 octahedral framework than the rigid tilting in the I4/mcm and Pnma structures.