As expected based on the crystal structure and phonon dispersion, the lattice thermal conductivity is anisotropic. However, in this case the anisotropy favours a lower thermal conductivity along the z direction, where the variation in the size and flavour of structural motifs is larger, and a higher thermal conductivity through the quasi-layers in the xy plane, where the electronic structure predicts the best transport properties. The calculations predict an in-plane thermal conductivity of 2.27 W m -1 K -1 at 1000 K, compared to a much smaller 0.76 W m -1 K -1 in the z direction (Figure ). At all temperatures, the in-plane lattice thermal conductivity is at least twice the out-of-plane conductivity, e.g. at 300 K the thermal conductivities are 7.59 W m -1 K -1 and 2.41 W m -1 K -1 respectively. Nonetheless, it can be seen that the 300 K lattice thermal conductivity of Y 2 Ti 2 S 5 O 2 , particularly the out-of-plane component, is competitive with or lower than that of other high-performance n-type thermoelectrics such as SrTiO 3 (11 W m -1 K -1 ), PbTe (4 W m -1 K -1 ) and BaBi 2 O 6 (3.6 W m -1 K -1 ).