Lower Miller index surfaces have lower cleavage and surface energies compared with higher order surfaces, likely a result of fewer bonds broken in the formation of the lower index surfaces. The (100) and (101) surfaces see modest 0.4 J m -2 reductions in energy upon relaxations, while the surface energy of (001) remains almost unchanged with a small 0.02 J m -2 difference in energy. The (101) surface is slightly lower in energy than (100) even though the opposite trend would be typically expected. This can be explained by considering the bonds broken during the cleavage as two Ti-O eq and four Y-S bonds were broken on the (100) surface, while on the (101) only one Ti-O eq , two Y-S and one Y-O bonds were broken. The 0.05 J m -2 difference in the cleavage energies between the two is retained after the relaxation.