and NiV 2 O 6 exclusively form vanadiumoxygen tetrahedra. According to a statistical analysis of experimentally realized oxides by Waroquiers et al., tetrahedral coordination for V 5+ is the most likely geometry (67.27%). The presence of V 5+ on this site would necessitate V 3+ within the material for charge balance because of the tight restriction on the composition seen in the diffraction co-refinement result. And the presence of V 3+ cations is evidenced by BVS analysis of the square pyramidal vanadium sites (V3), where a mixed +3/+4 oxidation state is likely. Waroquiers et al. present square pyramidal coordination geometries as the second most likely for V 4+ (13.35%) behind octahedral ones (71.08%). For V 3+ , they show that octahedra are by far the most likely (96.72%) whereas square pyramids are quite unlikely (0.01%). This suggests that V 4+ is more common on the V3 site and promotes the square pyramidal geometry derived from X-ray and neutron diffraction co-refinement while V 3+ cations also occupying the site distort the polyhedron between geometries with octahedral and square pyramidal character. BVS analysis of mixed occupancy sites can prove difficult, but Bosi demonstrates a technique where, in this case, BVS values obtained assuming a purely nickel or vanadium site are averaged while weighting by site occupancy. Using Bosi's procedure with the two Ni/V sites produces a predicted oxidation state of +3 for V1 and +4 for V2, more evidence for three vanadium oxidation states. If the V1, V2, and V4 sites contain only one vanadium oxidation state, as seems likely based on the BVS analysis, then in order to have charge balance, V3 would require an average oxidation state of +3.726. This seems plausible based on a +3/+4 weighted average using Bosi's method. It also supports the square pyramidal arrangement of the site in the average crystallographic cell since more V 4+ is present. It should be noted, however, that Bosi's analysis assumes the structure contains unstrained polyhedra, and although it provides a better BVS fit for V3 than a purely +3 or +4 state BVS calculation, there is enough error to cast doubt on this approximation in this case, and other options need to be considered. BVS results for this method are summarized in Ta-ble 2.