Type II Bi1 - xWxO1.5 + 1.5x: a (3 + 3)-dimensional commensurate modulation that stabilizes the fast-ion conducting delta phase of bismuth oxide.

The Type II phase in the Bi1 - xWxO1.5 + 1.5x system is shown to have a (3 + 3)-dimensional modulated δ-Bi2O3-related structure, in which the modulation vector ℇ `locks in' to a commensurate value of 1/3. The structure was refined in a 3 × 3 × 3 supercell against single-crystal Laue neutron diffraction data. Ab initio calculations were used to test and optimize the local structure of the oxygen sublattice around a single mixed Bi/W site. The underlying crystal chemistry was shown to be essentially the same as for the recently refined (3 + 3)-dimensional modulated structure of Type II Bi1 - xNbxO1.5 + x (Ling et al., 2013), based on a transition from fluorite-type to pyrochlore-type via the appearance of W4O18 `tetrahedra of octahedra' and chains of corner-sharing WO6 octahedra along 〈110〉F directions. The full range of occupancies on this mixed Bi/W site give a hypothetical solid-solution range bounded by Bi23W4O46.5 (x = 0.148) and Bi22W5O48 (x = 0.185), consistent with previous reports and with our own synthetic and analytical results.