Rational Design of a Commensurate (3 + 3)-D Modulated Structure within the Fast-Ion Conducting Stabilized δ-Bi₂O₃ Series

We report the systematic design, preparation, and characterization of the first commensurate member of the oxide-ionic conducting, (3 + 3)-D modulated, Type II phases of doped δ-Bi₂O₃. The incommensurate Type II modulation vector ϵ was previously described as continuously variable, but high-resolution synchrotron X-ray powder diffraction data show that close to the composition Bi₂₃CrNb₃O₄₅, it "locks in" to ϵ = 1/3. The space group of the resulting 3 × 3 × 3 fluorite-type supercell was found to be F43m by selected-area electron diffraction, and the structure was solved and Rietveld-refined against neutron powder diffraction data in conjunction with local structural information from X-ray absorption spectroscopy, high-resolution transmission electron microscopy, and ab initio geometry optimization calculations. The result unambiguously validates the crystal-chemical model of the Type II phases as being based on the local ordering of oxygen around transition metals M into tetrahedral clusters of MO₆ octahedra and isolated MO₄ tetrahedra, separating relatively disordered fluorite-type regions that facilitate the highest oxide-ionic conduction among transition metal-doped δ-Bi₂O₃ phases.