Structural Relationships among Bismuth-Rich Phases in the Bi₂O₃-Nb₂O₅, Bi₂O₃-Ta₂O₅, Bi₂O₃-MoO₃, and Bi₂O₃-WO₃ Systems

The crystal structures of bismuth-rich phases in the Bi₂O₃-M₂O₅ (M = Nb, Ta) and Bi₂O₃-M₂O₆ (M = W, Mo) systems are investigated, and the most probable model for the crystal structure of each phase is used to propose a crystal-chemical scheme unifying key features of these structures in terms of their relationships to a fluorite-type δ-Bi₂O₃-related parent structure. This scheme is based on the incorporation of pyrochlore-type structural motifs (e.g., strings of M atoms along 〈110〉_F directions) into the underlying fluorite-type metal atom array. The relative orientations of these M atom strings and their interactions are driven by the competing requirements of overall charge-balance (a function of mol% M₂O₅ or M₂O₆) and local coordination environment (a function of the element M) within the flexible fluorite-type oxygen atom array. These interactions interrelate the oxygen atom array, the metal atom array, and the composition. As the composition moves further from pure Bi₂O₃, they force the abandonment of pyrochlore-type structural motifs, and hence any meaningful relationship to a fluorite-type δ-Bi₂O₃-related parent structure is lost. The descriptive and predictive utilities of this crystal-chemical scheme are discussed.