Capabilities and limitations of a (3+d)-dimensional incommensurately modulated structure as a model for the derivation of an extended family of compounds:: example of the scheelite-like structures

The previously reported incommensurately modulated scheelite-like structure KNd(MoO4)(2) has been exploited as a natural (3 + 1)-dimensional superspace model to generate the scheelite-like three-dimensional structure family. Although each member differs in its space-group symmetry, unit-cell parameters and compositions, in ( 3 + 1)-dimensional space, they share a common superspace group, a common number of building units in the basic unit cell occupying Wyckoff sites with specific coordinates (x, y, z) and specific basic unit-cell axial ratios (c/a, a/b, b/c) and angles. Variations of the modulation vector q, occupation functions and t(0) are exploited for the derivation. Eight topologically and compositionally different known structures are compared with their models derived from the KNd(MoO4)(2) structure in order to evaluate the capabilities and limitations of the incommensurately modulated structure to act as a superspace generating model. Applications of the KNd(MoO4)(2) structure as a starting model for the refinement and prediction of some other modulated members of the family is also illustrated. The (3 + 1)dimensional presentation of the scheelite-like structures reveals new structural relations, which remain hidden if only conventional three-dimensional structure descriptions are applied.