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

Abstract

Author(s) of this paper may load this reprint on their own web site or institutional repository provided that this cover page is retained. Republication of this article or its storage in electronic databases other than as specified above is not permitted without prior permission in writing from the IUCr.For further information see http://journals.iucr.org/services/authorrights.html Acta Crystallographica Section B: Structural Science publishes papers in structural chemistry and solid-state physics in which structure is the primary focus of the work reported. The central themes are the acquisition of structural knowledge from novel experimental observations or from existing data, the correlation of structural knowledge with physicochemical and other properties, and the application of this knowledge to solve problems in the structural domain. The journal covers metals and alloys, inorganics and minerals, metal-organics and purely organic compounds.Crystallography Journals Online is available from journals.iucr.org Acta Cryst. (2008 The previously reported incommensurately modulated scheelite-like structure KNd(MoO 4 ) 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(MoO 4 ) 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(MoO 4 ) 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.

Validating the model of a (3 + 1)-dimensional incommensurately modulated structure as generator of a family of compounds for the Eu2(MoO4)3scheelite structure

“…It has been shown recently [7] that the structure of Eu 2 oe(WO 4 ) 3 (oe stands for a vacancy) can be described as a commensurately modulated member of the scheelite (3 þ 1)D structure type with the modulation vector q ¼ (2/3)a* þ (2/3)b*, the initial phase t 0 ¼ 0 and the crenel occupation functions Á Eu ¼ 2/3, Á oe ¼ 1/3. This q-vector and the occupation functions have been used for the simulation of its structure from the KNd(MoO 4 ) 2 prototype.…”

“…The structure can be produced with various chemical compositions defined by A ¼ K, Na, Li, Rb, Ag, La, Ca, Sr, Ba and X ¼ Mo, W, V among others. The A atoms, as well as the [XO 4 ] groups, can be either identical or not and also partially vacant [7]. The general formula of this family can thus be expressed as…”

“…0 or X ! 0 define vacancies on the corresponding sites [7]. Different combinations (ordered or not) of the building units lead to different members of the family.…”

“…Different combinations (ordered or not) of the building units lead to different members of the family. Eight known types of ordered distributions have already been described as three-dimensional (3D) periodic compounds [7]. Two incommensurately modulated structures, KNd(MoO 4 ) 2 and KSm(MoO 4 ) 2 , also belong to this family [7][8][9].…”

“…Recently, the possibility to use an incommensurately modulated structure belonging to a family of compounds as a superspace model for the description and prediction of the family members [7] has been postulated and discussed. In particular, the incommensurately modulated KNd(MoO 4 ) 2 structure was used as a prototype for the scheelite-like family.…”