Superspace description of trigonal and ortho-rhombic A1+xAx′B1-xO3 compounds as modulated layered structures;: application to the refinement of trigonal Sr6Rh5O15

The structures of the trigonal compounds A(1+x)A(x)'B1-xO3 are described, to a first approximation, as a hexagonal close-packed stacking of A(3)O(9) and A(3)A'O-6 layers. However, quantitative analyses are usually performed in superspace, with the structures considered as modulated composites made of two subsystems: chains of A cations, and columns of trigonal prisms, A'O-6, and octahedra, BO6. It is demonstrated that an alternative superspace description as a single modulated structure can be found in terms of the aforementioned layers, with a composition-dependent modulation parameter and discontinuous atomic domains. In this approach, these compounds fulfill layer-stacking rules analogous to those observed in other layered compounds. These rules translate into a so-called closeness condition for the discontinuous atomic domains in superspace; this condition is analogous to that postulated in quasicrystals. Both superspace models, the composite and the layered model, when considered without displacive modulations, can be taken as two limiting idealized paradigms and can be used as the starting point of a structure refinement. As an example, the structure of the trigonal phase Sr6Rh5O15, which was previously refined as a modulated composite [Stitzer, El Abed et al. ( 2001), J. Am. Chem. Soc. 123, 8790-8796], has been refined anew, with equivalent results, as a single modulated structure taking as reference the ideal layered structure. A similar superspace layer description is applied to the recently reported orthorhombic family A(4m+4n) A'(n) B4m+2nO12m+9n. This description allows the a priori derivation of a refineable superspace model that includes the superspace symmetry and crenel functions and is valid for the whole family. This model has been successfully applied to the refinement of the compound Ba12Co11O33 [Darriet et al. (2002), Chem. Mater. 14, 3349-3363].