Superspace description of trigonal and orthorhombic A1+xAx'B1-xO3 compounds as modulated layered structures; application to the refinement of trigonal Sr6Rh5O15
Résumé
The structures of the trigonal compounds A_{1+x}A_x^{'}B_{1-x}O_3 are described, to a first approximation, as a hexagonal close-packed stacking of A_3O_9 and A_3A^{'}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, BO_6. 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 Sr_6Rh_5O_{15}, 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...