- kommensurabel Modulation (1) (remove)
- Crystal Structures of Perovskite-related Can(Nb,Ti)nO3n+2 (n=5 and 6) (2006)
- In this thesis, the crystal structures at room temperature of perovskite-related materials belonging to the homologous series Can(Nb,Ti)nO3n+2 with n = 5 and 6 have been accurately determined by single-crystal X-ray diffraction. The three compounds Ca5Nb5O17 (n = 5), Ca5Nb4TiO17 (n = 5), and Ca6(Nb,Ti)6O20 (n = 6) have been investigated. Their general structural features are the same, independent of the composition n. The crystal structures are composed of slabs of corner-sharing (Nb,Ti)O6 octahedra stacked along the  direction of the cubic perovskite structure. Neighboring slabs are separated by additional layers of oxygen atoms and are shifted with respect to each other by half the body diagonal of an octahedron along a. The number of layers of octahedra in a slab, indicated by the parameter n, determines the structure type, which varies therefore with composition. The crystal structures are all monoclinic (b unique) with a centrosymmetric P21/c symmetry for the n = 5 type compounds and an acentric P21 symmetry for the n = 6 type compound (in the latter, pseudo-inversion symmetries have been observed). The distortion of the (Nb,Ti)O6 octahedra increases from the center to the borders of the slabs. For the Ti-doped compounds, an ordering of Nb and Ti ions is observed with Ti ions preferentially occupying the central region of the slabs where the octahedral is least distorted. Nb and Ti ions have computed valences close to their formal valences of 5+ and 4+, respectively, for all sites in the structure. This indicates that Nb and Ti ions are equally well accommodated by the different oxygen environments in the slabs and that the observed ordering of Nb and Ti ions can only be the result of the different octahedral distortions. For the undoped Ca5Nb5O17 (n = 5), computed valences of Nb ions are close to 5+ at the borders and smaller fractional valences are obtained in the middle of the slabs. This suggests that the electrical conduction in this compound is most likely accommodated by the least distorted octahedra. Owing to the similarity in the structural features, a common model was successfully employed in the structural descriptions of the compounds investigated. Applying the superspace approach to the Ti-doped compounds, the crystal structures were characterized as commensurately modulated structures with a common basic structure and a centrosymmetric superspace group valid for both compounds, while the modulation wave vectors and the modulation functions depend on the composition n. Structure refinements in superspace demonstrate the efficiency of the superspace approach. The different occupation factors of Nb and Ti ions in the slabs as obtained in the three-dimensional structure model have been reproduced in the superspace refinements. The higher quality of the structure model obtained from the superspace refinements is illustrated by the computed valences of Nb and Ti ions which are much closer to their formal values of 5+ and 4+, respectively, for all sites in the structure compared to the three-dimensional or supercell model. In the case of n = 6 compound, the application of a centrosymmetric superspace group leads to an equal Nb/Ti ratio on sites that are related by superspace inversion, but that are independent sites in the supercell. In this way, the superspace approach provides a natural explanation for the pseudo-inversion symmetries as they have been observed in the supercell structure, while removing the interdependencies between parameters. The displacive modulation functions for the two compounds exhibit similarities, but in general are not identical. The modulation functions in n = 6 may not be used to describe exactly the atomic displacements in n = 5. Thus it is concluded that for this homologous series, the idea of a unified superspace model does not extend towards the precise atomic positions of the two compounds which are characterized by the displacive modulation functions.