Intergrowth polytypoids as modulated structures: a superspace description of the Sr-n(Nb,Ti)(n)O3n+2 compound series

A new, unified superspace approach to the structural characterization of th e perovskite-related Sr-n(Nb,Ti)(n)O3n+2 compound series, strontium niobium /titanium oxide. is presented. To a first approximation, the structure of a ny member of this compound series can be described in terms of the stacking of (110)-bounded perovskite stabs, the number of atomic layers in a single perovskite slab varying systematically with composition. The various compo sition-dependent layer-stacking sequences can be interpreted in terms of th e structural modulation of a common underlying average structure. The avera ge interlayer separation distance is directly related to the average struct ure periodicity along the layer stacking direction, while an inherent modul ation thereof is produced by the presence of different types of layers (par ticularly vacant layers) along this stacking direction. The fundamental ato mic modulation is therefore occupational and can be described by means of c renel (step-like) functions which define occupational atomic domains in the superspace, similarly to what occurs for quasicrystals. While in a standar d crystallographic approach, one must describe each structure (in particula r the space group and cell parameters) separately for each composition, the proposed superspace model is essentially common to the whole compound seri es. The superspace symmetry group is unique, while the primary modulation w avevector and the width of some occupation domains vary linearly with compo sition. For each rational composition, the corresponding conventional three -dimensional space group can be derived from the common superspace group. T he resultant possible three-dimensional space groups are in agreement with all the symmetries reported for members of the series. The symmetry-breakin g phase transitions with temperature observed in many compounds can be expl ained in terms of a change in superspace group, again in common for the who le compound series. Inclusion of the incommensurate phases, present in many compounds of the series. lifts the analysis into a five-dimensional supers pace. The various four-dimensional superspace groups reported for this inco mmensurate phase at different compositions are shown to be predictable from a proposed five-dimensional superspace group apparently common to the whol e compound series. A comparison with the scarce number of refined structure s in this system and the homologous (Nb,Ca)(6)Ti6O20 compound demonstrates the suitability of the proposed formalism.