Intergrowth polytypoids as modulated structures: the example of the cationdeficient oxides LaTi1-xO3

A new, essentially composition-independent structural model is proposed for the perovskite-related compound series LanTin-deltaO3n, with delta less th an or equal to n/4, based on superspace formalism, Tn the standard 3-dimens ional crystallographic approach, one must specify space group and cell para meters separately fur each composition. In the superspace approach, the sup erspace group is invariant while the cell parameters and primary modulation wavevector vary slowly and continuously with composition. To a first appro ximation, the structure at any particular composition carl be described in terms of mixed cubic and hexagonal stacking of close-packed LaO3 (and Ti) l ayers along the z-axis. The actual layer stacking sequence varies abruptly with composition, and the titanium vacancies occur as entire layers between neighbouring hexagonal close-packed LaO3 layers. The continuously variable , composition-dependent character of reciprocal space indicates that the va rious layer stacking sequences must be intimately correlated and shows that all the compounds can be interpreted in terms of a structural modulation o ver a common average structure. It is shown that a very simple model in sup erspace is sufficient to describe the layer stacking sequences for any part icular composition. The atomic surfaces representing the atoms in superspac e are shown to be well described by means of crenel functions. The cation d isplacive modulations are approximately described by sawtooth functions. Th e only variable parameters are the composition-dependent (but smoothly vary ing) primary modulation wave-vector and associated Ti occupation domain wid th. Conventional space groups can be easily determined from the superspace group and the composition. From a practical point of view, this means that we have a very good single starting point to refine the actual atomic posit ions for any composition, including incommensurate or long period structure s. Even more importantly, the superspace approach has the flexibility to re present in a simple manner the symmetry-allowed deviations from the ideal m odel. A comparison with the scarce number of refined structures in this sys tem and in the homologous (Ba,La)(n)Tin-1O3n system, demonstrates the suita bility of the formalism for the analysis of these compound series and for t he analysis of compositionally flexible systems in general.