Superspace description of the homologous series Ga4Tim-4O2m-2 with the crystallographic shear structure based on that of rutile.

A generalized approach is proposed for the structure description of the homologous series Ga(4)Ti(m-4)O(2m-2) with crystallographic shear (CS) structures based on that of rutile. A (3 + 1)-dimensional model for an ideal CS structure is built up in connection with the CS operation in three-dimensional space. Its structural parameters are determined by m, the shear plane and the shear vector. The Rietveld fitting of the X-ray diffraction profile of Ga(4)Ti(13)O(32) (m = 17) was successfully carried out using the ideal CS structure as an initial model, where modulation functions of atomic positions are inherently discontinuous and sawtooth-like. The deviation of a real structure from the ideal one was described by a few additional Fourier terms. This method was confirmed to be efficient for reducing the number of structural parameters required in the refinement in comparison to the conventional three-dimensional description.