Investigation of the Cs_xRb_1-xTiOAsO₄ Series. II. The Problems of Interpretation of Residual Electron Densities in a Polar Space Group

The problems of refinements of structures in a polar space group, such as Pna2₁, are illustrated by the example of crystals in the Cs_2xRb_2-2xTi₂O₂As₂O₈, caesium rubidium titanyl arsenate, series, which are isostructural with the well known non-linear optical crystal KTiOPO₄. It is shown in particular that errors in the data collection and/or refinement tend to contribute positive residual electron density in sites which are related by an inversion operation to the real Cs/Rb sites. This phenomenon is a consequence of the presence of two minima in least-squares space, representing here the possible coordinate sets x,y,z and x,y,-z, for a polar structure and is exacerbated in these structures by the presence of strong inversion psuedo-symmetry. It is shown that in the worst case, the positive residual electron density can be eliminated and an improved agreement to the observed data obtained by refinement of a partially micro-twinned disordered structure in which the Cs/Rb occupancy is split between the main sites and the inversion-related sites. It is argued that the true structure is micro-twinned, including partial occupancy of the additional sites.

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