Structure-factor statistics and crystal symmetry

Abstract

This article briefly summarizes the ideal structure-factor statistics, which are usually the only ones that are applied at the stage of resolution of space-group ambiguities, and points out their disadvantages. Next, the non-ideal structure-factor statistics,i.e.those taking any atomic composition into account, are summarized and applied to several examples, based on real intensity data. The superiority of the non-ideal statistics, when applied to the problematic space group P\overline{1}, is obvious. It is also shown that statistics for some orthorhombic space groups are rather insensitive to atomic heterogeneity. A table of coefficients is presented from which non-ideal statistics can be computed for all the space groups of the triclinic, monoclinic and orthorhombic systems.