Analysing Friedel averages and differences

Various practical applications of the average (A) and difference (D) of Friedel opposites are described. Techniques based on the resonant-scattering contribution to Friedel differences are applied to see whether a crystal is centrosymmetric or not, and to determine the point group of the crystal. For the validation of a structural study, plots of A(obs) against A(model), and D-obs against D-model are used extensively. Moreover, it is useful to display both plots on the same graph. Intensity measurements on a crystal of NaClO3 were made at three different speeds, with two different radiations and two different diffractometers, and treated with two different software packages and four different absorption corrections. The evaluation of these numerous data sets reveals underlying deficiencies. For comparison, plots of A(obs) against A(model), and D-obs against D-model are presented for two centrosymmetric crystals.