Concise intensity statistics of Friedel opposites and classification of the reflections

Abstract

A previous extensive analysis of the mean-square intensity difference of Friedel opposites [Shmueli et al. (2008). Acta Cryst. A64, 476-483] is here concisely re-examined and confirmed by purely statistical methods. The analysis applies to noncentrosymmetric crystals only. For special reflections and centered lattices both mean-square intensity difference and average intensity of Friedel opposites depend on the centering factor of the crystal lattice and/or on the isotropy subgroup of the reflection. A complete classification of the reflections, based on the above intensity statistics, is presented. It is also shown that the experimentally important Bijvoet ratio is found to depend only on the chemical composition of the unit-cell content and the wavelength of the radiation.