Forbidden reflections due to anisotropic X-ray susceptibility of crystals

Methods have been developed for predicting the properties of the new type of structurally forbidden reflections arising from anisotropic X-ray susceptibility of crystals. The general symmetry properties of the spatially dependent tensor of X-ray susceptibility are described. From this tensor the structure amplitudes and new extinction rules for the screw-axis and glide-plane 'forbidden' reflections are derived. All these forbidden reflections may be excited except the 00l (l = 2n + 1) reflections for a 63 screw axis and the 00l (l = 6n + 3) reflections for 6₁ and 6₅ screw axes. The polarization properties of these forbidden reflections are very unusual. For example, a σ-polarized incident beam can give a π-polarized diffracted one and vice versa; in some cases only a circularly polarized beam is diffracted, etc. Some estimations show that near the X-ray absorption edges the structure amplitudes of these reflections can be of the order of a few electrons atom^-1. The general methods are illustrated by their application to the rutile structure.