Section 1.11.2.2.2. Screw-axis forbidden reflections

For the screw-axis forbidden reflections, the most general form of the tensor structure factor can be found as before (Dmitrienko, 1983; see Table 1.11.2.1). Again, as in the case of the glide plane, for each forbidden reflection all components of the tensor structure factor are determined by at most two independent complex elements and . There may, however, exist further restrictions on these tensor elements if other symmetry operations of the crystal space group are taken into account. For example, although there are screw axes in space group , and reflections remain forbidden because the lattice is body centred, and this applies not only to the dipole–dipole approximation considered here, but also within any other multipole approximation.

Table 1.11.2.1 | top | pdf | The indices of the screw-axis/glide-plane forbidden reflections () and independent components of their tensorial structure factors Other components: , , . The direction of the z axis is selected along the corresponding screw axes. The last column lists different types of polarization properties defined in Section 1.11.3. Screw axis or glide plane Type 0 0 I II II 0 0 I 0 0 II 0 0 II 0 0 I 0 0 II 0 0 I 0 0 II 0 0 0 0   0 0 II 0 0 0 0   0 0 II 0 0 I 0 0 II 0 0 0 0   0 0 II

In Table 1.11.2.1, resulting from the dipole–dipole approximation, some reflections still remain forbidden. For instance, in the case of a screw axis, there is no anisotropy of susceptibility in the plane due to the inevitable presence of the threefold rotation axis. For and axes, the reflections with also remain forbidden because only dipole–dipole interaction (of X-rays) is taken into account, whereas it can be shown that, for example, quadrupole interaction permits the excitation of these reflections.