Section 2.5.3.2.4. Zero-layer absences

Horizontal glides, a′, n′ (diperiodic, primed notation), generate zero-layer absent rows, or centring, rather than GS bands (see Fig. 2.5.3.3). This is an example of the projection approximation in its most universally held form, i.e. in application to absences. Other examples of this are: (a) appearance of both G and S extinction bands near their intersection irrespective of whether glide or screw axes are involved; and (b) suppression of the influence of vertical, non-primitive translations with respect to observations in the zero layer. It is generally assumed as a working rule that the zero-layer or ZOLZ pattern will have the rotational symmetry of the point-group component of the vertical screw axis (so that ). Elements included in Table 2.5.3.1 on this pretext are given in parentheses. However, the presence of rather than 2 ( rather than 3 etc.) should be detectable as a departure from accurate twofold symmetry in the first-order-Laue-zone (FOLZ) reflection circle (depicted in Fig. 2.5.3.3). This has been observed in the cubic structure of Ba₂Fe₂O₅Cl₂, permitting the space groups I23 and to be distinguished (Schwartzman et al., 1996). A summary of all the symmetry components described in this section is given diagrammatically in Table 2.5.3.2.

Figure 2.5.3.3| top | pdf | Diagrammatic representation of the influence of non-symmorphic elements: (i) Alternate rows of the zero-layer pattern are absent owing to the horizontal glide plane. The pattern is indexed as for an `a' glide; the alternative indices (in parentheses) apply for a `b' glide. (ii) GS bands are shown along the central row of the zero layer, for odd-order reflections.