International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 2.5, p. 288   | 1 | 2 |

Section 2.5.3.2.4. Zero-layer absences

P. Goodmanb

2.5.3.2.4. Zero-layer absences

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Horizontal glides, a′, n′ (diperiodic, primed notation), generate zero-layer absent rows, or centring, rather than GS bands (see Fig. 2.5.3.3[link]). 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 [2_{1} \simeq 2]). Elements included in Table 2.5.3.1[link] on this pretext are given in parentheses. However, the presence of [2_{1}] rather than 2 ([3_{1}] 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[link]). This has been observed in the cubic structure of Ba2Fe2O5Cl2, permitting the space groups I23 and [I2_{1} 3] to be distinguished (Schwartzman et al., 1996[link]). A summary of all the symmetry components described in this section is given diagrammatically in Table 2.5.3.2[link].

[Figure 2.5.3.3]

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.

References

First citation Schwartzman, A., Goodman, P. & Johnson, A. W. S. (1996). IUCr XVII Congress and General Assembly, Seattle, Washington, USA, August 8–16, Collected Abstracts, p. C-54, Abstract PS02.03.18.Google Scholar








































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