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

International Tables for Crystallography (2006). Vol. B. ch. 2.5, pp. 287-288   | 1 | 2 |

## Section 2.5.3.2.3. In-disc symmetries

P. Goodmanb

#### 2.5.3.2.3. In-disc symmetries

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• (a) Dark-field (diffracted-beam) discs . Other reciprocity-generated symmetries which are available for experimental observation relate to a single (zero-layer) disc and its origin , and are summarized here by reference to Fig. 2.5.3.2, and given in operational detail in Table 2.5.3.2. The notation subscript R, for reciprocity-induced symmetries, introduced by Buxton et al. (1976) is now adopted (and referred to as BESR notation). Fig. 2.5.3.2 shows a disc crossed by reference lines m and . These will be mirror lines of intensity if: (a) g is parallel to a vertical mirror plane; and (b) g is parallel to a horizontal diad axis, respectively. The third possible point symmetry, that of disc centrosymmetry ( in BESR notation) will arise from the presence of a horizontal mirror plane. Lines m and become the GS extinction lines G and S when glide planes and screw axes are present instead of mirror planes and diad axes.

 Table 2.5.3.2| top | pdf | Diagrammatic illustrations of the actions of five types of symmetry elements (given in the last column in Volume A diagrammatic symbols) on an asymmetric pattern component, in relation to the centre of the pattern at , shown as ⊕', or in relation to the centre of a diffraction order at , shown as +'
TypeSymmetry elementObservation and actionIn combinationInterpretation
Vertical 4
m; a
Horizontal 2′;

m′; a
• (b) Bright-field (central-beam) disc . The central beam is a special case since the point is the centre of the whole pattern as well as of that particular disc. Therefore, both sets of rotational symmetry (types I and II) discussed above apply (see Table 2.5.3.3).

In addition, the central-beam disc is a source of three-dimensional lattice information from defect-line scattering. Given a sufficiently perfect crystal this fine-line structure overlays the more general intensity modulation, giving this disc a lower and more precisely recorded symmetry.

### References

Buxton, B., Eades, J. A., Steeds, J. W. & Rackham, G. M. (1976). The symmetry of electron diffraction zone axis patterns. Philos. Trans. R. Soc. London Ser. A, 181, 171–193.Google Scholar