Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

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

Section In-disc symmetries

P. Goodmanb 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 [{\bf K}_{g} = {\bf 0}], and are summarized here by reference to Fig.[link], and given in operational detail in Table[link]. The notation subscript R, for reciprocity-induced symmetries, introduced by Buxton et al. (1976)[link] is now adopted (and referred to as BESR notation). Fig.[link] shows a disc crossed by reference lines m and [m_{R}]. 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 ([1_{R}] in BESR notation) will arise from the presence of a horizontal mirror plane. Lines m and [m_{R}] become the GS extinction lines G and S when glide planes and screw axes are present instead of mirror planes and diad axes.

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    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 [{\bf K}_{00} = {\bf 0}], shown as `⊕', or in relation to the centre of a diffraction order at [{\bf K}_{0g} = {\bf 0}], shown as `+'

    TypeSymmetry elementObservation and actionIn combinationInterpretation
    Vertical 4 [Scheme scheme1]   [Scheme scheme2]
    m; a [Scheme scheme3] [Scheme scheme5] [Scheme scheme6]
    Horizontal 2′; [2'_{1}] [Scheme scheme4]
    [i(\bar{1}')] [Scheme scheme7]   [Scheme scheme8]
    m′; a [Scheme scheme9]   [Scheme scheme10]
  • (b) Bright-field (central-beam) disc . The central beam is a special case since the point [{\bf K}_{0} = {\bf 0}] is the centre of the whole pattern as well as of that particular disc. Therefore, both sets of rotational symmetry (types I[link] and II[link]) discussed above apply (see Table[link]).

    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.


First citation 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

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