International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 1.6, p. 111

Section 1.6.2.5. Pitfalls in space-group determination

U. Shmuelia and H. D. Flackb

1.6.2.5. Pitfalls in space-group determination

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The methods described in Sections 1.6.2[link] and 1.6.5.1[link] rely on the crystal measured being a single-domain crystal, i.e. it should not be twinned. Nevertheless, some types of twin are easily identified at the measurement stage as they give rise to split reflections. Powerful data-reduction techniques may be applied to data from such crystals to produce a reasonably complete single-domain intensity data set. Consequently, the multi-domain twinned crystals that give rise to difficulties in space-group determination are those for which the reciprocal lattices of the individual domains overlap exactly without generating any splitting of the Bragg reflections. A study of the intensity data from such a crystal may display two anomalies. Firstly, the intensity distribution, as described and analysed in Section 1.6.2.2[link], will be broader than that of the monodomain crystal. Secondly, one may obtain a set of conditions for reflections that does not correspond to any entry in Section 1.6.4[link]. In this chapter we give no further information on the determination of the space group for such twinned crystals. For further information on this topic see Part 3[link] of Volume D (Boček et al., 2006[link]) and Chapter 1.3[link] on twinning in Volume C (Koch, 2006[link]). A supplement (Flack, 2015[link]) to the current section deals with the determination of the space group from twinned crystals and those displaying a specialized metric. However, it is apposite to note that the existence of twins with overlapping reciprocal lattices can be identified by recording atomic resolution transmission electron-microscope images.

In order to obtain reliable results from space-group determination, the coverage of the reciprocal space by the intensity measurements should be as complete as possible. One should attempt to attain full-sphere data coverage, i.e. a complete set of intensity measurements in the point group 1. All Friedel opposites should be measured. The validity and reliability of the intensity statistics described in Section 1.6.2.2[link] rest on a full coverage of reciprocal lattice. Any systematic omission by resolution, azimuth and declination, intensity etc. of part of the asymmetric region of the reciprocal lattice has an adverse effect. In particular, reflections of weak intensity should not be omitted or deleted.

There are a few other common difficulties in space-group determination due either to the nature of the crystal or the experimental setup:

  • (a) The crystal may display a pseudo-periodicity leading to systematic series of weak or very weak reflections that can be mistaken for systematic absences.

  • (b) The physical effect of multiple reflections can lead to diffraction intensity appearing at the place of systematic absences. However, the shape of these multiple-reflection intensities is usually much sharper than a normal Bragg reflection.

  • (c) Contamination of the incident radiation by a [\lambda/2] component may also cause intensity due to the 2h 2k 2l reflection to appear at the place of the hkl one. Kirschbaum et al. (1997)[link] and Macchi et al. (1998)[link] have studied this probem and describe ways of circumventing it.

References

Boček, P., Hahn, Th., Janovec, V., Klapper, H., Kopský, V., Přivratska, J., Scott, J. F. & Tolédano, J.-C. (2014). International Tables for Crystallography, Volume D, Physical Properties of Crystals, edited by A. Authier, 2nd ed., Part 3. Chichester: Wiley.
Flack, H. D. (2015). Methods of space-group determination – a supplement dealing with twinned crystals and metric specialization. Acta Cryst. C71, 916–920.
Kirschbaum, K., Martin, A. & Pinkerton, A. A. (1997). λ/2 Contamination in charge-coupled-device area-detector data. J. Appl. Cryst. 30, 514–516.
Koch, E. (2006). Twinning. In International Tables for Crystallography, Volume C, Mathematical, Physical and Chemical Tables, 1st online edition, edited by E. Prince, ch. 1.3. Chester: International Union of Crystallography.








































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