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

International Tables for Crystallography (2006). Vol. B. ch. 2.1, p. 196   | 1 | 2 |

Section 2.1.5.3. Effect of other symmetry elements on the ideal acentric and centric distributions

U. Shmuelia* and A. J. C. Wilsonb

aSchool of Chemistry, Tel Aviv University, Tel Aviv 69 978, Israel, and bSt John's College, Cambridge, England
Correspondence e-mail:  ushmueli@post.tau.ac.il

2.1.5.3. Effect of other symmetry elements on the ideal acentric and centric distributions

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Additional crystallographic symmetry elements do not produce any essential alterations in the ideal centric or acentric distribution; their main effect is to replace the parameter Σ by a `distribution parameter', called S by Wilson (1950[link]) and Rogers (1950[link]), in certain groups of reflections. In addition, in noncentrosymmetric space groups, the distribution of certain groups of reflections becomes centric, though the general reflections remain acentric. The changes are summarized in Tables 2.1.3.1[link] and 2.1.3.2[link]. The values of S are integers for lattice centring, glide planes and those screw axes that produce absences, and approximate integers for rotation axes and mirror planes; the modulations of the average intensity in reciprocal space outlined in Section 2.1.3.2[link] apply.

It should be noted that if intensities are normalized to the average of the group to which they belong, rather than to the general average, the distributions given in equations (2.1.5.8)[link] and (2.1.5.11)[link] are not affected.

References

First citationRogers, D. (1950). The probability distribution of X-ray intensities. IV. New methods of determining crystal classes and space groups. Acta Cryst. 3, 455–464.Google Scholar
First citationWilson, A. J. C. (1950). The probability distribution of X-ray intensities. III. Effects of symmetry elements on zones and rows. Acta Cryst. 3, 258–261.Google Scholar








































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