International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. B. ch. 2.1, p. 196
Section 2.1.5.3. Effect of other symmetry elements on the ideal acentric and centric distributions^{a}School of Chemistry, Tel Aviv University, Tel Aviv 69 978, Israel, and ^{b}St John's College, Cambridge, England |
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) and Rogers (1950), 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 and 2.1.3.2. 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 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) and (2.1.5.11) are not affected.
References
Rogers, 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 ScholarWilson, 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