Acta Crystallographica Section A

Foundations of Crystallography

Volume 63, Part 3 (May 2007)

research papers

Acta Cryst. (2007). A63, 257-265 [ doi:10.1107/S0108767307002802 ]

The mean-square Friedel intensity difference in P1 with a centrosymmetric substructure

H. D. Flack and U. Shmueli

Abstract: For non-centrosymmetric structures in space group P1 containing a centrosymmetric substructure, analytical expressions have been obtained for various functions of the diffraction intensity of Friedel opposites. These functions are the average intensity of Friedel opposites, the mean difference in intensity of Friedel opposites and the mean-square difference in intensity of Friedel opposites. A Bijvoet intensity ratio is defined for the evaluation of resonant-scattering effects in non-centrosymmetric and pseudo-centrosymmetric structures. Analysis of these expressions confirms that both resonant and non-resonant atoms are necessary to produce differences in intensity between Friedel opposites and also shows that in some circumstances atoms may lie on a centrosymmetric substructure without diminishing the Bijvoet intensity ratio. The effects of the real component of resonant scattering, of the variation of the scattering factors with sin [theta] / [lambda] , of isotropic atomic displacement parameters, of a crystal twinned by inversion, of atoms in special positions and of weak reflections are considered. Software is available for the evaluation of the Bijvoet intensity ratio.

Keywords: absolute configuration; absolute structure; anomalous scattering; Flack parameter; intensity statistics; pseudo-centrosymmetric structures; resonant scattering.


	Microsoft Excel (XLS) file (77.5 kbytes) [ doi:10.1107/S0108767307002802/sh5056sup1.xls ] Spreadsheet in Excel format (original version)

	Open Spreadsheet Text (ODS) file (32.1 kbytes) [ doi:10.1107/S0108767307002802/sh5056sup2.ods ] Spreadsheet in ODS format (original version)

	Extensible Markup Language (XML) file (286.4 kbytes) [ doi:10.1107/S0108767307002802/sh5056sup3.xml ] Spreadsheet in xml format (original version)

	Microsoft Excel (XLS) file (107.0 kbytes) [ doi:10.1107/S0108767307002802/sh5056sup4.xls ] Spreadsheet in Excel format (new version supplied by the author on 8 May 2008)

	Open Spreadsheet Text (ODS) file (36.6 kbytes) [ doi:10.1107/S0108767307002802/sh5056sup5.ods ] Spreadsheet in ODS format (new version supplied by the author on 8 May 2008)

	Extensible Markup Language (XML) file (287.5 kbytes) [ doi:10.1107/S0108767307002802/sh5056sup6.xml ] Spreadsheet in xml format (new version supplied by the author on 8 May 2008)

Notes:

To open or display or play some files, you may need to set your browser up to use the appropriate software. See the full list of file types for an explanation of the different file types and their related mime types and, where available links to sites from where the appropriate software may be obtained.

The download button will force most browsers to prompt for a file name to store the data on your hard disk.

Where possible, images are represented by thumbnails.

Search: From to Advanced search