Chapter

Chapter 2.2 Single-crystal X-ray techniques

Mathematical, physical and chemical tables

First Online Edition (2006)

Part 2. Diffraction geometry and its practical realization

  1. J. R. Helliwell

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000577

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Helliwell, J. R. 2006. Single-crystal X-ray techniques. International Tables for Crystallography. 26–41.

Author Information

  1. Department of Chemistry, University of Manchester, Manchester M13 9PL, England

Publication History

  1. Published Online: 1 JAN 2006

Abstract

The diffraction of beams of X-rays from single crystals involves very specific geometries that form the basis for the measurement of intensities used in crystal structure analysis. In terms of the incident beam itself, the two key approaches available involve either a monochromatic beam or a polychromatic ‘Laue’ white beam. Starting from Bragg’s law and the Ewald reciprocal-space construction, the methods for the collection of diffraction data, i.e. reflection intensities, using commonly available apparatus are then described. Monochromatic beam measuring methods such as rotating/oscillating crystal, stills, Weissenberg, precession and four-circle diffractometry are covered. The mathematical relationships between the reciprocal-lattice point (relp) coordinates in reciprocal space and the corresponding diffraction spot positions at the detector (flat, cylindrical or V-shaped) are given in detail. These coordinate transformations represent an idealized situation of relps (i.e. as points) and of diffracted rays as lines. Deviations from ideality arise from practical considerations such as the incident beam spectral purity, its divergence or convergence to the sample from the source via the optics, as well as the crystal perfection (‘mosaicity’), and of the point-spread factor of the detector. The reflection rocking curves and diffraction spot shapes and sizes are practical manifestations of these effects.

Keywords:

  • angular distribution of reflections in Laue diffraction;
  • area detectors;
  • blind region;
  • cone-axis photography;
  • conventional X-ray sources;
  • crystals;
  • diffraction;
  • diffractometry;
  • geometrical aberrations;
  • gnomonic transformations;
  • Laue geometry;
  • maximum oscillation angle;
  • monochromatic still exposure;
  • multiple-order reflections;
  • normal-beam equatorial geometry;
  • oscillation geometry;
  • photographs;
  • precession geometry;
  • reflections;
  • rocking curves;
  • rotation geometry;
  • single crystal monochromators;
  • single-order reflections;
  • spot size and shape;
  • stereographic transformations;
  • synchrotron radiation;
  • transformations;
  • upper-layer photographs;
  • Weissenberg geometry;
  • X-ray optics;
  • X-ray sources;
  • zero-layer photographs