International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by M. G. Rossmann and E. Arnold © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. F. ch. 11.4, p. 232
Section 11.4.6.2. Bragg's law for non-ideal conditions: mosaicity
a
UT Southwestern Medical Center at Dallas, 5323 Harry Hines Boulevard, Dallas, TX 75390-9038, USA, and bDepartment of Molecular Physiology and Biological Physics, University of Virginia, 1300 Jefferson Park Avenue, Charlottesville, VA 22908, USA |
The Bragg condition [equation (11.4.2.1)] assumes ideal crystals and a parallel X-ray beam. In reality, crystals are mosaic and the beam has some angular spread. The value of mosaicity describes the range of orientations of the crystal lattice within a sample. As the impacts of mosaicity and the beam's angular spread on the angular width of reflections are equivalent, the keyword mosaicity describes the sum of both effects.
DENZO
assumes the following model of angular shape of diffraction peaks: for
in the range (
,
where mos is mosaicity,
is the predicted angle and P is the predicted partiality of data collected by oscillating from
to
.
Partiality is a number that represents what fraction of the reflection intensity is present in one image. If partiality is 1, such reflections are called fully recorded; otherwise they are called partials. For partials, predictions of partiality can be compared with the observed fraction of the reflection intensity present in one image. The partiality model contributes the following term to the refinement:
The combined positional and partiality refinement used in DENZO is both stable and very accurate. The power of this method is in proper weighting (by estimated error) of two very different terms – one describing positional differences and the other describing intensity differences. Both detector and crystal variables are uniformly treated in the refinement process.