Orientation refinement and reflection integration.



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Orientation refinement and reflection integration.

The objects of the initial stages of crystallographic data analysis are to assign correct values of Miller indices to each reflection on a raw diffraction image, to evaluate the integrated intensities of each reflection and obtain realistic estimates of their errors for later use when calculating structure factor phases. In addition, corrections to the integrated intensities must be made to account for the polarisation of the incident X-ray beam and for the time taken by a particular reciprocal lattice point to traverse the Ewald sphere (Lorentz correction).

Accurate determination of the orientation of the crystallographic axes of the sample crystal in the laboratory frame corresponding to each diffraction image is an essential step in this procedure. The crystal orientation is described by three rotations around orthogonal axes X, Y and Z. The X axis points horizontally along the oscillation axes perpendicular to the X-ray beam direction which is defined as Z. The Y axis points vertically upwards. Approximate values describing the crystal orientation may be obtained either manually (as was done for all the cases described later) or via several automatic auto-indexing routines which are presently available but which will not be discussed here. Once a sufficiently correct orientation has been found (usually to within ) the refinement of the orientation is then performed using least-squares methods to minimise the differences between the observed diffraction spot positions and the predicted positions calculated from known values of the crystal cell dimensions, the space group, the sample to detector distance and the X-ray wavelength. With values of the predicted positions of the reflection centroids at hand, estimates of the intensities are made using profile fitting where a calculated 2-D profile is assigned to each reflection centred on the predicted spot positions. With an expected spot profile at hand each pixel reading provides its own estimate of the overall intensity of the spot. The intensity is taken as the weighted average of the intensity estimates provided by each pixel making up a diffracted spot. Error estimates are based on counting statistics. For this reason the values of the intensities obtained are largely dependent on the quality of fit obtained for the crystal orientation since this determines the positions on the image at which the profiles are set. The program used to perform the above task was DENZO [89].

In practice there are many parameters which are not accurately known and which must be refined along with the three rotations describing the crystal orientation. These additional parameters account for small systematic shifts in the detector position and orientation, and in the case of the imaging plate scanner (see Sec. gif), for systematic misalignment of the laser readout head. Additional refinement of the crystal lattice parameters and detector distance is also performed although these values tend to be highly correlated when only low angle reflection information is available.





next up previous contents index
Next: Orientational refinement. Up: Analysis of diffraction Previous: The rotation method.



Gwyndaf Evans
Fri Oct 7 15:42:16 MET 1994