The rotation method.



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The rotation method.

In the rotation method the Bragg condition for each reflection is satisfied for monochromatic radiation by rotating the sample crystal. Each lattice plane is brought in turn into the diffraction condition for a short period of time as the crystal rotates. An equivalent description is to imagine reciprocal lattice points traversing the Ewald sphere as the lattice rotates. This may be visualised with the aid of Fig. gif where

  
Figure: 2-dimensional section through reciprocal space showing how the Ewald sphere sweeps through reciprocal lattice points bringing them into the diffraction condition. For simplicity the reciprocal lattice has been held fixed and the Ewald sphere has been rotated whereas the opposite applies in the Rotation method. The rotation axis is normal to the paper. The Ewald sphere of radius is shown in two positions distinguished by a rotation about . The shaded areas show the regions of reciprocal space covered by this rotation. The limiting sphere is defined by the maximum attainable resolution which is dependent on detector geometry or sample crystals diffraction limit.

the Ewald sphere is shown in two positions with respect to the reciprocal lattice after a rotation about the axis which is normal to the paper. The shaded region represents that part of reciprocal space which cuts the sphere as it rotates. (In fact the Ewald sphere is fixed and the reciprocal lattice rotates but for simplicity the figure has been drawn in the opposite fashion; the two situations are however equivalent.) The view normal to the rotation axis is shown in Fig. gif. It is seen that there is a specific region of reciprocal space which is missed by the Ewald sphere as it rotates. This is called the blind region. Any reflections which are not collected due to being in the blind region can be collected by re-orienting the sample crystal so that they enter the region of space traversed by the Ewald sphere. Alternatively the presence of symmetry elements in the crystal may imply that symmetry equivalent reflections of those lost in the blind region may be observed elsewhere in reciprocal space where they do cut the Ewald sphere.

  
Figure: Orthogonal view of reciprocal space showing the blind region of space where the Ewald sphere does not cross any reciprocal lattice points.

The diffracted intensities produced by the rotation method are typically recorded with an area detector positioned behind the sample crystal. The most commonly used detectors have been X-ray film, Imaging plates (see Sec. gif), television type detectors and more recently CCDs (Charge-Couple Devices).

The crystal reciprocal lattice cannot be sampled in one rotation as this would produce many spots upon one image which would overlap making their individual intensities unmeasurable. The reciprocal lattice is therefore sampled by a series of oscillation images whereby only a few degrees of reciprocal space are sampled per image. Overlap is most likely to occur in that region of reciprocal space which traverses the Ewald sphere in a direction normal to the sphere surface. This corresponds to reciprocal lattice points for which the equivalent Bragg plane spacing is small, i.e. is large. Overlap will occur between adjacent reciprocal lattice points which lie on a line perpendicular to the rotation axis. If their separation is then the maximum allowable rotation, , which can be made without incurring overlapping spots is given by

where is a value representing the angular range over which the diffraction condition is satisfied for a particular reciprocal lattice point and is dependent on the crystal mosaicity, the angular spread of the X-rays incident on the crystal, and the range of X-ray wavelengths incident on the crystal (see for example Helliwell [47] p248). Detailed descriptions and theory of the rotation method may be found in [3] [39] [18] [47].



next up previous contents index
Next: Orientation refinement and Up: Analysis of diffraction Previous: Analysis of diffraction



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