Section 9.1.6.2. Diffraction pattern at a single orientation: the `still' image

For a stationary crystal in any particular orientation (a so-called `still' exposure), only a fraction of the total number of Bragg reflections will satisfy the diffracting condition. The number of reflections will be very limited for a small-molecule crystal, possibly zero in some orientations. Macromolecules have large unit cells, of the order of 100 Å, compared with the wavelength of the radiation, which is about 1.0 Å. In geometric terms, the reciprocal space is densely populated by points in relation to the size of the Ewald sphere. Thus, more reflections diffract simultaneously but at different angles, since many reciprocal-lattice points (reflections) lie simultaneously on the surface of the Ewald sphere in any crystal orientation. This is the great advantage of 2D detectors for large cell dimensions.

The real crystal is a regular and ordered array of unit cells. This means that reciprocal space is made up of a set of points organized in regular planes. For a still exposure, any particular plane of points in the reciprocal lattice intersects the surface of the Ewald sphere in the form of a circle. The corresponding diffracted rays, originating from the centre of the Ewald sphere, form a cone that intersects the sphere on the circle formed by the set of points. In most experiments, the detector is placed perpendicular to the direct beam and the cone of diffracted rays forms an ellipse of spots on its surface (Fig. 9.1.6.2). If a major axis of the crystal lies nearly parallel to the beam, then the ellipses will approximate a set of circles around the centre of the detector. All reflections within each circle will have one index in common, corresponding to the unit-cell axis lying along the beam. For non-centred unit cells, the index will increase by one in successive circles. The gaps between the circles depend on the spacing between the set of reciprocal-lattice planes and are inversely proportional to the real cell dimension related to these planes.

Figure 9.1.6.2| top | pdf | The plane of reflections in the reciprocal sphere that is approximately perpendicular to the X-ray beam gives rise to an ellipse of reflections on the detector.

Still exposures were used extensively in the early applications of the rotation method for estimation of crystal alignment. The geometric location of the spots with respect to the origin allows accurate determination of the unit-cell parameters and the crystal orientation. This approach has been superseded in modern software packages by autoindexing algorithms using real rotation images instead of stills.