Section 9.1.7.3. Blind region

Even after rotation of the crystal about a single axis by 360°, some reflections do not cross the surface of the Ewald sphere and cannot be measured. These lie in a cusp around the rotation axis which is referred to as the blind region. This is in principle a disadvantage of the single-rotation method, but for most systems the problems are easily overcome. Owing to the curvature of the Ewald sphere, the width of the blind region increases with the resolution and directly depends on a single parameter, the diffraction angle θ (Fig. 9.1.7.7). The variation of the fraction, , of unrecordable reflections lying in the blind region at a particular resolution with Bragg angle θ is given by The cumulative fraction, , of reflections in the blind region up to a certain resolution is given by is shown graphically as a function of resolution for selected wavelengths in Fig. 9.1.7.8.

Figure 9.1.7.7| top | pdf | Rotation by 360° leaves the part of the reciprocal space in the blind region unmeasured, since the reflections near the rotation axis do not cross the surface of the Ewald sphere. The rotation axis in this projection lies vertically in the plane of the figure.

Figure 9.1.7.8| top | pdf | Dependence of the total fraction of reflections in the blind region on the resolution for three different wavelengths: 1.54, 1 and 0.71 Å.

For a particular resolution limit, the blind region is narrower if the wavelength is short, since the surface of the Ewald sphere is flatter (Fig. 9.1.7.9). This is an advantage of using short-wavelength radiation. For Cu Kα radiation at 2.0 Å resolution, the blind region amounts to less than 5%. With shorter wavelengths, it falls below 2%.

Figure 9.1.7.9| top | pdf | For shorter wavelengths the blind region is narrower, since the Ewald sphere is flatter.

The two halves of the blind region on either side of the Ewald sphere are related by the centre of symmetry. In the triclinic case, the blind region is therefore unavoidable with a single mount of the crystal. The only solutions are to use a second mount of the crystal offset by at least 2θ from the first, easily achievable with a κ-goniostat, or to measure from a second sample.

For crystals with symmetry higher than P1, reflections that are symmetry equivalent to those in the blind region may be recorded, and there will be no loss of unique reflections. Only if the unique axis passes through the blind region approximately parallel to the spindle axis will the reflections lying close to it not be repeated by symmetry in another region of reciprocal space. To avoid the blind region, it is sufficient to misorient the unique symmetry axis by at least from the rotation axis (Fig. 9.1.7.10). To achieve full completeness, monoclinic crystals should not be oriented along the unique twofold axis or along any vector in the ac plane.

Figure 9.1.7.10| top | pdf | If the crystal has a symmetry axis, it should be skewed from the rotation axis by at least to be able to collect the reflections equivalent to those in the blind region.

The reciprocal-lattice points on the border of the blind region cross the surface of the Ewald sphere at a very acute angle or fail to cross it completely, staying in the diffracting position for a considerable time. Their intensity cannot be measured accurately, because the Lorentz factor is large and its magnitude is very sensitive to minor errors in the orientation matrix. These reflections are located on the detector window along the line parallel to the spindle axis and should not be integrated.

The detrimental effect of the blind region on the completeness of data is negligible at medium and low resolution or if the crystal is non-axially oriented. This means that a simple single rotation axis is sufficient for the majority of applications.