International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. C. ch. 2.2, p. 34

Section 2.2.3.5. Blind region

J. R. Helliwella

a Department of Chemistry, University of Manchester, Manchester M13 9PL, England

2.2.3.5. Blind region

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In normal-beam geometry, any relp lying close to the rotation axis will not be stimulated at all. This situation is shown in Fig. 2.2.3.4[link] . The blind region has a radius of [\xi_{\min}=d^*_{\max}\sin\theta_{\max}={\lambda^2\over2d^2_{\min}}, \eqno (2.2.3.31)]and is therefore strongly dependent on dmin but can be ameliorated by use of a short λ. Shorter λ makes the Ewald sphere have a larger radius, i.e. its surface moves closer to the rotation axis. At Cu Kα for 2 Å resolution, approximately 5% of the data lie in the blind region according to this simple geometrical model. However, taking account of the rocking width Δ, a greater percentage of the data than this is not fully sampled except over very large angular ranges. The actual increase in the blind-region volume due to this effect is minimized by use of a collimated beam and a narrow spectral spread (i.e. finely monochromatized, synchrotron radiation) if the crystal is not too mosaic.

[Figure 2.2.3.4]

Figure 2.2.3.4| top | pdf |

The rotation method. The blind region associated with a single rotation axis. From Arndt & Wonacott (1977[link]).

These effects are directly related to the Lorentz factor, [L=1/(\sin^{2}2\theta-\zeta^2)^{1/2}.\eqno (2.2.3.32)]It is inadvisable to measure a reflection intensity when L is large because different parts of a spot would need a different Lorentz factor.

The blind region can be filled in by a rotation about another axis. The total angular range that is needed to sample the blind region is [2\theta_{\max}] in the absence of any symmetry or [\theta_{\max}] in the case of mm symmetry (for example).

References

First citation Arndt, U. W. & Wonacott, A. J. (1977). The rotation method in crystallography. Amsterdam: North-Holland.Google Scholar








































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