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

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

Section 2.2.3.5. Blind region

J. R. Helliwella

aDepartment 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

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








































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