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, pp. 29-30

Section 2.2.2. Monochromatic methods

J. R. Helliwella

aDepartment of Chemistry, University of Manchester, Manchester M13 9PL, England

2.2.2. Monochromatic methods

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In this section and those that follow, which deal with monochromatic methods, the convention is adopted that the Ewald sphere takes a radius of unity and the magnitude of the reciprocal-lattice vector is λ/d. This is not the convention used in the Laue section above.

Some historical remarks are useful first before progressing to discuss each monochromatic geometry in detail. The original rotation method (for example, see Bragg, 1949[link]) involved a rotation of a perfectly aligned crystal of 360°. For reasons of relatively poor collimation of the X-ray beam, leading to spot-to-spot overlap, and background build-up, Bernal (1927[link]) introduced the oscillation method whereby a repeated, limited, angular range was used to record one pattern and a whole series of contiguous ranges on different film exposures were collected to provide a large angular coverage overall. In a different solution to the same problem, Weissenberg (1924[link]) utilized a layer-line screen to record only one layer line but allowed a full rotation of the crystal but now coupled to translation of the detector, thus avoiding spot-to-spot overlap. Again, several exposures were needed, involving one layer line collected on each exposure. The advent of synchrotron radiation with very high intensity allows small beam sizes at the sample to be practicable, thus simultaneously creating small diffraction spots and minimizing background scatter. The very fine collimation of the synchrotron beam keeps the diffraction-spot sizes small as they traverse their path to the detector plane.

The terminology used today for different methods is essentially the same as originally used except that the rotation method now tends to mean limited angular ranges (instead of 360°) per diffraction photograph/image. The Weissenberg method in its modern form now employed at a synchrotron is a screenless technique with limited angular range but still with detector translation coupled to crystal rotation.

2.2.2.1. Monochromatic still exposure

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In a monochromatic still exposure, the crystal is held stationary and a near-zero wavelength-bandpass (e.g. δλ/λ = 0.001) beam impinges on it. For a small-molecule crystal, there are few diffraction spots. For a protein crystal, there are many (several hundred), because of the much denser reciprocal lattice. The actual number of stimulated relp's depends on the reciprocal-cell parameters, the size of the mosaic spread of the crystal, the angular beam divergence as well as the small, but finite, spectral spread, δλ/λ. Diffraction spots are only partially stimulated instead of fully integrated over wavelength, as in the Laue method, or over an angular rotation (the rocking width) in rotating-crystal monochromatic methods.

The diffraction spots lie on curved arcs where each curve corresponds to the intersection with a film of a cone. With a flat film the intersections are conic sections. The curved arcs are obviously recognizable for the protein crystal case where there are a large number of spots.

2.2.2.2. Crystal setting

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Crystal setting follows the procedure given in Subsection 2.2.1.2[link] whereby angular mis-setting angles are given by equation (2.2.1.3)[link]. When viewed down a zone axis, the pattern on a flat film or electronic area detector has the appearance of a series of concentric circles. For example, with the beam parallel to [[00\bar1]], the first circle corresponds to l = 1, the second to l = 2, etc. The radius of the first circle R is related to the interplanar spacing between the (hk0) and (hk1) planes, i.e. λ/c (in this example), through [\theta], by the formulae [\tan2\theta=R/D;\quad\cos2\theta=1-\lambda/c. \eqno (2.2.2.1)]

References

Bernal, J. D. (1927). A universal X-ray photogoniometer. J. Sci. Instrum. 4, 273–284.
Bragg, W. L. (1949). The crystalline state: a general survey, pp. 30–33. London: Bell.
Weissenberg, K. (1924). Ein neues Röntgengoniometer. Z. Phys. 23, 229–238.








































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