Section 2.2.7.2. Conventional X-ray sources: spectral character, crystal rocking curve, and spot size

An extended discussion of instrumentation relating to conventional X-ray sources is given in Arndt & Willis (1966) and Arndt & Wonacott (1977). Witz (1969) has reviewed the use of monochromators for conventional X-ray sources.

It is generally the case that the Kα line has been used for single-crystal data collection via monochromatic methods. The continuum Bremsstrahlung radiation is used for Laue photog­raphy at the stage of setting crystals.

The emission lines of interest consist of the , doublet and the Kβ line. The intrinsic spectral width of the , or line is , their separation (δλ/λ) is , and they are of different relative intensity. The Kβ line is eliminated either by use of a suitable metal filter or by a monochromator. A mosaic monochromator such as graphite passes the , doublet in its entirety. The monochromator passes a certain, if small, component of a harmonic of the , line extracted from the Bremsstrahlung. This latter effect only becomes important in circumstances where the attenuated main beam is used for calibration; the process of attenuation enhances the short-wavelength harmonic component to a significant degree. In diffraction experiments, this component is of negligible intensity. The polarization correction is different with and without a monochromator (see Chapter 6.2 ).

The effect of the doublet components of the Kα emission is to cause a peak broadening at high angles. From Bragg's law, the following relationship holds for a given reflection: For proteins where is relatively small, the effect of the , separation is not significant. For small molecules, which diffract to higher resolution, this is a significant effect and has to be accounted for at high angles.

The width of the rocking curve of a crystal reflection is given by (Arndt & Willis, 1966) when the crystal is fully bathed by the X-ray beam, where a is the crystal size, f the X-ray tube focus size (foreshortened), s the distance between the X-ray tube focus and the crystal, and η the crystal mosaic spread (Fig. 2.2.7.1 ).

Figure 2.2.7.1| top | pdf | Reflection rocking width for a conventional X-ray source. From Arndt & Wonacott (1977, p. 7). (a) Effect of sample mosaic spread. The relp is replaced by a spherical cap with a centre at the origin of reciprocal space where it subtends an angle η. (b) Effect of (δλ/λ)conv, the conventional source type spectral spread. (c) Effect of a beam divergence angle, γ. The overall reflection rocking width is a combination of these effects.

In the moving-crystal method, Δ is the minimum angle through which the crystal must be rotated, for a given reflection, so that every mosaic block can diffract radiation covering a fixed wavelength band δλ from every point on the focal spot.

This angle Δ can be controlled to some extent, for the protein case, by collimation. For example, with a collimator entrance slit placed as close to the X-ray tube source and a collimator exit slit placed as close to the sample as possible, the value of (a + f)/s can approximately be replaced by (a′ + f′)/s′, where f′ is the entrance-slit size, a′ is the exit-slit size, and s′ the distance between them. Clearly, for a′ a, the whole crystal is no longer bathed by the X-ray beam. In fact, by simply inserting horizontal and vertical adjustable screws at the front and back of the collimator, adjustment to the horizontal and vertical divergence angles can be made. The spot size at the detector can be calculated approximately by multiplying the particular reflection rocking angle Δ by the distance from the sample to the spot on the detector. In the case of a single-counter diffractometer, tails on a diffraction spot can be eliminated by use of a detector collimator.

Spot-to-spot spatial resolution can be enhanced by use of focusing mirrors, which is especially important for large-protein and virus crystallography, where long cell axes occur. The effect is achieved by focusing the beam on the detector, thereby changing a divergence from the source into a convergence to the detector.

In the absence of absorption, at grazing angles, X-rays up to a certain critical energy are reflected. The critical angle is given by where N is the number of free electrons per unit volume of the reflecting material. The higher the atomic number of a given material then the larger is for a given critical wavelength. The product of mirror aperture with reflectivity gives a figure of merit for the mirror as an efficient optical element.

The use of a pair of perpendicular curved mirrors set in the horizontal and vertical planes can focus the X-ray tube source to a small spot at the detector. The angle of the mirror to the incident beam is set to reject the Kβ line (and shorter-wavelength Bremsstrahlung). Hence, spectral purity at the sample and diffraction spot size at the detector are improved simultaneously. There is some loss of intensity (and lengthening of exposure time) but the overall signal-to-noise ratio is improved. The primary reason for doing this, however, is to enhance spot-to-spot spatial resolution even with the penalty of the exposure time being lengthened. The rocking width of the sample is not affected in the case of 1:1 focusing (object distance = image distance). Typical values are tube focal-spot size, f = 0.1 mm, tube-to-mirror and mirror-to-sample distances ∼200 mm, convergence angle 2 mrad, and focal-spot size at the detector ∼0.3 mm.

To summarize, the configurations are

(a) is for Laue mode; (b)–(f) are for monochromatic mode; (f) is a fairly recent development for conventional-source work.