Section 2.2.7.3. Synchrotron X-ray sources

In the utilization of synchrotron X-radiation (SR), both Laue and monochromatic modes are important for data collection. The unique geometric and spectral properties of SR renders the treatment of diffraction geometry different from that for a conventional X-ray source. The properties of SR are dealt with in Subsection 4.2.1.5 and elsewhere; see Subject Index. Reviews of instrumentation, methods, and applications of synchrotron radiation in protein crystallography are given by Helliwell (1984, 1992).

(a) Laue geometry: sources, optics, sample reflection band-width, and spot size. Laue geometry involves the use of the fully polychromatic SR spectrum as transmitted through the beryllium window that is used to separate the apparatus from the machine vacuum. There is useful intensity down to a wavelength minimum of ∼λ_c/5, where λ_c is the critical wavelength of the magnet source. The maximum wavelength is typically 3 Å; however, if the crystal is mounted in a capillary then the glass absorbs the wavelengths beyond ∼2.6 Å.

The bandwidth can be limited somewhat under special circumstances. A reflecting mirror at grazing incidence can be used for two reasons. First, the minimum wavelength in the beam can be sharply defined to aid the accurate definition of the Laue-spot multiplicity. Second, the mirror can be used to focus the beam at the sample. The maximum-wavelength limit can be truncated by use of aluminium absorbers of varying thickness or by use of a transmission mirror (Lairson & Bilderback, 1992; Cassetta et al., 1993).

The measured intensity of individual Laue diffraction spots depends on the wavelength at which they are stimulated. The problem of wavelength normalization is treated by a variety of methods. These include:

Each of these methods produces a `λ-curve' describing the relative strength of spots measured at various wavelengths. The methods rely on the incident spectrum being smooth and stable with time. There are discontinuities in the `λ-curve' at the bromine and silver K-absorption edges owing to the silver bromide in the photographic emulsion case. The λ-curve is therefore usually split up into wavelength regions, i.e. λ_min to 0.49 Å, 0.49 to 0.92 Å, and 0.92 Å to λ_max. Other detector types have different discontinuities, depending on the material making up the X-ray absorbing medium. [The quantification of conventional-source Laue-diffraction data (Rabinovich & Lourie, 1987; Brooks & Moffat, 1991) requires the elimination of spots recorded near the emission-line wavelengths.]

The production and use of narrow-bandpass beams may be of interest, e.g. δλ/λ 0.2. Such bandwidths can be produced by a combination of a reflection mirror used in tandem with a transmission mirror. Alternatively, an X-ray undulator of 10–100 periods ideally should yield a bandwidth behind a pinhole of δλ/λ 0.1–0.01. In these cases, wavelength normalization is more difficult because the actual spectrum over which a reflection is integrated is rapidly varying in intensity. The spot bandwidth is determined by the mosaic spread and horizontal beam divergence (since γ_H γ_V) as where η = sample mosaic spread, assumed to be isotropic, γ_H = horizontal cross-fire angle, which in the absence of focusing is (x_H + σ_H)/P, where x_H is the horizontal sample size and σ_H the horizontal source size, and P is the sample to the tangent-point distance; and similarly for γ_V in the vertical direction. Generally, at SR sources, σ_H is greater than σ_V. When a focusing-mirror element is used, γ_H and/or γ_V are convergence angles determined by the focusing distances and the mirror aperture.

The size and shape of the diffraction spots vary across the film. The radial spot length is given by convolution of Gaussians as and tangentially by where L_c is the size of the X-ray beam (assumed circular) at the sample, and and where ψ is the angle between the vertical direction and the radius vector to the spot (see Andrews, Hails, Harding & Cruickshank, 1987). For a crystal that is not too mosaic, the spot size is dominated by L_c. For a mosaic or radiation-damaged crystal, the main effect is a radial streaking arising from η, the sample mosaic spread.

(b) Monochromatic SR beams: optical configurations and sample rocking width. A wide variety of perfect-crystal monochromator configurations are possible and have been reviewed by various authors (Hart, 1971; Bonse, Materlik & Schröder, 1976; Hastings, 1977; Kohra, Ando, Matsushita & Hashizume, 1978). Since the reflectivity of perfect silicon and germanium is effectively 100%, multiple-reflection monochromators are feasible and permit the tailoring of the shape of the monochromator resolution function, harmonic rejection, and manipulation of the polarization state of the beam. Two basic designs are in common use. These are (a) the bent single-crystal monochromator of triangular shape (Lemonnier, Fourme, Rousseaux & Kahn, 1978) and (b) the double-crystal monochromator.

In the case of the single-crystal monochromator, the actual curvature employed is very important in the diffraction geometry. For a point source and a flat monochromator crystal, there is a gradual change in the photon wavelength selected from the white beam as the length of the monochromator is traversed [Fig. 2.2.7.2(a)]. For a point source and a curved monochromator crystal, one specific curvature can compensate for this variation in incidence angle [Fig. 2.2.7.2(b)]. The reflected spectral bandwidth is then at a minimum; this setting is known as the `Guinier position'. If the curvature of the monochromator crystal is increased further, a range of photon wavelengths, (δλ/λ)_corr, is selected along its length so that the rays converging towards the focus have a correlation of photon wavelength and direction [Fig. 2.2.7.2(c)]. The effect of a finite source is to cause a change in incidence angle at the monochromator crystal, so that at the focus there is a photon-wavelength gradient across the width of the focus (for all curvatures) [Fig. 2.2.7.2(d)]. The use of a slit in the focal plane is akin to placing a slit at the tangent point to limit the source size.

Figure 2.2.7.2| top | pdf | Single-crystal monochromator illuminated by synchrotron radiation: (a) flat crystal, (b) Guinier setting, (c) overbent crystal, (d) effect of source size (shown at the Guinier setting for clarity). From Helliwell (1984).

The double-crystal monochromator with two parallel or nearly parallel perfect crystals of germanium or silicon is a common configuration. The advantage of this is that the outgoing monochromatic beam is parallel to the incoming beam, although it is slightly displaced vertically by an amount , where d is the perpendicular distance between the crystals and the monochromator Bragg angle. The monochromator can be rapidly tuned, since the diffractometer or camera need not be re-aligned significantly in a scan across an absorption edge. Between absorption edges, some vertical adjustment of the diffractometer is required. Since the rocking width of the fundamental is broader than the harmonic reflections, the strict parallelism of the pair of crystal planes can be relaxed, i.e. detuned so that the harmonic can be rejected with little loss of the fundamental intensity. The spectral spread in the reflected monochromatic beam is determined by the source divergence accepted by the monochromator, the angular size of the source, and the monochromator rocking width (see Fig. 2.2.7.3 ).

Figure 2.2.7.3| top | pdf | Double-crystal monochromator illuminated by synchrotron radiation. The contributions of the source divergence αV and angular source size Δθsource to the range of energies reflected by the monochromator are shown.

The double-crystal monochromator is often used with a toroid focusing mirror; the functions of monochromatization are then separated from the focusing (Hastings, Kincaid & Eisenberger, 1978).

The rocking width of a reflection depends on the horizontal and vertical beam divergences/convergences (after due account for collimation is taken) γ_H and γ_V, the spectral spreads (δλ/λ)_conv and (δλ/λ)_corr, and the mosaic spread η. We assume that η ω, where ω is the angular broadening of a relp due to a finite sample. In the case of synchrotron radiation, γ_H and γ_V are usually widely asymmetric. On a conventional source, usually .

Two types of spectral spread occur with synchrotron and neutron sources. The term (δλ/λ)_conv is the spread that is passed down each incident ray in a divergent or convergent incident beam; the subscript refers to conventional source type. This is because it is similar to the , line widths and separation. At the synchrotron, this component also exists and arises from the monochromator rocking width and finite-source-size effects. The term (δλ/λ)_corr is special to the synchrotron or neutron case. The subscript `corr' refers to the fact that the ray direction can be correlated with the photon or neutron wavelength. Usually, an instrument is set to have (δλ/λ)_corr = 0. In the most general case, for a (δλ/λ)_corr arising from the horizontal ray direction correlation with photon energy, and the case of a horizontal rotation axis, then the rocking width of an individual reflection is given by where and L is the Lorentz factor .

The Guinier setting of the instrument gives (δλ/λ)_corr = 0. The equation for then reduces to (from Greenhough & Helliwell, 1982). For example, for ζ = 0, γ_V = 0.2 mrad (0.01°), = 15°, (δλ/λ)_conv = 1 × 10⁻³ and η = 0.8 mrad (0.05°), then = 0.08°. But increases as ζ increases [see Greenhough & Helliwell (1982, Table 5)].

In the rotation/oscillation method as applied to protein and virus crystals, a small angular range is used per exposure (Subsection 2.2.3.4). For example, may be 1.5° for a protein, and 0.4° or so for a virus. Many reflections will be only partially stimulated over the exposure. It is important, especially in the virus case, to predict the degree of penetration of the relp through the Ewald sphere. This is done by analysing the interaction of a spherical volume for a given relp with the Ewald sphere. The radius of this volume is given by (Greenhough & Helliwell, 1982). For discussions, see Harrison, Winkler, Schutt & Durbin (1985) and Rossmann (1985).

In Fig. 2.2.7.4 , the relevant parameters are shown. The diagram shows (δλ/λ)_corr = 2δ in a plane, usually horizontal, with a perpendicular (vertical) rotation axis, whereas the formula for above is for a horizontal axis. This is purely for didactic reasons since the interrelationship of the components is then much clearer. For full details, see Greenhough & Helliwell (1982).

Figure 2.2.7.4| top | pdf | The rocking width of an individual reflection for the case of Fig. 2.2.7.2(c) and a vertical rotation axis. φR is determined by the passage of a spherical volume of radius (determined by sample mosaicity and a conventional-source-type spectral spread) through a nest of Ewald spheres of radii set by δ = ½ [δλ/λ]corr and the horizontal convergence angle γH. From Greenhough & Helliwell (1982).