Beamline components

Schoenborn, B. P.; Knott, R.

doi:10.1107/97809553602060000666

International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

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International Tables for Crystallography (2006). Vol. F. ch. 6.2, pp. 134-136 | 1 | 2 |

Section 6.2.1.3. Beamline components

B. P. Schoenborn^a ^* and R. Knott^b

^a Life Sciences Division M888, University of California, Los Alamos National Laboratory, Los Alamos, NM 8745, USA, and ^bSmall Angle Scattering Facility, Australian Nuclear Science & Technology Organisation, Physics Division, PMB 1 Menai NSW 2234, Australia
Correspondence e-mail: schoenborn@lanl.gov

6.2.1.3. Beamline components

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Until recently, instrument design has been largely based on experience; however, in many cases, it is now possible to formulate a comprehensive description of the instrument and explore the impact of various parameters on instrument performance using an extensive array of computational methods (Johnson & Stephanou, 1978; Sivia et al., 1990; Hjelm, 1996). In practice, it is the instrument design that provides access to the fundamental scattering processes, as briefly outlined in the following.

If a neutron specified by a wavevector $[{\bf k}_{1}]$ is incident on a sample with a scattering function $[S({\bf Q}, \omega)]$ , all neutron scattering can be reduced to the simple form $[{\hbox{d}^{2} \sigma \over \hbox{d}\Omega \hbox{ d}E} = AS({\bf Q}, \omega),]$ where A is a constant containing experimental information, including instrumental resolution effects. The basic quantity to be measured is the partial differential cross section, which gives the fraction of neutrons of incident energy E scattered into an element of solid angle Ω with an energy between [E'] and $[E' + \hbox{d}E']$ . The momentum transfer, Q, is given in Fig. 6.2.1.3(a). The primary aim of a neutron-scattering experiment is to measure $[{\bf k}_{2}]$ to a predetermined precision (Bacon, 1962; Sears, 1989) (Fig. 6.2.1.3b). A generic neutron-scattering instrument used to achieve this aim is illustrated in Fig. 6.2.1.4. The instrument resolution function will be determined by uncertainties in $[{\bf k}_{1}]$ and $[{\bf k}_{2}]$ , which are a direct consequence of (i) measures to increase the neutron flux at the sample position (to maximize wavelength spread, beam divergence, monochromator mosaic, for example) and (ii) uncertainties in geometric parameters (flight-path lengths, detector volume etc.).

Figure 6.2.1.3 | top | pdf |

(a) Schematic vector diagram for an elastic neutron-scattering event. A neutron, $[{\bf k}_{1}]$ , is incident on a sample, S, and a scattered neutron, $[{\bf k}_{2}]$ , is observed at an angle 2θ leading to a momentum transfer, Q. (b) Schematic of an elastic neutron-scattering event illustrating the consequences of uncertainty in defining the incident neutron, $[{\bf k}_{1}]$ , and determining the scattered neutron, $[{\bf k}_{2}]$ . The volumes ( $[\delta {\bf k}_{1_{x}}]$ , $[\delta {\bf k}_{1_{y}}]$ , $[\delta {\bf k}_{1_{z}}]$ ) and ( $[\delta {\bf k}_{2_{x}}]$ , $[\delta {\bf k}_{2_{y}}]$ , $[\delta {\bf k}_{2_{z}}]$ ) constitute the instrument resolution function.

Figure 6.2.1.4 | top | pdf |

A generic neutron-scattering instrument illustrating the classes of facilities and operators important to instrument design and assessment. Each class should be optimized and integrated into the overall instrument description.

6.2.1.3.1. Collimators and filters

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In general, neutron-beam applications are flux-limited, and a major advantage will be realized by adopting advanced techniques in flux utilization. A reactor neutron source is large, and stochastic processes dominate the generation, moderation and general transport mechanisms. Because of radiation shielding, background reduction and space requirements for scattering instruments, reactor beam tubes have a minimum length of 3–4 m and cannot exceed a diameter of about 30 cm. The useful flux at the beam-tube exit is thus between 10⁻⁵ and 10⁻⁶ times the isotropic flux at its entry.

The most important aspect of beam-tube design, other than the size, is the position and orientation of the tube with respect to the reactor core. The widespread utilization of D₂O reflectors enables significant gains to be obtained from tangential tubes with maximal thermal neutron flux, and minimal fast neutron and γ fluxes. A similar result is accomplished in a split-core design by orienting the beam tubes toward the unfuelled region of the reactor core (Prask et al., 1993).

There are two major groups of neutron-scattering instruments: those located close to and those located some distance from the neutron source. The first group is located to minimize the impact of the inverse square law on the neutron flux, and the second group is located to reduce background and provide more instrument space. In both cases, the first beamline component is a collimator to extract a neutron beam of divergence α from the reactor environment. The collimator is usually a beam tube of suitable dimensions for fully illuminating the wavelength-selection device. The angular acceptance of a collimator is determined strictly by the line-of-sight geometry between the source and the monochromator. Some geometric focusing may be appropriate, and a Soller collimator may be used to reduce α without reducing the beam dimensions. For technical reasons, the primary collimator is essentially fixed in dimensions and secondary collimators of adjustable dimensions may be required in more accessible regions outside the reactor shielding.

Neutron-beam filters are required for two main reasons: (i) to reduce beam contamination by fast neutron and γ radiation and (ii) to reduce higher- or lower-order harmonics from a monochromatic beam. Numerous single-crystal, polycrystalline and multilayer materials with suitable characteristics for filter applications are available (e.g. Freund & Dolling, 1995).

6.2.1.3.2. Crystal monochromators

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The equilibrium neutron-wavelength distribution (Fig. 6.2.1.2) is a broad continuous distribution, and in most experiments it is necessary to select a narrow band in order to define $[{\bf k}_{1}]$ . Neutron-wavelength selection can be achieved by Bragg scattering using single crystals to give well defined wavelengths; by polycrystalline material to remove a range of wavelengths; by a mechanical velocity selector; or by time-of-flight methods. The method chosen will depend on experimental requirements for the wavelength, λ, and wavelength spread, $[\Delta \lambda/\lambda]$ .

Neutrons incident on a perfect single crystal of given interplanar spacing d will be diffracted to give specific wavelengths at angle 2θ according to the Bragg relation. A neutron beam, $[\alpha_{1}]$ , incident on a single crystal of mosaicity β will provide $[\Delta \lambda /\lambda = [(\cot \theta \cdot \theta)^{2} + (\Delta d/d)^{2}]^{1/2},]$ where $[(\Delta \theta)^{2} = {\alpha_{1}^{2} \alpha_{2}^{2} + \beta^{2} (\alpha_{1}^{2} + \alpha_{2}^{2}) \over \alpha_{1}^{2} + \alpha_{2}^{2} + 4\beta^{2}}]$ and $[\alpha_{2}]$ is the divergence of the (unfocused) diffracted beam.

Crystals for neutron monochromators must not only have a suitable d, but also high reflectivity and adequate β. Under these conditions, neutron beams with a $[\Delta \lambda/\lambda]$ of a few per cent are obtained. Typical crystals are Ge, Si, Cu and pyrolytic graphite. In order to increase the neutron flux at the sample, a number of mechanisms have been developed. These include focusing monochromatic crystals, frequently using Si or Ge (Riste, 1970; Mikula et al., 1990; Copley, 1991; Magerl & Wagner, 1994; Popovici & Yelon, 1995), as well as stacked composite wafer monochromators (Vogt et al., 1994; Schefer et al., 1996).

One limitation of the use of crystal monochromators is the absence of suitable materials with large d. Indeed, the longest useable λ diffracted from pyrolytic graphite or Si is ~5–6 Å.

6.2.1.3.3. Multilayer monochromators and supermirrors

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Multilayers are especially useful for preparing a long-wavelength neutron beam from a cold source and for small-angle scattering experiments in which $[\Delta \lambda /\lambda]$ of about 0.1 is acceptable (Schneider & Schoenborn, 1984). Multilayer monochromators are essentially one-dimensional crystals composed of alternating layers of neutron-different materials (e.g. Ni and Ti) deposited on a substrate of low surface roughness. In order to produce multilayers of excellent performance, uniform layers are required with low interface roughness, low interdiffusion between layers and high scattering contrast. Various modifications (e.g. carbonation, partial hydrogenation) to the pure Ni and Ti bilayers improve the performance significantly by fine tuning the layer uniformity and contrast (Mâaza et al., 1993). The minimum practical d-spacing is ~50 Å and a useful upper limit is ~150 Å. Multilayer monochromators have high neutron reflectivity (>0.95 is achievable), and their angular acceptance and bandwidth can be selected to produce a neutron beam of desired characteristics (Saxena & Schoenborn, 1977, 1988; Ebisawa et al., 1979; Sears, 1983; Schoenborn, 1992a).

The supermirror, a development of the multilayer monochromator concept, consists of a precise number of layers with graded d-spacing. Such a device enables the simultaneous satisfaction of the Bragg condition for a range of λ and, hence, the transmission of a broader bandwidth (Saxena & Schoenborn, 1988; Hayter & Mook, 1989; Böni, 1997).

Polarizing multilayers and supermirrors (Schärpf & Anderson, 1994) facilitate valuable experimental opportunities, such as nuclear spin contrast variation (Stuhrmann & Nierhaus, 1996) and polarized neutron reflectometry (Majkrzak, 1991; Krueger et al., 1996). Supermirrors consisting of Co and Ti bilayers display high contrast for neutrons with a magnetic moment parallel to the saturation magnetization and very low contrast for the remainder. With suitable modification of the substrate to absorb the antiparallel neutrons, a polarizing supermirror will produce a polarized neutron beam (polarization >90%) by reflection.

6.2.1.3.4. Velocity selectors

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The relatively low speed of longer-wavelength neutrons (~600 m s⁻¹ at 6 Å) enables wavelength selection by mechanical means (Lowde, 1960). In general, there are two classes of mechanical velocity selectors (Clark et al., 1966). Rotating a group of short, parallel, curved collimators about an axis perpendicular to the beam direction will produce a pulsed neutron beam with λ and $[\Delta \lambda/\lambda]$ determined by the speed of rotation. This is a Fermi chopper. An alternate method is to translate short, parallel, curved collimators rapidly across the neutron beam, permitting only neutrons with the correct trajectory to be transmitted. This is achieved in the helical velocity selector, where the neutron wavelength is selected by the speed of rotation and $[\Delta \lambda/\lambda]$ can be modified by changing the angle between the neutron beam and the axis of rotation (Komura et al., 1983). The neutron beam is essentially continuous, the resolution function is approximately triangular and the overall neutron transmission efficiency exceeds 75% in modern designs (Wagner et al., 1992).

6.2.1.3.5. Neutron guides

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In order for a collimator to be effective, its walls must absorb all incident neutrons. The angular acceptance is strictly determined by the line-of-sight geometry. Neutron guides can be used to improve this acceptance dramatically and to transport neutrons with a given angular distribution, almost without intensity loss, to regions distant from the source (Maier-Leibnitz & Springer, 1963). The basic principle of a guide is total internal reflection. This occurs for scattering angles less than the critical angle, $[\theta_{c}]$ , given by $[\theta_{c} = 2(1 - n)^{1/2},]$ where n is the (neutron) index of refraction related to the coherent scattering length, b, of the wall material, viz, $[n = 1 - (\lambda^{2} \rho b/2\pi),]$ where ρ is the atom number density (in $[\hbox{cm}^{-3}]$ ). Among common materials, Ni with $[b = 1.03 \times 10^{-12}\;\hbox{cm}]$ , in combination with suitable physico-chemical properties, provides the best option, with a critical angle $[\theta_{c} = 0.1 \lambda]$ (in Å). The dependence of $[\theta_{c}]$ on λ implies that guides are more effective for long-wavelength neutrons. With the introduction of supermirror guides with up to four times the $[\theta_{c}]$ of bulk Ni, both thermal and cold neutron beams are being transported and focused with high efficiency (Böni, 1997).

While a straight guide transports long wavelengths efficiently, it continues to transport all neutrons within the critical angle, including non-thermal neutrons emitted within the solid angle of the guide. This situation may be modified significantly by introducing a curvature to the guide. Since a curved neutron guide provides a form of spectral tailoring (cutoff or bandpass filters), simulation is a distinct advantage in exploring the impact of guide geometry on neutron-beam quality (van Well et al., 1991; Copley & Mildner, 1992; Mildner & Hammouda, 1992).

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International Tables for Crystallography (2006). Vol. F. ch. 6.2, pp. 134-136