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2. Monochromatization

If a neutron beam with continuous wavelength distribution falls on a single crystal, various sets of lattice planes will give rise to Bragg reflections in appropriate directions, each such reflection being associated with a particular wavelength according to the Bragg law. Therefore, by aligning the single crystal appropriately with respect to the incident neutron beam, it can be achieved that only one particular wavelength will be `reflected' in the direction required. The angle between the incident and the reflected beams is called the `take-off angle' of the crystal monochromator. It is twice the Bragg-angle of the reflection ($2\theta_m$). Figure 1 shows the wavelength vs. the take-off angle graph of a germanium crystal monochromator for different sets of reflecting planes. Large single crystals of other materials such as lead, copper, zinc, aluminium, beryllium, graphite, $\dots$ are also used as monochromators in neutron diffraction studies. They can be used either in reflection or transmission.

 

Figure 1: Wavelength vs. take-off angle for GF Monochromator.

The reflectivity of a perfect single crystal is low caused by the large primary extinction due to the small angular misalignment of the mosaic blocks which the crystal is composed of (so-called mosaic spread, $\beta_1$). One way of increasing the reflectivity of a crystal monochromator is to increase the mosaic spread through a controlled and uniform distribution of imperfections such as the introduction of dislocations or impurities. The mosaic spread of a crystal monochromator can be estimated from the width-at-half-height of its `rocking curve' which is the intensity of the reflected neutron beam plotted as a function of the angular setting of the crystal in the immediate neighbourhood of a Bragg peak.

Germanium and silicon crystals both have diamond structure, hence the second order reflections from lattice planes whose Miller indices (hkl) are all odd--such as the 222, 622 and 662 reflections--are systematically absent. Hence using the 111, 311 or 331 reflecting planes of a germanium monochromator, there will be no $\lambda/2$ contamination in the monochromated beam. Another advantage of these crystal monochromators is their low absorption and low incoherent scattering cross section. Moreover, large single crystals of germanium and silicon are readily available, though are often `too perfect' for diffraction work resulting in a very low reflectivity. Increasing the mosaic spread by doping impurity into perfect single crystals of germanium has not been very successful. Barrett, Mueller and Heaton (1963) tried several ways of introducing imperfections into a germanium single crystal to increase its reflectivity. The best method turned out to be an uniaxial compression of a disc or slab of germanium along the [110] direction at 650$^\circ$C (`squashed' single crystal). This compression produced a uniform mosaic spread and a high neutron reflectivity. Barrett et al. reported an increase in the reflectivity of a compressed single crystal of germanium by a factor up to 30 as compared with the reflectivity of an `as-grown' crystal. By varying the amount of compression, a wide range of mosaic spread can be obtained. This method proved to be quite successful and was subsequently adopted by Dolling and Nieman (1967) at Chalk River Nuclear Laboratories, Canada and by Cooper and Nathans (1967) at Brookhaven National Laboratory, USA as well as at the A.E.R.E., Harwell. (Note: Herbstein, Boonstra, Dunn, Chipman, Boldrini and Loopstra, 1967, gave a brief abstract of 520 papers published up to the end of 1966 under the heading: `Methods of obtaining monochromatic X-rays and neutrons'. See also, Turberfield, 1968).

Some efforts have been made in recent years to develop multilayer monochromators for neutrons (see e.g. Saxena and Schoenborn, 1977). Alternating thin film of two materials such as Mn and Ge, deposited on a glass substrate, makes a periodic system in the direction normal to the plane of the multilayer with a periodicity determined by combined thickness of two films. By choosing the appropriate materials, the multilayer can give rise to very high reflectivities, and in addition to that, the diffracted beam has very low high-order contamination. According to Saxena and Schoenborn, the multilayers can also be used as excellent polarizers and filters for neutrons.

The study of curved neutron monochromators has recently attracted much attention and seems promising though not well understood as yet (see e.g. Rustichelli, 1969; Riste, 1970; Nunes and Shirane, 1971; Antonini et al., 1972; Boeuf and Rustichelli, 1973,1974; Kalus et al., 1973; Currant, 1973; Kalus, 1975; Frey, 1975; Albertini et al., 1977; Boeuf et al., 1979). A curved monochromator is either a bent single crystal or it is basically composed of bent perfect crystal slices (lamellae). The bending of the crystals is done either mechanically, chemically or thermally. The basic principles of these monochromators are the same as for the bent monochromators in X-ray experiments (see e.g. Parrish and Roberts, 1962; Herbstein et al., 1967 and Webb et al., 1977).

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