Neutron Scattering

10 .3 Beaur shaping
Due to the fact that neutrons are uncharged and thus may penetrate materials rather easily,
neutrons may bc bundled or focused to a limited extent, only . This aspect aggravates with increasing
neutron energy . Already in the source, there arises the problem to guide a suitable
number of neutrons through "holes" (beam tubes) in the biological shielding to the experimental
setup. From the total solid angle of 4n , only the fraction travelling in the direction of the
beam tube will contribute to the flux . The used divergence of the beam is can merely bc chosen
by annihilating all those neutrons by absorbing materials travelling outside a defmed angular
range . Thus a beam tube represents the simplest version of a collimator . It is comparable to
a system of two diaphragms positioned in a distance of some meters . With a typical length of
3 m for the beam tube and a cross section of 0 .1 m there results a divergence of about 2° for
the neutron beam .
Now it turns out that it is less meaningful to collimate the neutron beam in the vertical plane as
tight as in the horizontal (scattering) plane . Tilting the scattering triangle (Fig . 2) slightly out
ofthe scattering plane influences the selected (,0, 0) -point either not at all or in second order,
only . If collimation shall be achieved within a short distance, thereby making allowance for a
desired anisotropy, one uses a so-called Soller collimator. To this end, a set of coplanar foils
coated with absorbing material is mounted vertically with a distance of say 1 to 5 mm .
Choosing about 30 cm for the length of the foils, one may achieve a horizontal divergence of
the neutron beam in the order of 10 minutes of angle . Yet one has to take into account that
switching to half of the divergence entails about the saure reduction of the neutron flux! The
facts that the foils have a finite thickness and that their absorption is less than 100% modifies
the ideal triangular transmission curve by rounding the top and by the appearance of tails beyond
the base . This modiffed curve may well be represented by a normal distribution - a useful
property for folding operations. In regard to the interpretation of measured data the more
sharply limited resolution triangle as realized by the chopper of a time-of-flight machine
would be more desirable . Since a well defmed cut-off clearly separates the change from elastic
to inelastic scattering the difficulties in interpreting the quasi-elastic transition region which
involve the knowledge ofthe exact shape of the resolution function are greatly reduced .
The anisotropy of the divergence may be exploited by a vertically focusing arrangement of
monochromator and/or analyzer ciystal in order to increase the neutron flux at the sample as
shown in Fig. 4). It is well known from optics that the inverse focal length is given by
1 /f = (Ll +i2 ) and that the ratios of heights for image and source is equal to that of their distances
L IL, . Since, in general, the Bragg angle 0 -7~ 0°, the focal length depends on the
Bragg angle and the radius of vertical curvature by
f _
R
sin0
The distances 4,4 for a given spectrometer are to be considered as fixed quantities and thus
the curvature R of the crystal bas to be variable . This may e .g . bc realized by the parallel arrangement
of lamellae of single crystals which can be tilted individually . An additional gain
factor results from the height ratio of monochromator to source . Depending on the relative
heights of sample and crystals an increase ofthe neutron flux at the sample by a factor of 2 to
6 might be achieved. The possibility of a horizontal focusing - whereby the influence on the
resolution is no longer negligible - will be discussed further down.
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