Neutron Scattering

Choosing PG or Cu one gets contributions of higher order apart from the wavelength scattered
first order . It is important to eliminate those contributions carefully in order to avoid any
ambiguity of the measured signal . One may circumvent this problem by inserting suitable materials
as filter, however, at the expense ofweakened intensity . In addition, there result limitations
in regard of the freedom to ctroose the wavelength as can be seen by the example of the
frequently used PG-filter . The corresponding transmission curve is shown in Fig. 10) . The
goal is to choose a wavelength À for which the filter offers an especially large transmission
and, however, a large absorption for integer fractions  /n . With the choice of' =2.37 - 10-10
m, neutrons with 2 Â and 3Â =2 .37 - 10 -10 m will be largely suppressed. The wavelength
 =l .55 - 10-10 m offers itself, as well . Above  - 4 - 10-10 m , as in the case of a triple-axis
spectrometer at a cold source, one uses a Beryllium-filter cooled by liquid nitrogen as a cut-off
for shorter wavelengths .
Table 1) properties of frequently used mosaic crystals
material graphite (PG) Ge Cu
reflection (hkl (002 (111 (220)
À -range / 10-10m upper limit 6.708 6.533 2.556
( ~t 2d)
lower limit 1 .16 1 .13 0.444
(0=10 .)
peak- reflectivity  = 1 10 -10 m - - 14
(0/-) = 2 10 -10 m 74 24 32
= 3 10 -10 m 82 34 -
= 4 10 -10 m 87 43 -
absorption 5-10-4 0.058 0 .19
details (222) forbidden "bad" mosaic distribution
costs 20000 15000 5000
per crystal in DM (coarse)
Mosaic distribution of a crystal and beam divergence are not the only means to influence
resolution and intensity . Those properties may be varied also directly by the choice of k . In
order to offer more neutrons at the conespondingly large or small incident energies, one shifts
the maximum in the energy spectrum of the reactor neutrons by cooling (D2 at 25 K) or heating
(C at 2000 K) of a moderator. A spectrometer placed at a cold source (small k), has a
higher resolution as compared to ttrose placed at thermal or hot sources . Thus, by selecting different
moderation, one may vary AE between orders of 0 .01 meV, 1 meV, and 100 meV .
One notes that nearly all introduced components affect the resolution function of the spectrometer
. This function - a four dimensional ellipsoid - results by projecting the product of the
volume elements AV and AV' onto the (L), ü) -space (integration over the two dimensional
vector P in Fig . 2)[5] . In the upper part of Fig . 11), the orientation of the volume elements
with respect to k and k' are indicated as well as projections of the resolution function . Inclination
and widths of the ellipsoids depend strongly on the scattering sense - part (II) of the figure
. Part (III) shows that there results an appreciable increase of the wave vector spread for
scattering twice in the Same sense . Il is just those different projections on the various (Q, 0J)-
9-10