Neutron Scattering

Fig . 14) Dispersion surfaces for Barium in
the (110)-plane . The solidlines correspond
to the main symmetry directions,
the points to the various observed pealc
positions of intensity . The transition from
lighter to darker points corresponds to that
from longitudinal to transverse polarisation
of the phonons .
A fmal aspect for optimising the spectrometer shall now be mentioned . Considering the dispersion
for Barium it becomes obvious that the dependence on wave vector for the so called
acoustic phonons is not exceedingly large towards the zone boundary . Optical phonons (sec
the lecture on phonons and magnons) exhibit this property in most cases even more clearly .
This means that one could achieve more intensity or shorter measuring times by reducing the
-resolution and keeping the energy resolution constant, i.e . keeping the distinctness of the
various phonon branches . This can be achieved by means of a horizontally culved monochromator
and/or analyzer as drafted in Fig . 15) . About a factor of five in irrtensity may bc
gained by this horizontal arrangement. Experiments using doubly focusing deflection crystals
exist since a couple of years requiring, however, a high degree of skill and experience .
k
1
1
0#0#0#0#0 0=0=0=0=0
1 2 3 4 5 1 2 3 4 5
k#k#k#k#k
k=k=k=k=k
1 2 3 4 5 1 2 3 4 5
Fig. 15)LA hand side : energy and resolution are determined by the deflection angle O as well as by the collimators
absorbing all neutrons travelling outside the accepted divergence . Right hand side : for the so called
monochromatic focusing, all deflection angles and thus the energy of the neutrons are equal due to the curved
crystal such that the divergent (i .e . relaxed Q-resolution) but monochromatic neutrons merge together at the focusing
point . Caution! the average energy of the set-up bas now become dependent on the sample position due
to the omitted collimators . The resolution will depend on the size of source and sample relative to the radius of
curvature .
9- 13