PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

exploiting multiple successive identical Bragg reflections from two slabs of a channel-cut
monolithic single crystal, producing a highly collimated neutron beam [111,115].
For a crystal cut asymmetrically at S B to the reflecting planes, |b| –1 is large. For incidence at a
near grazing angle B – S , the crystal will thus accept a narrow beam of a large angular divergence
1/2
w / b and generate a highly collimated ( w b
1/2
) diffracted beam wider in cross section. The
enhancement by the factor |b| in the spatial width δx of the reflected beam vis-a-vis the incident
beam, reduces the angular divergence of the reflected beam by the same factor. This is a direct
consequence of conservation of the phase space volume spanned by the beam since the momentum
spread δp x =p 0 δ of a monochromatic beam is proportional to the angular width δ. Such an
arrangement therefore works as a collimator. The same setup with the beam directions reversed,
relating to the other extreme ( S – B , |b| –1 →0) in the Bragg case, may be employed where a small
sample is to be studied and the angular divergence is of no great consequence.
2.2.3 Laue Case
In a Laue configuration (Fig.4b), the line drawn through the point of incidence parallel to n i always
intersects the dispersion surface in two real points, such as A and B in Fig.5. The internal wave
vectors are thus always real for a nonabsorbing crystal. Further, since the diffracted wave does not
exit the incidence surface, the boundary condition II) implies
1
O O
0 H
H
. (29)
At the exit surface, each composite internal wave function (
or ) gives rise to a transmitted
and a diffracted wave. The situation where the exit surface normal, n e is not parallel to n i is
illustrated in Fig.5. The line drawn through A parallel to n e intersects the spheres of incident and
diffracted wave vectors in vacuum in the points E and R respectively. Thus, the exiting transmitted
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