PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

in forward diffracted (I O ) and diffracted (I H ) beams (Fig.9) [66,138]. Here, θ B and θ S imply their
usual meaning of Bragg angle and the angle between the front surface and the diffracting planes
respectively. We have coined the term ‘Bragg prism for this device [139-142].
3.0 Amorphous prism
Consider incidence of a monochromatic neutron plane wave
i k .
e O
r , on a non-absorbing amorphous
prism at an angle (Fig.9 (top)). Because of the refractive index n of amorphous prism being very
close to unity, these neutrons get almost fully transmitted through the prism (viz., I O ≈ I i ) and suffer
a small deflection, with reflection at the incidence face being negligibly small. As alluded to earlier
in Chapter 2, reciprocal space representation for an amorphous prism is depicted in Fig.10. Here,
incident wave vectors k O in vacuum can originate on sphere of incidence LR of radius k O centred
at reciprocal lattice point O and terminate at O of reciprocal lattice vector OH. For an amorphous
prism, the refracted wave vectors (|K|=n|k O |) must originate on sphere of refraction QR' of radius
nk O centred at reciprocal lattice point O and end at O. Let the vacuum wave vector k O is
represented by RO for an incidence angle equal to . The inside wave vector of prism is uniquely
selected by continuity of the tangential component of the wave vector across the vacuum-prism
interface and hence the allowed internal wave vector is T'O at incidence surface, since it differs
from RO only by a vector RT' along the incidence surface normal n i (Fig.10). By the triangle law
of vectors, T'O and RO thus have identical components tangential to the incidence surface as
required by the boundary conditions. We obtained the effected wave vector change –RM at
incidence surface by extending back the inside wave vector T'O upto incidence sphere and located
intersection point M. Negative sign indicates |n| less than unity. Thus, neutron gets deflected by
δ 1 =(n–1)cotθ, away from the inward surface normal at incidence surface of the prism, with (1-n)k O
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