PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

Therefore, the forward diffracted intensity (transmission) fraction as a function of incidence angle
is given by
sin sin(A )
(51)
B S
I ( )
.
O
sin(A )sin(
B S
)
The apex angle A of Bragg prism must lie between B + S and π–(θ B –θ S ) to make possible the
emergence of both I O and I H ( I H
1
I D
- I O
, expression derived in Chapter 4, cf. Eq.(61)), from the
side face. Outside the total reflectivity domain, as apex angle 'A' approaches B + S , all the
unreflected intensity (1–I D ) tends to propagate in I O (Fig.14), since the cross section for I H
approaches zero. As 'A' increases beyond B + S , the intensity fraction I H rises at the expense of I O .
3.3 Neutron deflection
We derive the neutron deflection formulae for the Bragg prisms of the forward diffracted beam by
delineating the wave vectors change in reciprocal space determined by the boundary conditions at
the incidence and exit faces of the prisms. The forward diffracted neutron (transmitted) beam show
strong deflections sensitivities for neutron incidence close to total reflectivity regime, accompanied
by a large concomitant loss of intensity due to appearance of Bragg reflection at front and Bragg
prism diffraction at side faces, respectively. These transmitted neutrons exit the side face with a
concomitant lateral displacement depending on the incidence angles θ and thus on the energy flow
inside the crystal (Fig.12).
3.3.1 Bragg prism
To obtain the neutron deflection by a Bragg prism, we follow the same procedure as outlined for
the amorphous prism except that now the internal wave vector must originate on the dispersion
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