PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

We shall confine our discussion henceforth to nonabsorbing centrosymmetric crystals, for the sake
of simplicity and clarity. The assumption of zero absorption is fairly accurate for instance, with
crystals of silicon which exhibit absorption lengths of a few metres for Å wavelength neutrons. The
quantities O , H (=– H ), K, K O and K H are thus all real.
The internal wave solutions can then be represented by
1 y
ψ
Oα
= 1- ψ
Oβ
= 1-
2
2
y +1
1 | b |
and ψ
Hα
= -ψ
Hβ
= - ,
2 2
y +1
(30)
with the associated wave vector magnitudes
k χ | b |
Oα
β
K = K ±
0 H
2
y +1 ± y
2
k0χ
H
K
Hα
= K ±
β
2
y +1 y .
2 | b |
(31)
For incidence at θ = θ C , i.e. y = 0, the incident wave splits equally into the α and β waves. ψ Oβ gets
stronger at the expense of ψ Oα , as θ increases beyond θ C (y >0), whereas ψ Oα becomes the dominant
component on the other side of θ C . The diffracted wave amplitudes on the other hand exhibit a
peak,
| b | / 2 in magnitude, at θ C and fall symmetrically on both sides of θ C . The diffracted
intensities
2
H
and 2 H
drop to half their peak values at y = ±1, corresponding to an FWHM equal
to w i of Eq.(22). Thus θ C represents the centre of diffraction in the Laue case as well. Only in the
symmetric Laue configuration, does θ C equal θ B represented by the point L, the centre of
diffraction within the kinematical model.
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