PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

Due to the rapid strides made lately by the semiconductor electronics industry, most relevant
properties of single crystal silicon have been determined to great precision over a wide temperature
range. Single crystal silicon is therefore an ideal candidate for high precision b c determination (cf.
Chapter 5). For Si, attn /(2 b c ) ~ 10 -5 for 2Å neutrons, implying negligible neutron absorption and
incoherent scattering. Some important neutron scattering properties of silicon cited in literature
[119] are summarised in the Table 1.
2.2 Dynamical diffraction from a single crystal
The dynamical theory [1,4,54-70] regards the incident and diffracted waves inside the crystal to be
coherently coupled forming a composite wave function
( r ) e e ,
(9)
i KO
. r ' i KH
. r
O
H
H
which behaves as a single entity. The sum extends over all reciprocal lattice vectors. The internal
wave vectors K O and K H are related through the Bragg condition
K H = K O + H. (10)
The interactions between the waves and the crystal are represented by the potential
V( r) V e V V e
i H. r
i H.
r
H O H
H H≠0
(11)
with
V
H
2 2 2
2
Nbc FH
k0
m F 2m
O
H
. (12)
Here m stands for the neutron mass, F O and F H , the structure factors for O and H reflections
respectively, N, the atomic number density, H , the susceptibility for the H reflection and b c , the
coherent scattering length.
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