PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

sample, i.e.,
R
2
{ln( ) / 2}
R m
1
D(R) e .
(69)
R 2
Here, R m and σ denote the median radius and dimensionless standard deviation of the distribution,
respectively. Substituting Eqs. (68) and (69) in Eq. (67), we express the scattered intensity as
6
2
. (70)
I(Q) R F(QR) D(R)dR
0
The rocking curve recorded with the sample is then least-square fitted to the convolution of I(Q)
with the instrument resolution curve, viz. the rocking curve observed without the sample, i.e.
I (Q) I (Q) I(Q).
(71)
S
nS
The log-normal size distribution of spherical agglomerates in the sample inferred [153] from the
least-squares fit is characterised by R m of 53 µm and σ = 0.38 respectively. This distribution peaks
at 46 μm, dropping to Half Maximum at 27 and 73 μm respectively. The greater half-maximum of
this distribution corresponds to the instrument capability of characterising agglomerates up to 150
μm in size.
4.4.2 Coherence properties of the beam
Coherence properties of the amplitude of a beam are described by the coherence function [1,51]
( ) g( k)e dk
, (72)
(1) i k.
viz. the Fourier transform of the wave vector (momentum) distribution g(k) of the beam. For
Gaussian wave vector distributions having widths k i in each of the three orthogonal directions
(i=x,y,z), a Gaussian coherence function of the form
81