PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

superior by a factor of about 6 to the Q-resolution of 2x10 -5 Å -1 possible at the next best USANS
facility on S18 beamport of ILL (France). The Q-resolution is inversely proportional to the spatial
extent of agglomerates that can be probed by the instrument. The hydroxyapatite casein protein
sample was placed between a pair of transparencies used for overhead projection. To ascertain the
small angle scattering contribution from the transparencies, a SUSANS spectrum was recorded
(Fig.41) with the transparencies as the sample. Within the experimental error, the transparencies
left the instrument rocking curve essentially unaltered over the Q-domain of interest. This enabled
us to ignore the scattering from transparencies during the final data analysis. Analyser rocking
curves were recorded without and with the protein sample placed in the holder (Fig.42). The
observed broadening of the SUSANS spectrum by the protein sample in the 10 -6 - 10 -5 Å -1 region
yielded information on the size distribution of agglomerates in the sample (Fig.43).
SUSANS data analysis
The intensity of neutrons scattered through a small wave vector transfer of magnitude Q from
spherical agglomerates in a homogeneous sample can be expressed as
2 2
2
s a (67)
o
I(Q) C[ ] N [V(R)] F(QR) D(R)dR ,
where C denotes a constant, N o signifies the number of scattering objects in the sample, V(R)
stands for the volume of the scattering object of radius R and ρ s and ρ a symbolise scattering
densities of the scattering sample and the surrounding ambient matrix respectively. The form factor
F(QR) is the Fourier transform of the spatial distribution of the scattering sphere, viz.
3{sin(QR) QR cos(QR)}
F(QR) .
(68)
3 3
Q R
We assumed a log-normal distribution function D(R) of spherical agglomerates with radii R in the
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