PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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4.4 Applications of novel SUSANS setup 4.4.1 Super Ultra small angle neutron scattering (SUSANS) of a protein sample With this highly collimated, nearly plane-wave neutron beam, we recorded the first SUSANS spectrum in the wave vector transfer Q ~ 10 -6 Å -1 regime with a hydroxyapatite casein protein sample placed between the monochromator and analyser. The virgin rocking curve that consists of a pair of 0.62 arcsec wide peaks separated by 2.2 arcsec constitutes the instrumental resolution. This is basically the convolution of the monochromator peak with the analyser acceptance curve riding on an unavoidable background. The bottom axis in Fig.41 labelled as Q (Å -1 ) is derived from the analyser Bragg prism rotation and neutron wave number k O through relation Q = 2k O sin(/2). The corresponding instrumental resolution of about 3.4x10 -6 Å -1 for this novel instrument is Fig.41 SUSANS spectra without and with a sample holder, viz. a pair of overhead projection transparencies. 78
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 79
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Studying neutron dynamical diffract
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DECLARATION I, hereby declare that
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ACKNOWLEDGEMENTS I sincerely, thank
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Fig.10 Boundary conditions on wave
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Fig.28 Theoretical curves for Si {1
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sample. Least-squares fit to the sa
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Fig.62 Interference contrast and av
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3.4 Experimental 49 3.5 Results and
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SYNOPSIS The present thesis aims to
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analytic expressions for intensity
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Research A, 634 (2011) S41. [9] S.
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spallation sources yield peak neutr
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SU(2) phase, and separation of geom
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[33-34,48]. The bi-refracting natur
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application of the dynamical theory
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I. One of the major disadvantages o
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nuclear physics very important as i
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potential for most nuclei in spite
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Due to the rapid strides made latel
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for a positive value of b c i.e. fo
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k b k O H . ni sin( B S) . (18)
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factor exp(-W). The centre, θ C ,
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exploiting multiple successive iden
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We shall confine our discussion hen
Page 50 and 51: The depth Z is measured from the in
Page 52 and 53: wings (large-y regions). The freque
Page 54 and 55: expressed as T(y, t )R(y, t )R(
Page 56 and 57: studies. With such beams, the and
Page 58 and 59: CHAPTER 3 Neutron forward diffracti
Page 60 and 61: eing the separation of points M and
Page 62 and 63: 3.1 Neutron forward diffraction Con
Page 64 and 65: excited by the incident wave (Fig.1
Page 66 and 67: Therefore, the forward diffracted i
Page 68 and 69: Fig.15 Calculated cr and I O for a
Page 70 and 71: (1 I ) D tan b . ID cot( B S)
Page 72 and 73: Fig.18 Experimental layout to measu
Page 74 and 75: Fig.20 Bragg reflection intensity f
Page 76 and 77: fraction I O through the Bragg pris
Page 78 and 79: Fig.22 Experimental (points) and th
Page 80 and 81: Table 2: Observed deflection sensit
Page 82 and 83: total reflectivity domain. These ar
Page 84 and 85: Here the term C() accounts for the
Page 86 and 87: Fig.28 Theoretical curves for Si {1
Page 88 and 89: I H (θ H ) peaks of 0.18 height an
Page 90 and 91: other with a compression factor lim
Page 92 and 93: an overall compression factor of 14
Page 94 and 95: 4.3 Experimental 4.3.1 Bragg prism
Page 96 and 97: 4.3.2 Experiment The experiment was
Page 98 and 99: Fig.38 Bragg reflection rocking cur
Page 102 and 103: Fig.42 First Q ~ 10 -6 Å -1 SUSANS
Page 104 and 105: 2 (1) -(δk i .Δ i ) /2 Γ (Δ) =
Page 106 and 107: 2 I( ) A( ) . (76) The least squa
Page 108 and 109: Fig.46 Analyser rocking curve for a
Page 110 and 111: This instrument was also employed t
Page 112 and 113: Fig.48 Theoretical flat-topped angu
Page 114 and 115: difference between the two neutron
Page 116 and 117: Fig.52 Phase dispersion in a 26.5 m
Page 118 and 119: the beam and remains visible up to
Page 120 and 121: cos bc 4NDd1 1 2cot 2 III 2 2
Page 122 and 123: yield about an order of magnitude r
Page 124 and 125: The refractive index, n = (1-Nb c
Page 126 and 127: with a white, and hence high-intens
Page 128 and 129: proposed dual sample. The dual samp
Page 130 and 131: The experiment was performed with =
Page 132 and 133: Fig.59 Typical interferograms for p
Page 134 and 135: Fig.63 Path I, II and I-II phases d
Page 136 and 137: Fig.65 Average intensity with the s
Page 138 and 139: Fig.69 New metrological mapping of
Page 140 and 141: Si at 26.2 o C, applying a correcti
Page 142 and 143: selected asymmetric Bragg prism may
Page 144 and 145: III. High precision determination o
Page 146 and 147: REFERENCES [1] H. Rauch and S. Wern
Page 148 and 149: [36] J. S. Nico and W. M. Snow, Ann
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[67] V. F. Sears, Can. J. Phys., 56
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[97] A. Cabello, S. Filipp, H. Rauc
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[127] A. Ioffe, D. L. Jacobson, M.
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2009, (Grenoble, France, 2010) 3-15
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PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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