PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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2 (1) -(δk i .Δ i ) /2 Γ (Δ) = e , (73) i=x,y,z is obtained. In this case, the wave vector distribution and coherence length i are related by Heisenberg uncertainty relation [95], δk Δ = 1/ 2 . (74) i i Diffraction from a macroscopic grating Diffraction of neutrons of wavelength for near normal incidence at a grating of period d>> gives rise to a pattern with an angular separation ~ /d between successive intensity maxima. With a grating period of even a few microns, scattering angles become as small as a few arcsec for thermal and cold neutrons. A collimation of the incident neutron beam to within ~ arcsec is therefore necessary to record a well resolved diffraction pattern. Our super collimated beam facilitated measurement of the diffraction pattern from a large-period grating and determination therefrom of the transverse coherence length of the beam. A grating of ~ 200 μm period, made by winding a steel wire of 100 μm diameter tightly on a 50x50 mm 2 aluminium frame (inset of Fig.44), was mounted between the monochromator and analyser for near normal neutron incidence. SUSANS (Super Ultra-Small Angle Neutron Scattering) spectra recorded with and without the grating in the mount are depicted in Fig.47. The two peaks in the grating pattern are considerably broadened due to multiple scattering and refraction in the cylindrical wires, and modulated by clearly resolved diffraction oscillations corresponding to the grating period [154]. The average peak broadening on transmission through the steel wires in the grating was least-square fitted to a Gaussian angular profile of standard deviation equal to about 0.41 arcsec, by deconvoluting each peak from that in the no-grating SUSANS pattern. At a 82
Fig.44 1 st neutron diffraction pattern of a macroscopic grating (inset) of period d ~ 200 μm. The least-squares fit to the pattern (smooth curve) corresponds to a transverse coherence length of 175 μm, the highest value reported to date for Å wavelength neutrons. scattering angle , partial neutron wave amplitudes diffracted from successive elements of the grating with concomitant phases add coherently to form a net complex amplitude (nd) 2 ¥ - 2πnd 2 i( sinθ) 2σ λ . (75) A(θ) = e e n=-¥ Here n is a running index for the illuminated elements of the grating and σ denotes the transverse coherence length for amplitudes of the incident neutron wave. The corresponding intensity is given by 83
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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
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The depth Z is measured from the in
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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 100 and 101: 4.4 Applications of novel SUSANS se
Page 102 and 103: Fig.42 First Q ~ 10 -6 Å -1 SUSANS
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
Page 150 and 151: [67] V. F. Sears, Can. J. Phys., 56
Page 152 and 153: [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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