PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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2 I( ) A( ) . (76) The least squares fit (smooth curves in Fig.44) to the data, yields a transverse coherence length σ equal to 74 μm for the monochromated neutron beam. The corresponding transverse coherence length for intensity equals 53 μm which is greater than 1/(2σ k ) = 35 μm expected for a Gaussian angular distribution with the observed FWHM of 0.58 arcsec. The corresponding FWHM transverse coherence length of 175 μm far exceeds the previous best value of 80 μm [112] obtained for a 1.4 arcsec wide beam as well as the highest (5 μm) achieved in neutron interferometry [1]. The peak broadening was also analysed by considering SUSANS from steel wires. The intensity of neutrons scattered through a small wave vector transfer of magnitude Q in a homogeneous sample is governed by Eq.(67) with the form factor term |F(QR)| 2 being replaced by /2 2 F(QR, ) sin d where F(QR,) is given by 0 sin(QL / 2 cos ) J (QR sin ) QL / 2 cos QR sin 1 F(QR, ) 2 . (77) Here J 1 (x) is the first order Bessel functions of the first kind, L is length of cylindrical wire, the angle between the scattering vector Q and wire axis, V cyl the volume of the wire and R denotes the radius of the wire. In our experiment, the wires are vertical and Q lies in the horizontal plane. Hence equals /2 and 2J (QR) (78) QR 1 F(QR) . We assumed a log- normal distribution in radii and a form factor given by Eq.(78) for steel wires. The least-squares fit to the broadened peaks vide Eq.(67) yielded a median radius of 54 μm with a standard deviation of 0.1, i.e. a peak radius of 53.5 μm and Half Maximum radii of 47.5 and 60 μm 84
espectively, for the grating wires. The least-squares fit (smooth curves in Fig.45) to the data with this broadening fit vide Eqs.(75-76) yielded the same transverse coherence length σ . Fig.45 Neutron diffraction pattern (points) from a macroscopic grating of period d ~ 200 m and the least-squares fit (smooth curve) to the pattern. 4.4.3 Versatility of the instrument We also investigated the mesoscopic length scale with this novel instrument. The analyser rocking curve was recorded with and without a magnetic sample Fe 73 Al 5 Ga 2 P 8 C 5 B 4 Si 3 placed between the monochromator and analyser. Since the neutron beam was unpolarised, we could infer only the nuclear scattering length density distribution in the sample. Fig.46 depicts the fitted scattering length density distribution which extends upto a few m. 85
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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
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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 104 and 105: 2 (1) -(δk i .Δ i ) /2 Γ (Δ) =
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
Page 154 and 155: [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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