PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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the beam and remains visible up to very high interference orders [1]. However, here the phase varies significantly with θ as 2 2 I0 c a a B B 2 Nb N b Dd 1 cot {1 2cot }/ 2 , (85) introducing dispersion due to a horizontal sample misalignment δθ. The nondispersivity condition therefore requires the sample to be aligned with arcsec precision (cf. Fig.52 and 0-I and II-0 curves in Fig.53 (bottom)). Only at the exact nondispersive setting (viz., θ= θ B , to within arcsec), can Ф I be increased to arbitrarily large values by increasing D without losing interference contrast. At even a slight misalignment δθ, the -dependence of the first order term in δθ of the Ф I-0 variation (85) is large enough to make the phase dispersive (Fig.52), thereby limiting b c precision. Ioffe et al. [127] obviated the need for this precise sample alignment by measuring the phase shift between interferograms recorded with the sample placed alternately in subbeams I and II (Fig.50). For a symmetric LLL IFM, this method requires that the sample be parallel translated from path I to path II. Upon translation, the horizontal misset angle δθ changes sign. The phase shift then equals ( ) ( ( )) ( ) ( ) . This eliminates the large first order variation of the phase (cf. Eq.(85) and 0-I and II-0 curves in Fig.53 (bottom) for 0 ) with δθ. The sample alignment thus requires only arcminute precision to locate the minimum in the magnitude of I-II (cf. I-II curves in Fig.53), occurring at the intersection of 0-I and II-0 curves. For small deviations in the incidence angles, the nondispersive phase shift 2 Nbc Naba Dd 2 2 2 {1 2cot B } , III cos (86) then determines the coherent scattering length 96
Fig.53 Variation in the difference Ф I -Ф II between phases arising with the sample on paths I and II with θ near θ B for three wavelengths (top). The approximate phases for 0 are also shown (bottom). Ф I -Ф II remains nondispersive over ~ arcminute, relaxing the required sample alignment precision. 97
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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(
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studies. With such beams, the and
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CHAPTER 3 Neutron forward diffracti
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eing the separation of points M and
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3.1 Neutron forward diffraction Con
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excited by the incident wave (Fig.1
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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 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 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.
Page 156: 2009, (Grenoble, France, 2010) 3-15
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PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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