PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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proposed dual sample. The dual sample affords greater precision than the single sample due to its greater effective thickness of 36 mm. 5.2 EXPERIMENTAL The experiment was performed at the S18 beam port of 58 MW Institut Laue Langevin (ILL) reactor in Grenoble, France. The Si perfect-crystal monochromator and IFM are operated in a nondispersive configuration which provides a narrow rocking curve with 1.8" FWHM at a wavelength of 1.8Å. To attain greater contrast and phase stability, the optical bench is shielded against Fig.57 A photograph of the experimental setup at S18 ILL, depicting a pair of amorphous Si prisms each of 120 o apex angles placed before the symmetric {220} LLL IFM to remove the λ/2 from monochromatic neutron beam. Dual sample mounted on a plate, is hanging from the top. 106
vibrations and thermal drifts. A pair of amorphous Si prisms each of 120 o apex angles is placed before the symmetric {220} LLL IFM to remove the second harmonic (λ/2) from monochromatic neutron beam (Fig.57). The 93 mm long sample had a 6 mm wide groove in the middle to accommodate the mirror blade of IFM (Fig.56). The sample was cut and ground from a single crystal Si ingot, at an orientation carefully selected so that neutrons incident at 38 o to the sample surface would be at least 10 o away from exciting any major reflection in Bragg or Laue configuration, at a company in Grenoble. 5.2.1 Recording of the interferograms The relative intensity patterns recorded for the O and H exit beams, depend upon the phase difference of the neutron subbeams traversing path I relative to path II. We record an interferogram with a 4 mm thick Al flat phase flag positioned between the splitter and mirror blades of the IFM such that it intercepts both neutron paths (Fig.55). A rotation ζof this phase flag from parallelity to IFM blades induces a differential thickness between the two paths given by 2sin sin D ( ) D ( ) D ( ) D cos sin B Al II I 0 2 2 B (93) and a phase shift ( )=-N AlbAlD Al( ), (94) proportional to D Al (ζ). Here D 0 , N Al and b Al denote thickness, atom density and coherent scattering length of aluminum phase shifter respectively. O and H intensity patterns recorded by varying χ through ζ, are governed by Eqs.(41a and 41b). 107
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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
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Fig.15 Calculated cr and I O for a
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(1 I ) D tan b . ID cot( B S)
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Fig.18 Experimental layout to measu
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Fig.20 Bragg reflection intensity f
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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 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 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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