PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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I. One of the major disadvantages of neutrons, also shared by X-rays, is their very small magnitude of refractive power |n – l| ~ 10 -6 –10 -5 [4-5]. Therefore, thermal neutrons traversing an amorphous prism undergo a deflection in the arcsec regime and a few-degree variation in the incidence angle brings about only ~ arcsec change in the neutron deflection. Further, contrary to light, since refractive index is usually smaller than unity for neutrons, the deflection will be towards the apex of prism. Schneider and Shull [108] have carried out precision measurements of prism deflection angles from which refractive indices, and hence scattering lengths, were determined. Wagh and Rakhecha [109] showed that for neutron propagation parallel to the prism base, the neutron deflection just equals the product of the refractive power and base-height ratio of the prism. Over the past five decades, variations of the forward diffracted (I O ) and diffracted (I H ) intensities from single crystal prisms with the incidence angle have been observed for X-rays [38,110] and neutrons [79]. Due to the nonavailability of arcsec wide neutron beams at that time however, the neutron I H (θ) variation could only be mapped by scanning a narrow slit across the diffracted beam. However, deflection sensitivities of the amorphous prisms remained abysmally low. In Chapter 3, we overcome this problem by presenting a novel Bragg prism, viz., a single crystal prism operating in the vicinity of a Bragg reflection, offering deflection sensitivity of more than three orders of magnitude greater than an amorphous prism achieved with a 2 arcsec wide neutron beam [111- 112]. II. Experimenters’ insatiating thirst for more and more parallel monochromatic neutron beam, has led to development of numerous types of monochromator–collimator setup using single crystal [4,24-27]. Ultra-small angle neutron (or X-ray) scattering (USANS/USAXS) studies [113] which probe wavevector transfers Q ~ 10 -5 Å -1 , require an incident beam collimation down to a few arcsec, to characterize samples [26-27,114] containing agglomerates of μm dimensions. A Bragg 10
diffracted neutron beam from a single crystal monochromator is typically a few arcsec wide but with long tails. The Darwin profile is sharper, with an intensity nearly half that for the Ewald profile in the tail region. Yet even the Darwin tail intensity drops gradually, in inverse proportion to the square of the incidence angle measured from the centre of Bragg reflection. Bonse and Hart in 1965 [115] proposed a number p of successive identical Bragg reflections from two slabs of a channel-cut monolithic single crystal to achieve collimation without the tail contamination. The tails of the multiply reflected intensity fraction R p (R
Page 1: Studying neutron dynamical diffract
Page 4 and 5: DECLARATION I, hereby declare that
Page 6 and 7: ACKNOWLEDGEMENTS I sincerely, thank
Page 8 and 9: Fig.10 Boundary conditions on wave
Page 10 and 11: Fig.28 Theoretical curves for Si {1
Page 12 and 13: sample. Least-squares fit to the sa
Page 14 and 15: Fig.62 Interference contrast and av
Page 16 and 17: 3.4 Experimental 49 3.5 Results and
Page 18 and 19: SYNOPSIS The present thesis aims to
Page 20 and 21: analytic expressions for intensity
Page 22 and 23: Research A, 634 (2011) S41. [9] S.
Page 24 and 25: spallation sources yield peak neutr
Page 26 and 27: SU(2) phase, and separation of geom
Page 28 and 29: [33-34,48]. The bi-refracting natur
Page 30 and 31: application of the dynamical theory
Page 34 and 35: nuclear physics very important as i
Page 36 and 37: potential for most nuclei in spite
Page 38 and 39: Due to the rapid strides made latel
Page 40 and 41: for a positive value of b c i.e. fo
Page 42 and 43: k b k O H . ni sin( B S) . (18)
Page 44 and 45: factor exp(-W). The centre, θ C ,
Page 46 and 47: exploiting multiple successive iden
Page 48 and 49: 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
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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
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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 =
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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
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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.
Page 156:
2009, (Grenoble, France, 2010) 3-15
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PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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