PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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sample. Least-squares fit to the sample spectrum (smooth curve) implies the instrument capability of characterising ~ 150 μm-size agglomerates in a sample. 80 Fig.43 Sphere size distribution inferred from Fig.42. 80 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. 83 Fig.45 Neutron diffraction pattern (points) from a macroscopic grating of period d ~ 200 μm and the least-squares fit (smooth curve) to the pattern. 85 Fig.46 Analyser rocking curve for an iron sample (top) and inferred scattering length density distribution (bottom). 86 Fig.47 Analyser rocking curve for amorphous aluminium prisms of apex angles 120 o (top) and 90 o (bottom) to observe ~ arcsec deflections. 87 Fig.48 Theoretical flat-topped angular profile from the optimally tailored Bragg prism monochromator (A=172 o and θ S =50.1 o ) for 1.75 Å neutrons. 90 Fig.49 Theoretical acceptance curve (black) of the optimal Bragg prism analyser (A=16 o and θ S =−51 o ) for 1.75 Å neutrons and its convolution (red) with the monochromator angular profile of Fig.48. 90 Fig.50 Our proposal depicting the phase measurement by recording the interferograms with the thick sample placed alternately in subbeams I and II of the symmetric LLL IFM. 91 Fig.51 In a symmetric LLL IFM, neutrons of wavelengths λ and λ+δλ propagate at corresponding Bragg angles θ B and θ B +δθ B to the IFM Bragg planes and hence
are incident at angles θ and θ+δθ B on the sample. Neutron refraction at the airsample interfaces introduces a small correction to the phase due to the sample. 93 Fig.52 Phase dispersion in a 26.5 mm thick Si sample placed on path I of an IFM as a function of neutron incidence angle θ at central wavelength λ 0 (=5.14Å). The phase becomes nondispersive only for incidence at the Bragg angle θ B and hence mandates sample alignment to arcsec precision. 94 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 λ 0 are also shown (bottom). Ф I -Ф II remains nondispersive over ~ arcminute, relaxing the required sample alignment precision. 97 Fig.54 Variation of the allowed sample thickness with Bragg angle of the IFM. 99 Fig.55 The experimental setup (schematic) employing a large symmetric LLL IFM with dual sample placed in subbeam II. 103 Fig.56 Dual Si-sample mounted on a plate. 104 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 Fig.58 Optimisation of the sample rotation and tilt. 109 Fig.59 Typical interferograms for path I and II as a function of phase flag. 110 Fig.60 Variation in phase with the interferogram oscillation frequency normalised to that expected theoretically. 110 Fig.61 Oscillation frequency and phase with scan number. 111
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 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 32 and 33: I. One of the major disadvantages o
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
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I H (θ H ) peaks of 0.18 height an
Page 90 and 91:
other with a compression factor lim
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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
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with a white, and hence high-intens
Page 128 and 129:
proposed dual sample. The dual samp
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The experiment was performed with =
Page 132 and 133:
Fig.59 Typical interferograms for p
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Fig.63 Path I, II and I-II phases d
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Fig.65 Average intensity with the s
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Fig.69 New metrological mapping of
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Si at 26.2 o C, applying a correcti
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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
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[67] V. F. Sears, Can. J. Phys., 56
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[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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