PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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Fig.15 Calculated cr and I O for a symmetric Bragg prism. Fig.16 Calculated cr and I O for an asymmetric Bragg prism. 46
The high sensitivity of neutron deflection cr of Bragg prism stems from dynamical diffraction effects. Figs.15 and 16 depict the deflection and forward diffracted intensity fraction by a rightangled Bragg prisms for symmetric and asymmetric {220} configurations. At incidence angles well off a Bragg reflection, cr equals the amorphous prism deflection am . As the Bragg reflection is approached from the low θ-side, cr increases monotonically, reaching a maximum at the onset of total reflectivity. On approaching the Bragg reflection from the higher angle side, the deflection decreases symmetrically by the same amount, attaining a corresponding minimum at the other extreme of total reflectivity. Si {220} being a full reflection (F H ≈ F O ), the maximum in cr at y = –1 nearly equals zero in the symmetric (cf. Eq.(54)) configuration (Fig.15). In the asymmetric case (Fig.16), the deflection even changes sign on the low θ-side, eventually exceeding –7 am and displaying a much greater sensitivity to θ-variation. For partial reflection like Si {111}, cr deviation from am is reduced to 70.7% of the full reflection value as F H /F O ≈.707. Contrary to the typical |d am /dθ| values of arcsec/deg attainable with an amorphous prism, a Bragg prism affords several orders of magnitude greater sensitivities |d cr /dθ| ~ arcsec/arcsec. 3.3.2 Back Face contribution to neutron forward diffraction If the crystal is thin in the direction normal to the incidence surface, at moderate values of the angle Δ, the neutron flow along J T reaches the back face (assumed parallel to the incidence surface). At the back face, two beams viz., partially transmitted and partially reflected, are generated with amplitudes and wave vectors determined by the respective boundary conditions. Boundary conditions at the back face excite the other tie point B. These partially reflected neutrons travel along current density vector J B at an angle Δ b , say, to the back face, (Figs.12-13) given by 47
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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
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 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
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the beam and remains visible up to
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cos bc 4NDd1 1 2cot 2 III 2 2
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yield about an order of magnitude r
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The refractive index, n = (1-Nb c
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with a white, and hence high-intens
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proposed dual sample. The dual samp
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The experiment was performed with =
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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
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REFERENCES [1] H. Rauch and S. Wern
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[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.
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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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