PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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Therefore, the forward diffracted intensity (transmission) fraction as a function of incidence angle is given by sin sin(A ) (51) B S I ( ) . O sin(A )sin( B S ) The apex angle A of Bragg prism must lie between B + S and π–(θ B –θ S ) to make possible the emergence of both I O and I H ( I H 1 I D - I O , expression derived in Chapter 4, cf. Eq.(61)), from the side face. Outside the total reflectivity domain, as apex angle 'A' approaches B + S , all the unreflected intensity (1–I D ) tends to propagate in I O (Fig.14), since the cross section for I H approaches zero. As 'A' increases beyond B + S , the intensity fraction I H rises at the expense of I O . 3.3 Neutron deflection We derive the neutron deflection formulae for the Bragg prisms of the forward diffracted beam by delineating the wave vectors change in reciprocal space determined by the boundary conditions at the incidence and exit faces of the prisms. The forward diffracted neutron (transmitted) beam show strong deflections sensitivities for neutron incidence close to total reflectivity regime, accompanied by a large concomitant loss of intensity due to appearance of Bragg reflection at front and Bragg prism diffraction at side faces, respectively. These transmitted neutrons exit the side face with a concomitant lateral displacement depending on the incidence angles θ and thus on the energy flow inside the crystal (Fig.12). 3.3.1 Bragg prism To obtain the neutron deflection by a Bragg prism, we follow the same procedure as outlined for the amorphous prism except that now the internal wave vector must originate on the dispersion 44
surface instead of sphere QT'R' for an amorphous prism. For neutron incidence along RO on the Bragg prism, the allowed internal wave vector in forward diffracted direction is hence TO, differing from RO only by the vector RT (Fig.13) along the incidence surface normal n i . Likewise, at the exit surface, the emergent wave vector SO can be arrived at. The exit angle of the forward diffracted beam B +LS/k O , thus differs from the incidence angle ( B +LR/k O ) by the Bragg prism deflection –RS/k O , written as . (52) cr O (n 1 ) cot( B S) cot(A B S) kO Here O symbolises the difference between magnitudes of TO and T'O and is obtained as sin( ) F O 1/2 B S H 2 bCN y(1 1 y ) sin( B S) FO . (53) Here, symbols have their usual meanings viz., y denotes scaled deviation of incidence angle from centre of Bragg diffraction C (cf. Eq.(27)), F O and F H stand for structure factor magnitude for O and H reflection respectively. O is positive and negative respectively for (y0) branches of the dispersion surface. The difference between cr and am thus originates from O which vanishes for an amorphous material. O and hence the deflection cr vary sharply with incidence angle, the reflection {hkl} and asymmetry of Bragg configuration S . cr reaches extrema at either end of the total reflection domain, viz., y=±1 and can be enhanced for the opposite asymmetry (viz., S ~ – B ) and by employing full {hkl} reflections (F O ≈ F H ). Eqs.(53) in (52), lead to the relation, F sin( ) cr am FO sin( B S) H B S 2 1 y 1 1 y . (54) 45
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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
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 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
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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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