PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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CHAPTER 3 Neutron forward diffraction by Bragg prisms For a single crystal prism operating in a Bragg configuration, dynamical diffraction effects bring about strong deviations from the amorphous prism scenario. For a single crystal prism, if neutron incidence is set close to a Bragg reflection i.e., θ ~ θ B - θ S just outside the total reflection domain, unreflected neutrons traverse the prism at an angle Δ to the incidence surface and exit the side face Fig.9 Neutron propagation through amorphous and single crystal prisms. For the single crystal prism, additional beams emerge from front and side faces and the transmitted beam undergoes a significant lateral displacement. 36
in forward diffracted (I O ) and diffracted (I H ) beams (Fig.9) [66,138]. Here, θ B and θ S imply their usual meaning of Bragg angle and the angle between the front surface and the diffracting planes respectively. We have coined the term ‘Bragg prism for this device [139-142]. 3.0 Amorphous prism Consider incidence of a monochromatic neutron plane wave i k . e O r , on a non-absorbing amorphous prism at an angle (Fig.9 (top)). Because of the refractive index n of amorphous prism being very close to unity, these neutrons get almost fully transmitted through the prism (viz., I O ≈ I i ) and suffer a small deflection, with reflection at the incidence face being negligibly small. As alluded to earlier in Chapter 2, reciprocal space representation for an amorphous prism is depicted in Fig.10. Here, incident wave vectors k O in vacuum can originate on sphere of incidence LR of radius k O centred at reciprocal lattice point O and terminate at O of reciprocal lattice vector OH. For an amorphous prism, the refracted wave vectors (|K|=n|k O |) must originate on sphere of refraction QR' of radius nk O centred at reciprocal lattice point O and end at O. Let the vacuum wave vector k O is represented by RO for an incidence angle equal to . The inside wave vector of prism is uniquely selected by continuity of the tangential component of the wave vector across the vacuum-prism interface and hence the allowed internal wave vector is T'O at incidence surface, since it differs from RO only by a vector RT' along the incidence surface normal n i (Fig.10). By the triangle law of vectors, T'O and RO thus have identical components tangential to the incidence surface as required by the boundary conditions. We obtained the effected wave vector change –RM at incidence surface by extending back the inside wave vector T'O upto incidence sphere and located intersection point M. Negative sign indicates |n| less than unity. Thus, neutron gets deflected by δ 1 =(n–1)cotθ, away from the inward surface normal at incidence surface of the prism, with (1-n)k O 37
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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
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 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 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
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
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Fig.46 Analyser rocking curve for a
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This instrument was also employed t
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Fig.48 Theoretical flat-topped angu
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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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