PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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total reflectivity domain. These arise since unreflected neutrons propagate into the crystal at an angle Δ to the incidence surface due to dynamical diffraction and emerge from the side face, if the apex angle A between the front and side faces lies between θ B +θ S and π−θ B +θ S (cf. Fig.12, Chapter 3). The prism diffracted beam, albeit weaker than the Bragg reflection, can be made much narrower. Its intensity can furthermore be made to drop to zero within a fraction of an arcsec on either side of the peak centre by judiciously positioning the incident beam and tailoring the exit face orientation at large depths. We have named this super collimator-monochromator device a ‘Bragg prism collimator’ (Fig.26). 4.1 Bragg prism diffraction We revisit neutron beam incidence on a single crystal prism (Fig.12) just outside the total reflectivity domain such that the incident vacuum wave vector is RO in reciprocal space corresponding to the angle of incidence, B +LR/k O (Fig.27). Continuity of the tangential components of the wave vectors at the incidence interface and physical constraint on the energy flow direction into the thick single crystal allow the excitation of only a single tie point T on the dispersion surface (Chapter 3). At the exit surface, which subtends an angle A with the front face, following the same boundary condition, a line is drawn from T along the exit surface normal n e to intersect vacuum spheres of incidence and diffraction at point S and E respectively. The emergent wave vectors are therefore SO and EH in forward diffracted and Bragg diffracted directions, respectively. The Bragg diffracted intensity fraction I H of the Bragg prism as a function of the incidence angle can be written as I ( ) C( ) H 2 H . (58) O 60
Fig.27 Bragg diffraction of a neutron beam in reciprocal space. At each incidence angle, continuity of tangential components of wave vectors across the incidence and exit faces of the prism yields unique tie points as well as internal and emergent wave vectors. 61
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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
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SYNOPSIS The present thesis aims to
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analytic expressions for intensity
Page 22 and 23:
Research A, 634 (2011) S41. [9] S.
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spallation sources yield peak neutr
Page 26 and 27:
SU(2) phase, and separation of geom
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[33-34,48]. The bi-refracting natur
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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 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
Page 118 and 119: 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
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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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