PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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analytic expressions for intensity fraction I H and exit angle θ H of neutrons diffracted from a Bragg prism, are derived. With a judicious choice of the Bragg reflection, its asymmetry and the apex angle, a Bragg prism can collimate a neutron beam to sub-arcsec widths (Section 4.2). In conjunction with an analyser in the opposite asymmetry likewise tailored to accept a pair of even narrower peaks, it would yield a rocking curve comprising a pair of sub-arcsec peaks separated by up to a few arcsec. Experimental achievement of the first ever neutron beam of sub-arcsec widths is presented in Section 4.3. This novel setup has facilitated SUSANS (Super Ultra-Small- Angle Neutron Scattering) experiments probing wave vector transfers Q ~ 10 -6 Å -1 (Section 4.4) and hence characterisation of up to 150 μm-size agglomerates in samples. The transverse coherence length of 175 μm of the monochromated beam is the highest achieved to date, allowing us to record the first neutron diffraction pattern from a macroscopic grating of 200 μm period [8-16]. Chapter 5 describes high-precision interferometric determination of the coherent scattering length b C by optimising various parameters of the experiment. A finely surfaced thick dual sample in the nondispersive configuration and a large interferometer (IFM) with spacious splitter-mirror and mirror-analyser gaps operating at a large Bragg angle reduce imprecision in previous b C measurements down to a few ppm. It is then imperative to correct the b inferred C from the observed phase for neutron refraction effects at the sample-ambient interfaces. The refractive index for neutrons can thus be determined to a phenomenal precision of a few parts in 10 12 . Section 5.2 describes the interferometric experiment which thus determined b C of silicon to within 27 parts in 10 6 [17-22]. Chapter 6 concludes this thesis and provides a summary of the main results and future directions for the use of these novel techniques and devices in research. It enumerates several firsts scored III
y us in the field of neutron optics such as: • Enunciation and observation of neutron forward diffraction by single crystal prisms which enables smooth control over the neutron deflection due to the arcsec/arsec sensitivity of the deflection to the incidence angle. • Design, fabrication and operation of a novel Bragg prism monochromator-analyser pair which achieved the first rocking curve of sub-arcsec angular width. • SUSANS (Super Ultra Small Angle Neutron Scattering) spectrum probing wave vector transfers Q ~ 10 -6 Å -1 . • Neutron diffraction pattern from a macroscopic grating (period ~ 200 μm). • Measurement of the largest non-dispersive phase (911 interference orders) to date, determining b C to within 27 parts per million. REFERENCES [1] S. Abbas, A. G. Wagh, M. Strobl and W. Treimer, Nuclear Instruments and Methods in Physics Research A, 634 (2011) S144. [2] A. G. Wagh, S. Abbas and W. Treimer, Journal of Physics (CS), 251 (2010) 012074. [3] S. Abbas, A. G. Wagh, and W. Treimer, Pramana- J. Phys., 71 (2008) 1109. [4] S. Abbas, A. G. Wagh, M. Strobl and W. Treimer, Sol. St. Phys. (India), 51 (2006) 351. [5] M. Strobl, W. Treimer, Ch. Ritzoulis, A. G. Wagh, S. Abbas and I. Manke, J. Apl. Cryst., 40 (supplement) (2007) s463. [6] A. G. Wagh, S. Abbas , M. Strobl and W. Treimer, BENSC experimental reports 2005 (HMI, Germany, 2006) 115. [7] S. Abbas and A. G. Wagh, Sol. St. Phys. (India), 50 (2005) 317. [8] A. G. Wagh, S. Abbas and W. Treimer, Nuclear Instruments and Methods in Physics IV
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 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 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
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Fig.20 Bragg reflection intensity f
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fraction I O through the Bragg pris
Page 78 and 79:
Fig.22 Experimental (points) and th
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Table 2: Observed deflection sensit
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total reflectivity domain. These ar
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Here the term C() accounts for the
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Fig.28 Theoretical curves for Si {1
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I H (θ H ) peaks of 0.18 height an
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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
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4.3.2 Experiment The experiment was
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Fig.38 Bragg reflection rocking cur
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4.4 Applications of novel SUSANS se
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Fig.42 First Q ~ 10 -6 Å -1 SUSANS
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2 (1) -(δk i .Δ i ) /2 Γ (Δ) =
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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
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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
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.
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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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