PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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yield about an order of magnitude reduction in the D/D contribution to b c /b c . In addition, the phase also increases by the same factor as D, reducing the Ф/ contribution. Further, one can maximise d to 3.14 Å by choosing the {111} Bragg reflection for the Si IFM (hence λ = 5.14 Å) to enhance by about 63% over that obtainable with the {220} Bragg reflection and reduce Ф/. A thermal enclosure around and vibration isolation of the IFM reduces the phase drift to a fraction of a degree over a day [1,127]. The effect of this phase drift over a typical measurement duration of a few hours, is minimised by recording the O and H detector intensities (Fig.50) for the three positions (I, II and Out) of the sample in succession at each angular setting of the phase flag. A phase error of about 0.3 deg, thus routinely achieved in interferometric experiments, is included in Table 3. Good interference contrast can be achieved even for this high interference order due to the nondispersive configuration [1,126-127]. The contribution from the uncertainty in the refractive index of air, dependent on variations in the temperature, pressure and relative humidity, can be larger than that assumed for N a b a /N =9.137(9) x 10 -3 fm in [127]. However, this assumed uncertainty of 2.2 parts per million in b c precision due to air can be eliminated by performing the experiment in vacuum. If the sample happens to be a single crystal, extreme care needs to be exercised to ensure neutron incidence far off any Bragg reflection of the sample. The sample then just presents an average refractive index to neutrons. With a crystalline Si sample (Nd =1.57x10 15 cm -2 ), our proposed phase Ф I-II = -394284.8 o will yield b c with ultrahigh precision of a few parts per million (ppm) as shown in the last column of Table 3. The exact and approximate phases for δγ=0 in our proposal are plotted in Fig.53 (bottom curve). The exact phase is greater by about 2.6 o at θ=θ B . 100
The refraction corrections (cf.. Eq.(90)) in b c of – 6.5 * 10 -6 for Si{111}, slightly exceeds the proposed precision in magnitude (cf. Table 3), underscoring the importance of refraction effects. Therefore, when such ultrahigh precision is achieved, it becomes mandatory to account for neutron refraction at the ambient-sample interfaces and use the exact formulas for the Φ and b c respectively (cf. Eqs.(88-89)). Table 3: Comparison between various b c /b c contributions at Ioffe et al. [127] and our proposal for a Si sample. Ioffe et al. Source Proposed [111] [220] 5.0 * 10 -5 Thickness: D 0.1 μm 3.8 * 10-6 (Precision grinding) 9.0 * 10 -6 Phase: Ф = 0.3 o , typical 7.6 * 10 -7 1.2 * 10 -6 2.2 * 10 -6 Air: ( N a b a /N)=9 * 10 -6 fm 2.2 * 10 -6 Eliminate: Vacuum expt 1.1 * 10 -7 Rotation: δθ 0.01 o , typical 3.0*10 -8 1.4 * 10 -7 Tilt: δγ 0.01 o , typical 1.5 * 10 -8 3.7 * 10 -9 {Nd} Si = 6 * 10 6 cm -2 3.7 * 10 -9 5.1 * 10 -5 Total 4.4 * 10 -6 4.5 * 10 -6 Vacuum experiment 3.9 * 10 -6 4.0 * 10 -6 101
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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
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Research A, 634 (2011) S41. [9] S.
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spallation sources yield peak neutr
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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
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I. One of the major disadvantages o
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nuclear physics very important as i
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potential for most nuclei in spite
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Due to the rapid strides made latel
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for a positive value of b c i.e. fo
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k b k O H . ni sin( B S) . (18)
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factor exp(-W). The centre, θ C ,
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exploiting multiple successive iden
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We shall confine our discussion hen
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The depth Z is measured from the in
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wings (large-y regions). The freque
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expressed as T(y, t )R(y, t )R(
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studies. With such beams, the and
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CHAPTER 3 Neutron forward diffracti
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eing the separation of points M and
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3.1 Neutron forward diffraction Con
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excited by the incident wave (Fig.1
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Therefore, the forward diffracted i
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Fig.15 Calculated cr and I O for a
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(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
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 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 =
Page 132 and 133: Fig.59 Typical interferograms for p
Page 134 and 135: Fig.63 Path I, II and I-II phases d
Page 136 and 137: Fig.65 Average intensity with the s
Page 138 and 139: Fig.69 New metrological mapping of
Page 140 and 141: Si at 26.2 o C, applying a correcti
Page 142 and 143: selected asymmetric Bragg prism may
Page 144 and 145: 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
Page 150 and 151: [67] V. F. Sears, Can. J. Phys., 56
Page 152 and 153: [97] A. Cabello, S. Filipp, H. Rauc
Page 154 and 155: [127] A. Ioffe, D. L. Jacobson, M.
Page 156: 2009, (Grenoble, France, 2010) 3-15
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PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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