PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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potential for most nuclei in spite of the attractive nature of basic neutron-nuclear interaction. The dependence of b c on the atomic mass (Fig.2) is quite irregular [119] with only a few nuclei displaying negative scattering lengths [5,131]. If all scattering nuclei are identical, neutrons scattered from different nuclei have a definite phase relationship and coherent scattering results. On the contrary, there is no definite phase relationship between waves from scattered different isotopes (isotopic incoherent scattering) or from nuclei with random spin orientations in the sample (spin incoherent scattering) [1-2,4,24-27,119,129- 130]. If the sample contains different isotopes with fractional isotopic abundances f i , distributed randomly, the coherent b c , the isotopic incoherent b I , and the total b, scattering lengths are computed by accounting for the isotopic abundances, viz., bC fi b i , (5) i 2 b f f b b (6) I i j i j i j Fig2. The distribution of coherent scattering lengths as a function of atomic mass number [5,119]. 14
and b f b . (7) i i 2 i Absorption is accounted for by a complex interaction potential and therefore by a complex scattering length 2 b b / 2 i / 2 , (8) ' 2 C C attn attn where the attenuation cross section attn includes both absorption a and incoherent scattering I . The coherent, incoherent and total scattering cross sections ' 2 2 C C C 4 b 4 b , I 4 bI and 2 S C I 2 ( ) 4 b respectively of a bound nucleus, are determined by the moduli of the respective complex scattering lengths. In general, b c varies for different isotopes of an element, allowing isotopic substitution methods to yield structural and dynamical information in great detail. It also facilitates the use of contrast variation to selectively mask specific components of a complex system to observe scattering only from the rest of the system in small angle neutron scattering (SANS) studies. Table 1: Isotopic abundance, spin, neutron scattering lengths and cross sections for the Si. Silicon Abundance Spin b c b I σ C σ I σ a (%) (fm) (fm) (barn) (barn) (barn) 14Si - - 4.15071(22) 0.178 2.1633(10) 0.004(8) 0.171(3) 14Si 28 92.2 0 4.106(6) 0 2.120(6) 0 0.177(3) 14Si 29 4.7 1/2 4.7(1) 0.089* 2.78(12) 0.001(2) 0.101(14) 14Si 30 3.1 0 4.58(8) 0 2.64(9) 0 0.107(2) *For the isotope Si 29 with a spin ½, b I arises from different scattering lengths for the up and down spin states. 15
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 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 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 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 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 =
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
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[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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