PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

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nuclear physics very important as it would shed light on the basic nucleon- nucleon interaction, charge independence and charge symmetry of the nuclear forces and thus on validity of different nuclear models [1,2,68,119]. Neutron scattering studies of condensed matter clearly require accurate values for the coherent (b c ) and incoherent (b I ) scattering lengths of the elements present in the sample. There are many methods for b c determination such as, Christiansen filter [120], mirror reflection [121-122], gravity refractometer [123], prism refraction [49,124] and transmission [125] etc. However, the most accurate value with a relative error of about 0.03 was obtained by Shull et al. [66,78-79] using the dynamical diffraction of neutrons from a Si single crystal in Laue geometry and observing the Pendellösung oscillation for various thicknesses of Si crystal. Perfect crystal interferometry affords most precise determination of the coherent scattering length [1,2,4,69,119] of samples. Following Scherm’s suggestion of placing the sample with its surface parallel to the Bragg planes of the interferometer to attain a wavelength-independent phase, Rauch et al. [126] determined b c to within a few parts in 10 4 . Ioffe et al. [127] reduced the b c imprecision to a few parts in 10 5 by measuring the phase shift between two interferograms recorded with the sample placed alternately on the two beam paths of the interferometer in this non-dispersive configuration. Wagh and <strong>Abbas</strong> have proposed a comprehensive optimisation of this method to attain a further order of magnitude improvement in b c precision and pointed out that a correction for neutron refraction at the air-sample interfaces would then become mandatory. Using a monolithic dual sample, proposed by Lemmel and Wagh [128], in the non-dispersive configuration, b c has been determined with a precision of 27 parts per million [Chapter 5]. 12
CHAPTER 2 Optics and dynamical diffraction theory of neutrons This Chapter presents the basic theoretical framework underlying our work on neutron dynamical diffraction and its application in neutron optics. First, I briefly summarise the relevant results from the theory of neutron optics needed to understand the scattering length and its importance. 2.1 Scattering length: Basic relations Thermal neutrons are scattered by a nucleus through the strong interaction. The strong interaction being short-ranged, the relevant impact parameter R (~ fm) is much smaller than the neutron wavelength (~ Å) and the neutron angular momentum mvR = hR/ < 10 -4 ħ. Hence only l = 0 (swave) scattering need be considered which by the first Born approximation [51-52], is isotropic. Consider a neutron plane wave ψ inc i = e kr incident on a single nucleus bound within a solid sample. Here k denotes the incident wave vector. The condition of kR
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 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 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
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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