PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

More documents

Recommendations

Info

exploiting multiple successive identical Bragg reflections from two slabs of a channel-cut monolithic single crystal, producing a highly collimated neutron beam [111,115]. For a crystal cut asymmetrically at S B to the reflecting planes, |b| –1 is large. For incidence at a near grazing angle B – S , the crystal will thus accept a narrow beam of a large angular divergence 1/2 w / b and generate a highly collimated ( w b 1/2 ) diffracted beam wider in cross section. The enhancement by the factor |b| in the spatial width δx of the reflected beam vis-a-vis the incident beam, reduces the angular divergence of the reflected beam by the same factor. This is a direct consequence of conservation of the phase space volume spanned by the beam since the momentum spread δp x =p 0 δ of a monochromatic beam is proportional to the angular width δ. Such an arrangement therefore works as a collimator. The same setup with the beam directions reversed, relating to the other extreme ( S – B , |b| –1 →0) in the Bragg case, may be employed where a small sample is to be studied and the angular divergence is of no great consequence. 2.2.3 Laue Case In a Laue configuration (Fig.4b), the line drawn through the point of incidence parallel to n i always intersects the dispersion surface in two real points, such as A and B in Fig.5. The internal wave vectors are thus always real for a nonabsorbing crystal. Further, since the diffracted wave does not exit the incidence surface, the boundary condition II) implies 1 O O 0 H H . (29) At the exit surface, each composite internal wave function ( or ) gives rise to a transmitted and a diffracted wave. The situation where the exit surface normal, n e is not parallel to n i is illustrated in Fig.5. The line drawn through A parallel to n e intersects the spheres of incident and diffracted wave vectors in vacuum in the points E and R respectively. Thus, the exiting transmitted 24
and diffracted waves generated by will propagate in the directions EO and RH respectively. Since in general, the points E and T are distinct, the transmitted wave vector EO subtends an angle, ET/k O , with the incident wave vector TO. The tie point B will similarly result in another set of exiting waves. In the case where the incidence and exit surfaces are parallel, each of the tie points A and B, excites points T and I on the k O and k H spheres respectively. Each transmitted wave thus propagates exactly in the incident direction TO and each diffracted wave, along IH. In particular, for the symmetric Laue configuration, where n i is parallel to LQ ( S =–/2, b=l), a wave incident at an angle ( B +ω) to the crystal planes gives rise to diffracted waves exiting at ( B –ω) thus always maintaining an angle 2 B between the incident and diffracted waves. The amplitudes of the exiting waves are derived by applying the boundary condition II) at the exit surface. Fig.5 Reciprocal space diagram of the Laue diffraction in a single crystal. 25
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 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 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
show all

PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

Create successful ePaper yourself

Delete template?

Save as template?