Elementary scattering theory: for X-ray and neutron users
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2011
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 201 S. Ill., graph. Darst. |
| ISBN: | 9780199228676 9780199228683 |
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| 245 | 1 | 0 | |a Elementary scattering theory |b for X-ray and neutron users |c D. S. Sivia |
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2011 | |
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| adam_text | Titel: Elementary scattering theory
Autor: Sivia, Deviderjit S
Jahr: 2011
Contents
I Some preliminaries 1
1 Studying matter at the atomic and molecular level 3
1.1 Length scales and logarithmic axes 3
1.2 Resolution, magnification and microscopy 6
1.3 Structure, dynamics and spectroscopy 9
1.4 Atomic building blocks and interactions 11
1.4.1 The basic structure ofthe atom 12
1.4.2 The fundamental forces of nature 13
1.4.3 Probing matter by scattering particles 14
1.5 Energy, length and temperature scales 16
1.6 A table of useful constants 18
2 Waves, complex numbers and Fourier transforms 19
2.1 Sinusoidal waves 19
2.1.1 The direction of propagation 21
2.1.2 The principle of superposition 23
2.2 Complex numbers 25
2.2.1 Definition 25
2.2.2 Basic algebra 26
2.2.3 The Argand diagram 27
2.2.4 The imaginary exponential 27
2.3 Fourier series 29
2.3.1 Orthogonality and the Fourier coefficients 30
2.3.2 The complex Fourier series 32
2.4 Fourier transforms 32
2.4.1 Convolution theorem 34
2.4.2 Auto-correlation function 36
2.5 Fourier optics and physical insight 38
2.5.1 Young s double slit 40
2.5.2 A Single wide slit 41
2.5.3 A diffraction grating 42
2.5.4 The convolution theorem in action 43
2.5.5 Multi-dimensional generalization 44
2.6 Fourier data analysis 48
2.6.1 The phase problem 48
2.6.2 Truncation effects and windowing 50
2.6.3 Noise and probability theory 52
x Contents
2.7 Alist of useful formulae 56
2.7.1 Dimensional analysis 59
II Elastic scattering 61
3 The basics of X-ray and neutron scattering 63
3.1 An idealized scattering experiment 63
3.1.1 Elastic scattering and mornentum transfer 64
3.1.2 The differential cross-section 66
3.1.3 Elastic versus total scattering 67
3.2 Scattering by a Single fixed atom 67
3.2.1 Nuclear scattering lengths 69
3.2.2 Atomic form factors 71
3.2.3 Magnetic form factors 73
3.2.4 Scattering cross-sections 75
3.3 Scattering from an assembly of atoms 77
3.3.1 Scattering density and Fourier transforms 79
3.3.2 Temperature and Debye-Waller factors 81
3.3.3 Coherent and incoherent scattering 82
3.3.4 Mixed scattering events 84
3.4 X-rays and Synchrotron sources 84
3.4.1 Wigglers and undulators 88
3.5 Reactors and pulsed neutron sources 89
3.5.1 The time-of-flight technique 91
4 Surfaces, Interfaces and reflectivity 93
4.1 Reflectivity and Fourier transforms 93
4.1.1 Substrate only 98
4.1.2 One uniform layer 100
4.1.3 A short multilayer 101
4.1.4 A phaseless Fourier ambiguity 102
4.2 Reflectivity and geometrical optics 104
4.2.1 Refractive index 105
4.2.2 A Single boundary 105
4.2.3 Multiple boundaries 108
4.3 X-rays, neutrons and other techniques 110
5 Small-angle scattering and the big picture 113
5.1 Diffraction and length scales 113
5.2 Size, shape and molecular form factors 114
5.2.1 Absolute intensities 118
5.2.2 The Guinier approximation 119
5.2.3 Porod slaw 122
5.2.4 Polydispersity 124
5.3 Assemblies and correlations 125
5.3.1 Orientational alignment 125
5.3.2 Positional correlation 126
5.4 Pair-distribution function 127
Contents xi
5.5 Contrast matching 129
Liquids and amorphous materials 131
6.1 The middle phase of matter 131
6.2 Radial distribution functions 132
6.3 Structure factors 134
6.3.1 Partial structure factors 137
6.4 Comparison with small-angle scattering 139
6.5 The Placzek correction 139
Periodicity, symmetry and crystallography 141
7.1 Repetitive structures and Bragg peaks 141
7.1.1 Atomic planes and Bragg s law 144
7.1.2 Simple consequences and applications 146
7.2 Patterns and symmetries 147
7.2.1 Reality and Friedel pairs 147
7.2.2 Centrosymmetry and reality 148
7.2.3 Space groups and systematic absences 148
7.2.4 Geometry and Space groups 150
7.2.5 Symmetry and statistics 151
7.3 Circumventing the phase problem 151
7.3.1 Patterson maps 152
7.3.2 Heavy atoms and partial structure 153
7.3.3 Isomorphous replacement 154
7.3.4 Direct methods and prior knowledge 155
7.4 Powdered samples 156
7.4.1 Texture 158
7.4.2 Twinning 159
7.4.3 Fibre diffraction 160
7.5 Magnetic structures 160
III Inelastic scattering 163
8 Energy exchange and dynamical information 165
8.1 Experimental considerations 165
8.1.1 The partial differential cross-section 166
8.1.2 Triple-axis spectrometer 167
8.1.3 Time-of-flight Instruments 168
8.2 Scattering from time-varying structures 169
8.2.1 Elastic scattering 170
8.2.2 Space-time correlation function 170
8.2.3 Total scattering 171
8.2.4 Coherent and incoherent scattering 172
8.3 A quantum transitions approach 173
9 Examples of inelastic scattering 175
9.1 Compton scattering 175
9.1.1 The impulse approximation 177
xii Contents
9.1.2 Single particle wave function 178
9.2 Lattice vibrations 179
9.2.1 Heat capacities 182
9.2.2 Spin waves 183
9.3 Molecular spectroscopy 184
9.3.1 Quasi-elastic scattering 185
9.3.2 Energy resolution and time-scales 186
A Discrete Fourier transforms 187
B Resonant scattering and absorption 191
References 193
Index 197
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:51:35Z |
| institution | BVB |
| isbn | 9780199228676 9780199228683 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020874898 |
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| physical | XII, 201 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
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| publisher | Oxford Univ. Press |
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| spelling | Sivia, Devinder S. Verfasser aut Elementary scattering theory for X-ray and neutron users D. S. Sivia Oxford [u.a.] Oxford Univ. Press 2011 XII, 201 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Streutheorie (DE-588)4183697-2 gnd rswk-swf Streutheorie (DE-588)4183697-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020874898&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sivia, Devinder S. Elementary scattering theory for X-ray and neutron users Streutheorie (DE-588)4183697-2 gnd |
| subject_GND | (DE-588)4183697-2 |
| title | Elementary scattering theory for X-ray and neutron users |
| title_auth | Elementary scattering theory for X-ray and neutron users |
| title_exact_search | Elementary scattering theory for X-ray and neutron users |
| title_full | Elementary scattering theory for X-ray and neutron users D. S. Sivia |
| title_fullStr | Elementary scattering theory for X-ray and neutron users D. S. Sivia |
| title_full_unstemmed | Elementary scattering theory for X-ray and neutron users D. S. Sivia |
| title_short | Elementary scattering theory |
| title_sort | elementary scattering theory for x ray and neutron users |
| title_sub | for X-ray and neutron users |
| topic | Streutheorie (DE-588)4183697-2 gnd |
| topic_facet | Streutheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020874898&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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