Dynamical theory of x-ray diffraction:
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| Format: | Book |
| Language: | English |
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Oxford [u.a.]
Oxford Univ. Press
2008
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| Edition: | Reprinted |
| Series: | International Union of Crystallography monographs on crystallography
11 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 678 S. Ill., graph. Darst. |
| ISBN: | 9780198528920 |
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| 100 | 1 | |a Authier, André |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Dynamical theory of x-ray diffraction |c André Authier |
| 250 | |a Reprinted | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2008 | |
| 300 | |a XVIII, 678 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International Union of Crystallography monographs on crystallography |v 11 | |
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| 830 | 0 | |a International Union of Crystallography monographs on crystallography |v 11 |w (DE-604)BV005455767 |9 11 | |
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| adam_text | Contents
I Background and basic results
1
1
Historical developments
3
1.1
Prologue
3
1.2
The discovery of X-ray diffraction
4
1.3
The geometrical theory of diffraction
5
1.4
Darwin s dynamical theory of diffraction
6
1.5
Extinction theories
8
1.6
Ewald s dynamical theory
11
1.7
Early confirmations of the dynamical theory
13
1.8
Laue s dynamical theory
14
1.9 Umweganregung
and
Aufhellung 14
1.10
The properties of wavefields
16
1.10.1
Anomalous absorption (the Borrmann effect)
16
1.10.2
Wavefield trajectories
20
1.10.3
Pendellösung
23
1.11
Diffraction by deformed crystals
25
1.12
Modern times
26
2
Properties of the electromagnetic field
—
propagation and
scattering
28
2.1
Maxwell s equations
28
2.2
The electrodynamic potentials in vacuum
29
2.2.1
The vector and scalar potentials
29
2.2.2
The retarded potentials
30
2.3
The electrodynamic potentials in polarized media
31
2.4
Hertz vectors (polarization potentials)
31
2.5
Propagation of an electromagnetic wave in vacuum
33
2.6
Scattering of X-rays by an electron
33
2.7
Polarizability of matter for X-rays
36
2.7.1
Elementary dispersion theory
36
2.7.2
Fourier expansion of the polarizability
37
2.7.3
Index of refraction
41
2.7.4
Absorption
41
2.8
Ewald s dispersion theory
43
2.9
Propagation equation of an electromagnetic wave in
materials in Laue s dynamical theory
49
2.9.1
Laue s basic assumption
49
CONTENTS
2.9.2
Propagation
equation
49
2.10
Specular reflection
—
Fresnel relations
50
Geometrical theory of X-ray diffraction
57
3.1
Classical scattering by an electron
—
polarization
57
3.2
Amplitude diffracted by a periodic electron distribution
58
3.3
Intensity diffracted by a small crystal
61
3.4
Reflectivity
63
3.5
Integrated intensity
65
3.6
Mosaic crystals
67
Elementary dynamical theory
68
4.1
Limitations of the geometrical theory
68
4.2
Introduction of the dispersion surface
69
4.3
Analogy with the band theory of solids
71
4.4
Propagation equation
73
4.5
Fundamental equations of dynamical theory
74
4.6
Amplitude ratio of the refracted and reflected waves
79
4.7
Solutions of plane-wave dynamical theory
80
4.7.1
Boundary conditions
80
4.7.2
Departure from Bragg s angle of the incident wave
81
4.7.3
Transmission and reflection geometries
82
4.7.4
Deviation parameter
85
4.7.5
Determination of the tiepoints
85
4.7.6
Effective absorption coefficient
87
4.8
The diffracted waves in the transmission geometry
88
4.8.1
Double refraction
88
4.8.2
Boundary conditions for the amplitudes at
the entrance surface
88
4.8.3
Intensities of the reflected and refracted waves
89
4.8.4
Anomalous absorption
90
4.8.5
Boundary conditions at the exit surface
92
4.8.6
Reflectivity
94
4.8.7
Pendellösung
96
4.8.8
Integrated intensity
98
4.9
The diffracted waves in the reflection geometry
99
4.9.1
Tiepoints
99
4.9.2
Thick crystals
—
total reflection
99
4.9.3
Thin crystals
102
4.10
Influence of the asymmetry on the position and width of the
rocking curve and of the angular distribution of the
reflected beam
104
4.11
Comparison with geometrical theory
107
4.12
Dynamical diffraction by quasicrystals
110
CONTENTS xi
II
Advanced
dynamical theory
11
3
5
Properties of wavefields
115
5.1
Relations between the field vectors
115
5.2
Fundamental equations of the dynamical theory
117
5.3
The dispersion equation in the two-beam case
118
5.4
Poynting vector of the wavefields
121
5.5
Determination of the tiepoints
—
geometrical interpretation
of the deviation parameter
123
5.5.1
Boundary condition for the wavevectors
123
5.5.2
Deviation from Bragg s angle of the middle of the
reflection domain
125
5.5.3
Coordinates of the tiepoint
126
5.5.4
Deviation parameter,
Pendellösung
distance and
Darwin width in the transmission geometry
128
5.5.5
Deviation parameter, extinction distance, penetration
depth and Darwin width in the reflection geometry
132
5.5.6
Index of refraction for dynamical diffraction
135
5.6
The deviation parameter in absorbing crystals
136
5.7
Amplitude ratio of the refracted and reflected waves
136
5.7.1
Phase of the amplitude ratio in the transmission
geometry
137
5.7.2
Phase of the amplitude ratio in the reflection
geometry
138
5.8
Anomalous absorption
139
5.8.1
Effective absorption coefficient in the transmission
geometry
139
5.8.2
Absorption coefficient in the propagation direction
141
5.8.3
Discussion of anomalous absorption
—
properties
of the standing wavefield
142
5.8.4
Anomalous absorption in the reflection
geometry
—
penetration depth
147
5.9
Dispersion surface when the Bragg angle is close to
π/2
148
5.9.1
Deviation from Bragg s angle and Darwin width
148
5.9.2
Dispersion surface
151
5.9.3
Penetration depth
153
5.9.4
Applications
154
6
Intensities of plane waves in the transmission geometry
155
6.1
Boundary conditions for the amplitudes at the entrance
surface
155
6.2
Amplitudes of the refracted and reflected waves
157
CONTENTS
6.3
Boundary conditions for the wavevectors at the exit surface
161
6.3.1
Condition for the existence of two outgoing waves
161
6.3.2
Wavevectors of the outgoing waves (Laue-Laue
geometry)
163
6.3.3
Laue-Bragg geometry
165
6.4
Rocking curves of the reflected and refracted beams
166
6.4.1
Boundary conditions for the amplitudes at the
exit surface
166
6.4.2
Reflectivity
168
6.4.3
Properties of the rocking curves
169
6.5
Integrated intensity
171
Intensities of plane waves in the reflection geometry
173
7.1
Thick absorbing crystals
173
7.1.1
Reflectivity
173
7.1.2
Shape of the rocking curves
175
7.2
Standing waves
181
7.3
Thin crystals
185
7.3.1
Boundary conditions for the amplitudes
185
7.3.2
Reflectivity
186
Dynamical diffraction in highly asymmetric coplanar and
non-coplanar geometries
189
8.1
Introduction
189
8.2
Diffraction at grazing incidence or grazing emergence
190
8.3
Deviation from Bragg s incidence of the middle of the
reflection domain
192
8.3.
1 Grazing incidence and Bragg geometry
192
8.3.2
Grazing incidence.
Laue
geometry
195
8.3.3
Grazing emergence
196
8.4
Variation of the Darwin width for a grazing incidence
197
8.5
Variation of the width of the diffracted beam for a grazing
emergence
200
8.6
Equation of the dispersion surface
201
8.7
Relation with the traditional dynamical theory
206
8.8
Specularly and Bragg-reflected intensities
207
8.8.1
Boundary conditions for the amplitudes at the
entrance surface
207
8.8.2
Specularly and Bragg-reflected intensities for a
grazing incidence and the Bragg geometry
(semi-infinite crystal)
210
8.8.3
Specularly and Bragg-reflected intensities for a
grazing incidence and the
Laue
geometry
213
8.9
Grazing incidence diffraction (non-coplanar geometry)
213
CONTENTS
xiii
8.9.1
Introduction
213
8.9.2
Three-dimensional representation of the dispersion
surface
216
8.9.3
Tiepoints excited by the incident wave
216
8.9.4
Equation of the dispersion surface
223
8.9.5
Amplitudes of the waves
224
9
«-beam dynamical diffraction
225
9.1
Introduction
225
9.2
The general three-beam case
226
9.2.1
Renninger-scans
226
9.2.2
Fundamental equations of the dynamical theory
227
9.2.3
Solution in the general case
233
9.2.4
Energy flow
235
9.3
The three-beam coplanar case
236
9.4
Determination of phases using/(-beam diffraction
236
9.5
The super-Borrmann effect
242
9.5.1
Experimental evidence
242
9.5.2
Solution of the
11
1
.
Ï
11
case
243
9.5.3
Anomalous absorption coefficient
246
10
Spherical-wave dynamical theory: I. Kato s theory
249
10.1
Extension of the dynamical theory to any kind of incident
wave
249
10.2
Fourier expansion of a spherical wave in plane waves
250
10.2.1
Principle of Kato s spherical-wave theory
250
10.2.2
The incident wave is a scalar wave
250
10.2.3
The incident wave is a vector wave
253
10.3
Direct integration in the transmission geometry
255
10.3.1
The geometrical conditions
255
10.3.2
Stationary phase method
257
10.3.3
Amplitude distribution on the exit surface
—
reflected
wave
257
10.3.4
Amplitude distribution on the exit surface
—
refracted
wave
260
10.4
Intensity distribution on the exit surface
260
10.5
Equal-intensity
(Pendellösung)
fringes
263
10.6
Integration by the stationary phase method
264
10.7
Integrated intensity
268
10.8
Influence of polarization
269
10.9
Bragg geometry
269
10.10
Diffraction of
ultrashort
pulses
274
Appendix: Geometrical interpretation of
η/
j S
(γι,) + η2
in the transmission geometry
274
xiv CONTENTS
11
Spherical-wave dynamical theory: II. Takagi s theory
277
11.1
Introduction
277
11.2
Generalized fundamental equations
279
11.2.1
Modulated waves
279
11.2.2
Takagi s equations
280
11.2.3
Boundary conditions for the amplitudes at the
entrance surface
283
11.3
Reduction of Takagi s equations in the plane-wave case
285
11.4
Absorbing crystals
286
11.5
Analytical resolution of Takagi s equations for perfect
crystals
286
11.6
Analytical solution for a point source using the method
of integral equations
287
11.6.1
Transmission geometry
288
11.6.2
Reflection geometry
290
11.7
Analytical resolution of Takagi s equations using the
Riemann function
291
11.7.1
Hyperbolic nature of Takagi s equations
291
11.7.2
General expression of the reflected and refracted
waves
292
11.7.3
Determination of the Riemann function
293
11.7.4
General solution of Takagi s equations
295
11.8
Analytical solution for an incident spherical wave using the
method of Riemann functions
295
1
1.8.1
The incident wave is a point source located on the
entrance surface
295
11.8.2
The incident wave is a point source located away
from the entrance surface
296
11.8.3
Conservation of energy
298
Appendix: Hyperbolic partial differential equations
299
Characteristics
299
Adjoint differential expression
301
12
Ray tracing in perfect crystals
304
12.1
Ray tracing
304
12.2
The structure of real waves
305
12.3
Wavepackets made of the superposition of separate plane
waves
306
12.4
Wavepackets made of a continuous distribution of
wavevectors
308
1
2.5
Group velocity and Poynting vector
310
12.6
Angular amplification
311
12.7
Intensity distribution along the base of the Borrmann
triangle (transmission geometry)
3
1
7
CONTENTS xv
12.8
Geometrical properties of wavefield trajectories within
the Borrmann triangle
323
12.8.1
Wavefields propagating along the median, AE,
of the Borrmann triangle
323
12.8.2
Properties of the trajectories of the two wavefields
excited by a plane wave
323
12.9
Experimental proof of double refraction
324
12.10
Experimental observation of the separation of the
wavefield paths
326
12.10.1
Experimental setup
326
12.10.2
Focalization of the various wavelengths
328
12.10.3
Separation of wavefield paths in the transmission case
329
12.10.4
Plane-wave
Pendellösung
330
1
2.10.5
Application to the measurement of the index of
refraction
332
12.11
Fresnel diffraction near the Bragg incidence
335
12.
1
2
Ray tracing in finite crystals
339
12.12.1
Introduction
339
12.12.2
Bragg-Laue geometry
—
pseudo-plane waves
341
1
2.12.3
Bragg-Bragg geometry; multiple reflections of
a pseudo-plane wave in thin crystals
343
12.12.4
Laue-Bragg geometry
—
Borrmann-Lehmann fringes
344
12.13
Coherence of extended, non-strictly monochromatic sources
349
III Extension of the dynamical theory to
deformed crystals
353
1
3
Ray tracing in slightly deformed crystals
355
1
3.1
X-ray propagation in deformed materials
355
13.1.1
The different degrees of deformation
355
13.1.2
Principle of ray theories for weak deformations
356
13.2
Effective misorientation
357
13.2.1
Local reciprocal lattice vector
357
13.2.2
Effective misorientation in direct space
359
13.2.3
Effective misorientation in reciprocal space
360
13.2.4
Strain gradient
362
13.3
Polarizability of a deformed crystal
363
13.4
The Eikonal approximation
363
13.4.1
Justification of the concept of local dispersion surface
363
13.4.2
Fermat s principle
365
13.5
Ray trajectories
368
13.5.1
Local dispersion surface
368
13.5.2
Local wavevectors
369
13.5.3
Differential equation of the wavefield trajectories
369
xvi CONTENTS
13.6
The case of a constant strain gradient
375
13.6.1
Equation of the ray trajectory with respect to the
lattice planes
375
13.6.2
Ray trajectories in the transmission geometry
377
13.6.3
Pure bending
379
13.6.4
Temperature gradient
382
13.6.5
Ray trajectories in the reflection geometry
382
13.7
Diffracted intensities
—
plane-wave case
386
13.7.1
Zero absorption
386
13.7.2
Absorbing crystals (transmission geometry)
389
13.7.3
Expression of the diffracted intensities for a constant
strain gradient
389
1
3.7.4
Discussion of the intensity distribution for a constant
strain gradient
391
13.8
Diffracted intensities
—
spherical-wave case
395
13.8.1 Pendellösung in
slightly deformed crystals
395
13.8.2
Phase of the refracted wave in a deformed crystal
397
1
3.8.3
Expression of the phase in terms of the coordinates
in direct space
401
1
3.8.4
Shape of the
Pendellösung
fringes in a deformed
crystal
403
13.9
Lameller
model
405
14
Propagation of X-rays in highly deformed crystals
406
14.1
Introduction
406
14.2
Takagi s equations in a deformed crystal
406
14.3
Resolution of Takagi s equations in the deformed crystal case
409
14.3.1
Small deformations, limit of the validity of the
Eikonal approximation
409
14.3.2
Analytical resolution of Takagi s equations
410
14.3.3
Numerical integration
415
14.3.4
Applications
420
14.4
Ray concept applied to highly distorted crystals
421
14.4.1
Generalization of the notion of wavefields,
interbranch scattering
421
14.4.2
Example: X-ray propagation in a crystal with a
concentration gradient (Keitel
et al. 1
999) 423
14.5
Statistical dynamical theories
426
14.5.1
Introduction
426
14.5.2
Principle of Kato s statistical dynamical theory
428
14.5.3
Experimental tests of the statistical dynamical theory
431
Appendix: Resolution of Takagi s equations in the case of
a constant strain gradient using Laplace transforms
(Katagawa and
Kato
1974) 432
CONTENTS xvii
IV
Applications 435
15
X-ray
optics
437
15.1
X-ray sources
437
15.
I.I X-ray tubes
437
15.1.2
Synchrotron radiation
439
15.2
Flat monochromators
445
15.2.1
Introduction
445
15.2.2
Monochromator crystals
446
15.2.3
Multiple-reflection monochromators
449
15.3
Applications of multiple-crystal arrangements to beam
conditioning
456
15.3.1
Suppression of tails
456
15.3.2
Wavelength scanner
459
15.3.3
Production of beams with a very narrow angular spread
459
15.3.4
Harmonic suppression
461
15.3.5
Production of polarized radiation
467
15.4
Focusing optics
473
15.4.1
Introduction
473
15.4.2
Mirrors
474
15.4.3
Multilayers
476
15.4.4
Curved crystals
477
15.4.5
Fresnel zone plates
478
15.4.6
Bragg-Fresnel lenses
480
15.4.7
Refractive lenses
481
15.4.8
X-ray wave-guides
482
15.5
X-ray interferometers
483
15.5.1
Principle
483
15.5.2
Applications
485
15.6
Imaging with X-rays
489
15.6.1
Introduction
489
15.6.2
Phase contrast imaging
489
16
Location of atoms at surfaces and interfaces using X-ray
standing waves
495
16.1
Principle
495
16.2
Theory
498
16.2.1
Fluorescence yield
498
16.2.2
Influence of thermal vibrations
502
16.3
Bulk crystals
502
16.3.1
Extinction effect
502
16.4
16.3.2
Determination of the polarity of
heteropolar
crystals
Solution to the. surface reeistration problem
503
504
CONTENTS
17
16.5
Thin films and buried interfaces
507
16.5.1
Simple model
507
16.5.2
Calculation of the standing pattern in an overlayer with
the dynamical theory
509
16.6
Standing waves in deformed crystals
510
16.7
Standing waves due to specular reflection
511
X-ray
diffraction topography
513
17.1
Introduction
513
17.2
Single-crystal reflection topography (Berg-Barrett
technique)
514
17.2.1
Principle
514
17.2.2
Image formation
516
17.2.3
Penetration depth
518
17.2.4 Stereographic
views
519
17.2,5
Applications
520
17.3
Single-crystal transmission topography
520
17.3.1
Early history
520
17.3.2
Principle of section topographs
523
17.3.3
Projection topographs
528
17.3.4
Dislocation images
538
17.3.5
Images of planar defects
551
17.3.6
Applications
561
17.4
Double- or multiple-crystal topography
564
17.4.1
Principle of double-crystal topography
564
17.4.2
Plane-wave crystal topography
567
17.4.3
Synchrotron double-crystal topography
568
17.4.4
Mapping of distortions and of lattice parameter
variations
569
17.4.5
Equal-strain or equal-lattice parameter contours
569
17.4.6
Double-crystal setting for high spatial resolution
topography
570
Appendices
Appendix
1
Useful formulae
572
Appendix
2
The early days of dynamical theory
577
References
584
List of symbols
55
j
Index of Names
^55
Index of Subjects
¿,65
|
| any_adam_object | 1 |
| author | Authier, André |
| author_facet | Authier, André |
| author_role | aut |
| author_sort | Authier, André |
| author_variant | a a aa |
| building | Verbundindex |
| bvnumber | BV035455125 |
| classification_rvk | UQ 5100 |
| ctrlnum | (OCoLC)633953425 (DE-599)BVBBV035455125 |
| discipline | Physik |
| edition | Reprinted |
| format | Book |
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| id | DE-604.BV035455125 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:35:39Z |
| institution | BVB |
| isbn | 9780198528920 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017375088 |
| oclc_num | 633953425 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM DE-20 |
| owner_facet | DE-703 DE-19 DE-BY-UBM DE-20 |
| physical | XVIII, 678 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | International Union of Crystallography monographs on crystallography |
| series2 | International Union of Crystallography monographs on crystallography |
| spelling | Authier, André Verfasser aut Dynamical theory of x-ray diffraction André Authier Reprinted Oxford [u.a.] Oxford Univ. Press 2008 XVIII, 678 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier International Union of Crystallography monographs on crystallography 11 Röntgenbeugung (DE-588)4178306-2 gnd rswk-swf Röntgenstreuung (DE-588)4178324-4 gnd rswk-swf Röntgenbeugung (DE-588)4178306-2 s DE-604 Röntgenstreuung (DE-588)4178324-4 s International Union of Crystallography monographs on crystallography 11 (DE-604)BV005455767 11 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017375088&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Authier, André Dynamical theory of x-ray diffraction International Union of Crystallography monographs on crystallography Röntgenbeugung (DE-588)4178306-2 gnd Röntgenstreuung (DE-588)4178324-4 gnd |
| subject_GND | (DE-588)4178306-2 (DE-588)4178324-4 |
| title | Dynamical theory of x-ray diffraction |
| title_auth | Dynamical theory of x-ray diffraction |
| title_exact_search | Dynamical theory of x-ray diffraction |
| title_full | Dynamical theory of x-ray diffraction André Authier |
| title_fullStr | Dynamical theory of x-ray diffraction André Authier |
| title_full_unstemmed | Dynamical theory of x-ray diffraction André Authier |
| title_short | Dynamical theory of x-ray diffraction |
| title_sort | dynamical theory of x ray diffraction |
| topic | Röntgenbeugung (DE-588)4178306-2 gnd Röntgenstreuung (DE-588)4178324-4 gnd |
| topic_facet | Röntgenbeugung Röntgenstreuung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017375088&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005455767 |
| work_keys_str_mv | AT authierandre dynamicaltheoryofxraydiffraction |