Dynamical theory of x-ray diffraction / André Authier.

Format:

Book

Author/Creator:

Authier, André.

Series:

International Union of Crystallography monographs on crystallography ; 11.

International Union of Crystallography monographs on crystallography ; 11

Language:

English

Subjects (All):

X-ray crystallography.

Physical Description:

xviii, 661 pages : illustrations ; 24 cm.

Place of Publication:

Oxford ; New York : Oxford University Press, 2001.

Summary:

This is the first comprehensive book on the dynamical diffraction of x-rays since the development of synchrotron radiation. There is an introduction to the subject presenting early developments and the basic results, followed by a detailed development of the diffraction and propagation properties of x-rays in perfect crystals and by an extension of the theory to the case of slightly and highly deformed crystals. The last section gives three applications of the theory: x-ray optics for synchrotron radiation, locations of atoms at surfaces, and x-ray diffraction topography. The book is well illustrated and contains a wide range of references to the literature.

Contents:

I Background and basic results 1

1 Historical developments 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

1.11 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

2.3 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

2.8 Ewald's dispersion theory 43

2.9 Propagation equation of an electromagnetic wave in materials in Laue's dynamical theory 49

2.10 Specular reflection

Fresnel relations 50

3 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

4 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

4.8 The diffracted waves in the transmission geometry 88

4.9 The diffracted waves in the reflection geometry 99

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

II Advanced dynamical theory 113

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

5.6 The deviation parameter in absorbing crystals 136

5.7 Amplitude ratio of the refracted and reflected waves 136

5.8 Anomalous absorption 139

5.9 Dispersion surface when the Bragg angle is close to [pi]/2 148

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

6.3 Boundary conditions for the wavevectors at the exit surface 161

6.4 Rocking curves of the reflected and refracted beams 166

6.5 Integrated intensity 170

7 Intensities of plane waves in the reflection geometry 173

7.1 Thick absorbing crystals 173

7.2 Standing waves 181

7.3 Thin crystals 185

8 Dynamical diffraction in highly asymmetric coplanar and non-coplanar geometries 189

8.2 Diffraction at grazing incidence or grazing emergence 189

8.3 Deviation from Bragg's incidence of the middle of the reflection domain 192

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

8.9 Grazing incidence diffraction (non-coplanar geometry) 213

9 n-beam dynamical diffraction 225

9.2 The general three-beam case 226

9.3 The three-beam coplanar case 236

9.4 Determination of phases using n-beam diffraction 236

9.5 The super-Borrmann effect 242

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

10.3 Direct integration in the transmission geometry 255

10.4 Intensity distribution on the exit surface 260

10.5 Equal-intensity (Pendellosung) 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

Appendix Geometrical interpretation of [eta] / [square root]S([gamma]h) + [eta superscript 2] in the transmission geometry 274

11 Spherical-wave dynamical theory: II. Takagi's theory 277

11.2 Generalized fundamental equations 279

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

11.7 Analytical resolution of Takagi's equations using the Riemann function 291

11.8 Analytical solution for an incident spherical wave using the method of Riemann functions 295

Appendix Hyperbolic partial differential equations 299

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

12.5 Group velocity and Poynting vector 310

12.6 Angular amplification 311

12.7 Intensity distribution along the base of the Borrmann triangle (transmission geometry) 317

12.8 Geometrical properties of wavefield trajectories within the Borrmann triangle 323

12.9 Experimental proof of double refraction 324

12.10 Experimental observation of the separation of the wavefield paths 326

12.11 Fresnel diffraction near the Bragg incidence 335

12.12 Ray tracing in finite crystals 339

12.13 Coherence of extended, non-strictly monochromatic sources 349

III Extension of the dynamical theory to deformed crystals 353

13 Ray tracing in slightly deformed crystals 355

13.1 X-ray propagation in deformed materials 355

13.2 Effective misorientation 357

13.3 Polarizability of a deformed crystal 363

13.4 The Eikonal approximation 363

13.5 Ray trajectories 368

13.6 The case of a constant strain gradient 375

13.7 Diffracted intensities

plane-wave case 386

13.8 Diffracted intensities

spherical-wave case 395

14 Propagation of X-rays in highly deformed crystals 406

14.2 Takagi's equations in a deformed crystal 406

14.3 Resolution of Takagi's equations in the deformed crystal case 409

14.4 Ray concept applied to highly distorted crystals 421

14.5 Statistical dynamical theories 426

Appendix Resolution of Takagi's equations in the case of a constant strain gradient using Laplace transforms (Katagawa and Kato 1974) 432

IV Applications 435

15 X-ray optics 437

15.1 X-ray sources 437

15.2 Flat monochromators 445

15.3 Applications of multiple-crystal arrangements to beam conditioning 456

15.4 Focusing optics 473

15.5 X-ray interferometers 483

15.6 Imaging with X-rays 489

16 Location of atoms at surfaces and interfaces using X-ray standing waves 495

16.2 Theory 498

16.3 Bulk crystals 502

16.4 Solution to the surface registration problem 504

16.5 Thin films and buried interfaces 507

16.6 Standing waves in deformed crystals 510

16.7 Standing waves due to specular reflection 511

17 X-ray diffraction topography 513

17.2 Single-crystal reflection topography (Berg-Barrett technique) 514

17.3 Single-crystal transmission topography 520

17.4 Double- or multiple-crystal topography 564

Appendix 2 The early days of dynamical theory 576.

Notes:

Includes bibliographical references (pages [583]-636) and indexes.

ISBN:

0198559607

OCLC:

45799622