## X-Ray Multiple-Wave Diffraction: Theory and ApplicationX-ray multiple-wave diffraction, sometimes called multiple diffraction or N-beam diffraction, results from the scattering of X-rays from periodic two or higher-dimensional structures, like 2-d and 3-d crystals and even quasi crystals. The interaction of the X-rays with the periodic arrangement of atoms usually provides structural information about the scatterer. Unlike the usual Bragg reflection, the so-called two-wave diffraction, the multiply diffracted intensities are sensitive to the phases of the structure factors in volved. This gives X-ray multiple-wave diffraction the chance to solve the X-ray phase problem. On the other hand, the condition for generating an X ray multiple-wave diffraction is much more strict than in two-wave cases. This makes X-ray multiple-wave diffraction a useful technique for precise measure ments of crystal lattice constants and the wavelength of radiation sources. Recent progress in the application of this particular diffraction technique to surfaces, thin films, and less ordered systems has demonstrated the diver sity and practicability of the technique for structural research in condensed matter physics, materials sciences, crystallography, and X-ray optics. The first book on this subject, Multiple Diffraction of X-Rays in Crystals, was published in 1984, and intended to give a contemporary review on the fundamental and application aspects of this diffraction. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Introduction | 1 |

12 Development of Theories for XRay TwoWave Diffraction | 3 |

13 Development of MultipleWave Diffraction | 6 |

Elements of XRay Physics and Crystallography | 13 |

212 Synchrotron Radiation Sources | 15 |

22 Interaction of XRays with Matter | 19 |

23 Reciprocal Lattice Structure Factor and Electron Density Distribution | 25 |

24 Factors Affecting the Diffraction Intensity | 27 |

714 Numerical Computing Procedures | 152 |

72 Approximations | 156 |

722 Born Approximation | 180 |

723 QuantumMechanical Approach | 184 |

724 Quantitative Approach for Phasing An Iterative Approximation | 200 |

725 Approach Using TakagiTaupin Equation | 204 |

726 Expanded DistortedWave Born Approximation | 215 |

727 Resonance Perturbation Bethe Approximation | 219 |

242 LorentzPolarization Factor | 28 |

243 Temperature Factor | 29 |

Diffraction Geometry | 31 |

312 Systematic Coplanar and Coincidental MultipleWave Diffraction | 33 |

32 Grazing Incidence Diffraction Versus WideAngle Incidence Diffraction | 34 |

33 LorentzPolarization Factor in MultipleWave Cases | 36 |

34 MultipleWave Diffraction in MultiCrystal Systems | 39 |

Experimental Techniques | 43 |

411 ReferenceVector Method for Indexing Renninger Scan | 45 |

42 DivergentBeam Method Kossel Diagram | 48 |

421 Indexing Kossel Diagrams | 51 |

43 RotationCrystal Methods ReferenceBeamStereoscopic Imaging | 53 |

431 Indexing Multiple Wave Diffraction Diagram by Crystal Orientation Matrix | 62 |

44 Diffractometer and Detector | 65 |

Kinematical Theory of XRay Diffraction | 71 |

51 PowerTransfer Equation | 72 |

511 TwoWave Laue Diffraction and Bragg Reflection | 74 |

512 Multiple Wave Diffraction | 76 |

52 Approximate Solutions to the PowerTransfer Equation | 77 |

53 HigherOrder Approximation and Iterative Calculation | 80 |

54 Integrated Intensity and XRay Path Length in Crystals | 82 |

55 MultipleWave Diffraction Profile | 85 |

Dynamical Theory of XRay Diffraction | 89 |

61 Fundamental Equation of Wavefield | 90 |

62 Formalism of Photonic Band Theory | 94 |

63 Polarization of Wavefields | 95 |

64 Equation of Dispersion and Excitation of Dispersion Surface | 98 |

65 Energy Flow and Group Velocity | 109 |

66 Mode of WavePropagation | 112 |

661 Wavefields of Modes for Symmetric TwoWave Transmission Diffraction | 113 |

662 Wavefields of Modes for Symmetric ThreeWave Transmission Diffraction | 115 |

663 Wavefields of Modes for Symmetric iVWave Diffraction | 119 |

67 Number of Modes and Number of Permitted Modes | 122 |

68 Absorption | 125 |

69 Boundary Conditions | 127 |

691 Boundary Conditions at an Entrance Surface | 128 |

692 Boundary Conditions at an Exit Surface | 131 |

Scattering Matrix | 135 |

611 Excitation of Mode and Intensity of Wavefield | 137 |

612 SphericalWave Nature of XRays | 139 |

613 Dynamical Diffraction in Distorted Crystals | 141 |

Theoretical Approaches | 143 |

71 Numerical Calculation Procedures | 144 |

712 Linear Approximation | 145 |

713 Cartesian Coordinates Representation of Eigenvalue and Eigenvector | 146 |

Dynamical Diffraction Properties and Behaviors | 223 |

812 Extremely Asymmetric TwoWave Diffraction | 230 |

813 Grazing Incidence TwoWave Diffraction | 238 |

814 TwoWave Back Diffraction | 244 |

82 ThreeWave Diffraction | 246 |

821 ThreeWave LaueLaue Diffraction | 247 |

822 ThreeWave BraggLaue Diffraction | 253 |

823 ThreeWave BraggBragg Diffraction | 258 |

824 ThreeWave BraggSurface Diffraction | 259 |

825 ThreeWave Grazing Incidence Diffraction | 262 |

826 ThreeWave Coplanar Diffraction | 271 |

83 Polarization Aspects of Three Wave Diffraction | 280 |

831 Indirect Excitation of Three wave Diffraction with a PolarizationForbidden Reflection | 282 |

832 Polarization Suppression of Multiple Wave Interaction | 284 |

833 PolarizationResolved MultipleWave Diffraction | 286 |

84 HighOrder MultipleWave Diffraction | 289 |

842 Coincidental TwentySixWave Diffraction | 291 |

843 MultipleWave Back Diffraction | 294 |

9 Applications | 299 |

911 Qualitative and Quantitative Determination of Phase | 300 |

912 Determination of Absolute Configuration of Crystals | 317 |

913 Phase Determination for ChargeDensityWave Reflections | 318 |

914 Phase Determination for Diffraction in QuasiCrystals | 321 |

915 Determination of Phase Shift due to Resonance | 322 |

916 Phase Determination of Surface InPlane Reflection | 326 |

917 Phase Determination for Diffraction in Thin Films and Substrates and Reconstructed Surfaces | 329 |

92 Phasing Macromolecular Structures and Structure Determination with Triplet Phases | 333 |

922 Structure Determination with Triplet Phases | 334 |

93 Determination of Crystal Lattice Constants and Perfection | 339 |

932 Strain Measurements of Epitaxy Layer on Crystal Substrate | 341 |

933 Characterization of Crystal Perfection of Semiconductor Surfaces | 348 |

94 MultipleWave Diffraction Excited Fluorescence | 353 |

MDAFS | 359 |

95 Studies of Phase TransitionTransformation | 364 |

96 MultipleWave XRay Optics | 368 |

961 MultipleWave XRay Monochromators | 369 |

962 MultiWave Phase Plate and XRay Polarimeter | 378 |

97 Other Applications | 382 |

972 MultipleWave XRay Topography | 383 |

98 Prospects of Future Development | 384 |

References | 387 |

409 | |

413 | |

### Other editions - View all

### Common terms and phrases

7r-polarized Acta Cryst angular asymmetry beam divergence boundary conditions Bragg angle Bragg reflection Bragg's law components crystal surface defined detector diffracted intensity diffracted waves diffraction position diffraction profiles dispersion sheets dispersion surface eigenvalue electron Ewald sphere experimental fluorescence four-wave fundamental equation G reflection geometry given GIXD grazing incidence Green function incident beam incident wave intensity distribution intensity profiles interaction involved Kossel lattice constants Laue diffraction Lett linear absorption coefficient Lorentz factor matrix monochromator multiple-wave diffraction normal permitted modes perpendicular phase determination photon photon energy Phys plane of incidence polarization factors Poynting vector primary reflection reciprocal lattice points reciprocal lattice vector reflected wave reflection G Renninger scan resonance respectively rotation scattering secondary reflection shown in Fig Stetsko surface normal symmetric three-wave diffraction tion transmission triplet phase two-wave diffraction unit vectors wavefield amplitudes wavelength wavevectors X-ray diffraction

### Popular passages

Page 409 - S.-L. Chang, C.-H. Chao, Y.-S. Huang, Y.-C. Jean, H.-S. Sheu, F.-J. Liang, H.-C. Chien, C.-K. Chen,