Dynamical theory of X-ray diffraction

Authier, A.

doi:10.1107/97809553602060000779

International Tables for Crystallography (2010). Vol. B. ch. 5.1, pp. 626-646 | 1 | 2 |
https://doi.org/10.1107/97809553602060000779

Chapter 5.1. Dynamical theory of X-ray diffraction

5.1. Dynamical theory of X-ray diffraction (pp. 626-646) | html | pdf | chapter contents |
A. Authier
- 5.1.1. Introduction (p. 626) | html | pdf |
- 5.1.2. Fundamentals of plane-wave dynamical theory (pp. 626-630) | html | pdf |
  - 5.1.2.1. Propagation equation (pp. 626-628) | html | pdf |
  - 5.1.2.2. Wavefields (p. 628) | html | pdf |
  - 5.1.2.3. Boundary conditions at the entrance surface (p. 628) | html | pdf |
  - 5.1.2.4. Fundamental equations of dynamical theory (pp. 628-629) | html | pdf |
  - 5.1.2.5. Dispersion surface (pp. 629-630) | html | pdf |
  - 5.1.2.6. Propagation direction (p. 630) | html | pdf |
- 5.1.3. Solutions of plane-wave dynamical theory (pp. 630-633) | html | pdf |
  - 5.1.3.1. Departure from Bragg's law of the incident wave (p. 630) | html | pdf |
  - 5.1.3.2. Transmission and reflection geometries (p. 631) | html | pdf |
  - 5.1.3.3. Middle of the reflection domain (p. 631) | html | pdf |
  - 5.1.3.4. Deviation parameter (pp. 631-632) | html | pdf |
  - 5.1.3.5. Pendellösung and extinction distances (pp. 632-633) | html | pdf |
  - 5.1.3.6. Solution of the dynamical theory (p. 633) | html | pdf |
  - 5.1.3.7. Geometrical interpretation of the solution in the zero-absorption case (p. 633) | html | pdf |
    - 5.1.3.7.1. Transmission geometry (p. 633) | html | pdf |
    - 5.1.3.7.2. Reflection geometry (p. 633) | html | pdf |
- 5.1.4. Standing waves (p. 633) | html | pdf |
- 5.1.5. Anomalous absorption (pp. 633-634) | html | pdf |
- 5.1.6. Intensities of plane waves in transmission geometry (pp. 634-638) | html | pdf |
  - 5.1.6.1. Absorption coefficient (p. 634) | html | pdf |
  - 5.1.6.2. Boundary conditions for the amplitudes at the entrance surface – intensities of the reflected and refracted waves (pp. 634-635) | html | pdf |
  - 5.1.6.3. Boundary conditions at the exit surface (p. 635) | html | pdf |
    - 5.1.6.3.1. Wavevectors (p. 635) | html | pdf |
    - 5.1.6.3.2. Amplitudes – Pendellösung (p. 635) | html | pdf |
  - 5.1.6.4. Reflecting power (pp. 635-636) | html | pdf |
  - 5.1.6.5. Integrated intensity (p. 637) | html | pdf |
    - 5.1.6.5.1. Non-absorbing crystals (p. 637) | html | pdf |
    - 5.1.6.5.2. Absorbing crystals (p. 637) | html | pdf |
  - 5.1.6.6. Thin crystals – comparison with geometrical theory (pp. 637-638) | html | pdf |
- 5.1.7. Intensity of plane waves in reflection geometry (pp. 638-640) | html | pdf |
  - 5.1.7.1. Thick crystals (pp. 638-639) | html | pdf |
    - 5.1.7.1.1. Non-absorbing crystals (p. 638) | html | pdf |
    - 5.1.7.1.2. Absorbing crystals (pp. 638-639) | html | pdf |
  - 5.1.7.2. Thin crystals (pp. 639-640) | html | pdf |
    - 5.1.7.2.1. Non-absorbing crystals (pp. 639-640) | html | pdf |
    - 5.1.7.2.2. Absorbing crystals (p. 640) | html | pdf |
- 5.1.8. Real waves (pp. 640-642) | html | pdf |
  - 5.1.8.1. Introduction (pp. 640-641) | html | pdf |
  - 5.1.8.2. Borrmann triangle (p. 641) | html | pdf |
  - 5.1.8.3. Spherical-wave Pendellösung (pp. 641-642) | html | pdf |
- Appendix 5.1.1. Basic equations (pp. 642-644) | html | pdf |
  - A5.1.1.1. Dielectric susceptibility – classical derivation (pp. 642-643) | html | pdf |
  - A5.1.1.2. Maxwell's equations (p. 643) | html | pdf |
  - A5.1.1.3. Propagation equation (pp. 643-644) | html | pdf |
  - A5.1.1.4. Poynting vector (p. 644) | html | pdf |
- References | html | pdf |
- Figures
  - Fig. 5.1.2.1. Bragg reflection (p. 627) | html | pdf |
  - Fig. 5.1.2.2. Boundary condition for wavevectors at the entrance surface of the crystal (p. 628) | html | pdf |
  - Fig. 5.1.2.3. Intersection of the dispersion surface with the plane of incidence (p. 629) | html | pdf |
  - Fig. 5.1.2.4. Intersection of the dispersion surface with the plane of incidence shown in greater detail (p. 629) | html | pdf |
  - Fig. 5.1.2.5. Dispersion surface for the two states of polarization (p. 630) | html | pdf |
  - Fig. 5.1.3.1. Departure from Bragg's law of an incident wave (p. 630) | html | pdf |
  - Fig. 5.1.3.2. Transmission, or Laue, geometry (p. 631) | html | pdf |
  - Fig. 5.1.3.3. Reflection, or Bragg, geometry (p. 631) | html | pdf |
  - Fig. 5.1.3.4. Boundary conditions at the entrance surface for transmission geometry (p. 632) | html | pdf |
  - Fig. 5.1.3.5. Boundary conditions at the entrance surface for reflection geometry (p. 632) | html | pdf |
  - Fig. 5.1.6.1. Variation of the effective absorption with the deviation parameter in the transmission case for the 400 reflection of GaAs using Cu Kα radiation (p. 634) | html | pdf |
  - Fig. 5.1.6.2. Variation of the intensities of the reflected and refracted waves in an absorbing crystal for the 220 reflection of Si using Mo Kα radiation, t = 1 mm (μt = 1.42) (p. 635) | html | pdf |
  - Fig. 5.1.6.3. Boundary condition for the wavevectors at the exit surface (p. 636) | html | pdf |
  - Fig. 5.1.6.4. Decomposition of a wavefield into its two components when it reaches the exit surface (p. 636) | html | pdf |
  - Fig. 5.1.6.5. Cross sections of the incident, $[{\bf K}_{{\bf o}}^{(a)}]$ , refracted, $[{\bf K}_{{\bf o}}]$ , and reflected, $[{\bf K}_{{\bf h}}]$ , waves (p. 636) | html | pdf |
  - Fig. 5.1.6.6. Theoretical rocking curves in the transmission case for non-absorbing crystals and for various values of $[t/\Lambda_{\rm L}]$ (p. 637) | html | pdf |
  - Fig. 5.1.6.7. Variations with crystal thickness of the integrated intensity in the transmission case (no absorption) (arbitrary units) (p. 637) | html | pdf |
  - Fig. 5.1.7.1. Theoretical rocking curve in the reflection case for a non-absorbing thick crystal in terms of the deviation parameter (p. 638) | html | pdf |
  - Fig. 5.1.7.2. Theoretical rocking curve in the reflection case for a thick absorbing crystal (p. 639) | html | pdf |
  - Fig. 5.1.7.3. Bragg case: thick crystals (p. 639) | html | pdf |
  - Fig. 5.1.7.4. Bragg case: thin crystals (p. 639) | html | pdf |
  - Fig. 5.1.8.1. Borrmann triangle (p. 641) | html | pdf |
  - Fig. 5.1.8.2. Packet of wavefields of divergence Δα excited in the crystal by an incident wavepacket of angular width $[\delta (\Delta \theta)]$ (p. 641) | html | pdf |
  - Fig. 5.1.8.3. Intensity distribution along the base of the Borrmann triangle (p. 642) | html | pdf |
  - Fig. 5.1.8.4. Interference at the origin of the Pendellösung fringes in the case of an incident spherical wave (p. 642) | html | pdf |
  - Fig. 5.1.8.5. Spherical-wave Pendellösung fringes observed on a wedge-shaped crystal (p. 643) | html | pdf |

Chapter 5.1. Dynamical theory of X-ray diffraction

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