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

Chapter 5.1. Dynamical theory of X-ray diffraction

Contents

  • 5.1. Dynamical theory of X-ray diffraction  (pp. 626-646) | html | pdf | chapter contents |
    • 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 K α 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 K α radiation, t = 1 mm (μ t = 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 |