Chapter 5.1 Dynamical theory of X‐ray diffraction

Reciprocal space

Second Online Edition (2010)

Part 5. Dynamical theory and its applications

  1. A. Authier

Published Online: 1 JUN 2010

DOI: 10.1107/97809553602060000779

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Authier, A. 2010. Dynamical theory of X‐ray diffraction. International Tables for Crystallography. B:5:5.1:626–646.

Author Information

  1. Institut de Minéralogie et de la Physique des Milieux Condensés, Bâtiment 7, 140 rue de Lourmel, 75015 Paris, France

Publication History

  1. Published Online: 1 JUN 2010



This chapter presents the dynamical theory of the diffraction of X‐rays by perfect crystals. The most important part is devoted to the case of plane waves (Section 5.1.2). The solutions of the propagation equation of plane waves in crystals are given in Section 5.1.3 using the concept of wavefields introduced by Ewald for X‐rays in 1913 and by Bloch for electrons in 1928 (known in solid‐state physics as Bloch waves). They are applied to the interpretation of the main properties of dynamical diffraction: anomalous transmission, standing waves and Pendellösung. The expressions for the diffracted intensity are given in both the transmission (Section 5.1.6) and the reflection (Section 5.1.7) cases. The last part (Section 5.1.8) concerns the diffraction of real and spherical waves, which is described in a qualitative way.


  • dynamical theory;
  • X‐ray scattering;
  • propagation equation;
  • wavefields;
  • wavevectors;
  • boundary conditions;
  • dispersion surfaces;
  • Bragg’s law;
  • transmission geometry;
  • reflection geometry;
  • Laue case;
  • extinction;
  • Pendellösung;
  • dielectric susceptibility;
  • standing waves;
  • anomalous absorption;
  • absorption coefficients;
  • total reflection;
  • Borrmann triangle;
  • Maxwell’s equations;
  • Poynting vector