Standard Article

Kinematic Diffraction of X-Rays

Computation and Theoretical Methods

  1. Haydn Chen

Published Online: 18 MAY 2012

DOI: 10.1002/0471266965.com018.pub2

Characterization of Materials

Characterization of Materials

How to Cite

Chen, H. 2012. Kinematic Diffraction of X-Rays. Characterization of Materials. 1–21.

Author Information

  1. University of Illinois at Urbana-Champaign Urbana, Illinois, USA

Publication History

  1. Published Online: 18 MAY 2012

Abstract

Diffraction by x-rays, electrons, or neutrons has enjoyed great success in crystal structure determination. For a perfectly ordered crystal, diffraction results in arrays of sharp Bragg reflection spots periodically arranged in reciprocal space. Analysis of the Bragg peak locations and their intensities leads to the identification of crystal lattice type, symmetry group, unit cell dimensions, and atomic configuration within a unit cell. On the other hand, for crystals containing lattice defects such as dislocations, precipitates, local ordered domains, surface, and interfaces, diffuse intensities are produced in addition to Bragg peaks. The distribution and magnitude of diffuse intensities are dependent on the type of imperfection present and the x-ray energy used in a diffraction experiment.

Diffuse scattering is usually weak, and thus more difficult to measure, but it is rich in structure information that often cannot be obtained by other experimental means. Since real crystals are generally far from perfect, many properties exhibited by them are therefore determined by the lattice imperfections present. Consequently, understanding of the atomic structures of these lattice imperfections and of the roles these imperfections play is of paramount importance if these materials properties are to be exploited for optimal use.

This article addresses the fundamental principles of diffraction based upon the kinematic diffraction theory for x-rays. Nevertheless, the diffraction principles described here may be extended to kinematic diffraction events involving thermal neutrons or electrons. In practice, most x-ray diffraction experiments are carried out on crystals containing a sufficiently large number of defects that kinematic theory is generally applicable.

This article is divided into two major sections. In the first section, the fundamental principles of kinematic diffraction of x-rays are discussed and a systematic treatment of theory is given. In the second section, the practical aspects of the method are discussed; specific expressions for kinematically diffracted x-ray intensities are described and used to interpret diffraction behavior from real crystals containing lattice defects. Neither specific diffraction techniques and analysis nor sample preparation methods are described in this article.

Keywords:

  • scattering processes;
  • kinematic diffraction;
  • Bragg reflection;
  • diffraction;
  • x-rays;
  • thermal diffuse scattering;
  • small-angle scattering;
  • structure factor;
  • Guinier approximation;
  • Porod approximation