Chapter 1.2 The structure factor

Reciprocal space

First Online Edition (2006)

Part 1. General relationships and techniques

  1. P. Coppens

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000550

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Coppens, P. 2006. The structure factor. International Tables for Crystallography. B:1:1.2:10–24.

Author Information

  1. Department of Chemistry, Natural Sciences & Mathematics Complex, State University of New York at Buffalo, Buffalo, New York 14260-3000, USA

Publication History

  1. Published Online: 1 JAN 2006


This chapter summarizes the mathematical development of the structure-factor formalism. It starts with the definition of the structure factor appropriate for X-ray and neutron scattering, and includes the derivation of the appropriate expressions. Beyond the isolated-atom case, the atom-centred spherical harmonic (multipole) model is treated in detail. Expressions for thermal motion in the harmonic approximation and for treatments including anharmonicity are given and their relative merits are discussed.


  • structure factors;
  • X-ray scattering;
  • magnetic scattering;
  • spherical harmonic expansion;
  • orbital products;
  • temperature factors;
  • rigid-body motion;
  • cumulant expansion;
  • Gram–Charlier series;
  • one-particle potential model