Chapter 4.6 Reciprocal‐space images of aperiodic crystals

Reciprocal space

Second Online Edition (2010)

Part 4. Diffuse scattering and related topics

  1. W. Steurer,
  2. T. Haibach

Published Online: 1 JUN 2010

DOI: 10.1107/97809553602060000778

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Steurer, W. and Haibach, T. 2010. Reciprocal‐space images of aperiodic crystals. International Tables for Crystallography. B:4:4.6:590–624.

Author Information

  1. Laboratory of Crystallography, Department of Materials, ETH Hönggerberg, HCI G 511, Wolfgang‐Pauli‐Strasse 10, CH‐8093 Zurich, Switzerland

Publication History

  1. Published Online: 1 JUN 2010



This chapter presents an aid to the characterization of aperiodic crystals based on information from diffraction experiments and gives a survey of aperiodic crystals from the viewpoint of the experimentally accessible reciprocal space. Characteristic features of the diffraction patterns of the different types of aperiodic crystals are shown. A standard way of determining the metrics and finding the optimum nD embedding is described. Structure‐factor formulae for general and special cases are given.


  • reciprocal space;
  • aperiodic crystals;
  • icosahedral phases;
  • composite structures;
  • incommensurately modulated structures;
  • crystalline approximants;
  • hyperatoms;
  • satellite reflections;
  • main reflections;
  • Fibonacci sequence;
  • Fibonacci chains;
  • fractal atomic surfaces;
  • decagonal phases;
  • Penrose tiling