Chapter 3.4 Classification and use of modulated and composite structures data

Definition and exchange of crystallographic data

First Online Edition (2006)

Part 3. CIF data definition and classification

  1. G. Madariaga

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000736

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Madariaga, G. 2006. Classification and use of modulated and composite structures data. International Tables for Crystallography. G:3:3.4:131–140.

Author Information

  1. Departamento de Física de la Materia Condensada, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain

Publication History

  1. Published Online: 1 JAN 2006


The core CIF dictionary has been extended to provide a formalism for the description in software of certain types of aperiodic crystal structures. Aperiodic structures do not have lattice periodicity, but show long-range order; their diffraction patterns exhibit sharp Bragg peaks that have to be indexed using more than three Miller indices; and they can be classified in one of the three groups: incommensurately modulated structures, incommensurate composite structures or quasicrystals. Modulated structures are described by periodic distortions of an underlying (reference) crystal structure. Composite structures can be thought of as being built of two or more periodic subsystems whose lattices are mutually incommensurate. Both may be described using a CIF dictionary of terms (msCIF) that express the modulation or superposition of structural models according to the standard established by the IUCr Commission on Aperiodic Crystals. Quasicrystals not only lack three-dimensional lattice periodicity but also show noncrystallographic symmetry. Theoretical descriptions of quasicrystal structures are still relatively poorly developed, and are not described by the terms in the msCIF dictionary.


  • aperiodic structures;
  • cell subsystems;
  • displacive modulations;
  • occupational modulations;
  • atom properties;
  • chemistry;
  • satellite reflections;
  • superspace;
  • data collection;
  • modulated structures Crystallographic Information File;
  • experimental measurements;
  • incommensurate structures;
  • metadata;
  • msCIF dictionary;
  • refinement;
  • special modulation functions;
  • structural models;
  • structure analysis;
  • symmetry