International Tables for Crystallography

Classification and use of modulated and composite structures data
G. Madariaga. International Tables for Crystallography (2006). Vol. G, ch. 3.4, pp. 131-140  [ doi:10.1107/97809553602060000736 ]


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.

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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The series consists of eight volumes and comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.