Dear Colleagues,

There are solids that, like crystals, give X-ray patterns with essentially sharp diffraction peaks, but do not fall within the well-known definition of a crystal as a solid with a three-dimensional periodicity of structure. These solids, called aperiodic crystals, form two large families, namely, modulated crystals and quasicrystals. The atoms of a modulated crystal are displaced from the sites of a three-dimensional lattice according to a periodic law. In other words, the atoms lie on the modulation wave. If the wave period is incommensurate with at least one of the three lattice periods, the structure loses three-dimensional periodicity. The diffraction patterns of modulated crystals contain additional satellite reflections at the interstices of the reciprocal lattice. A special part of this family consists of composites whose atoms form at least two lattices with mutually incommensurate periods. Traditional methods of structural analysis, entirely based on the concepts of atoms at the sites of the crystal lattice and translational symmetry, which is obligatory for any crystal, do not work for incommensurately modulated crystals. The X-ray diffraction patterns of quasicrystals contain elements of non-crystallographic point symmetry, such as axes of the fifth or tenth order. Consequently, their structures, in principle, cannot be described in terms of a crystal lattice consisting of identical unit cells. The structural analysis of aperiodic crystals forms a separate area of research with its own theoretical and computational base, its own experimental features, methods of searching and refining the structural model. The structures of modulated crystals and quasicrystals are effectively explored in spaces of more than three dimensions. Geometric and group-theoretic approaches to the description of the structure of quasicrystals are being developed.

All researchers whose studies cover any aspects of the structural analysis of crystals with a modulated structure, incommensurate composites, quasicrystals, united by the common name "aperiodic crystals", are invited to participate in the Special Issue "Aperiodic Crystals: Theory, Structure and Properties". Theoretical and methodological works, as well as new results of the analysis of aperiodic structures, can be submitted for consideration.

Dr. Nadezhda B. Bolotina
Guest Editor

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• structure analysis
• aperiodic crystals
• modulated crystals
• incommensurate composites
• quasicrystals
• theory
• methods
• data collection
• structure solution
• structure refinement