Subperiodic groups, line groups and their applications

Understanding the symmetries described by subperiodic groups – frieze, rod and layer groups – has been instrumental in predicting various properties (band structures, optical absorption, Raman spectra, diffraction patterns, topological properties etc.) of `low‐dimensional' crystals. This knowle...

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Bibliographic Details
Published in:Journal of applied crystallography 2024-06, Vol.57 (3), p.623-629
Main Authors: de la Flor, Gemma, Milošević, Ivanka
Format: Article
Language:English
Subjects:
Crystallography
Crystals
Diffraction patterns
Group theory
layer groups
line groups
Materials engineering
nanostructures
Optical properties
Raman spectra
Raman spectroscopy
rod groups
Symmetry
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Summary:Understanding the symmetries described by subperiodic groups – frieze, rod and layer groups – has been instrumental in predicting various properties (band structures, optical absorption, Raman spectra, diffraction patterns, topological properties etc.) of `low‐dimensional' crystals. This knowledge is crucial in the tailored design of materials for specific applications across electronics, photonics and materials engineering. However, there are materials that have the property of being periodic only in one direction and whose symmetry cannot be described by the subperiodic rod groups. Describing the symmetry of these materials necessitates the application of line group theory. This paper gives an overview of subperiodic groups while briefly introducing line groups in order to acquaint the crystallographic community with these symmetries and direct them to pertinent literature. Since line groups are generally not subperiodic, they have thus far remained outside the realm of symmetries traditionally considered in crystallography, although there are numerous `one‐dimensional' crystals (i.e. monoperiodic structures) possessing line group symmetry. Since they do not belong to the class of subperiodic groups, line groups thus far have been beyond the scope of symmetries traditionally studied in crystallography, although they describe the symmetry of numerous `one‐dimensional' crystals (i.e. monoperiodic structures). Therefore, together with an overview of frieze, rod and layer groups, a brief introduction to line groups is presented.
ISSN:1600-5767
0021-8898
1600-5767
DOI:10.1107/S1600576724003418