Please use this identifier to cite or link to this item: https://physrep.ff.bg.ac.rs/handle/123456789/1407
Title: Subperiodic groups, line groups and their applications
Authors: Gemma de la Flor
Ivanka Milošević
Editors: S. Moggach
Keywords: layer groups; rod groups; line groups; symmetry; nanostructures
Issue Date: 31-May-2024
Publisher: International Union of Crystallography (co-published with Wiley)
Project: 451 03-66/2024-03/200162 - RS Ministry of Science
DEAL
Related Publication(s): This article is part of a collection of articles from the IUCr 2023 Congress in Melbourne, Australia, and commemorates the 75th anniversary of the IUCr.
Journal: Journal of Applied Crystallography
Conference: IUCr 2023 Congress in Melbourne, Australia
Abstract: 
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 crystal
lography, although there are numerous ‘one-dimensional’ crystals (i.e. mono
periodic structures) possessing line group symmetry.
URI: https://physrep.ff.bg.ac.rs/handle/123456789/1407
DOI: https://doi.org/10.1107/S1600576724003418
Appears in Collections:Journal Article

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