Highly symmetric aperiodic structures -INVITED

The symmetries of periodic structures are severely constrained by the crystallographic restriction. In particular, in two and three spatial dimensions, only rotational axes of order 1, 2, 3, 4 or 6 are possible. Aperiodic tilings can provide perfectly ordered structures with arbitrary symmetry prope...

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Bibliographic Details
Published in:EPJ Web of conferences 2021, Vol.255, p.9001
Main Author: Grimm, Uwe
Format: Article
Language:English
Subjects:
Axes of rotation
Crystallography
Homogeneous structure
Periodic structures
Symmetry
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Summary:The symmetries of periodic structures are severely constrained by the crystallographic restriction. In particular, in two and three spatial dimensions, only rotational axes of order 1, 2, 3, 4 or 6 are possible. Aperiodic tilings can provide perfectly ordered structures with arbitrary symmetry properties. Random tilings can retain part of the aperiodic order as well the rotational symmetry. They offer a more flexible approach to obtain homogeneous structures with high rotational symmetry, and might be of particular interest for applications. Some key examples and their diffraction are discussed.
ISSN:2100-014X
2101-6275
2100-014X
DOI:10.1051/epjconf/202125509001