The Curled Up Dimension in Quasicrystals

Article


Fang, Fang, Clawson, Richard and Irwin, Klee. 2021. "The Curled Up Dimension in Quasicrystals." Crystals. 11 (10), pp. 1-9. https://doi.org/10.3390/cryst11101238
Article Title

The Curled Up Dimension in Quasicrystals

ERA Journal ID210328
Article CategoryArticle
AuthorsFang, Fang (Author), Clawson, Richard (Author) and Irwin, Klee (Author)
Journal TitleCrystals
Journal Citation11 (10), pp. 1-9
Article Number1238
Number of Pages9
Year2021
Place of PublicationSwitzerland
ISSN2073-4352
Digital Object Identifier (DOI)https://doi.org/10.3390/cryst11101238
Web Address (URL)https://www.mdpi.com/2073-4352/11/10/1238
Abstract

Most quasicrystals can be generated by the cut-and-project method from higher dimensional parent lattices. In doing so they lose the periodic order their parent lattice possess, replaced with aperiodic order, due to the irrationality of the projection. However, perfect periodic order is discovered in the perpendicular space when gluing the cut window boundaries together to form a curved loop. In the case of a 1D quasicrystal projected from a 2D lattice, the irrationally sloped cut region is bounded by two parallel lines. When it is extrinsically curved into a cylinder, a line defect is found on the cylinder. Resolving this geometrical frustration removes the line defect to preserve helical paths on the cylinder. The degree of frustration is determined by the thickness of the cut window or the selected pitch of the helical paths. The frustration can be resolved by applying a shear strain to the cut-region before curving into a cylinder. This demonstrates that resolving the geometrical frustration of a topological change to a cut window can lead to preserved periodic order.

Keywordsquasicrystals; aperiodic order; periodic order; perpendicular space; geometric frustration; curled-up
ANZSRC Field of Research 2020401699. Materials engineering not elsewhere classified
Byline AffiliationsQuantum Gravity Research, United States
University of Southern Queensland
Institution of OriginUniversity of Southern Queensland
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