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Local growth of icosahedral quasicrystalline tilings

Author(s): Hann, Connor T.; Socolar, Joshua E.S.; Steinhardt, Paul J.

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Abstract: Icosahedral quasicrystals (IQCs) with extremely high degrees of translational order have been produced in the laboratory and found in naturally occurring minerals, yet questions remain about how IQCs form. In particular, the fundamental question of how locally determined additions to a growing cluster can lead to the intricate long-range correlations in IQCs remains open. In answer to this question, we have developed an algorithm that is capable of producing a perfectly ordered IQC yet relies exclusively on local rules for sequential, face-to-face addition of tiles to a cluster. When the algorithm is seeded with a special type of cluster containing a defect, we find that growth is forced to infinity with high probability and that the resultant IQC has a vanishing density of defects. The geometric features underlying this algorithm can inform analyses of experimental systems and numerical models that generate highly ordered quasicrystals.
Electronic Publication Date: 14-Jul-2016
Citation: Hann, Connor T, Socolar, Joshua ES, Steinhardt, Paul J. (2016). Local growth of icosahedral quasicrystalline tilings. PHYSICAL REVIEW B, 94. doi:10.1103/PhysRevB.94.014113
DOI: doi:10.1103/PhysRevB.94.014113
ISSN: 2469-9950
EISSN: 2469-9969
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW B
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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