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Local growth of icosahedral quasicrystalline tilings

Publication ,  Journal Article
Hann, CT; Socolar, JES; Steinhardt, PJ
Published in: Physical Review B
July 14, 2016

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.

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Published In

Physical Review B

DOI

EISSN

2469-9969

ISSN

2469-9950

Publication Date

July 14, 2016

Volume

94

Issue

1

Related Subject Headings

  • 51 Physical sciences
  • 40 Engineering
  • 34 Chemical sciences
 

Citation

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Hann, C. T., Socolar, J. E. S., & Steinhardt, P. J. (2016). Local growth of icosahedral quasicrystalline tilings. Physical Review B, 94(1). https://doi.org/10.1103/PhysRevB.94.014113
Hann, C. T., J. E. S. Socolar, and P. J. Steinhardt. “Local growth of icosahedral quasicrystalline tilings.” Physical Review B 94, no. 1 (July 14, 2016). https://doi.org/10.1103/PhysRevB.94.014113.
Hann CT, Socolar JES, Steinhardt PJ. Local growth of icosahedral quasicrystalline tilings. Physical Review B. 2016 Jul 14;94(1).
Hann, C. T., et al. “Local growth of icosahedral quasicrystalline tilings.” Physical Review B, vol. 94, no. 1, July 2016. Scopus, doi:10.1103/PhysRevB.94.014113.
Hann CT, Socolar JES, Steinhardt PJ. Local growth of icosahedral quasicrystalline tilings. Physical Review B. 2016 Jul 14;94(1).

Published In

Physical Review B

DOI

EISSN

2469-9969

ISSN

2469-9950

Publication Date

July 14, 2016

Volume

94

Issue

1

Related Subject Headings

  • 51 Physical sciences
  • 40 Engineering
  • 34 Chemical sciences