Local growth of icosahedral quasicrystalline tilings

Published

Journal Article

© 2016 American Physical Society. 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.

Full Text

Duke Authors

Cited Authors

  • Hann, CT; Socolar, JES; Steinhardt, PJ

Published Date

  • July 14, 2016

Published In

Volume / Issue

  • 94 / 1

Electronic International Standard Serial Number (EISSN)

  • 2469-9969

International Standard Serial Number (ISSN)

  • 2469-9950

Digital Object Identifier (DOI)

  • 10.1103/PhysRevB.94.014113

Citation Source

  • Scopus