Local growth of icosahedral quasicrystalline tilings

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.

13 pages, 15 figures, 1 table

References in corpus (3)

• Self-Assembly of Monatomic Complex Crystals and Quasicrystals with a Double-Well Interaction Potential
• Growth modes of quasicrystals
• Dynamics of particle flips in two-dimensional quasicrystals

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• Automating Blueprints for Colloidal Quasicrystal Assembly
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• Starobinsky Inflation and Dark Energy and Dark Matter Effects from Quasicrystal Like Spacetime Structures
• Icosahedral Polyhedra from D6 lattice and Danzer's ABCK tiling
• Dodecahedral Structures with Mosseri-Sadoc Tiles