A Model of Quasicrystal Growth

Joseph, Dieter; Elser, Veit

doi:10.1103/physrevlett.79.1066

Cited by 45 publications

(28 citation statements)

References 6 publications

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“…While the tessellation patterns proposed for all regions of dd-Ta 1. 6 Te observed yet agree quite well with those generated by theoretical growth models [36], the disorder in direction of the ''periodic'' axis perpendicular to the dodecagonal planes remains unaccounted for.…”

Section: Resultssupporting

confidence: 70%

The structure of dodecagonal (Ta,V)1.6Te imaged by phase-contrast scanning transmission electron microscopy

Krumeich

Müller

Wepf

et al. 2012

Journal of Solid State Chemistry

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Section: Resultssupporting

confidence: 70%

The structure of dodecagonal (Ta,V)1.6Te imaged by phase-contrast scanning transmission electron microscopy

Krumeich

Müller

Wepf

et al. 2012

Journal of Solid State Chemistry

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“…In contrast to the unrestricted case where the zipper move is ergodic this is not the case for restricted tilings. A solution might be to apply a growth algorithm [12] which can produce open clusters without restrictions.…”

Section: Resultsmentioning

confidence: 99%

Restricted square-triangle tilings

Roth¹

2008

Zeitschrift Für Kristallographie

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Abstract. Restricted square-triangle tilings are tilings of regular squares and triangles where the number of vertex types has been limited to a subset of all possible vertex types. Such structures have recently been observed in several places: for example as strip phases in colloidal patterns on laser fields with pentagonal symmetry, and as square-pair-free tilings in patterns formed by dipolar magnetic binary colloidal mixtures. In general there are four vertex configurations: A (4 squares, 4 4 ), Z (6 triangles, 3 6 ), H (4 2 3 3 ), and S (43433). Strip phases belong to type AHZ, square-pair-free phases to SZ, standard inflation generated quasicrystals to HSZ, and unrestricted dodecagonal random tilings to AHSZ. We study several vertex type combinations and describe the properties of the patterns generated. AHZ tilings can be mapped to binary necklaces and classified completely. A similar mapping is possible for many HS tilings. Defect-free SZ tilings can be transformed into a triangle-square-hexagon (TSH) supertiling with matching rules. Monte-Carlo (MC) simulations are used to examine the properties of several classes of restricted tilings.

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“…Recently Joseph and Elser [16] succeeded in improving a long-known method to generate quasicrystals: the growth mechanism. Up to their breakthrough this method produced quasicrystals of low quality [17] with tears and strong deviations of the lifted hypersurface from the ideal orthogonal space direction.…”

Section: Construction Of Random Tilingsmentioning

confidence: 99%