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Abstract
We exhibit a toy model of a binary decagonal quasicrystal of composition Al80.1 Co19.9–closely related to actual structures–in which realistic pair potentials yield a ground state which appears to perfectly implement Penrose's matching rules, for Hexagon–Boat–Star (HBS) tiles of edge 2.45 Å. The second minimum of the potentials is crucial for this result.
Keywords:
Acknowledgements
This work was supported by US DOE grant DE-FG02-89ER-45405; MM was also supported by Slovak research grants VEGA 2-5096/27 and APVV-0413-06.
Notes
Notes
1. There are four violations per cell necessitated by the periodic boundary conditions, and a few more violations that we ascribe to incomplete minimization. The energy correlates with the number of violations.
2. S. Lim, M. Mihalkovič, and C. L. Henley, unpublished results.
3. This tile was introduced and called an ‘E’ tile by M. Mihalkovič and M. Widom Citation20
4. Note the effective interactions can't always be written in terms of adjoining tiles. In particular, at either tip of each Boat, if the matching rules are both satisfied (V-rule on one side, Fat/Fat on the other), then an additional (favourable) 4.67 Å Al–Co interaction is created between the Co atom on the V-rule side and the internal Al atom on the Fat/Fat side.