Tile Hamiltonian for Decagonal AlCoCu

Details Tile Hamiltonian for Decagonal AlCoCu Tile Hamiltonian for Decagonal AlCoCu

2002-05-23

arxiv.org/abs/cond-mat/0205489v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

19 pages, 8 figures. Submitted to PRB

Scientific paper

A tile Hamiltonian (TH) replaces the actual atomic interactions in a quasicrystal with effective interactions between and within tiles. We studied Al-Co-Cu decagonal quasicrystals described as decorated Hexagon-Boat-Star (HBS) tiles using {\em ab-initio} methods. The dominant term in the TH counts the number of H, B and S tiles. Phason flips that replace an HS pair with a BB pair lower the energy. In Penrose tilings, quasiperiodicity is forced by arrow matching rules on tile edges. The edge arrow orientation in our model of AlCoCu is due to Co/Cu chemical ordering. Tile edges meet in vertices with 72$^\circ$ or 144$^\circ$ angles. We find strong interactions between edge orientations at 72$^\circ$ vertices that force a type of matching rule. Interactions at 144$^\circ$ vertices are somewhat weaker.

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