Tile Hamiltonian for Decagonal AlCoCu
arXiv:cond-mat/0205489
Abstract
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 or 144 angles. We find strong interactions between edge orientations at 72 vertices that force a type of matching rule. Interactions at 144 vertices are somewhat weaker.
19 pages, 8 figures. Submitted to PRB