2002/05/23 by Ibrahim Al-Lehyani, Al-Lehyani, Ibrahim, Mike Widom +1
Engineering · Materials Science · Physics and Astronomy · #Aluminum Alloy Microstructure Properties #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Hydrogen Storage and Materials #Quasicrystal Structures and Properties #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.cond-mat/0205489
19 pages, 8 figures. Submitted to PRB
arxiv created 2002/05/23 · openalex publication_date 2002/05/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.