2002/12/26 by M. Widom, Michael Widom, Ibrahim Al-Lehyani +6
Materials Science · Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #Quasicrystal Structures and Properties #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/0212605
Proceedings of the 8th International Conference on Quasicrystals, to be published in J. Noncryst. Solids (2003), 6 pages and 8 figures
arxiv created 2002/12/26 · openalex publication_date 2002/12/26 · 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 study Al-Co-Ni and Al-Co-Cu decagonal quasicrystals described as decorated Hexagon-Boat-Star (HBS) tiles using \em ab-initio methods. A dominant term in the TH counts the number of H, B and S tiles, favoring tilings of H and B only. In our model for Al-Co-Cu, chemical ordering of Cu and Co along tile edges defines tile edge arrowing. Unlike the edge arrowing of Penrose matching rules, however, the energetics for Al-Co-Cu do not force quasiperiodicity. Energetically favored structures resemble crystalline approximants to which the actual quasicrystalline compounds transform at low temperature.