Tile Hamiltonians for Decagonal Phases
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/0212605,
title = {Tile Hamiltonians for Decagonal Phases},
author = {M. Widom and I. Al-Lehyani and M. Mihalkovic},
journal= {arXiv preprint arXiv:cond-mat/0212605},
year = {2007}
}
Comments
Proceedings of the 8th International Conference on Quasicrystals, to be published in J. Noncryst. Solids (2003), 6 pages and 8 figures