Tile Hamiltonians for Decagonal Phases

Details Tile Hamiltonians for Decagonal Phases Tile Hamiltonians for Decagonal Phases

2002-12-26

arxiv.org/abs/cond-mat/0212605v1

Physics

Condensed Matter

Proceedings of the 8th International Conference on Quasicrystals, to be published in J. Noncryst. Solids (2003), 6 pages and 8

Scientific paper

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.

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