Tile Hamiltonians for decagonal phases

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 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. (C) 2004 Elsevier B.V. All rights reserved.