Tile decoration model of the W-(Al–Co–Ni) approximant

We use ab-initio total energy calculations to refine chemical ordering of the W-(Al–Co–Ni) approximant structure and calculate its stability relative to other ternary and binary competing compounds. This approximant structure has 8 Å stacking periodicity along its pseudofivefold axis and can be interpreted as stacking of two identical adjacent 4 Å slabs with stacking vector inclined relative to the pseudofivefold axis. We generalize this stacking motif to model the 8 Å quasicrystal. Starting with 4 Å slabs forming a ‘binary’ (three-level) decagonal tiling, we introduce tile flips between adjacent slabs analogous to the ‘octagon’ tile-reshuffling update move for binary Penrose tiling. These tile flips lower the total energy, implying 8 Å superorder for the quasicrystal at low temperatures, consistent with experiment.