**PUBLICATION:** M. Mihalkovic and M. Widom,
"Tile-decoration model of the W-AlCoNi approximant",
*Phil. Mag.* **86** (2005) p.557-65
(reprint)

**ABSTRACT:**
We use ab-initio total energy calculations to refine chemical ordering
of the W-AlCoNi approximant structure, and calculate its stability
relative to other ternary and binary competing compounds. This
approximant structure has 8A stacking periodicity along its
pseudo-5-fold axis and can be interpreted as stacking of two identical
adjacent 4A slabs with stacking vector inclined relative to the
pseudo-5-fold axis. We generalize this stacking motif to model the
8A quasicrystal. Starting with 4A slabs forming a ``binary''
(3-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 8A superorder for the quasicrystal at low temperatures,
consistent with experiment.