  One may predict a quasicrystal structure starting from electrons and quantum
mechanics, as approximated by interatomic pair potentials calibrated with
ab-initio total-energy calculations, combined with the experimentally known
composition and lattice constants. Here we report our progress on the "basic
Ni" decagonal phase d(Al70 Ni21 Co9). Atomic configurations are represented as
decorations of (possibly) random tilings. Our method was Monte Carlo simulation
using both lattice-gas hops by atoms and tile-flip rearrangements, eventually
followed by molecular dynamics and relaxation of the atom positions. Initially
allowing the greatest freedom of atom positions, we observed nearly
deterministic structural rules and enforced these as constraints involving
larger tiles; this procedure was repeated at the next level of modeling. In
crude and preliminary form, the effective Hamiltonian for tile-tile
interactions is known, which is needed for further simulations to infer the
long-range order. Our atomic arrangements in the 20 A decagonal cluster are
compared with three structure models based on recent experiments.
