Abstract
Quasicrystals are metal alloys whose noncrystallographic symmetry and lack of
structural periodicity challenge methods of experimental structure
determination. Here we employ quantum-based total-energy calculations to
predict the structure of a decagonal quasicrystal from first principles
considerations. We employ Monte Carlo simulations, taking as input the
knowledge that a decagonal phase occurs in Al-Ni-Co near a given composition,
and using a few features of the experimental Patterson function. The resulting
structure obeys a nearly deterministic decoration of tiles on a hierarchy of
length scales related by powers of $\tau$, the golden mean.