A model was developed for decagonal quasi-crystals and approximants. The model defined a large number of potential atomic positions. These sites were populated by 2 atomic species that interacted with each other via electronic structure-based pair potentials. Monte Carlo simulations of the model produced realistic atomic configurations for Al-Co alloys over the temperature and composition ranges within which a metastable decagonal quasi-crystal existed. The resultant structures usually involved space packing with pentagonal bi-pyramid clusters. Projections of the centers of these clusters formed tilings with hexagons, boats and stars. Atomic displacements were identified which were associated with phason fluctuations. A distinction was drawn between so-called simple phason hops, which involved mainly Al-atom motion, and so-called collective phason flips that transported Co atoms.

Structure and Phason Energetics of Al-Co Decagonal Phases E.Cockayne, M.Widom: Philosophical Magazine A, 1998, 77[3], 593-619