  Thermodynamic properties of Ne, Ar, Kr, and Xe adsorbed on an Al-Ni-Co
quasicrystalline surface (QC) are studied with Grand Canonical Monte Carlo by
employing Lennard-Jones interactions with parameter values derived from
experiments and traditional combining rules. In all the gas/QC systems, a
layer-by-layer film growth is observed at low temperature. The monolayers have
regular epitaxial fivefold arrangements which evolve toward sixfold
close-packed structures as the pressure is increased. The final states can
contain either considerable or negligible amounts of defects. In the latter
case, there occurs a structural transition from five to sixfold symmetry which
can be described by introducing an order parameter, whose evolution
characterizes the transition to be continuous or discontinuous as in the case
of Xe/QC (first-order transition with associated latent heat). By simulating
fictitious noble gases, we find that the existence of the transition is
correlated with the size mismatch between adsorbate and substrate's
characteristic lengths. A simple rule is proposed to predict the phenomenon.
