  This paper reviews recent progress in the study of rare gas films on
quasicrystalline surfaces. The adsorption of Xe on the 10-fold surface of
decagonal Al-Ni-Co was studied using low-energy electron diffraction (LEED).
The results of these studies prompted the development of a theoretical model,
which successfully reproduced the thermodynamic parameters found in the
experiment. Grand canonical Monte Carlo (GCMC) simulations for Xe produced
structures agreed with the experimental observations of the adsorption
structures and provided a deeper insight into the nature of the ordering. A
first-order commensurate-incommensurate transition that involves a transition
from a quasicrystalline five-fold stucture to a periodic hexagonal structure
was discovered and characterized for the Xe monolayer. The five rotational
domains of the hexagonal structure observed in the LEED study were shown in the
GCMC study to be mediated by pentagonal defects that are entropic in nature,
and not by substrate defects. The GCMC study found an absence of any such
transition for Kr, Ar and Ne on the same surface. A detailed analysis of this
transition led to the conclusion that the formation of the hexagonal layer
depends on matching the gas and substrate characteristic lengths.
