Ordering of rare gas films on a decagonal Al-Ni-Co quasicrystal

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 that 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, which involves a transition from a quasicrystalline five-fold structure 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, which 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.