Low-energy electron diffraction and He-atom scattering experiments will be carried out to study the adsorption geometries of adsorbed atoms on nominally flat and vicinal crystalline surfaces, and to characterize the adsorption of weakly-adsorbed atoms on quasicrystalline surfaces. This research program centers on increasing our understanding of the fundamental interactions and properties which give rise to the equilibrium structures of simple adsorbates, and the phase transitions which are peculiar to low-dimensional systems. It also aims to increase our understanding of the properties of the quasicrystalline structure which give rise to the unusual properties of quasicrystals, such as low friction coefficients and high hardness, properties which are important to the development of wear-resistant coatings in machines and tools. This research program includes the participation of postdoctoral researchers, graduate and undergraduate researchers, as well as two faculty from primarily-undergraduate institutions. It includes a significant component of collaborative research with researchers in the UK and Finland. %%% Experiments will be carried out to study the structures and other physical properties of layers of atoms on crystalline and quasicrystalline surfaces. Quasicrystals are a relatively new type of solid which appear to have particularly hard, slippery surfaces. The origin of these unusual physical properties is not well understood. Part of this research involves the study of clean quasicrystal surfaces and the growth of two-dimensional quasicrystalline layers in order to identify the properties of the quasicrystalline sold which give rise to these unusual physical properties. Understanding these properties will facilitate the development of new materials such as wear-resistant coatings in machines and tools. This research program includes the participation of postdoctoral researchers, graduate and undergraduate researchers, as well as two faculty from primarily-undergraduate institutions. It includes a significant component of collaborative research with researchers in the UK and Finland. ***