The system of methane on grafoil has the unusual property that melting always takes place from an incomensurate phase- an expanded solid phase at coverage less than the full commensurate monolayer coverage, and the familiar compressed solid phase at highter coverages. Detailed line-shape analyses in the fluid and imcommensurate solid phase and across the melting transitions show that (a) Lorentzian stucture factors account well for the observed fluid lineshapes, with correlation lengths ~ 30A well within the fluid phase; (b) ''tails'' in the incommensurate solid lineshapes indicate the presence of substantial 'thermal diffuse scattering' and can be fitted with power-law structure factors; (c) The expanded solid has only been observed indistinguishable from continuous. However, outside the coexistence region, the approach to the transition region from either side is in all cases indicative of Kosterlitz-Thouless melting

Nanostructured magnetic materials are intensively studied due to their unusual properties and promise for possible applications. The key issues in these materials relate to the connection between their physical properties (transport, magnetism, mechanical, etc.) and their chemical-physical structure. In principle, a detailed knowledge of the chemical and physical structure allows calculation of their physical properties. Theoretical and computational methods are rapidly evolving so that magnetic properties of nanostructured materials might soon be predicted. Success in this endeavor requires detailed quantitative understanding of the magnetic structure and properties.