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There is much interest today in novel nanostructuredmaterials. For instance Pt-plated nanoporous gold(NPG), a catalytic heterostructure with an ultrathin(5 nm) film of Pt grown on the nanoscopically curvedand rough surfaces of NPG, is a promising catalystfor fuel-cell applications. But unlike film growthon planar surfaces, epitaxial growth onnanoscopically non-planar surfaces is not wellunderstood. Indeed, nanoscale effects are expectedto cause non-planar epitaxial growth to deviatesubstantially from classical thin-film growth. Asepitaxially layered nanostructures gain industrialapplications, these deviations in film growth becomeimportant to consider. This book presents anintroduction to thin-film growth mechanics, followedby a review of the Pt-on-Au system. The thermodynamiceffects of high curvatures on film growth areexamined, and the impact of nanoscopic roughness ongrowth is explored experimentally. Some novel growthcharacteristics observed for the first time arediscussed, and an atomistic strain-energy mediatedmodel for 3d thin film growth is proposed. This modelmay be applied to any lattice-mismatched epitaxialsystem.