Deposition of metals on binary alloy surfaces offers new possibilities for guiding the formation of functional metal nanostructures. This idea is explored with scanning tunneling microscopy studies and atomistic-level analysis and modeling of nonequilibrium island formation. For Au/NiAl(110), complex monolayer structures are found and compared with the simple fcc(110) bilayer structure recently observed for Ag/NiAl(110). We also consider a more complex codeposition system, ðNi þ AlÞ∕NiAlð110Þ, which offers the opportunity for fundamental studies of self-growth of alloys including deviations for equilibrium ordering. A general multisite lattice-gas model framework enables analysis of structure selection and morphological evolution in these systems.S elf-assembly involves the autonomous organization of components into structures (1). This process requires mobility of aggregating components, and usually occurs on smooth surfaces or in fluids. Some degree of relaxation in the aggregated state is typically also operative. Self-assembly can be manifested in either complex equilibrium structures, e.g., reflecting competing interactions, or in far-from-equilibrium growth structures (1). The latter can be very different and more diverse than the equilibrium forms (2). Significantly, self-assembly provides a practical strategy for creating ensembles of nanostructures with unique size and shape dependent properties, a central goal of nanotechnology.A broad range of systems self-assemble, spanning hard and soft matter, with a wide variety of interactions and component sizes. We consider the formation of metal nanostructures motivated by applications ranging from catalysis to plasmonics (3-5). Our specific focus is vapor deposition of metal atoms on single-crystal metal surfaces under the well controlled conditions of ultrahigh vacuum (UHV). This process leads to the self-assembly of metal nanostructures and growth of epitaxial metal films. Here, the nonaggregated components are rapidly diffusing adsorbed atoms (adatoms) which assemble into islands. Relaxation in the aggregated state can be achieved via diffusion of adatoms along island edges or via detachment-reattachment. Understanding these processes on the atomic scale facilitates guided formation of functional nanostructures with tailored morphologies and (for alloys) compositions. Ideally, control over formation allows tuning of desired properties, e.g., for heterogeneous catalysis (6).Despite the complexity of self-assembly processes, significant advances are being made in the development of predictive models even in soft material systems (7). Our focus on epitaxial growth on perfect single-crystal surfaces (hard materials) under UHV has a special advantage in facilitating extremely detailed and realistic atomistic-level modeling. Localization of adatoms to a periodic array of adsorption sites enables the use of lattice-gas (LG) models for which nonequilibrium evolution can be efficiently analyzed on the appropriate time-and length-scales via kinetic Monte Carlo (KMC)...