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Atomistic simulations are carried out to investigate the nano-indentation of single crystal Cu and the sliding of the Cu–Zn alloy. As the contact zone is extended due to adhesive interaction between the contact atoms, the contact area on a nanoscale is redefined. A comparison of contact area and contact force between molecular dynamics (MD) and contact theory based on Greenwood–Williamson (GW) model is made. Lower roughness causes the adhesive interaction to weaken, showing the better consistency between the calculated results by MD and those from the theoretical model. The simulations of the sliding show that the substrate wear decreases with the mol% of Zn increasing, due to the fact that the diffusion movements of Zn atoms in substrate are blocked during the sliding because of the hexagonal close packed (hcp) structure of Zn.