Coexisting lattice contractions and expansions with decreasing thicknesses of Cu (100) nano-films

Abstract Lattice parameters are a basic quantity in material characterization and a slight alteration in lattice parameters directly affects the properties of materials. However, there is still considerable controversies on whether lattice expansion or contraction occurs in metallic nanomaterials with size reduction. Here, the size dependence of lattice parameter and surface free energy of clean Cu (100) films are investigated by simulations. Lattice parameters of the exposed surfaces contract whereas lattice expansion occurs along the direction perpendicular to the surfaces with decreasing film thicknesses. This is striking since the metallic bonds are usually lack of strong directionality and it is always regarded that the lattice variations in all directions are consistent. The contraction parallel to the surface is severer than the expansion perpendicular to the surface in films. Lattices changes from cubic to tetragonal with decreasing film thickness. Consequently, common contractions and occasional expansions of lattice parameters of Cu nanoparticles are observed in previous experiments. Increasing free energy and surface free energy with decreasing thicknesses is the thermodynamic origin of the lattice variations. Our study therefore provides a comprehensive physical basis for the surface effects on the lattice variations.