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 are still considerable controversies as to whether lattice expansion or contraction occurs in metallic nanomaterials with size reduction. Here, the size dependences of the lattice parameter and surface free energy of clean Cu (100) films are investigated via 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 usually lack strong directionality, and it is always regarded that the lattice variations in all directions are consistent. The contraction parallel to the surface is more severe than the expansion perpendicular to the surface in films. The lattices change from cubic to tetragonal with decreasing film thickness. Consequently, common contractions and occasional expansions of the lattice parameters of Cu nanoparticles have been 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.