Nanocrystalline copper films are never flat

We used scanning tunneling microscopy to study low-angle grain boundaries at the surface of nearly planar copper nanocrystalline (111) films. The presence of grain boundaries and their emergence at the film surface create valleys composed of dissociated edge dislocations and ridges where partial dislocations have recombined. Geometric analysis and simulations indicated that valleys and ridges were created by an out-of-plane grain rotation driven by reduction of grain boundary energy. These results suggest that in general, it is impossible to form flat two-dimensional nanocrystalline films of copper and other metals exhibiting small stacking fault energies and/or large elastic anisotropy, which induce a large anisotropy in the dislocation-line energy.