Finite-size effects on the structure of grain boundaries.

We present a combined experimental and theoretical analysis of the structure of finite-sized Sigma 3 [112] grain boundaries in Au. High-resolution electron microscopy shows lattice translations at the grain boundary, with the magnitude of the translation varying along the finite-sized grain boundaries. The presence of this structural profile is explained using continuum elasticity theory and first-principles calculations as originating from a competition between elastic energy and the energy cost of forming continuous [111] planes across the boundary. This competition leads to a structural transition between offset-free and nontrivial grain boundary structures at a critical grain boundary size, in agreement with the experiments. We also provide a method to estimate the energy barrier of the gamma surface.