Free energy of grain boundaries from atomistic computer simulation

A thermodynamic integration (TI) scheme is presented that allows us to compute the free energy of grain boundaries (GBs) in crystals from an atomistic computer simulation. Unlike previous approaches, the method can be applied at arbitrary temperatures and allows for a systematic extrapolation to the thermodynamic limit. It is applied to a Sigma 11 GB in a face-centered-cubic Lennard-Jones crystal. At a constant density, the GB free energy shows a nonmonotonic temperature dependence with a maximum at about half the melting temperature, and the GB changes from a rigid to a rough interface with distinct finite-size scaling above this temperature.