  A novel thermodynamic integration (TI) scheme is presented that allows
computing the free energy of grain boundaries (GBs) in crystals from 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 $\Sigma11$ GB in a face centered cubic
(FCC) Lennard-Jones crystal. At a constant density, the GB free energy shows a
non-monotonic 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.
