Extracting the grain boundary character free energy relationship from the microstructure: Pure [100] and [111] tilt boundaries

Analysis is described to extract the excess free energy of grain boundaries from the mesotexture of well-equilibrated polycrystalline samples. The approach is based upon the force and torque balances at triple junctions described in the classical work of Herring [1]. The main advantage of the approach is that the free energy function is obtained over the full fundamental zone of grain boundary types. For the purposes of exposition, the method is described for specified two-parameter hypersurfaces in the fundamental zone for cubic polycrystals (the sets of pure < 100 > and < 111 > tilt boundaries) and the free energy is assumed to depend only upon the lattice misorientation. Results from testbed simulations are presented.