Method to calculate the grain boundary energy distribution over the space of macroscopic boundary parameters from the geometry of triple junctions

Abstract Details of a numerical method for reconstructing the grain boundary energy distribution over the complete space of macroscopic boundary parameters are presented. The reconstruction is based on the analysis of the dihedral angles between homophase grain boundaries of polycrystalline triple junctions. Instead of the Herring equilibrium condition, the procedure uses the Hoffman–Cahn formalism of the capillarity vector. This turns the reconstruction into the problem of solving a homogeneous system of algebraic linear equations. A numerical example demonstrating a reasonably good performance of the method is also given.