Determining Grain Boundary Energies from Triple Junction Geometries without Discretizing the Five-Parameter Space

Grain boundary energy anisotropy plays an important role in many science and engineering problems. This paper presents a new numerical method for determining the grain boundary energy distribution (GBED) from the microstructures of polycrystalline materials. The method assumes that triple junctions are in local equilibrium, that this equilibrium is described by the Herring equation, and can be expressed using the Hoffman-Cahn formalism of the capillarity vector. The conventional method discretizes the five-parameter space and then fits the energy for each discrete bin. The new method minimizes the difference between similar boundaries in the dataset while obeying the equilibrium equation at triple junctions. This non-parametric approach shows smaller error than the conventional method, and it can also determine the grain boundary energies from datasets that have small numbers of triple junctions if their configurations are clustered in the five-parameter space, which is not possible using the conventional method. In addition, the proposed non-parametric approach performs better when the number of triple junctions increases, which is not always true for the conventional method.