Extracting grain boundary and surface energy from measurement of triple junction geometry

Measurement of the geometry of triple junctions between grain boundaries in polycrystalline materials generates large sets of dihedral angles from which maps of the grain boundary energy may be extracted. A preliminary analysis has been performed for a sample of magnesia based on a three-parameter description of grain boundaries. An extended form of orientation imaging microscopy (OIM) was used to measure both triple junction geometry via image analysis in the SEM and local grain orientation via electron back scatter diffraction. Serial sectioning with registry of both in-plane images and successive sections characterizes triple junction tangents from which true dihedral angles are calculated. We apply Herring's relation at each triple junction, based on the assumption of local equilibrium at the junction. By limiting grain boundary character to a (three parameter) specification of misorientation for the preliminary analysis, we can neglect the torque terms and apply the sine law to the three boundaries. This provides two independent relations per triple junction between grain boundary energies and dihedral angles. Discretizing the misorientation and employing multiscale statistical analysis on large data sets allows (relative) grain boundary energy as a function of boundary character to be extracted from triple junction geometry. A similar analysis of thermal grooves allows the anisotropy of the surface energy to be measured in MgO.