It was noted that measurement of the geometry of the triple junctions between grain boundaries in polycrystalline materials generated large sets of dihedral angles, from which maps of the grain-boundary energy could be extracted. An initial analysis was carried out, for a sample of MgO, which was based upon a 3-parameter description of the grain boundaries. An extended form of orientation-imaging microscopy was used to measure both the triple junction geometry, via image analysis in a scanning electron microscope, and the local grain orientation (via electron back-scattering diffraction). Serial-sectioning (with registry of the in-plane images and of successive sections) characterized the triple-junction tangents. The true dihedral angles were then calculated. Herring's relationship was applied to each triple junction, on the basis of an assumed local equilibrium at the junction. By limiting the grain-boundary characteristics to a 3-parameter specification of misorientation, at first, it was possible to neglect the torque terms and to apply the sine law to the 3 boundaries. This then provided 2 independent relationships, per triple junction, between grain-boundary energies and dihedral angles. Discretization of the misorientation, and the use of multi-scale statistical analysis of large data sets, permitted the (relative) grain boundary energy to be deduced, as a function of boundary type, from the triple-junction geometry. A similar analysis of thermal grooving permitted the anisotropy of the surface energy to be measured in MgO.

Extracting B.L.Adams, S.Taasan, D.Kinderlehrer, I.Livshits, D.E.Mason, C.T.Wu, W.W.Mullins, G.S.Rohrer, A.D.Rollett, D.M.Saylor: Interface Science, 1999, 7[3-4], 321-38