Equilibrium at triple junctions under the influence of anisotropic grain boundary energy

We study the conditions required of equilibrium configurations at triple junctions, under the influence of grain boundary energy that can vary with boundary inclination, through application of the Hoffman-Cahn capillarity vector. It is shown that relatively simple geometric constructions can be used, which are analogous to the usual force-triangle method used under isotropic conditions. Particular attention is paid to cases in which one, two or three of the boundaries are trapped in orientations that are associated with energy cusps, and it is shown that these are often able to accommodate wide variations of grain boundary energy and/or inclination. Some cases generate "bi-stable" configurations in which one or two of the boundaries can flip between different stable inclinations.