The equilibrium shape of anisotropic interfacial particles

The Wulff construction yields the equilibrium shape of a particle of fixed volume embedded in a single phase at constant temperature. When the particle attaches to an interface (boundary) between two distinct phases or grains of the same phase, the Wulff construction must be modified to account for the abutment of Wulff shapes at the boundary as well as the boundary energy that is replaced by the particle. If the boundary is non-deformable, a portion of the particle interface is constrained to replace the image (i.e. the exact position) of the boundary that is removed, and the Winterbottom construction yields the equilibrium particle shape. If the boundary can deform, the particle is not constrained to replace the image of removed boundary, and the particle shape is determined by a more general modification of the Wulff construction. In two dimensions, the particle attaches to an initially flat boundary and creates two disjoint segments that remain flat at equilibrium. In three dimensions, the boundary surrounding the particle is contiguous, and numerical calculations show that such a boundary is not necessarily flat but maintains a constant mean curvature of zero at equilibrium.