Knowing the equilibrium shape of an interfacial particle can provide insight into material properties and microstructures. Until now, there has been no method available to rapidly analyze the geometry and energetics of such a system which includes the anisotropy of the interfacial energies. WulffSOAP (Wulff Shape Of Anisotropic Particles) is a platform-independent software tool that quickly and easily models any particle shape at an interface, such as a droplet sitting on the free surface of a substrate, or a faceted precipitate phase sitting at a grain boundary. The user specifies the Wulff shapes of the particle (or hole) within the two media sharing the interface, and the crystal and plane orientation of this interface; then the program returns images and energetic information, such as the dihedral angle (or the equivalent wetting angle). The program assumes that each particle-medium interface may be fully-faceted, partially-faceted, or isotropic, and that the medium-medium interface is isotropic and deformable. The tool runs in Mathematica, and a free online tool is in development.
WulffSOAP finds the equilibrium configuration by using a modified Winterbottom-like construction, and employs tools from computational geometry and group theory to expedite the calculation. Then, it finds the morphology of the surrounding interface by energetically relaxing the shape, much like the program Surface Evolver [Brakke, Experimental Math., 1992].
WulffSOAP can be used to analyze experimental results, like equilibrated lead crystals at copper surfaces which have a cube-on-cube orientation relationship and reveal a partially faceted free surface on the lead, a fully facetted lead-copper interface, and a raised ridge along the triple line [Chatain and Galy, J. Mater. Sci. 2006]. Other examples are analyzing the shapes of wholly facetted Pb inclusions on twin boundaries in silicon [Hagege, Interface Sci., 1999], or Pb particles at general grain boundaries in Al, facetted on one side and isotropic on the other [Dahmen et al., Phil. Mag., 2004 and Dahmen et al., Microscopy and Microanalysis, 2003]. Bicrystal inclusions within a homogeneous medium, such as eutectic-composition Pb-Cd inclusions in an aluminum matrix, can also be modeled [Hagege and Dahmen, Phil. Mag. Lett., 1996]. By comparing micrographs of particles with the model, the relative magnitudes of interfacial energies can be estimated. This is particularly important for many experimentally observed cases when the orientation relationship between the particle and the substrate, or the orientation of the interface, is variable.