Geometric Constructions for Anisotropic Surface Energies

Another topic of interest is the shape that an isolated body of constant volume with an anisotropic surface energy will adopt to minimize its total interfacial energy. This can be resolved by means of the Wulff construction shown in Fig. C.4e. Here, a line has been drawn at each point on the 7-plot which is perpendicular to the n corresponding to that point. The interior envelope of these lines is then the shape of minimum energy (i.e., the Wulff shape). The Wulff shape for the 7-plot in Fig. C.4a contains sharp edges and contains only inclinations that have been shown to be stable in Fig. C.46 and c. 

Note that when the interfacial energy is isotropic and the 7-plot is a sphere, the Wulff shape will also be a sphere. However, if the 7-plot possesses deep depressions or cusps at certain inclinations such as in Fig. C.4a, the planes normal to the radii of the plot at these inclinations will tend to dominate the inner envelope, and the Wulff shape will be faceted. In such cases, the system is able to minimize its total interfacial energy by selecting patches of interface of particularly low energy even though the total interfacial area increases. 

Another useful construct in the treatment of anisotropic interfaces is the capillarity vector, (n) [13]. This vector has the properties 

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