 where α, β, and θ are the angles shown and γij is the surface energy between the two indicated phases. These relations can also be expressed by an analog to a triangle known as Neumann ’ s triangle, shown in Figure 4. Neumann ’ s triangle is consistent with the geometrical restriction that <formula>, and applying the law of sines and law of cosines to it produce relations that describe how the interfacial angles depend on the ratios of surface energies.
