Microstructure in Metals:Capillarity

3. Wulff Construction I [10 points]: Prove the Wulff construction for the equilibrium shape of a parallelopiped crystal shown below with surface energies yx (YZ plane); Vy (XZ plane); and Vz (XY plane). [Hint: Minimize the total surface energy of the body while keeping the volume constant. Here you need to use Lagrange multiplier (review your calculus notes). The resultant relation is the Wulff construction]. 2x Yy YA AX 2y Yx Z YZ 2z