Wulff construction

The Wulff construction is a method to determine the equilibrium shape of a droplet or crystal of fixed volume inside a separate phase (usually its saturated solution or vapor). Energy minimization arguments are used to show that certain crystal planes are preferred over others, giving the crystal its shape.

In 1878 Josiah Willard Gibbs proposed that a droplet or crystal will arrange itself such that its surface Gibbs free energy is minimized by assuming a shape of low surface energy. He defined the quantity

Here ${\displaystyle \gamma _{j}}$ represents the surface (Gibbs free) energy per unit area of the ${\displaystyle j}$th crystal face and ${\displaystyle O_{j}}$ is the area of said face. ${\displaystyle \Delta G_{i}}$ represents the difference in energy between a real crystal composed of ${\displaystyle i}$ molecules with a surface and a similar configuration of ${\displaystyle i}$ molecules located inside an infinitely large crystal. This quantity is therefore the energy associated with the surface. The equilibrium shape of the crystal will then be that which minimizes the value of ${\displaystyle \Delta G_{i}}$.

...
Wikipedia