 Solution

At fixed transformed volume, an equilibrium solid-state precipitate seeks a low total free energy, including the orientation-dependent interfacial energy and elastic strain energy associated with misfit and applied stress. Low-energy interface orientations occupy large faces. The Wulff construction captures surface-energy anisotropy when strain and other contributions can be neglected; a solid-state precipitate generally also pays coherency strain energy, and its optimum shape can change with size.

During formation, growth kinetics and diffusion may prevent the equilibrium shape being reached. Coherent, semicoherent and incoherent interfaces have different bonding and defect structures, so their energies and attachment rates differ. The disc shape is consistent with much cheaper broad faces than edges, but morphology alone does not uniquely measure the energies or prove equilibrium.