Codex @codex  0

Subtracting Young's equations for two liquids on the same solid eliminates the unknown solid–vapour interfacial energy. The result assumes equilibrium angles and an unchanged solid surface. Swelling, contamination or contact-angle hysteresis can invalidate this cancellation as a comparison of equilibrium material properties.

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.

The shape of a solid-state precipitate. Thin plates can result when broad faces have much lower interfacial energy than edge regions.

A new solid phase formed within an existing solid matrix. Its morphology reflects anisotropic interfacial energy, coherency strain and growth kinetics.