As discussed in Sect. 1.5.2, phase transformations can occur continuously or discontinuously. The discontinuous case begins with the appearance of a small but distinct volume of material having a structure and composition that differ from those of the parent phase. A discontinuous transition can be forced by symmetry, as formalized for some cases in Sect. 14.4. There is no continuous way to rearrange the atoms of a liquid into a crystal, for example. The new crystal must appear in miniature in the liquid, a process called “nucleation.” If the nucleation event is successful, this crystal will grow. The process of nucleation is an early step for most phase transformations in materials. It has many variations, but two key concepts can be appreciated immediately.

• Because the new phase and the parent phase have different structures, there must be an interface between them. The atom bonding across this interface is not optimal, so the interfacial energy must be positive. This surface energy is most significant when the new phase is small, because a larger fraction of its atoms are at the interface. Surface energy plays a key role in nucleation.

• For nucleation of a new phase within a solid, a second issue arises when the new phase differs in shape or specific volume from the parent phase. The mismatch creates an elastic field that costs energy. This is not a concern for nucleation in a liquid or gas, since the surrounding atoms can flow out of the way.