Referring again to Figure 7.1, above an equilibrium temperature, TE, alpha is the stable phase and below TE, beta is the stable phase. So below TE in a transformation from α to β, there is a negative Gibbs energy change; that is, ΔGα-β = G(β) − G(α). Although the Gibbs energy of β is lower than that of α, the phase transformation does not occur instantly. Most phase transformations require a density or composition change and the generation of some phase interface surface energy all of which require either a diffusion process or a surface reaction or both (and sometimes heat transfer) that take time. In addition, the formation of a second phase, beta, requires that the new phase starts somewhere in the old phase, alpha. ese particles of the new phase, perhaps very small containing only tens or hundreds of atoms, are the nuclei of the new phase. Even though the new phase is thermodynamically more stable, these nuclei have a surface or interfacial energy that needs to be overcome before they are stable and can grow. Once the stable nuclei of the second phase are formed, they grow by either a diffusion control or surface reaction control (Chapter 5), eventually transforming all of the original alpha to beta. As noted earlier, nucleation and growth is a major mechanism of phase transformations of interest in materials science and engineering. Figure  7.7  shows the nucleation and growth of silicon crystals in an amorphous thin film of silicon. Now, nucleation can be either homogeneous or heterogeneous. Homogeneous nucleation is the process where the small nuclei form spontaneously throughout the bulk of the material undergoing the phase change. In reality, homogeneous nucleation is hard to achieve in practice but it is easier to model. In contrast, heterogeneous nucleation is more common and it occurs when the new phase forms on particles of dust or another phase that allows the nucleus to lower its interfacial energy thereby allowing the nucleus to form more easily. erefore, heterogeneous nucleation is the process where the small, stable particles of the new phase are formed at the interface with another phase (could be the free surface) that lowers the interfacial energy of the nuclei. An important example of heterogeneous nucleation is the process of cloud seeding with silver iodide, AgI, smoke particles that act as heterogeneous nuclei for ice formation, which will ultimately lead to rain (hopefully) during drought. Another classic and visual result of heterogeneous nucleation is the intentional production of crystalline glazes on ceramic art pieces where the heterogeneous nuclei are dust particles or small pieces of the kiln-furnace-insulation that fall onto the glaze surface serving as heterogeneous nucleation sites for crystals (Figure 7.8). e large round areas are the crystals of willemite, Zn2SiO4, that have grown out of the glaze. Notice the deeper coloration of the crystals compared to the glass glaze. is is due to the optical absorption of electrons in the d-shells of transition metal ions, such as cobalt, that have different optical absorption characteristics depending on their local electronic environments-number and proximity of anions-that are different in the crystal and glass.