From AMS Glossary
The process of initiation of a new phase in a supercooled (for liquid) or supersaturated (for solution or vapor) environment; the initiation of a phase change of a substance to a lower thermodynamic energy state (vapor to liquid condensation, vapor to solid deposition, liquid to solid freezing).
In nature, heterogeneous nucleation is the more common where such a change takes place on small particles of different composition and structure. Homogeneous nucleation occurs when the change of state centers upon embryos that exist in the same initial state as the changing substance. In this case, the nucleation system contains only one component, and it is termed homogeneous nucleation. In meteorology, particularly in cloud physics, a number of types of nucleation are of interest. The process by which cloud condensation nuclei initiate the phase change from vapor to liquid is important in all cloud formation problems. The physical nature of freezing nuclei that may be responsible for the conversion of drops of supercooled water into ice crystals is critically important in precipitation theory, as is the clarification of the role of homogeneous nucleation near -40°C. Thermodynamically, all nucleation processes involve free energy decrease associated with the bulk phase change and the free energy increase associated with the creation of new interfaces between phases.