Nucleation

Nucleation forms a sufficiently large region of a new phase within an old metastable phase. In classical nucleation theory, positive surface energy competes with bulk free-energy gain, producing a critical nucleus and a barrier to conversion. The Arrhenius nucleation time depends exponentially on this barrier; boundaries and impurities can alter it. This explains how metastability and hysteresis can persist despite a different globally stable phase.

Formation of most nuclei within an interval short compared with subsequent particle growth. A common birth period can help narrow a particle size distribution if mixing and later growth are sufficiently uniform and secondary nucleation is suppressed.

A schematic time history of growth-species concentration showing buildup, a short nucleation interval above an effective nucleation threshold, then growth above the equilibrium solubility but below substantial new nucleation. The concentration history suggests how to separate particle birth from growth; it does not establish that every particle synthesis follows that mechanism.

Formation of a critical nucleus at a pre-existing surface or interface. Favorable wetting can replace part of the cost of a free nucleus and lower its barrier; later deposition of a free particle on a support is a different process.

Ice forms from ice-supersaturated vapour at a suitable foreign surface. The relevant temperature and surface properties differ from liquid-droplet immersion freezing.

A suitable particle colliding with a supercooled droplet can trigger heterogeneous freezing. This is distinguished from nucleation around an inclusion already inside it.

Ice nucleates on an inclusion already immersed in supercooled water. The interfacial nucleation barrier, inclusion properties, droplet volume and observation time affect freezing probability.

Formation of a critical nucleus within the bulk parent phase without assistance from a pre-existing interface. Its interfacial cost competes with the bulk free-energy gain.

Ice embryos form without a foreign nucleating surface once thermal fluctuations can overcome the free-energy barrier on the relevant timescale. An apparent freezing threshold depends on droplet volume and measurement duration.