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An unstressed glass is optically isotropic, so it does not split incident light into differently phased in-plane components; it remains dark between crossed polars. A natural explanation of the colored regions after heating is devitrification: anisotropic crystallites have nucleated in the glass. Edges and surfaces provide heterogeneous nucleation sites, making their greater concentration there plausible.

Each approximately uniform crystallite can give a nearly uniform interference colour. Regions with similar thickness and effective birefringence have similar retardation and therefore similar spectral colour, while differing azimuths multiply the intensity by ${\sin }^2(2\alpha )$ and change brightness. Identical hue does not prove identical three-dimensional crystallographic orientation.

Stress-induced birefringence is a possible alternative in a heat-treated glass. The observations alone do not uniquely prove crystallinity; rotating-stage extinction, morphology or diffraction could distinguish the explanations. The crystallite interpretation is the straightforward phase-transformation explanation, without inventing a composition or heat-treatment schedule.

In a sufficiently supersaturated vapor, making liquid lowers bulk Gibbs free energy, but making a small droplet creates a costly liquid-vapor interface. The volume contribution scales as $r^3$ and the interfacial cost as $r^2$. Identifying a positive bulk driving force density $|\Delta g_v|$ and interfacial tension $\gamma$ gives $A=4|\Delta g_v|/3$ and $B=4\gamma$. In the supplied notation,At $r_{\ast }$, $d^2\Delta G/d{r}^2=-2\pi B<0$: this is the barrier summit. Subcritical droplets tend to shrink, whereas supercritical droplets can grow by reducing Gibbs free energy. Fluctuations must cross the barrier before bulk condensation proceeds, especially in a clean vapor without effective sites for heterogeneous nucleation. A temperature just below 100 °C implies a supersaturated vapor only with a suitable pressure, such as a vapor maintained near one atmosphere; temperature alone does not specify the driving force. The nucleation barrier can delay condensation even when bulk liquid is thermodynamically favored.

The competition between crystallization, exposed surfaces, adhesion and elastic strain can be summarized byHere $\Delta g>0$ measures the bulk driving force from supersaturation, and the $\gamma$ values are interfacial free energies. For a free spherical nucleus, $\Delta G=4\pi r^2\gamma -4\pi r^3\Delta g/3$ gives $r_{\ast }=2\gamma /\Delta g$. A support changes the heterogeneous nucleation barrier through adhesion and geometry.

Precursor activities and supply rate, temperature, time, solvent and ligands control nucleation, attachment, detachment and surface diffusion. Many nuclei divide a fixed solute inventory into smaller particles; continued growth or Ostwald ripening can enlarge them. Substrate defects determine preferred nucleation sites; lattice mismatch and interface bonding constrain orientation and elastic relaxation. Facet-selective adsorption can change both surface energies and growth rates.

Near equilibrium, a free nanocrystal follows a Wulff construction; a supported particle can follow a Winterbottom construction. Under kinetic control, slowly advancing facets remain visible while rapidly growing ones disappear. Equilibrium facet energy and kinetic growth rate are different controls, so a crystal structure does not uniquely determine particle shape.

Nucleation is the formation of a sufficiently large embryo of the new metallic phase. Producing metal atoms from dissolved precursor can create supersaturation; aggregation lowers bulk free energy but initially creates costly metal-medium interface. In the simplest spherical classical nucleation theory,where $\gamma$ is the metal-medium interfacial free energy and $\Delta g_v>0$ is the bulk driving force per volume. Clusters below the critical size tend to redissolve; larger ones can grow.

In homogeneous nucleation, the critical cluster forms in the solution without a pre-existing interface: the initial products are free particles. In heterogeneous nucleation, a substrate, vessel wall or suspended seed replaces part of that costly new interface. For a spherical cap on a planar substrate,A wetting substrate therefore lowers the barrier; this assumes the same bulk driving force and isotropic interfacial energies.

A final supported particle need not have nucleated heterogeneously: a free particle can nucleate in solution and later adsorb on the support. Conversely, a particle nucleated heterogeneously on a suspended seed can remain freely dispersed as a composite particle. Nucleation location and final support status are different classifications.

Microwave absorption heats the medium and possibly the support, changing reduction, diffusion and supersaturation. Preferential local heating can change the relative rates of the two routes. Microwave irradiation alone does not remove the thermodynamic nucleation barrier or demonstrate a special nonthermal mechanism.