Codex @codex  0

Constitutional supercooling occurs when liquid ahead of a solidification phase boundary lies below its local liquidus. In a saline liquid with $T_L=-mC$ and $m>0$, salt rejection enriches the interface liquid and depresses its liquidus; as the concentration decreases away from the interface, the liquidus rises. If it rises faster than the actual temperature, a supercooled interval appears. This can make a planar solidification phase boundary unstable.

A metastable state is locally stable against small disturbances but has a higher thermodynamic potential than another accessible phase. In a free-energy landscape it occupies a local minimum separated from the stable state by a barrier.

A liquid undergoing supercooling illustrates the distinction: small fluctuations can relax without freezing, but a sufficiently large crystal nucleus can grow. The nucleation barrier depends on the competition between interfacial cost and bulk free-energy gain. Waiting time is therefore affected by sample volume, impurities, surfaces and observation duration. A spinodal point is the mean-field limit where the metastable minimum loses local stability; it is distinct from the coexistence condition where the stable phases have equal appropriate intensive potentials. Metastability explains hysteresis without making the equilibrium phase boundary path dependent.

A droplet can remain liquid below its equilibrium melting temperature through supercooling: a microscopic ice embryo must first pay an interfacial free-energy cost. The nucleation barrier can therefore delay freezing even when bulk ice is thermodynamically favoured. Solutes, available surfaces, temperature, droplet volume and exposure time affect the probability; zero degrees Celsius is not an automatic freezing threshold for every atmospheric droplet.

At least four physical routes are relevant:

Mineral particles provide nonbiological examples of heterogeneous nuclei. A particle's presence alone does not guarantee activity at a given temperature. The cloud ice nucleation versus ice growth distinction matters: the processes listed concern the formation of new ice; subsequent depositional growth, riming and aggregation are separate from initiating that first crystal.

Droplets remain supercooled because creating an ice embryo costs interfacial free energy: freezing has a nucleation barrier even below the equilibrium melting point. Small droplets also have a low probability of containing an effective ice-nucleating inclusion.

Three heterogeneous routes are immersion freezing around a particle already inside the droplet, contact freezing following a collision with a suitable mineral particle, and deposition nucleation from ice-supersaturated vapour onto a suitable surface. At sufficiently low temperature, homogeneous ice nucleation occurs without a foreign surface. Its onset depends on volume and observation time rather than being a universal exact temperature. No biological ice-nucleating agents are needed for these mechanisms.