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I recently asked a question over on the Earth Science stack exchange about cumulus cloud formation from (roughly) point sources. These points can form around the same time across large areas, such as this example of 10-15 appearing all around Mississippi, pulled from GOES-East satellite data:

image description: clouds form from about 10-15 points across the state of Mississippi and begin to combine.

or this example from the same source and date in Guatemala:

image description: clouds energetically form from numerous small points over Guatemala

It's likely these point sources are thermals, warm updrafts that form over heated ground. The warm air rises and cools as it expands in lower-pressure surroundings, then sinks again along the outside of the column, as in this image from Wikipedia of the plume thermal model:

image description: a column of warm air rises and spreads out before falling back down along the column's boundary

To summarize in physics language: a medium is brought near a phase transition, but the nuclei that form are able to, to some extent, self-stabilize against further growth in area. That is, their own dynamics act to impede their further growth.

Of course, this stability is partly due to the system being near criticality. If it were brought above its critical temperature (holding other parameters fixed), the thermals would grow. This is true of many (all?) systems near a phase transition. But if thermals lacked their boundary -- the cooler air sinking around them -- they would grow anyway! (And decrease in intensity, unless the incoming solar energy was strong enough.)

So my question is: what other examples are there of phase transition nuclei whose dynamics somehow impede their own growth?

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Many crystals grow once started, but they can be difficult to start.

Water has a number of unusual properties. One is the ice is less dense than water. Suppose you have pure water. Neighboring water molecules attract each other when separated. When too close, they repel. You can describe this as a force, or as potential energy. There is a distance where the potential energy is a minimum.

In liquid water, molecules have a fair amount of kinetic energy. Water is continually forming small ordered groups. But they immediately break up.

Image from https://royalbcmuseum.bc.ca/exhibits/living-landscapes/thomp-ok/env-changes/water/introduction.html

Image from https://royalbcmuseum.bc.ca/exhibits/living-landscapes/thomp-ok/env-changes/water/introduction.html

It is similar in ice crystals. The molecules fit in a different, more separated, configuration. There is a different, lower, minimum potential energy. This structure is stable at low temperatures. But at higher temperatures, the kinetic energy of the molecules is strong enough to break these bonds.

Image from https://royalbcmuseum.bc.ca/exhibits/living-landscapes/thomp-ok/env-changes/water/introduction.html

Water freezes at $0$ C. But it is densest at $4$ C. Between these temperatures, small groups of molecules form ice like structures that immediately break up, as well as water like structures. Near $0$ C, there are enough momentary ice like structures to make water less dense.

And yet, ice does not form at this temperature. In fact, it is possible to super cool water - to cool it below $0$ C in its liquid state. Once ice starts forming in super cooled water, the water freezes instantly. But something can prevent it from starting to form ice crystals.


It is energetically favorable for water molecules to be near each other in a water like structure. Also in an ice like structure. But less favorable for a water like structure to be near an ice like structure. This is a higher energy configuration.

When bulk ice meets bulk water, almost every molecule is in the interior of ice or water. Relatively few are right at the surface.

Right at $0$ C, ice and water are in equilibrium. As many molecules are ripped out of the ice and become water as freeze out of the water to become ice. At a little lower temperature, it is more likely for water molecules to freeze into the ice. The ice grows.

But what if there was no ice and the temperature dropped? Small ice like structures continually form randomly. These contain perhaps dozens of molecules in an ice like solid. But in a small sphere or similar blob, few molecules are in the interior and many are at the surface. The energy of such a blob is high. It quickly falls apart into a liquid.

Ice cannot start forming until a blob forms that is so big that low energy of the larger interior overcomes the high energy of the surface. Once this happens, the solid will grow.

This can happen a number of ways. First the temperature can drop so low that the solid form is strongly favored over liquid. Even a small blob can overcome the surface energy.

Second, water might be in contact with a surface. Even if the surface does not strongly attract water, it might have imperfections or impurities where the attraction is stronger. A blob can form there without so big an energy penalty.

Third, simply disturbing the water, for example shaking it, can help the momentary formation of a larger blob.


This example has talked about water, which is an unusual substance. But many substances can have similar behavior nucleating crystals.

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