How Ice Crystals Are Born and Grow

Foundations Chapter 5 and Advanced Chapter 7 said that smoothness rests on how fine the ice crystals are. That fineness rests on how fast the freezing goes. Advanced Chapter 1 counted ice crystals as one of the four components. But how does an ice crystal come to be in the first place, and how does it grow? The physical root of smoothness is here. The life of an ice crystal is taken in two parts: nucleation, where a crystal is born, and growth, where it gets bigger.

Supercooling — at the freezing point, nothing freezes yet

Oddly enough, water does not begin to freeze merely on reaching its freezing point. To become ice it must first grow a tiny seed of ice, a nucleus. That seed forms only at a temperature lower still. This state, below the freezing point and not yet frozen, is supercooling (sottoraffreddamento).

An experiment makes it visible. Cool a beaker of water and the temperature passes 0 °C without pausing, going on down, and no ice appears. Then, at some moment, the temperature jumps back up to 0 °C and flattens there. The jump is a nucleus finally born: freezing begins, and the latent heat it lets go warms the water itself. The latent heat of water is large. The heat given off as one kilogram of ice freezes would raise one kilogram of water from 0 °C to 80 °C. Holding out below the freezing point, then snapping all at once at the limit — supercooling is a state under strain.

The depth of the supercooling — how far below the freezing point the cooling has gone — drives everything that follows. Sugar has already pulled the freezing point itself down (Approfondimento 1). On top of that, this kinetic supercooling settles how fast nucleation and growth go.

Nucleation — where a crystal is born

Why should freezing need a nucleus at all? When ice grows, a lattice is already there, and water molecules climb onto it one at a time. Where no lattice has formed yet, there is nothing to climb onto. So, before freezing can happen, a seed has to appear — a nucleus, where water molecules have chanced to gather into an orderly arrangement.

Two energies contend here. Below 0 °C, ice sits at a lower energy than water, so making a nucleus carries a gain. But making one also opens a new surface at the border with the water, and that surface exacts a cost. For a spherical nucleus of radius r, the balance can be written like this.

The first term, the gain, works as the cube of the radius; the second, the cost of surface, as the square. While the seed is small the cost of surface wins, so a newborn seed breaks apart at once and is gone. Past a certain radius the cube catches up, and from there the energy falls as the seed grows larger. Which is to say that growth no longer stops. That parting of ways is the critical radius (r*), the top of the hill on the curve. The height of the hill is the energy barrier to nucleation.

And here is what decides the matter: the deeper the supercooling, the lower this hill and the nearer it stands. At −10 °C the critical radius is about 5 nanometers; cooled to −30 °C it shrinks to 1.5. The barrier to be crossed comes down at the same time. A small seed can survive, and the wall in front of it is low. So the deeper the supercooling, the more readily nuclei are born.

And here lies the key to smoothness. For a given amount of ice, the more nuclei there are, the smaller each crystal is. The same water can be made into a few large crystals or into many small ones. Which it becomes is settled by the number of nuclei — that is, by how fast nucleation goes.

Nucleation, resting as it does on molecules gathering by chance, is a matter of probability. It does not happen without fail at some set temperature. In theory, perfectly pure water can stay unfrozen down to −40 °C. That real water freezes higher than that is owing to what comes next.

A nucleus comes easily where there is something to build on

Real water has fine particles drifting in it — dust and the like — and it has the walls of its vessel. These surfaces give water molecules a pattern to fall into line against. With a pattern, a stable nucleus is reached with fewer molecules than building a seed from nothing. Which means a nucleus can form on a shallower supercooling. Pure water holds out to −40 °C, while the water in a real beaker begins to freeze at around −2 °C — this is why.

This property — that a nucleus comes easily where there is something to build on — runs straight into the machine taken up below.

Growth — where a crystal gets bigger

Once a nucleus exists, water molecules around it spread to the crystal surface, bind there, and the crystal gets bigger. This is growth.

Here is the asymmetry that matters most in this piece. Nucleation asks for a supercooling of several degrees. Growth moves on less than a hundredth of one. The reason is plain: a molecule joining the growth has no new crystal to build from nothing. A lattice is there, and it need only climb on. Making a nucleus is hard; growing one is easy.

The consequence is heavy. Growth begins the moment a nucleus is born and does not stop until the supercooling is eaten up. It does not wait for conditions to come right, as nucleation does. So the fineness of the ice is not settled by whether growth can be stopped. It cannot be stopped. What settles it is the race between nucleation and growth.

Freeze fast — that is, supercool deeply — and nuclei are born in quantity, with little time left for growth. The result is many small crystals. Freeze slowly and few nuclei are born, and that few grow at leisure. The result is a few large crystals. The amount of ice is the same; the fabric is wholly different. Freezing in the region where nucleation beats growth is the condition for smoothness.

Freezing ends, but it is not over

When all the water has frozen, or the supercooling is spent, growth stops. The amount of ice grows no further. But — that is not equilibrium.

Compared at the same volume, small crystals have more surface than large ones. And surface exacts a cost in energy — the same cost seen in the second term of the nucleation equation. So the state of many small crystals, built at such pains, is a state that loses on energy. The system wants that lowered. The road down is recrystallization.

Making smoothness and keeping smoothness are thus two different jobs. The first is letting nucleation beat growth — which is what this piece has followed so far. The second is a fight over how far the coarsening demanded by thermodynamics can be slowed (Approfondimento 3). From the moment it leaves the mantecatore, gelato has begun to roll down a slope.

The mantecatore is a machine for mass-producing nuclei

With all this in hand, what the mantecatore does comes into view. Its heart is the inner wall of the cylinder, cooled hard by the refrigerant. That wall gives, at one stroke, the two things nucleation needs. It supercools the mix deeply, and it is itself the pattern the nuclei line up against. So the nuclei are born first of all, and in numbers, at the wall. Left alone, though, they would grow large there and become a layer of ice.

This is where the scraper blade comes in. The blade shaves off the layer of ice on the wall without pause. It scatters the newborn nuclei through the mix before they can grow. Make nuclei at the wall in quantity; scrape them off and spread them before they grow. Repeated, that spreads countless tiny crystals evenly. The mantecatore is, in effect, a machine that mass-produces nuclei and allows no growth.

And this carries a heavy meaning. In the whole road from making to selling, new nuclei are born in one place only: inside this machine. What waits beyond it — hardening, storage — is change in one direction, fewer crystals and a larger mean size: recrystallization (Approfondimento 3). No later step will add crystals. So as many nuclei as possible must be made in these few minutes. Advanced Chapter 7 asked for a machine of high performance because everything hangs on whether this one chance is used to the full.

Turning it faster is not the answer

But here is a fact that betrays the intuition. "The more often it is scraped, the finer the crystals must be" — so it is tempting to think, yet the reverse can be true.

What settles the total count of crystals at the exit is chiefly how long the mix stays and how fast the blade turns. A short stay and a slow blade give many small crystals. Hold the mix longer and turn faster, and the count drops instead, and the crystals get larger.

Why? Turn the blade faster and the interval between scrapes does shorten. But the stirring itself makes heat. The energy shed by the rotation becomes heat, and pushes up the temperature in the middle of the barrel. That holds even with the outlet temperature kept steady. Crystals exposed to that higher temperature recrystallize faster as they travel along the barrel. So by the time they reach the exit, their number has fallen.

The power to cool has its limit too. A good part of the cooling capacity goes to removing the heat the stirring makes. In the end the energy the blade puts in balances the heat the refrigerant takes out. That balance is the floor that can be reached. In an industrial continuous freezer, the lowest outlet temperature attainable is put at about −5 to −6 °C. About half the cooling capacity goes to removing this heat of stirring. The batch mantecatore of the artisan usually delivers at −6 to −8 °C (Advanced Chapter 7). Those are different machines under different conditions, and the numbers are worth keeping apart. Running a machine hard and making the crystals fine are not the same thing. The tug of war between nucleation and growth happens inside the running of the machine as well.

Why the critical band must be crossed fast

Advanced Chapter 7 urged that the critical band, from the freezing point down to −8 °C, be crossed as fast as possible. The reason too can be told as the tug of war between nucleation and growth. Linger slowly in that band and a limited number of nuclei grow large over time. Growth takes the lead, and the crystals come out coarse. Cross it fast, and the deep supercooling holds, nucleation takes the lead, and the crystals stay fine. Giving no time is giving no growth.

And the tug of war does not end at the moment of freezing. Crystals once made fine will try to grow again under the swings of temperature in storage. How the crystals born here grow during storage — that story goes on into Approfondimento 3. The glass transition, where freeze concentration finally arrives (Approfondimento 1), is the end point that stops this growth for good.