# When can water be supercooled?

Qualitatively, I understand that water can be supercooled when:

1. It is relatively pure.
2. It is in a container that is relatively smooth of defects.

The effect of both of these is to reduce nucleation points, which are needed to provide a place for the ice crystals to start growing.

Rate of cooling may also be a factor- this is less clear to me.

But.... surely water that is experimentally supercooled is not perfectly free of impurities, nor is its container smooth at the atomic level. So there must be some critical amount of nucleation sites available.

Is it possible to quantify somehow, whether in general or at least for a specific impurity, exactly what the critical amount is to prevent supercooling? Is it a critical density of these sites that matters, or just a critical total number, since each site has some probability of starting crystallization? Even better, is there some general energetic or thermodynamic inequality that describes what conditions are needed for successful supercooling?

• another necessary condition for supercooling liquid water is no agitation and no shock disturbance. A water sample which can sit in a metastable supercooled state for ~hours can be triggered into freezing simply by tapping the side of its container with a pencil. Jan 19 '18 at 1:11
• I went to a non heated barn in winter to get some water from a bucket. In an instant the backet crystallized by rays of ice exploding from the mag to the walls of the bucket. The mug was now frozen solid inside a full bucket of ice. The bucket was a zinc plated steel with water from a well. The rate of temperature change was slow inside the barn. Jan 19 '18 at 8:36
• @Farcher that study is very interesting, and relevant- feel free to adapt it into an answer. However, it does not quite address the question as stated, since it deals with the extreme case of water without any external nucleation sites. Jan 20 '18 at 16:37
• It is not only a matter of concentration: a single nucleation site can start the freezing of the sample, and the probability that this happens will depend on its size, its surface structure and its interaction potential with the water molecules. See for example B.J.Mason, Nucleation of Water Aerosols, 1960. Jan 23 '18 at 12:17

Qualitatively, I understand that water can be supercooled when:

• It is relatively pure.
• It is in a container that is relatively smooth of defects.
• ...

Yes, but it's actually very complicated ...

See here for a huge chart of ice types - this site seems to be down, with the last complete capture by Wayback on Oct. 9 2020); some later captures are incomplete, missing some of the images and links to other webpages.

 Phase Diagram


Is it possible to quantify somehow, whether in general or at least for a specific impurity, exactly what the critical amount is to prevent supercooling? ... Even better, is there some general energetic or thermodynamic inequality that describes what conditions are needed for successful supercooling?

It is explained relatively simply at Wikipedia's Supercooling webpage; and at great length, but still relatively simply, at the "Amorphous Ice and Glassy Water" and "Explanation of the Phase Anomalies of Water (P1-P13)" webpages (so, 14 webpages, more than you likely wanted to know).

Conditions such as: cooling rate, impurities, pressure, container, shock waves, all have an effect on the results you obtain, sometimes a bit of luck is involved (something you don't account for, experimental error).

You can make syrup if you do it correctly.

Wikipedia gives a simplified explanation of heterogeneous nucleation which in water usually occurs when a crystal of ice water is added to supercooled water.

Some experimental results were published in the Journal of Physics article "High-density amorphous ice: nucleation of nanosized low-density amorphous ice", the Journal of the American Chemical Society article "Heterogeneous Nucleation of Ice on Carbon Surfaces", and in the Proceedings of the National Academy of Sciences article "Observing the formation of ice and organic crystals in active sites".

• Thanks for the info and links. I'm aware that this is venturing into a very complicated system in general. For the purposes of this question, I'm mostly interested in region of the phase diagram around 1 atm, and more generally conditions that don't require special equipment to access. Jan 23 '18 at 6:42
• And actually I disagree that wiki is very useful... it doesn't address in any depth the quantitative conditions required for supercooling, and it (as of right now) has a whole bunch of incorrect information that confuses supercooling with freezing point depression- preceded by a statement that points out this mistake! Jan 23 '18 at 6:45
• @Rococo - Yes, the Wikipedia webpage is too simple and indeed someone did make an edit to point out shortcomings on the webpage: "The following paragraphs are about freezing-point depression.". -- Read prior to that if you desire the 'Wikipedia explanation', otherwise there's the more thorough explanation provided by the following links. Quick and dirty or in-depth ... There's really no stone unturned on the second offering but it's likely to take over a week of study.
– Rob
Jan 23 '18 at 7:19
• @Rococo - One of the places it is dealt with is here: www1.lsbu.ac.uk/water/cluster_evidence.html#amor --- It is also possible to find almost everywhere it is dealt by clicking here: encrypted.google.com/… . --- Pulling off the "site: xxx" gives 236K returns, so not too bad.
– Rob
Jan 27 '18 at 23:52
– Rob
Jan 28 '18 at 2:03

Hopefully I can dig into these a bit more and flesh out the answer, but for now here are some relevant resources & quotes:

"Effect of solutes on the heterogeneous nucleation temperature of supercooled water: an experimental determination" Physical Chemistry Chemical Physics (2009):

Homogeneous nucleation
Homogeneous nucleation occurs only in water not influenced by surfaces and devoid of foreign particles or substances. Only the water molecules are involved in the freezing event and at some homogeneous nucleation temperature, $T_{hom}$, estimated to be $\approx -41^\circ$$C^5$ they form an ice-like nucleus, or cluster, large enough to then cause spontaneous freezing. The practicalities of the experimental determination of this temperature are difficult and usually involve an emulsion technique and an averaging of the measured $T_{hom}$ values in an attempt to smooth out the inherent stochastic nature of nucleation.$^6$

Heterogeneous nucleation
Ice nucleation can also occur at the surface of so called ‘‘ice nuclei’’ by heterogeneous nucleation.7 The nuclei can be dirt, large molecules, bacteria, or simply the container wall. In each case a specific nucleating surface allows scaling of the free energy barrier (in classical theory) and causes the freezing event to proceed. The study of heterogeneous nucleation is of much more practical importance than homogeneous nucleation because most nucleation events in nature are heterogeneous.

Effects of solutes on $T_{hom}$ and $T_{het}$

It is well established that for homogeneous nucleation in aqueous solutions the lowering of $T_{hom}$ is linearly related to solute concentration and is independent of the solute, at least for small molecules, i.e.

$\Delta T_{hom} = \lambda \Delta T_m$

$^{8,9}$ The multiplying factor $\lambda$ is generally cited as 2.0$^{10,11}$ although there is some debate, with values as low as 1.7 being quoted.$^{12}$ We are not aware of a molecular explanation of this factor. It has also been reported that high molecular weight solutes have a larger effect than smaller molecules and that l can reach values as high as five for large molecules.$^{13,14}$ It is clear that the effects of solute on the heterogeneous nucleation temperature, $T_{het}$, have wide-ranging consequences in areas as diverse as cloud formation,15 ice-cream and other foods16 and in freeze-tolerant organisms.17 As an example, if sugar is added to ice-cream prior to manufacture the freezing point is reduced by B1.86 1C per mole but the nucleation temperature is reduced by B3.7 1C, allowing for deeper supercooling and so causing more, but smaller, nuclei at the time of nucleation, and so smoother ice-cream. Accurate determination of $\lambda$ is of importance to all of these fields of study.

"Measurements of the concentration and composition of nuclei for cirrus formation" Proceedings of the National Academy of Sciences (2003):

measurements of the concentration and composition of tropospheric aerosol particles capable of initiating ice in cold (cirrus) clouds are reported

• It's nice how much great physics seems to be driven by ice cream: physics.stackexchange.com/questions/373276/… . Jan 23 '18 at 6:37
• The first study is close to but not quite what I am looking for. The authors study ice nucleation with a single nucleating site (a grain of sand) in each sample, and find the temperature at which 50% of the samples have frozen (which is -12 degrees C for pure water). But it is not clear how this survival probability would change as they, for example, added more grains of sand. Jan 27 '18 at 21:07
• (contd.) I've looked at a few of the references but have yet to find a study that addresses this. Most studies seem to focus on the homogeneous nucleation rate instead, despite (as the authors note) the fact that heterogeneous nucleation is the more common process out in the world. Jan 27 '18 at 21:07

When pure water is cooled below freezing point,it may remain in a super cooled state.Super cooling is a state where liquids do not solidify even below their normal freezing point. This concept can applied in why water in cloud do not freeze.