# What happens to the crystal structure of ice as it gets colder and colder [duplicate]

Not sure if this belongs on Chemistry or Physics stackexcahnge.

As water freezes into ice, it turns into a solid, and expands as it forms a crystal structure. But what happens to this crystal structure as it continues to cool? For example, if you take ice and cool it down to -50C, how does the crystal structure alter? -100C?

I would assume that it contracts, similar to any other crystal as it cools.

I'm familiar with the different phases of ice, which require different amounts of pressure and such to create. For my example above, I'm talking about taking a cup of water, and slowly freezing it over time with roughly no change to the pressure in the room.

• Not all exotic phases of ice require pressure to create. – Ivan Neretin Feb 7 at 15:16
• en.wikipedia.org/wiki/Ice#Phases – Karl Feb 7 at 17:14
• May have an answer here – Mathew Mahindaratne Feb 7 at 18:49
• Not all crystals contract monotonically as the temperature is lowered. Some start to expand again in some temperature range. Thermal expansion coefficients are not constants. – Jon Custer Feb 10 at 14:03

Well, the easiest way to address this question is take a look at the phase diagram for ice. Ordinary ice as we know consists of lots of hexagonal rings of water molecules. First off, as temperature is decreased well below $$0~^\circ$$C, there will be a slight contraction of the lattice due to decreased thermal contribution to vibrational frequencies. This will cause the average $$\ce{OH}$$ bond length to decrease which will cause a subsequent contraction of the average $$\ce{OO}$$ distance.

It is not obvious in any way that there should be another phase transition at low temperatures and pressure for ice Ih, but it turns out there is. One can understand why there is a phase transition by observing that in the low temperature limit, entropic effects will make a diminishing contribution to the free energy of any state, and the ground state will in the low temperature, low pressure limit will simply be the global minimum of the potential energy surface.

Now, experiments demonstrate that while the oxygen atoms in ice Ih are all arranged in these hexagonal rings, the hydrogen atoms are essentially distributed randomly subject to the conditions that two hydrogen atoms are covalently bound to each oxygen atom, each oxygen receives two hydrogen bonds, and no two hydrogen atoms point towards each other. These are known as the ice rules (or sometimes Bernal-Fowler rules). This, however, is not the most stable structure that one can imagine as the protons are disordered, and hence there is not optimal cooperativity in the direction of the hydrogen bonds.

For this reason, people thought there might be a low-temperature phase of ice which is proton-ordered. That is, you have the same lattice as in regular ice Ih, but the protons all point in the same direction when forming hydrogen bonds. This is easier to see, so I have put a picture of the lattice below.

This phase of ice is called ice XI. I think they are numbered based on the order they were discovered, which is very annoying.

In practice, even though this is essentially the ground state of bulk water, it is very uncommon to find in nature, and very difficult to synthesize in a lab. This is because at such low temperatures, the rates of proton rearrangements are very slow. These rearrangements occur by proton transfer in ice, or by rotating to rearrange which oxygen the hydrogen bonds are donated to. These processes individually have high barriers, and hence have low rates even at relatively high temperatures and pressures. So, going from ice Ih to ice XI occurs much more slowly than most phase transitions.

You can read about how ice XI is prepared in practice on the wikipedia page for ice XI, but basically you introduce defects which act as catalysts for the rearrangements for the hydrogen atoms.

TL;DR: To be really pedantic, the answer to your question depends on how long you are willing to wait as you keep cooling down the block of ice. That is, if you have an ice cube and cool to e.g. 5K, then nothing will happen besides a slight contraction of the lattice. If you keep it at that temperature for, literally something like 1,000 years (evidence from Antarctic ice cores), then your ice cube will look exactly the same, but microscopically, the protons will be organized much more neatly. How pleasant.

There are two structures of ice that are found in that temperature range, hexagonal (common on earth) and cubic (less common on earth). To read more about those, see e.g. https://www.pnas.org/content/110/29/11757.

In the absence of a phase change, the density increases with decreasing temperature (for comparison, the density of water is on the order of 1000 g/L): Data from: https://www.engineeringtoolbox.com/ice-thermal-properties-d_576.html