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Name: Connor
Status: Student
Grade: 4-5
Location: CO
Country: United States
Date: June 2007

My 12 year old son asked the following question to which we're having a difficult time getting a conclusive (and consistent) answer from our scientist friends: If you take a 1 ft x 1 ft x 1 ft infinitely strong and rigid cube and fill it completely with water such that absolutely no additional space exists in the cube, and then place the cube in a deep freeze (as low as almost 0 K), will the water ever freeze since it cannot expand at all?

The short answer is yes, it will be a solid at nearly zero Kelvin, regardless of pressure.

Water's expansion during freezing at atmospheric pressure is well known, but water is still compressible. If you have sufficiently high pressure or very low temperature, water will be solid.

Reference this water phase diagram for more information:

That is a bit oversimplified, though. The simple phases (solid, liquid, etc) lose their distinctions at these extreme conditions. Our common-sense knowledge of how things works tends to break down. We cannot actually achieve 0K experimentally anyway, and even if we could, the thermodynamics would make things act really squirrely. At massive pressures, the terms solid and liquid start to lose meaning. You have a system so highly constrained that it is no longer hydrogen bonding or van der Waals forces, but nuclear repulsive forces that dominate the structure. The fact that molecules cannot jump around as readily is what makes a solid a solid, although technically molecules can jump around, just at a much slower rate. But I digress...

And, for all you ever wanted to know about water, here is the terrific site from which I got the phase diagram:

Hope this helps,
Burr Zimmerman

The reason your "scientist friends" are having a problem is that this "simple" question is not at all simple. Ice is a very complicated substance -- possibly not more complicated than other substances, but certainly the most thoroughly studied. What you are "really" asking for is the "phase diagram of ice", which term you can use to search the topic in as much detail and complexity as you can stand. A rather inclusive site is:

If you refer to the insert figure on that site you will see that at temperatures just below 0 C. and hold the temperature fixed but increase the pressure several different transitions from one crystal structure to another will occur. This is a bit different than the "experimental setup" you proposed, but it ends up doing the same "experiment". As you can see, below 0 C. and - 60 C. and pressures less than 1000 MPa there are 5 different arrangements of water molecules that can occur in solid ice. In total there are between 11 and 13 structures of ice known (depending upon whose data you believe). Yes the water will freeze, but the water molecules will rearrange themselves in different shapes depending upon the specific temperature and pressure.

Vince Calder

Yes, the water will indeed freeze, but determining the exact temperatures and pressures where this happens is for an expert familiar with the properties of ice. I will explain.

There are at least 12 different forms of ice. Each form has a different arrangement f atoms and can exist at different pressures and temperatures. There are "phase diagrams" easily available on the Internet that show the stability of water, ice, steam, and fluid for various pressures and temperatures. Ordinary ice is Ice 1 - hexagonal.

Water stays liquid at temperatures below 0C when subjected to high pressures. But there comes a limit to this, and this limit is about –20C and a pressure of 200 megapascals. At higher pressures, the trend reverses and the high pressures tend to make the water solid. At really high pressures, water is solid up to many hundreds of degrees.

The diagrams show that solid ice is ALWAYS the stable phase of water below –20C, regardless of how much pressure there is. So, if you cool your box to –20C or so, you are guaranteed to have solid ice (assuming no nucleation problems).

But let us do a little calculation, because you are worrying that the pressure will suppress the freezing.

As a first approximation, suppose you pour water into the container and seal it at room temperature. As the water is cooled, the water will become more dense and the water will exert a pulling force on the container. (yes, fluids can "pull" on the container that they are inside of).

At 0C and below, ice will start to form. Water expands about 9% when it freezes, and so the water-ice mixture will start to experience pressure as the first bits of ice form. As more and more ice freezes, there will be more and more pressure in the box.

Let us do a simple calculation. Then we will find out why the simple calculation is not quite right.

The bulk modulus of ice is about 8.8E9 pascals. That means that if you completely froze the ice cube (let us say, pretty cold), and tried to stuff it back into the box, you would need to squeeze with a pressure of about 790 megapascals of force to compress 9% to make it fit. That is about 114,000 pounds per square inch, so you would need a strong box. But during the process of compressing it into the box, the pressures would be high enough for the ice to transform to types 3 and 5 and maybe even 6. It is difficult to determine what the compressibility of these ice forms are. So, as the ice is squeezed into the box (or as it is made cooler and cooler), it takes a real expert to figure out what the pressures are. But, solid ice is ALWAYS the stable phase of water at about –20C and below, so that the water in the infinitely strong and rigid cube will indeed freeze.

Robert Erck

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