Ice cube left in water at 0 °C for a thousand years

Let's say we take an ideal calorimeter with a liter of water at +5 °C and throw a 5×5×5 cm cube of ice having temperature of –70 °C. I choose these initial parameters so that the stationary temperature would come to zero after melting about 10 grams of ice. The calorimeter is then closed an isolated.

How would the contents of this calorimeter evolve with time? How would it look like after a day? a year? a thousand years? Let's suppose that ice never touches walls and floats in the middle.

This may sound as a "homework" problem, but it's just a question I came up with and I found it to be quite a complicated one — so I formulate it this way just to be specific.

I suppose that the ice cube would eventually recrystallize to take the least-energy shape of some hexagonal kind. What would this shape be like? I have never heard of a single hexagonal ice crystal. I have seen large single crystals of quartz, but not of ice.

How can I estimate the rate of recrystallization? Can you point me to some relevant papers on this?

Also, as surface tension of ice is about two times less than that of water, the least-energy state of the system would have all it's water-air surface frozen. Am I right? How can I estimate the depth of the surface ice?

Another factor is that top of the ice is always above water. Eventually it would recrystallize through sublimation and desublimation. But the rate would be different from that in water. How can this rate be estimated?

• I considered (3): first, because water is a little bit denser and ice, and second, because the very "beautiful" crystals are very well-organized states, with low entropy. Your system is a high-entropic system because it is in a dynamical equillibrium. This is because I don't think some beautiful effect will happen. But it is only my hypotese. – peterh Dec 12 '14 at 15:56