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?
 A: I have done some builded shots with Vodka and Ice in a -18 C degrees. And because I don't have fotos or links, I just tell you how it goes; 
1. Put a bit water on a shot glas and let it freeze. -18 C
2. Put -18 C Vodka (I actually used Amaro del Capo) in the glass above the ice. 
-Let it stay. What happens?
First, the vodka melts the ice and forms a snow shot. - This is the goal to do this shot. But if you leave it too long, it forms an solid Ice surface.
Why? It's finally all about density differences. So in your case you should expect to have air, Ice, water sortet out according to their amounts.
And you don't need even a Month do have it that way. 

But why the shot makes this Ice surface? It's simple; because you normally have too much water in it at the beginning, and because alcohol and water mixes and forms this snow, with freezing point exactly as your fridge. And then the rest of the Ice just moves to where it belongs. -> At the top of it all.
And, btw. This snow is really nice. Hold your shot in your hand for a while, and you see how it reacts.
