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Assume we let some water freeze in freezer under normal conditions. We then measure its density. We then chill it down towards 0K. Does it get denser? I assume so but how much?

Does the fact that the ice is a solid with a "set" crystaline structure mean that this structure stays the same from 253K down to 0K or does this change? Also does the distance between the H20 molecules reduce?

(by all means makes assumptions like pure water or rates of cooling)

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A quick Google will tell you the density of ice increases with decreasing temperature. For example see this data from the Engineering Toolbox.

At around 72K ice undergoes a phase transition to a structure called ice-XI. I can't find density figures for ice-XI, but I think it is just an order-disorder transition and any density change is likely to be small.

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