Can we obtain a permanently polarized ice?

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oxivixo
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What is the result of the following experiment?

We put an amount of water in a uniform electrostatic field. We get a polarisation.
Keeping the polarizing field, we cool rapidly the water until it became solid.
We turn off the polarizing field.
Do we obtain a permanently polarized piece of ice? If not, what prevents that from
happening?
 
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I did not realize that you could polarise water given it's diamagnetic nature. I would imagine that the water would set up an orbital magnetic field under the influence of an external magnetic field, I'm not sure that you actually could freeze magnetic force lines into frozen water, but if you could; it would be a diamagnetic orbital field and not a polarised one...I think?