When water freezes, all the individual water molecules (which are roughly “V” shaped) click together into a highly structured repeating 3D crystal [pattern that looks like this.](https://www.chemtube3d.com/images/aleximages/ice.png) Note all the waters form hexagons, kind of like a honeycomb – that’s why snowflakes are hexagonal and have 6-sided symmetry.
So yes the water does “purify” itself as it crystallizes into solid ice. Basically, the salt molecules don’t really fit or snap into this hexagonal pattern very well, so they mostly get left behind as all the waters start clicking together into their big solid scaffold.
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