Why does ice float after it crystallizes?
Water Ice floats on water for the same reason anything floats on water: solid ice is LESS DENSE than is liquid water.
When we put ice cubes in a drink and watch them float to the surface, we become a bit blase with respect to the peculiarity of the phenomenon.
A body floats because it displaces a mass of water that is LESS than the mass of the volume of the body that is immersed in the water. This is Archimedes' principle, and there should be many discussions and treatments of this on the web.
It follows that since both ice cubes and ice bergs float, solid ice water must be less dense than the liquid water from which it is composed. We also note that sea water contains a substantial amount of solute, which makes more floating bodies more buoyant.
Water is an unusual liquid in that the density of the solid phase is less than that of the liquid phase. And the result is that both ice cubes and ice bergs float.