What is Equilibrium and fractional crystallisation?

In equilibrium crystallisation the crystals remain in chemical equilibrium with the whole of the liquid until the end, re-equilibrating as the liquid changes; the system ends with the composition it started with. In fractional crystallisation each crystal, once formed, is removed from reaction with the liquid, by settling, by being plastered on the walls of the chamber, or by being armoured by later growth; the liquid then evolves as if the crystals had been taken out of the system.