In most cases of solidification, the material is cooled too quickly to allow the equilibrium phases, predicted by the phase diagram, to form. This is because the material does not spend sufficient time at high temperatures where diffusion is faster. The non-equilibrium phases that result can be explained qualitatively by using the phase diagram to predict the composition of the first solid formed. When diffusion is not sufficient for the first solid formed to reach the equilibrium composition, this will result in an excess of solute in the last solid formed, which is often sufficient to cause the formation of a non-equilibrium eutectic.
Quantitative analysis also allows us to predict the compositions of the solid and liquid as a material solidifies, if we assume complete mixing in the liquid and no diffusion in the solid (Scheil equation), or if we assume finite diffusion in the liquid and no diffusion in the solid (Steady state solidification).
We can qualitatively understand the reasons why a planar solidification front breaks down into cells or dendrites, from the fact the solute is partitioned into the liquid at the interface, and any random protuberance will be in a liquid of lower solute concentration, therefore favouring its growth compared to the rest of the solid.
Using the knowledge of the solute profile in the liquid, we can quantitatively predict when dendrites will form as a result of this constitutional undercooling, and also make predictions about the scale and morphology of the structure formed.