How does the equilibrium distribution coefficient differ from the effective distribution coefficient?

In the context of zone melting, the distribution coefficient ($k$) represents the ratio of an impurity's concentration in the newly forming solid to its concentration in the liquid phase. The distinction between the equilibrium and effective coefficients is based on the rate of the freezing process:1

• Equilibrium distribution coefficient ($k_0$): This value exists under conditions of very slow freezing, where the liquid and solid phases are in true thermodynamic equilibrium.1
• Effective distribution coefficient ($k$): This value applies at moderate freezing rates (typically 1 to 30 centimeters per hour). Because the impurity is rejected by the solid, it accumulates in the liquid layer immediately ahead of the advancing solid interface. Consequently, the solid forms from a liquid that is more impure than the bulk liquid, causing the effective coefficient to shift toward unity.1

If freezing occurs rapidly, the effective coefficient may approach unity, effectively eliminating the refining process because the impurity concentration becomes uniform across both phases.1