How does freezing speed affect the effectiveness of zone refining?

The effectiveness of zone refining is heavily dependent on the speed at which the molten zone travels through the material, as this rate dictates the distribution of impurities between the liquid and solid phases.1

• Slow Freezing Rates: At very slow speeds, the system maintains an equilibrium state where the distribution coefficient, $k$, is at its ideal value, $k_0$. This allows for the most effective separation of impurities, as they are efficiently rejected by the advancing solid and concentrated into the liquid zone.1
• Moderate Freezing Rates: At typical industrial speeds (roughly 1 to 30 centimeters per hour), the effective distribution coefficient $k$ shifts toward unity. Because impurities accumulate in the liquid just ahead of the solid interface, the forming solid is exposed to a more impure liquid than the bulk, which reduces the efficiency of the purification process.1
• Rapid Freezing Rates: If the freezing speed is too high, $k$ approaches unity, meaning the impurity concentration becomes identical in both the liquid and solid phases. Under these conditions, zone refining ceases to be effective, and the interface may become dendritic or branching in shape.1