What does a distribution coefficient below one mean for an impurity during freezing?

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zone melting Figure 1: Schematic representation of (A) normal freezing, (B) zone refining

When the distribution coefficient ( $k$ ) is below one, it indicates that the impurity atoms or molecules prefer the liquid phase over the solid phase during the freezing process.

In the context of zone melting, this preference means that as the material freezes, the impurity is rejected by the advancing solid and accumulates in the remaining liquid. Consequently, the impurity becomes concentrated in the last-to-freeze region of the material. Because the impurity is effectively "pushed" ahead of the solid-liquid interface, this property allows for the purification of the solid as the molten zone travels along the ingot.1