Solidification partition ratio

At the solid/liquid interface, the concentration of the impurities in the solidified Si will be in equilibrium with the molten metal. The ratio between the two concentrations is defined as the partition coefficient, given by k = Cs/C, where Cs and C are the concentrations of solid and liquid. For k values less than 1, there will be a refining effect. The principle of refining by solidification is illustrated in Fig. 1.12. 

Recall from Chapter 12 that the partition coefficient k was defined as the ratio of solid component Cs to the liquid component Cl at the solidification interface. In the phase diagram shown in Figure 13.3, the fc = Ci/Co at Ti and = Co/C2 at Tq. In this case, k is seen to vary with temperature. For dilute systems (alloys in which the second component is a small fraction of the host component), k can be taken to be a constant and can be defined as the ratio of the slope of the liquidus to the slope of the solidus. Even for nondilute alloys, assuming k to be constant is a reasonable approximation for most systems. 

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