## Solid solution formation

Mixtures of components that exhibit solid solution behaviour cannot be separated in a single step as can, for example, simple eutectic systems. Multistage or fractional precipitation schemes must therefore be employed (section 7.1). The distribution of an impurity between the solid (i.e. solid solution) and liquid phases may be represented by the Chlopin (1925) equation:

y \b - yj where a and b are the amounts of components A and B in the original solid, - and y are the amounts of A and B in the crystallized solid and a-x and b-y are the amounts of A and B retained in the solution. D is a distribution coefficient. Alternatively, the logarithmic Doerner-Hoskins (1925) equation may be used:

The constant A has been called a heterogeneous distribution coefficient to distinguish it from the homogeneous distribution coefficient D in equation 8.15. Under ideal conditions D = A.

If component A is the impurity, A > 1 indicates that the impurity will be enriched in the precipitate. Conversely, if A < 1 it will be depleted. A schematic diagram of the effect of precipitation rate on A is shown in Figure 8.6 (Walton, 1967). In enrichment systems, A ^ Ae = De as the precipitation rate tends to zero. For fast rates of precipitation A ^ 1. For depletion systems, an analogous situation exists with A ^ Ad = Dd for very slow precipitation and A ^ 1 for rapid precipitation.

Both the Chlopin and Doerner-Hoskins relationships have been widely used to correlate the results of fractional precipitation and recrystallization schemes

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