laws of distribution in precipitation

During the formation of a mixed crystal from a solution containing two components 'A' and 'B', the latter may be distributed according to the equation

$K A , B = b ( a 0 − a ) a ( b 0 − b )$ .

In this homogeneous distribution, $a 0$ and $b 0$ are the respective concentrations in the solution before crystallization and $a$ and $b$ are the respective concentrations in the solution after crystallization. $K A , B$ is usually called the separation factor. The term homogeneous distribution coefficient is not recommended. Alternatively the distribution of the micro-component may follow the equation of Doerner and Hoskins

$ln ( a 0 a ) = λ ln ( b 0 b )$

(logarithmic distribution) where $λ$ is usually called the logarithmic distribution coefficient, the meaning of the other symbols remaining the same. Exactly homogeneous or logarithmic distributions are extreme cases and very seldom encountered.

Source:

Orange Book, p. 85