This refining procedure, which has been theoretically suggested by Petrov [1] and realized by Pfann [2], is the main industrial method used in the production of extra-high-purity metals and semiconductors. The principle of the method lies in the partitioning of solute atoms between the liquid and the solid phases, with solid being much purer in certain solute elements than the liquid. In this method, a narrow zone of liquid metal is made to travel slowly through the ingot, thus moving impurities by partitioning and diffusion from the refined part of the ingot to the untreated part. In the general case, the efficiency of this method is characterized by the equilibrium partition coefficient k0, which is defined as the ratio of the solute impurity concentrations in the solid and liquid phases, taken according to the phase diagram,



= (11.1)

where Cs and Cl are, respectively, the concentrations of the solute element in the solid and liquid phases in equilibrium at the same temperature. The partition coefficient is smaller or greater than unity, depending on whether the liquidus and solidus of the alloy decrease (eutectic systems) or increase (peritectic systems) with increasing the amount of the solute impurity.