Effective segregation coefficient in cluster crystallization model

An expression for the effective segregation coefficient keff is derived at the assumption that the crystallization begins in the melt within the supercooled diffusion layer by the formation of complex anion structures (clusters). The dependence of keff on the equilibrium segregation coefficient k0, the thickness of the supercooled boundary layer σ and the crystal growth rate V is determined for a low supercooling at the melt-crystal interface. There is no necessity to introduce the concept of the interface segregation coefficient (which is equal to the ratio of the concentration in the crystal to that in the melt at the interface), when the presence of the anion structures in the melt is taken into account. The mutual dependence of V and σ is considered. The formula derived fits well to the experimental data for the range of the low crystal growth rates.