Application of Equilibrium State Diagrams for Calculating Segregation Kinetics during Cooling of a Two-Component Melt

According to equilibrium state diagrams, compositions of liquid and solid phases are determined by corresponding diagram curves at the melt cooling to below the liquidus temperature. For equilibrium to occur, the following is necessary: the melt is kept indefinitely at each temperature; or the thermal conductivity of the liquid and solid phases, as well as the diffusion coefficients of their components, are infinitely large. This study attempts to find out how these processes occur in reality. An individual crystal growth during cooling of a two-component melt is considered. A mathematical model is designed based on the following standings: (i) a melt region with a volume per one grain, the periphery of which is cooled according to a certain law, is selected; (ii) at the initial time, the crystal nucleus with a certain minimal size is in the liquid; (iii) near the crystal surface, the compositions of the liquid and solid phases correspond to a state diagram for the considered temperature on its surface; and (iv) changes in temperature and composition in the liquid and solid phases occur according to the heat conduction and diffusion laws, respectively. As the melt cools and the crystal grows, the liquid phase is enriched in one component and depleted in another, while the solid phase occurs in reverse. The component’s diffusion coefficient in the solid phase is small. Therefore, its composition does not completely equalize over the cross section. The model proposed here makes it easier to study this phenomenon and to calculate the crystal composition for each cooling mode as it moves away from its center. The calculations showed that the temperature equalizes almost instantly while the composition equalization of the liquid phase occurs much slower. The solid phase’s composition during observation practically does not equalize. The obtained results will be useful for improving the production technology for alloys with an optimal structure.