A mathematical model of segregation during cooling of the melt of iron with phosphorus

The purpose of this work is to study in detail the process of phosphorus segregation during steel solidification. A mathematical model considering a spherical melt cell with the nucleus of a solid phase in the center has been created. It has assumed that the thermal processes in this system are in accordance with the law of thermal conductivity and the mass transfer of phosphorus in the liquid and solid phases obeys the law of diffusion. In addition, it has assumed that a local equilibrium is maintained at the interface between these phases and the parameters of this equilibrium can be determined from the equilibrium phase diagram Fe-P. It has been assumed that the outer boundary of the system is cooled according to a mode that is set arbitrarily. Based on the obtained equations, a computer program has been created, that allows obtaining the temperature and the phosphorus content at any point at any time. The calculations have shown that the temperature alignment in of the system is almost instantaneous, and the concentration of phosphorus in the liquid phase has aligned quickly. However, the phosphorus concentration in the solid phase aligns much slower due to the small phosphorus diffusion coefficient in the solid phase. The principal factors determining the segregation of phosphorus are the initial concentration and the melt cooling mode. The results will help to calculate the cooling mode of the melt to produce a metal with the desired properties.