Phase-field Model for Solidification of Ternary Alloys

Abstract

The phase-field model for dilute ternary alloys is proposed and the relationships between phase-field parameters and material properties are derived at a thin interface limit. One-dimensional and two-dimensional numerical simulations show that the model reproduces the equilibrium conditions including Gibbs–Thomson effect. We apply the model for ternary alloys to micro-segregation analysis in Fe–C–P alloy and the results are compared with analytical models. The results show good agreement with those of Clyne–Kurz equation. For two-dimensional computations, isothermal dendritic growth is simulated for Fe–C and Fe–C–P alloys. The change in phosphorous concentration affects significantly the interface velocity and the dendrite shape even when the phosphorous concentration is much lower than that of carbon because of the small diffusivity of phosphorous.