Peritectic transformation with non-linear solute distribution in all three phases: Analytical solution, phase-field modeling and experiment comparison

Abstract

An analytical model is derived to predict the kinetics of a peritectic transformation involving solute diffusion in the L-, δ- and γ-phases with non-zero constant diffusivities. A similarity method is adopted to solve the diffusion equations in the bulk L-, δ-, and γ-phases coupled with the solute conservation equations at the γ/L and γ/δ interfaces. The proposed model is applied to predict the kinetics of the isothermal peritectic transformation of Fe-C alloys for two conditions, zero and non-zero supersaturation, in the δ- and L-phases. An excellent match between the analytical solutions and phase-field simulations is achieved. In the case of zero supersaturation, the time evolution of γ-phase thickness and non-linear concentration distribution in the γ-phase predicted by the present analytical model agree well with the experimental data reported in the literature. When the holding temperature decreases, the parabolic rate constant at the γ/δ interface increases non-linearly, while it remains nearly unchanged at the γ/L interface. Additionally, the non-zero supersaturation in the parent phases increases the diffusion flux jump significantly at the γ/L interface but only slightly at the γ/δ interface. As a result, the growth velocity increases noticeably at the γ/L interface, but it is nearly unchanged at the γ/δ interface.