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

An analytical model is derived to predict the kinetics of a peritectic transformation involving solute diffusion in the L-, delta- and gamma-phases with non-zero constant diffusivities. A similarity method is adopted to solve the diffusion equations in the bulk L-, delta-, and gamma-phases coupled with the solute conservation equations at the gamma/L and gamma/delta 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 delta- 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 gamma-phase thickness and non-linear concentration distribution in the gamma-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 gamma/delta interface increases non-linearly, while it remains nearly unchanged at the gamma/L interface. Additionally, the non-zero supersaturation in the parent phases increases the diffusion flux jump significantly at the gamma/L interface but only slightly at the gamma/delta interface. As a result, the growth velocity increases noticeably at the gamma/L interface, but it is nearly unchanged at the gamma/delta interface. (C) 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.