Concurrent γ-phase nucleation as a possible mechanism of δ-γ Massive-like phase transformation in carbon steel: Numerical analysis based on effective interface energy

Effective interface energies of various homo- and hetero-interfaces of iron were calculated with an aid of phase-field modeling, taking into account geometric constraints by competition among grains or interfaces. Calculated effective interface energies for δ/γ, δ/δ, and γ/γ interfaces are 0.56, 0.44 and 0.37 J/m2, respectively. Using two simple geometric models for nucleation on or off an interface in the matrix, the optimal shape of a nucleus at a given radius and undercooling, a critical radius and an energy barrier for nucleation for each possible circumstance were numerically calculated. It is found that, although the energy barrier for γ-phase nucleation in homogeneous δ-phase matrix is more than three orders of magnitude greater than that for homogeneous solidification of δ-phase, the γ nucleation on a δ/δ grain boundary in the solidifying matrix suppresses the energy barrier, increasing a nucleation rate. Furthermore, it is found that the γ-phase nucleation on an existing γ nucleus halves undercooling needed with smaller critical radius. This suggests that, once γ nucleation is initiated, then following γ nucleation is promoted by doubled driving force, enabling multiple γ nucleation as in chain reaction. These findings are sufficient to explain experimentally observed phenomena during the δ-γ massive-like phase transformation even if other factors such as solute re-distribution or transformation is neglected.