Modeling competitive precipitations among iron carbides during low-temperature tempering of martensitic carbon steel

Upon tempering of martensitic carbon steels, transition carbides (TCs), as precipitated precursors that compete for available C atoms among multiple iron carbides, have tremendous influences on the microstructural evolution and the final properties of steels. Although two similar structures of TCs, i.e. the hexagonal ε-Fe₂C and the orthorhombic η-Fe₂C, were successively identified, they still cannot be clearly distinguished experimentally, so far. It is timely to grasp the corresponding atomic-scale nature to predict the real structure of TCs. Based on the maximal entropy production principle and the atomic-scale computations, a Fokker-Planck type equation (FPE) following a modified multi-scale modeling framework, is solved for competitive precipitations among the potential iron carbides (including ε-Fe₂C, η-Fe₂C and θ-Fe₃C) during the low-temperature tempering of carbon steel. The obtained microstructural evolution path dominated by synergy of thermodynamics and kinetics indicates a precipitation sequence for TCs, i.e. ε → η, which is further verified by the minimum energy path in terms of the solid-state nudged elastic band (SSNEB) method. On this basis, the potential hexagonal-orthorhombic transformation (HOT) of TCs is discussed, by which the probable structure of TCs can be accurately identified in experiment. The current modeling framework is expected to be a worthy paradigm for reference to predict the structural evolution of TCs in engineering materials.