Thermodynamic Analysis of the Formation Mechanism of Metastable Carbides during Tempering of Fe–C Martensite

A thermodynamics analysis based on first-principles calculations was used to establish the behavior of carbon in the matrix during the preliminary stage of the tempering process of steel, as well as the formation mechanism of the η-carbide and cementite phases. Models were constructed in which carbon occupied three octahedral interstitial sites in BCC-Fe, and the cluster expansion and variation method was applied to evaluate the free energy of forming the solid solution. Furthermore, the thermal equilibrium distribution of carbon was obtained using the Monte Carlo simulation method by using the effective cluster interactions. The variable-cell nudged elastic band method was applied to evaluate the energy barrier that exists in the transition process. In addition, transition models considering the influence of interfaces were constructed. The Monte Carlo simulations of BCC-Fe showed well-defined clustering of carbon atoms. Furthermore, the free energies calculated from the cluster expansion and variation method showed two-phase separations between Fe and Fe2C, suggesting that these clusters are formed by two-phase separation based on atomic ordering. The energies of the transition processes to η-carbide and cementite were calculated from the structural models created based on these local structural findings. By comparing the energy barriers in each transition process, it is shown here that the metastable carbides may occur because of a series of following processes: η-carbide precipitates preferentially in the initial stage of tempering; consequently, cementite precipitates in the third stage using the η-carbides as precipitation sites, and finally, η-carbide transitions to cementite.