Energy for the interface system of (Nb, Mo)C/γ-Fe

Abstract

The interfacial energies of MC/γ-Fe and formation energies of MC carbides have been investigated using first-principles calculations based on density functional theory (DFT). Results show that the replacement of Nb by Mo in the NbC lattice is unfavorable with respect to the formation energy. However, it reduces the lattice parameter of MC and decreases the $$\sigma_{\text{chemical}}$$ (interfacial chemical energy) of MC/γ-Fe, thus favoring the formation of complex (Nb, Mo)C carbide. The substitution of Nb by Mo at the interface of MC/γ-Fe system promotes the hybridizations of Mo–1NNFe and C–1NNFe (or 2NNFe) (the first or second nearest neighboring Fe atoms), which leads to a decrease in $$\sigma_{\text{chemical}}$$ . The influence of bond energy is estimated using the discrete lattice plane/nearest neighbor broken bond (DLP/NNBB) model. It is found that the reduced $$\sigma_{\text{chemical}}$$ is attributed to the much smaller value of $$e_{{{\rm{Fe-C}}}} - e_{{{\rm{Mo-C}}}}$$ (the difference between Fe–C and Mo–C interactions) compared to $$e_{{{\rm{Fe-C}}}} - e_{{{\rm{Nb-C}}}}$$ (the difference between Fe–C and Nb–C interactions). The results obtained from the analysis of the precipitates in Nb- and Nb–Mo-bearing steels are in a good agreement with the calculations.