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The Finnis-Sinclair (FS) potential is one of the three-body potentials and the potential function is the simplest in them. We developed the FS potential for an Fe-C binary system without changing the original form of the function. The potential parameters for the Fe-C and C-C interactions were determined to fit the physical properties (structural parameters, bulk modulus and cohesive energy) of five iron carbides (γ′-Fe4C, θ-Fe3C, χ-Fe5C2 ο-Fe7C3 and NaCl type-FeC). The developed potential reproduced fourteen iron carbides and migration energy barriers of interstitial carbon atoms in body-centered cubic (bcc) and face-centered cubic (fcc) irons. Moreover, the reproducibility of the phonon densities of states for the iron atoms of cementite (θ-Fe3C) and hexagonal-Fe7C3 (h-Fe7C3) was confirmed and the diffusion coefficient of carbon atoms in bcc iron was good agreement with the experimental value.

A new empirical potential for the Fe-N binary system based on the Finnis–Sinclair (FS) potential was developed in order to analyze the strengthening mechanism of N addition in ferritic and austenitic steels. The potential parameters for the Fe-N and N-N interactions were determined to reproduce the physical properties of the first principles calculation data of four iron nitrides (ZnS type-FeN, e - F e 3 N , γ ′ - F e 4 N and α ′ ′ - F e 16 N 2 ) obtained in this study. Furthermore, we investigated the reproducibility of physical properties of the other nitrides (NaCl type-FeN, e - F e 2 N and ζ - F e 2 N ) and the N behavior in body-centered cubic (bcc) and face-centered cubic (fcc) iron. The results showed good agreement with reference data.