Interactions between interstitial and substitutional elements of solute diatomic and triatomic clusters in α-Fe from first-principles calculations

In this study, we investigated the interaction energies of solute diatomic clusters (M-C/M-N) and triatomic clusters (M-C-M/M-N-M) in α-Fe, where M represents substitutional elements (Al, Si, Ti, V, Cr, Mn, Co, Ni, Cu, Zr, Nb, Mo) and X represents C or N atoms. Key findings include: (1) Positive interaction energies at the first nearest neighbor (1nn) indicate repulsion, while specific M-X pairings, such as Ti-C/N and Zr-C/N, exhibit negative interaction energies at the second nearest neighbor (2nn), indicating attraction. (2) Attractive triatomic clusters, observed in Fe-Zr-C, Fe-Zr-N, Fe-Ti-N, Fe-V-N, and Fe-Nb-N systems, were limited to (2,2,2) and (2,2,3) configurations. (3) A larger metallic radius correlates with 1nn repulsion and 2nn/3nn attraction, while increased valence p electrons in M-X clusters cause repulsion, and more valence d electrons in M-M clusters lead to attraction. The stable (2,2,2) and (2,2,3) triatomic clusters in Fe-Ti-N, Fe-V-N, and Fe-Nb-N systems align with experimentally observed monolayer clusters of Ti-N, V-N, and Nb-N. However, our linear combination model of M-X and M-M interactions could not fully explain the formation of B1-type MX compounds, such as MoN and TiC, highlighting the need for further computational studies.