Vacancy Formation and Trapping by Carbon in Ferritic Iron: A First‑Principles Study

The vacancy-carbon interactions control defect kinetics and the properties of ferritic iron. Here we use spin‑polarized density‑functional theory on 3×3×3 bcc‑Fe supercells with one to four carbon atoms in octahedral interstitial sites to quantify how carbon modifies vacancy energetics. Two limiting families are considered: dilute configurations with C far from the vacancy and compact VCₙ clusters ( n=1-4 ) with C placed in the nearest octahedral shell. For the dilute case, the vacancy formation energy remains close to that of pure Fe. In contrast, for compact clusters the effective formation energy of a vacancy bound to carbon, E f_VC , decreases markedly with increasing n, while the total binding energy increases and then saturates. The incremental stabilization E add stays positive up to n = 3 and turns negative for n=4 . E trap is small and positive for n=1-2, but becomes negative for n ≥ 3, consistent with carbon‑rich microenvironments biasing vacancies into VCₙ states. Increasing n moderately reduces N(E F ) , particularly in the minority-spin channel, which is consistent with strengthened Fe-C hybridization and the larger binding energies of the VC n complexes. Finally, using a Seydel thermodynamic trapping model parameterized by our ab initio E bind ( VC n ) we predict effective vacancy diffusivities D v_eff ( T,C tot ) that exhibit trends in line with prior analyses, while reflecting the stronger trapping implied by our energetics. Consistent with our DOS analysis, increasing carbon content strengthens Fe-C hybridisation, shifts Fe d states to lower energies and reduces N(E F ) , indicating a gradual transition from metallic Fe-Fe bonding to a more covalent Fe-C bond character. This work closes an important gap between electronic-structure data and mesoscale modelling by providing a consistent set of vacancy-carbon energetics and effective vacancy diffusivities for dilute C in α-Fe, which serves as a model system for ferritic Fe-based alloys.