Metallic-covalent interatomic potential for carbon in iron

Existing interatomic potentials for the iron-carbon system suffer from qualitative flaws in describing even the simplest of defects. In contrast to more accurate first-principles calculations, all previous potentials show strong bonding of carbon to overcoordinated defects (e.g., self-interstitials, dislocation cores) and a failure to accurately reproduce the energetics of carbon-vacancy complexes. Thus any results from their application in molecular dynamics to more complex environments are unreliable. The problem arises from a fundamental error in potential design—the failure to describe short-ranged covalent bonding of the carbon $p$ electrons. We describe a resolution to the problem and present an empirical potential based on insights from density-functional theory, showing covalent-type bonding for carbon. The potential correctly describes the interaction of carbon and iron across a wide range of defect environments. It has the embedded atom method form and hence appropriate for billion atom molecular-dynamics simulations.

Figure 1

Fitted forms for the embedding functions showing the implementation of solvation and bonding via the embedding parts of our potential. The regions associated with solvation and bonding within the carbon embedding function, $F^{\left(\text{C}\right)}$, are indicated. Energies are in electron volts and distances in angstroms.

Figure 2

(a) $O$ and $T$ interstitial sites for carbon (black circles) in an unrelaxed bcc unit cell of iron atoms (white circles). (b) Configurations containing two interacting carbon atoms in neighboring octahedral sites. Distinct configurations are labeled by the position of the second carbon atom.

Figure 3

Distinct octahedral sites for carbon surrounding a $⟨110⟩$-self-interstitial defect. The site nomenclature is also valid for a vacancy defect after removing the superfluous letter.