Diffusion properties of Fe-C systems studied by using kinetic activation-relaxation technique

Diffusion of carbon in iron is associated with processes such as carburization and the production of steels. In this work, the kinetic activation-relaxation technique (k-ART) - an off-lattice self-learning kinetic Monte Carlo (KMC) algorithm - is used to study this phenomenon over long time scales. Coupling the open-ended ART nouveau technique to generate on-the-fly activated events and NAUTY, a topological classification for cataloging, k-ART reaches timescales that range from microseconds to seconds while fully taking into account long-range elastic effects and complex events, characterizing in details the energy landscape in a way that cannot be done with standard molecular dynamics (MD) or KMC. The diffusion mechanisms and pathways for one to four carbon interstitials, and a single vacancy coupled with one to several carbons are studied. In bulk Fe, k-ART predicts correctly the 0.815 eV barrier for a single C-interstitial as well as the stressed induced energy-barrier distribution around this value for 2 and 4 C interstitials. For vacancy-carbon complex, simulations recover the DFT-predicted ground state. K-ART also identifies a trapping mechanism for the vacancy through the formation of a dynamical complex, involving C and neighboring Fe atoms, characterized by hops over barriers ranging from ∼0.41 to ∼0.72 eV that correspond, at room temperature, to trapping time of hours. At high temperatures, this complex can be broken by crossing a 1.5 eV barrier, leading to a state ∼0.8 eV higher than the ground state, allowing diffusion of the vacancy. A less stable complex is formed when a second C is added, characterized by a large number of bound excited states that occupy two cells. It can be broken into a V-C complex and a single free C through a 1.11 eV barrier.