Carbon diffusion paths and segregation at high-angle tilt grain boundaries inα-Fe studied by using a kinetic activation-relation technique

Abstract

Carbon diffusion and segregation in iron is fundamental to steel production but is also associated with corrosion. Using the kinetic activation-relaxation technique (k-ART), a kinetic Monte Carlo (KMC) algorithm with an on-the-fly catalog that allows to obtain diffusion properties over large time scales taking into account long-range elastic effects coupled with an EAM force field, we study the motion of a carbon impurity in four Fe systems with high-angle grain boundaries (GB), focusing on the impact of these extended defects on the long-time diffusion of C. Short and long-time stability of the various GBs is first analyzed, which allows us to conclude that the $\mathrm{\ensuremath{\Sigma}}3(1\phantom{\rule{0.16em}{0ex}}1\phantom{\rule{0.16em}{0ex}}1)\ensuremath{\theta}=109.{53}^{\ensuremath{\circ}}\ensuremath{\langle}110\ensuremath{\rangle}\phantom{\rule{0.16em}{0ex}}\mathrm{GB}$ is unstable, with Fe migration barriers of \ensuremath{\sim}0.1 eV or less, and C acts as a pinning center. Focusing on three stable GBs, in all cases, these extended defects trap C in energy states lower than found in the crystal. Yet, contrary to general understanding, we show, through simulations extending to 0.1 s, that even tough C diffusion takes place predominantly in the GB, it is not necessarily faster than in the bulk and can even be slower by one to two orders of magnitude depending on the GB type. Analysis of the energy landscape provided by k-ART also shows that the free cavity volume around the impurity is not a strong predictor of diffusion barrier height. Overall, results show rather complex diffusion kinetics intimately dependent on the local environment.