Ab initio thermodynamics of carbon segregation on dislocation cores in bcc iron

The equilibrium segregation of carbon atoms in the core of screw dislocations in body-centred cubic Fe is modelled using a generalized Ising model parametrized on density functional theory calculations and solved using both mean-field calculations and Monte Carlo simulations. Recently, a strong carbon-dislocation attraction was evidenced, resulting in a spontaneous reconstruction of the dislocation core towards a hard core configuration, where the carbon atom is located at the centre of a regular trigonal prism called a prismatic site. Here we show that the fourth neighbour octahedral sites of the reconstructed core are also attractive for carbon with a binding energy similar to that of the prismatic core site reported previously. This suggests that the dislocation may be decorated by lines of carbon atoms on both types of sites. Moreover, all carbon-carbon interactions including intra-line and inter-line interactions, are found repulsive. Segregation therefore results from a competition between the dislocation-carbon attraction and the carbon-carbon repulsion, leading to complex ordering phenomena that are analysed here in detail. Notably, we evidence a high temperature regime, in the regime of dynamical strain ageing of steels, where the prismatic line is half-occupied on average with every other prismatic site occupied by a carbon atom while the octahedral lines are empty. The iso-concentrations for the prismatic and octahedral lines obtained with the mean-field approach and with Monte Carlo simulations are qualitatively similar.