Magnetism is largely responsible for the body centered cubic to face centered cubic structural phase transition occurring in iron at 1185 K and to many anomalies in the vicinity of the ferromagnetic to paramagnetic phase transition at 1043 K, as for instance an anomalous softening of the tetrahedral shear modulus. Current atomistic models including magnetism are either limited to the treatment of perfect lattice models or to zero temperatures, while research and development of candidate materials for future fission and fusion power plants requires the modeling of irradiation induced defects in ferritic/martensitic steels at high temperatures. An attempt to fill this gap is the Dudarev-Derlet potential, which includes zero temperature magnetism in an embedded atom method formalism, together with a more recent extension of the method to the inclusion of spin rotations at non zero temperature with nearly half the computational speed of an embedded atom method potential. In this work, we report on the optimization of the Dudarev-Derlet potential to the zero temperature bulk properties of the non-magnetic and ferromagnetic bcc and fcc phases, including the third order elastic constants of the ferromagnetic bcc phase, the point defects formation and migration energies and the core structure of the screw dislocation with Burgers vector 1/2[111], either from experiments or from density functional theory calculations, where we develop a method to fit the core structure of the screw dislocation based on the Suzuki-Takeuchi model. Three representative fits from the optimization of the Dudarev-Derlet potential are compared with recent semi empirical potentials for iron, with density functional theory and experiments. The migration energies of the self-interstitial range from 0.31 eV to 0.42 eV, compared to a density functional theory value close to 0.35 eV and an experimental value close to 0.3 eV, and the vacancy migration energies range from 0.85 eV to 0.94 eV, compared to a density functional theory value close to 0.65 eV. Clusters composed of parallel self-interstitials are oriented along ‹110› if the number of interstitials composing the cluster is smaller or equal than 3, while for bigger clusters the ‹111› orientation is more stable, in qualitative agreement with density functional theory. Depending on which one of the three representative fits is chosen, the formation entropy of one ‹110› dumbbell calculated by the thermodynamical integration method in the range from 300 K to 600 K varies from 0.28 kB to 4.02 kB. The diffusion coefficient of the ‹110› dumbbell at 600 K ranges from 1×10-6 cm2/s to 10×10-6 cm2/s, while at room temperatures the scatters extends over three orders of magnitude. The main difficulties, common to all the semi empirical potentials considered in the work, are related to the description of the fcc phase and the migration mechanism of the screw dislocation. The semi empirical potentials are unable to distinguish the anti-ferromagnetic fcc from the low spin ferromagnetic fcc or the high spin ferromagnetic fcc. Considering the equilibrium volume and the bulk magnetic moment, the high spin phase is the one which most resembles the ferromagnetic fcc phase of the Dudarev-Derlet potentials. Finally, for those fits with a non-degenerate core structure, we investigate some fundamental aspects of the migration mechanism of the screw dislocation with Burgers vector 1/2[111] at zero temperature and at zero applied stress, by calculating the Peierls potential in the [211] direction between two structurally equivalent soft cores. This confirms the existence of a stable core structure in the middle of the migration path not observed in density functional theory, which is actually found to be energetically degenerate with the soft core. The consequences of this are discussed in terms of formation energies of double kinks in the [211] direction.
EPFL2010
