Migration of Cr-vacancy clusters and interstitial Cr in α-Fe using the dimer method

The migration mechanisms and the corresponding activation energies of Cr-vacancy (Cr-V) clusters and Cr interstitials in α-Fe have been investigated using the dimer and the nudged elastic-band methods. Dimer searches are employed to find the possible transition states of these defects and the lowest-energy paths are used to determine the energy barriers for migration. A substitutional Cr atom can migrate to a nearest-neighbor vacancy through an energy barrier of 0.56 eV but this simple mechanism alone is unlikely to lead to the long-distance migration of Cr unless there is a supersaturated concentration of vacancies in the system. The Cr-vacancy clusters can lead to long-distance migration of a Cr atom that is accomplished by Fe and Cr atoms successively jumping to nearest-neighbor vacancy positions, defined as a self-vacancy-assisted migration mechanism, with the migration energies ranging from 0.64 to 0.89 eV. In addition, a mixed Cr-Fe dumbbell interstitial can easily migrate through Fe lattices, with the migration energy barrier of 0.17, which is lower than that of the Fe-Fe interstitial. The on-site rotation of the Cr-Fe interstitial and Cr atom hopping from one site to another are believed to comprise the dominant migration mechanism. The calculated binding energies of Cr-V clusters are strongly dependent on the size of clusters and the concentration of Cr atoms in clusters.