Interstitials and Vacancies inαIron

The migration energies and atomic configurations for mono- and di-interstitials and mono- and divacancies in $\alpha$ iron have been calculated using a classical model. About 530 atoms surrounding the defect were treated as individual particles, each with three degrees of freedom, while the remainder of the crystal was treated as an elastic continuum with atoms imbedded in it. A two-body central force was devised which matched the elastic moduli, was sharply repulsive at close separation, and which went to zero midway between the second and third neighboring atoms. Configurations were found by choosing a starting configuration roughly approximating the situation under consideration and successively adjusting the value of each variable occurring in the energy equation so that the magnitude of the generalized force associated with it was zero until equilibrium was reached. The energy calculations include changes in bond energy in the discrete region, energy in the elastic field, and work done against cohesive forces, but neglect changes due to the redistribution of electrons. Calculated activation energies for motion of mono- and di-interstitials and mono- and di-vacancies were 0.33, 0.18, 0.68, and 0.66 eV, respectively, and binding energies of di-interstitials and di-vacancies were 1.08 and 0.20 eV, respectively. The stable interstitial was a "split" configuration in which two atoms were symmetrically split in a $〈110〉$ direction about a vacant normal lattice site, and the stable di-interstitial consisted of two parallel split interstitials at nearest-neighbor lattice sites with their axes perpendicular to the line joining their centers. In the vacancy configuration an atom was missing from a normal lattice site, and the divacancy consisted of two vacancies at second-nearest-neighbor lattice sites.