Point-defect calculations for tungsten

Abstract

Computer-model calculations have been carried out for vacancies, divacancies, and interstitials in tungsten using an interatomic potential developed by Johnson and White. Full relaxation of the 531 atoms closest to the defect is carried out by the model, and surrounding atoms are constrained to displace elastically. With an input into the model of a vacancy formation energy of 3.60 eV, the vacancy migration energy, formation volume, and migration volume were 2.00 eV, $0.79\ensuremath{\Omega}$, and $\ensuremath{-}0.08\ensuremath{\Omega}$, respectively ($\ensuremath{\Omega}$ is the atomic volume). The second-neighbor divacancy was most stable and migrated through partial separation to the fourth neighbor divacancy. The binding energy and volume were 0.78 eV and $0.08\ensuremath{\Omega}$, respectively, and migration was similar to that for single vacancies. The potential had to be modified for interstitial calculations to provide repulsion at near separations. For a hard repulsion, the formation energy was large (13.04 eV), the migration energy large (1.05 eV), and the formation volume small ($0.13\ensuremath{\Omega}$), while for a soft repulsion, the formation and migration energies were smaller (9.30 and 0.20 eV, respectively) and the formation volume was negative ($\ensuremath{-}0.65\ensuremath{\Omega}$). Although these calculations do not yield unambiguous results, they suggest that high-temperature curvature in self-diffusion data for tungsten is not caused by divacancies or by single interstitials.