Point-Defect Calculations for an fcc Lattice

Formation and migration energies and atomic configurations have been calculated for interstitials and vacancies in an fcc lattice, and the interaction of close Frenkel pairs has been studied. A mathematical model was used in which the atoms in a spherical crystallite of about 530 atoms are treated as individual particles, each with three degrees of freedom, while the remainder of the crystal is treated an an elastic continuum with atoms imbedded in it. A two-body central force previously used in calculations for $\alpha$-iron (a bcc metal), was used to simulate the interaction of atoms in the fcc lattice. Configurations were found using a digital computer 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 object of this calculation was to investigate the consequences of using an interatomic interaction for an fcc metal with a form similar to that used for previous bcc calculations. The interaction used should be reasonably appropriate for both $\gamma$-iron and nickel and the results are compared with experimental values for both metals. The stable interstitial was a "split" configuration in which two atoms were symmetrically split in a $〈100〉$ direction about a vacant normal lattice site. The formation energy was 4.08 eV and the activation energy for motion was 0.15 eV. A number of metastable configurations were found, the most important of which was the $〈111〉$ "split" interstitial, which was metastable by 0.16 eV and had a migration energy of 0.13 eV. The vacancy formation energy and activation energy for migration were 1.49 and 1.32 eV, respectively. The interaction between a vacancy and an interstitial was very complex and short in range. Configurations were found which were bound, repulsive, and trapped, and there were 32 unstable lattice sites.