Point Defects in Copper

The atomic configurations and energies for point defects in copper have been studied theoretically using a classical model. The atoms near the defect are treated explicitly while the remainder of the crystal is treated as an elastic continuum with atoms imbedded in it. A Born-Mayer repulsive force law, $A{e}^{-\alpha r}$, is assumed to act between nearest neighbors. Vacancies, interstitials, di-vacancies, and di-interstitials have been considered. Configurations are found by choosing a starting configuration roughly approximating the situation under consideration, and an iterative process of successively adjusting the value of each variable occurring in the equation for energy such that the magnitude of the generalized force acting on it is minimized. 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. Various aspects of the model and method of calculation have been investigated, and the effects of electron redistribution are discussed. Predicted activation energies for motion of interstitials and vacancies are 0.05 and 0.43 eV, respectively. An upper limit of 0.26 eV has been found for the activation energy for migration of di-interstitials. The isolated interstitial has been thoroughly investigated, and eight well-defined equilibrium configurations have been found. Only one of these is stable, being the case in which two atoms are symmetrically split in the $〈100〉$ direction about a vacant normal lattice site. The configuration in which the interstitial is located at a body center is found to be a local maximum, but the saddle point configuration for migration of interstitials is quite close to it.