Calculations of Small Vacancy and Interstitial Clusters for an fcc Lattice

Binding and migration energies and atomic configurations have been calculated for small vacancy and interstitial clusters in an fcc lattice with a model which should be applicable to nickel. The mathematical model consisted of a spherical crystallite containing about 530 atoms which were treated as individual particles surrounded by an elastic continuum with atoms imbedded in it. A two-body central force was used to simulate the interaction between nearest-neighbor atoms in the crystallite, and the elastic continuum provided a pressure which held the crystallite in equilibrium. The binding and migration energies for divacancies and di-interstitials were ${E_{2V}}^B=0.25\mathrm{}$, ${E_{2V}}^M=0.90\mathrm{}$, ${E_{2I}}^B=1.16\mathrm{}$, and ${E_{2I}}^M=0.29\mathrm{}$ eV. The binding energy of larger vacancy clusters was approximately equal to the energy in the nearest-neighbor "bonds" between vacancies, each "bond" contributing 0.25 eV. The vacancy-cluster migration energy increased slowly with the size of the cluster but was still less than the single-vacancy migration energy, ${E_{\mathrm{IV}}}^M=1.32\mathrm{}$ eV, for small clusters. Spherical vacancy clusters were the most stable, although an estimate was made that a platelet on a {111} plane would collapse into a dislocation loop after absorbing somewhat more than 180 vacancies and that this loop might be more stable than a spherical cluster which had absorbed the same number of vacancies. Interstitial clustering was more complex, but in general binding energies were large and migration energies increased with cluster size, although they never got as large as that for the divacancy, the most easily migrating vacancy complex.