Distortion of the Lattice around an Interstitial, a Crowdion, and a Vacancy in Copper

Abstract

A general method for calculating lattice distortions around point defects is proposed. Atoms in a sufficiently large region I around the defect and in a "boundary" region II around region I are treated as discrete particles. A set of proper elastic solutions is joined to the displacements of the atoms in region II. The equilibrium state of the lattice is determined by successive solution of sets of linear algebraic equations. Actual calculations have been done with the help of the Illiac digital computer for an interstitial, a crowdion, and a vacancy in copper. The changes in volume of the crystal arising from these defects are found to be 1.7, 1.1, -0.53 and 2.0, 1.3, -0.45 atomic volumes respectively for the two Born-Mayer repulsive potentials we have used. [See Eqs. (7).] In addition to the distortion of the lattice around an isolated defect, we treat the distortion around an interstitial-vacancy pair. The electronic contributions to the formation energies of the defects considered are estimated in a way similar to that used by Fumi in the case of a vacancy. However, the change in the effective charge of the defect with lattice dilation is also taken into account. The formation energy of a crowdion is found to be about 0.6 ev higher than that of an interstitial. The calculated values of the change in volume are discussed in connection with recent experimental results on radiation damage in copper.