Zwischengitteratome in kubisch-flächenzentrierten kristallen, insbesondere in kupfer

Abstract

We give a comprehensive discussion of the geometry of all the possible equilibrium or non-equilibrium configurations of interstitial atoms in f.c.c. crystals. It is shown that these occur within a polyhedron which occupies only a small fraction of the atomic volume. The interstitial in the stable equilibrium configuration, the so-called 〈100〉 dumb-bell, has two elementary modes of movement (migration and rotation). We characterize them by specifying the side of the polyhedron through which the interstitial atom has to move. The reorientation process of the dumb-bells under external strains gives rise to a relaxation effect, which is discussed in some detail. This relaxation process has been experimentally verified for cold-worked and irradiated nickel. The quantitative calculations of energies and displacements in seven symmetric equilibrium configurations is carried out for copper, employing an improved version of the model due to Seeger and Mann. The improvements allow, in particular, for the anisotropy of the elastic displacement field and for the large relative displacements of neighbouring atoms. The influence of the choice of the Born-Mayer potential and of various cut-off and correction procedures are discussed and allowed for in some detail. The more important numerical results are: energy of migration of an interstitial atom in copper, 0·5 ev; energy of formation, 2·8 ev; increase of the volume of a finite crystal due to one interstitial atom, 0·4 atomic volumes. The expansion of the crystal in the environment of the interstitial atoms was found to be slightly less than one atomic volume. Contrary to previous views, the region of the crystal containing the interstitial atom appears to be more densely packed than the ideal crystal. The relative change in the elastic constants due to the relaxation process of an atomic concentration c of interstitial atoms in copper is calculated to be of the order 20 c. As far as they could be checked, these results are in fair agreement with the experimental data. By introducing additional data, we find for the electrical resistivity in copper 2·5 μΩ cm/per cent Frenkel pairs and 0·9 μΩ cm/per cent interstitials.