Interstitial substitutional model for the anomalous diffusion in Pb and Pb alloys

A model is proposed which involves interstitial, substitutional, and disubstitutional defects along with the equilibrium fraction of each defect type. The lead diffusivity data from a variety of experimental measurements are reinterpreted in terms of this model. Both enhancement and de-enhancement diffusivity results as a function of impurity content are discussed for both impurity and self-diffusion. Impurity diffusion in the limit of small impurity concentration is analyzed. The resulting system reduces to a two-defect interstitial-substitutional model. Questions pertaining to the large variation in the measured activation energies and volumes are discussed. The model explains why impurity-lead diffusion couples that appear to be predominantly interstitial or substitutional in nature give activation volume results which are not characteristic of either an interstitial or substitutional mechanism. The isotope effect has been reanalyzed in terms of the proposed model and the small values of $f\Delta K$ of 0.12, 0.25, and 0.23 for Cd, Ag, and Cu, respectively, in Pb are interpreted in terms of small changes in the interstitial and substitutional energy states, amounting to about 2 × ${10}^{-4\mathrm{}}$ eV/atomic mass unit. The equilibrium fraction of interstitial defects as a function of temperature and pressure was calculated for each of the diffusion couples, Cu, Ag, Au, Ni, Pd, Pt, Zn, Cd, Hg, and Sn in Pb, as was the pressure and temperature dependence of pure interstitial substitutional diffusivity.