Vacancies and Complexes in the Noble Metals

Abstract

In part I, the changes in resistivity of a noble metal on the introduction of vacancies into the lattice are calculated, taking into account the relaxation of the lattice around the defect site. The agreement between calculated and experimental resistivities is satisfactory for a particular model of the scattering power of the vacancy. Using this same model, it is then shown how the calculations of Fumi and Brooks concerning vacancy formation energies can be modified in the light of known surface energy data to yield quite reasonable predictions of formation energies of relaxed vacancies in noble metal lattices. The agreement between calculated and experimental resistivity data implies that the phase shift of electron waves at the Fermi surface are accurate and this in turn permits the prediction of the electron density in the neighborhood of the vacancy. In part II, this electron density is used in a treatment of the interaction energy between vacancies and substitutional impurities in the noble metals. The binding energies deduced in this way from scattering theory exhibit a strong dependence on the valence of the solute atom and are invariably positive for positive valence solutes at nearest neighboring lattice sites to a vacancy. The computed binding energies are quantitatively compatible with the available experimental data.The long-range characteristics of interaction between vacancies and both point and extended defects are also investigated in part II. Particular attention is drawn (a) to the oscillatory nature of the interaction as a function of the separation of the defects, and (b) to the different dependence on this separation for interactions concerning the different types of defect. Thus, in every case, the interaction energy oscillates with period $\frac{{k}_{F}}{\ensuremath{\pi}}$, ${k}_{F}$ being the Fermi energy, while the decay of amplitude with separation takes the form ${r}^{\ensuremath{-}3}$, ${r}^{\ensuremath{-}\frac{5}{2}}$, or ${r}^{\ensuremath{-}2}$ contingent upon the vacancy interacting with a second point defect, a dislocation, or a crystal boundary, respectively.