LXXXVI. Fields around impurity atoms in metals

Abstract

Detailed calculations of the potential around impurity atoms with valency Z+l dissolved in a monovalent metal are reported. The first order or linearization approximation usually employed is avoided, and the basic Thomas-Fermi equation must then be solved numerically. The potentials thus obtained differ significantly from those, predicted by the first order approximation. The differences are always in the direction of a more effective shielding of the point charge Ze. The shielding depends appreciably on the valency of the dissolved impurity, whereas the first order result is a screened potential with a screening radius independent of Z. The connection between the present results and Friedel's second order approximation is briefly discussed. The calculations have then been extended to cover the case when we are dealing with a finite concentration of impurities, using the model of Friedel. Again we find that the results given by the first order approximation are appreciably in error. In all the numerical calculations we have taken copper as the solvent metal; the essential conclusions will however hold more generally.