Effect of Point Imperfections on the Electrical Properties of Copper. I. Conductivity

Abstract

Changes in resistivity due to the addition of substitutional impurities and due to the presence of vacancies or interstitials in copper have been evaluated. It was assumed that the free-electron approximation is valid and that Matthiessen's rule holds. Relaxation of the lattice about the imperfections was neglected. The scattering potentials for the various imperfections were derived from the appropriate Hartree fields, and the partial wave method was employed in the evaluation of the scattering cross sections. In each case, the potentials were adjusted until the phase shifts satisfied the Friedel sum rule. The phase-shift calculations were carried out on the ILLIAC (University of Illinois Graduate School High Speed Electronic Digital Computer).The calculated resistivities due to small concentrations of gallium, germanium, and arsenic in copper, though consistently too large, are in fair agreement with measurements of Linde. The calculated change in resistivity due to interstitials in copper, 1.4 \ensuremath{\mu}ohm-cm per atomic percent, is essentially the same as that due to an equal concentration of vacancies. This result is at variance with earlier predictions based on annealing experiments on irradiated copper. A recent interpretation of the annealing spectrum of irradiated copper by Cooper, Koehler, and Marx appears to be consistent with the present results and offers agreement with a variety of theoretical and experimental work, although some difficulties remain unresolved.On the basis of the calculations reported here and comparison with Linde's results for dilute substitutional alloys of copper, it is concluded that the resistivity increase due to a concentration of one atomic percent of Frenkel defects in copper is probably between 1.5 and 2.0 \ensuremath{\mu}ohm-cm, with vacancies and interstitials contributing about equally to the scattering of conduction electrons.