Impurity and temperature dependence of the electrical resistivity of dilute alloys of aluminum

Abstract

The low-temperature electrical resistivity of dilute alloys of aluminum is calculated by the variational method, based on the special properties of the electron distribution function for electron-phonon scattering. Excellent agreement is obtained with the resistivity data, both as a function of temperature and as a function of impurity concentration. The calculation is based on a multiple-OPW (orthogonalized planewave) description for all relevant properties of aluminum. The interference terms, resulting from the coupling between the transition probabilities for electron-phonon scattering and electron-impurity scattering, are explicitly calculated and found to be generally small. However, in the dirty limit, the interference terms become important and are responsible for the observed lack of saturation of the resistivity as a function of impurity concentration. Including the interference terms leads to agreement between theory and experiment for the resistivity over five decades of impurity concentration. Finally, the humps observed in the resistivity-versus-temperature curves at somewhat higher temperatures are accurately reproduced by the calculation.