Electrical Resistivity and Deviations from Matthiessen's Rule in Dilute Alloys of Aluminum, Cadmium, Silver, and Magnesium

Abstract

Absolute values of the electrical resistivity of polycrystalline silver, aluminum, cadmium, and magnesium and over 20 dilute binary alloys of these metals with different solute concentrations have been measured from 1.5 to 300 °K. From the resistivity data, deviations $\Delta$ from Matthiessen's rule have been evaluated for the alloys. Deviations with positive as well as negative sign have been observed at temperatures above 50 °K. These deviations, for all except the hcp alloys of cadmium containing magnesium as a solute ($\mathrm{Cd}-\mathrm{M}\mathrm{g}$ alloys), can be explained in terms of a two-band contribution, which can only be positive, and an interference term between the scattering of electrons by lattice vibrations of the host atoms and the excess potential due to the vibrating impurities, which can have either sign. The deviations for $\mathrm{Ag}-\mathrm{C}\mathrm{d}$, $\mathrm{Ag}-\mathrm{M}\mathrm{g}$, $\mathrm{Ag}-\mathrm{A}\mathrm{l}$, and $\mathrm{Al}-\mathrm{M}\mathrm{g}$ alloys increase linearly with temperature and those for $\mathrm{Al}-\mathrm{A}\mathrm{g}$, $\mathrm{Cd}-\mathrm{A}\mathrm{g}$, and $\mathrm{Mg}-\mathrm{A}\mathrm{l}$ decrease linearly with temperature in this range. Combined with published data for $\mathrm{Mg}-\mathrm{A}\mathrm{g}$ alloys, these results are in excellent qualitative agreement with the predictions of Bhatia and Gupta, who showed that the interference term should be important at high temperatures and should change sign when the ions on the host and impurity sites are interchanged. This agreement is further strengthened by comparison of the slope $\frac{d\Delta }{\mathrm{dT}}$ of the experimental results for the alloys of magnesium and aluminum with a semiquantitative calculation by Gupta. Near 250 °K $\Delta$ is negative and $\frac{d\Delta }{\mathrm{dT}}$ is temperature dependent for $\mathrm{Cd}-\mathrm{M}\mathrm{g}$ alloys, and further work is required to clarify this result. Below about 50 °K deviations for all alloys are positive, and the various contributions are discussed. The precise resistivity results obtained over a wide temperature range extend our knowledge of deviations from Matthiessen's rule, but the complexity of the scattering processes makes a detailed comparison with theory difficult, particularly at low temperatures.