Deviations from Matthiessen's Rule in Aluminum, Tin, and Copper Alloys

The electrical resistance of aluminum, tin, and copper alloys was measured at 4.2°K, 77°K, and from 198°K to 348°K. The aluminum alloys contained zinc, magnesium, germanium, or silver in various concentrations. The alloys of tin contained indium, antimony, or bismuth; and those of copper contained zinc. At temperatures above 77°K, the impurity resistivity, $\delta \rho$, for a given solvent may be described by the equation $\delta \rho =\alpha \mathrm{}\left(T\right)\mathrm{}{\rho }_r$, where ${\rho }_r$ is the residual resistivity, measured at 4.2°K, and $T$ is the temperature. This result is indepent of the nature of the solute. $\alpha$ is constant in the temperature region 198°K to 348°K. For aluminum and tin $\alpha \mathrm{}\left(273\right)=1.12\mathrm{}$, whereas for copper $\alpha \mathrm{}\left(273\right)=1.05\mathrm{}$. The value of $\alpha \mathrm{}\left(77\right)\mathrm{}$ is about the same as at 273°K for aluminum and copper, but for tin $\alpha \mathrm{}\left(77\right)=1.08\mathrm{}$. The temperature coefficient of the impurity resistivity for $198°\mathrm{K}<T<\mathrm{}348\mathrm{}°\mathrm{K}$ was no larger than 1×${10}^{-3\mathrm{}}$ ${\left(\mathrm{°}\mathrm{K}\right)}^{-1\mathrm{}}$. It is pointed out that while several different theoretical models qualitatively describe these results, none can be quantitatively compared with experiment.