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

Abstract

The electrical resistance of aluminum, tin, and copper alloys was measured at 4.2\ifmmode^\circ\else\textdegree\fi{}K, 77\ifmmode^\circ\else\textdegree\fi{}K, and from 198\ifmmode^\circ\else\textdegree\fi{}K to 348\ifmmode^\circ\else\textdegree\fi{}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\ifmmode^\circ\else\textdegree\fi{}K, the impurity resistivity, $\ensuremath{\delta}\ensuremath{\rho}$, for a given solvent may be described by the equation $\ensuremath{\delta}\ensuremath{\rho}=\ensuremath{\alpha}(T){\ensuremath{\rho}}_{r}$, where ${\ensuremath{\rho}}_{r}$ is the residual resistivity, measured at 4.2\ifmmode^\circ\else\textdegree\fi{}K, and $T$ is the temperature. This result is indepent of the nature of the solute. $\ensuremath{\alpha}$ is constant in the temperature region 198\ifmmode^\circ\else\textdegree\fi{}K to 348\ifmmode^\circ\else\textdegree\fi{}K. For aluminum and tin $\ensuremath{\alpha}(273)=1.12$, whereas for copper $\ensuremath{\alpha}(273)=1.05$. The value of $\ensuremath{\alpha}(77)$ is about the same as at 273\ifmmode^\circ\else\textdegree\fi{}K for aluminum and copper, but for tin $\ensuremath{\alpha}(77)=1.08$. The temperature coefficient of the impurity resistivity for $198\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}<T<348\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$ was no larger than 1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ ${(\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\mathrm{K})}^{\ensuremath{-}1}$. It is pointed out that while several different theoretical models qualitatively describe these results, none can be quantitatively compared with experiment.