Deviations from Matthiessen's Rule in Dilute Gold and Platinum Alloys

Abstract

The electrical resistivity of dilute alloys of gold with Ag, Cu, Pt, and Co and of platinum with Au and Rh has been measured, together with the resistivity of the pure solvent metals, between 1.6 and 373\ifmmode^\circ\else\textdegree\fi{}K. The solute concentration ranged, in general, between 0.1 and 5 at.%. Also the resistivity change caused by quenched-in lattice vacancies in platinum has been measured between 1.6 and 295\ifmmode^\circ\else\textdegree\fi{}K. A data analysis method has been used which eliminates the sensitivity of the results to the geometrical factor of the sample. In all systems, positive deviations $\ensuremath{\Delta}(T)$ form Matthiessen's rule are observed. For the alloys $\mathrm{Au}$-Co and $\mathrm{Pt}$-Rh, $\ensuremath{\Delta}(T)$ is found to be proportional to $\mathrm{ln}T$ between 30 and 200\ifmmode^\circ\else\textdegree\fi{}K. For the other systems, the $\ensuremath{\Delta}(T)$ curves can be described approximately by a Kohler-Sondheimer-Wilson equation. At low temperatures, the temperature dependence of $\ensuremath{\Delta}$ is found to be somewhat lower than that of the resistivity of the pure solvent metal. For the low solute concentrations, a sharp peak in the $\ensuremath{\Delta}(T)$ curves at about 30-50\ifmmode^\circ\else\textdegree\fi{}K is observed. Various possibilities for explaining the results are discussed, including the two-band model, the anisotropy of the electron scattering, and the shift in the Fermi surface due to alloying.