Thermal and Electrical Conductivities of Dilute Solutions of Iron in Gold

The thermal and electrical conductivities of a specimen of pure gold and 12 dilute gold-iron alloys ranging in iron concentration from 0.01 to 1 at.% have been measured over the temperature range 1-4.2 °K. In addition, the electrical conductivities of six other gold-iron alloys ranging in iron concentration from 0.05 to 2 at.% were measured over the same temperature range. The electrical resistivities of the more dilute specimens exhibit the Kondo logarithmic dependence on temperature; those of the more concentrated samples show the linear dependence on temperature predicted by Harrison and Klein. The data for samples of intermediate concentration show maxima in the resistivity-versus-temperature curve $\rho \mathrm{}\left(T\right)\mathrm{}$. The corresponding temperature $T_{max}$ is found to vary linearly with impurity concentration $c$. The ratio $\frac{T_{max}}{c}$ is about 24 °K/at.% of iron. The slope of the linear region of $p\left(T\right)\mathrm{}$ varies with the impurity concentration as $c^{\frac{1}{5}}$. A detailed comparison of the dilute-concentration data with Kondo's theory yields a value of -(0.28 ± 0.05) eV for the $s-d$ exchange energy of gold-iron. The product of the electronic thermal resistivity $W_e$ and the temperature $T$ for the more dilute specimens varies logarithmically with the temperature. The fractional magnitude of the logarithmic term in $W_{e}T$ is the same as in the electrical resistivity, indicating that, in this range of impurity concentration and temperature, impurity scattering of conduction electrons is predominantly elastic. The Lorenz ratios of these samples are, as a result, independent of temperature, but are a few percent higher than the theoretical Lorenz number $L_0$. The Lorenz ratios of the more concentrated specimens are found to decrease slowly with decreasing temperature because of the onset of small-angle inelastic conduction-electron scattering. At the upper end of the concentration range, the Lorenz ratio is temperature independent, but depressed by about 15% relative to $L_0$. The absence of any firm indication of a return of the Lorentz ratio back towards $L_0$ is discussed in terms of an interaction between an electron and a system of coupled impurities.