Effect of Electron-Electron Scattering on the Low-Temperature Lorenz Numbers of DilutePd-Ni Alloys

The thermal and electrical resistivities of $\mathrm{Pd}$-Ni alloys at concentrations ranging from 0 to 1.0 at.% Ni have been measured at temperatures between 2 and 20 K. The Lorenz numbers $L_e$ appropriate to electron-electron scattering have been extracted from the data and are found to be relatively insensitive to Ni concentration. A theoretical calculation of $L_e$ has been carried out under the assumption that the entire current is carried by $s$ electrons which are scattered from spin-density fluctuations of the electrons in the $d$ band. A consistent interpretation of the data is obtained by employing the local-enhancement model, while the uniform-enhancement model is found to yield values of $L_e$ which decrease too rapidly with increasing Ni concentration to reasonably represent the experimental results. The calculated value of $L_e$ is significantly smaller than the experimental value for pure Pd; it is felt this may be due to the neglect of detailed band-structure effects in this work. Lorenz numbers for Baber scattering have also been calculated by using Coulomb interaction screened by the $d$ electrons. It is found that the presence of Baber scattering cannot remove the discrepancy between theory and experiment for pure Pd. The Baber-scattering model is also used to calculate $L_e$ for rhenium and gives very good agreement with experiment.