Effect of Phonon Drag on the Electrical Resistivity of Metals

It is shown that the phonon-drag component ${\rho }_g$ of the electrical resistivity and the phonon-drag component $S_g$ of the thermoelectric power of a metal are related through the equation ${\rho }_g=\frac{{S_g}^{2}T}{{\kappa }_L}$, where $T$ and ${\kappa }_L$ are the absolute temperature and the lattice thermal conductivity, respectively. The relation is used to calculate the influence of phonon drag on the electrical resistivity of gold and platinum from the experimentally determined quantities $S_g$ and ${\kappa }_L$. It is found that in gold and platinum phonon-drag effects reduce the electrical resistivity by less than 0.5 and 1.6%, respectively, above 20°K. The relation can serve to calculate the deviations from the Matthiessen rule in the lattice-defect electrical resistivity which are caused by changes in ${\rho }_g$ due to the phonon scattering by the imperfections. Such deviations from the Matthiessen rule are estimated for lattice vacancies in gold and platinum and are found to be negligible.