Deviations from Matthiessen's rule for dilute alloys of polyvalent and noble metals

An analysis is presented of the low-temperature deviations from Matthiessen's rule (DMR) for the polyvalent and noble metals. For these metals, the Fermi surface intersects the Brillouin-zone boundaries, leading to an enormous enhancement, at low temperatures, of the electron-phonon scattering probability for the electrons near the Brillouin-zone intersections. An electron distribution function is introduced which takes explicit account of these localized regions of extremely strong electron-phonon scattering. This electron distribution function is shown to provide the basis for understanding (i) the large magnitude of the low-temperature DMR, (ii) their temperature dependence, (iii) their dependence on residual resistivity, and (iv) their variation from metal to metal. Moreover, it is found that by including the contribution of the interference term, one may explain the observed lack of saturation of the DMR for large values of the residual resistivity. Finally, it is demonstrated that normal electron-phonon scattering constitutes a large part of the total calculated DMR.