Mathiessen's Rule and Anisotropic Relaxation Times

Departures from Matthiessen's rule were measured for dilute alloys of copper with gold, tin, or germanium, and of silver with gold or tin; and for strained copper and silver. The concentration of alloyed elements ranged from 0.01 to 1 at.%; residual resistivities per atomic percent impurity are estimated to be known within better than 1% accuracy and were compared with Linde's values. In evaluating the deviations, corrections were applied for the volume dependence of the residual resistivity due to thermal expansion and the ideal resistivity due to alloying. The results were interpreted on a simple two-band model as due to different anisotropies of the relaxation times associated with different scattering processes; the expected temperature dependence of the anisotropy of phonon scattering was taken into account. At temperatures where the residual resistivity dominates, deviations from Matthiessen's rule become comparable to or greater than the ideal resistivity, making experimental determination of the ideal resistivity in this region open to criticism.