Electrical resistivity of the noble metals at low temperatures. II. Effect of electron-dislocation scattering

An analysis is presented of the effect of electron-dislocation scattering on the temperature-dependent part of the electrical resistivity of the noble metals at low temperatures. The basic idea is that for any given sample, the degree to which the relaxation time varies over the Fermi surface is determined by the 'competition' between small-angle electron-dislocation scattering and large-angle electron-impurity scattering. Detailed calculations of the low-temperature resistivity are carried out, based on the variational method, that yield quantitative agreement with the recent resistivity data for Ag and Cu. The analysis also leads to the following results. (i) For the ultra-pure samples, the residual dislocations are shown to eliminate the T⁴ dependence that characterises the resistivity of the less pure samples. (ii) Electron-dislocation scattering is shown to produce a variety of possible deviations from Matthiessen's rule (DMR), including large negative DMR, small positive DMR or even a complete absence of DMR, in agreement with the resistivity data for strained samples of Ag and Al. (iii) Dislocations are shown to increase the magnitude of the electron-electron scattering term for the noble metals, in agreement with the recent Kaveh-Wiser theory (1980-1982).