Relaxation time for electron-dislocation scattering for noble and polyvalent metals

An analysis is presented of the relaxation time for electron-dislocation scattering for the polyvalent and noble metals. It is shown that for these metals the relaxation time is significantly anisotropic, i.e., its magnitude varies markedly with position over the Fermi surface. This anisotropy of the relaxation time results from the nonsphericity of the Fermi surface for these metals and from the dominance of very-small-angle scattering events for electron-dislocation scattering. The explicit form of the relaxation time is determined by a variational solution to the Boltzmann equation. The degree of anisotropy of the relaxation time is calculated for A1, Cu, Ag, and Au. The analysis is then generalized to include the effects of both electron-dislocation scattering and electron-impurity scattering. It is shown that the large-angle scattering events that characterize electron-impurity scattering tend to reduce the anisotropy of the relaxation time. Finally, a discussion is presented of the implications of the present results to the recent theories of the effect of electron-dislocation scattering on the low-temperature electrical resistivity of the polyvalent and noble metals.