Theory of the sample dependence of the electron-electron scattering resistivity in metals

A theory is presented of the sample dependence of the electron-electron scattering contribution to the electrical resistivity, rho _ee(T)= A_eeT². A central role in the analysis is played by anisotropic electron scattering processes such as those caused by dislocations, stacking faults, grain boundaries, etc. The main idea is that such anisotropic scattering centres lead to anisotropy in the electron scattering relaxation time, which in turn leads to an enhancement of A_ee. As a result, samples which are strained or unannealed, and thus contain a relatively high density of anisotropic scattering centres, will exhibit a larger value for A_ee than samples which are annealed; this implies a sample dependence for A_ee. It is shown for the alkali metals that the enhancement of A_ee can be as large as an order of magnitude, whereas for the noble and polyvalent metals the enhancement is much smaller. These results are in accord with all the available data. A model is introduced for the anisotropy of the electron scattering relaxation time for the alkali metals, and an explicit calculation is carried out for the sample dependence of A_ee. The results of the calculation are applied to potassium and yield excellent agreement with experiment. Finally, the data of A_ee for lithium are also explained.