Correlation between electron-dislocation scattering and electron-impurity scattering in metals

An analysis is presented of the correlation between electron-dislocation scattering and electron-impurity scattering and its effect on the specific dislocation resistivity rho _D/N_D of metals. It is shown that, in contrast to the usual assumption, rho _D/N_D is not independent of the dislocation density N_D. For very large values of N_D, of the order of 10⁹ cm^-2 for pure samples, rho _D/N_D is indeed independent of N_D. However, for lower values of N_D, of the order of 10⁷-10⁸ cm^-2, the calculation yields that rho _D/N_D depends on N_D, varying approximately as C₁-C ₂lg(N_D/N_D^th) where N _D^th is a threshold value. The variation of rho _D/N_D with N_D is found to be about an order of magnitude for aluminium and for the noble metals. An experiment is proposed for measuring this predicted dependence of rho _D/N_D on N _D. The few available experimental data for the N_D dependence of rho _D/N_D for Cu and Be are found to be in close agreement with the present theory.