Abstract
We calculate the electron-phonon scattering rate in polycrystalline metals, e.g., Ti 1-x Al x , in the limit of dilute impurity concentration. We consider the additional contribution due to the Umklapp process of impurity scattering, which has been neglected in all previous nearly free-electron calculations but is important for the present problem. We find that, as a result of including the Umklapp process, the scattering rate in the dirty limit q T l≪1 is enhanced by the disorder due to substitutional impurities and random lattice shift of crystallites, where q T =thermal phonon wave vector and l = electron mean free path. Specifically, we obtain the scattering rate 1/τ ep ∼ T 2 l -1 , where T = temperature, in agreement with previous experiments both in order of magnitude and in functional dependence. This work satisfactorily explains the long-standing discrepancy between theories and experiments regarding the effect of disorder on electron-phonon scattering, for the case of polycrystalline metals with dilute impurity concentration.