Abstract
In this thesis, we calculate the electron-phonon scattering rate in polycrystalline metals, e.g., Ti1-xAlx, 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 (i.e. thermal phonon wave vector times electron mean free path <<1) is enhanced by the disorder due to substitutional impurities in the presence of random lattice shift of crystallites. Specifically, we obtain the scattering rate directly proportion to temperature squared divided by electron mean free path 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. We also study the electron-phonon scattering rate in impure metals in the case of single crystals doped with impurities. We show that, if all impurities are substitutional, the previous Reizer-Sergeyev result, the electron-phonon scattering rate is directly proportion to temperature to the fourth power, holds even when discreteness of the lattice structure is taken into account. However, the result is modified when we also allow for random positional shift of impurities, in which case the result, the electron-phonon scattering rate is directly proportion to temperature squared, is obtained.