Electrical resistivity in amorphous metals: Consequences of phonon ineffectiveness in the diffraction model

Electrical transport in amorphous metals is analyzed in the context of the Baym-Faber-Ziman theory. The theory is generalized to incorporate electron mean-free-path effects through the Pippard-Ziman condition on the electron-phonon interaction. Various model $t$ matrices are considered. The geometrical structure factors are modeled by Percus-Yevick hard-sphere forms and a single-branch Debye phonon spectrum is assumed. Detailed results for electrical resistivity $\rho$ versus temperature $T$ and the temperature coefficient of resistivity are presented for extensive ranges of $\frac{2k_F}{k_p}$ and electron mean free path. The results, incorporating the Pippard-Ziman condition, are consistent with the observed $\rho$ versus $T$ in low-resistivity glassy metals. However, although inclusion of the Pippard-Ziman condition dramatically improves agreement with the data, quantitative agreement is not obtained in high-resistivity amorphous metals.