Electrical transport in transition-metal liquids and metallic glasses

The extended Ziman-Faber theory is developed in terms of a consistent single-site approximation to the density of states that permits a simple interpretation and evaluation of the effective valence $Z^{*}$ and other relevant parameters without reference to crystalline-band calculations. Results for four transition-metal liquids (Fe, Co, Ni, Cu) and two amorphous alloys ($\mathrm{Ni}\mathrm{P}$ and $\mathrm{Co}\mathrm{P}$) yield $Z^{*}\gtrsim 1$ for the former and $Z^{*}\simeq 2$ for the latter. In contrast with previous calculations, the electrical resistivity is greatly overestimated when the theory is applied consistently to strong-scattering liquids such as Fe and Co, while better results are found for Cu and Ni, in which the scattering is weaker. It is concluded that for the former type of system the Ziman formula should not be used to compute the magnitude of the resistivity. Similar results are obtained for $\alpha -Co\mathrm{P}$ and $\alpha -Ni\mathrm{P}$. The effect of the metalloid on the resistivity of the glass and its relationship to the corresponding transition-metal liquid is explained within the context of the model.