Theory of Electrical Conductivity in Disordered Binary Alloys. The Effect ofs−dHybridization

The coherent-potential approximation (CPA) of the conductivity theory of disordered alloys is generalized in order to calculate and to discuss the static conductivity of a two-$s-d$-band-alloy model relevant to noble- and transition-metal alloys. The vertex corrections are calculated and can be expressed in the CPA as a sum of single-site contributions. As in the one-band model and for the same physical reasons, these vertex corrections vanish if the potentials are short ranged. Three contributions are obtained for the electrical conductivity. They correspond to the propagation of a pair of $s$ electrons, a pair of $d$ electrons, and two hybridized $s-d$ electrons. The scattering of $s$ electrons is viewed as indirectly caused by the randomness of $d$ levels acting through the hybridization interaction $s-d$. Two limiting cases are investigated and compared with previous treatments. In the weak-scattering limit, the present theory is shown to be equivalent to the Boltzmann approach. In the dilute-concentration limit, it is possible to reduce this formalism to previous calculations of the impurity-induced resistivity by defining in that limit an effective $s-d$ scattering potential. A numerical application is presented. It is not directly related to any particular alloy but the physical parameters are reasonably chosen such that the computed resistivity reproduces qualitatively two types of deviations from the Nordheim behavior observed in some transition-metal-based alloys: (a) a change of slope of the resistivity-versus-concentration curve correlated with a minimum of the specific heat, and (b) an asymmetry of the resistivity curve with a peak in a range of concentration where the influence of $s-d$ hybridization is dominant.