Structural Aspects of the Electrical Resistivity of Binary Alloys

Using the weak scattering approximation and the Van Hove correlation-function technique, it is shown that the scattering function for a binary alloy (solid or liquid) is quite generally expressible in terms of three structure factors $S_{\mathrm{NN}}\left(\overrightarrow{\mathrm{q}}\right)$, $S_{\mathrm{NC}}\left(\overrightarrow{\mathrm{q}}\right)$, and $S_{\mathrm{CC}}\left(\overrightarrow{\mathrm{q}}\right)$ constructed from the Fourier transforms of the local number density and concentration in the alloy. These structure factors have the property that at temperatures above the Debye temperature and in the long-wavelength limit ($q\to 0$), $S_{\mathrm{NN}}\mathrm{}\left(0\right)\mathrm{}$ and $S_{\mathrm{CC}}\mathrm{}\left(0\right)\mathrm{}$ represent, respectively, the mean square thermal fluctuations in the particle number and concentration, and $S_{\mathrm{NC}}\mathrm{}\left(0\right)\mathrm{}$ the correlation between these two fluctuations. Thermodynamic formulas for these fluctuations are given and their concentration and temperature dependence examined for various types of mixtures (regular, order-disorder type, athermal, etc.). It is concluded that the present formalism, because of its ready link with the thermodynamic properties of the alloy, can be helpful in interpreting the various experimental data and provides useful insight into the partial structure factors introduced in the Faber-Ziman theory of liquid alloys.