Critical test of the diffraction model in amorphous and disordered metals

The transport properties of amorphous metals below their Debye temperatures $\Theta$ are examined within the framework of the diffraction model. The electrical resistivity $\rho$ is predicted to exhibit the following features: (i) All curves deviate from their $T=0\mathrm{}$°K values as $+T^2$; (ii) Negative temperature coefficients of resistivity (TCR) occur at $T\approx \Theta$ for $K\approx K_p$, where $K_p$ is the position of the principal peak in the structure factor $a\left(K\right)\mathrm{}$ and $K=2\mathrm{}{k}_F$. Positive TCR occur at all $T$ for $K$ outside the vicinity of $K_p$, i.e., to the left- and right-hand sides of $K_p$; (iii) Small maxima in $\rho$ (of the order of tenths of a percent) are seen for $K\approx K_p$. The position of the maximum shifts to lower temperatures as $K\to K_p$. The largest maximum occurs for the nearly flat curve; (iv) The amplitude of the variations of $\rho$, and the size of the maxima are sensitive to $\Theta$ and the sharpness of the main peak in $a\left(K\right)\mathrm{}$; (v) For fixed $\Theta$, the positions of the maxima in $\rho$ generally approach $\Theta$ as the main peak in $a\left(K\right)\mathrm{}$ becomes smaller; (vi) The curves which display only positive TCR are generally $S$ shaped; (vii) The electron-to-atom ratio for negative TCR is estimated to range from $1.3\mathcal{z}$ to $3\mathcal{z}$. The predictions are compared with experimental findings in a variety of amorphous alloys. The agreement is excellent. The question of breakdown of the diffraction model is discussed; some of the apparent paradoxes seen in high-resistivity metals are resolved through a redefinition of saturation. The implications of these results for disordered and liquid metals are also discussed.