Critical test of the diffraction model in amorphous and disordered metals

Abstract

The transport properties of amorphous metals below their Debye temperatures $\ensuremath{\Theta}$ are examined within the framework of the diffraction model. The electrical resistivity $\ensuremath{\rho}$ is predicted to exhibit the following features: (i) All curves deviate from their $T=0$\ifmmode^\circ\else\textdegree\fi{}K values as $+{T}^{2}$; (ii) Negative temperature coefficients of resistivity (TCR) occur at $T\ensuremath{\approx}\ensuremath{\Theta}$ for $K\ensuremath{\approx}{K}_{p}$, where ${K}_{p}$ is the position of the principal peak in the structure factor $a(K)$ and $K=2{k}_{F}$. 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 $\ensuremath{\rho}$ (of the order of tenths of a percent) are seen for $K\ensuremath{\approx}{K}_{p}$. The position of the maximum shifts to lower temperatures as $K\ensuremath{\rightarrow}{K}_{p}$. The largest maximum occurs for the nearly flat curve; (iv) The amplitude of the variations of $\ensuremath{\rho}$, and the size of the maxima are sensitive to $\ensuremath{\Theta}$ and the sharpness of the main peak in $a(K)$; (v) For fixed $\ensuremath{\Theta}$, the positions of the maxima in $\ensuremath{\rho}$ generally approach $\ensuremath{\Theta}$ as the main peak in $a(K)$ 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.