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Here, we present the measurements of $R_H$ in a series of $Ti_xSi_{100-x}$amorphous reaching the critical concentration, $x_c\approx9-9.5$. For$x\geq17$, the Hall coefficient displays the behavior predicted by theperturbation theory, $R_H^{-1}\left(T\right)=R_H^{-1}\left(0\right)+bT^{1/2}$,which extends up to the temperature 150 K. The temperature dependence getsstronger in alloys with lower $x$; $R_H\left(0\right)$ diverges at $x_c$displaying critical behavior. We used the combined conductivity and Hallcoefficient data for alloys with high Ti content to test the theories ofquantum corrections to conductivity. We found that the correction due to weaklocalization is dominated by the electron-phonon scattering with the ratevarying with temperature as $\tau_{ep}^{-1}=A_{ep}T^2$. The extracted parameter$A_{ep}$ is in good agreement with the theory that considers the incompletedrag of impurities by lattice vibrations. The spin-orbit scattering timeextracted from the weak localization correction was found to be two orders ofmagnitude larger than the time given by the standard estimate$\tau_{so}\approx\tau\left(\hbar c/e^2Z\right)^4$. The theory of the EEIquantum correction was tested using the Hall coefficient and specific heat datafor Ti-Si and $\left(Ag_{0.5}Cu_{0.5}\right)_{100-x}Ge_x$ amorphous alloys,which allowed us to estimate all microscopic parameters needed by the theory.We found that, within the accuracy of our measurements, the EEI theory worksexactly for alloys that follow the free electron model[$\left(Ag_{0.5}Cu_{0.5}\right)_{100-x}Ge_x$ with $x\le50$.] The deviation fromthe theory observed in all Ti-Si alloys and in Ag-Cu-Ge alloys with $x\geq60$can be qualitatively explained by weakening of the electron screening in thesystems.

Hall coefficient in amorphous alloys: critical behavior and quantitative  test of quantum corrections due to weak localization and electron-electron  interactions