Calculation of electrical resistivity of highly resistive metallic alloys

The new feature in an otherwise standard calculation is the inclusion of the temperature-dependent Debye-Waller factor. At low temperature a resistance minimum is predicted which is not of the logarithmic form, such as occurs in the Kondo system, but is instead a polynomial in $T$. Its magnitude scales with the residual resistivity $\rho \mathrm{}\left(0\right)\mathrm{}$ and is unobservably small unless $\rho \mathrm{}\left(0\right)\mathrm{}$ is very large. At higher temperature a contribution linear in $T$ is predicted with coefficient small in magnitude and possibly of either sign, becoming more negative as $\rho \mathrm{}\left(0\right)\mathrm{}$ increases. Behavior almost in line with these predictions has been observed for many metallic glass alloy systems containing transition-metal atoms. But two drawbacks are the uncertain validity of the model for these systems and the prominence of competing effects due to the $d$ electrons.