Explanation of the apparentT2dependence of the surface-induced electrical resistivity in pure metals from measurements on high-purity Au foils

From previously reported, detailed size-effect measurements in the range $4.2 \mathrm{K}\lesssim T\lesssim 20 \mathrm{K}$ on chlorine annealed, high-purity Au foils of thicknesses $2 \mu \mathrm{m}\lesssim d\lesssim 25 \mu \mathrm{m}$, the surface contribution to the electrical resistivity ${\rho }_S\mathrm{}\left(T\right)\mathrm{}$ has been extracted accurately at several $T$'s, with the use of Soffer's surface-scattering theory. It is shown that this theory, combined with the correct intrinsic $T$ dependence of the metal concerned, consistently predicts the observed behavior of ${\rho }_S$ against $T$ over the entire $T$ range covered and shows that the relation between ${\rho }_S$ and $T$ is effectively nowhere a quadratic one, contradicting herewith the apparent general behavior of ${\rho }_S\propto T^2$ over various pure metals and $T$ ranges as suggested by van der Maas et al. It is shown that it is only due to the scatter in experimental size-effect data collected over several temperatures that one can easily select a low-$T$ range (i.e., $T\lesssim 13$ K) where the data seem to fit a $T^2$ dependence.