Low-temperature resistance and its temperature dependence in nanostructured silver

The dc resistance and the temperature coefficient of resistance (TCR) of bulk nanostructured silver ($n$-Ag), synthesized by inert gas condensation and in situ vacuum compaction as well as by the sol-gel method, was investigated in the temperature range from 4.2 to 300 K. The results indicated that for all of the $n$-Ag specimens with larger grain sizes $(d>\mathrm{}20\mathrm{}\mathrm{nm})$ and higher densities (relative density $D>\mathrm{}88\%$) investigated, their resistivity decreased with decreasing temperature, showing metallic behavior; however, it was found that for the $n$-Ag with smaller grain sizes and lower density $(D=45\mathrm{}–50\%),$ the resistance increased with decreasing temperature (negative TCR) as its mean size $d<\mathrm{}9\mathrm{}\mathrm{nm},$ exhibiting nonmetallic behavior. Furthermore, it was found that generally at a certain (fixed) temperature (at 280 K, for instance), there were approximately linear relations (with negative slope) between its TCR and reciprocals of both grain size and density. In addition, the absolute magnitudes of the resistivity of $n$-Ag were higher than that of polycrystalline silver (poly-Ag), and increased with decreasing both grain size and density. With the model of grain boundary reflection, it was evaluated that the electron mean free path at room temperature was 44 and 33 nm for the $n$-Ag with grain size 38.5 and 25 nm, respectively, both of which are smaller than that of poly-Ag (51 nm). It was also evaluated that the electron transmission coefficient through boundaries decreased monotonically from 0.83 to 0.42 as $n$-Ag density decreased from 98.5 to 88%, suggesting greater boundary barriers in the $n$-Ag’s with lower densities. The fact that transition of TCR sign from positive to negative can be attributed mainly to the dominant scattering caused by interfaces as compared to that caused by intragranular phonons in $n$-Ag with extremely fine grain sizes and low densities.