Determination of Contributions to the Residual Resistivity of Gallium at 4.2°K

Abstract

Resistivity measurements have been carried out on single-crystal wires of high-purity gallium in the temperature range of 1.27° to 43°K, and also at 4.2°K on gallium with added impurities, and with varying wire diameter. The last measurements indicated the electron mean free path to be 1.2 mm at 4.2°K at a resistivity of about 3×${10}^{-22\mathrm{}}$ esu, implying that the effective number of free electrons per atom in gallium is 0.2. Diffuse surface scattering was found to be an important scattering mechanism in wires of high-purity gallium at 4.2°K, and its contribution to the ratio of resistivity at 4.2 to 295°K in a 1-mm diam crystal is 1.5×${10}^{-5\mathrm{}}$. The temperature measurements indicated that no resistivity minimum occurs, and also that along the $b$ axis, the lattice scattering contributes 0.4×${10}^{-5\mathrm{}}$ to the resistivity ratio. The effect of grain boundaries on the resistivity ratio is negligible. The presence of as little as one atomic part per million of impurities such as Cu, Ag, Zn, Tl, Ge, Sn, Pb, and As can be detected by residual resistivity measurements.