Measurements of the High-Temperature Electrical Resistance of Aluminum: Resistivity of Lattice Vacancies

The electrical resistance of a 99.995% aluminum wire was measured at temperatures from 14 to 655°C. Values of temperature coefficient of resistance and of resistivity are derived; they differ somewhat from earlier work. The resistivity values show a progressive increase above the expected values at high temperatures; this is ascribed to scattering by thermally generated point defects of the type which add atomic sites (vacancy-type defects), whose equilibrium concentrations have been measured directly in identical material at identical temperatures by Simmons and Balluffi. Three different semiempirical methods were used to estimate the expected values of the ideal lattice resistivity in the absence of defects; they gave similar results. The limitations of extrapolation methods are discussed. The resistivity increment ascribed to the vacancy-type defects was then obtained by difference and can be represented by $\Delta \rho =(4.4\mathrm{}\times {10}^{-3\mathrm{}} \mathrm{o}\mathrm{h}\mathrm{m}-\mathrm{c}\mathrm{m})\exp (-0.77\mathrm{} \mathrm{ev}/kT)$. The observed formation energy is in close agreement with that obtained by direct concentration measurements and with that obtained in various quenching investigations. This increment is nearly twice the value expected from extrapolation of recent quenching work from the interval 260° to 320°C, however. This relatively small discrepancy can be ascribed to three factors, whose relative importance cannot be precisely evaluated at present. They are (1) failure of quenching techniques to retain all of the equilibrium defect concentrations, (2) the presence of appreciable divacancy concentrations at the highest temperatures, and (3) a contribution to the high temperature resistivity arising from lattice anharmonicity. The increment of about 0.30 μohm-cm at the melting point (660°C) corresponds to a resistivity 3 μohm-cm/atom% monovacancies in agreement with a crude estimate based upon known effects of solute atoms of different valence.