Energy of formation of lattice vacancies in lead from equilibrium resistivity and quenching studies

Abstract

Estimates of the electrical resistivity of lattice vacancies in 99·999% pure lead wires have been made in two ways; firstly from measurements of the equilibrium resistivity between 0°c and the melting point, and secondly from determinations of the quenched-in defect resistivity of specimens rapidly cooled to liquid nitrogen temperatures in an atmosphere of helium. The precision of the equilibrium resistance measurements is a few parts in 10⁴ and the quenched-in resistivity could be determined to about 1 × 10⁻¹⁰ ohm cm. In the temperature range 0–250°c the resistivity is given within experimental error by the equation: and the present results join smoothly with existing data below 0°c. Due to the uncertainty in the extrapolated lattice resistivity for T < 250°c and the difficulty of retaining the equilibrium defect concentration in the quenching experiments, the analysis of equilibrium and quenching data gives respectively upper and lower limits for the vacancy resistivity and the energy of formation of a vacancy. The following mean values were obtained, E _V ^f=0·58±0·13 ev and Δe_v(m.p.)∼5 × 10⁻⁸ ohm cm. Using a value for the vacancy concentration at the m.p. of 2 × 10⁻⁴ as determined from expansivity and lattice parameter measurements, values for the excess entropy of formation of a vacancy S _V ^f/k=2·6 and of Δe_v∼2·5 μ ohm cm/at. % vacancies are found. The latter value can only be considered to be a rough estimate.