Equilibrium vacancy concentration in pure Pb and dilute Pb-Tl and Pb-In alloys

Abstract

The equilibrium concentration of vacancies near the melting point was measured for pure Pb, and for Pb + 1 % In, Pb + 0·5 % T1 and Pb + 5% T1 alloys by comparison of the macroscopic thermal expansion with the microscopic expansion obtained from precision lattice parameter measurements. Previous work (d'Heurle et al. 1963) had indicated that the alloys have a much lower vacancy concentration at the melting point, Δ/N(T _m) than pure Pb. The present work has repeated the dilatometric measurements, using an inter -ferometric dilatometer for the absolute expansion of pure Pb, and a high precision differential method for the alloys. The results for pure Pb show that Δ/N(T _m) = 17×10⁻⁵, and give a vacancy formation energy of 0·49±0·10 ev and formation entropy of 0·7±2·0 (in units of k), from the semi-logarithmic plot of ΔN/N versus 1/T. The results for the alloys show no detectable difference from those for the pure Pb.