Measurement of Equilibrium Concentrations of Lattice Vacancies in Gold

The linear thermal expansion of a 99.999% gold bar has been measured throughout the range 15^∘{} to 1057^∘{}C by direct observation of the length expansion ΔLL, with filar micrometer microscopes and by measurement of the lattice parameter expansion Δaa, by x-ray diffraction with a rotating-single-crystal method. The expansions agree within the experimental precision of about 1:10⁵ at the lower temperatures. However, the values of thermal expansion obtained are about 1.5% larger than those in the literature. At the higher temperatures (ΔLL-Δaa) becomes positive, proving that thermally-generated defects are formed which are predominantly vacant lattice sites. The net added concentration of substitutional atomic sites, ΔNN=3(ΔLL-Δaa), just below the melting temperature, is (7.2±{}0.6)×{}10^-4 as obtained by an extrapolation of the data of only 6^∘{}C. ΔNN can be described by exp(1.0)exp(-0.94 ev/kT). These results are independent of any aggregation of the defects and of any lattice dilatation about the individual defects. Just below the melting temperature, more than 80% of the vacant sites are single vacancies if the divacancy and trivacancy binding energies are less than 0.4 ev and 1.0 ev, respectively.The present concentrations are about 40% larger than those reported by DeSorbo from a calorimetric study of quenched foil. A critical assessment of the relationship between the present equilibrium measurements and results obtained by quenching methods is attempted. Combination of present ΔNN values with Δρ and (ΔLL)Δρ values of Bauerle and Koehler and with ΔLL values of Takamura on quenched and annealed wires gives an electrical resistivity ρᵥ=1.5±0.3 {μ}ohm cm/at.% of vacancies and a volume expansion χ=0.45±0.10 atomic volume/vacancy.