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 $\frac{\Delta L}{L}$, with filar micrometer microscopes and by measurement of the lattice parameter expansion $\frac{\Delta a}{a}$, by x-ray diffraction with a rotating-single-crystal method. The expansions agree within the experimental precision of about 1:${10}^5$ 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 ($\frac{\Delta L}{L}-\frac{\Delta a}{a}$) becomes positive, proving that thermally-generated defects are formed which are predominantly vacant lattice sites. The net added concentration of substitutional atomic sites, $\frac{\Delta N}{N}=3(\frac{\Delta L}{L}-\frac{\Delta a}{a})$, just below the melting temperature, is (7.2±0.6)×${10}^{-4\mathrm{}}$ as obtained by an extrapolation of the data of only 6°C. $\frac{\Delta N}{N}$ can be described by $\exp \mathrm{}\left(1.0\right)\mathrm{}\exp (-0.94\mathrm{} \mathrm{ev}/kT)$. 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 $\frac{\Delta N}{N}$ values with $\Delta \rho$ and $\frac{\left(\frac{\Delta L}{L}\right)}{\Delta \rho }$ values of Bauerle and Koehler and with $\frac{\Delta L}{L}$ values of Takamura on quenched and annealed wires gives an electrical resistivity ${\rho }_v=1.5\mathrm{}\pm 0.3$ μohm cm/at.% of vacancies and a volume expansion $\chi =0.45\mathrm{}\pm 0.10$ atomic volume/vacancy.