Annealing of Pure Gold Quenched from above 800°C

Abstract

The decrease of quenched-in resistivity as a function of time of Au wires quenched from above 800°C and then annealed in the vicinity of room temperature, is observed to be an $S$-shaped curve. The time $t_{\frac{1}{2}}$ required for half of the initially quenched-in resistivity ${\rho }_0$ to anneal out decreases from 15 to 0.5 h as quenching temperature is raised from 840 to 1000°C. It is observed that $\frac{1}{t_{\frac{1}{2}}}\propto {{\rho }_0}^{(2.60\mathrm{}\pm 0.2)}$. The fraction of ${\rho }_0$ that remains after infinite annealing times is independent of the quenching temperature with $\frac{{\rho }_r\left(\infty \right)}{{\rho }_0}=0.074\mathrm{}\pm 0.006$. All the $S$-shape annealing data combine into one universal curve if $f=\frac{[\rho -{\rho }_r(\infty \left)\right]}{[{\rho }_0-{\rho }_r(\infty \left)\right]}$ is plotted against the reduced time $\frac{t}{t_{\frac{1}{2}}}$. The universality of the curves indicates that the supersaturated concentrations of defects in Au disappear by one unique process. The following process is proposed: The defects in freshly quenched specimens are present as single vacancies, divacancies, and trivacancies, which are in thermal equilibrium with one another. The concentration of other complexes is negligible. Tetrahedra of stacking faults, as observed by Hirsch, act as the sinks for singles and divacancies. They are formed during annealing by the collapse of six aggregated vacancies; their nucleation sites are the tetravacancy complexes, which are the smallest vacancy clusters in Au which are not in thermal equilibrium. The tetravacancy converts into a tetrahedron if struck by a divacancy. The remaining resistivity is due to the stacking faults of the tetrahedra. If it is assumed, in addition, that all the quenched-in defects disappear at the tetrahedra, then $\frac{{\rho }_r\left(\infty \right)}{{\rho }_0}$ is shown to be a constant as observed and the parameter $f$ then represents the fraction of the initially quenched-in defects that has not yet been absorbed. The model predicts that $\frac{1}{t_{\frac{1}{2}}}\propto {c_0}^{2.5}$ and that the number of tetrahedron $n_{\infty }$ at infinite annealing times is $n_{\infty }\propto {c_0}^{1.5}$ in agreement with the experiments. The resistivity of stacking faults per unit area was calculated to be (1.3±0.4)×${10}^{-13\mathrm{}}$ Ω${\mathrm{cm}}^2$.