Quenching Rate and Quenched-In Lattice Vacancies in Gold

The quenched-in resistivity in gold was measured for cooling rates from 104 to 105 °C/sec. The quenched-in resistivity increases considerably with increasing cooling rate and depends strongly on the quenching temperature over much of the range investigated; for example, for a cooling rate of 20 000°C/sec about 12% of the residual resistivity recovers during the quenching process for a quench from 700°C and about 20% recovers for a quench from 800°C. For the lower quenching temperatures the quenched-in resistivity appears to approach saturation at the fastest quenching rates obtained. A linear relation between the logarithm of quenched-in resistivity and the reciprocal of quenching rate was observed. This allowed linear extrapolation to infinite quenching rate. The quenched-in resistivity ρ∞ obtained by extrapolating to infinite rate, is expressed by ρ∞=ρ0 exp(−Hf/kT), where ρ0=5.0×10−4 Ω-cm and the formation enthalpy, Hf=0.97 eV. Assuming ρ∞ corresponds to single vacancies rather than clusters, measurements of the length change of the quenched specimens and using Tewordt's result that a vacancy has 0.47 atomic volume, the following constants were obtained: The resistivity of 1 at. % of vacancies, 1.7×10−6 Ω-cm; the entropy of formation of a vacancy, 0.95×10−4 eV/°K; and the fractional concentration at the melting point, 6.4×10−4.