Pressure Effect on Vacancy Migration Rate in Gold

The effect of hydrostatic pressures up to 10 000 kg/${\mathrm{cm}}^2$ on the annealing rate of vacancies quenched in gold is studied. Highpurity gold wires are quenched from 700°C, trapping in the equilibrium concentration of vacancies at that temperature. The vacancies are then observed to anneal out in the vicinity of room temperature at various pressures by observing the decay of the quench-induced residual resistance increase. A simple relation for the temperature dependence of the annealing rate is derived, assuming a random distribution of vacancies and vacancy sinks. By applying thermodynamic relations to the expression for the vacancy annealing rate, a volume of motion is derived in terms of the experimentally determined pressure effect on the annealing rate. For gold, the motional volume is found to be 1.50±0.14 ${\mathrm{cm}}^3$/mole compared with the atomic volume of 10.2 ${\mathrm{cm}}^3$/mole. A hard-spheres model for the jump process predicts about a one atomic volume increase of the lattice for the saddle-point configuration as well as a one atomic volume increase when a vacancy is formed. Many theoretical calculations of the lattice distortion around a vacancy and indirect experimental measurements of the volume change of the lattice on forming a vacancy indicate that there is considerable relaxation of the neighboring atoms about a vacancy. These results are used to explain the small value of the motional volume. Activation volumes derived from measurements of the effect of pressure on the rate of self-diffusion are seen to be consistent with the present experimental vlue.