A study of vacancies in tungsten wires quenched in superfluid helium

Abstract We have studied the dependence of quenched-in resistance upon quench temperature and quenching speed for fine tungsten wires quenched under superfluid helium. We ascribe this resistance to vacancies trapped in the wires by the rapid quench. Extrapolation of the data to infinite quench speed produced a vacancy formation energy larger than the value of 3.3 eV proposed by Schultz. Analysis in terms of the theory of Flynn, Bass, and Lazarus yielded a vacancy formation energy of 3.6±0.2 eV and a vacancy motion energy of 2.5±0.5 eV, assuming an activation energy for self-diffusion of 6.1 ±0.3 eV. We have also examined the isochronal annealing spectrum after quenches from above 2800 K. Over 80% of the quenched-in resistance annealed away in a single, narrow stage, centred in the temperature range 850 to 1150K. After quenches from below 3100 K, this stage was centred in the upper portion of this temperature range and contained essentially all of the quenched-in resistance. After quenches from higher temperatures, the annealing stage shifted toward lower temperatures, and some resistance remained after the stage was completed. Finally, isothermal annealing studies were made in the range 800 to 1040 K after quenches from above 3200 K. The isothermal annealing curves had a complex shape-the rate of annealing initially increasing with increasing annealing time. Measurements of changes in the rate of annealing upon changing the annealing temperature yielded an activation energy for migration of l.5±0.2 eV. This is considerably smaller than the high temperature estimate of 2.5 eV for the single vacancy motion energy. This low activation energy, the complex form of the isothermal annealing curves, and the persistence of some quenched-in resistance to high temperatures during isochronal annealing, are all suggestive of vacancy clustering during the quench and subsequent annealing.