Kinetic Study of Vacancy Clustering and Annealing in Metals

Abstract

The rate equations governing the clustering and annealing of vacancies in metals have been studied. Single vacancies were considered to be immobile at temperatures at which small clusters migrate. Clusters with up to seven vacancies were explicitly treated, and approximations were made to account for larger clusters. A variety of cases for different cluster binding and migration energies were run. Since the annealing curves generally gave little indication of the actual processes occurring, the input data could not be inferred from standard analyses of isothermal and isochronal data. For small binding energies the annealing was small, as some clusters reached sinks, and the single-vacancy concentration increased. For large binding energies the annealing was also small, as clustering dominated the recovery and few clusters reached sinks. Between these limits, complex results were obtained; the total annealing could be quite large with an appreciable decrease in concentration of single vacancies, and anomalously low activation energies were often found.