A mathematical lattice model was used to compute the kinetic and static aspects of vacancy-cluster nucleation, growth, and dissociation in $\alpha$-iron. Persistent attention is paid to the kinetics of changes among metastable configurations as well as the formation of stable configurations. The tetravacancy was the smallest immobile vacancy cluster and the mono-, di-, and trivacancy essentially share a common migration-energy value (0.65-0.70 eV). There exists a well-defined hierarchy of different types of stable clusters, the most stable structure being compact clusters, followed in order of decreasing stability by double layers, linear chains, tetravacancies, single layers, trivacancies, and divacancies. The gain in binding energy per additional vacancy increased as the cluster size increased from two to six vacancies. Between 6 and 10 vacancies this gain approached an upper limit of about 0.8 eV/vacancy and remained at this value for larger clusters.

• Received 21 October 1966

DOI:https://doi.org/10.1103/PhysRev.156.677