Abstract
The possible distinct crystallographic configurations of small vacancy clusters and vacancy-solute clusters in body centred cubic structures have been enumerated and classified. Clusters with up to four point defects have been considered, with the condition that each vacancy or solute has at least one point defect as a first- or second-nearest neighbour. A large number of clusters is possible and each type has a group of crystallographically equivalent variants. Computer simulation techniques have been used to determine the binding energies of these clusters. In this work the well established potentials for alpha-iron due to Johnson and for molybdenum due to Miller have been employed. A modified form of the alpha-iron potential has been used when dealing with host-solute interactions. The possible collapsed structures have also been investigated. The calculations were carried out on an IBM 360/195 computer, using a model containing up to 105 atoms. The migration energies of clusters have also been determined using computer experiments. In particular first-, second-, third- and fourth-neighbour divacancies have been considered in both alpha-iron and molybdenum. Selected clusters of three and four point defects have also been examined in details. The growth and contraction of clusters have been investigated using computer simulation. For selected cases all possible ways in which a vacancy can be attached to or detached from a cluster have been studied. It is found that the growth and contraction mechanisms are very anisotropic. In addition to clusters of up to four point defects a few of the most compact clusters of five and six point defects were also examined. Computer experiments have been performed to investigate some of their relevant properties such as stability, migration, growth and contraction. Time-independent and time-dependent Markov chain analyses relating to the migration of these clusters have been carried out. This allowed the equilibrium distribution of clusters to be determined. The model has been extended to incorporate the different migration energies that have been computed for the vacancy jumps. Equilibrium distributions have been calculated. As these calculations are based on migration mechanisms and the corresponding migration energies, rather than binding energies, the results obtained are different from those deduced using conventional methods of statistical physics.