Abstract
A new method based on representation matrices, for classifying and enumerating close-packed clusters of vacancies or substitutional solutes in crystals is described. In particular it is shown how a scalar quantity, related to the determinant of the representation matrix, can be used in the classification procedure. This has proved to be especially valuable in the computational method adopted. Results are presented for clusters of up to five point defects in all single-lattice and selected double-lattice structures. Relationships between the results for different structures are discussed and some inaccuracies in earlier analyses noted. The method of representation matrices has been extended to include clusters with more than one type of point defect. All possible cases are considered, from pure clusters with just one type of solute to mixed clusters in which each solute is different. In each case the number of distinct configurations and the total number of variants is recorded. Non-central Lifson-Warshel type four-body interatomic potentials for silicon and germanium have been developed. These potentials are matched to the experimental lattice parameter, the elastic constants, and the vacancy formation, divacancy binding and {111} stacking fault energies. The geometries of bond reconstruction among neighbouring atoms of vacancy and vacancy-solute clusters in the diamond structure have been studied. Computer simulation techniques have been used to determine the formation and binding energies of vacancy and vacancy-impurity clusters of up to five points by employing these potentials. Two or more structures for some low index twin and fault boundaries, e. g. {Ill}, {211}, {113}, {122} and {233} in silicon and germanium have been investigated and their low energy configurations established. One of the possible stable structures for each of the {211}, {122} and {233} boundaries observes a two-fold screw orientation relation and for {211} and {122} this has the lower energy. The theoretical results are discussed and compared with available experimental information and suggestions are made for future work.