The classification of close-packed clusters of substitutional point defects in crystals

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. For example, there are 458 different configurations of five point defects in h.c.p. structures, and these have a total of 9728 variants. Relationships between the results for different structures are discussed and some inaccuracies in earlier analyses noted.