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

Abstract

Abstract The method of classifying and enumerating close-packed clusters of vacancies or substitutional solutes in crystals by using representation matrices has been extended to include clusters with more than one type of point defect. Examples are provided for a few simple cases in order to clarify the notation adopted. Results are then presented for clusters of up to four point defects in all single-lattice and selected double-lattice structures. All possible cases are included, 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. For example, in h.c.p. structures there are 1043 configurations of clusters with four points, each occupied by a different solute, and these have a total of 22 800 variants. In all there are 106 possible decorated topologies for the configurations and these are illustrated. Relationships between the results for different structures are discussed.