Modified Wulff constructions for twinned particles

This paper reports the application of a modified form of the Wulff construction to derive theoretical shapes and total surface energies for twinned particles. It is proposed that the incorporation of twin boundaries in faceted particles leads to a number of constrained local minimum in the total surface energy (at constant volume), in addition to the minimum of a single crystal Wulff polyhedron. A procedure for generating these constrained local minima is described. The model is then applied to determine the structures of twinned particles in face-centred materials. Two possible configurations are examined, an arrangement where the crystals are symmetric about the twin boundaries, and an asymmetric configuration. Shapes and total surface energies for a large number of twinned structures are given using a simple model which includes only (111) and (100) surface facets. Excellent agreement is obtained between the theoretical model and experimental results.