Size effect on the crystal phase of cobalt fine particles

We have synthesized Co fine particles with the average diameter $(D)$ of less than 500 \AA{} by sputtering Co in a somewhat high inert-gas pressure. It has been found that there is a close relationship between the particle size and the crystal phase; that is, pure fcc (\ensuremath{\beta}) phase for $D<~200\AA{},$ a mixture of hcp (\ensuremath{\alpha}) and \ensuremath{\beta} phases for $D\ensuremath{\sim}300\AA{},$ and \ensuremath{\alpha} phase with inclusion of a very small amount of \ensuremath{\beta} phase for $D>~400\AA{}.$ Precise structural characterizations have revealed that the \ensuremath{\beta} particles are multiply twinned icosahedrons and the \ensuremath{\alpha} particles are perfect single crystals with external shape of a Wulff polyhedron. In order to explain the size effect on the crystal phase of Co fine particles, we have performed theoretical calculations for total free energies of an \ensuremath{\alpha} single crystal, a \ensuremath{\beta} single crystal, and a multiply twinned \ensuremath{\beta} icosahedron. The present calculations well explain the size dependence of the crystal phase of the Co fine particles, and have revealed that the stabilization of \ensuremath{\beta} phase, confirmed by previous studies, is the intrinsic effect caused by the small dimensionality of fine particles. Moreover, the phase transformations that occurred in annealing experiments can also be explained by the theory.