How the shape of catalyst nanoparticles determines their crystallographic orientation during carbon nanofiber growth

A theoretical model is presented that explains spontaneous changes in the crystalline orientation of nanoparticles. The spontaneous changes in crystalline orientation are attributed to the crystal anisotropy of the surface energy of nanocrystalline particles. We consider an important specific case of the chemical vapor deposition growth of carbon nanofibers, where previous studies have shown that both the catalyst nanoparticle shape and the nanofiber growth rate change with changes in the chemical potential of diluted carbon. Energetic considerations of the nanoparticle’s free surface and its interfacial energy with the nanofiber during these shape changes are shown to force a reorientation of the nanoparticle crystallographic axes at a critical growth rate. The model therefore reveals the mechanism by which the shape and crystallographic orientation of the catalyst nanoparticle are linked to the nanofiber growth rate. The model suggests a new way, based upon measurable geometry of nanoparticles during in situ growth experiments, to estimate the role of chemisorption in the attraction of the graphene film to the curved catalyst surface and the anisotropy energy of this interface.