Reduced carbon solubility in Fe nanoclusters and implications for the growth of single-walled carbon nanotubes

Fe nanoclusters are becoming the standard catalysts for growing single-walled carbon nanotubes via chemical vapor decomposition. Contrary to the Gibbs-Thompson model, we find that the reduction of the catalyst size requires an increase of the minimum temperature necessary for the growth. We address this phenomenon in terms of solubility of C in Fe nanoclusters and, by using first-principles calculations, we devise a simple model to predict the behavior of the phases competing for stability in Fe-C nanoclusters at low temperature. We show that, as a function of particle size, there are three scenarios compatible with steady state growth, limited growth, and no growth of single-walled carbon nanotubes, corresponding to unaffected, reduced, and no solubility of C in the particles.