Thermodynamic instabilities in nano-catalysts and their effects on the diameter of grown nanotubes*

Fe and Fe:Mo nanoclusters are becoming the standard catalysts for growing single-walled carbon nanotubes (SWCNTs) via chemical vapor decomposition (CVD). Contrary to the Gibbs-Thomson formalism, experimental results show that reducing the size of the catalyst beyond a certain limit requires increasing the (minimum) growth temperature. This apparent paradox is addressed in terms of solubility of C in Fe nanoclusters. By using first principles calculations, an innovative thermodynamic model is constructed to determine the behavior of the phases competing for stability. As a function of particle size, there are three scenarios: steady state-, limited-, or no-growth of SWCNTs, corresponding to unaffected, reduced, and zero solubility of C in the clusters. The results are extended to Fe-Mo binary catalysts. The 15+ year long-standing question about the effects of Mo concentration on the growth capability is finally answered. Phys. Rev. Lett. {\bf 100}, 195502 (2008), Phys. Rev. B, {\bf 77}, 115450 (2008), Phys. Rev. B {\bf 75}, 205426 (2007).