Catalyst nanoparticles play a crucial role in the synthesis of single-walled carbon nanotubes by chemical vapor deposition technique. Understanding the thermal behavior of the nano-catalysts, their interaction with Carbon and stability of nanocarbides can give better insight into the growth mechanism and control over selective, yield of nanotubes. In this work, we present results using first-principle calculations and classical molecular dynamics simulations to understand the thermodynamics of free and Al2O3 supported Fe-C nanoparticles. We observe that the substrate plays an important role during the growth reaction by increasing the melting temperatures of small and medium size Fe nanoparticles. We investigate Fe-C phase diagrams for small Fe nanoparticles (d∼2nm) and discover that as the size of the Fe nanoparticle is reduced, the eutectic point shifted significantly toward lower temperatures, as expected from the Gibbs-Thomson law, and also toward lower concentrations of C. We devise a simple model based on the Young-Laplace pressure-radius relation, to predict the behavior of the phases competing for stability in Fe-C nanoclusters at low temperature. We identify ranges of nanoparticle sizes which are compatible for steady state-, limited- and no-growth of SWCNTs corresponding to unaffected, reduced and no solubility of C in the Fe nanoparticles. We also calculate Fe-Mo-C ternary phase diagrams to investigate the behavior of bimetallic Fe:Mo catalyst nanoparticles. Our results show that addition of Mo (upto small concentrations) lowers the minimum radius when stable carbides nucleate and poison the catalyst, which enables a larger range of catalyst nanoparticles sizes to nucleate nanotubes. We also find that pure Fe has the highest surface concentration in Fe:Mo nanoparticles and is likely to be the active nucleation site for nanotubes.
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