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.

Figure 1

Evolution of minimum synthesis temperature ($T_{\mathrm{synth}}^{\min }$) for growing SWCNTs with $\mathrm{Fe}:{\mathrm{Al}}_2{\mathrm{O}}_3$ molar ratio. The inset shows the Raman spectra for minimum synthesis temperature versus $\mathrm{Fe}:{\mathrm{Al}}_2{\mathrm{O}}_3$ molar ratio. The inset shows the Raman spectra for samples obtained with a catalyst molar ratio of $1:50$.

Figure 2

Size-pressure approximation for Fe nanoparticles. Given a spherical particle, we estimate the hydrostatic pressure due to the surface curvature by calculating the deviation of the average bond length inside the cluster, $\Delta d_{nn}\equiv d_{nn}^0-d_{nn}$, and comparing it to the deviation of the bond length for the bulk material as a function of hydrostatic pressure.

Figure 3

The scenarios described in the text with their implication in CVD SWCNT growth with Fe nanocatalysts. $P$ is the pressure at which the calculations are performed and $R$ is the radius of the corresponding SWCNT within the size-pressure approximation. $E_f[{\mathrm{Fe}}_3\mathrm{C}]=E_f[\alpha \mathrm{\text{−}}{\mathrm{FeC}}_{\sim 0.00102}^{\mathrm{sol}}]$ for $R_{\min }\sim 0.58\mathrm{nm}$ ($P\sim 4.3\mathrm{GPa}$).