Surface Diffusion: The Low Activation Energy Path for Nanotube Growth

We present the temperature dependence of the growth rate of carbon nanofibers by plasma-enhanced chemical vapor deposition with Ni, Co, and Fe catalysts. We extrapolate a common low activation energy of 0.23–0.4 eV, much lower than for thermal deposition. The carbon diffusion on the catalyst surface and the stability of the precursor molecules, ${\mathrm{C}}_2{\mathrm{H}}_2$ or ${\mathrm{CH}}_4$, are investigated by ab initio plane wave density functional calculations. We find a low activation energy of 0.4 eV for carbon surface diffusion on Ni and Co (111) planes, much lower than for bulk diffusion. The energy barrier for ${\mathrm{C}}_2{\mathrm{H}}_2$ and ${\mathrm{CH}}_4$ dissociation is at least 1.3 eV and 0.9 eV, respectively, on Ni(111) planes or step edges. Hence, the rate-limiting step for plasma-enhanced growth is carbon diffusion on the catalyst surface, while an extra barrier is present for thermal growth due to gas decomposition.

Figure 1

(a) Schematic of the growth process. (b) Bright field image and electron energy loss spectroscopy Ni $L$ edge (854 eV) and carbon $K$ edge (284 eV) elemental maps of a PECVD CNF at 500 °C. Scale bar: 20 nm.

Figure 2

Arrhenius plots for CNF growth rates on different catalysts in ${\mathrm{NH}}_3$ diluted ${\mathrm{C}}_2{\mathrm{H}}_2$. The activation energies are calculated from the slope of the linear fit to the data. Temperature dependent changes in the CNFs crystallinity are not considered. The dotted line is the growth rate variation for Ni thermal CVD ($E_{\mathrm{act}}=1.21\mathrm{eV}$ [11, 42]).

Figure 3

(a) The incorporation of a new C atom into an existing graphene sheet on a Ni(111) surface proceeds spontaneously when started from this configuration, with the additional C atom placed at a nearby hollow site; (b)–(e) Equilibrium (left) and transition state (right) geometries: dissociation of ${\mathrm{C}}_2{\mathrm{H}}_2$ on (b) the Ni(111) surface; (c) Ni(111) step edge, where the large dark spheres indicate metal atoms of the topmost layer; (d) diffusion of a C atom on Ni(111) surface; (e) a subsurface pathway one layer below the Ni(100) surface. The transition barrier height is shown next to each TS geometry.