Heat-Induced Transformation of Nanodiamond into a Tube-Shaped Fullerene: A Molecular Dynamics Simulation

Heat-induced structural transformation in nanodiamond of diameter $\sim 1.4\mathrm{n}\mathrm{m}$ is investigated by tight-binding molecular dynamics simulations using the environment-dependent tight-binding carbon potential. The nanodiamond is found to transform into a tube-shaped fullerene via annealing. Three interesting mechanisms for promoting inner carbon atoms of the nanodiamond into the surface carbon atoms of the tubular structure are observed. The “flow-out” mechanism prevails at temperatures lower than 2500 K and the “direct adsorption” and “push-out” mechanisms are observed at higher temperatures.

Figure 1

Atomic processes of structural transformation of nanodiamond to tube-shaped fullerene by successive annealings. (a) 0 K (at time $t=0\mathrm{p}\mathrm{s}$), (b) $\sim 2500\mathrm{K}$ ($t\approx 3\mathrm{p}\mathrm{s}$), (c) $\sim 2500\mathrm{K}$ ($t\approx 19\mathrm{p}\mathrm{s}$), (d) $\sim 2100\mathrm{K}$ $t\approx 35\mathrm{p}\mathrm{s}$), (e) $\sim 1900\mathrm{K}$ $t\approx 50\mathrm{p}\mathrm{s}$), and (f) $\sim 20\mathrm{K}$ $t\approx 120\mathrm{p}\mathrm{s}$). Simulated annealings with temperatures up to 3000 K are performed during the process $(\mathrm{e})\to (\mathrm{f})$. The white color indicates atoms and bonds of two and less-fold coordination. Red and yellow colors indicate atoms and bonds of threefold coordination and fourfold coordination, respectively. Green colors indicate atoms and bonds of five and higher-fold coordination. Note that two holes H1 and H2 are created in (d). See the text for the part A in (e).

Figure 2

Flow-out mechanism observed around the hole H1 on the top side of the cluster labeled in Fig. 1d. The process corresponds to the steps of Figs. 1c, 1d, 1e. (a) $\sim 2500\mathrm{K}$ ($t\approx 19\mathrm{p}\mathrm{s}$), (b) $\sim 2600\mathrm{K}$ ($t\approx 24\mathrm{p}\mathrm{s}$), (c) $\sim 2500\mathrm{K}$ ($t\approx 25\mathrm{p}\mathrm{s}$), (d) $\sim 2100\mathrm{K}$ ($t\approx 33\mathrm{p}\mathrm{s}$), (e) $\sim 2000\mathrm{K}$ ($t\approx 45\mathrm{p}\mathrm{s}$), and (f) $\sim 1900\mathrm{K}$ ($t\approx 50\mathrm{p}\mathrm{s}$). $t$ is the total simulation time. The blue color indicates the inner atoms and bonds and the yellow color indicates the surface atoms and bonds at the starting configuration (a). The motion of blue atoms and bonds shows the process of promoting inner carbon atoms into surface carbon atoms.

Figure 3

Conversion of inner carbon atoms into surface carbon atoms by the direct adsorption mechanism. (a) $\sim 2500\mathrm{K}$ $\Delta t=0\mathrm{p}\mathrm{s}$), (b) $\sim 2900\mathrm{K}$ ($\Delta t=0.31\mathrm{p}\mathrm{s}$), (c) $\sim 3000\mathrm{K}$ ($\Delta t=1.29\mathrm{p}\mathrm{s}$), (d) $\sim 3000\mathrm{K}$ ($\Delta t=1.46\mathrm{p}\mathrm{s}$). (e) $\sim 3000\mathrm{K}$ ($\Delta t=1.54\mathrm{p}\mathrm{s}$), (f) $\sim 3000\mathrm{K}$ ($\Delta t=1.84\mathrm{p}\mathrm{s}$). (a) corresponds to the step of Fig. 1e. $\Delta t$ is the elapsed time relative to the moment of (a). The figure shows the part of the cluster marked by A in Fig. 1e. Blue atoms indicate the inner atoms of the cluster at the moment of (a). Red and yellow atoms indicate surface atoms. See the text for a detailed description of the colors.

Figure 4

Conversion of inner carbon atoms into sur-face carbon atoms by the push-out mechanism. (a) $\sim 2900\mathrm{K}$ ($\Delta t=0\mathrm{p}\mathrm{s}$), (b) $\sim 2900\mathrm{K}$ ($\Delta t=0.05\mathrm{p}\mathrm{s}$), (c) $\sim 2800\mathrm{K}$ ($\Delta t=0.11\mathrm{p}\mathrm{s}$), (d) $\sim 2800\mathrm{K}$ ($\Delta t=0.18\mathrm{p}\mathrm{s}$), (e) $\sim 2700\mathrm{K}$ ($\Delta t=0.24\mathrm{p}\mathrm{s}$), and (f) $\sim 2700\mathrm{K}$ ($\Delta t=0.32\mathrm{p}\mathrm{s}$). $\Delta t$ is the elapsed time relative to the moment of (a). The figure shows only a part of the cluster. Blue and red colors indicate inner and surface atoms, respectively, at the moment of (a).