Tight-binding molecular dynamics simulations of radiation-induced fragmentation of ${\mathrm{C}}_{60}$

The fragmentation of the ${\mathrm{C}}_{60}$ fullerene was investigated using tight-binding molecular dynamics simulations based on the parametrization of Papaconstantopoulos et al. [MRS Symposia Proceedings No. 491 (Materials Research Society, Pittsburgh, 1998), p. 221]. Averaged fragment size distributions over random sets of initial configurations were obtained from simulations of radiation-induced fragmentation in the $50–500\mathrm{eV}$ excitation energy range. The excitation caused by the radiation was simulated simply by ascribing suddenly random velocities to each atom of the fullerene cage. For low excitation energies, the size distributions are peaked for dimers (reflecting a preferential ${\mathrm{C}}_2$ emission) and a bimodal size dependence characterizes the distributions of the complementary small and large fragments. For high excitation energies, predominantly multifragmentation occurs, but a genuine power-law dependence of small fragments is not yet observable. A phase transition is found for rather low excitation energies $(100–120\mathrm{eV})$.

Figure 1

Normalized number of fragments for selected excitation energies. The fragmentation is characterized by U-shaped and bimodal distributions for low energies, and by power laws for very high energies and small fragment sizes.

Figure 2

Comparison of fragmentation probabilities as functions of excitation energy for small fragments $(n=1–4)$. Probabilities increase faster for monomers than for other fragments.

Figure 3

Relative fragmentation probabilities for small-sized fragments as function of the excitation energy.

Figure 4

The average fragment size shows its steepest decrease in the excitation energy interval of $100–120\mathrm{eV}$, indicating a certain type of phase transition.

Figure 5

Average minimum and maximum fragment sizes plotted against the excitation energy. The minimum fragment size exhibits a distinctive peak at approximately $110\mathrm{eV}$, indicating a special energy interval for the fullerene’s stability.

Figure 6

Overall minimum maximum fragment size plotted against the excitation energy. A considerable ratio of fullerenes remains unfragmented for energies up to $150\mathrm{eV}$. The continuous lines are just a visual aid.

Figure 7

Average number of fragments per trajectory vs excitation energy (semilogarithmic plot).

Figure 8

Simulated and theoretical average binding energy per atom vs excitation energy. The slightly lower simulated values are responsible for the nonfragmenting deformations of the fullerene.

Figure 9

The cumulative fragmentation probability shows a phase transition in the $100–120\mathrm{eV}$ excitation energy range.