Simulating the thermal stability and phase changes of small carbon clusters and fullerenes

The thermal stability, phases and phase changes of small carbon clusters and fullerenes are investigated by constant energy Molecular Dynamics simulations performed over a wide range of temperatures, i.e., from $T=0 {\rm K}$ to above the melting point of graphitic carbon. The covalent bonds between the carbon atoms in the clusters are represented by the many-body Tersoff potential. The zero temperature structural characteristics of the clusters, i.e., the minimum energy structures as well as the isomer hierarchy can be rationalized in terms of the interplay between the strain energy (due to the surface curvature) and the number of dangling bonds in the cluster. Minimization of the strain energy opposes the formation of cage structures whereas minimization of the number of dangling bonds favors it. To obtain a reliable picture of the processes experienced by carbon clusters as a function of temperature, both thermal and dynamical characteristics of the clusters are carefully analyzed. We find that higher excitation temperatures are required for producing structural transformations in the minimum energy structures than in higher lying isomers. We have also been able to unambiguously identify some structural changes of the clusters occurring at temperatures well below the melting-like transition. On the other hand, the melting-like transition is interrupted before completion, i.e., the thermal decomposition of the clusters (evaporation or ejection of $\rm C_2$ or $\rm C_3$ units) occurs, from highly excited configurations, before the clusters have fully developed a liquid-like phase. Comparison with experiments on the thermal decomposition of $\rm C_{60}$ and a discussion of the possible implications of our results on the growth mechanisms leading to the formation of different carbon structures are included