Carbon Nucleation from ring seeds on Icosahedral Fe$_{13}$

Using ab initio molecular dynamics calculation, we computed the initial stages of carbon nanotube growth from ten -- atom carbon rings on icosahedral Fe$_{13}$. The carbon ring interacts with Fe$_{13}$ to form a zigzag structure due to a mismatch between the number of atoms on the ring and the atoms on the pentagonal ring of Fe$_{13}$, with formation energy of 2.2 ev. A mixture of carbon dimers and carbon atoms interact with the Fe$_{13}$ + C$_{10}$ structure to yield a tubular structure with the lowest energy. Another configuration of carbon atoms distributed in the vicinity hexagonal lattice sites interacts with Fe$_{13}$ + C$_{10}$ structure to form also a tubular structure that is almost degenerate in energy to the ground state. The results indicate that the icosahedral symmetry of the Fe$_{13}$ with its magnetic moment almost intact is retained whenever the tubular structure is formed.