  Transformation of graphene flakes to fullerenes assisted by Ni clusters is
investigated using molecular dynamics simulations. The bond-order potential for
Ni-C systems is developed. The potential reproduces the experimental and
first-principles data on the physical properties of pure Ni as well as on
relative energies of carbon species on Ni surfaces and in Ni bulk. The
potential is applied for molecular dynamics simulations of the transformation
of graphene flakes consisting of 50 - 400 atoms with and without Ni clusters
attached. Free fullerenes, fullerenes with Ni clusters attached from outside
and fullerenes encapsulating Ni clusters (Ni endofullerenes) are observed to
form in the presence of Ni clusters consisting of 5 - 80 atoms. Moreover, a new
type of heterofullerenes with a patch made of a Ni cluster is found to form as
an intermediate structure during the transformation. The Ni clusters are shown
to reduce the activation energy for the graphene-fullerene transformation from
4.0 eV to 1.5 - 1.9 eV, providing the decrease of the minimal temperature at
which such a transformation can be observed experimentally from about 1400 K
for free graphene flakes to about 700 - 800 K. While the transformation of free
graphene flakes is found to occur through formation of chains of
two-coordinated carbon atoms at the flake edges, the mechanism of the
Ni-assisted graphene-fullerene transformation is revealed to be based on the
transfer of carbon atoms from the graphene flake to the Ni cluster and back.
The way of controlled synthesis of endofullerenes with a transition metal
cluster inside and heterofullerenes with a transition metal patch is also
proposed.
