We use a density-functional based tight-binding method to study diamond
growth steps by depositing dicarbon species onto a hydrogen-free diamond (110)
surface. Subsequent C_2 molecules are deposited on an initially clean surface,
in the vicinity of a growing adsorbate cluster, and finally, near vacancies
just before completion of a full new monolayer. The preferred growth stages
arise from C_2n clusters in near ideal lattice positions forming zigzag chains
running along the [-110] direction parallel to the surface. The adsorption
energies are consistently exothermic by 8--10 eV per C_2, depending on the size
of the cluster. The deposition barriers for these processes are in the range of
0.0--0.6 eV. For deposition sites above C_2n clusters the adsorption energies
are smaller by 3 eV, but diffusion to more stable positions is feasible. We
also perform simulations of the diffusion of C_2 molecules on the surface in
the vicinity of existing adsorbate clusters using an augmented Lagrangian
penalty method. We find migration barriers in excess of 3 eV on the clean
surface, and 0.6--1.0 eV on top of graphene-like adsorbates. The barrier
heights and pathways indicate that the growth from gaseous dicarbons proceeds
either by direct adsorption onto clean sites or after migration on top of the
existing C_2n chains.Comment: 8 Pages, 7 figure