General description of the calculations

The Oxford Order N (OXON) [77] package was used in the present work. This is a set of programs for carrying out atomistic static and dynamic calculations using potentials which are based on tight-binding methods.

The tight-binding method was employed in the calculations to describe interactions between carbon atoms. With this method, the molecular dynamics technique was applied to calculate the positions and the velocities of the atoms as function of the time. In the MD calculation, Newton's equations of motion were solved using the predictor-corrector algorithm. The MD time step was 0.5 $\times$ 10$^{-15}$ s. Periodic boundaries conditions were applied to the problem.

In order to calculate the ratio of $sp^2$ to $sp^3$ bonded atoms, as well as the radial and angle distribution functions of the structures of amorphous carbon generated a FORTRAN program was written.