For each potential, four MD simulations with densities of 1.5, 2.0, 2.5 and 3.0 g/cc are performed in an NVT ensemble. The same general protocol is applied to all simulations and involves three steps: (i) the creation and equilibration of the liquid, (iii) the quenching of the liquid to produce an amorphous solid and (iii) the annealing of the amorphous solid to induce graphitization. An example of the temperature profile throughout this protocol is shown in Fig. 1. Note that the values of Tliquid and Tanneal are specific to the combination of the potential and density as discussed below.
The liquid is created starting from a slightly randomized simple cubic lattice at the desired density. A supercell of 32 32 32 carbon atoms (i.e. 32,768 atoms) is used, and the initial temperature is 100 K. This structure is highly unstable and immediately collapses and melts, leading to a rapid increase in temperature. For the Tersoff, REBO and EDIP potentials the initial stage of melting is followed in the NVE ensemble, and after 0.25 ps a thermostat is activated to equilibrate the liquid at the desired temperature Tliquid. For ReaxFF, LCBOP-I and COMB3, the thermostat is applied from the beginning as otherwise the temperature becomes too high and the simulation becomes numerically unstable. To ensure the liquid is highly diffusive, the value of Tliquid (see Table 2) is chosen such that the mean-squared-displacement (MSD) increases linearly with time. A value of 6000 K is sufficient for REBO-II, EDIP, ReaxFF and COMB3, but a higher temperature of 8000 K is required for Tersoff and LCBOP-I. These high temperature are not surprising, as the melting point of the Tersoff potential is approximately 1700 K higher than the experimental value , and similar values in the range of 5500e6000 K were reported for the LCBOP family . The liquid is maintained at the chosen temperature Tliquid until the potential energy equilibrates. In all cases the liquid is equilibrated for 5 ps, except in the case of LCBOP-I which requires an equili- bration of 15 ps.
Graphitization of Amorphous Carbons: