2.2 The distribution of C concentration in Ni at different C/Ni ratios was evaluated to verify the growth mechanism of graphene
Based on the above analysis, it can be inferred that the formation of graphene through the inter-diffusions of Ni and Cu, resulting in a gradual decrease in the proportion of Ni and a corresponding increase in the proportion of C, and finally converted into graphene on the substrate promoted via the catalysis effect the Cu-Ni alloy. Molecular dynamics (MD) simulations are performed to further verify this graphene growth mechanism by evaluating the concentration distribution of C in the Ni with different C/Ni ratios using the ReaxFF as a measure.[37] The initial models of the Ni-C system were built by randomly replacing Ni atoms with C atoms, as shown in Supplementary Figure S3 . In Figure 2 , the First line (black), Heat line (orange), and Last line (blue) are the representative concentration distribution of C atoms along the z-direction (the normal direction of the substrate) at initial structures at 300 K, heated structure at1800 K, and the final annealed structure at 1800 K.Figures 2a-2b show representative snapshots of the annealed C-Ni systems for 75% and 85% C concentration, respectively. With the processing of annealing, the first peak and the second peak both rise significantly, indicating that C atoms are more easily stabilized to a certain plane to form stable graphene. The proportion of C atoms does not affect the position of graphene. However, the peaks inFigure 2d are higher than the peaks in Figure 2c , further demonstrating that the Ni−C alloy with a higher concentration of carbon atoms (85%) is more suitable for the growth of graphene than that with a lower concentration of carbon atoms (75%).
The kinetic process of graphene forming is shown in Figure 3 . There are 85% C atoms and 15% Ni atoms in the initial system, and its front views are displayed at 0 ps. Figures 3a-3e provide the evolution of the surface morphology of this system revealing four steps in the formation of graphene. At the first stage, randomly distributed atoms began to diffuse freely, and free C atoms tended to form C chains in 0 to 150 ps due to the strong bonding energy between C atoms. Soon afterward, a few elongated C chains were spontaneously folded into isolated C rings. These isolated C rings were easy to connect with free C chains or free C atoms as a nucleus, and the nucleus expanded into small pieces of graphene at 160 ps as the connected C chains folded again into new C rings around it. When the time is up to 500 ps, small pieces of graphene grow more significantly, merge with other ones, and finally become a large piece of graphene. After 500 ps, the size of the large graphene changed slightly. However, the graphene self-optimized itself into a more regular shape, and its internal defects reduced as the annealing continued to 1650 ps, suggesting that the quality of the resulting graphene was improved by extending the annealing time. The pair distribution function for C-C bonds is shown in Figure 3f , suggesting that with annealing, the peak at ~1.4 Å is very sharp. Since the length of the C-C bond in graphene is approximately 1.42 Å, the more C-C bonds formed at ~1.4 Å indicates that more graphene ring structures are formed during the annealing and cooling process.