Supplementary Figure 1. Schematic of rapid thermal annealing process: (a) indicates schematics and SEM cross-section of the initial layer-by-layer film configuration, (b) demonstrates schematic and cross-section of the different layers after annealing process.
Supplementary Figure 2. AFM image of the graphene grown at 800 C and transferred using a thermal release tape procedure onto a SiO 2 substrate. (a) Topography images of the graphene transferred on silicon dioxide with scaled up profile of the uniform flake (b) are shown. (c) Heigh profile of the area highlighted in (a) by the line confirms the flake thickness of approximately 0.6 nm and the Raman signature indicates single layer graphene (I 2D /I G =1.9, fwhm of 2D peak = 50 cm -1 ). D-peak presence in Raman signature originates from the folds and residual contamination of the thermal release tape transfer method.
Supplementary Figure 3. Raman mapping of 2D to G peak intensity ratio. (a) The area of graphene on diamond sample selected for Raman mapping is highlighted with rectangle. (b) Raman mapping of I 2D /I G intensity ratio demonstrates the uniformity of the graphene films grown on UNCD. Small dots are possibly due to contamination on the surface of graphene. (c) The typical Raman signature of the sample is provided. Supplementary Figure 4. SEM images of the free-standing graphene growth procedure: (a) FIB patterning to produce the hole in UNCD film (b) Nickel evaporation (c) lateral growth of graphene film over the hole after RTA annealing procedure.
Supplementary Figure 5. Selective growth of graphene on diamond for nickel through nickel patterned through a shadow mask. (a) demonstrates SEM images of graphene grown on diamond with selective growth of graphene with (b) representing the scaled up SEM image of the selected square. Raman signatures indicate the outside of the pattern area to remain UNCD (c) and the patterned area to selectively grow graphene (d).
Supplementary Figure 6. XRD analysis of 50 nm Ni film on UNCD wafer. The size of nickel crystals is estimated to be 15 nm, calculated from full width half maximum (FWHM) of Ni (111) peak (at 2θ=44.1) using Debye-Scherrer equation. Supplementary Figure 7. Initial configuration of nickel on diamond. The configuration shows the Ni(111) slab on top of ultra-nano-crystalline diamond (UNCD) with typical grain boundary (13 twist (100)).
At ~300 K, t = 0 Top view At ~1600 K, t = 2 ns Supplementary Figure 8. Simulation snapshots of Ni(111) slab on single crystal diamond. Compared to bi-crystal UNCD, we observe very little amorphization at the Ni/diamond interface. At t=2ns, we observe very little penetration of this amorphized C into Ni bulk. Top view at 2 ns shows very little segregation of C atoms to the free surface.
Supplementary Figure 9. Effect of orientation of the underlying Ni substrate on graphene growth. Snapshots of atomic configuration are shown at different times during annealing of amorphous carbon deposited on Ni substrates in our MD simulations. The Ni substrates are oriented with surface normal along 111 (a d) and 001 (e h) directions. During the annealing process, amorphous carbon undergoes ordering resulting in a monolayer graphene sheet with nearly full coverage on Ni(111), while graphene patches with significant number of holes and defects are obtained on Ni(001). Graphene growth on Ni(111) is favored due to the presence of close-packed triangular moiety of Ni atoms (d) as compared to the square arrangement of Ni atoms in 001 plane (h). Supplementary Note 1 Molecular dynamics simulations of Ni(111) deposited on UNCD with a twist grain boundary. For our MD simulations on Ni/polycrystalline UNCD, we constructed a UNCD bicrystal containing a 13 twist (100) GB. It was reported previously that this particular GB presents a good compromise between the computational requirements and the need of a reasonably large cell size needed to reproduce a general high-angle GB 7. The procedure for the construction of the grain boundary is as follows: First, we perform a relative rotation of the two halves of the diamond crystal by 67.4 about the z axis that is normal to the common (100) plane. Such a rotation gives a coincident site lattice periodic in two dimensions with a planar cell containing 13 atoms per (100) plane. We construct a three- dimensional periodic model of the crystal with planar repeating grain boundaries. Note that the periodicity in the third dimension is achieved by extending the two grain boundaries per repeating cell. Each cell has a thickness of 16 layers and thus contains 208 carbon atoms. This generated grain boundary was subjected to a relaxation or an equilibration procedure. During the initial relaxation, the dimensions of the cell in the GB plane were fixed because of the rigidity of the diamond lattice. However, we do allow for expansion in the z direction to reproduce the volume increase in the grain boundary region. Subsequently, we performed thermal equilibration of this initial structure by simulating at a high
temperature of 1500 K for 100 ps. We then use a simulated annealing to gradually lower the temperature, and the final structure was optimized by a conjugate gradient method. The initial equilibrated grain boundary structure is shown in Supplementary Figure 7. A schematic representation of the initial configuration used for the simulations on Ni/UNCD bicrystal is shown in Supplementary Figure 7. The computational supercell comprised of a Ni thin film of approximate dimensions12å x 200Å x 24 Å placed on top of the 13 twist (100) GB of UNCD (constructed using methods detailed in Supplementary Note 2). All the MD simulations in this study were performed using the MD simulation package LAMMPS. 8 Prior to running high temperature annealing, the system comprising of Ni on top of the UNCD GB was equilibrated at 300 K within canonical ensemble for 50 ps. The temperature was maintained constant using a Nose-Hoover thermostat (NVT) 9. Both the Ni thin film and the diamond surfaces forming the grain boundary are allowed to freely relax during these equilibration runs with no charge transfer. The equilibrated samples are then simulated in a NVT ensemble for 1 ps with dynamic charge transfer using the ReaxFF potential model to generate the relaxed configuration for use in subsequent simulations. The slab of Ni (111) is then placed on top of the diamond surfaces; the grain boundary is normal to the Ni(111) surface (Supplementary Figure 7). Several simulations of Ni-induced amorphization of carbon and subsequent graphization were then performed at high temperatures ranging from 1200 K up to 1600 K. To facilitate comparisons with the experiments, we have performed the graphene growth simulations in both hydrogen and hydrogen-free environments. The hydrogen atmosphere was created by introducing H 2 molecules in the simulation box with their x, y, and z positions chosen randomly. In the case of simulations in the hydrogen environment, reflecting boundary conditions are imposed in the z-direction to confine the molecules that might reach the simulation box limit. The initial atomic velocities were chosen from a Maxwell-Boltzmann distribution corresponding to the target temperature. The equations of motion were integrated using a velocity-verlet scheme with time steps of 1 fs. The atomic charges were updated every 10 MD timesteps to afford long runs. We have confirmed that a more frequent charge update does not have any impact on the results of our MD simulations.
Supplementary Note 2 Reactive Force Field details. The interactions between Ni and C atoms were modelled using a reactive bond-order potential, namely, reactive force field (ReaxFF) developed by van Duin and co-workers; 1 the parameters used in this works are taken from Mueller et al. 2. In particular, the bond-order based formalism of ReaxFF enables it to provide a continuous description of formation/dissociation of chemical bonds. This in conjunction with dynamic charge transfer between atoms via the electronegativity equalization scheme, (implemented in ReaxFF framework) enables the accurate description of chemical reaction pathways, and associated barriers. 1 In terms of the mathematical framework of ReaxFF, the total energy is composed of several contributions (Supplementary Equation 1) from bonded (i.e, bond, over/under coordination, angle bending, dihedral torsion, lone-pair) and non-bonded (i.e., hydrogen bond, van der Waals, Coulomb) interactions. E total = E bond + E over + E under + E lp + E val + E tors + E H + E VdW + E Coul (1) In addition, the atomic charges at every MD step are obtained using a electronegativity equalization method, which minimizes the overall electrostatic energy contribution (Supplementary Equation 2) while conserving the charges. qiq 2 j E( q) iqi iqi T( rij) kc 2 3 1 / 3 i rij ij (2) In the above equation, q, χ, η, T(r), γ, and k c are atomic charge, electronegativity, atomic hardness, 7th order taper function, shielding parameter, and dielectric constant, respectively. Detailed implementation and development of ReaxFF models for Ni-C interactions can be found in the work by van Duin and co-workers. 1,3 Owing to this unified framework, ReaxFF is capable of treating metallic, ionic, and covalent systems equally well; 1 more relevant to this work, ReaxFF has been extensively used to study formation of graphene and carbon nanotubes. 4,5 Additionally, it can take into account the presence of multiple coordination as well as valence states in the growing graphene film. 3,6
Supplementary Note 3 MD simulations of Ni(111) deposited on single crystal diamond. To understand the role of UNCD GB on the nucleation of graphene on free surface of Ni, we performed a set of control simulations with conditions identical to those detailed in Supplementyary Note 1 but using a single crystal diamond (instead of a UNCD bi-crystal). From these simulations, we observed that in the absence of a GB in diamond, Ni atoms do not penetrate into diamond, and consequently, the kinetics of Ni induced amorphization of diamond is drastically impaired. Even after 2 ns of MD simulation time at temperatures as high as 1600 K, only the interfacial layer in diamond gets amorphized; in addition, very few C atoms diffuse into the Ni slab (Supplementary Figure 8). In comparison, in the presence of a twist GB in UNCD, there is extensive penetration of Ni into UNCD. Within approximately 1 ns of MD simulation time at the same temperature (i.e, 1600 K) there is a rapid Ni induced amorphization. The rapid amorphization of UNCD results in higher flux of C into the Ni slab which supersaturates rapidly. Once the Ni slab is super-saturated, C tends to segregate to the free surface, which is followed by the graphenization process. In the case of single crystal diamond, the kinetics of amorphization is much slower which translates into much slower C flux into Ni. The time required for super-saturation and subsequent segregation to the free surface is also considerably higher in single crystal compared to UNCD. This is consistent with other experimental studies we have mentioned in references 10,11 wherein it requires much longer annealing time to observe graphene growth, which are mostly spotty and with Ni seggegration, which has nowhere to go unlsess etched from the surface. Supplementary Note 4 MD simulations of surface diffusion of C atoms on Ni. Our second set of MD simulations explore the fast kinetics of surface diffusion of carbon atoms on the free surface of Ni that underlies rapid growth of graphene. In this set of simulations, we also investigated the impact of crystallographic orientation of Ni surface by employing Ni slabs with surface normal oriented along the crystallographic 111 and 001 planes. For each of these simulations, we first generated
an initial configuration (t = 0) by placing a layer of completely disordered (amorphous) carbon (with nearest C-C spacing of approximately 2-2.5 Å) on a Ni substrate with dimensions approximately 40 Å 40 Å 50 Å with the desired surface orientation, as shown in Supplementary Figures 9a and 9e. The initial coverage of C on Ni slabs of different orientations are kept identical to facilitate comparison. Periodic boundary conditions were imposed in the plane of the surface. The temperature of the system was ramped from 300 K to several high temperatures (1200 K 1600 K) over 50 ps in a canonical ensemble (NVT) with a Nosé-Hoover thermostat, as implemented in LAMMPS; 8 subsequently, the temperature was held at the high temperature for an additional 150 ps. Direct visualization of the MD trajectories (Supplementary Figure 9) showed that in the initial approximately 5 ps, when the temperature is around 300 K, the density of amorphous carbon tends to increase, along with ordering of C atoms and the formation of C-C bonds (Supplementary Figures 9b and 9f). As indicated by Supplementary Figures 9b and 9f, the formation of carbon rings occurs on all Ni surfaces; however, the Ni (111) exhibits much higher formation of graphene like C-rings as compared to a Ni(001) surface. To provide a quantitative assessment of this orientation preference, we calculated the rate of formation of C-rings containing 5-8 C members on Ni substrates of different orientations in the initial approximately 5 ps. From these calculations, we found that among the low-index surfaces of Ni, the C rings form at the highest rate on Ni (111) approximately 30 rings per ps; this rate is more than twice as fast as that on Ni (001) surface (approximately 12 rings per ps). Interestingly, most of the rings (approximately 65%) that form on a Ni (111) surface are 6-membered (like the hexagons in graphene), while the population of 6-membered rings nucleated on a Ni (001) surface is fairly limited, which is ~25% of the total nucleated C-rings (Supplementary Figure 9f). This clearly indicates that graphene formation is most favorable on Ni (111) among the low-index planes. After this initial time period, the C atoms continue to re-arrange to reduce the number of defects (i.e., off 6-membered rings, holes) but no new C-rings appear. As shown in Supplementary Figure 9c, the monolayer graphene that forms on a Ni (111) surface features the least number of defects, and covers nearly the entire substrate. On the other hand, on Ni (001), graphene forms as patches and is highly defective (Supplementary Figure 9g). We note that these results are robust; the effect of the Ni surface orientation on graphene growth is unaffected by the temperature
schedule and the highest temperature achieved during the annealing. The kinetics of reorganization of C-atoms to reduce the defects, as expected, is slow at lower temperatures. The preferential formation of 6-membered C rings on Ni (111) as opposed to Ni (001) surfaces can be attributed to the higher commensurability between Ni (111) and graphene, as compared to that between Ni (001) and graphene. Such a commensurability has been reported in previous MD works (a comprehensive review has been published recently by Elliot and co-workers 12 ). The Ni atoms on (111) plane are arranged on a close-packed triangular lattice (Supplementary Figure 9d), which closely resembles the honeycomb structure of graphene; this enables Ni (111) substrate to provide a suitable template for the formation of nuclei for graphene growth, i.e., 6- membered C-rings. Ni (001) plane, on the other hand, exhibit a square lattice (Supplementary Figure 9h) and cannot provide such a template. Furthermore, recent first-principle calculations have reported that the diffusion of C on a Ni (111) surface is much lower than that on Ni (001) [around 0.5 ev on Ni (111); and around 1.9 ev on Ni (001)] 13. This leads to substantially higher diffusion of C on Ni (111) plane, which explains the faster rate of graphene growth on Ni (111). Even a sub-surface diffusion pathway for C over Ni (001) has a high barrier (1.0 ev). 13 Finally, the diffusion barrier for C in bulk Ni is 1.6 ev 13 our MD simulations are consistent with these reports, wherein the diffusion of C occurs primarily over the surface rather than in the bulk.
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