Literature review The behavior of the Cu-C system has been extensively studied. Several attempts to grow graphene on copper are available in the literature using somewhat different methods to either grow them from solid or gas-like phases. Injected carbon atoms attaching to pre-deposited graphene Hot LJ-solid with Cu-like structure but much higher mp Initial (red) and growing (blue) graphene region after ~0.7 ns

Term project idea Show that Graphene can be grown in a similar manner using the COMB3 potential and LAMMPS http://lammps.sandia.gov/doc/pair_comb.html The Charge-Optimized Many-Body (COMB) potential in version 3 includes the fully optimized Cu-C interaction. For style comb3, in addition to ffield.comb3, a special parameter file, lib.comb3, that is exclusively used for C/O/H systems, will be automatically loaded if carbon atom is detected in LAMMPS input structure.

Preliminaries (1) Reproduce simple properties of copper to ensure that the potential can be applied For example study the behavior of a copper block (32000 atoms) with (ppp) bounds LAMMPS: it is suggested to use langevin thermostat and NVE ensemble for heating runs

Preliminaries (2) How about graphene (a 2 dimensional structure) Boundaries (ppf) or (pps) – shrink wrapped might produce artifacts #graphene island variable alat equal 2.46 lattice custom ${alat} & a1 1 0 0 & a2 0 1.732050807569 0 & a3 0 0 3.35 & basis 0 0 0 & basis 0.5 0.166666666667 0 & basis 0.5 0.5 0 & basis 0.0 0.666666666667 0 & region sheet block 0 10 0 10 0.0 0.5 300K equilibrating 1 ns (C193-C190) = 1.42026(0) Å Step Temp PotEng TotEng Press Volume 0 300 -7.3515051 -7.312824 8925.8713 4319.4076 50 240.63396 -7.3176361 -7.2866094 7667.5257 4319.4076 100 298.41618 -7.3137675 -7.2752906 8164.3517 4319.4076 150 319.2247 -7.308583 -7.2674231 6031.9098 4319.4076 200 318.90352 -7.3083392 -7.2672208 6776.6484 4319.4076 250 315.11179 -7.3083525 -7.267723 6180.2545 4319.4076 300 299.75036 -7.3072195 -7.2685706 4675.9149 4319.4076 The C-C bond length of graphene at RT after several ns equilibration is correctly reproduced The cohesive energy compares well to literature (7.3-7.4, cf. D’ Souza, Handbook of Carbon Nano Materials)

Preliminaries (3) The growth temperature should be as high as possible as to “enhance” the growth rate due to very limited total simulation time (real-scale graphene growth takes place around >800K and on 5 minutes timescale) In a small (400 C atoms, pps boundary) graphene test system heating up to 1400K and cooling back down to RT leads to no visible instability of the system

Trial (1) Equilibrate a sheet of graphene (a “flake”) on copper to see if it adapts a reasonable equilibrium distance (f) 431 atoms in group graphene 8000 atoms in group copper 8431 atoms in group mobile (@100K) Graphene flake (p) Mobile Cu layer Fixed bottom layer (f) (starting distance Cu-C was 3.5 A, Equilibrium distance Cu-C here ~ 2.6, reported for BOB: 3.4)

Problem Atoms randomly displaced (0.1 a) (@100K) (@1000K) (@300K) The attempt to see the re-assembly of previously randomly in-plane displaced graphene at 1000K fails.

Possible reason The studied system is small (pp boundaries) and size dependence has been suggested A comparable system (Klaver et al., Carbon 82 (2015)) Melts at 1140 K (MEAM~1360K) Studied system has 180,000 atoms compared to 10,000 in my case Upon request Dr. Klaver told me that they needed to set the time constant very low (0.0005 ps) compared to my 1 fs Currently running a larger system with smaller time constant