Figure 2: Graphene bands and density of states.

Figure 3: Joined Bi-layer Graphene bands, and density of states.

Potential Energy Per Atom = 0.878 eVDefect Formation Energy = 0.001 eV

Figure 4: 3d Prints

2016 Research Experience for Undergraduates: Physics @ Rensselaer

Simulation and Printing of Joined Bi-Layer GrapheneTimothy W. Kilmer1,2, Humberto Terrores2

1State University of New York (SUNY) Oneonta2Rensslear Polytechnic Insitute

Project Goals Methods

Introduction

Results and Discussion Conclusions and Impact

Future Directions

Acknowledgments

The purpose of this project is to simulate the density of states and bands structure of two layer graphene connected by a hole (Figure 1) and compare properties to Graphene. On the side, to develop a process to print proposed structure, Buckminsterfullerene, and large fullerenes intended to demonstrate crystal structures.

DFT SimulationSimulations for Joined Bi-Layer Graphene and Graphene were done on CCI BlueGene q/amos and SDCS Comet both running the Quantum Espresso (QE) programs. Each sample was relaxed to the lowest total energy. Self Consistent Field (SCF) and band calculations were done on both structures using QE pw.x program. Finally the density of states were calculated using QE dos.x program.

Printing The models start as Cartesian coordinates generated from Mathematica and is made into a Protein Data Bank (PDB) file. These Files are then imported into Blender using Atomic Blender to show atoms as spheres and bonds as cylinders. The file size of the model was reduced and a thickness is applied so the model can be processed. The model was then exported as a STL and sent to RPI’s Rapid Prototyping Facility to be printed.

Future directions to be done involve simulating lattice vibrations, carrier density, and electron flow. Comparisons can also be made to graphene anti-dots and bi-layer graphene. The process to of improving the 3D printing process to print large complex fullerenes.

Thanks to Humberto Terrones, Aldo , Micheal Lucking, Larry Ruff, CCI RPI, Comet Exede, SUNY Oneonta, Quantum EspressoProject was supported by NSFReferencesH. Terrones M Terrones, Journal of Phys. 5, 1 (2003) W. Kohn and L. J. Sham, Physical Review 140, pp. 1333 (1965) L.A Chernozatonskii, V.A. Demin, & AA Artyukh, JETP Let. 5, pp 353-359 (2014)

With the use of DFT, the bi-layer graphene system was not spin polarized due to no change in the total energy of the system. Also the formation energy of the system per atom was 0.001 eV. However this could be changed by doping or changing the geometry of the hole. Such as, the hole radius and hole depth.

Figure 1:Joined bi-layer graphene side view (Left) and top view (Right).

Images generated in Mathematica.

Using density functional theory (DFT) will give insight on the band structure, density of states, spin polarization , and the total energy per atom of the system. Molecular structures can be represented as a file such as xyz, vasp, or PDB, which will be used to define the STL mesh for 3D printing and be used for DFT.

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