This project generates 3D visual models of various carbon nanostructures like graphene, graphite, carbon nanotubes, and buckyballs using C++ programs and modeling software. The models are then analyzed by comparing their calculated densities to experimental values, proving the models accurately represent the real materials. The project also determines the critical bond distance between carbon atoms in the models.

1. Generating 3D Visual Models of
Carbon Nano-structures
Shangzhou Xia
under the direction of
Professor Ju Li
Massachusetts Institute of Technology
Research Science Institute
July 30, 2014

2. Abstract
As the study on carbon nano-materials has become a hot field of research and appli-
cation, three-dimensional visual modeling of the carbon nano-structures is essential for a
thorough and scientific comprehension of their patterns, properties, and subsequently ap-
plicative values. This project uses C++ programs and the atomistic configuration viewing
software AtomEye to generate three-dimensional models of carbon nano-structures includ-
ing monolayer graphene sheets, graphite crystal, armchair and zigzag graphene nano-ribbons,
carbon nanotubes of di↵erent chiralities, and buckminsterfullerene (C60). The project then
compares the calculated average mass densities of these models to their experimental val-
ues, and these models proved close to the actual nano-materials and therefore scientific. The
project also finds the critical distance of chemical bond formation between carbon atoms in
AtomEye models.
Summary
When the age of carbon nano-materials has come, 3D visual models of these materials are
needed to help people better understand their patterns, properties and applicative values.
This project uses modeling softwares to make models of carbon nano-structures such as
graphene, carbon nanotubes, and buckyballs. Later data analyses prove the models correct
in describing the materials. The project also finds the critical distance of bond formation
between carbon atoms.

3. 1 Introduction
1.1 Overview
The age of carbon nano-structures began in 1947 when the theory on the band structure of
graphene was first established by Canadian theoretical physicist Philip Russell Wallace[1].
Ever since then, this particular topic has attracted intense attention of experts in physics,
chemistry, and engineering. One of the most notable breakthroughs was made by Andre
Konstantin Geim, Konstantin Sergeevich Novoselov et al.[2, 3], who successfully isolated
the first free-standing, atomically thin membrane, graphene in 2005. Consequently, they
were jointly awarded the Nobel Prize in Physics by the Nobel Foundation[4] in 2010, “for
groundbreaking experiments regarding the two-dimensional material graphene.”
Interestingly, many other carbon nano-structures that have been discussed and studied,
including the well-known carbon nanotubes and buckminsterfullerene (C60) are based on the
structure of graphene. Therefore, all these studies, as studies on some complicated combi-
nations of di↵erent nano-materials done by Geim and Grigorieva[5], start with a thorough
perusal of graphene; correspondingly, all constructions of carbon nano-structure models be-
gin with a clear understanding of their significance, which mostly concerns the properties
and applicative values of carbon nano-structures.
1.2 Graphene
Graphene is a planar (two-dimensional) carbon nano-structure similar to hexagonal hives in
which each carbon atom is connected to three other carbon atoms through chemical bonds.
Experiments concerning mechanical properties of graphene by Georgia Tsoukleri et al.[7, 8]
have shown that graphene is extraordinarily strong with its low mass density (allegedly 100
times stronger than steel), and has high e ciency in conducting heat[9] and electricity[10].
Theoretical researches done by Feng et al.[11] and experiments done by Geim and Kim[12]
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4. References
[1] P. R. Wallace. The band structure of graphite. Physical Review, 77:622–634, 1947.
[2] A. K. Geim and K. S. Novoselov. The rise of graphene. Nature Materials, 6:183–191,
2007.
[3] A. K. Geim. Graphene: Status and prospects. Science, 324:1530–1534, 2009.
[4] The Nobel Foundation. The Nobel Prize in Physics 2010. Available at http://
www.nobelprize.org/nobel_prizes/physics/laureates/2010/index.html (2014-
07-08).
[5] A. K. Geim and I. V. Grigorieva. Van der Waals heterostructures. Nature, 499:419–425,
2013.
[6] J. Hedberg. A graphene lattice. Available at http://www.jameshedberg.com/
scienceGraphics.php?sort=all&id=graphene-lattice-onSubstrate-3Dmodel
(2014-07-09).
[7] G. Tsoukleri, J. Parthenios, K. Papagelis, R. Jalil, A. C. Ferrari, A. K. Geim, K. S.
Novoselov, and C. Galiotis. Subjecting a graphene monolayer to tension and compres-
sion. Available at http://arxiv.org/pdf/0910.0622.pdf (2014-07-24).
[8] Graphene properties. Available at http://www.graphene-battery.net/graphene-
properties.htm (2014-07-16).
[9] E. Pop, V. Varshney, and A. K. Roy. Thermal properties of graphene: Fundamentals
and applications. Available at http://poplab.stanford.edu/pdfs/PopVarshneyRoy-
GrapheneThermal-MRSbull12.pdf (2014-07-24).
[10] K. Bolotin, K. Sikes, Z. Jiang, M. Klimaand, G. Fudenberg, J. Hone, P. Kim, and
H. Stormer. Ultrahigh electron mobility in suspended graphene. Solid State Communi-
cations, 146:351, 2008.
[11] J. Feng, W. Li, X. Qian, J. Qi, L. Qi, and J. Li. Patterning of graphene. Nanoscale,
4:4883–4899, 2012.
[12] A. K. Geim and P. Kim. Carbon wonderland. Scientific American, 4:90–97, 2008.
[13] Available at http://www.intechopen.com/source/html/10021/media/image1.png
(2014-07-09).
[14] E. N. Ganesh. Single walled and multi walled carbon nanotube structure, synthesis and
applications. IJITEE, 2:311–320, 2013.
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