Chapter 3 Epoch Making Simulation

Large Scale Simulations for Carbon Nanotubes
Project Representative

Kazuo Minami

Research Organization for Information Science & TechnologyAuthors

Syogo Tejima 1, Kazuo Minami 1, Satoshi Nakamura 1, Kohji Makino 1,
Yoshiyuki Miyamoto 2, Mari Ohfuti 3, Mamoru Sakaue 3,
Yoshikazu Fujisawa 4 and Hisashi Nakamura 1
1 Research Organization for Information Science &Technology (RIST)
2 Fundamental and Environmental Research Laboratories, NEC Corporation
3 Nanotechnology Research Center, Fujitsu Laboratories Ltd.
4 Honda R&D Co., Ltd.
CARBON NANOTUBE RESARCH GROUPE

Morinobu Endo, Eiji Osawa, Atushi Oshiyama, Yasumasa Kanada, Susumu Saito,Riichiro Saito, Hisanori Shinohara, David Tomanek, Tsuneo Hirano, Shigeo Maruyama,Kazuyuki Watanabe, Takahisa Ohno, Yoshiyuki Miyamoto, Hisashi Nakamura

Nano carbon materials as nanotubes (CNTs) and fullerenes in nanotechnology have a lot of potential for industrial applications. On the efforts of developing applications, it has been recognized that computational simulations are powerful and efficient tools to find and create new materials from nano scale. Aiming at realistic simulations for nonmaterial, we have developed a large-scale computation technique utilizing tight binding molecular dynamic method, ab initio density functional theory (DFT), GSW rearrangement and time-dependent DFT method. We have studies various physical properties of nano-carbon
and applications e.g., (1) Nano-structural deformation by ion irradiation, (2) Atomic and Electronic Structures of Contact
between Carbon Nanotube and Titanium, (3) Generation of new atomic structure using GSW rearrangement, (4) Composite
material formed from twisted CNTs, (5) Hole-doped diamond superconductor. In addition to nano carbon as nanotube, diamond and graphite of traditional carbon material came into limelight. Along these works, we have realized that the Earth
Simulator is a very powerful tool for large-scale material simulations.
Keywords: Large scale simulation, TB theory, ab initio theory, DFT, Carbon Nanotube, Fullerenes
GSW, Hole-doped Diamond superconductor

1. INTRODUCTIONof symmetrical arrangement. The Eliashberg equation linearized with respect to the anomalous Green's function
applied to the prediction of high Tc superconductivity for ahole-doped diamond. The Generalized Stone-Wales (GSW)
rearrangement is used to find new novel nano carbon structures. We have carried out some subjects in this work, which
are described in the next section. There are three primaryobjectives with this work: (1) design of innovative nonmaterial with certain desired properties; (2) obtaining fundamental properties in nano-scale matter, and (3) nano-applications. Our purpose is to give the clear explanation of properties and phenomena of nano-scale events and deduce guiding
principle to design new materials for applications fromnanostructures using super-computers.

Carbon materials have been expected to make a breakthrough in material science and nanotechnology. A lot ofpotential applications of nanotubes and fullerenes e.g., electronic field emitter and electronic devices have attracted scientific community. In the investigation and utilizing theirmaterial properties, numerical simulation using supercomputer has turned to be a very efficient tool. A recent development in nanotechnology has required a more efficient supercomputing capable of a large-scale simulation of up to 104
atoms. Aiming large-scale simulations utilizing Earth
Simulator, we have developed computational package basedon ab initio DFT theory and parameterized tight-binding(TB) method. The TB code we have developed is shown tobe suitable for the very large systems even though the lack155

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2. PHYSICAL STUDIES ON NANOMATERIALS

as 125 eV, single vacancies are formed not only on thegraphene surface layer but also on the third layer below thesurface. The most interesting structural change is seen when
the incident energy is 225 eV. The simulation shows roll-up
structure of graphene sheet obtained by connecting the thirdand fourth layers.
Figure 2 (a) shows more detailed viewgraph of the final
geometry in Fig. 1 obtained with incident energy of 225 eV.
One can be interested in how this rolled geometry sustains
until the system is cooled down. Figure 2 (b) shows how
kinetic energies of C atoms are distributed after the collisionof Ar8+ ion on the graphene layers. Surprisingly, even in
short time constant as 0.1 ps (100fs), the kinetic energy distribution on each carbon layers seems to be equal suggestingsemi-equilibrium condition. The estimated temperature for

2.1 Nano-structural deformation by ion irradiation
Ion beam irradiation is one of important technology for
nano-scale fabrication. The structural deformation fromgraphite to nano-diamond upon irradiation of Ar8+ ion (highcharged ion) was suggested by the RIKEN group [1].
Motivated by this report, the mechanisms of the structuralchange are studied by means of electron-ion dynamics.
Experimentalists of RIKEN thought that the high charge ofAr is essential to determine the structure, and thus they
expected that the resulting structure appearing on the graphite
surface was independent on the Ar8+ incident energy. From
theoretical point of view, speed of electron flow fromgraphite and Ar ion should be a key factor during the collision, thus electron dynamics in addition to MD should playvery important roles.
Last year, we investigated the structural deformation by
first-principles electron-ion dynamics simulation based on
the time-dependent density functional theory (TDDFT) coupled with Ehrenfest approximation for classical MD. We set
the incident energy of Ar8+ ion as 400 eV, the same value asthat in experiment, and found significant destruction ofgraphitic structure causing transient formation of local sp3
configuration.
This year, we examined the dependence of the structuraldeformation on the incident energy by testing several values
as 40 eV, 125 eV and 225 eV. In sharp contrast to experimentalists' expectation, the resulting geometry is highly
dependent on the incident energy of Ar8+[3].
Figure 1 shows how resulting geometries differ. In case of
Ar8+ irradiation with incident energy of 40 eV, the Ar ion is
simply reflected dressing electron cloud and graphite retains
its honeycomb network. When incident energy is increased

Fig. 1 Varieties of structures obtained upon Ar8+ irradiation with several
incident energies denoted in each panel. The charge contour
maps are also shown indicating semi-neutralization of Ar8+ ion ineach case.

Fig. 2 (a) The modified structure of graphene sheets irradiated by an Ar+8 ion with incident energy of 225 eV.
(b) The corresponding distribution of kinetic energies of Ar ions, of C atoms in the 1st, 2nd, 3rd, and 4thlayers, as a function of time.

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Chapter 3 Epoch Making Simulationeach layer is around 3100 K but should be lower when thicker model are available to test. We thus expect formation ofrolled structure is very likely.
In next year, we will examine effect of the charge on Ar
ions by comparing current results with the cases of neutral
Ar irradiation.

2.3 Generation of new atomic structure using GSW
rearrangement
The purpose of the research is to search for the possibilityof the creation of new novel nano carbon structures by using
only Generalized Stone-Wales (GSW) rearrangement. We
have explored the procedure of sequential GSW rearrangement (it is named to "path".) from initial structure to objective structure. The various kinds of paths were found out.
For example, one was the path from 2 connected C60 toshort CNT, another was the path from a certain CNT to other
CNT that has different chirality, and so on.
In this report, the objective structure is periodic carbon
structure with hexagon and octagon rings of carbon, known
as P-surface of Schwarzites. The structure is very interestingfor many researchers, and is analyzed the characteristics inthe simulations, because it has negative curves and highsymmetry. However, the procedures of the generation havenot been clarified yet. Two types of the P surface have beenknown. One is called as P688, the other is P8BAL. The
number of atoms per primitive cell of P688 is 48. The cell ofP8BAL consists of 192 atoms. Furthermore, we discover the2.2 Atomic and Electronic Structures of Contact between
Carbon Nanotube and Titanium
For electronics applications of carbon nanotubes (CNTs)
the contact with metal is important. We have studied theatomic and electronic structures of the contact between
metallic nanotube and titanium (Ti) as a possible contact
material by using ab-initio molecular dynamics (Fig. 3). The
atomic structure was stabilized from the simple contact by
the Ti atoms sticking out around the CNT. The Ti and C
atoms have been found to form the structure like a TiC
nanoparticle. The electronic structure has also changed especially near the Fermi level, where the more charge is distribute to the contact layers and the CNT than the simple contact.
This suggests that Ti plays the role as a contact material.

(b)(a)
4(nm)
32

10(c)

(d)

(e)

Fig. 3 (a) Simple and (b) stabilized atomic structures of the contact between carbon nanotube (CNT) and titanium (Ti).
The blue and orange spheres represent C and Ti atoms, respectively. (c) Nanoparticle-like structure at the root of
the CNT and (d) the Ti8C12 nanoparticle. (e) Initial (blue) and stabilized (red) charge distributions near the Fermi
level along the tube direction.

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structure that consists of 144 atoms per cell. This reportdeals with two types (P688 and the new structure with 144atoms) of three, because P8BAL is too large to be explored
all the paths by this program. It is assumed that initial structure is (8, 8) CNTs that are connected with 4 CNTs. The difference of them is a distance of the connecting position.
First, in the case of P688, snapshot are shown in Fig. 4. 16
GSW steps are necessary for isomerization. Secondly, Fig. 5
illustrates snapshot of isomerization of another objectivestructure. The isomerization is realized by 164 GSW steps.
Though this report deals with only P-surface, there are G andD surfaces and they have interesting characteristics as wellas P-surface. In the next step of the research, the paths tothese surfaces will be found out.

multi-CNT to complex structures as a composite CNT. The
characteristic structure and properties of single and multi
CNTs play an important role in synthesizing more complex
composite materials. Therefore, stage by stage, we launched
our simulations.
Two years ago, we presented a the technique to create
CNTs in the bundles using van-del walls attractive interaction. But the interaction is too week to remain CNT bundle
under even low temperatures.
In expectation of creating atomic bonding between CNTs
to keep bundle, we tried to twist the CNTs presented in Fig. 6.
Because of the torque caused by twisted CNTs, CNTs in
the bundles at the initial state changed to come loose under
the free edgy. So as to hold CNTs twisted under the freeedgy condition, we have to induce atomic bonding between
CNTs. From the results of any trial simulations, we foundthe suitable condition of applied temperature and a rate oftwist per length to generate atomic bonding between CNTs.
The sp3 hybridization bonding appears on the surface ofCNTs. Three orbitals contribute to intra atomic bonding and

2.4 Composite material formed from twisted CNTs
The aim in this section is to present a design for strong
and functional composite materials formed from CNT. We
have been investigating mechanical properties of nano carbon structure from basic structures as a single CNT andFig. 4 Snapshot of isomerization (P688).

Fig. 5 Snapshot of isomerization(Structure consisting of 144 atoms per cell).

Fig. 6 Rope of nanotube.

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Chapter 3 Epoch Making Simulation

Fig. 7 The sp3 hybridization between CNTs.

one orbital to inter atomic bonding presented in Fig. 7. As aresult, sp3 hybridization might prevent CNTs in the bundles
from coming loose. But for a long time simulation the site ofatomic bonding rearrange on the surface. The most important thing in this simulation is that there is no impurity withthe exception of Carbon in the structure. So we think thestructure expressed here is one of the stronger structures
among the composite material formed from pure CNTs.
2.5 hole-doped diamond superconductor
Recently, hole-doped diamonds have attracted considerable attention. Our aim is to investigate by simulation experiment that at what temperature hole-doped diamond becomessuperconducting if holes are ideally doped into pure diamond without using impurities. To this end, we have formulated from microscopic point of view a general non-perturbation scheme of the calculation of dielectric response functions. Specifically, we simulated the time evolution ofcharge density r(t) of the carbon atoms using PVCRTMD(Parallel Vector Carbon Recursion Technique MolecularDynamics) code for order-N tight-Binding moleculardynamics simulation. In the present simulation, the numberof carbon atoms in the diamond was 4096 and the simulationof the charge density. ρ(t) was performed up to 8.2 ps with
0.5 fs time step. The sustained performance of 4.82 Tflops
was achieved by utilizing 130 nodes (1040 PEs) of the EarthSimulator.
From the simulated charge density ρ(t), the dielectric
response function is given by adopting the linear-response
theory. And also the effective interaction between electrons
is defined as a bare Coulomb interaction divided by response
function. Thus, solving the Eliashberg equation with theeffective interaction, we can obtaine the relation between thehole concentration and Tc.
Since we is concerned with Tc , the Eliashberg equation islinearized with respect to the anomalous Green's function.
Then, the Eliashberg equation reduces to a eigenvalue problem: MX=λX, where M is a function of the single Green'sFig. 8 Eigenvalues for the linearized Eliashberg equation are plotted asfunctions of temperature.

function and effective interaction, and X corresponds to gap
function. Tc is determined as the temperature at which thelargest eigenvalue λmax of the kernel M crosses 1. From Fig. 8
we see that the attractive interaction between electrons occurs
due to strong interplay between electrons and lattice vibration. We also see that Tc suddenly increases with hole concentration.
The results of our simulation show that hole-doped diamond within a rigid-band approach is promising superconductor. We hope that the results presented here could stimulate further experimental work on the synthesis and characterization of diamond into which holes are ideally injectedwith no impurity.

3. SUMMARY
The large-scale simulations on nonmaterial have been carriedout by ab initio density functional method and the parameterizedtight-binding calculations. The optimized codes
showed that the computation on the Earth Simulator could
give an exceptional performance and enables us morechance for large-scale and realistic simulations. Our large
scale simulations can provide the nanotechnology industries
valuable information on novel nano material properties andon nano electrical designs for application.
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References[3] Y. Miyamoto, "Ultra-fast phenomena in nano-scaled
materials with the aid of supercomputer", SC2006, HPC
Nano workshop 2006, November 15, 2006, Tampa.
[4] Satoshi Nakamura, "Study of carbon-based superconductor using large scale simulation", The Physical Society ofJapan, March 21, 2007, Kagoshima.

[1] T. Meguro et al., Appl. Phys. Lett. 79, 3866 (2001).
[2] S. Tejima, H. Nakamura, T. Fututa, D.Tomanek andM.Endo, "Large Scale Simulations for Composite nanoCarbon Materials", SC2006, HPC Nano workshop 2006,
November 15, 2006, Tampa.

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