Chapter 4 Epoch Making Simulation

Large-Scale Simulation on the Properties of CarbonNanotube
Group Representative

Kazuo Minami

Research Organization for Information Science & Technology, Senior technical staffAuthors

Syogo Tejima 1
Noboru Jimbo 1
Hisashi Nakamura 1

Kazuo Minami 1

Noejung Park 1

1 Research Organization for Information Science &Technology
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
Yoshiyuki Miyamoto
Hisashi Nakamura.

Carbon nanotubes (CNTs) and fullerenes have a lot of potential applications in nanotechnology. In the stream of efforts to exploit
these nanoscale materials, the computational simulations have turned out to be powerful and efficient tools. Especially, as the recent
trend in technology made it possible to manipulate further miniaturized structures, required simulations for emerging material become
bigger and bigger. Aiming at realistic simulations for nanomaterials, we have developed a large-scale computation technique utilizingtight-binding (TB) molecular dynamic method, ab-initio density functional theory (DFT), and time-dependent DFT method. By an efficient optimization on ES, we get the performance of 7.04 Tera flops using 435 nodes for TB calculation for CNT thermal conductivity.
We have studied various physical properties of nano-carbon material e.g., the thermal conductivity of the single wall CNT, stabilityof super-diamond, synthetic diamond, stability of nanotube peapod with a defective wall, and designing of a purification of CNT.
During these works, we have realized that the Earth Simulator is very powerful tool for large-scale material simulations.
Keywords: Large scale simulation, TB theory, ab initio theory, DFT, Carbon Nanotube, Nano Diamond

1. INTRODUCTION

2. PHYSICAL STUDIES ON NANOMATERIALS

Carbon materials have been expected to make a breakthrough in material science and nanotechnology. A lot of
potential applications of nanotubes and fullerenes e.g., electronic field emitter and electronic devices have attracted scientific community. In the investigation and utilizing their material properties, numerical simulation using supercomputer hasturned out to be a very efficient tool. A recent development innanotechnology has required a more efficient supercomputings
capable of a large-scale simulation of up to 10 4 atoms.
Aiming large-scale simulations utilizing Earth Simulator,
we have developed computational package based on ab initio
DFT theory and parameterized TB method. The TB code wehave developed is shown to be suitable for the very large
systems even though the lack of symmetrical arrangement.
We have carried out six subjects in this work, which aredescribed in the next section. Our purpose is to give the clear
explanation of properties and phenomena of nano-scale
events and deduce guiding principle to design new materials
from nano-structures using super-computers.

2.1. Thermal Conductivity of CNT [1]
The stiff sp 3 bonds between carbon atoms make diamondone of the best thermal conductors. The thermal conductivityof diamond, 3320[W/m. K], is eight times larger than that ofcupper. An unusually high thermal conductivity should also
be expected in carbon nanotubes, which are held together byeven stronger sp 2 bonds.
Some molecular dynamics simulations showed very
high thermal conductivity, however the estimated valuesof thermal conductivity were widely difference from one
another. These results arise from the lack of atoms usedin simulation.
We calculate the thermal conductivity in our simulationfrom head transport coefficients. The artificial "hot" and"cold" layer are introduced within the system and a heat
flux of the particles inside the artificial regions is fixed.
After all, thermal flux from hot to cold region on nanotube
creates a temperature gradient because of phonon collisions.
Once the steady state reaches we can determine the thermal157

Annual Report of the Earth Simulator Center April 2002 - March 2003

conductivity from Fourier's law:material in designing electronic devices and in mechanicalcoating because of hardness, chemical stability, and highthermal conductivity. While the high pressure, condition
which is believed to be realized during the detonation experiment, is so generally accepted as a sufficient condition forstabilizing the diamond phase over graphite, various diamond synthesis under low pressure conditions have cast
doubts on the ingredients in the growth mechanism.
Although the presence of atomic hydrogen has been
considered to be a crucial factor in the low pressure synthesisof diamond, the understanding on the exact role of them israther ambiguous. Several recent studies reported the synthesisof diamond without the presence of atomic hydrogen, which
revived the interests in the growth mechanism. Especially, theexperimental results which showed the possibility that thediamond particles formed in the vapor phase are negativelycharged, are now triggering the question about the charging
effect on the nucleation stage. Also the bias-enhanced nucleation on the substrate leads to the same question.
Our calculation results show that a negative charge canstabilize the diamond surface from reconstruction into
graphitic layer as the atomic hydrogen does shown in Fig. 3.
Excess charge is mostly localized around the dangling

The mean free path is limited by the size of the system. If
a sample were shorter than the length of mean free path,phonons could get no scattering except the edges. In thatcase we could not get correct thermal conductivity byphonon scattering in bulk materials. Thus to measure precise
thermal conductivity, we need enough length nanotube. Alsoa large number of iterations are required in order to averagetemperatures to compensate the unavoidable large fluctuation. In our simulation the number of atoms is more than
10 4, then the tube is more length of 100 nm. The large-scale
simulation is essentially important of precise simulation.
The thermal conductivity of CNT in our simulations in
Fig.1 is strongly dependent on length of CNT and is diverging with the power-law characteristic. This behavior issimilar to that of the model calculation of thermal conductivity in one dimension.
2.2. Stability of Super-diamond
We simulated the stability of super-diamond structure inFig. 2 which is formed from the carbon nanotube connecting
between the diamond structure lattice points. Because of
the high structural stability of sp 2 bonding, the diamondstructure is very hard. We performed a detailed dynamics
study up to melting and evaporation temperature.
Simulations are carried out after initial velocities of atoms
have been randomized following Maxwell distribution. The
temperature is increased from 1000k to 4000K with steps of
T=1000K. Super-diamond keeps the stability of structure
up to 3000 K. This structure looks like very hard material.
2.3. Charging effects on synthetic diamond [2,3]Synthetic diamond has been considered to be an important

Thermal conductivity:k [arb.units]

Fig. 2 Diamond-Structure at 3000k

Endo, Exp. (1984)

101

102

103

104

105

Length of nanotube:L (nm)Fig. 1 Length dependence of thermal conductivity in CNT.

Fig. 3 Reconstruction of diamond nanoparticle into fullerene-like structure.

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bonds. More over, the C-H bonding at the surface is substantially reduced by the presence of negative charge. Theseresults are believed to be quite meaningful to rationalize thesuggested hypothesis claiming the carbon particle is likely tobe remained as a pure carbon structure under a negatively
charging environment. In addition, this explains the reason
why the diamond formation under the discharge condition is
so independent of hydrogen partial pressure.

Fig. 5. In the initial state, the nanotube have a defect in the walland ends of tubes are opened. Nine fullerenes are inserted withsame intervals in the nanotube of 12 nm. Simulation results
show that encapsulation of fullerenes are stable even if the walland cap have substantial defect and opening. We suggest thisstable encapsulation to be utilized as a nanoscale reactor.
2.6. Searching for superhard carbon structure [5]The sp2-bonded carbon structures with a negative Gaussian
curvature, so called Schwarzites, have been suggested by several authors. While positively curved structures, fullerenes orthe cap of nanotubes, have been intensively studied focusing
on the various electronic behaviors, the negatively curved
structures have been limited to preliminary suggestions
because of difficulties in synthesizing process. However, a
few recent progresses in making a kind of random Schwarzite
revive interests in that structure as a new carbon-based novel
material. Whereas the positive curvature eventually leads tothe closure of the surface and consequently to the isolated
fullerene molecule, the Schwarzites form a three-dimensional
covalent solid and have been suspected to have an enhanced
mechanical properties: lightness and hardness.
Focusing on the hardness, we performed first-principles
calculations on the three-dimensional carbon Schwarzites of668D and 668P in Fig. 6. Although the synthesized samples
so far are nanoclusters rather than a crystalline sold, our theoretical works on the perfect Schwarzite could be a reference
for a further experimental study. Our calculation results
show that most Schwarzites are very strong and their bulk
modulus are about 25 % of bulk diamond. Noting that they
have a small band gap of 0.5 eV and higher structural stability, an application in the electronic devices is also suggested.

2.4. Purification of CNT for Electronic Circuits [4]Design of purification method of carbon nanotubes areused for electronic circuits. Aim of the present simulations iscleaning of oxidized nanotubes without aid of thermal
processing, which is unreliable for nano-scale materials. In
case of oxidized nanotube, thermal extraction of oxygen (O)is atoms always accompanied by carbon extraction which
gives more damage on nanotubes. Methods of cleaning
process proposed here is optical excitation and subsequentultra-fast chemical dynamics, which can locally break C-O
bonds and extract O atoms from carbon nanotubes in Fig. 4.
Simulation technique is the time-dependent density functional approach combined with the molecular dynamics, whichenables us to stably follow the dynamics under electronicexcitations. Spontaneous oxygen ejection from nanotube byresonant Auger process initiated by O-1s core-excitation wasmonitored by the present simulations.
Furthermore, de-activation of ejected O atoms is found to
be possible by introduction of H 2 molecules. The applicationof photo-chemical reaction can be alternative tool to thermal
process especially nano-scaled materials.
2.5. Peapod stability during fulleren actionWe have performed TB molecular dynamic simulations
to investigate stability of the fullerenes encapsulated inside thecarbon nanotube, the so-called 'carbon nano-peapods' shown

Fig. 5 Peapod structure after 15ps

Fig. 4 Cleaning process for CNT. Optical excitation locally breaks C-Obonds and extract O atoms from carbon nanotubes. Red sphereand blue spheres show O atom and H2 molecules, respectively.

Fig. 6 Super Jungle Gym Structure

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3. PERFORMANCE OPTIMIZATION
3.1. Strategy of Performance Optimization
The tuning to parallelization of CRTMD Code was, firstly,
executed on SR8000 at Information Technology Center(ITC), the University of Tokyo tow years ago. The optimization performance to the vector processors was tested on theEarth Simulator.

4Speed Up

7.052 Tflops

5.249 Tflops2

3.1.1. Parallelization(1) Parallelization by particle
As for the CRTMD code, the main calculation is composed of 'particle loop' part to compute the atomic energies
and forces acting on atoms. The percentage of CPU time andflop count at this part are 94.6% and 99.6%, respectively.
This part was parallelized completely because calculations
can be accomplished on each particle independently.
(2) Parallelization of nearest atoms map
Each particle interacts with only adjacent particles in cutoff
radius. To find the interacting atoms we have to compute interatomic distances and make a map on distance information.
In the case of less than hundreds of processors in parallels, communication between processors for the map issmooth. But for more than thousands processors, the communications are the bottleneck. So we have adopted themethod that it is not necessary to transfer atoms map by setting cutoff distance twice.

3.740 Tflops

1.965 Tflops

0100002000

3000

Number of Processors
Fig. 7 Speed Up on Earth Simulator

7.05 Tera flops by use of 435 node (3480 PE) shown in
Fig. 7. It is a 25.3% performance in the peak on each node.
The amount of flop count 89 Peta flop as a whole, and when
435nodes are used, is executable in 3.5 hours.

4. SUMMARY
The large-scale simulations on nanomaterials have been
carried by ab-initio density functional method and the parameterized tight-binding calculations. Various physical material properties e.g., thermal conductivity, mechanical hardness, charging effect on the stability have been studied. The
optimized codes showed that the computation on Earth
Simulator could give an exceptional performance andenables more large-scale realistic simulations.
[1] S.Tejima et al., Massively Parallel Simulation on LargeScale Carbon Nanotubes, NANOTECH 2003, February,2003, San Francisco, CA.
[2] N.Park et al., Charging effects on the stability of diamond nanoclusters, APS, A6.011, March 3-7, 2003,
Austin, TX.
[3] N.Park et al., Charging effects on the diamond nanocluster. The 10th International Symposium on Advanced
Materials, March 10-13, 2003, Tsukuba, Japan[4] Y.Miyamoto et al., Photo-induced cleaning of oxidized carbon nanotubes, APS, B27.004, March, 2003, Austin, TX[5] N.Park et al., Diamondoids as functional building blocks
for nanotechnology, APS, G27.010, March, 2003,Austin, TX.

3.1.2. Vectorization(1) Coefficient Matrix by Recursive Method
The main calculation of this part is matrix and vector
operation as a matrix-vector product and dot product. In thispart, a high vector performance was realized by reducingthoroughly data-load-latency in coding.
(2) Integration Calculation Part
This part has a complex coding composed of the subroutine and function call of six hierarchies. In loop structure,
this part are composed by eight piles's DO Loops and theGOTO Loops.
A thorough change in the program structure and the loop
structure was done, and innermost loop was vectorized invector lengths as three times of the number of cluster atoms.
A high vector performance has been obtained because ofthe changes in such coding.
3.2 Performance
For the thermal conductivity simulation with 48000 particles and 10000 steps we accomplished high performance,

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