Download - Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

Ying Wang, Alister J. Page, Yoshio Nishimoto, Hu-Jun Qian, Keiji Morokuma, Stephan Irle

Department of Chemistry, Graduate School of Science, Nagoya University, JapanFukui Institute for Fundamental Chemistry, Kyoto University, Japan

.

Kyoto University Nagoya University

http://kmweb.fukui.kyoto-u.ac.jp/nano http://qc.chem.nagoya-u.ac.jp

Talk XX5.62012 Materials Research Society Spring Meeting, San Francisco, CA

April 11, 2012

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Haeckelite

Overview

Crespi et al. Phys. Rev. B 53, R13303 (1996); Terrones et al. Phys. Rev. Lett. 84, 1716 (2000); Rocquefelte et al. Nano Lett. 4, 805 (2004)

DE(TB) (meV/C atom)DE(PBE) (meV/C atom)

00

307261

304246

408375

419380

C60:

Ernst Haeckel(1834-1919)

Thrower-Stone-Wales Transformation

Radiolara

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Haeckelite

Overview

Rocquefelte et al. Nano Lett. 4, 805 (2004) a) graphite b) rectangular

c) oblique d) hexagonal

& Haeckelite Nanotubes

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Overview Experiments

Graphene CVD SynthesisNagashima et al. Phys. Rev. B 4, 17487 (1994)

• “monolayer graphite (MG)”

• C2H4 decomposition on Ni(111) at 600°C

• No bulk carbide

Graphene Formation from Ni-C AlloyShelton et al. Surf. Sci. 43, 493 (1974)

• “graphitic monolayer” = modern picture

• Carbon doping of Ni(111) with CO at 1200°C

• Phase transition: Carbon segregationGrüneis et al. Phys. Rev. B 77, 193401 (2008)

Overview Theoretical Studies

How Does Graphene Form on Ni(111)?Gao et al. J. Am. Chem. Soc. 133, 5009 (2011)

• GGA PW91/UPP-PW (VASP) geometry optimizations• individual clusters on Ni(111) C1-C24

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Geometries and energetics only

No information on structure evolution with time (growth)!

Want QM/MD Simulations!

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Self-consistent-charge density-functional tight-binding (SCC-DFTB)

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2tot i i repi

E f E q q

0vi iv

c H S Second order-expansion of DFT total energy with respect to charge fluctuation

TB-eigenvalue equation

Method SCC-DFTB

Single-zeta STO basis set

Finite temperature approach (Mermin free energy EMermin)

1

exp / 1ii B e

fk T

2 ln 1 ln 1e B i i i ii

S k f f f f

Te: electronic temperatureSe: electronic entropy

0 1

2N

repi i i i

i

EH H SF f c c q q

SR R R R

0 1if

Atomic force

M. Weinert, J. W. Davenport, Phys. Rev. B 45, 13709 (1992)

EMermin = Etot - TeSe

E

2fi0 1 2

m

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DFTB/MD Results H model

QM/MD of 30 C2 on Ni(111), 1180 KY. Wang, A. J. Page, Y. Nishimoto, H.-J. Qian, K. Morokuma, SI, JACS (2011)

Haeckelite!

A

t = 0

100 ps 410 ps

0 50 100 150 200 250 300 350 4000

1

2

3

4

5

6

7

8

Num

ber

of poly

gonal rings

Time [ps]

five-membered ring six-membered ring seven-membered ring

200 ps 300 ps

0 50 100 150 200 250 300 350 4000

1

2

3

4

5

6

7

8

Num

ber

of poly

gonal rings

Time [ps]

five-membered ring six-membered ring seven-membered ring

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Average 5- and 6-ring counts over 10 annealing

trajectories

Formation of first condensed 2-ring

system (5/5 or 5/6)

Always pentagon first!

Hollow in Fe is required

Y. Ohta, Y. Okamoto, A. J. Page, SI, K. Morokuma, ACS Nano 3, 3413 (2009)

Nanotube cap nucleation

DFTB/MD Results Why Pentagons?

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DFTB/MD Results H model

QM/MD of 30 C2 on Ni(111), 1180 KY. Wang, A. J. Page, Y. Nishimoto, H.-J. Qian, K. Morokuma, SI, JACS (2011)

top side

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DFTB/MD Results G Model

QM/MD of 18 C2 + C24 on Ni(111), 1180 KY. Wang, A. J. Page, Y. Nishimoto, H.-J. Qian, K. Morokuma, SI, JACS (2011)

• Pentagon-first vs. template effect.• Suppression of heptagons and

pentagons

Wang et al., Nano Lett., (2011)

Graphene!

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• Pentagon-first vs. template effect.• Suppression of heptagons and

pentagons

Wang et al., Nano Lett., (2011)

Graphene!

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top side

DFTB/MD Results Templating effect

Ring count analysis(average over 10 trajectories)

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Our “haeckelite index” h

Y. Wang, A. J. Page, Y. Nishimoto, H.-J. Qian, K. Morokuma, SI, JACS (2011)

Haeckelite is a Metastable Phase

DFTB/MD Results Ostwald’s rule

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F. W. Ostwald, Z. Phys. Chem. 22, 289 (1897)

MC Study: Karoui et al., ACS Nano 4, 6114 (2010)

Self-Organized Criticality Random Graph Theory

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S. Kauffman, At Home in the Universe (1996)

Phase Transformation in Random Graph Theory

20 nodesedgesnodes

= 520

largest cluster:

3

1020

5

1520

15

2020

18

2520

20

largest cluster:

edgesnodes

x x

xx x

Self-Organized Criticality Random Graph Theory

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S. Kauffman, At Home in the Universe (1996)

Edges Number of BondsNodes Number of Atoms

Phase transition!

Self-Organized Criticality Carbon phase transition

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Haeckelite/Graphene Formation: Carbon spsp2 Phase Transition?

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What is Self-Organized Criticality (SOC)?P. Bak, C. Tang, K. Wiesenfeld (BTW), Phys. Rev. Lett. 59, 381 (1987)

Avalanche sizes (time)

frequency P over size x

P(x) x∝ -α (x>1)

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What is Self-Organized Criticality (SOC)?P. Bak, C. Tang, K. Wiesenfeld (BTW), Phys. Rev. Lett. 59, 381 (1987)

Universality of self-organized critical state and 1/f noise:Gutenberg-Richter Law N/NTOT = 10-bM

(Earthquake probability vs magnitude)

Source: wikipedia

Marine extinction on geological time scale

Source: wikipedia

time (Ma)

Others: Stock market, epidemics, solar flares, rivers, mountain ranges, etc. etc. = FRACTALS!

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Michael Hilke, McGill Universityhttp://www.physics.mcgill.ca/webgallery/michael1/

• Universality of pentagon-first mechanism in carbon condensation

• Possibility to synthesize Haeckelite: fast carbon supply, rapid cooling

• Graphene nucleation follows pentagon-first mechanism; subsequent annealing required (Ostwald’s rule of stages)

• C24 template imprints hexagonal structure on growing flat carbon network: suggestion to experiment

• spsp2 condensation at high [C] is a phase transition with fractal characteristics of self-organized criticality (SOC)

Summary http://qc.chem.nagoya-u.ac.jp

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Acknowledgements

July 8, 2011

The Group:

Dr. Oraphan Saengsawang (Visitor)Dr. Ying WangDr. Hu-Jun QianDr. Matt Addicoat (JSPS)Dr. Cristopher CamachoMs. Lili Liu (D3)Mr. Yoshifumi Nishimura (D1)Ms. Elena Vyshnyakova (D1, visitor)Mr. Yoshio Nishimoto (M2)Undergraduates

CREST “Multiscale Physics” (2006-2011)CREST “Soft -p materials: (2011-2015)

SRPR tenure track program (2006-2011) JSPS KAKENHI

Funding: