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Quantum chemical molecular dynamics (QM/MD) simulations of ensembles of C2 molecules on the Ni(111) terrace show that, in the absence of a hexagonal template, hydrogen, or step edge, Haeckelite as a metastable intermediate is preferentially nucleated over graphene [1]. The nucleation process is dominated by the swift transition of long carbon chains towards a fully connected sp2 carbon network. Starting from a pentagon as nucleus, pentagons and heptagons condense during ring collapse reactions, which results in zero overall curvature. To the contrary, in the presence of a coronene-like C24 template, hexagonal ring formation is clearly promoted, in agreement with recent suggestions from experiments. In the absence of step edges or molecular templates, graphene nucleation follows Ostwald’s ‘rule of stages’ cascade of metastable states, from linear carbon chains, via Haeckelite islands that finally anneal to graphene. Furthermore, we found similarities between graphene nucleation and other critical phase transition phenomena [2]. Our analysis confirms the existence of a critical nC-C/NC value close to 1.0 (‘H’ model) and 1.1 (‘G’ model), where nC-C is the number of C-C bonds and NC is the number of carbon atoms. As in random graph theory, above this critical value, the further conversion of linear carbon chains to sp2 carbon polygons leads to the emergence of a fully networked carbon structure. Thus we find the theory of selforganized criticality [2] applicable to discuss the sp2 network formation from sp chains in the formation mechanism of graphenes. References: [1] Wang, Y.; Page, A. J.; Nishimoto, Y.; Qian, H.-J.; Morokuma, K., Irle, S.; JACS (just accepted) (2011). [2] Bak, P.; Tang, C.; Wiesenfeld, K., Phys. Rev. Lett. 1998, 59, 381.
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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, Japan Fukui 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 XX5.6 2012 Materials Research Society Spring Meeting, San Francisco, CA April 11, 201
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Page 1: 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

Page 2: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

2

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

Page 3: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

3

Haeckelite

Overview

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

c) oblique d) hexagonal

& Haeckelite Nanotubes

Page 4: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

4

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)

Page 5: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

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

5

Geometries and energetics only

No information on structure evolution with time (growth)!

Want QM/MD Simulations!

Page 6: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

6

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

12

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

Page 7: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

7

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!

Page 8: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

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

5

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?

8

Page 9: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

9

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

Page 10: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

10

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!

Page 11: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

11

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!

Page 12: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

12

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)

top side

Page 13: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

DFTB/MD Results Templating effect

Ring count analysis(average over 10 trajectories)

13

Our “haeckelite index” h

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

Page 14: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

Haeckelite is a Metastable Phase

DFTB/MD Results Ostwald’s rule

14

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

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

Page 15: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

Self-Organized Criticality Random Graph Theory

15

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

Page 16: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

Self-Organized Criticality Random Graph Theory

16

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

Edges Number of BondsNodes Number of Atoms

Phase transition!

Page 17: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

Self-Organized Criticality Carbon phase transition

17

Haeckelite/Graphene Formation: Carbon spsp2 Phase Transition?

Page 18: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

18

Self-Organized Criticality Carbon phase transition

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)

Page 19: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

19

Self-Organized Criticality Carbon phase transition

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!

Page 20: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

20

Self-Organized Criticality Carbon phase transition

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

Page 21: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

• 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

21

Page 22: Haeckelite and Graphene Formation on a Metal Surface: Evidence for a Phase Transition at the Edge of Criticality

22

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:


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