Insights in the CVD synthesis of carbon
nanotubes from computer simulation
Christophe Bichara
CINaM - CNRS and Aix Marseille University - France
SOS_Nanotubes
ANR-09-Nano-028
1
Let’s start by the end : our findings in a video (1)
Grand Canonical Monte Carlo
o Starting from a NT cap on a
Nickel nanoparticle
o Carbon wall grows along
nanoparticle
o Some C atoms dissolved
o Nanoparticle tends to
escape the tube
What are the driving forces ?
Ni : orange
Initial C cap : blue
added C atoms : black
2
Let’s start by the end : our findings in a video (2)
Starting from last configuration and
removing carbon atoms dissolved in
nanoparticle after growth
o Canonical Monte Carlo
o No Carbon dissolved
o Nanoparticle re-enters the tube
Wetting / dewetting behavior ?
3
Outline
Model for Ni+C interaction; Computer simulation technique
o Tight binding + 4th moment’s method = O(N) and fast
o Grand canonical Monte Carlo
Thermodynamic properties of Ni+C alloys
o Melting of Ni bulk and clusters
o Carbon solubility in bulk and clusters
Wetting of (Ni+C) clusters on sp2 carbon layers
o Carbon dissolution controls wetting properties
SWNT growth
o Chemical potential and temperature conditions for growth
o Growth modes
o Growth mechanisms
4
Tight binding model
Hopping integrals :
Minimal basis set :
–
–
- C-C : ss, sp, pp, pp
C s and p electrons
Ni d electrons
- Ni-Ni : dd, dd, dd
- Ni-C : sd, pd, pd
Total energy :
 Ef


E
Eni (E)dE 


i  

 
Band structure term
Local densities of states
 1V(rij )
2 i, j
Empirical repulsive term
Moments :
Local DOS on red atom depends on
- 1st neighbors (2nd moment); cut off = 2.7 Å for C
- 1+2nd neighbors (4th moment)
4th moment and beyond : directional bonding (p)
Parameters :
Energy levels, hopping integrals, repulsion, cut off dist.
Amara et al. Phys. Rev. B 73, 113404 (2006)
Phys. Rev. B 79, 014109 (2009)
J. H. Los et al. Phys. Rev. B 84, 085455 (2011)
5
Grand Canonical Monte Carlo simulations
C insertion
C removal
Insertion


V
Pacc  min 1, 3
exp((   E ) / k BT )

(
N

1
)


Atoms displacts
Removal
Ni cluster
3


  N

Pacc  min 1,
exp( (   E ) / k BT )
V




μ : carbon chemical potential
ΔE : energy variation (new-old)
T : temperature
Random changes in configurations (atoms displacements, insertion, destruction, …)
Accepted according to thermodynamic criterion  Leads to thermodynamic equilibrium
Reasonable because growth (μs to ms / ring) is very slow at atomic level (0.1 ps)
6
Melting of small Ni clusters
Internal energy (eV/ at.)
Melting temperature of Ni clusters
1400 K
Temperature (K)
Pure Ni clusters with more than 55 atoms are
still solid up to 1400 K in our model
Melting temperatures
 Extrapolated (Gibbs-Thompson) 2360 K
 « Exact » calculated
2050 K
 Experimental
1728 K
J. H. Los et al. PRB 81, 064112 (2010)
7
Carbon solubility in bulk Ni
Temperature rescaled to compare
with experimental phase diagram
Liquid Ni+C
Tcalc. rescaled by 0.85
Calculated solubility limit
below 5% in crystal
Crystal Ni+C
8
How does carbon solubility change at nanoscale ?
Option 1 :
Option 2 :
• Nanosize induces Laplace
Pressure inside NP
• C in subsurface interstitial sites
• C in interstitial sites
• Smaller size induce more
pressure and hence smaller
solubility
• Surface/volume ratio larger for
smaller sizes
• Smaller size induces larger
solubility
Harutyunyan et al. PRL 100, 195502 (2008)
9
Carbon solubility in nanoparticles ?
Outer C atoms
C - C dist. < 1.7 Å
Calculate « sorption » isotherms
Average carbon contents inside,
on surface and outside particles
Surface C atoms
Ni-C bonds  5
Bulk C atoms
(often subsurface)
Ni-C bonds > 5
Ni particles sizes and structures
o 55 and 147 atoms, icosahedral :
compact (111)-like surface
o 201, 405 and 807 atoms, Wulff shape :
(111) and (100) facets
10
Carbon solubility in nanoparticles: effect of particle size
At given μC, smaller clusters have
larger C concentration
Solubility limit
slightly larger for smaller NPs
depends on the state of the NP
… might explain why tubes grow
from smaller NPs while larger
ones are encapsulated …
see below
11
Carbon solubility in nanoparticles: effect of particle size
Molten
Crystalline core/
Molten shell
12
State of Nanoparticles
405 Ni atoms
1000 K
6%C
Pure Ni
« Phase diagram »
1000 K
Relative thickness of liquid layer
Crystalline
11 % C
Core: crystal, no Carbon
Outer layer: C-rich, molten
Molten/amorphous
201
405
807
13
Carbon solubility in nanoparticles: effect of temperature
Same data, plotted as function of :
… Carbon chemical potential C
C/ kT ~ Ln (Pressure ), if ideal gas
Solubility limits
increase with T
Pressure to reach this solubility limit also increases with T
Explains pressure threshold for nucleation of SWNT
o
Cf : in situ Raman during SWNT growth
M. Picher et al. Nano Letters (2009), 9 (2), 542–547
14
Effect of C solubility on wetting of NP on graphite/ene ?
Sessile drop method to measure contact
angle of macroscopic Ni drops on graphite:
Yu V. Naidich et al. 1971
o Pure Ni wets graphite Θ = 50°
o Θ > 90° for C wt% > 2.5
o Same effect observed for Co and Fe
What about :
o Nanosized particles ?
o Plays a role for SWNT growth ?
15
Wetting of Ni+C nanoparticles on graphene
405 Ni
1000 K
1400 K
405 Ni +11 % C
Carbon rich Ni nanoparticles
tend to dewet graphene
405 Ni + 24 % C
1400 K
Relaxed at 0 K
16
Try and grow a tube from an existing cap
What we did:
o Fix a SWNT butt on a pure Ni Nanoparticle and relax to 0 K
o Different tube diameters, chiralities and NP sizes
o Play with (μC, T) conditions to grow tube walls
Controlling carbon chemical potential via GCMC calculations is essential !
Low temperature and high μC :
encapsulation by growing walls
High temperature and low μC :
detachment of tube cap from NP
17
Nucleation and growth modes
CVD growth aborted at different synthesis times
M.F. Fiawoo + A. Loiseau + ..
TEM observation through SiO2 or Si3N4 membrane
Statistical analysis of tube and attached NP diameters
Perpendicular and tangential modes coexist
Tangential mode dominates at longer times
M.F.C. Fiawoo et al.
PRL 108, 195503 (2012)
18
Growth modes : perpendicular vs tangential
perpendicular
Tangential incorporation favored
over perpendicular one
No need for a step edge on which
tube can « push »
Dewetting of side walls is essential
to avoid encapsulation
tangential
Statistics over 19 successful
growth simulation runs
M.F.C. Fiawoo et al.
PRL 108, 195503 (2012)
19
Under correct (μC, T) conditions : tube grows !
Starting configuration
Last configuration
Tube cap tends to dewet from catalyst NP when C is incorporated in Ni
Tube walls develop through polyyne chains … no evidence for C2 dimers addition
Still challenging :
o (µC, T) conditions to grow defectless tube
o Effect of tube chirality ?
M. Diarra et al. submitted, available on ArXiv
20
Dewetting when C concentration is large enough
M. Diarra et al. submitted, available on ArXiv
21
If Carbon is removed from the NanoParticle …
(… easy to do on a computer …)
One recovers wetting conditions,
Nanoparticle tends to move inside
tube
M. Diarra et al. submitted, available on ArXiv
22
Conclusions : towards a NT growth model ?
Carbon solubility in Ni nanoparticles ?
o depends on T and µC
o larger for smaller sizes
o Surface of NP ≤ 807 is not crystallline under growth conditions
Dewetting of Ni nanoparticle from sp2 carbon wall ?
o controlled by carbon dissolved
o Essential for NT growth
o … other metals ?
also for graphene ?
metal contacts ?
Growth modes ?
o Tangential mode favored
o C incorporation at tube lip by short chains
wall quality still challenging
for computer simulation
Elementary steps
o Feedstock decomposition
o Carbon diffusion
surface diffusion via chains faster
o Dewetting of NP from growing tube
o Growth of tube wall
weakly chirality dependent ?
strongly chirality dependent ??
23
Thank you for your attention !
And thanks to
Hakim Amara
François Ducastelle
LEM - ONERA/CNRS
Chatillon France
Kim Bolton
Anders Börjesson
Univ. Gothenburgh
+ Borås Sweden
Alexandre Zappelli
Jan H. Los
Mamadou Diarra
Dominique Chatain
CINaM - CNRS and Aix Marseille University
MRS Fall 2011 – Christophe Bichara
24/16
Why is it important to control chemical potential ?
T = 1200 K ; 10 relaxation steps/atom = unphysical !
Mu_C = - 7.0 eV / C
Mu_C = -4.5 eV / C
Low carbon chemical potential :
Higher carbon chemical potential :
 only favorable incorporation sites are accepted
 Chains are growing on surface
 Less selective incorporation
 More disordered structures
25
How do we grow Carbon Nanotubes ?
Chemical Vapor Deposition
1) Decomposition of a carbon bearing
precursor (e. g. : C2H2, CH4, CO,…)
catalyzed by metallic Nanoparticle
2) Nucleation and growth of a CNT
800-1100 K
or
Zhu et al., Small 2005
Carbon NT
Metal Nanoparticle
Carbon NT
Fe, Ni, Co …
Substrate e. g. SiOx, Al2O3
26
Some important features
Catalyst particle nanosized (1-5 nm) to produce Single Wall tubes
o Obtained by dewetting thin metal layer on substrate
o Size range accessible to computer simulation
Growth kinetics
o Orders of magnitude too slow for Molecular Dynamics simulations
o Local thermodynamic equilibrium
0 sec
96 sec
120 sec
150 sec
Lin et al. Nano Lett 2006
27
Experimental evidence for pressure threshold for nucleation
In situ Raman during SWNT growth : V. Jourdain et al.
G-band kinetics
: no growth
T=850°C
M. Picher, et al., Nano Letters (2009), 9 (2), 542–547
Below a threshold precursor pressure, NO carbon deposition
Temperature increases  threshold pressure increases
MRS Fall 2011 – Christophe Bichara
28/16
Can we explain wetting / dewetting behavior ?
Can we calculate the different terms ?
Surface energy is well defined for flat
interface. For pure Ni
Calculated
γ(100) = 1.64 N/m
γ(111) = 1.35 N/m
Experimental
solid : γ = 2.10 N/m
liquid : γ = 1.77 N/m
Graphene adhesion on Ni
Wadh ~
0.6 N / m
(Ni+C) clusters adhesion on Graphene
Wadh ~
2-3 N /m pure Ni
0.5 N /m C saturated Ni
Can we explain wetting/dewetting behavior ?
solid
liquid
Taking into account the state of the NP
30
Growth from a larger particle
Catalyst Ni with 15% C attached to piece of tube … then start GCMC
31
Tight binding model : important features
Pure Carbon :
o Carbon linear chain about 1 eV/ atom less stable than
sp2 carbon (DFT-GGA calculation)
L
Pure Ni : melting temperature is
DA
G
GA
o 2040 K (model) instead of 1728 K (expt)  15 % too high
Solubility of C in bulk Ni
o Heat of solution = + 0.5 eV / C (experimental value)
Tendency to favor C or C2 species in subsurface sites.
o Surface Ni layer distorted by adsorbed C atoms
o ‘Clock’ reconstruction of (100) surface
Klink PRL 1993
Amara et al.
Phys. Rev. B 73, 113404 (2006)
Phys. Rev. B 79, 014109 (2009)
M. Moors et al., ACS Nano, 2009, 3 (3), 511-516
Our TB 4 model
MRS Fall 2011 – Christophe Bichara
32/16
Grand canonical Monte Carlo calculations (1)
Thermochemistry of precursor decomposition yields atomic C at given chemical potential (C)
C is an essential control parameter
Idea is to use GCMC algorithm to control growth (nb. of Ni atoms fixed, C atoms incorporated)
Thermodynamic probability of a configuration
Pi 
V

N
3N
N!
exp(   ( E  N ))
Randomly alternate canonical displacement moves
+ attempts to insert a particle with acceptance probability:


V
Pacc (i  j )  min 1, 3
exp(  (   E ))
  ( N  1)

+ attempts to remove a particle with acceptance probability:
 3 N

Pacc (i  j )  min 1,
exp(   (   E ))
V


Random
“move” of
atoms
+
insertion
removal
33
Grand Canonical Monte Carlo simulations
Bulk : no surface
C removal
Nanoparticle
C insertion
C insertion
C removal
Atoms displacts
Atoms displacts
Ni cluster
Box relax x, y and z
Slab : free surface
C removal
Metropolis Monte Carlo :
C insertion
Changes in configurations (atoms displacements, insertion,
destruction, box relaxation) attempted at random, but accepted
according to thermodynamic criterion
Atoms displacts
 Leads to thermodynamic equilibrium
Box relax x and y
34
Carbon solubility in bulk Ni
Amorphous or molten Ni + C
Crystalline Ni+C
Carbon incorporation isotherms in bulk Ni (576 Ni atoms)
o Difficult to converge : intermediate region with mix of crystal + liquid
o Phase boundary of crystal is an upper bound
35
Evidence for subsurface C dimers
Hsol
TB Calculations :
Field Ion Microscopy + mass spectrometry
Subsurface dimers are stable at dCC1.9Å
Bulk behaviour (C unstable) below 3rd layer
Evidence for C2 and C3 species when
exposing a Ni tip to C2H2 under CVD
conditions
M. Moors et al., ACS Nano, 2009, 3 (3), 511-516
Already evidenced in catalysis literature 70’s-90’s
MRS Fall 2011 – Christophe Bichara
36/16
Tube/catalyst contact
start
end
start
end
end
Once formed, the tube remains attached at the
catalyst NP surface
TB 1000K :
Börjesson et al.,
Randomly dispersed Ni atoms coalesce at tube lip
Nano Lett., 2009, 9 (3), 1117-1120
Relevant for:
• contacting with electrode
• regrowth of nanotubes
MRS Fall 2011 – Christophe Bichara
37/16
Graphene formation : C incorporation in/on Ni slab
We get same three regimes as in Eisenberg et al.



Thick amorphous C layer
Graphene layer (128 C atoms for 64 Ni)
C atoms on Ni surface and nothing ouside
38
Conclusions
Tight binding 4th moment + GCMC simulations : unique and reliable tool
o Thoroughly tested for Ni-C
o Can be extended to other metal-carbon systems
Carbon solubility in Ni nanoparticles increases when size becomes smaller
Wetting of NP by sp2 carbon walls controlled by C concentration
o Important for SWNT growth
o Might also be of interest for contacting nanotubes or graphene
Growth of SWNT :
o C solubility, NP dewetting and polyyne chains are essential ingredients
o side wall quality still challenging issue. When solved, address chiral selectivity
Growth of graphene on metal : … ongoing work
39
Graphene formation
800 K
μC = -6.10 eV/at.
Low μC and T :
o crystalline structure preserved
o low C concentration
o oscillating C concentration profile
1000 K
μC = -5.95 eV/at.
Larger μC and T :
o Amorphous structure
o ~ 20-25 % C
o Note that we cannot obtain Ni3C
structure (orthorhombic box)
40