Application du modèle métal-carbone en liaisons fortes à la croissance de nanostructures de carbone M. Diarra, H. Amara, F. Ducastelle C. Bichara LEM CNRS and ONERA CINaM - CNRS and Aix-Marseille Université
Why trying to make Single Wall Carbon Nanotubes? They are cute? It s rolled graphene? Outstanding features : mechanical properties; aspect ratio; quasi 1-dimensional metallic or semiconducting depending on its «chirality» controlling chirality during growth quite challenging! 2
Applications Transparent Conducting films : Smartphones already on Chinese market (Foxconn + Tsinghua Univ.) Flexible electronics: Nature Nanotech 6, 156 (2011) (Nagoya + Aalto Univ.) Carbon Nanotube Computer Nature 501, 7468, 526-30 (2013) (Stanford Univ.) Christophe Bichara 3
Chemical Vapor Deposition 1) Decomposition of a carbon bearing precursor (e. g. : C 2 H 2, CH 4, CO, ) catalyzed by metallic Nanoparticle 2) Nucleation and growth of a CNT 800-1100 K or Carbon NT Zhu et al., Small 2005 Metal Nanoparticle Fe, Ni, Co Carbon NT Christophe Bichara Substrate e. g. SiO x, Al 2 O 3 4
In situ video of SWNT growth Titan 80-300 ETEM Accelerating voltage: 300 kv, Tip growth Co NP s on MgO CO pressure: < 10 mbar. Temperature: 600 o C~ 700 o C Courtesy : Maoshuai He + + E. Kauppinen (Aalto Univ. Finland) Microscope at DTU (Denmark) Christophe Bichara 5
What we can do now by atomistic computer simulation start growth Final Nickel nanoparticle with 147 atoms (1.3 nm diameter) Size is almost comparable to experiments (x 2-4) Time scale is still challenging Christophe Bichara 6
Today s menu Simulation tools o Tight Binding model for Ni+C and Grand Canonical Monte Carlo o Check of Bulk Carbon solubility Solubility of carbon in Ni nanoparticles o Size and Temperature dependance, state of NPs o Wetting properties Growth mechanisms o Carbon incorporation via C chains o Nanotubes : narrow chemical potential + temperature window o Graphene : easier than SWNT s? o Role of dissolved C? Christophe Bichara 7
Tight binding model Total energy is a sum of local terms : E E Eni (E)dE f i Band structure term Local densities of states 1 2 V(r ij ) i,j Empirical repulsive term Moments method (order N and fast) : Local DOS on red atom depends on - 1 st neighbors (2 nd moment); cut off = 2.7 Å for C - 1+2 nd neighbors (4 th moment) 4 th moment and beyond : directional bonding (p) Parameters (fitted on experimental data and DFT calculations) : 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) Christophe Bichara 8
Grand Canonical Monte Carlo Idea is to mimic complex CVD reaction C insertion C removal e.g. C 2 H 2 2 C + H 2 With P, T, H 2, O 2, H 2 O, Ar etc We neglect all the thermochemistry and assume we simply have: Atoms displacts Carbon atoms Ni cluster close to the surface At a given chemical potential Random changes in configurations (atoms displacements, insertion, removal, ) Accepted according to thermodynamic criterion Drives system towards thermodynamic equilibrium Christophe Bichara 9
Importance of chemical potential to control C incorporation T = 1200 K ; 10 relaxation steps/atom = unphysical! Mu_C = - 7.0 ev / C Mu_C = -4.5 ev / C Low carbon chemical potential : only favorable incorporation sites accepted Chains growing on surface Higher carbon chemical potential : Less selective incorporation More disordered structures 10/30
Internal energy (ev/ at.) Melting of small Ni clusters Melting temperature of Ni clusters Melting temperatures Temperature (K) Pure Ni clusters with more than 55 atoms are solid up to 1400 K in our model Extrapolated (Gibbs-Thompson) 2360 K «Exact» calculated 2050 K Experimental 1728 K Christophe Bichara 11
Carbon solubility in bulk Ni Liquid Ni+C Crystal Ni+C Temperature rescaled to compare with experimental phase diagram Calculated solubility limit below 5% in crystal Christophe Bichara 12
How does carbon solubility change at nanoscale? Simple idea. : Nanosize induces Laplace Pressure (~ γ / R) inside NP Assumes that surface energy remains constant when C is adsorbed C in interstitial sites Smaller size induce more pressure and hence smaller solubility Harutyunyan et al. PRL 100, 195502 (2008) Christophe Bichara Carbon on Fe DFT calculations @ 0 K PRB 82, 125459 (2010) 13
Carbon solubility in nanoparticles? Calculate «sorption» isotherms: Mole fraction of carbon inside Ni NP, as a function of C chemical pot. At different temperatures For different Nano Particle sizes 55 147 201 405 807 1.1 1.5 1.8 Diameter (nm) Christophe Bichara 2.3 2.9 14
Carbon solubility in nanoparticles: effect of particle size At given μ C, smaller clusters have larger C concentration Solubility limit slightly larger for smaller NPs depends on the state of the NP μ C region for growth Christophe Bichara 15
State of Nanoparticles Order parameter S : Core : crystalline (S > 6) Outer shell : liquid or amorphous (S < 2) P. Steinhardt, D. Nelson, and M. Ronchetti, Bond-orientational order in liquids and glasses, Phys. Rev. B, 28, 2, 784 805, 1983. Towards a phase diagram : In this example, nanoparticles are molten for % C > 10 % 16
Carbon solubility in nanoparticles: effect of particle size Molten Melting line? Crystalline core/ Molten shell Christophe Bichara 17
Effect of C solubility on wetting of NP on graphite/ene? Sessile drop method to measure contact angle of macroscopic Ni drops on graphite: o Pure Ni wets graphite Θ = 50 o Θ > 90 for C wt% > 2.5 o Same for Co and Fe Yu V. Naidich et al. 1971 What about : o Nanosized particles? o Plays a role for SWNT growth? Christophe Bichara 18
Wetting of Ni+C nanoparticles on graphene 405 Ni 1000 K 1400 K 405 Ni +11 % C 405 Ni + 24 % C Carbon rich Ni nanoparticles tend to dewet graphene 1400 K Relaxed at 0 K Christophe Bichara 19
Under correct (μ C, 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 C 2 dimers addition Still challenging : o (µ C, T) conditions to grow defectless tube o Effect of tube chirality? Christophe Bichara 20
Nucleation and growth of multiwall tube Yoshida et al., Nano Letters 2008 Two steps 1) Metal NP is deformed and sticking to the carbon wall 2) Quick detachment and retraction of NP after some delay. Looks very similar to what we see in simulated system Christophe Bichara 21
Dewetting when C concentration is large enough Christophe M. Diarra Bichara et al. Phys. Rev. Lett. 109, 185501 (2012) 22
If Carbon is removed from the NanoParticle ( easy to do on a computer ) One recovers wetting conditions, Nanoparticle reenters inside tube Could explain formation of bamboo tubes Stop and go growth observed by in situ TEM M. Diarra et al. Phys. Rev. Lett. 109, 185501 (2012) Christophe Bichara 23
Competing growth kinetics NP dewetting Wall growth Starting conf. Dewetting ~ wall growth efficient growth Dewetting > wall growth NP detaches Wall growth > dewetting NP encapsulation Christophe Bichara 24
Graphene growth Top view Side view Using similar method, we can grow graphene on Ni (111) surface, starting from a C 10 nucleus o 1000 K o Almost perfect graphene structure o Carbon atoms dissolved in bulk Ni See : Amara et al. PRB 73, 113404 (2006) Haghighatpanah et al. PRB 85, 205448 (2012) Christophe Bichara 25
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 26
Much narrower (μ C, T) domain for SWNT growth SWNT Growth possible Graphene Growth possible Christophe Bichara 27
Under suitable conditions, no subsurface carbon atoms Tight-binding GCMC simulations T = 800 K, μ C = -6.10 ev/at T = 1000 K, μ C = -5.95 ev/at Tendency for carbon depletion in subsurface interstitial layer Is this realistic? Christophe Bichara 28
Dissolution energy calculations Tight Binding Without graphene With graphene overlayer Subsurface : Binding energy -8.21 ev Subsurface : Binding energy -6.79 ev Subsubsurface : Binding energy -7.31 ev Subsubsurface : Binding energy -7.77 ev Our Tight Binding overestimates Graphene adhesion energy Christophe Bichara 29
Dissolution energy calculations DFT calculations d o o o VASP code (PAW; GGA; spin-polarized, ) 6 atomic planes (9 Ni atoms) Graphene (18 C atoms) 1 2 o Graphene - Ni distance varied : d(a) ΔE (1-2) (ev) 3.50-0.90 2.00-0.10 1.80 +0.31 When graphene is closer to surface, subsurface carbon atoms are less stable than subsubsurface Qualitative agreement with Tight Binding model Christophe Bichara 30
Conclusions Under growth conditions: Smaller NPs are liquid/amorphous Core shell structure when bigger Ni nanoparticles surface is not crystalline Carbon solubility : influences interfacial properties plays important role in growth mechanisms Growth mechanisms: Controlling C chemical potential is essential Carbon addition via chains/strings Growth conditions influence diameter and selectivity Contrasted role of C solubility in SWNT or graphene growth Christophe Bichara 31
Merci pour votre attention! Et merci à Annick Loiseau LEM - ONERA/CNRS Kim Bolton Anders Börjesson Univ. Gothenburgh + Borås Sweden Alexandre Zappelli Jan H. Los CINaM - CNRS and AMU SOS_Nanotubes ANR-09-Nano-028 2 post docs wanted! Maseille et Paris Christophe Bichara 32