Insights in the CVD synthesis of carbon nanotubes from computer simulation

1. Insights in the CVD synthesis of carbon nanotubes from computer simulation Christophe Bichara CINaM - CNRS and Aix Marseille University - France

2. Let’s start by the end : our findings in a video (1) Grand Canonical Monte Carlo • Starting from a NT cap on a Nickel nanoparticle • Carbon wall grows along nanoparticle • Some C atoms dissolved • Nanoparticle tends to escape the tube What are the driving forces ? Ni : orangeInitial C cap : blue added C atoms : black

3. 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 • Canonical Monte Carlo • No Carbon dissolved • Nanoparticle re-enters the tube Wetting / dewetting behavior ?

4. Outline Model for Ni+C interaction; Computer simulation technique • Tight binding + 4th moment’s method = O(N) and fast • Grand canonical Monte Carlo Thermodynamic properties of Ni+C alloys • Melting of Ni bulk and clusters • Carbon solubility in bulk and clusters Wetting of (Ni+C) clusters on sp2 carbon layers • Carbon dissolution controls wetting properties SWNT growth • Chemical potential and temperature conditions for growth • Growth modes • Growth mechanisms

5. Tight binding model Band structure termLocal densities of states Empirical repulsive term Hopping integrals : - C-C : ss, sp, pp, pp - Ni-Ni : dd, dd, dd - Ni-C : sd, pd, pd Minimal basis set : • C s and p electrons • Ni d electrons Total energy : Moments : Local DOS on red atom depends on - 1stneighbors (2nd moment); cut off = 2.7 Å for C - 1+2ndneighbors (4th moment) 4th moment and beyond : directional bonding (p) Parameters : Energylevels, hoppingintegrals, 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)

6. Grand Canonical Monte Carlo simulations C removal C insertion Ni cluster Atoms displacts Insertion Removal μ : carbon chemical potentialΔE : energy variation (new-old)T : temperature Random changes in configurations (atomsdisplacements, insertion, destruction, …) Acceptedaccording to thermodynamiccriterion  Leads to thermodynamicequilibrium Reasonablebecausegrowth (μs to ms / ring) isvery slow atatomiclevel (0.1 ps)

7. Melting of small Ni clusters Meltingtemperature of Ni clusters Internal energy (eV/ at.) 1400 K Temperature (K) Pure Ni clusters with more than 55 atoms are stillsolid up to 1400 K in our model Meltingtemperatures • Extrapolated(Gibbs-Thompson) 2360 K • « Exact » calculated2050 K • Experimental1728 K J. H. Los et al. PRB 81, 064112 (2010)

8. Carbon solubility in bulk Ni Temperature rescaled to compare with experimental phase diagram Calculated solubility limit below 5% in crystal Tcalc. rescaled by 0.85 Liquid Ni+C Crystal Ni+C

9. How does carbon solubility change at nanoscale ? Option 1 : Nanosizeinduces Laplace Pressure inside NP C in interstitialsites Smaller sizeinduce more pressure and hencesmallersolubility Harutyunyanet al. PRL 100, 195502 (2008) Option 2 : C in subsurfaceinterstitial sites Surface/volume ratio larger for smaller sizes Smaller sizeinduceslargersolubility

10. Carbon solubility in nanoparticles ? Outer C atoms C - C dist. < 1.7 Å Surface C atoms Ni-C bonds  5 Bulk C atoms (often subsurface) Ni-C bonds > 5 Ni particles sizes and structures • 55 and 147 atoms, icosahedral : compact (111)-like surface • 201, 405 and 807 atoms, Wulff shape : (111) and (100) facets Calculate « sorption » isotherms Average carbon contents inside, on surfaceand outside particles

11. 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

12. Carbon solubility in nanoparticles: effect of particle size Molten Crystalline core/ Molten shell

13. State of Nanoparticles 405 Ni atoms 1000 K 6 % C Pure Ni 11 % C Core: crystal, no Carbon Outer layer: C-rich, molten Crystalline Molten/amorphous 201 405 « Phase diagram » 1000 K Relative thickness of liquid layer 807

14. Carbon solubility in nanoparticles: effect of temperature … Carbon chemical potential C C/ kT ~ Ln (Pressure ), if ideal gas Same data, plotted as function of : Solubility limits increase with T Pressure to reach this solubility limit also increases with T Explains pressure threshold for nucleation of SWNT • Cf : in situ Raman during SWNT growthM. Picher et al. Nano Letters (2009), 9 (2), 542–547

15. Effect of C solubility on wetting of NP on graphite/ene ? Sessile drop method to measure contact angle of macroscopic Ni drops on graphite: • Pure Ni wets graphite Θ = 50° • Θ > 90° for C wt% > 2.5 • Same effect observed for Co and Fe What about : • Nanosized particles ? • Plays a role for SWNT growth ? Yu V. Naidich et al. 1971

16. Wetting of Ni+C nanoparticles on graphene Carbon rich Ni nanoparticles tend to dewet graphene 405 Ni 1000 K 1400 K 405 Ni +11 % C 405 Ni + 24 % C 1400 K Relaxed at 0 K

17. Try and grow a tube from an existing cap Whatwedid: • Fix a SWNT butt on a pure Ni Nanoparticle and relax to 0 K • Different tube diameters, chiralities and NP sizes • Play with (μC, T) conditions to grow tube walls Controllingcarbonchemicalpotential via GCMC calculationsis essential ! Low temperature and high μC : encapsulation by growing walls High temperature and low μC : detachment of tube cap from NP

18. 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)

19. Growth modes : perpendicular vs tangential perpendicular M.F.C. Fiawoo et al. PRL 108, 195503 (2012) 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

20. Under correct (μC, T) conditions : tube grows ! Tube cap tends to dewetfromcatalystNP when C isincorporated in Ni Tube wallsdevelopthroughpolyynechains… no evidence for C2dimers addition Stillchallenging: • (µC, T) conditions to growdefectless tube • Effect of tube chirality ? Starting configuration Last configuration M. Diarra et al. submitted, available on ArXiv

21. Dewetting when C concentration is large enough M. Diarra et al. submitted, available on ArXiv

22. 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

23. Conclusions : towards a NT growth model ? Carbonsolubility in Ni nanoparticles ? • dependson T and µC • larger for smaller sizes • Surface of NP ≤ 807 is not crystalllineundergrowth conditions Dewetting of Ni nanoparticlefrom sp2carbonwall? • controlled by carbondissolved • Essential for NT growthalso for graphene ? • … othermetals ? metal contacts ? Growth modes ? • Tangential mode favoredwallqualitystillchallenging • C incorporation at tube lip by short chainsfor computer simulation Elementarysteps • Feedstockdecomposition • Carbon diffusion surface diffusion via chainsfaster • Dewetting of NP fromgrowing tube weaklychiralitydependent ? • Growth of tube wallstronglychiralitydependent ??

24. Thank you for your attention ! • And thanks to • Hakim Amara LEM - ONERA/CNRS • François Ducastelle Chatillon France • Kim Bolton Univ. Gothenburgh • Anders Börjesson + Borås Sweden • Alexandre Zappelli CINaM - CNRS and Aix Marseille University • Jan H. Los • Mamadou Diarra • Dominique Chatain MRS Fall 2011 – Christophe Bichara

25. 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 : • only favorable incorporation sites are accepted • Chains are growing on surface Highercarbonchemicalpotential : • Lessselective incorporation • More disordered structures

26. How do we grow Carbon Nanotubes ? Zhu et al., Small 2005 ChemicalVaporDeposition Decompositionof a carbonbearingprecursor (e. g. : C2H2, CH4, CO,…)catalyzed by metallicNanoparticle Nucleation and growth of a CNT 800-1100 K or Carbon NT Metal Nanoparticle Fe, Ni, Co … Carbon NT Substrate e. g. SiOx, Al2O3

27. Some important features Catalystparticlenanosized(1-5 nm) to produceSingle Wall tubes • Obtained by dewettingthinmetal layer on substrate • Size range accessible to computer simulation Growthkinetics • Orders of magnitude too slow for Molecular Dynamics simulations • Local thermodynamicequilibrium 0 sec 96 sec 120 sec 150 sec Lin et al. Nano Lett 2006

28. 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

29. 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

30. Can we explain wetting/dewetting behavior ? solid liquid Taking into account the state of the NP

31. Growth from a larger particle Catalyst Ni with 15% C attached to piece of tube … then start GCMC

32. Tight binding model : important features LDA GGA Klink PRL 1993 Our TB 4 model • Pure Carbon : • Carbon linear chain about 1 eV/ atom less stable than sp2 carbon (DFT-GGA calculation) • Pure Ni : melting temperature is • 2040 K (model) instead of 1728 K (expt)  15 % too high • Solubility of C in bulk Ni • Heat of solution = + 0.5 eV / C (experimental value) • Tendency to favor C or C2 species in subsurface sites. • Surface Ni layer distorted by adsorbed C atoms • ‘Clock’ reconstruction of (100) surface 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 MRS Fall 2011 – Christophe Bichara

33. Grand canonical Monte Carlo calculations (1) Random “move” of atoms insertion removal 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 Randomly alternate canonical displacement moves + attempts to insert a particle with acceptance probability: + attempts to remove a particle with acceptance probability: +

34. Grand Canonical Monte Carlo simulations C removal C removal C insertion C insertion Ni cluster Atoms displacts Box relax x, y and z Slab : free surface C removal C insertion Metropolis Monte Carlo : Changes in configurations (atoms displacements, insertion, destruction, box relaxation) attempted at random, but accepted according to thermodynamic criterion  Leads to thermodynamic equilibrium Box relax x and y Bulk : no surface Nanoparticle Atoms displacts Atoms displacts

35. Carbon solubility in bulk Ni Amorphous or molten Ni + C Crystalline Ni+C Carbon incorporation isotherms in bulk Ni (576 Ni atoms) • Difficult to converge : intermediate region with mix of crystal + liquid • Phase boundary of crystal is an upper bound

36. Evidence for subsurface C dimers Hsol Subsurface dimers are stable at dCC1.9Å Bulk behaviour (C unstable) below 3rd layer TB Calculations : Field Ion Microscopy + mass spectrometry 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

37. Tube/catalyst contact start end start end end • Once formed, the tube remains attached at the catalyst NP surface • TB 1000K : • Randomly dispersed Ni atoms coalesce at tube lip • Relevant for: • contacting with electrode • regrowth of nanotubes Börjesson et al., Nano Lett., 2009, 9 (3), 1117-1120 MRS Fall 2011 – Christophe Bichara

38. Graphene formation : C incorporation in/on Ni slab Wegetsamethreeregimes as in Eisenberget al. • Thickamorphous C layer • Graphene layer (128 C atoms for 64 Ni) • C atoms on Ni surface and nothingouside

39. Conclusions Tight binding 4th moment + GCMC simulations : unique and reliable tool • Thoroughly tested for Ni-C • 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 • Important for SWNT growth • Might also be of interest for contacting nanotubes or graphene Growth of SWNT : • C solubility, NP dewetting and polyyne chains are essential ingredients • side wall quality still challenging issue. When solved, address chiral selectivity Growth of graphene on metal : … ongoing work

40. Graphene formation Low μC and T : • crystalline structure preserved • low C concentration • oscillating C concentration profile 800 K μC = -6.10 eV/at. 1000 K μC = -5.95 eV/at. LargerμC and T : • Amorphous structure • ~ 20-25 % C • Note thatwecannotobtain Ni3C structure (orthorhombic box)