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Growing a SWNT on the computer … March 2011

Growing a SWNT on the computer … March 2011. Christophe Bichara Centre Interdisciplinaire de Nanoscience de Marseille (CINaM) Mamadou Diarra Hakim Amara LEM ONERA/CNRS Chatillon France François Ducastelle. Tight Binding model. Band structure term Local densities of states.

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Growing a SWNT on the computer … March 2011

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  1. Growing a SWNT on the computer … March 2011 Christophe Bichara Centre Interdisciplinaire de Nanoscience de Marseille (CINaM) Mamadou Diarra Hakim Amara LEM ONERA/CNRS Chatillon France François Ducastelle

  2. 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 - 1st neighbors (2nd moment); cut off = 2.7 Å - 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).

  3. Original algorithm • Moments calculations: • Use recursion algorithm • stable, efficient beyond 4th moment • At each MC step calculate only moments that have changed • very fast, possible only for limited nb. of moments • Continued fraction to calculate DOS and total energy with 3 choices • CF truncated at 4th moment level : (b3=0) • simple but not efficient • Constant ai and bi coefs up to Mth level + diagonalizing (MxM) tridiagonal matrix • efficient and stable, but slow (older version) • Asymptotic expansion (M) + numerical integration • very fast but not very stable.

  4. Faster algorithm (thanks to Jan H. Los) • Moments calculations: • Use recursion algorithm • stable, efficient beyond 4th moment • At each MC step calculate only moments that have changed • very fast, possible only for limited nb. of moments • Continued fraction to calculate DOS and total energy with 3 choices • CF truncated at 4th moment level : (b3=0) • simple but not efficient • Constant ai and bi coefs up to Mth level + diagonalizing (MxM) tridiagonal matrix • efficient and stable, but slow (older version) • Asymptotic expansion (M) + numerical integration • very fast but not very stable.

  5. Tools : Grand canonical Monte Carlo calculations Random “move” of atoms 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: insertion removal • Carbon chemical potential () is an essential control parameter • Idea is to use GCMC algorithm to control growth • number of Ni atoms fixed, C atoms incorporated +

  6. Tools : Grand canonical Monte Carlo calculations C insertion C removal displacement C atoms are tentatively inserted close to Ni cluster surface, with a given chemical potential, to simulate CVD reaction Ingredients of GCMC calculations • Temperature • Carbon : tells you how often a random attempted insertion will be accepted  sticking coefficient if pure adsorption • Number of relaxation steps between insertions/destructions of C atoms 1/flux … but no time scale in MC

  7. Tight binding model : important features LDA GGA Klink PRL 1993 Our TB 4 model • Carbon : • Carbon linear chains about 1 eV/ atom less stable than sp2 carbon (DFT-GGA calculation) • Melting temperature of pure Ni is 2040 K (model) instead of 1728 K (experiment)  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

  8. Melting of small Ni clusters Internal energy (eV/ at.) Temperature (K) Extrapolating melting temperature of clusters (Gibbs-Thompson) Calculated Tm = 2360 K Experimental Tm = 1728 K Pure Ni clusters with more than 55 atoms are still solid up to 1400 K in our model J. H. Los et al. PRB 81, 064112 (2010)

  9. Melting temperature of bulk Ni Better estimate by calculating Gibbs energies of bulk liquid and solid phases (thermodynamic integration on 864 atoms boxes) Calculated Tm = 2040 K Experimental Tm = 1728 K

  10. Menu of the day • Play with GCMC calculations varying • Structures : (6,5), (6,6), (9,1) and (10,0) tube butts sitting on Ni clusters (55, 85 and 147 atoms) • Temperature : 1000 to 1400 K • Flux : 10000 to 50000 relaxation MC steps attempted between insertions/destruction • Carbon chemical potential • Work is still going on …

  11. First tests of role of C and flux on graphene growth • T fixed at 1200 K, 10000 MC displacements between ins/ext . • Not really significant … Alex Z. will do better GRAZNI20 GRAZNI27 -6.0 eV/C 95 C added; 41 rings (5, 6 or 7) formed -5.5 eV/C 93 C added; 43 rings (5, 6 or 7) formed

  12. Chemical potential controls C incorporation … • T=1200 K • When C increases, the insertion of C atoms is less energy selective(less favorable insertion sites are accepted) Mu_C = - 7.0 eV / C Mu_C = -4.5 eV / C

  13. Low temperature, fast flux : encapsulation T91_NI85.CT2 T65_NI85.C10 1000 K; 10000 MC disp./at. 1000 K; 50000 MC disp./at. • At T= 1000 K, we almost systematically obtain a encapsulation of Ni cluster, specially when flux is fast (small number of realxation steps between ins./dest.)

  14. Too hot : tube detaches from NP T100NI85.C50 T66N147.C30 1400 K; 50000 MC disp./at. 1400 K; 50000 MC disp./at. • At T = 1400 K, tube almost systematically detaches from Ni cluster, before or after closing … • Note that our model seems to give too small an adhesion energy of tubes on Ni cluster when a carbide is formed close to surface…

  15. Growth of sp2 layers is tangential to particle T65_NI85.C10 1000 K; 50000 MC disp./at. • T= 1000 K : sp2 structure tends to form on left side, tangential to Ni surface, while right side (perpendicular) hardly grows.

  16. Intermediate temperature and/or slow enough flux : growth T66_NI85.C20 T100NI85.C40 1200 K; 10000 MC disp./at. 1200 K; 50000 MC disp./at. • Around 1100-1200 K, tube growth is possible. • In most succesful growth situations, Ni is pumped in the tube, than expelled … Why ? • What is the role of + or – short C chains ?

  17. Tube vs. Nanoparticle diameter ratio seems important T91_NI55.CTU T100NI55.CTU 1000 K; 10000 MC disp./at. 1000 K; 10000 MC disp./at. • Ni55 particles don’t seem to promote growth

  18. Growth mechanism involves chains … T66_NI85.C30 1400 K; 10000 MC disp./at. • Chains attach to tube lip ?

  19. Ni pumped inside tube then expelled … T100NI85.C70 • What is the driving force ? 1100 K; 50000 MC disp./at.

  20. Conclusions / Open questions : • Before growth, Ni catalyst gets saturated with subsurface C atoms • It would be reverse in real situation (saturation/nucleation/growth) • We always see + or – long C chains forming • Compatible with mechanism proposed by B. Yakobson ? • Controlling this length might be important: • Too long chains have lower probability to get attached to tube lip • cf. role of NH3 for chiral selection Kauppinen • Seen in Graphene as well (cf. Loginova+Bartelt) • The size ratios are important, • we never see growth perpendicular to the surface, always tangential… • In line with observations by Annick and Marie Faith • With caps tested, no growth on Ni55, difficult on Ni147, best on Ni85 • The pumping/expelling of Ni in tube butt is frequent when tube starts to grow. • Competing tendencies to encapsulate and to grow … • Other evidences • Model ??? • What about inserting C dimers to model C2H4 decomposition ?

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