1 / 48

FULLERÉNEK ÉS SZÉN NANOCSÖVEK

FULLERÉNEK ÉS SZÉN NANOCSÖVEK. előadás fizikus és vegyész hallgatóknak ( 2008 tavaszi félév – május 07.) Kürti Jenő ELTE Biológiai Fizika Tanszék e-mail: kurti@virag.elte.hu www: virag.elte.hu/kurti. G. Kresse et al. FIRST PRINCIPLES CALCULATIONS DFT: LDA

quin-king
Download Presentation

FULLERÉNEK ÉS SZÉN NANOCSÖVEK

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. FULLERÉNEK ÉS SZÉN NANOCSÖVEK előadás fizikus és vegyész hallgatóknak (2008 tavaszi félév – május 07.) Kürti Jenő ELTE Biológiai Fizika Tanszék e-mail: kurti@virag.elte.hu www: virag.elte.hu/kurti

  2. G. Kresse et al FIRST PRINCIPLES CALCULATIONS DFT: LDA plane wave basis set, cutoff: 400 eV Wien Budapest Lancaster

  3. arrangement: tetragonal (hexagonal for test) distance between tubes: l = 0.6 nm (1.3 nm for test) hexa tetra

  4. d building block r1 bond lengths r2 r3 c q1 bond angles q2 q3 (4,2) 56 atoms

  5. tube axis ideal hexagonal lattice

  6. c decreases tube axis d increases

  7. b1 tube axis extra bond misalignment

  8. GEOMETRY OPTIMIZATION

  9. diameter

  10. 1/d vs 1/d0DFT optimized diameter . ZZ AC CH 1/d (nm-1) 1/d0 (nm-1) r0 = 0.1413 nm

  11. (d-d0)/d0 vs 1/d0relative change . ZZ AC CH (d-d0)/d0 (%) 1/d0 (nm-1) (9,0) : 1.06 ± 0.01 % r0 = 0.1413 nm

  12. (d-d0)/d0 vs 1/d0relative change . ZZ AC CH (d-d0)/d0 (%) 1/d0 (nm-1) (9,0) : 1.06 ± 0.01 % r0 = 0.1413 nm

  13. length of the unit cell

  14. unit cell lengths vs 1/d0relative change . ZZ AC CH (c-c0)/c0 (%) 1/d0 (nm-1) (9,0) : -0.05 ± 0.01 % r0 = 0.1413 nm ZZ triads

  15. bond lengths

  16. (r1-r0)/r0 vs 1/drelative change . ZZ AC CH (r1-r0)/r0 (%) 1/d (nm-1) r0 = 0.1413 nm (9,0) : -0.32 ± 0.004 % ZZ triads

  17. (r2-r0)/r0 vs 1/drelative change . ZZ AC CH (r2-r0)/r0 (%) 1/d (nm-1) r0 = 0.1413 nm ZZ triads

  18. bond angles

  19. bond angle q1 vs 1/d0DFT optimized . ZZ AC CH q1 (deg) 1/d0 (nm-1) r0 = 0.1413 nm

  20. pyramidalization or s-p rehybridization sp2 sp3 S.Niyogi et al., Acc. Chem. Res. 35, 1105 (2002)

  21. pyramidalization angle qP vs 1/d0DFT optimized . C60: 11.6° ZZ AC CH qP (deg) 1/d0 (nm-1) r0 = 0.1413 nm

  22. BAND STRUCTURE

  23. tight binding (nearest neighbour)

  24. DFT (VASP)

  25. (6,5) - DFT

  26.  1/d zigzag (11,0) (10,0) (14,0) (13,0) (8,0) (17,0) (16,0) (20,0) (19,0) (4,0) (5,0) (7,0) ZF-TB DFT  1/d chiral (4,3) (5,3) (6,4) (6,2) (4,2) (3,2) (6,1) (5,1)

  27. (5,0) ZF-TB: Eg = 2.3 eV DFT: Eg = 0 ! s* - p*

  28.  1/d zigzag (11,0) (10,0) (14,0) (13,0) (8,0) (17,0) (16,0) (20,0) (19,0) (4,0) (5,0) (7,0) ZF-TB DFT  1/d chiral (4,3) (5,3) (6,4) (6,2) (4,2) (3,2) (6,1) (5,1)

  29. ZF-TB METALLIC non-armchair: zigzag, chiral K tube axis dkF kF - kF (d) = f(1/d2) opening of a secondary gap dkF

  30. secondary gap in (7,1) 0.14 eV

  31. ZF-TB METALLICarmchair K tube axis dkF kF - kF (d) = f(1/d2) NO secondary gap dkF

  32. (6,6) F dkF (4,4) F dkF kF (d)=2/3

  33. AC (11,11) (10,10) (9,9) (8,8) (7,7) (6,6) (5,5) (4,4) (3,3)

  34. n m N Θ0 d0 dDFTDc/c0234/dDFTwDFT w*DFT n m N Θ0 d0 dDFTDc/c0234/dDFTwDFT w*DFT

  35. REZGÉSI TULAJDONSÁGOK

  36. D band Radial Breathing Mode

  37. DFT (5,3) quadratic fit force constant RBM-frequency

  38. RBM vs 1/d0 linear fit for large diameters Alarge_d= 233.1 ZZ AC CH n (cm-1) 1/d0 (nm-1)

  39. RBM vs 1/ddeviation from linear fit 5,3 7,0 ZZ AC CH Dn (cm-1) d=0.5546 nm 1/d (nm-1)

  40. AAC= 236 AZZ= 232 ZZ AC CH

  41. COUPLING of TOTALLY SYMMETRIC MODES (RBM + G (HFM)) radial tangential 1 for achiral 2 for chiral

  42. ZZ AC CH

  43. Raman Stokes: w2=w1 – w (Anti-Stokes: w2=w1+w) b a 0 w, 0 w, w, w1 w w1 w2=w1 –w w1 w2=w1 +w w w1

  44. hin hout hin hout hin hout (incoming) resonance Raman C. V. Raman

  45. (a) RBM spectra of HiPCO produced carbon nanotubesatdifferent excitationenergies. The spectra are vertically offset forclarity. From top to bottom the laser energy increases between 1.51and 1.75 eV. Each peak arises from a different (n,m)nanotube. (b) Resonance profiles for the peaks marked in aby vertical lines.Thedots are experimental data; the lines are fits.

  46. 2D RBM Two-dimensional plot of the radial-breathing-mode range vs. laser excitation energy. Note the various laola-like resonance enhancements, from which we can determine both the optical transition energies and the approximate diameter of the nanotubes. The spectra were each calibrated against the Raman spectrum of CCl4.

  47. Contour plot of 2D RBM

  48. Contour plot of 2D RBM A. Jorio et al., (in press)

More Related