1. Electron diffraction on carbon nanotubes Marko Viršek adviser: doc. dr. Maja Remškar

2. 21.11.06Electron difraction on carbon nanotubes Outline Transmission electron microscope: Electron diffraction on graphite Geometry of carbon nanotubes Kinematical diffraction theory for carbon nanotubes Simulations and experimental diffraction patterns Other helical structures

3. 21.11.06Electron difraction on carbon nanotubes Transmission electron microscope (TEM) TEM components: HV source Vacuum sistem Electron gun EM lenses Apertures Specimen holder Viewing screen Basic TEM modes: Imaging Selected area diffraction

4. 21.11.06Electron difraction on carbon nanotubes Interaction of electrons with the sample Specimen thickness < 100 nm Electron energies ~ 100 - 400 keV (unscattered + elastically Bragg scattered e - ) diffraction pattern scattering: nonuniform distribution of electrons spatial distributionangular distribution image (unscattered e - ) σ elastic ~(Z e / V θ) 2 mean free path of e - ~ 10 nm Electrons interact stronger than x-rays

5. 21.11.06Electron difraction on carbon nanotubes Electron lenses 1/u + 1/v = 1/f u....object plane v....image plane f.....focal plane General properties: Changable strength (f) of the lense Collecting from small angles Limiting the resolution of TEM Using apertures for selecting electrons

6. 21.11.06Electron difraction on carbon nanotubes Selected area diffraction diffraction mode imaging mode object planesample focal plane (obj. aperture) image of the diffraction image plane (SAD aperture) image of the sample Objective lens : Intermediate lense object plane: at image plane of objective lense at back focal plane of obj. lense Selecting TEM mode: remove

7. 21.11.06Electron difraction on carbon nanotubes Elastic scattering k K K0K0 X-rayselectrons KK0K0 C Bragg: nλ = 2d hkl sinθ B λ - electron wavelength ~2,5 pm at 200 keV von Laue: k = K - K 0 = ha*+kb*+lc* and |k|=1/d hkl Many points in electron diffraction: small λ + relrods

8. 21.11.06Electron difraction on carbon nanotubes Electron diffraction on graphite Structure factor for primitive celll: Intensity of diffraction waves: (hk.0) spots structure of hexagonal graphite TED pattern (00.1) forbidden (00.2) allowed (hk.o) allowed

9. 21.11.06Electron difraction on carbon nanotubes Geometry of single-shell carbon nanotubes η XX’ Chiral vector: XX’ = L a 1 +M a 2 ; L > 0 Circumference of the tube: |XX’| = 2πR 0 = a Chiral angle: tg η = M / (2L + M) armchair: (L, L ); η = ±30º zigzag: (L, 0); η = 0º chiral: (L, M); −30° < η < 30° rolling up

10. 21.11.06Electron difraction on carbon nanotubes Geometry of carbon nanotubes d a = d 3 helical ribbons

11. 21.11.06Electron difraction on carbon nanotubes Geometry of carbon nanotubes 30°+ |η| L helical ribbons M > 0: right handed tube M < 0: left handed tube tube: (L > 0, M) (4,1) nanotube

12. 21.11.06Electron difraction on carbon nanotubes Geometry of carbon nanotubes L paralel zigzag helices L paralel double helices a u z After rolling up: u Ф u = ФR 0

13. 21.11.06Electron difraction on carbon nanotubes Geometry of carbon nanotubes ∆z 1,∆Φ 1 ∆z 2,∆Φ 2 = function (a, L, M) u z a ∆z1∆z1 ∆u1∆u1 ∆u2∆u2 ∆z2∆z2

14. 21.11.06Electron difraction on carbon nanotubes Geometry of carbon nanotubes Positions of carbon atoms on a single helix: zigzag pair from primitive helix by a screw displacement (Δz 1, ΔФ 1 ) L-1 pairs of helices from the first pair by (j Δz 2, j ΔФ 2 ), where j = 0,…, L-1 r j = (ρ j, z j, Φ j ) = Function (R 0, z 0, Φ 0, a, L, M) Arangement of the atoms in the complete single-shell nanotube: ∆u2∆u2 ∆z2∆z2 a ∆z1∆z1 ∆u1∆u1

15. 21.11.06Electron difraction on carbon nanotubes Kinematical diffraction theory Scattering amplitude for identical atoms: For a single primitive helix: r j = (ρ j, z j, Φ j ) Ф k = arctg (k y / k x ) discrete values of k z layer lines m, n integers

16. 21.11.06Electron difraction on carbon nanotubes Kinematical diffraction theory The amplitude A 2 (k) for a pair of parallel helices: generated by screw displacement (Δz 1, ΔФ 1 ) The amplitude A SS (k) of the complete single-shell carbon nanotube: generated by L-1 screw displacements (Δz 2, ΔФ 2 ) where T translational period in z direction2 independent integers

17. 21.11.06Electron difraction on carbon nanotubes Simulation of diffraction for single-shell tubes for e beam normal to the tube axis bc (10, 10) armchair(36, 0) zigzag tube(18, 1) chiral tube (nearly zigzag) graphite Zero order line represents zero order Bessel function The oscilations represent slit function from upper/bottom tube edge Spots are not circular as in 3D crystals Spots are diffuse streaks elongated normal to the tube axis and fading away

18. 21.11.06Electron difraction on carbon nanotubes bc (10, 10) armchair(36, 0) zigzag tube 2η2η graphite Simulation of diffraction for single-shell tubes for e beam normal to the tube axis (18, 1) chiral tube (nearly zigzag) Two hexagonal patterns rotaded by η from z-axis Hexagonal (hk.0) pattern, rotated by 30 ° from armchair to zigzag

19. 21.11.06Electron difraction on carbon nanotubes Multi-shell nanotubes First observations in 1991 by Iijima on multi-shell nanotubes: Multi-shell tubes contain coaxial single-shells of different chiralities: The amplitude A MS (k) of the multi-shell carbon nanotube: 7 layer nanotubeElectron diffractionSimulation 7 tubules: (29, 0) (38, 0) (47, 0) (48, 13) (55, 16) (63, 17) (70, 20) 7 zigzag and achiral tubules with η = 12° 24° S. Iijima, Nature, 354, 56, 1991

20. 21.11.06Electron difraction on carbon nanotubes Diffraction pattern A constant honeycomb lattice along the axis Sharp diffraction spots along the axis Shrinking lattice parameter along the tubule circumference Smaller lattice parameter – larger scattering angle Spots are elongated away from the axis

21. 21.11.06Electron difraction on carbon nanotubes Tilting experiment (00.2) spots remain anafected axis of rotation all other spots move away from z= 0 axis A, B, C, D climb up and finnaly coincide lattice distance is shrinkened

22. 21.11.06Electron difraction on carbon nanotubes Tilting simulation (25, 10) chiral tube, η = 16° tilt angle θ: from 0° to 30° distances between layer lines increase like 1/cosθ θ 1 cosθ coalescence of spots beggins at chiral angle!

23. 21.11.06Electron difraction on carbon nanotubes Helical structures: DNA Franklin R. E. and Gosling R. G., Nature 171, 740, 1953 Watson J. D. and Crick F. H. C., Nature 171, 737, 1953 DNA structure from x-ray diffraction pattern and CCV theory

24. 21.11.06Electron difraction on carbon nanotubes Helical structures: WS 2 and MoS 2 nanotubes WS 2 nanotube revealing the main chirality of 6.5° and 13° Achiral Au–WS 2 nanotubeAu-WS 2 nanotube M. Remskar, Z. Skraba, C. Ballif, M. Regula, R. Sanjinés, F. Lévy, Adv. Mater. 10, 246, 1998

25. 21.11.06Electron difraction on carbon nanotubes The End