determination of the chirality of carbon nanotubes - it is ... · determination of the chirality of...

1

LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07

Determination of the Determination of the ChiralityChiralityof Carbon of Carbon NanotubesNanotubes

-- it is easy now it is easy now --

W.M. Keck Laboratory for Atomic Imaging and ManipulationW.M. Keck Laboratory for Atomic Imaging and ManipulationDepartment of Physics and Astronomy andDepartment of Physics and Astronomy and

Curriculum in Applied and Materials SciencesCurriculum in Applied and Materials SciencesUniversity of North Carolina at Chapel Hill, USAUniversity of North Carolina at Chapel Hill, USA

Qin Lu-Chang秦禄昌


AcknowledgementsAcknowledgementsHakanHakan DenizDenizZejianZejian LiuLiuGongpuGongpu ZhaoZhaoHan ZhangHan ZhangQiQi ZhangZhang

W.M. Keck FoundationW.M. Keck FoundationUNCUNCAFOSR, DOE, AFOSR, DOE, XintekXintek

2


Carbon NanotubeCarbon Nanotube

Ph. Lambin


Schematic showing the formation and definition of a single-walled carbon nanotube. The chiral indices (u,v) are related to diameter and helicity. For example, when u – v is divisible by 3, it is metallic, otherwise it is semiconducting.

Diameter2 2

0u v uvd a

π+ +

=

Helicity

3tan2

vu v

α =+

Notation of Chiral Indices: (u,v) = (n,m)

3


CNT AFM ProbeCNT AFM Probe

LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07Nanotube gas sensorNanotube display

Nanotube FET

Battery

Nanotube ApplicationsNanotube Applications

FET-CT (UNC)

4


Why Why ChiralityChirality ((u,vu,v) is Important?) is Important?

Properties of a CNT are Properties of a CNT are chiralitychirality--sensitive!sensitive!Precision of measurement matters!Precision of measurement matters!Electronic: Electronic: (u (u –– v) divisible by 3: Metallicv) divisible by 3: Metallic

Otherwise: Otherwise: SemiconductingSemiconductingMechanical:Mechanical: Molecular frictionMolecular friction

Mechanical strengthMechanical strengthOptical:Optical: Transition energyTransition energyElectron Emission:Electron Emission:


CNT-Based Field Effect Transistor

Metal-Semiconductor CNT-Based Schottky Diode

Metallic CNT for Electron TransportR. H. Baughman et al., Science 287, 787 (2002).

Semiconducting nanotube

5


Carbon Nanotube Field EmitterCarbon Nanotube Field EmitterSingle CNT Emitter

G. Zhao et al., Appl. Phys. Lett. 89, 193113 (2006).

0.170.17--0.30.31010--77--1010--881%1%3X103X109922CNT EmitterCNT Emitter

0.40.4--0.60.61010--99<1%<1%1010881515Thermal Thermal Field EmitterField Emitter

Energy Energy Spread (Spread (evev))

Vacuum Vacuum ((TorrTorr))

Stability (% Stability (% RMS)RMS)

Brightness Brightness (A/cm(A/cm--22sr)sr)

Source Size Source Size (nm)(nm)

For a single CNT field emitter, a current density of more than 104 A/cm2 could be easily achieved at an extraction electric field of 2 V/um.

Carbon nanotube has a diameter ranging from a few to below 100 nm, the small r greatly enhances local electric field;


Scanning Scanning Tunneling Tunneling MicroscopyMicroscopy

T. W. Odom et al. Nature 391, 62(1998).

6


Raman SpectroscopyRaman Spectroscopy

Breathing ModeBreathing Mode

dRBM /248=ω

A. Jorio et al., Phys. Rev. Lett. 86, 1118 (2001); New J. Phys. 5, 139 (2003).


Optical AbsorptionOptical Absorption

SemiconductingSemiconducting SWNTsSWNTs of small diameterof small diameter–– Electronic absorptionElectronic absorption–– Emission transitionsEmission transitions–– Resonance Raman dataResonance Raman data

Metallic Metallic SWNTsSWNTs–– InterbandInterband transitionstransitions

S.M. Bachilo et al., Science 298, 2361 (2002).M.S. Strano et al., Nano Lett. 3, 1091 (2003).

7


Precision Measurement is CrucialPrecision Measurement is Crucial

Properties of a CNT are Properties of a CNT are chiralitychirality--sensitive!sensitive!Precision of measurement matters!Precision of measurement matters!


0 5 10 15 20 25 300

1

2

3

4

5

Dia

met

er (n

m)

Helicity (degrees)

Metallic Semiconducting

Distribution of all possible single-walled carbon nanotubes within the range of 0.5 nm to 4.5 nm in diameter.

Zigzag

Armchair

(10,10)(17,0) (12,8)(14,5)(16,2)

1.356 nm

1.331 nm

1.338 nm

1.336 nm

1.365 nm

8


Electron Diffraction and Imaging in TEMElectron Diffraction and Imaging in TEM

Specimen

Objective Lens

Back Focal Plane - Diffraction

Image Plane – Magnified


(u,v)

Electron Diffraction

9


Schematic demonstrating the formation of electron diffraction pattern from a carbon nanotube.

(0,1)(-1,0)

(1,1)

(1,0)(0,-1)

(-1,-1)


DNA DNA -- Watson & Crick (April 25, 1953)Watson & Crick (April 25, 1953)

10


Radial Projection of HelixRadial Projection of Helix

Single Strand


...3,2,0 )(

helix fold-m

...4,2,0 )(

helix Double

,...3,2,1 )(

helix Single

2

2

2

mmldRJI

ldRJI

ldRJI

ll

ll

ll

=

=

=

=

=

=

π

π

π

W. Cochran, F.H.C. Crick & V. Vand, Acta Cryst. 5, 581 (1952).L.-C. Qin, J. Mater. Res. 9, 2450 (1994).

Scattering Intensities from HelicesScattering Intensities from Helices

11


Bessel FunctionBessel Function

0)( 222

22 =−++ ynx

dxdyx

dxydx

)()(

)(

)(

cos

)/1)(2/(

xJixJ

exJie

txJe

nn

n

n

inxn

nix

n

nn

ttx

=

=

=

−

∞

−∞=

∞

−∞=

−

∑

∑φ

Wikipedia & http://www.mpimf-heidelberg.mpg.de/~holmes/fibre/branden.html


Airy Disc Airy Disc –– Aperture DiffractionAperture Diffraction2

0

010 /)sin(2

)/)sin(2()(λθπλθπθ

rrJII =

Wikipedia

12


Radial Projection of HelicesRadial Projection of Helices

Single Strand Double Strands

Triple Strands Quadruple Strands


L.-C. Qin, J. Mater. Res. 9, 2450 (1994).

Scattering Intensities from HelicesScattering Intensities from Helices

13


Diffraction from HelicesDiffraction from Helices

Intensities appear on discrete lines (layer Intensities appear on discrete lines (layer lines) due to axial periodicity;lines) due to axial periodicity;On each layer line of order On each layer line of order ll, the , the intesnityintesnityis proportional to the square of Bessel is proportional to the square of Bessel function of order function of order ll;;When there is a mWhen there is a m--fold rotational fold rotational symmetry (m helices), the nonsymmetry (m helices), the non--extinction extinction reflections appear on layer line reflections appear on layer line mlml; ;


XX--Ray Diffraction from DNA (1953)Ray Diffraction from DNA (1953)

R.E. Franklin & R.G. Goslin, Nature 171, 740 (1953).

14


Structure Factor of Carbon Structure Factor of Carbon NanotubesNanotubes

∑

∑

∑ ∫ ∫ ∫

∫

+=

+Φ=Φ

Φ=Φ

+−+Φ=

⋅=∞

=

∞

j

jjjnl

nn

nnln

n

c

n

clz

Anx

ifT

inrRJRB

TRBlRF

dzrdrdclznirRJzrVin

c

rdrqrVqF

)](2exp[

)]2

(exp[)2(),(

),(),,(

)]2(exp[)2(),,()]2

(exp[1

)2exp()()(

10

2

0 0

π

ππ

φπφπφπ

π

π

vvvvv

Bn: Taking care of cylindrical curvatureTnl: Planar structure factor of graphene

L.-C. Qin, J. Mater. Res. 9, 2450 (1994).


On the base line, there is one (v) helix parallel to a1 (blue), seven (u) helices parallel to a2 (orange), and eight (u+v) helices parallel to a3 (green). Example: [7,1]

15


Structure Factor of Carbon Structure Factor of Carbon NanotubesNanotubes

⎩⎨⎧ =++

=

++−+=

+Φ=Φ ∑

otherwise ,0(integer) /])([ when ,

),(

]3

)2(2exp[1),(

)]2

(exp[)2(),(),(),,(,

Nvmvunvmn

vmvunimn

inrRJmnmnflRF

uv

uv

mnnuvuv

γ

πχ

ππγχ

Z. Liu & L.-C. Qin, Chem. Phys. Lett. 400, 430 (2004).L.-C. Qin, Phys. Chem. Chem. Phys. 9, 31 (2007).


Schematic demonstrating the formation of electron diffraction pattern from a carbon nanotube.

(0,1)(-1,0)

(1,1)

(1,0)(0,-1)

(-1,-1)

l1

l2l3

16


Diffraction from Carbon Nanotube [Diffraction from Carbon Nanotube [u,vu,v]]

v helices parallel to a1u helices parallel to a2u+v helices parallel to a3

L.-C. Qin, Rep. Prog. Phys. 69, 2781 (2006).


The intensities of principal layer lines are directly related to the orders of Bessel functions.

L.-C. Qin, Chem. Phys. Lett. 297, 23 (1998).Z. Liu & L.-C. Qin, Chem. Phys. Lett. 408, 75 (2005).L.-C. Qin, Rep. Prog. Phys. 69, 2781 (2006).

Only one Bessel function dominates the scattering intensity on each layer line.

200

23

22

21

)(

)(

)(

)(

dRJI

dRJI

dRJI

dRJI

vul

ul

vl

π

π

π

π

∝

∝

∝

∝

+

17


Electron diffraction from a carbon nanotube.

Electron Beam

( ) ( ) ( )

( )

,, , , ,

exp2

uv uv uvl n m

n

lF R Z Z f n m n mc

J dR in

δ χ γ

ππ

⎛ ⎞Φ = −⎜ ⎟⎝ ⎠

⎡ ⎤⎛ ⎞× Φ +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∑ ∑

( ) (2 ), 1 exp 23uv

n u v mn m iu

χ π + +⎡ ⎤= + ⎢ ⎥⎣ ⎦

( ) , integer,

0, otherwiseuv

n mvun m uγ

+⎧ =⎪= ⎨⎪⎩

( ) ( )2 22 2n u v m u v uvl

uM+ + + +

=

( ) ( ) 2, , , ,uv uvI R Z F R ZΦ = Φ

L.-C. Qin, J. Mater. Res. 9, 2450 (1994). Z. Liu & L.-C. Qin, Chem. Phys. Lett.

400, 430 (2004).


1.1881.18830301.2471.24720201.3981.3981010

1.1921.19229291.2561.25619191.4281.42899

1.1961.19628281.2661.26618181.4651.46588

1.2011.20127271.2751.27517171.5071.50777

1.2061.20626261.2871.28716161.5651.56566

1.2111.21125251.3011.30115151.6391.63955

1.2181.21824241.3151.31514141.7511.75144

1.2261.22623231.3321.33213131.9071.90733

1.2321.23222221.3501.35012122.1972.19722

1.2391.23921211.3731.37311112.8922.89211

XX22/X/X11nnXX22/X/X11nnXX22/X/X11nn

Ratio of peak positions for various orders of Bessel functions. It is unique for each order of Bessel function.

( ) : nJ X X dRπ=

2 2

1 1

X RX R

=

Determination of Order of Bessel Function

18


(a)

Electron diffraction pattern of a single-walled carbon nanotube [17,2]. (a) Electron diffraction pattern. (b) Intensity line profile on layer line l1. (c) Intensity line profile on layer line l2.

(b)2.190

(c)

1.279


Single-walled carbon nanotube of chiral indices [17,1] --- a semiconducting nanotube.

19


Electron diffraction patterns of two branches of a sharp carbon nanotube kink. Analysis indicates that they have the same (u,v) chiral indices (16,4).

A

A

BB


Geometry of Graphene in Fourier SpaceGeometry of Graphene in Fourier Space

)60cos(

)60cos(

)cos(

3

2

1

α

α

α

+°=

−°=

=

∗

∗

∗

aD

aD

aD

A = (u, v)(Equator)

C (Meridian)

D2 (1,0)D1 (0,-1)

D3 (-1,-1)

D4 (1,-1)

α

D3 = D1 – D2

D4 = D1 + D2

21

12

22

DDDD

uv

−−

=

Index Ratio:

20


16.76416.7641.8811.8818819190.42110.421112.73012.7302.7702.7709930300.30000.300016.62716.6272.3702.370101024240.41670.416712.73012.7301.8461.8466620200.30000.300016.62716.6271.1851.1855512120.41670.416712.73012.7300.9230.9233310100.30000.300016.53716.5372.8592.859121229290.41380.413812.59812.5982.4872.4878827270.29630.296316.47416.4741.6741.6747717170.41180.411812.52012.5201.5641.5645517170.29410.294116.39016.3902.1632.1639922220.40910.409112.43212.4322.2052.2057724240.29170.291716.33716.3372.6522.652111127270.40740.407412.21612.2162.5642.5648828280.28570.285716.10216.1022.9342.934121230300.40000.400012.21612.2161.9231.9236621210.28570.285716.10216.1022.4452.445101025250.40000.400012.21612.2161.2821.2824414140.28570.285716.10216.1021.9561.9568820200.40000.400012.21612.2160.6410.64122770.28570.285716.10216.1021.4671.4676615150.40000.400012.00812.0082.2822.2827725250.28000.280016.10216.1020.9780.9784410100.40000.400011.92711.9271.6411.6415518180.27780.277816.10216.1020.4890.48922550.40000.400011.85711.8572.6402.6408829290.27590.2759alphaalphad (nm)d (nm)vvuuv / uv / ualphaalphad (nm)d (nm)vvuuv / uv / u

Chart of Index Ratios ( v / u )

L.-C. Qin, Phys. Chem. Chem. Phys. 9, 31 (2007).


Ratio of Layer Line Spacings (D1/D2)u \ v 0 1 2 3 4 5 6 7 8 9 10

1 2.0000 1.0000

2 2.0000 1.2500 1.0000

3 2.0000 1.4000 1.1429 1.0000

4 2.0000 1.5000 1.2500 1.1000 1.0000

5 2.0000 1.5714 1.3333 1.1818 1.0769 1.0000

6 2.0000 1.6250 1.4000 1.2500 1.1429 1.0625 1.0000

7 2.0000 1.6667 1.4545 1.3077 1.2000 1.1176 1.0526 1.0000

8 2.0000 1.7000 1.5000 1.3571 1.2500 1.1667 1.1000 1.0455 1.0000

9 2.0000 1.7273 1.5385 1.4000 1.2941 1.2105 1.1429 1.0870 1.0400 1.0000

10 2.0000 1.7500 1.5714 1.4375 1.3333 1.2500 1.1818 1.1250 1.0769 1.0357 1.0000

11 2.0000 1.7692 1.6000 1.4706 1.3684 1.2857 1.2174 1.1600 1.1111 1.0690 1.0323

12 2.0000 1.7857 1.6250 1.5000 1.4000 1.3182 1.2500 1.1923 1.1429 1.1000 1.0625

13 2.0000 1.8000 1.6471 1.5263 1.4286 1.3478 1.2800 1.2222 1.1724 1.1290 1.0909

14 2.0000 1.8125 1.6667 1.5500 1.4545 1.3750 1.3077 1.2500 1.2000 1.1563 1.1176

15 2.0000 1.8235 1.6842 1.5714 1.4783 1.4000 1.3333 1.2759 1.2258 1.1818 1.1429

mnvumnmn

vuvu

DD

≥≥++

=++

= ; ,2

22

2

2

1

秦禄昌，中国电子显微学报 (2007).

21


Electron diffraction pattern of a double-walled carbon nanotube of chiral indices (15,11) (1.77 nm, 24.9°) and (30,3) (2.48 nm, 4.7°), respectively.

l1

l3

l2

l3

l1l2

Double-Walled Carbon Nanotube


Chiral indices of three shells of a triple-walled nanotube are (35,14), (37,25) and (40,34), respectively. All of them are metallic.

Triple-Walled Carbon Nanotube

22


Structure determination of a quadruple-walled carbon nanotube by electron diffraction. Three helicities exist in the tubule with two shells having the same helicity.

Calculating

from the layer line spacings.

Quadruple-Walled Carbon Nanotube

21

12

22

DDDD

uv

−−

=


0.360.365.085.081.51.5SS[[64,0264,02]]

0.490.494.374.3722.822.8SS[[39,2539,25]]

0.430.433.393.3928.728.7SS[[26,2426,24]]

------2.542.541.51.5SS[[32,0132,01]]

IntertubularIntertubulardistance distance

(nm)(nm)

Diameter Diameter (nm)(nm)

Helicity Helicity (DEG)(DEG)M/SM/S[[u,vu,v]]

Atomic structure of a quadruple-walled carbon nanotube.

All the four shells in the nanotube are semiconducting which dictates that this nanotube is a semiconductor.

Z. Liu, Q. Zhang, L.-C. Qin, Appl. Phys. Lett. 86, 191903 (2005).

23


Quintuple-Walled Carbon Nanotube

16.416.48.28.2

21.521.510.010.021.521.5

2.162.162.852.853.703.704.694.695.555.55

SSMMSSSSMM

[[22,922,9]][[33,633,6]][[34,2034,20]][[53,1253,12]][[51,3051,30]]

Helicity Helicity (DEG)(DEG)

Diameter Diameter (nm)(nm)MM//SS[[u,vu,v]]

Quintuple-walled carbon nanotube of assigned chiral indices. The inner and outer diameters are 2.16 nm and 5.55 nm, respectively.


Electron Electron EmissionEmission

15.7415.746.9996.999SS(72,28)(72,28)5515.6015.606.3036.303SS(65,25)(65,25)4415.4315.435.6075.607MM(58,22)(58,22)3315.6015.605.0425.042SS(52,20)(52,20)2216.3816.384.3274.327SS(44,18)(44,18)11

(deg)(deg)dd (nm)(nm)MetaMetallicityllicity((uu,,vv))ShellShell

Chiral indices (Chiral indices (uu,,vv), ), metallicitymetallicity, diameter , diameter dd, and , and helicityhelicity of each shell of the carbon nanotube.of each shell of the carbon nanotube.

G. Zhao et al. Appl. Phys. Lett. 89, 263113 (2006).

24


For chiral carbon nanotubes with chiral indices (u,v) (u ≠ v), two enantiomers exist, which are mirror images of each other.

Left-handed Right-handed

(u,v)(v,u)


Handedness of Handedness of SWNTsSWNTs

25

LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07Z. Liu & L.-C. Qin, Chem. Phys. Lett. 405,205 (2005).

Twisting a nanotube about the tubule axis tells its handedness.


http://www.physics.unc.edu/project/lcqin/www1/qin.htmhttp://www.physics.unc.edu/project/lcqin/www1/qin.htm

( )

( )

( )

21

22

23

:

:

:

v

u

u v

l J X

l J X

l J X+

⎧⎪⎪⎨⎪⎪⎩

SummarySummary A systematic method has A systematic method has been established to obtain been established to obtain the chiral indices (the chiral indices (u,vu,v) of ) of carbon nanotubes from their carbon nanotubes from their electron diffraction patterns. electron diffraction patterns.

UNC Nanotube Diffraction Simulator 21

12

22

DDDD

uv

−−

=

26


1. L.-C. Qin, “Electron diffraction from cylindrical nanotubes”; J. Mater. Res. 9, 2450 (1994).2. L.-C. Qin, T. Ichihashi, S. Iijima, “On the measurement of helicity of carbon nanotubes”; Ultramicroscopy 67, 181 (1997).3. L.-C. Qin, S. Iijima, H. Kitaura, Y. Maniwa, S. Suzuki and Y. Achiba, “Helicity and packing of single-walled carbon

nanotubes studied by electron nanodiffraction”; Chem. Phys. Lett. 268, 101 (1997). 4. L.-C. Qin, “Measuring the true helicity of carbon nanotubes”; Chem. Phys. Lett. 297, 23 (1998).5. L.-C. Qin, “Helical diffraction from tubular structures”; Mater. Characterization 44, 407 (2000).6. L.-C. Qin, “Determining the Helicity of Carbon Nanotubes by Electron Diffraction”; in Progress in Transmission Electron

Microscopy 2: Applications in Materials Science. Eds. X.-F. Zhang and Z. Zhang, Springer Series in Surface Sciences Vol. 39, (Tsinghua University Press and Springer-Verlag, 2001) pp.73-104.

7. L.-C. Qin, “Diffraction and Imaging of Single Walled Carbon Nanotubes”; in Electron Microscopy of Nanotubes and Nanowires. Eds. Z.L. Wang and C. Hui. (Kluwer Academic Publisher, 2003) pp.1-41.

8. Z. Liu, L.-C. Qin, “Symmetry of electron diffraction from single-walled carbon nanotubes”, Chem. Phys. Lett. 400, 430 (2004).

9. Z. Liu, L.-C. Qin, “Breakdown of the 2mm symmetry of electron diffraction from multiwalled carbon nanotubes”, Chem. Phys. Lett. 402, 202 (2005).

10. Z. Liu, L.-C. Qin, “A practical approach to determine the handedness of single-walled carbon nanotubes”, Chem. Phys. Lett. 405, 205 (2005).

11. Z. Liu, L.-C. Qin, “Electron diffraction from elliptical nanotubes”; Chem. Phys. Lett. 406, 106 (2005).12. Z. Liu, L.-C. Qin, “A direct method to determine the chiral indices of carbon nanotubes”, Chem. Phys. Lett. 408, 75 (2005).13. Z. Liu, L.-C. Qin, “Measurement of handedness in multiwalled carbon nanotubes by electron diffraction”, Chem. Phys. Lett.

411, 291 (2005).14. Z. Liu, L.-C. Qin, “Extinction and orientational dependence of electron diffraction from single-walled carbon nanotubes”,

Chem. Phys. Lett. 412, 399 (2005).15. Z. Liu, Q. Zhang, L.-C. Qin, “Accurate structure determination of multiwalled carbon nanotubes by nondestructive

nanobeam electron diffraction”; Appl. Phys. Lett. 86, 191903 (2005).16. Z. Liu, Q. Zhang, L.-C. Qin, “Determination and mapping diameter and helicity of single-walled carbon nanotubes by

nanobeam electron diffraction”, Phys. Rev. B 71, 245413 (2005).17. L.-C. Qin, “Electron diffraction from carbon nanotubes”; Rep. Prog. Phys. 69, 2781 (2006).18. L.-C. Qin, “Determination of the chiral indices of carbon nanotubes by electron diffraction”; Phys. Chem. Chem. Phys. 9,

31 (2007).19. 秦禄昌，精确测定碳纳米管螺旋度的电子衍射方法；《中国电子显微学报》2007.

determination of the chirality of carbon nanotubes - it is ... · determination of the chirality of...

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