determination of the chirality of carbon nanotubes - it is ... · determination of the chirality of...
TRANSCRIPT
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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
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
AcknowledgementsAcknowledgementsHakanHakan DenizDenizZejianZejian LiuLiuGongpuGongpu ZhaoZhaoHan ZhangHan ZhangQiQi ZhangZhang
W.M. Keck FoundationW.M. Keck FoundationUNCUNCAFOSR, DOE, AFOSR, DOE, XintekXintek
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
Carbon NanotubeCarbon Nanotube
Ph. Lambin
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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)
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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:
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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;
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
Scanning Scanning Tunneling Tunneling MicroscopyMicroscopy
T. W. Odom et al. Nature 391, 62(1998).
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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).
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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).
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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!
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
Electron Diffraction and Imaging in TEMElectron Diffraction and Imaging in TEM
Specimen
Objective Lens
Back Focal Plane - Diffraction
Image Plane – Magnified
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
(u,v)
Electron Diffraction
9
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
Schematic demonstrating the formation of electron diffraction pattern from a carbon nanotube.
(0,1)(-1,0)
(1,1)
(1,0)(0,-1)
(-1,-1)
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
DNA DNA -- Watson & Crick (April 25, 1953)Watson & Crick (April 25, 1953)
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
Radial Projection of HelixRadial Projection of Helix
Single Strand
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
...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
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
Airy Disc Airy Disc –– Aperture DiffractionAperture Diffraction2
0
010 /)sin(2
)/)sin(2()(λθπλθπθ
rrJII =
Wikipedia
12
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
Radial Projection of HelicesRadial Projection of Helices
Single Strand Double Strands
Triple Strands Quadruple Strands
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
L.-C. Qin, J. Mater. Res. 9, 2450 (1994).
Scattering Intensities from HelicesScattering Intensities from Helices
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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; ;
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
XX--Ray Diffraction from DNA (1953)Ray Diffraction from DNA (1953)
R.E. Franklin & R.G. Goslin, Nature 171, 740 (1953).
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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).
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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]
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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).
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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).
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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).
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
(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
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
Single-walled carbon nanotube of chiral indices [17,1] --- a semiconducting nanotube.
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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:
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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).
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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).
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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
−−
=
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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).
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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.
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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).
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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)
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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.
LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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
−−
=
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LuLu--Chang QinChang Qin IMR, Shenyang 07/12/07IMR, Shenyang 07/12/07
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.