Direct Observation of Six-Membered Rings in the ... - ACS Publications

Feb 27, 2006 - was imaged successfully by employing a spherical aberration-corrected HRTEM operated at 120 kV acceleration voltage. Utilizing two ...
0 downloads 0 Views 291KB Size
Download PDF
NANO LETTERS

Direct Observation of Six-Membered Rings in the Upper and Lower Walls of a Single-Wall Carbon Nanotube by Spherical Aberration-Corrected HRTEM

2006 Vol. 6, No. 8 1778-1783

Kaori Hirahara,*,† Koh Saitoh,†,‡ Jun Yamasaki,†,‡ and Nobuo Tanaka*,†,‡ EcoTopia Science Institute, Nagoya UniVersity, Chikusa-ku, Nagoya, 464-8603, Japan, and Department of Crystalline Materials Science, Nagoya UniVersity, Chikusa-ku, Nagoya, 464-8603, Japan Received February 27, 2006; Revised Manuscript Received June 14, 2006

ABSTRACT Atomic arrangements of the continuous network of six-membered rings in a single graphene sheet constituting a single-wall carbon nanotube was imaged successfully by employing a spherical aberration-corrected HRTEM operated at 120 kV acceleration voltage. Utilizing two advantages of the aberration-corrected HRTEM, the images separately resolved the rings in the upper and lower walls. Such images can be considered to be the first “tomographic” atomic images taken by HRTEM. This is a striking result that changes the conventional concept of HRTEM as a projection image.

Introduction. Carbon nanotubes (CNT) consist of cylindrically rolled-up graphene sheets. Individual CNTs have various chiral structures, and the chiral structures determine their electronic structures.1 For discussing physical and chemical properties unique to CNTs, it is essential to observe the chiral structure individually. Hexagonal lattice images of CNTs have been obtained by using a scanning tunneling microscope (STM).2,3 STM images of the CNTs, however, contain huge and artificial distortions, especially at the edge region of CNTs in the perpendicular direction of the tube axis. On the contrary, high-resolution transmission electron microscopy (HRTEM) does not employ a probe but a parallel beam of electrons so that it can provide images reflecting the electrostatic potential of whole CNTs within the pointspread function of the objective lens. As HRTEM techniques developed, direct imaging of the chiral structures was tried in various ways4-7 in addition to the diffraction studies.8-10 The spatial resolution for conventional HRTEM has been improved recently, sufficient to visualize the hexagonal lattices in graphene sheets, ∼0.2 nm. However, it is still difficult to visualize the atomic arrangement for only a single graphene sheet: HRTEM images of CNTs obtained by conventional HRTEM are a kind of Moire´ pattern of multiple hexagonal-lattice images of graphene sheets constituting the individual CNTs.4-7 The reason is the lack of structural information in the depth direction of the * Corresponding authors. E-mail: [email protected]; [email protected]. † EcoTopia Science Institute. ‡ Department of Crystalline Materials Science. 10.1021/nl060458k CCC: $33.50 Published on Web 07/19/2006

© 2006 American Chemical Society

Figure 1. (a) Structure model of a SWNT with diameter D. Upper and lower portions of the rolled-up graphene sheet comprising the SWNT perpendicular to the incident electron beam are shown in L1 and L2, respectively. (b) Hexagonal lattices of these two portions observed from the inverse direction of the incident electron beam. We can see that they have 180° rotational symmetry, and inclination angles of arrays of hexagons with respect to the tube axis correspond to the chiral angle of the SWNT.

specimen due to the large value of defocus (∆f). In particular, for weak-phase objects such as carbon, the HRTEM images obtained have been approximately interpreted as two-dimensional projections of the electrostatic potential. Even for a SWNT, the upper and lower portions of rolled-up graphene sheets, shown by squares L1 and L2 in Figure 1, could not be individually resolved when overlapping.5,7 For these reasons, three-dimensional structures of CNTs were not able to be discussed on the basis of HRTEM images. HRTEM imaging combined with tilting the specimen has been generally employed to obtain the structural information in the depth direction.11 Concerning CNTs, Friedrichs et al. first utilized the visibility of periodic structures with 0.21 nm

spacing, which is clearly observable only when a CNT is tilted by a specific angle, to deduce the chirality of the CNT.12 Lack of resolution in the depth direction for HRTEM images stems mainly from spherical aberration of the objective lens, which is caused by problems in electron optics, and the genuine property of Fourier images.13,14 To put it another way, a specifically small value of the spherical aberration coefficient (CS) should make drastic changes in phase contrast imaging for changing the defocus even by a few nanometers around the exact focus (∆f ) 0).14 Images taken in such a situation will include the structural information in the depth direction, which corresponds to a kind of “tomographic” image data set. Therefore, by taking a set of HRTEM images, and changing defoci a small amount, threedimensional structures of materials can be discussed with atomic resolution, which were not obtainable with conventional TEM. In the present study, a SWNT was observed by using an instrument with a CS-corrector developed in recent years (CScorrected HRTEM,15), which enabled us to use a CS 1/1000 smaller than the conventional value. Six-membered rings in a single graphene sheet constituting a SWNT was visualized successfully by utilizing two advantages of the CS correction, a spatial resolution with atomic scale and a shallow focal depth. Experimental Section. SWNTs used in this experiment were prepared by the pulse-arc discharge method. Details of the preparation procedure will be reported in another paper.16 Most of the CNTs found in the products are SWNTs with rather large diameters between 2 and 3 nm. The products containing SWNTs were dispersed in ethanol by using a conventional ultrasonic bath. The colloidal suspension prepared was collected onto standard carbon microgrids for HRTEM observation. HRTEM experiments were performed by using a thermal field-emission TEM (JEM-2100F) with a hexapole-type CS corrector.14,15 The CS corrector is based on two electromagnetic hexapoles as well as two additional transfer roundlens doublets located below the objective lens, which enables us to correct the spherical aberration of the objective lens electron-optically, down to the submicrometer scale.15 In the present experiment, the value of CS was chosen as positive 600 nm. At this time, other second to fourth order aberrations were also measured, A2 ) 8.2 nm, B2 ) 8.1 nm, S3 ) 400 nm, A3 ) 400 nm and A4 ) 2.4 µm.17 It should be noted here that the CS-corrected TEM was operated at 120 kV acceleration voltage (E) in order to reduce the electron beam irradiation damage. In addition, decreasing the acceleration voltage is effective for increasing the phase contrast using elastic scattering from atom clusters and crystallites, but not for single atoms.18 Because the scattering amplitude for the weak-phase object is generally proportional to E -1/2, the phase contrast at 120 kV is greater than that at 200 kV by ∼1.3 times. HRTEM images of individual SWNTs were recorded mainly using a CCD camera (Tietz, TemCam F114), where the electron dose for taking an image is 1.2 × 106 electrons/ nm2, respectively. The original image data was 1k × 1k Nano Lett., Vol. 6, No. 8, 2006

pixels, with a corresponding physical size of 18.5 × 18.5 nm2 on the specimen. The images shown in this paper are enlarged parts of the originals and are not treated by any filtering method. Note that the HRTEM images shown in this paper are taken from an edge region of a rope-like bundle of SWNTs. Recording hexagonal-lattice images was carried out not only for SWNTs located at such a region but also for isolated (free-standing) ones found in the same specimen. In most cases, however, the lattice images of the latter one seem slightly blurred, compared with those of former one, although such a blurring might be as small as several hundred picometers or less. It is considered that the blurring may be related to the charging effect due to electron irradiation, or possibly mechanical vibration of the tubes. Simulations of the HRTEM images were performed for verifying the images obtained in this study. The calculations were carried out by using a multi-slice program MacHREM2.5, which was developed by Ishizuka et al.19 It is noted that the simulations demonstrate convincingly that we are imaging the upper and lower graphene sheets individually. Results and Discussion. Two nonfiltered HRTEM images taken from the same part of a SWNT with different defocus are shown in Figure 2a and b. The SWNT is located at the edge region of a bundle of SWNTs as illustrated in Figure 2c.20 Figure 2a and b are so-called over- and under-focus images, respectively, and the difference in defocus is about 3 nm. The most important point of those images is that hexagonal lattices can be seen at the central portion of the SWNT with opposite contrast, as shown by arrays of white and black hexagons in Figure 2a and b, respectively. Such lattice images correspond to the arrangements of carbon atoms in the graphene monolayer constituting the SWNT. Moreover, the line profile in Figure 2d, which is the averaged one of 10 different pairs of neighboring carbon atoms, seems to be resolved. It was confirmed that the mutual distance between intensity maxima corresponded to the carboncarbon bond length in sp2-type carbon. This result is direct evidence of the spatial resolution being less than 0.14 nm at 120 kV acceleration voltage. The pair of hexagonal lattice images of the SWNT in Figure 2a and b has two considerable characteristics as follows: One is that they have a complementary contrast as described above. This is due to the difference of defoci between the two images, which is verified later with the aid of simulations. The other important characteristic is that the two hexagonal lattice images indicate different orientations. For example, the array of six-membered rings outlined by white hexagons in Figure 2a rotates by about 2.5° against the tube axis, whereas that pointed by black hexagons in Figure 2b rotates by about -2.3 °, where the positive value corresponds to the clockwise direction. Such different orientations shown in over- and under-focus images are expected if the upper and lower walls in the SWNT are individually imaged because the hexagonal lattices in those walls have a mirrorsymmetric orientations with respect to the tube axis. This suggests that the individual hexagonal lattice images shown 1779

Figure 2. (a and b) Over- and under-focus images taken from the same part of a SWNT. The SWNT is located at the edge of a bundle as illustrated in c. The difference value of defoci between a and b is about 3 nm. (d) Intensity profiles taken along two neighboring carbon atoms, as indicated by black lines in the images. Experimental and simulated data are shown by solid and dotted lines, respectively. Experimental data are averaged over 10 different pairs of carbon atoms. (e and f) Simulated HRTEM images of a (21, 8) SWNT, which is tilted by c.a. 20° to the incident plane of the electron beam, with -0.5 and -3 nm in defoci.

in Figure 2a and b are not Moire´ images of the upper and lower walls as reported so far by using conventional HRTEM, but the structural images of the individual graphene monolayers. To confirm this interpretation, simulations of the HRTEM images were carried out. To simulate HRTEM images of a SWNT, first we should determine the structural parameter of the SWNT and the incident direction of electron beam. The structural parameter of a SWNT is designated by a “chiral index”, which is a pair of two integers (n, m), and the index can be examined by measuring the tube diameter and chiral angle.21 The SWNT in Figure 2 was measured as about 2.6 nm diameter and 26.4° chiral angle22 so that the chiral index was determined as (21, 18). Next, the incident direction of the electron beam is roughly deduced by examining the intensity profiles of two portions on the HRTEM images. Comparing image intensities between two portions indicated by A-A′ and B-B′ in Figure 2a, it was found that the defoci of these two portions differed; namely, the SWNT is inclined to the horizontal axis. Then, the 1780

intensity profile taken along A-A′ corresponds to that taken along B- B′ on another HRTEM image taken with about 1 nm greater defocus than the image shown in Figure 2a. The portion indicated by A-A′ is about 1 nm below the portion indicated by B-B′. Because the distance between A-A′ and B-B′ is about 3 nm, it is accordingly estimated that the SWNT observed is tilted by about 20°. A through-focus series of the HRTEM image of a (21, 18) SWNT with a tilt by 20° was simulated by employing a 600 nm CS value. Then simulated images at -0.5 nm and -3 nm in defoci (Figure 2e and f) were found to match the experimental images in Figure 2a and b, respectively. The same arrays of white and black hexagons as those in Figure 2a and b are drawn in the corresponding places in Figure 2e. The simulated hexagonal lattice image seen in Figure 2e agrees well with the atomic arrangement at the lower wall of the structural model of the (21, 18) SWNT, whereas that in Figure 2f agrees with the upper wall. In addition, the simulated focal-image series of a (39, -18) SWNT, which is an optical isomer of the (21, 18) SWNT, did not match the experimental data in terms of the orientations of the hexagonal lattice. The simulated data support the interpretation that the over- and under-focus images in Figure 2a and b individually correspond to structural images of the upper and lower walls of the SWNT. In the following section, we consider why the upper and lower portions of the rolled-up graphene sheet constituting the SWNTs are individually visualized in this study. This is due to two effects caused by correcting the CS of the objective lens. One is the small spatial resolution down to atomic scale, although the spatial resolution is made worse by decreasing the acceleration voltage (E).18 The other, which might be more essential in this study, is the small value of the Scherzer defocus. At CS ) 600 nm and E ) 120 kV, the value of Scherzer defocus is reduced to ∼2 nm (see appendix). Such a small value results in the phase contrast image changing drastically with defocus even in a few nanometers around Gaussian focus. We next consider the phase contrast image of a planar graphene sheet at CS ) 600 nm. The phase contrast transfer function (PCTFs) is generally used for describing the imaging property of the objective lens (see the Appendix). Concerning the phase contrast imaging of a hexagonal lattice of a planar graphene sheet, two specific values of q are dominant: One is q ) ∼6.9 nm-1 corresponding to the inverse of the carboncarbon bond-length (0.144 nm21), and the other is q ) ∼4.9 nm-1 corresponding to the inverse of the (10) lattice spacing of a graphene (0.216 nm). Therefore, we consider the PCTFs with such fixed q values. Two PCTFs are presented as functions of defoci in Figure 3a, where the solid- and dottedlines correspond to, respectively, those at q ) 6.9 nm-1 and 4.9 nm-1. The calculations are on the basis of CS ) 600 nm, λ ) 0.0035 nm (E ) 120 kV), 0.5 mrad for the semiangle of beam convergence, and 3 nm for the half width of Gaussian spread of defocus. This figure indicates that the phase contrast becomes almost zero at exact focus (∆f ) 0), and sensitively changes from minimum to maximum values with changes of only several nanometers around the Nano Lett., Vol. 6, No. 8, 2006

Figure 3. (a) Partially coherent phase transfer functions as functions of defoci (∆f) for fixed values of two different spatial frequencies (q). Solid and dotted lines correspond to q ) 6.9 nm-1 and q ) 4.9 nm-1, respectively. Calculations are carried out by using the values λ ) 0.0035 nm (at 120 kV), CS ) 600 nm, 0.5 mrad for the semi-angle of beam convergence, and 3 nm for the half width of Gaussian spread of defocus. (b) Through focal series of simulated images of a graphene sheet. Images i-v are calculated under the same condition as a, and the values of defocus are indicated by arrows i-v in a, respectively. (c) Definition of the definite defocus for experimental and simulated HRTEM images of the (21, 18) SWNT shown in Figure 2. The upper and lower walls (L1 and L2) have different values of relative defoci by ∼3 nm as shown in this figure.

exact focus. For q ) 4.9 nm-1, the phase contrast is maximized (or minimized) at ∆f ) 3 nm (or -3 nm), where the positive value of ∆f indicates overfocus. For q ) 6.9 nm-1, it is maximized (or minimized) at ∆f ) 6 nm (or -6 nm). Figure 3c shows a focal series of simulated HRTEM images of a graphene sheet with 0.144 nm of carbon-carbon bond length. Values of defoci for the simulated images Figure 3b i-v is, respectively, indicated by arrows i-v in Figure 3a. In the case of underfocus images shown in Figure 3b i and ii, we can see black hexagonal lattice images corresponding to six-membered rings in the graphene sheet. Overfocus images shown in Figure 3b iv and v indicate hexagonal lattices with opposite contrast. In particular, individual carbon atoms are resolved most clearly at ∆f ) -3 and 3 nm (Figure 3b iv and ii) because the PCTF at q ) 6.9 nm-1 becomes maximum and minimum. On the images at ∆f ) -6 and 6 nm (Figure 3b i and v), carbon atoms cannot be resolved but the hexagonal lattice image is clearly seen because the PCTF at q ) 4.9 nm-1 is close to zero and that at q ) 6.9 nm-1 is minimized or maximized. Accordingly, the phase contrast of a single sheet of graphene drastically changes with changing defoci between -6 and 6 nm. Next let us consider phase contrast imaging of a real SWNT. A TEM image of the central portions of the SWNT is generally considered as a superposition of two images of two graphene sheets perpendicular to the incident electron beam, L1 and L2 in Figure 1 as well as Figure 3c. These two images should have different values of the relative defoci, and the difference is equal to the diameter of the SWNT. The relations between the definite and relative values of defoci are illustrated in Figure 3c. The definite defoci of the experimental images in Figure 2a and b were estimated as -0.5 and -3 nm, respectively, with aid of simulation. In the former case, the image was focused at the lower wall of the SWNT so that the relative values of defoci of the upper and lower walls (L1 and L2 in Figure 3c) become overfocused by about 3 and 0 nm. Therefore, graphitic networks at the Nano Lett., Vol. 6, No. 8, 2006

upper and lower walls are individually imaged with similar contrasts as Figure 3b iv and iii, respectively. Because the image intensity at exact focus is almost zero as shown in Figure 3b iii, mainly the upper wall contributes to the phase contrast of the SWNT, and the white hexagonal lattice image should be observed as seen in Figure 2a. In the latter case, the relative values of defoci for the upper and lower walls are about 0 nm and -3 nm. Therefore, the total phase contrast corresponds to the sum of the two images shown in Figure 3b ii and iii; that is, the hexagonal lattice structure image of only the lower wall is visualized as seen in Figure 2b. Consequently, it can be concluded that the upper and lower walls of the SWNT are able to be observed individually by changing the value of defocus by ∼3 nm around the exact focus. This is direct evidence that the CS-corrected HRTEM images contain structural information in the depth direction, which is a noteworthy fact that changes the conventional concept of TEM. Finally, we consider the depth sensitivity for HRTEM imaging with CS-correction. As described above, spacing 0.14 nm can be resolved with the maximum contrast at ∆f ≈ 3 nm (or -3 nm). In the view of PTCF referring to the Thon’s curve24 with the damping function, the value of defocus d2/ 2λ gives us a z resolution with a maximized black or white contrast.25 If maximized phase contrast is not required for the observation, however, the z resolution can be smaller, although the actual limit will depend on the detectability of the recording media actually used for experiments. When the z resolution is about 1 nm, for example, the phase contrast for q ) 0.69 nm-1 is over 0.2 (Figure 3a), which may still be detectable by using a conventional CCD camera. In addition, we should note that if more than three layers are superposed then it would be difficult to visualize the individual layers independently, as shown in the present experiment for the upper and lower walls of SWNT. This is because of the periodicity of Thon’s curve.24,25 Even in such a case, however, individual HRTEM images in a through 1781

focal series undoubtedly contain structural information of the specimen in the depth direction rather than its projection. It might furnish a new kind of hint for extracting the novel 3D atomic structures by using such image processing. Summary. In the present study, we succeeded for the first time in visualizing the hexagonal lattice structure in a single graphene sheet by using CS-corrected TEM at 120 kV of an acceleration voltage. Furthermore, it was indicated that CScorrected HRTEM images cannot be regarded simply as a two-dimensional projection of the electrostatic potential for materials observed, but contains structural information in the depth direction. Such images can be interpreted as a kind of tomographic series of images. Nanometer-scale depth information has been extracted from through focal series in scanning TEM,26 although they should be interpreted carefully, taking account of the probe channeling effect for a crystalline specimen as discussed in ref 27. We can say that the present experiment is the first time that such information was obtained in HRTEM. Through focal series with subnanometer steps of defoci may realize three-dimensionaltomographic characterization more accurately than the tilting methods employed so far.28 The present three-dimensional tomographic method with high resolution and low voltage must be attractive especially for organic molecules. Various organic molecular materials have now gotten attention in the world of materials science in recent years. Some of them, however, are still difficult to characterize by using conventional methods such as X-ray diffraction because of their lower crystallinity. In such cases, accurate characterization techniques on the basis of the present HRTEM imaging at low acceleration voltage must become more important, although some improvement for avoiding damage is necessary. The results obtained by CS-corrected HRTEM in this paper suggest a new possibility for 3D structural characterization with atomic resolution for single molecules or soft materials. Appendix. Phase Contrast Images of Graphene Obtained by Cs-Corrected HRTEM. In a TEM with a given wavelength (λ) and a fixed value of spherical aberration coefficient of the objective lens (CS), contrast transfer is modulated by adjustment of the defocus (∆f). In particular, images of weakphase objects such as SWNTs have maximal phase contrast at a specific defocus called Scherzer’s defocus (∆f ) ∆fSch). The value of ∆fSch is given by ref 29 ∆fSch) - x(4/3)Csλ

(1)

where the positive value of ∆f indicates overfocus. For a conventional HRTEM operated with a 120 kV acceleration voltage (λ ) 0.0035 nm), the value of ∆fSch is -48 nm with CS ) 0.5 mm. The value reduces to -2 nm after the spherical aberration is corrected to CS ) 600 nm. Such a small value of ∆fSch is the important point for observing a single graphene layer as discussed in this paper. The HRTEM image of weak-phase objects such as carbon is predominantly described by the phase contrast transfer function (PCTF). The PCTF T(∆f, q) is given by refs 18 and 25 1782

T(∆ f, q) ) D(∆ f, q) sin(χ(∆ f, q)), 1 1 χ(∆ f,q) ) 2π CSλ3q4 + λ q2∆ f (2) 4 2

(

)

where D(∆f, q) is the damping envelope function describing effects of the beam convergence as well as the spatial incoherency including instabilities such as fluctuations in the lens currents and the defocus spread due to a chromatic aberration and so forth. The function χ(∆f, q) is called the wave aberration. Acknowledgment. We thank M. Haider and his colleagues of CEOS GmbH for technical support. Thanks are also due to T. Sugai and H. Shinohara for providing us the SWNT samples. The present study is partially supported by special coordination grants of “Active nano characterization” and “Nano-CMOS”, grants-in-aid for scientific research (A) as “Fluctuation of structures and electronic states” (no. 17201022) and for young scientists (B) (no. 018710097), from Ministry of Science, Technology, Education and Sports in Japan. Finally, K.H. acknowledges Dr. S. Iijima of Meijo University for his kind encouragement through the work. Note Added after ASAP Publication. A sentence was added to the acknowledgment. The paper was published ASAP July 19, 2006; the corrected version was published ASAP July 24, 2006. References (1) Dresselhaus M. S.; Dresselhaus G.; Eklund P. C. Science of Fullerenes and Carbon Nanotubes; Academic Press: San Diego, CA; p 809. (2) Wido¨ler, J. W. G.; Venema, L. C.; Rinzler, A. G.; Smalley, R. E.; Dekker, C. Nature 1998, 391, 59. (3) Odom, T. W.; Huang, J.-L.; Kim, P.; Lieber, C. M. Nature 1998, 391, 62. (4) Zhang, X. B.; Zhang, X. F.; Amelinckx, S.; Tendeloo, G.; Van Landuyt, J. Ultramicroscopy 1994, 54, 237. (5) Hashimoto, A.; Suenaga, K.; Gloter, A.; Urita, K.; Iijima, S. Nature 2004, 430, 870. (6) Urita, K.; Suenaga, K.; Sugai, T.; Shinohara, H.; Iijima, S. Phys. ReV. Lett. 2005, 94, 155502. (7) Meyer, R. R.; Friedrichs, S.; Kirkland, A. I.; Sloan, J.; Hutchison, J. L.; Green, M. L. H. J. Microsc. 2003, 212, 152. (8) Kociak, M.; Hirahara, K.; Suenaga, K.; Iijima, S. Eur. Phys. J. B 2002, 32, 457. (9) Hirahara, K.; Bandow, S.; Kataura, H.; Kociak, M.; Iijima S. Phys. ReV. B 2004, 70, 205422. (10) Zuo, J. M.; Vartanyants, I.; Gao, M.; Zhang, R.; Nagahara, L. A. Science 2003, 300, 1419. (11) Yamasaki, J.; Tanaka, N.; Baba, N.; Kakibayashi, H.; Terasaki, O. Philos. Mag. 2004, 84, 2819. (12) Friedrichs, S.; Sloan, J.; Green, M. L. H.; Huchison, J. L.; Meyer, R. R.; Kirkland, A. I. Phys. ReV. B 2001, 64, 045406. (13) Reimer, L. Transmission Electron Microscopy; Springer-Verlag: Berlin Heidelberg, 1984; p 37. (14) Tanaka, N.; Yamasaki, J.; Kawai, T.; Pan, H. Nanotechnology 2004, 15, 1779. (15) Haider, M.; Rose, H.; Uhlemann, S.; Schwan, E.; Kabius, B.; Urban, K. Ultramicroscopy 1998, 75, 53. (16) Sugai, T.; Yoshida, H.; Shimada, T.; Okazaki, T.; Shinohara H.; Bandow, S. Nano Lett. 2003, 3, 769. (17) Kirkland, A. I.; Meyer, R. R. Microsc. Microanal. 2004, 10, 401. (18) Reimer, L. Transmission Electron Microscopy; Springer-Verlag: Berlin Heidelberg, 1984; Chapter 6. (19) Ishizuka, K. Acta Crystallogr., Sect. A 1982, 38, 73. (20) The SWNT shown in Figure 2 is partially overlapped by other neighboring SWNTs in the same bundle. By examining the through focal series of 30 images, however, it was confirmed that no obstacles were overlapped around the region where the hexagonal lattice images appear in Figure 2a and b.

Nano Lett., Vol. 6, No. 8, 2006

(21) Saito, R.; Dresselhaus, G.; Dresselhaus, M. S. Physical Properties of Carbon Nanotubes; Imperial College Press: London, 1998. (22) As described in ref 20, a part of the SWNT is hidden by other ones in the same bundle. It is difficult to measure the diameter of such a SWNT from the images with small values of defocus as shown in Figure 3a and b because of the lower contrast of the edge region. Therefore, the diameter was measured on the other images with increasing the defoci to enhance the contrast of the edge region of the SWNT. Then, the apparent value of the diameter was corrected by taking into account the relation between the values of apparent diameter and defocus.23 (23) Qin, C.; Peng, L.-M. Phys. ReV. B 2002, 65, 155431.

Nano Lett., Vol. 6, No. 8, 2006

(24) Thon, F. Naturforscher 1966, 21a, 179. (25) Tanaka, N. J. Electron Microsc. 1998, 47, 217. (26) Van Benthem, K.; Lupini, A. R.; Kim, M.; Baik, H. S.; Doh, S.; Lee, J. H.; Oxley, M. P.; Findlay, S. D.; Allen, L. J.; Luck, J. T.; Pennycook, S. J. Appl. Phys. Lett. 2005, 87, 034104. (27) Voyles, P. M.; Grazul, J. L.; Muller, D. A. Ultramicroscopy 2003, 96, 251. (28) Midgley, P. A.; Weyland, M. Ultramicroscopy 2003, 96, 413. (29) Lentzen, M.; Jahnen, B.; Jia, C. L.; Thust, A.; Tillmann, K.; Urban, K. Ultramicroscopy 2002, 92, 233.

NL060458K

1783