Stretching of carbon-carbon bonds in a $0.7\mathrm{nm}$ diameter carbon nanotube studied by electron diffraction

We studied a carbon-carbon bond-length of single-wall carbon nanotube with the diameter in the class of $\sim 0.7\mathrm{nm}$ by the electron diffraction. The nanotube, used in this study, was grown as an inner tube of a double wall carbon nanotube (DWNT) from peapod. Taking advantage of the use of DWNT, we can accurately determine the direction of incident electron beam, chiral indices, and both intensities and positions of diffraction spots. Due to careful analyses of these electron diffraction data, it was found that the carbon-carbon bond-length for $\sim 0.7\mathrm{nm}$ diameter class of an inner tube is stretched by $0.9\pm 0.1\%$ as compared with that for $\sim 1.4\mathrm{nm}$ outer tube. This is experimental evidence indicating a stretching of carbon-carbon bond in the small diameter tube.

Figure 1

Electron diffraction from an isolated double-wall carbon nanotube (DWNT) (a) and schematic of $hk$ diffractions (b). Mean diameter $D$ and interlayer distance $d$ can be measured on the equatorial line, and they are, respectively, $1.16\pm 0.2\mathrm{nm}$ and $0.37\pm 0.04\mathrm{nm}$. One layer line between a pair of arrows is perpendicular to the tube axis. Schematic of $hk$ diffraction rods corresponded to the first peaks of layer lines in (a) is in (b). Apparent chiral angles for inner $\left({\alpha }_{\text{inner}}\right)$ and outer tubes $\left({\alpha }_{\text{outer}}\right)$ can be measured, respectively, to be $30.0°\pm 1°$ and $18.1°\pm 0.2°$.

Figure 2

Schematic of a (5, 5)@(14, 6) DWNT (a), intensity profiles of the parts of equatorial lines (b) and tilt angle dependence of intensity ratio between 11 and $\overline{1}\overline{1}$ spots $(I_{\overline{1}\overline{1}}∕I_{11})$ of (5, 5) tube (c). We define the tilt angle $\theta$ and rotation angle $\varphi$ as indicated in (a). In (b), the top is taken from the enclosed region on the experimental diffraction pattern inserted, and those in the bottom are simulated patterns obtained by rotating the DWNT around the tube axis in the range between $0°<\varphi <18°$. Curve in (c) is calculated under the fixed value of $\varphi$ at 4.5° and obtained by integrating the whole of first peaks of the layer lines.

Figure 3

Line profiles of experimental and simulated electron diffraction patterns taken for DWNT. A part of the experimental pattern in Fig. 1a is in (a). Simulated pattern of (5, 5)@(14, 6) at $\theta =2.5°$ and $\varphi =4.5°$ is in (b). Intensity profiles along $\mathrm{A}\text{−}{\mathrm{A}}^{\prime }$ and $\mathrm{B}\text{−}{\mathrm{B}}^{\prime }$ in (a) are shown in (c), and that from the enclosed region in (b) is in (d). These profiles are taken along the axial direction and obtained by integrating in the direction perpendicular to the tube axis.

Figure 4

Expanded intensity profiles around 11 diffraction spots of (14, 6) outer and (5, 5) inner tubes. Experimental diffraction profiles are in (a). Simulated diffraction profiles by changing the ratio of $\mathrm{C}-\mathrm{C}$ bond-lengths of inner tube $\left(a_{\text{inner}}\right)$ and outer tube $\left(a_{\text{outer}}\right)$ are in (b), (c), and (d) with ratios in the figure. We find that the profile (c) matches well the experimental results shown in (a).

Figure 5

Simulations of the reciprocal space for (5, 5)@(14, 6). Simulated electron diffraction pattern for (5, 5)@(14, 6) at $\theta =2.5°$ with $\varphi =4.5°$ is in (a). Disklike distributions of (10) and (11) reciprocal lattice for (5, 5) inner tube are shown, respectively, in (b) and (c), which are normal to the tube axis. At $\varphi =4.5°$, a plane perpendicular to the vector ${\mathit{k}}_0$, which is the wave vector of incident electron beam, passes the disks along the dotted line as shown in (b) and (c). Enlarged patterns around the center regions of (b) and (c) are, respectively, in (d) and (e), indicating that the Ewald-sphere does not pass the center of disks due to the curvature of the Ewald sphere. In addition, when the tube is inclined against the electron beam, the cross section of the layer line and the Ewald sphere apart from the center with a function of $\theta$. The distance between the Ewald sphere and the center of the $\left(hk\right)$ disk causes asymmetric diffraction intensities for the crystallographically equivalent reflections. Diffraction intensity profiles of (10) and (11) disks along the intersection of the Ewald sphere at $\varphi =4.5°$ with various values of $\theta$ are shown in (f). The profiles of (10) reflection at the values of $\theta =2.5°$ and $-2.5°$ are, respectively, equal to those along${\mathrm{A}}_1\text{−}{\mathrm{A}}_1^{\prime }$ and ${\mathrm{A}}_2\text{−}{\mathrm{A}}_2^{\prime }$ in (a). Furthermore, the profiles of (11) reflection at $\theta =2.5°$ and $-2.5°$ are, respectively, equal to those along ${\mathrm{B}}_1\text{−}{\mathrm{B}}_1^{\prime }$ and ${\mathrm{B}}_2\text{−}{\mathrm{B}}_2^{\prime }$ in (a).