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The extinction and orientational dependence of electron diffraction from single-walled carbon nanotubes have been observed experimentally and investigated in detail theoretically using both algebraic analysis and numerical simulations. Electron diffraction from only achiral carbon nanotubes of zigzag or armchair structure shows observable orientational dependence and extinction of certain layer lines in experiment due to the interference of two primary Bessel functions of the same order that contribute to the scattering intensities on these layer lines.

A direct method is described to determine the chiral indices ( u, v ) of a carbon nanotube from a nanobeam electron diffraction pattern of the nanotube with high accuracy. This method is a one-step procedure and allows rapid and precise assignment of the chiral indices of carbon nanotubes. Using a contemporary electron microscope, we have been able to achieve an accuracy that enables us to assign the chiral indices unambiguously up to the range of (30, 30), corresponding to a diameter of 4.0 nm. Examples of determination of the chiral indices for two single-walled carbon nanotubes are presented as an illustration of the method.

A quantitative method for the structural determination by electron diffraction of nanotubes of elliptical cross-section is developed as a general case while the cylindrical nanotubes are treated as a special class. We found that the chiral indices of a carbon nanotube can always be measured from the electron diffraction pattern regardless if the nanotube is circular or elliptical. An experimental electron diffraction pattern from a partly-deformed carbon nanotube is also analyzed. Assisted with numerical simulations, it is determined that the observed carbon nanotube has chiral indices (15,7) with 8° tilt relative to the horizontal plane and eccentricity of 0.553.

A practical procedure has been proposed to determine the handedness of a carbon nanotube from its electron diffraction patterns. When a nanotube is twisted, the diffraction layer line spacings change, although the intensity distribution on the layer lines stays unchanged. The handedness can be assigned by observing the directions in which the principal layer lines shift under known direction of twisting and the twisting angle can be derived directly from the ratio of the diffraction layer line spacings. Simulated electron diffraction patterns of a carbon nanotube twisted both clockwise and counterclockwise are also presented as an example to corroborate the theoretical analysis.

Electron diffraction patterns of single-walled carbon nanotubes always have 2mm symmetry regardless if the nanotubes themselves have such symmetry. We here show that, for the case of multiwalled carbon nanotubes, the 2mm symmetry can break down when coherent interferences of the electron waves from two different shells take place such as when two shells of the same helicity but their chiral indices (u,v) have opposite evenness/oddity. Both an experimental electron diffraction pattern and analytic analysis are presented to demonstrate the conditions under which the 2mm symmetry breaks down in the electron diffraction patterns of multiwalled carbon nanotubes.

We show that, even when the atomic structure of a single-walled carbon nanotube does not have mirror symmetry perpendicular to the tubule axis, the electron diffraction patterns of the single-walled carbon nanotube always possess 2mm symmetry. We have also analyzed the contributions of higher order Bessel functions to the intensity distribution on the layer lines and found that (a) their contributions are negligible and (b) they would not affect the symmetry of the diffraction pattern. Both experimental and simulated electron diffraction patterns of a single-walled carbon nanotube of indices (14, 9) are presented to illustrate the 2mm symmetry and to corroborate the theoretical analysis.

Current commercial micro-CT scanners have the capability of imaging objects ex vivo with high spatial resolution, but performing in vivo micro-CT on free-breathing small animals is still challenging because their physiological motions are non-periodic and much faster than those of humans. In this paper, we present a prototype physiologically gated micro-computed tomography (micro-CT) scanner based on a carbon nanotube field emission micro-focus x-ray source. The novel x-ray source allows x-ray pulses and imaging sequences to be readily synchronized and gated to non-periodic physiological signals from small animals. The system performance is evaluated using phantoms and sacrificed and anesthetized mice. Prospective respiratory-gated micro-CT images of anesthetized free-breathing mice were collected using this scanner at 50 ms temporal resolution and 6.2 lp mm(-1) at 10% system MTF. The high spatial and temporal resolutions of the micro-CT scanner make it well suited for high-resolution imaging of free-breathing small animals.

We report a detailed study on the design of carbon nanotube based microfocus x-ray tube with one electrostatic focusing electrode. Based on the electron optics simulations, such parameters as geometrical distances and applied voltages among all the electrodes are considered, respectively, in relation to the size of x-ray focal spot. The stability of the x-ray focal spot size is also examined with respect to the variation of gate and anode voltages. Experimental results that agree well with the simulated data are also provided to corroborate the design method. We also discuss the operating stability and limitations when designing a carbon nanotube based microfocus x-ray tube with only one electrostatic focusing electrode. The designed x-ray tube with an isotropic focal spot sees wide applications in in vivo medical imaging studies.

The atomic structures of 124 single-walled carbon nanotubes, described by their diameter and helicity or equivalently by the two chiral indices $(u,v)$ that define the perimeter of each nanotube, have been determined unambiguously by nanobeam electron diffraction. A mapping of 70 possible nanotubes in the range of 1.20--1.65 nm in diameter with all possible helicities has been constructed experimentally for a carbon nanotube sample produced by arc discharge. Among the total 124 nanotubes characterized experimentally, 58 nanotubes of different structure have been identified. By examining the histogram of occurring helicities, we find that, while certain nanotubes were observed slightly more often than others, the overall feature showed a rather uniform distribution in occurrence. Basing on a nucleation-and-growth model, we suggest that the uniform distribution of helicity be originated from the weak dependence on helicity of the formation energy of carbon nanotubes, while the growth prefers slightly the structure with helicity 15\ifmmode^\circ\else\textdegree\fi{}--30\ifmmode^\circ\else\textdegree\fi{} for which the addition of carbon dimers would facilitate the growth of carbon nanotubes.

We report a method that allows direct, systematic, and accurate determination of the atomic structure of multiwalled carbon nanotubes by analyzing the scattering intensities on the nonequatorial layer lines in the electron diffraction pattern. Complete structure determination of a quadruple-walled carbon nanotube is described as an example, and it was found that the intertubular distance varied from 0.36 nm to 0.5 nm with a mean value of 0.42 nm.

Microcomputed tomography is now widely used for in vivo small animal imaging for cancer studies. Achieving high imaging quality of live objects requires the x-ray source to have both high spatial and temporal resolutions. Preliminary studies have shown that carbon nanotube (CNT) based field emission x-ray source has significant intrinsic advantages over the conventional thermionic x-ray tube including better temporal resolution and programmability. Here we report the design and characterization of a CNT based field emission x-ray source that also affords a high spatial resolution. The device uses modified asymmetric Einzel lenses for electron focusing and an elliptical shaped CNT cathode patterned by photolithography. Stable and small isotropic x-ray focal spot sizes were obtained.