1. Field of the Invention
The present invention relates to a method, computer program and device for determining the crystal structure and/or the range of crystal structures of one or more crystalline tubular molecules from a set of calibration-free properties of a diffraction pattern of the one or more crystalline tubular molecules.
2. Description of the Related Art
Various crystalline tubular molecules have been discovered in recent years including carbon Nanotubes and nanobuds and boron-nitride Nanotubes. Carbon Nanotubes have received the most attention because of their unique physical, chemical, thermal and electrical properties. A fundamental problem in both basic and applied research on crystalline tubular molecules such as single-walled carbon nanotubes (SWCNTs) exists because many physical properties of nanotubes can be extremely sensitive to their atomic structure. For instance, the structure of a SWCNT can be conveniently described by a pair of integers known as the chiral indices (n, m). A well-known example of the sensitivity of structure to properties is that a carbon nanotube can be metallic if (n−m) is divisible by 3, otherwise they are semiconducting. A slight change in the value n or m can, thus, dramatically alter the electronic properties of a nanotube. For instance, a (13, 1) tube is metallic while a (14, 1) tube is semiconducting though they are geometrically very similar to each other. Therefore, unambiguous (n, m) determination of individual SWCNTs is of crucial value for progressing CNT-based nanotechnology.
Current efforts for structural characterization of SWCNTs can be categorized into two broad classes, i.e., optical and non-optical. Optical spectroscopy includes, for example, resonant Raman scattering and photoluminescence, where (n, m) are identified by using the characteristic optical transition energies and photon frequencies (in Raman scattering) or optical absorption and emission energies (in photoluminescence). Optical measurements are usually limited in that they require a range of laser wavelengths for detecting a variety of tubes and they are only valid for a limited range of tube diameters. Laborious tasks are usually involved for both measurement and data interpretation. Photoluminescence has an additional drawback since the method can only detect semiconducting nanotubes. In addition, the insufficient spatial resolution of optical measurements makes it impossible to probe individual SWCNTs for analysis without considering effects from the tube environment. Moreover, there is no known calibration technique to correlate the intensity of excitations for tubes of given chiral indices to their concentrations, thus it is difficult to accurately map the chirality distribution in a SWCNT sample with optical measurements.
In the non-optical communities, the chiral indices are usually assigned by first determining the characteristic tube diameter D0 and chiral angle α by means of direct imaging techniques in real space (e.g. scanning tunneling microscopy (STM) and high-resolution transmission electron microscopy (HRTEM)), or in reciprocal space by the electron diffraction technique. Direct imaging techniques are faced with the problem that the tubes are usually not stable enough for acquiring high-quality images with atomic-resolution and at a high magnification.
Electron diffraction was the first technique to be used to characterize SWCNTs at the time of their discovery and has remained one of the most powerful means for their structural analysis. Advanced nano-beam electron diffraction techniques uniquely allow direct probing of individual nanotubes and characterization of their structure. However, the measurements are typically made by assuming a normal incidence condition or a small tube tilting angle, e.g. less than 6°. In contrast, it is not rare for a nanotube to have a tilt angle of 20° from the horizontal plane. In practice, it is difficult to establish an experimental setup to ensure such small tilt angle requirements. Although determination of the chiral angle α from electron diffraction patterns (EDPs) was shown to be independent of tube inclination, evaluation of the tube diameter may rely on the tilt of the tube unless the diffraction patterns are actually calibrated by internal standard materials, which are in practice unavailable in the measurement. In the absence of such standards, absolute calibration of an EDP of a SWCNT depends on the value of the carbon-carbon (C—C) bonding distance, which has uncertainty between 0.142 nm and 0.144 nm. Additionally the C—C bond can be stretched when the tube diameter is small. Also, calibration of the EDP by using the C—C bonding distance is either tilt sensitive or complicated by the curvature of the tube. In order to take into account the tilting effect of the tube on the determination, a tedious trial-and-error simulation procedure has to be applied.
Moreover, when D0 and α are required to be determined prior to (n, m) assignment, as by previous methods, they must both be determined with high accuracy in order to determine chiral indices n and m unambiguously. For instance, the metallic (13, 1) tube where D0=1.06 nm and α=3.7°, is very similar to the semi-conducting (14, 1) tube where D0=1.14 nm and α3.4°. Obviously, a slight error in either D0 or α easily leads to an ambiguity in indexing a SWCNT.