Electron diffraction study of small bundles of single-wall carbon nanotubes with unique helicity
The selected-area electron diffraction technique has been used to investigate the structure of bundles of single-wall carbon nanotubes synthesized by the catalytic chemical vapor deposition method. The helicity and lattice packing of the single-wall carbon nanotubes within the bundles have been deduced from the experimental diffraction patterns on the basis of the geometry of the reciprocal space of carbon nanotubes and computer simulations based on the kinematical theory. We show that a precise helicity can be found within a given small bundle. We attribute this selectivity to the small number of nanotubes ~20‐30! in the bundles.
Summary In this abstract, we propose a new finite-difference scheme for solving wave equations. This scheme splits the multidimensional system into different directions and solves each direction implicitly. Unlike most splitting methods in the literature which produce numerical anisotropy in diagonal directions, this method gives perfect circular impulse responses and allows lateral velocity variations. In this paper, we prove that the proposed scheme is unconditionally stable. In the numerical examples, we show some impulse response tests and compare them with the results from some high-order explicit finite-difference methods. The new method allows larger time step and requires less memory storage during the reverse time