ABSTRACT
Controlling the structure of single-wall carbon nanotubes during their synthesis by chemical vapor deposition remains a challenging issue. Here, using a specific synthesis protocol and ex situ transmission electron microscopy, we perform a statistical analysis of the structure of the tubes and of the catalyst particles from which they grow. We discriminate two nucleation modes, corresponding to different nanotube-particle junctions, that occur independently of the particle size. With the support of tight binding calculations, we show that a direct control of the nanotube diameter by the particle can only be achieved under growth conditions close to thermodynamic equilibrium.
ABSTRACT
Sample thinning for TEM observation introduces large changes with respect to the initial strain state of the bulk sample and particularly relaxation via the free surfaces which leads to HOLZ lines splitting in the CBED pattern. This phenomenon has been simulated owing to extensive calculations either in the kinematical or the dynamical framework of electron diffraction mainly using displacement fields resulting from finite element modelling of the sample relaxation. HOLZ line splitting is well reproduced and numerical fits can be used to compare experimental and calculated curves. This paper proposes new analytical solutions for the kinematical equation of electron diffraction. Simple mathematical functions are used to approximate the deformation profiles. We showed that, under certain conditions, the rocking curve profile can be analytically calculated, thus providing some clue to separate different contributions to the rocking curves against deformation profile. These simplified analytical expressions are used to extract the maximum amplitude displacement within the sample with about 10% accuracy. This accuracy can even be improved to 1% with a short adjustment routine. The influence of the shape of the displacement profile on the rocking curves is demonstrated.
