Density functional theory calculations of the carbon ELNES of small diameter armchair and zigzag nanotubes: core-hole, curvature and momentum transfer orientation effects

TL;DR

This study uses density functional theory to analyze how curvature, electron beam orientation, and core-hole effects influence the carbon ELNES in small diameter armchair and zigzag nanotubes, revealing significant curvature effects and the importance of core-hole inclusion.

Contribution

It provides a detailed theoretical analysis of curvature, core-hole, and orientation effects on carbon ELNES in small nanotubes, highlighting differences from flat graphene and graphite.

Findings

Curvature significantly affects ELNES spectra.

Core-hole effects are essential for accurate spectral reproduction.

ELNES anisotropy is reduced compared to graphite.

Abstract

We perform density functional theory calculations on a series of armchair and zigzag nanotubes of diameters less than 1nm using the all-electron Full-Potential(-Linearised)-Augmented-Plane-Wave (FPLAPW) method. Emphasis is laid on the effects of curvature, the electron beam orientation and the inclusion of the core-hole on the carbon electron energy loss K-edge. The electron energy loss near-edge spectra of all the studied tubes show strong curvature effects compared to that of flat graphene. The curvature induced $\pi-\sigma$ hybridisation is shown to have a more drastic effect on the electronic properties of zigzag tubes than on those of armchair tubes. We show that the core-hole effect must be accounted for in order to correctly reproduce electron energy loss measurements. We also find that, the energy loss near edge spectra of these carbon systems are dominantly dipole selected and that they can be expressed simply as a proportionality with the local momentum projected density of states, thus portraying the weak energy dependence of the transition matrix elements. Compared to graphite, the ELNES of carbon nanotubes show a reduced anisotropy.