Energy-loss near-edge structure changes with bond length in carbon systems

Abstract

We show that when the graphene planes of graphite are uniformly expanded, thereby increasing the CC bond length to $1.7\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, the ${\ensuremath{\sigma}}^{*}$ edge onset of the energy-loss near-edge structure (ELNES) spectrum shifts to lower energies by almost $5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, meanwhile the ${\ensuremath{\pi}}^{*}$ edge shifts by less than $0.2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The shift of the ${\ensuremath{\sigma}}^{*}$ edge demonstrates that for bond lengths which are typical of some carbon systems such as amorphous carbon, it is possible to find ${\ensuremath{\sigma}}^{*}$ features in the ELNES spectra at energies as low as $286--288\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Calculations on 64-atom amorphous carbon $(a\text{\ensuremath{-}}\mathrm{C})$ and amorphous carbon nitride model structures characterized by a wide range of bond lengths confirm this. Most of the $s{p}^{2}∕s{p}^{3}$ quantification techniques that are available overlook this issue of ${\ensuremath{\sigma}}^{*}$ contamination of the ${\ensuremath{\pi}}^{*}$ region and assume that all features within this energy range are entirely of ${\ensuremath{\pi}}^{*}$ origin. We show that the effect of bond length variation on the ${\ensuremath{\pi}}^{*}$ spectrum of graphite and $a\text{\ensuremath{-}}\mathrm{C}$ is minor, thereby supporting the reliability of the former spectrum for $s{p}^{2}∕s{p}^{3}$ quantification purposes, as was recently demonstrated [see J. T. Titantah and D. Lamoen, Phys. Rev. B 70, 075115 (2004)].