We describe a technique to determine the $s{p}^3∕s{p}^2$ ratio of carbon materials which is based on the electron-energy-loss spectroscopy and which uses the theoretical spectrum of graphite obtained from ab initio electronic structure calculations. The method relies on the separation of the $\pi *$ and $\sigma *$ components of the carbon $K$ edge of graphite. The resulting $\pi *$ spectrum is adopted and assumed to be transferable to other carbon systems given an appropriate parametrization of the broadening. The method is applied on a series of Monte Carlo generated amorphous carbon structures and is shown to be stable over a wide range of the energy windows for which spectral integration is performed. The $s{p}^3$ fractions obtained using this method are found to be in good agreement with those obtained from a microscopic scheme which uses the $\pi$-orbital axis vector analysis (POAV1). From the electron energy loss calculations on the generated amorphous carbon structures, we conclude that the interchangeable use of coordination number and hybridization state can lead to an underestimation of the $s{p}^3$ fraction of generated amorphous carbon structures for low and moderate densities. For high densities the coordination method and the POAV1 approach gave the same results. The technique was also applied on a series of spectra of plasma deposited amorphous carbon and was found to be in good agreement with the results obtained from a functional fitting approach.

• Received 20 October 2003

DOI:https://doi.org/10.1103/PhysRevB.70.075115