Calibration of the Measurement of sp2-Type Bonding in Carbon Using Eeels in an Electron Microscope

Electron Energy Loss Spectroscopy (EELS) in an electron microscope is an accurate method for the measurement of the sp2-type bonding in carbon, due to the presence of a clearly defined sharp peak in the specific carbon K spectral edge, whose area is directly proportional to the number of empty states in the local density of states. However, an absolute measurement of sp2 bonds requires to be scaled to the total number of sp2 and sp3 bonded atoms and then normalized to a 100% sp2-bonded standard. Usually, pure graphite is used as a 100% sp2- bonded standard. However, this normalizing value is affected by the anisotropy of the empty states, as their excitation probability depends on the amount of momentum that is transferred by the incident electron beam in the direction of the empty states, which is orientation dependent. Here we review the theoretical prediction of a magic angle for an electron microscope, when sp2 measurements are independent of the experimental conditions and support it with experimental verification. Furthermore, we analyze the implications of anisotropy on the measurements of the sp2-type bonding in amorphous carbon samples and in carbon nanotubes.