Experimental and theoretical evidence for the magic angle in transmission electron energy loss spectroscopy

We present experimental measurements of the C K-ELNES of high temperature pyrolysed graphite and related crystalline materials as a function of collection angle and sample tilt. These results together with a corresponding theoretical analysis indicate that the so-called "magic angle" for EELS measurements of an anisotropic crystal such as graphite, where spectra are independent of sample orientation, is approximately two times the characteristic scattering angle. We briefly discuss the implications of this result for the experimental measurement of anisotropic structures, including interfaces, as well as for the detailed modelling of ELNES structures using advanced electronic structure calculations.