Reciprocity in electron energy-loss spectra from non-centrosymmetric crystals

The energy losses of fast electrons propagating through a thin crystal show a strong effect associated with the interference term between Bloch-wave eigenstates. Reversing the direction of the electrons gives the same spectrum, and reciprocity is observed in the interference term between eigenstates in inelastic electron scattering. The reciprocity principle may be used to advantage to observe for GaAs a very large difference in the characteristic energy-loss spectra for pairs of experimental arrangements related by a mirror operation around the polar (111) planes. This provides a sensitive way of determining the polarity of a crystal based on simple two-beam arguments, and may also be used to obtain direct structure-factor phase information.