Trichroism in energy-loss near-edge structure spectroscopy:: Polarization dependence of near-edge fine structures

The goal of this paper is to relate the current of inelastically scattered electrons collected in a transmission electron microscope (TEM) to the double differential electron energy-loss cross section. Up to now, this relationship, which depends on the point symmetry around the probed atom site, has been essentially studied in a situation called dichroism. This situation can be encountered when a principal threefold, fourfold, or sixfold rotation axis through the probed atom site exists. The electron energy-loss cross section is then a linear combination of longitudinal and transversal cross sections, and the weights of these components are cos(2) theta(q) and sin(2) theta(q), where theta(q) is the angle between the scattering wave vector q and the principal rotation axis. The first aim of this paper is to find the dependence on q of the cross section in all other cases, that is to say, when the symmetry around the probed atom site is described with one of the eight low symmetry point groups C-1, S-2, C-1h, C-2, C-2h, C-2v, D-2, and D-2h. In these eight cases of low symmetry, three distinct situations called trichroism can be distinguished. In these situations, the cross section is expressed in terms of the cross sections obtained for six, four, or three particular orientations of the scattering wave vector. The second aim of this paper is to provide an expression of the inelastically scattered electron current collected in a TEM for these three situations of trichroism. This current is expressed in terms of experimental parameters, such as the incident beam convergence, the collector acceptance, the electron beam kinetic energy, and the sample orientation. As in the case of dichroism, magic conditions can be found, for which the collected current becomes independent of the single-crystal sample orientation. The case of the C K edge in the nonstoichiometric V6C5 metallic carbide with a trigonal symmetry is given as an illustration.