THEORETICAL DETERMINATION OF ANGULARLY-INTEGRATED ENERGY-LOSS FUNCTIONS FOR ANISOTROPIC MATERIALS

The general expression for angularly integrated electron-energy-loss functions for anisotropic materials is derived for arbitrary specimen orientations with respect to the incident angle of a fast electron. For uniaxial (tetragonal, trigonal and hexagonal) and biaxial (orthorhombic) crystal systems, the angularly integrated electron-energy-loss functions in the core loss region are linear combinations of the components of the dielectric function for the electron beam travelling along any one of the principal crystallographic axes. This suggests a novel method of determining the anisotropic dielectric function tensor from angularly integrated energy-loss spectra, which can be implemented for a convergent probe. The spatial resolution of the anisotropy in the localized electronic structure is then only limited by the probe size and can be as small as a few nanometres in a dedicated scanning transmission electron microscope.