Quantitative analysis of the effect of probe convergence on electron energy loss spectra of anisotropic materials

We present a quantitative analysis of core level electron energy loss (EEL) spectra for uniaxial anisotropic materials, taking into consideration the presence of a convergent electron probe as is the case in a scanning transmission electron microscope (STEM) or transmission electron microscope in convergent probe mode. The analysis assumes the dipole allowed, non-relativistic scattering angular distribution for inelastic electrons which have suffered core losses and the anisotropic effect is included by taking proper account of the projection of the electric field along different crystal axes. The physical response of a uniaxial material is represented by the dielectric function tensor, which has two components ε‖ and ε⊥. The detected core loss intensity is shown to be a linear superposition of the imaginary parts of these two components, with the `weightingʹ coefficients dependent on the experimental conditions. Their calculated values compare very well with the experimental measurement acquired from graphite, which is a well-known uniaxial material. We have presented the numerical result in a parameterized form for easy applications, such as to minimize or maximize the linear dichroic signal from uniaxial materials. We also discuss the condition in detail for minimizing the orientation dependence of the EELS signal in anisotropic materials.