Quantitative atomic cross section analysis by 4D-STEM and EELS

We demonstrate the use of a 4-dimensional scanning transmission electron microscope (4D-STEM) to extract atomic cross section information in amorphous materials. We measure the scattering amplitudes of 200 keV electrons in several representative specimens: amorphous carbon, silica, amorphous ice of pure water, and vitrified phosphate buffer solution. Diffraction patterns are recorded by 4D-STEM with or without energy filter at the zero-loss peak. In addition, Electron Energy Loss Spectroscopy (EELS) data are acquired at several thicknesses and energies. Mixed elastic and inelastic contributions for thick samples can be decoupled based on a convolution model. Measured differential cross sections between 1 and 3 mrad are due primarily to plasmon excitations and follow precisely a 1/θ² angular distribution. The measured intensities match Inokuti's calculations of total dipole matrix elements for discrete dipole transitions alone, i.e., transitions to bound states of the atom and not to continuum states. We describe the fundamental mechanism of plasmon excitation in insulators as a two-step interaction process with a fast electron. First, a target electron in the specimen is excited, the probability for which follows from the availability of atomic transitions, with a strong dependence on the column of the periodic table. Second, the dielectric response of the material determines the energy loss. The energy of the loss peak depends primarily on the valence electrons. Elastic scattering is dominant at higher angles, and can be fitted conveniently to 1/θ^3.7 with a linear dependence on atomic number for light atoms. In order to facilitate the interpretation of 4D STEM measurements in terms of material composition, we introduce two key parameters. Zeta is an analytical equivalent of classical STEM Z-contrast, determined by the ratio of elastic to inelastic scattering coefficients, while eta is the elastic coefficient divided by thickness. The two parameters may serve for identification of basic classes of materials in biological and other amorphous organic specimens.