Elastic Scattering of Electrons by Atoms

An electron penetrating into the electron cloud of an atom is attracted by the positive potential of the nucleus (Coulombic interaction), and its path is deflected towards the core as a result. The Coulombic force F is defined as:

F = Q₁Q₂ / 4πε₀r²

with r being the distance between the charges Q₁ and Q₂ and ε₀ the dielectric constant. The closer the electron comes to the nucleus, i.e. the smaller r, the larger is F and consequently the scattering angle. In rare cases, even complete backscattering can occur (back scattered electrons BSE). These interactions can be treated as elastic, which means that no energy is transferred from the scattered electron to the atom.

This simple model helps to explain the basic mechanisms of amplitude contrast in TEM and STEM. The mass-thickness contrast is somehow related to the contrast in optical microscopy, but it is the local scattering power that determines contrast in TEM instead of absorption of light. The interaction of electrons with heavy atoms having a high charge Q is stronger than with light atoms so that areas in which heavy atoms are localized appear with darker contrast than such with light atoms (mass contrast). In thick areas, more electron scattering events occur of course; thus, these thick areas appear darker than thin areas (thickness contrast). In particular, this mass-thickness contrast is important in bright and dark field imaging.

The strong Coulomb interaction of the negatively charged electrons with the positive potential of an atom core, which leads to high angle scattering (designated as Rutherford scattering) and even to back-scattering, is employed in STEM (Z-contrast imaging) and in SEM (imaging with back-scattered electrons). By the HAADF-STEM method, small clusters (or even single atoms) of heavy atoms (e.g. in catalysts) can be imaged in a matrix of light atoms since the local intensity is approximately proportional to Z² (Z: atomic number).

If a crystalline specimen is transmitted by electrons, then Bragg diffraction happens as well. Each atom in such a regular arrangement acts as a scattering center. The scattered electron waves may interact with each other either in a constructive or in a destructive way, which gives rise to a diffraction pattern. If a crystal is oriented along a zone axis so that many electrons are strongly scattered to contribute to the reflections in the diffraction pattern, then only a few electrons pass without interactions and therefore this crystal appears with dark contrast in the BF image (diffraction contrast). In real specimens, all contrast mechanisms, namely mass-thickness and Bragg contrast, occur simultaneously, making the interpretation of TEM images sometimes difficult.