electron microscopy



Electron Diffraction (ED)

Electron diffraction is a collective scattering phenomenon with electrons being (nearly elastically) scattered by atoms in a regular array (crystal). This can be understood in analogy to the Huygens principle for the diffraction of light. The incoming plane electron wave interacts with the atoms, and secondary waves are generated which interfere with each other. This occurs either constructively (reinforcement at certain scattering angles generating diffracted beams) or destructively (extinguishing of beams).
As in X-ray diffraction (XRD), the scattering event can be described as a reflection of the beams at planes of atoms (lattice planes). The Bragg law gives the relation between interplanar distance d and diffraction angle
Θ which is the distance between the reflection and the origin of the reciprocal lattice:

nλ = 2dsinΘ

Each set of parallel lattice planes, which correspond to planes decorated with atoms in the structure, generates a pair of spots in the electron diffraction pattern with the direct beam in their center (see scheme below).
Since the wavelength λ of the electrons is known, interplanar distances can be calculated from ED patterns. Furthermore, information about crystal symmetry can be obtained. Consequently, electron diffraction represents a valuable tool in crystallography.

Estimate of scattering angles

λel = 0.00197 nm (1.97 pm) for 300 kV electrons. A typical value for the interplanar distance is d = 0.2 nm.
If these values are put in the Bragg law, then the scattering angle is:
Θ = 0.28°.

As a rule, the scattering angles in ED are rather small (e.g., compared to those in XRD): 0 < Θ < 2.

From this follows that
(i) the reflecting lattice planes are almost parallel to the direct beam (left figure),
(ii) the incident electron beam is the zone axis of the reflecting sets of lattice planes (right figure).


Ewald sphere | Bragg law | ED vs. XRD | Examples


ETH Zürich | ETH chemistry department | ETH inorganic chemistry

modified: 20 April, 2020 by F. Krumeich | © ETH Zürich and the authors