Dynamical Scattering of Electrons in Thick TEM Specimen
- Practical Electron Microscopy and Database -
- An Online Book -


This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.


Dynamical electron scattering affects the application of electron diffraction to structural fingerprinting strategy.

If the TEM specimen is so thick that the electron waves are scattered more than once, the kinematical approximation no longer holds and the multiple, dynamical scattering must be considered. However, if the electron beam is tilted slightly away from the zone axis of the crystal in the specimen, the dynamical effects will be reduced.

Dynamical scattering exists in many cases. For instance, in the case of double diffraction, the wave is first diffracted by a set of parallel lattice planes (h1k1l1) and then by another set of planes (h2k2l2) according to the following equations,

         h3 = h1 + h2 --------------------------------------- [2732a]
         k3 = k1 + k2 --------------------------------------- [2732b]
         l3 = l1 + l2 ----------------------------------------- [2732c]

       hkl -- Miller indices.

Therefore, the reflections that are kinematically forbidden due to the presence of screw axes or glide planes will appear in the diffraction pattern of a crystal that scatters dynamically. However, the kinematically forbidden reflections due to unit-cell centering [1] do not show in dynamical scattering.

XRD obeys Friedel's Law because it can be approximately described by kinematical scattering. This limits the number of the space groups of crystals that can be determined by XRD to fifty. For electron diffraction, multiple (dynamical) scattering of the incident electrons in the TEM specimen occurs so that the Friedel's law is broken down, and thus the crystals with all the 230 space groups can be identified.






[1] D. E. Sands. Introduction to crystallography. Dover Publications, 1993.



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