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



The periodic potential in crystals causes the amplitude of the accelerating electron (e.g. 200 keV in TEM) to be transferred back-and-forth between the transmitted and diffracted wavefunctions. This transfer process can be explained by dynamical theory. The crystal has a periodic potential that is weak compared with an electron energy of 200 keV. At the Laue condition ( s= 0), the physical distance between two back-and-forth transfers is called the “extinction distance.”

Assuming the TEM specimen is a perfect crystal, in two beam condition the intensity (Ig) of diffracted electron beam can be given by (based on dynamical theory),

             intensity (Ig) of diffracted electron beam ------------------------- [4134a]
            intensity (Ig) of diffracted electron beam ------------------------- [4134b]

            intensity (Ig) of diffracted electron beam ------------------------- [4134c]

           seff -- Effective deviation parameter
           ξg -- Extinction distance
           V -- Volume of the unit cell
           λ -- Electron wavelength
           Γg -- Structure factor of the unit cell for diffraction g
           s -- Deviation parameter
           t -- Crystal thickness

Equation 4134a for dynamical theory is valid when the TEM sample is thick and s is about zero, but is not valid in kinematical theory. From Equation 4134c we can know that the extinction distance decreases with increase of scattering (increase of Γg). When s is equal to zero (exact Bragg condition) we have seff = 1/ξg, meaning the transmitted (I0) and diffracted (Ig) intensities has a periodicity of ξg in TEM specimen depth indicated in Figure 4134 in two beam condition. Here, I0 = 1 - Ig in two beam condition.

diffracted intensity (Ig) showing a periodicity of ξg

Figure 4134. The diffracted intensity (Ig) showing a periodicity of ξg in TEM
specimen depth in two beam condition. Ig is the intensity of transmitted beam.



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