Electron Extinction Distance
- Practical Electron Microscopy and Database -
- An Online Book -

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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.

 

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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]

where,
           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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