Mean Free Path of Electron Elastic Scattering
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In TEM analysis, the mean free path of elastic scattering of an electron represents how thin the specimen needs to avoid or minimize plural scattering.

The inelastic scattering of electrons occurs at smaller angles than that for elastic scattering. Figure 2863a shows an example of angular-resolved electron scattering profiles in logarithmic scale. The reference spectrum (vacuum) in blue is dominated by unscattered electrons in the range −4 to 4 mrad. Due to the scattering of the incident electrons with a rhenium (Re) TEM specimen, the modified spectrum in red was formed.

angular-resolved electron scattering profiles of electrons in vacuum and rhenium film

Figure 2863a. An example of angular-resolved electron scattering profiles of electrons in vacuum and Re film in logarithmic scale. The reference spectrum (vacuum) is dominated by unscattered electrons in the range −4 to 4 mrad. [1]

The mean free path of elastic scattering (λel) is given by, [1]

                                                                                       λel = −t/ln(ISample/IVacuum) ----------------------------- [2863]

For instance, ISample is equal to IRe in Figure 2863a.

Figure 2863b shows the experimental values of λel [1] and λin(Z) [2] as oscillatory functions of Z for Z > 20. Comparison of λel and λin values suggests that the elastic component should dominate scattering of incident high-energy electrons for most inorganic solids and of incident electrons penetrating thin TEM specimens.

Mean free path of elastic and inelastic scattering of electrons

Figure 2863b. The mean free path of elastic scattering λel of 200 keV electrons (solid squares) [1] and that of inelastic values λin (open circles) (Adapted from [2]).

 

 

 

 

[1] Konstantin Iakoubovskii and Kazutaka Mitsuishi, Elastic scattering of 200 keV electrons in elemental solids: experimental observation of atomic-number-dependent oscillatory behavior, J. Phys.: Condens. Matter 21 (2009) 155402.
[2] Iakoubovskii K, Mitsuishi K, Nakayama Y and Furuya K (2008) Phys. Rev. B 77, 104102.

 

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