Dependence of Inelastical Scattering of Electrons on Atomic Number
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The elements with larger atomic number (Z) has stronger elastic and thermal diffuse scattering and thus, a solid composed of element with larger Z can have larger mean free path value λ, i.e. weaker inelastic scattering. In the measurements of electron diffractions in TEM, the contribution of inelastically scattered electrons increases with decreasing atomic number and increasing foil thickness.

The fraction F of electron scattering (including both elastic and inelastic scatterings) at angles smaller than a scattering angle β can be given by, [1]

         fraction F of electron scattering (including both elastic and inelastic scatterings) at angles --------------------------------- [3504]
          θ0 -- (≈λZ1/3/(2πa0)) The soft cutoff to the Lorentzian angular distribution,
          θE ≈ 0.5Em/E0 (non-relativistically)

Figure 3504 shows the experimental values of λel [2] and λin(Z) [3] 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 3504. The mean free path of elastic scattering λel of 200 keV electrons (solid squares) [2] and that of inelastic values λin (open circles) (Adapted from [3]).













[1] F. Lenz, Z. Naturforsh 9A (1954) 185.
[2] 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.
[3] Iakoubovskii K, Mitsuishi K, Nakayama Y and Furuya K (2008) Phys. Rev. B 77, 104102.



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