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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.
Figure 2880a 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.
Figure 2880a. 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]).
In general, the higher the effective atomic number, the higher is
the inelastic differential cross-section. However, the ratio of the
inelastic to the elastic scattering cross-section is inversely
proportional to the effective atomic number, [3]
------------------------ [2880]
where,
σi --
the inelastic scattering cross-section,
σe --
the elastic scattering cross-section,
Zeff -- the effective atomic number,
C -- a coefficient,
-- the characteristic angle corresponding to the mean energy loss.
Figure 2880b shows the angle at which inelastic and elastic differential cross-sections are equal, as a function of the atomic number Z at the energy loss of 10 eV.
Figure 2880b. Plot of the scattering angle at which elastic and inelastic differential cross-sections are equal, as a function of the atomic number at an energy loss of 10 eV. [4] |
[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.
[3] A.V. Crewe, J.P. Langmore, M.S. Isaacson, Physical aspects of electron microscopy and microbeam analysis, in: B.M. Siegel, D.R. Beaman (Eds.),
Wiley, New York, 1975, p. 47.
[4] Lin Gu, Wilfried Sigle, Christoph T. Koch, Jaysen Nelayah, Vesna Srot, Peter A. van Aken, Mapping of valence energy losses via energy-filtered annular dark-field scanning transmission electron microscopy, Ultramicroscopy 109 (2009) 1164–1170.
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