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Small fraction of incident electrons are scattered through large angles and the extreme case is 180° backscattering as shown in Figure 4755a. The scattering angle has been discussed in Section Elastic Scattering Angle of Electrons. In electron microscopes, a collection angle higher than 50 mrad allows acquisition of mainly incoherent electrons. The incoherent images are directly interpretable.
Figure 4755a. Elastic scattering of electrons from an atomic nucleus for a largeangle collision and a 180 ° collision.
Darkfield images in TEMs/STEMs are constructed using electrons scattered at relatively large (≥ 30 mrad for STEM) angles and are dominated by elastic and thermal diffuse scattering. Scattering in the range of high angles is dominated by Rutherford (elastic) scattering and thermal diffuse (quasielastically) scattering (TDS). Such scattering is very sensitive to the atomic number (Z) of the scattering atoms and therefore provides information of the local chemical composition [1]. The scattering cross section is proportional to Z^{2}. In electron microscopic imaging, highangle annular darkfield (HAADF) method is used to remove the complexity of conventional brightfield scattering in HRTEM and the associated diffraction complications.
In general, the higher the effective atomic number, the higher is
the inelastic differential crosssection. However, the ratio of the
inelastic to the elastic scattering crosssection is inversely
proportional to the effective atomic number, [3]
 [4755]
where,
σ_{i} 
the inelastic scattering crosssection,
σ_{e} 
the elastic scattering crosssection,
Z_{eff}  the effective atomic number,
C  a coefficient,
 the characteristic angle corresponding to the mean energy loss.
Figure 4755b shows the angle at which inelastic and elastic differential crosssections are equal, as a function of the atomic number Z at the energy loss of 10 eV.
Figure 4755b. Plot of the scattering angle at which elastic and inelastic differential crosssections are equal, as a function of the atomic number at an energy loss of 10 eV. [2] 
[1] Characterization of III–V semiconductor interfaces by Z contrast imaging, EELS and CBED, Hubert Lakner, Bernd Bollig, Stefan Ungerechts and Erich Kubalek, J. Phys. D: Appl. Phys. 29 1767–1778 (1996).
[2] Lin Gu, Wilfried Sigle, Christoph T. Koch, Jaysen Nelayah, Vesna Srot, Peter A. van Aken, Mapping of valence energy losses via energyfiltered annular darkfield scanning transmission electron microscopy, Ultramicroscopy 109 (2009) 1164–1170.
[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.
