Chapter/Index: Introduction  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  Appendix
The cross section of elastic scattering of an electron, when divided by the actual area of an atom, gives the probability that a scattering event will occur. Rutherford crosssection gives convenient formulas to calculate the elastic scattering angle and total elastic cross section so that it is often used to describe the elastic scattering of electron. However, its accuracy becomes worse in lowenergy region or in high atomicnumber materials. Figure 4667a shows schematically electron scattering by an atom. Ω here is solid angle. Figure 4667a. Schematic of electron scattering. The crosssection of elasticscattering is given by,  [4667a] where is a function, which defines the scattering properties by [4667b] The element of solid angle (Ω) can be written as, dΩ= 2πsinθdθ [4667c] Figure 4667b. scattering vector for elastic scattering. Based on Turner–Doyle scattering factors [1], σ_{e} can be plotted by the curve in Figure 4667c. On the other hand, by simple estimation, σ_{e} can be plotted by the straight line using Lenz model given by [2],  [4667d]
Figure 4667d below shows the cross section of elastic scattering process in Al as a function of the incident electron energy at the scattering angles of ~ 0°. For comparison, the figure also shows cross sections for the various inelastic scattering processes. Figure 4667d. Cross sections for the elastic and various inelastic scattering processes in Al as a function of In ADF (Annual Dark Field) imaging, assuming the detector has a large outer
reciprocal radius, then the crosssection of elastic scattering can be expressed by the empirical relation, The elastical scattering crosssection
for the electrons scattered by an atom to the corresponding scattering angles of the
HAADF detector can also be given by,
[1] Humphreys, C. J., HartDavis, A., and Spencer, J. P. (1974). Optimizing the signal/noise in the dark field
imaging of single atoms. Proc. 8th Int. Congr. Electron. Microsc., Canberra, p. 248.
