Elastic Scattering of Electrons
- Practical Electron Microscopy and Database -
- An Online Book -





Elastic scattering means that the electron energy lost by the primary electron is too small to be detected. Simply speaking, the elastic scattering of electrons occurs mainly from electron interaction with the atomic nuclei or the whole electrostatic field of the atoms. The elastic scattering is responsible for electron diffraction from the specimens in TEM.

Elastic scattering is represented by the peak at zero energy loss, illustrated in EELS profiles, and and is often described in terms of Rutherford scattering from atoms or ions. For single scattering, elastic scattering can be treated as independent atomic scattering events and the cross-section of the scattering can be extracted by the relation,
         1/λ = Nσ -------------------------- [4108]
         N = ρ/(Am)
         N -- The atomic density,
         ρ -- The mass density,
         A -- The dimensionless atomic mass,
         m -- The proton mass.

Thermal diffuse scattering (TDS) can also be described by elastic scattering modified by the atomic vibrations.

Table 4108a shows that electrons interact with 1 electron, many electrons, 1 nucleus, and many nuclei in solids.

Table 4108a. Effects of interactions of electrons in solids.
  Interaction with electron(s) Interaction with nucleus/nuclei
  1 electron Many electrons 1 nucleus Many nuclei
Scattering type Inelastic Inelastic Quasi-elastic Elastic Inelastic
Scattering effect Electron Compton effect; electron excitation (from 50 eV to a few keV: EDS and EELS) Plasmon excitation (< 50 eV, ~100 nm TEM specimen); Cerenkov effect Rutherford scattering; phonon scattering (< 1 eV, heat) Bragg scattering Bremsstrahlung

Kikuchi lines are more pronounced in CBED patterns than in SAD patterns because:
        i) CBED patterns arise from a smaller, and thus more uniform region than SAD patterns,
        ii) The enhancement of coherent and elastic scattering in CBED.

Table 4108b. Electron scattering from a specimen in TEM measurements (Incoherent does not imply inelastic scattering; however, inelastic scattering is necessarily incoherent in EM measurements).
Scattering type
Energy loss
Wave (phase) property
Scattering direction
Scattering angle
Electron property
Full name
Elastic No energy change of the wave after scattering Usually coherent (when the specimen is thin and crystalline) Forward scattering 1° ~ 10° Wave Coherent elastic scattering
Incoherent > 10° Particle Incoherent elastic scattering
Back scattering  
Inelastic There is energy change of the wave after scattering Almost always incoherent Forward scattering < 1° Incoherent inelastic scattering
Coherent Does not exist in EM measurement, but it shows in neutron scattering     Coherent inelastic scattering
*   Incoherence does not imply inelastic scattering, while inelastic electron scattering is incoherent in electron microscopy.
** Inelastic scattering is not necessarily incoherent in neutron scattering.