Momentum Transfer of Incident Electrons
after Atomic Ionization/Energy loss
- Practical Electron Microscopy and Database -
- An Online Book -

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This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.
 

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In the case of an incident electron beam irradiates a specimen in TEM, the beam can be described by a plane wave. Figure 3799 shows the schematic illustration of momentum transfer and scattering angle of the incident electron beam in an atomic ionization process. Before the interaction of the incident beam with the specimen, the beam has a wave vector k0 (=2π/λ0) and an energy E0. This beam is scattered through an angle θ and loses energy E due to the ionization process. After the interaction it has a wave vector k and a smaller energy E' (=E0 - E). The momentum transferred to the specimen is q (=k0 - k). Their relationship is given by,

           momentum transferred to the specimen ------------------------------- [3799a]

where,
           θE -- The characteristic scattering angle (or called most probable scattering angle) for the given energy loss E.

θE is given by

           characteristic scattering angle (or called most probable scattering angle) (For general expression) ------------------- [3799b]
           characteristic scattering angle (or called most probable scattering angle) (For an energy of incident electrons is less than 100 keV) ------------------- [3799c]
Where,
           γ -- The relativistic factor (=(1 - v2/c2)-1/2)
           m0 -- The rest mass of the electron
           v -- The velocity of the incident electron

schematic illustration of momentum transfer and scattering angle in the atomic ionization process due to incident electron irradiation

Figure 3799. Schematic illustration of momentum transfer and scattering angle of the incident
electron beam in an atomic ionization process.

 

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