Electron-Phonon Scattering due to Incident Electrons
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In EM measurements, electrons also scatter inelastically with phonons. These energy losses are of the order of a few tens of millielectronvolts (meV) and can therefore not be detected with transmission EELS measurement in an electron microscope. However, these quasi-elastic scattering processes broaden the zero-loss peak of EELS on the high-energy side.

In EM systems, the development of energy-filtered imaging attachments [1 - 5] has allowed removing the intensity from electrons scattered inelastically by any mechanism other than phonon scattering.

Diffuse scattering induced by thermal vibrations can be treated as electron–phonon scattering using a Debye phonon model [6 - 7].

Table 4759. Energy losses and scattering angles of various inelastic electron scatterings in electron interaction with materials.
Process Phonon excitation Inter of intra band transitions Plasmon excitation Inner shell ionization
Region of energy loss
Low loss (< 50 eV)
High loss (> 50 eV)
Energy loss E [eV] ~0.02 3 - 25 5 - 25 10 - 2000
Scattering angle θE [mrad] 5 - 15 5 - 10 < 0.1 0.1 - 10
Oscillation Collective oscillations of atoms (e.g. lattice vibrations)   Collective oscillations of free electrons, a quantum of a collective longitudinal
wave in the electron gas of a solid
Detectability by EELS Is not resolved Yes Yes Yes
Effects Causes specimen to heat up      
Time     Damped out in < 10−15 s  
Localization     Localized to < 10 nm  
Interaction     Most common inelastic interaction due to high free electron density  
Cross sections     Relatively large Relatively small
    Relatively short Relatively large
Intensity     Much intense Much smaller
Materials     Predominant in metals  
Modification     Can reduce the number of phonons by cooling the specimen.  
Other names Thermal diffuse scattering      
Characteristics Diffuse background, don’t carry any useful information Signature of the structure   Elemental information









[1] T. Honda, T. Tomita, T. Kaneyama, Y. Ishida, Ultramicroscopy 54 (2–4) (1994) 132–144.
[2] O.L. Krivanek, A.J. Gubbens, N. Dellby, C.E. Meyer, Microsc. Microanal. Microstruct. 3 (1992) 187–199.
[3] K. Tsuno, J. Electron Microsc. 48 (6) (1999) 801–820.
[4] K. Tsuno, T. Kaneyama, T. Honda, Y. Ishida, Nucl. Instrum. Methods A 427 (1–2) (1999) 187–196.
[5] M. Tanada, K. Tsuda, M. Terauchi, K. Tsuno, T. Kaneyama, T. Honda, Y. Ishida, J. Microsc. 194 (1999) 219–227.
[6] P. Rez, C. J. Humphreys and M. J. Whelan: “The distribution of intensity in electron diffraction patterns due to phonon scattering.” Philos. Mag. 35, 81–86 (1977).
[7] C. R. Hall and P. B. Hirsch: “Effect of thermal diffuse scattering on propagation of high energy electrons through crystals.” Proc. R. Soc. (London) A 286, 158 - 177 (1965).