Back حيود الإلكترونات Arabic Дыфракцыя электронаў Byelorussian Difracció d'electrons Catalan Elektronenbeugung German Difracción de electrones Spanish پراش الکترون Persian Elektronidiffraktio Finnish Diffraction des électrons French Díraonadh leictreon Irish इलेक्ट्रान विवर्तन Hindi

Electron diffraction

Electron diffraction pattern showing white spots on a dark background, as a general example.
Figure 1: Selected area diffraction pattern of a twinned austenite crystal in a piece of steel

Electron diffraction is a generic term for phenomena associated with changes in the direction of electron beams due to elastic interactions with atoms.[a] It occurs due to elastic scattering, when there is no change in the energy of the electrons.[1]: Chpt 4 [2]: Chpt 5 [3][4] The negatively charged electrons are scattered due to Coulomb forces when they interact with both the positively charged atomic core and the negatively charged electrons around the atoms. The resulting map of the directions of the electrons far from the sample is called a diffraction pattern, see for instance Figure 1. Beyond patterns showing the directions of electrons, electron diffraction also plays a major role in the contrast of images in electron microscopes.

This article provides an overview of electron diffraction and electron diffraction patterns, collective referred to by the generic name electron diffraction. This includes aspects of how in a general way electrons can act as waves, and diffract and interact with matter. It also involves the extensive history behind modern electron diffraction, how the combination of developments in the 19th century in understanding and controlling electrons in vacuum and the early 20th century developments with electron waves were combined with early instruments, giving birth to electron microscopy and diffraction in 1920–1935. While this was the birth, there have been a large number of further developments since then.

There are many types and techniques of electron diffraction. The most common approach is where the electrons transmit through a thin sample, from 1 nm to 100 nm (10 atoms to 1000 thick), where the results depending upon how the atoms are arranged in the material, for instance a single crystal, many crystals or different types of solids. Other cases such as larger repeats, no periodicity or disorder have their own characteristic patterns. There are many different ways of collecting diffraction information, from parallel illumination to a converging beam of electrons or where the beam is rotated or scanned across the sample which produce information that is often easier to interpret. There are also many other types of instruments. For instance, in a scanning electron microscope (SEM), electron backscatter diffraction can be used to determine crystal orientation across the sample. Electron diffraction patterns can also be used to characterize molecules using gas electron diffraction, liquids, surfaces using lower energy electrons, a technique called LEED, and by reflecting electrons off surfaces, a technique called RHEED.

There are also many levels of analysis of electron diffraction, including:

  1. The simplest approximation using the de Broglie wavelength[5]: Chpt 1-2  for electrons, where only the geometry is considered and often Bragg's law[6]: 96–97  is invoked. This approach only considers the electrons far from the sample, a far-field or Fraunhofer[1]: 21–24  approach.
  2. The first level of more accuracy where it is approximated that the electrons are only scattered once, which is called kinematical diffraction[1]: Sec 2 [7]: Chpt 4-7  and is also a far-field or Fraunhofer[1]: 21–24  approach.
  3. More complete and accurate explanations where multiple scattering is included, what is called dynamical diffraction (e.g. refs[1]: Sec 3 [7]: Chpt 8-12 [8]: Chpt 3-10 [9][10]). These involve more general analyses using relativistically corrected Schrödinger equation[11] methods, and track the electrons through the sample, being accurate both near and far from the sample (both Fresnel and Fraunhofer diffraction).

Electron diffraction is similar to x-ray and neutron diffraction. However, unlike x-ray and neutron diffraction where the simplest approximations are quite accurate, with electron diffraction this is not the case.[1]: Sec 3 [2]: Chpt 5  Simple models give the geometry of the intensities in a diffraction pattern, but dynamical diffraction approaches are needed for accurate intensities and the positions of diffraction spots.


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  1. ^ a b c d e f Cite error: The named reference Cowley95 was invoked but never defined (see the help page).
  2. ^ a b Reimer, Ludwig (2013). Transmission Electron Microscopy : Physics of Image Formation and Microanalysis. Springer Berlin / Heidelberg. ISBN 978-3-662-13553-2. OCLC 1066178493.
  3. ^ Cite error: The named reference Form was invoked but never defined (see the help page).
  4. ^ Humphreys, C J (1979). "The scattering of fast electrons by crystals". Reports on Progress in Physics. 42 (11): 1825–1887. doi:10.1088/0034-4885/42/11/002. ISSN 0034-4885. S2CID 250876999.
  5. ^ Cite error: The named reference Broglie was invoked but never defined (see the help page).
  6. ^ Cite error: The named reference :7 was invoked but never defined (see the help page).
  7. ^ a b Cite error: The named reference HirschEtAl was invoked but never defined (see the help page).
  8. ^ Cite error: The named reference Peng was invoked but never defined (see the help page).
  9. ^ Cite error: The named reference Pendry71 was invoked but never defined (see the help page).
  10. ^ Cite error: The named reference Maksym was invoked but never defined (see the help page).
  11. ^ Cite error: The named reference Schroedinger was invoked but never defined (see the help page).

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