Editing Electron diffraction (section)

{{Short description|Bending of electron beams due to electrostatic interactions with matter}}
{{Good article}}
{{anchor|Figure 1}}[[Image:Austenite ZADP.jpg|thumb|Figure 1: Selected area diffraction pattern of a twinned [[austenite]] crystal in a piece of [[steel]]|alt=Electron diffraction pattern showing white spots on a dark background, as a general example.]]

'''Electron diffraction''' is a generic term for phenomena associated with changes in the direction of [[electron beams]] due to [[Elastic collision|elastic]] interactions with [[atoms]].{{efn|name=Diff}} It occurs due to [[elastic scattering]], when there is no change in the energy of the electrons.<ref name="Cowley95" />{{Rp|location=Chpt 4}}<ref name="Reimer">{{Cite book |last=Reimer |first=Ludwig |url=http://worldcat.org/oclc/1066178493 |title=Transmission Electron Microscopy : Physics of Image Formation and Microanalysis. |date=2013 |publisher=Springer Berlin / Heidelberg |isbn=978-3-662-13553-2 |oclc=1066178493}}</ref>{{Rp|location=Chpt 5}}<ref name="Form" /><ref name=":11">{{Cite journal |last=Humphreys |first=C J |date=1979 |title=The scattering of fast electrons by crystals |url=https://iopscience.iop.org/article/10.1088/0034-4885/42/11/002 |journal=Reports on Progress in Physics |volume=42 |issue=11 |pages=1825–1887 |doi=10.1088/0034-4885/42/11/002 |s2cid=250876999 |issn=0034-4885|url-access=subscription }}</ref> The negatively charged electrons are scattered due to [[Coulomb's law|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|Figure 1]]. Beyond patterns showing the directions of electrons, electron diffraction also plays a major role in the contrast of images in [[electron microscope]]s.

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 [[#A primer on electron diffraction|general way]] electrons can act as waves, and diffract and interact with matter. It also involves the extensive [[#History|history]] behind modern electron diffraction, how the combination of developments in the 19th century in understanding and controlling [[#Electrons in vacuum|electrons in vacuum]] and the early 20th century developments with [[#Waves, diffraction and quantum mechanics|electron waves]] were combined with early [[#Electron microscopes and early electron diffraction|instruments]], giving birth to electron microscopy and diffraction in 1920–1935. While this was the birth, there have been a large number of [[#Subsequent developments in methods and modelling|further developments]] since then.

There are many [[#Types and techniques|types and techniques]] of electron diffraction. The most common approach is where the electrons [[#In a transmission electron microscope|transmit]] through a thin sample, from 1&nbsp;nm to 100&nbsp;nm (10 to 1000 atoms thick), where the results depending upon how the atoms are arranged in the material, for instance a [[#Selected area electron diffraction|single crystal]], [[#Polycrystalline pattern|many crystals]] or [[#Multiple materials and double diffraction|different types]] of solids. Other cases such as [[#Bulk and surface superstructures|larger repeats]], [[#Aperiodic materials|no periodicity]] or [[#Diffuse scattering|disorder]] have their own characteristic patterns. There are many different ways of collecting diffraction information, from parallel illumination to a [[#Convergent beam electron diffraction|converging beam]] of electrons or where the beam is [[#Precession electron diffraction|rotated]] or [[#4D STEM|scanned]] across the sample which produce information that is often easier to interpret. There are also many other types of instruments. For instance, in [[#In a scanning electron microscope|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|gas electron diffraction]], liquids, surfaces using lower energy electrons, a technique called [[#Low-energy electron diffraction (LEED)|LEED]], and by reflecting electrons off surfaces, a technique called [[#Reflection high-energy electron diffraction (RHEED)|RHEED]].

There are also many levels of analysis of electron diffraction, including:
# The simplest approximation using the de Broglie wavelength<ref name="Broglie" />{{Rp|location=Chpt 1-2}} for electrons, where only the [[#Plane waves, wavevectors and reciprocal lattice|geometry]] is considered and often [[Bragg's law]]<ref name=":7" />{{Rp|pages=96–97}} is invoked. This approach only considers the electrons far from the sample, a far-field or [[Fraunhofer diffraction|Fraunhofer]]<ref name="Cowley95" />{{Rp|pages=21–24}} approach.
# The first level of more accuracy where it is approximated that the electrons are only scattered once, which is called [[#Kinematical diffraction|kinematical diffraction]]<ref name="Cowley95" />{{Rp|location=Sec 2}}<ref name="HirschEtAl" />{{Rp|location=Chpt 4-7}} and is also a far-field or Fraunhofer<ref name="Cowley95" />{{Rp|pages=21–24}} approach. 
# More complete and accurate explanations where multiple scattering is included, what is called [[#Dynamical diffraction|dynamical diffraction]] (e.g. refs<ref name="Cowley95" />{{Rp|location=Sec 3}}<ref name="HirschEtAl" />{{Rp|location=Chpt 8-12}}<ref name="Peng" />{{Rp|location=Chpt 3-10}}<ref name="Pendry71" /><ref name="Maksym" />). These involve more general analyses using relativistically corrected [[Schrödinger equation]]<ref name="Schroedinger" /> methods, and track the electrons through the sample, being accurate both near and far from the sample (both [[Fresnel diffraction|Fresnel]] and [[Fraunhofer diffraction|Fraunhofer]] diffraction).

Electron diffraction is similar to [[X-ray crystallography|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.<ref name="Cowley95" />{{Rp|location=Sec 3}}<ref name="Reimer" />{{Rp|location=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.