Editing Electron diffraction (section)

== History ==
The historical background is divided into several subsections. The first is the general background to electrons in vacuum and the technological developments that led to [[cathode-ray tube]]s as well as [[vacuum tube]]s that dominated early television and electronics; the second is how these led to the development of electron microscopes; the last is work on the nature of electron beams and the fundamentals of how electrons behave, a key component of [[quantum mechanics]] and the explanation of electron diffraction.

=== Electrons in vacuum ===
{{See also|Cathode ray|Electron#History|label 2=History of the electron}}
{{anchor|Figure 3}}{{multiple image
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| image1            = Katódsugarak mágneses mezőben(1).jpg
| image2            = Katódsugarak mágneses mezőben(2).jpg
| footer            = Figure 3: A Crookes tube – without emission (top, grey background) and with emission and a shadow due to the [[cross pattée]] blocking part of the electron beam (bottom, black background); see also [[Cathode ray | cathode ray tube]]
| alt1              = Image of a Crookes tube when it is not actively being used.
| alt2              = Image of a Crookes tube when it is operating, showing luminescence when the electrons hit the glass walls.
}}

Experiments involving electron beams occurred long before the discovery of the electron; [[wiktionary:ἤλεκτρον|ēlektron]] (ἤλεκτρον) is the Greek word for [[amber]],<ref name="DictOrigins">
{{cite book
 | last = Shipley | first = J.T.
 | title = Dictionary of Word Origins
 | page = 133
 | publisher = [[The Philosophical Library]] | year = 1945
 | isbn = 978-0-88029-751-6
 | url = https://archive.org/details/dictionaryofword00ship/page/133
 | url-access = registration
}}</ref> which is connected to the recording of electrostatic charging<ref name="Lacks">{{Cite journal |last1=Iversen |first1=Paul |last2=Lacks |first2=Daniel J. |date=2012 |title=A life of its own: The tenuous connection between Thales of Miletus and the study of electrostatic charging |url=https://www.sciencedirect.com/science/article/pii/S0304388612000216 |journal=Journal of Electrostatics |language=en |volume=70 |issue=3 |pages=309–311 |doi=10.1016/j.elstat.2012.03.002 |issn=0304-3886|url-access=subscription }}</ref> by [[Thales of Miletus]] around 585 BCE, and possibly others even earlier.<ref name="Lacks"/>

In 1650, [[Otto von Guericke]] invented the [[vacuum pump]]<ref name="Harsch 2007">
{{cite journal
| last=Harsch
| first=Viktor
| date=2007
| title=Otto von Gericke (1602–1686) and his pioneering vacuum experiments
| url=https://pubmed.ncbi.nlm.nih.gov/18018443/
| journal=Aviation, Space, and Environmental Medicine
| volume=78| issue=11
| pages=1075–1077
| doi=10.3357/asem.2159.2007
| issn=0095-6562| pmid=18018443
}}</ref> allowing for the study of the effects of high voltage electricity passing through [[rarefied air]]. In 1838, [[Michael Faraday]] applied a high voltage between two metal [[electrode]]s at either end of a glass tube that had been partially evacuated of air, and noticed a strange light arc with its beginning at the [[cathode]] (negative electrode) and its end at the [[anode]] (positive electrode).<ref name=":1">Michael Faraday (1838) [https://books.google.com/books?id=ypNDAAAAcAAJ&pg=PA125 "VIII.  Experimental researches in electricity. — Thirteenth series.,"] ''Philosophical Transactions of the Royal Society of London'', '''128''' :  125–168.</ref> Building on this, in the 1850s, [[Heinrich Geissler]] was able to achieve a pressure of around 10<sup>−3</sup> [[Atmosphere (unit)|atmospheres]], inventing what became known as [[Geissler tube]]s. Using these tubes, while studying electrical conductivity in [[rarefied]] gases in 1859, [[Julius Plücker]] observed that the radiation emitted from the negatively charged cathode caused phosphorescent light to appear on the tube wall near it, and the region of the phosphorescent light could be moved by application of a magnetic field.<ref name=":3">{{Cite journal|last=Plücker|first=M.|date=1858|title=XLVI. Observations on the electrical discharge through rarefied gases|url=https://doi.org/10.1080/14786445808642591|journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science|volume=16|issue=109|pages=408–418|doi=10.1080/14786445808642591|issn=1941-5982|url-access=subscription}}</ref>

In 1869, Plücker's student [[Johann Wilhelm Hittorf]] found that a solid body placed between the cathode and the phosphorescence would cast a shadow on the tube wall, e.g. [[#Figure 3|Figure 3]].<ref name="Martin 1986">{{Citation |last=Martin |first=Andre |title=Advances in Electronics and Electron Physics, Volume 67 |pages=183–186 |year=1986 |editor-last=Hawkes |editor-first=Peter |contribution=Cathode Ray Tubes for Industrial and Military Applications |publisher=Academic Press |isbn=9780080577333}}
</ref> Hittorf inferred that there are straight rays emitted from the cathode and that the phosphorescence was caused by the rays striking the tube walls. In 1876 [[Eugen Goldstein]] showed that the rays were emitted perpendicular to the cathode surface, which differentiated them from the incandescent light. [[Eugen Goldstein]] dubbed them [[cathode ray]]s.<ref>{{Cite book |last=Goldstein |first=Eugen |url=https://books.google.com/books?id=7-caAAAAYAAJ&pg=PA279 |title=Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin |date=1876 |publisher=The Academy |pages=279–295, pp 286 |language=de}}</ref><ref name="Whittaker">
{{cite book
 |last=Whittaker
 |first=E.T.
 |author-link=E. T. Whittaker
 |title=[[A History of the Theories of Aether and Electricity]]
 |volume=1
 |publisher=Nelson |place=London
 |year=1951
}}</ref> By the 1870s [[William Crookes]]<ref name=":2">{{Cite journal |last=Crookes |first=William |date=1878 |title=I. On the illumination of lines of molecular pressure, and the trajectory of molecules |url=https://royalsocietypublishing.org/doi/10.1098/rspl.1878.0098 |journal=Proceedings of the Royal Society of London |language=en |volume=28 |issue=190–195 |pages=103–111 |doi=10.1098/rspl.1878.0098 |s2cid=122006529 |issn=0370-1662|url-access=subscription }}</ref> and others were able to evacuate glass tubes below 10<sup>−6</sup> atmospheres, and observed that the glow in the tube disappeared when the pressure was reduced but the glass behind the anode began to glow. Crookes was also able to show that the particles in the cathode rays were negatively charged and could be deflected by an electromagnetic field.<ref name=":2" /><ref name="Martin 1986" />

In 1897, [[J. J. Thomson|Joseph Thomson]] measured the mass of these cathode rays,<ref>{{Cite journal |last=Thomson |first=J. J. |date=1897 |title=XL. Cathode Rays |url=https://doi.org/10.1080/14786449708621070 |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |volume=44 |issue=269 |pages=293–316 |doi=10.1080/14786449708621070 |issn=1941-5982|url-access=subscription }}</ref> proving they were made of particles. These particles, however, were 1800 times lighter than the lightest particle known at that time – a [[hydrogen]] atom. These were originally called ''corpuscles'' and later named electrons by [[George Johnstone Stoney]].<ref>{{Cite journal |last=Stoney | first=George Johnstone |url=https://www.biodiversitylibrary.org/item/51466 |title=Cause of Double Lines in Spectra| journal=The Scientific Transactions of the Royal Dublin Society |year=1891 |volume=4 |location=Dublin |pages=563, pp 583}}</ref>

The control of electron beams that this work led to resulted in significant technology advances in electronic amplifiers and television displays.<ref name="Martin 1986" />

=== Waves, diffraction and quantum mechanics ===
{{See also|Introduction to quantum mechanics|matter wave}}
{{anchor|Figure 4}}[[File:Wave packet propagation (phase faster than group, nondispersive).gif|thumb|Figure 4: Propagation of a wave packet demonstrating the movement of a bundle of waves; see [[group velocity]] for more details.|alt=A video illustrating a wavepacket of electrons, a small bundle.]]
Independent of the developments for electrons in vacuum, at about the same time the components of quantum mechanics were being assembled. In 1924 [[Louis de Broglie]] in his PhD thesis ''Recherches sur la théorie des quanta''<ref name=Broglie>{{cite web |last1=de Broglie |first1=Louis Victor |title=On the Theory of Quanta |url=https://fondationlouisdebroglie.org/LDB-oeuvres/De_Broglie_Kracklauer.pdf |access-date=25 February 2023 |website=Foundation of Louis de Broglie |edition=English translation by A.F. Kracklauer, 2004.}}</ref> introduced his theory of [[electron]] waves. He suggested that an electron around a nucleus could be thought of as [[standing wave]]s,<ref name="Broglie" />{{Rp|pages=Chpt 3}} and that electrons and all matter could be considered as waves. He merged the idea of thinking about them as particles (or corpuscles), and of thinking of them as waves. He proposed that particles are bundles of waves ([[wave packet]]s) that move with a [[group velocity]]<ref name="Broglie" />{{Rp|location=Chpt 1-2}} and have an [[Effective mass (solid-state physics)|effective mass]], see for instance [[#Figure 4|Figure 4]]. Both of these depend upon the energy, which in turn connects to the [[Wave vector|wavevector]] and the relativistic formulation of [[Albert Einstein]] a few years before.<ref>{{Cite book |last=Einstein |first=Albert |url=https://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory |title=Relativity: The Special and General Theory}}</ref>

This rapidly became part of what was called by [[Erwin Schrödinger]] ''undulatory mechanics'',<ref name="Schroedinger">{{Cite journal |last=Schrödinger |first=E. |date=1926 |title=An Undulatory Theory of the Mechanics of Atoms and Molecules |url=https://link.aps.org/doi/10.1103/PhysRev.28.1049 |journal=Physical Review |language=en |volume=28 |issue=6 |pages=1049–1070 |doi=10.1103/PhysRev.28.1049 |bibcode=1926PhRv...28.1049S |issn=0031-899X|url-access=subscription }}</ref> now called the [[Schrödinger equation]] or wave mechanics. As stated by [[Louis de Broglie]] on September 8, 1927, in the preface to the German translation of his theses (in turn translated into English):<ref name="Broglie" />{{Rp|page=v}}<blockquote>''M. Einstein from the beginning has supported my thesis, but it was M. E. [[Erwin Schrödinger|Schrödinger]] who developed the propagation equations of a new theory and who in searching for its solutions has established what has become known as “Wave Mechanics”.''</blockquote>
The Schrödinger equation combines the kinetic energy of waves and the potential energy due to, for electrons, the [[Coulomb potential]]. He was able to explain earlier work such as the quantization of the energy of electrons around atoms in the [[Bohr model]],<ref>{{Cite journal |last=Bohr |first=N. |date=1913 |title=On the constitution of atoms and molecules |url=https://www.tandfonline.com/doi/full/10.1080/14786441308634955 |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |language=en |volume=26 |issue=151 |pages=1–25 |doi=10.1080/14786441308634955 |bibcode=1913PMag...26....1B |issn=1941-5982|url-access=subscription }}</ref> as well as many other phenomena.<ref name="Schroedinger" /> Electron waves as hypothesized<ref name="Broglie" />{{Rp|location=Chpt 1-2}} by de Broglie were automatically part of the solutions to his equation,<ref name="Schroedinger" /> see also [[introduction to quantum mechanics]] and [[matter waves]].

Both the wave nature and the undulatory mechanics approach were experimentally confirmed for electron beams by experiments from two groups performed independently, the first the [[Davisson–Germer experiment]],<ref name="DG0">{{Cite journal |last1=Davisson |first1=C. |last2=Germer |first2=L. H. |date=1927 |title=The Scattering of Electrons by a Single Crystal of Nickel |url=http://dx.doi.org/10.1038/119558a0 |journal=Nature |volume=119 |issue=2998 |pages=558–560 |doi=10.1038/119558a0 |bibcode=1927Natur.119..558D |s2cid=4104602 |issn=0028-0836|url-access=subscription }}</ref><ref name="DG1">{{Cite journal |last1=Davisson |first1=C. |last2=Germer |first2=L. H. |date=1927 |title=Diffraction of Electrons by a Crystal of Nickel |journal=Physical Review |volume=30 |issue=6 |pages=705–740 |doi=10.1103/physrev.30.705 |bibcode=1927PhRv...30..705D |issn=0031-899X|doi-access=free }}</ref><ref name="DG2">{{Cite journal |last1=Davisson |first1=C. J. |last2=Germer |first2=L. H. |date=1928 |title=Reflection of Electrons by a Crystal of Nickel |journal=Proceedings of the National Academy of Sciences |language=en |volume=14 |issue=4 |pages=317–322 |doi=10.1073/pnas.14.4.317 |issn=0027-8424 |pmc=1085484 |pmid=16587341|bibcode=1928PNAS...14..317D |doi-access=free }}</ref><ref name=":0">{{Cite journal |last1=Davisson |first1=C. J. |last2=Germer |first2=L. H. |date=1928 |title=Reflection and Refraction of Electrons by a Crystal of Nickel |journal=Proceedings of the National Academy of Sciences |language=en |volume=14 |issue=8 |pages=619–627 |doi=10.1073/pnas.14.8.619 |issn=0027-8424 |pmc=1085652 |pmid=16587378 |bibcode=1928PNAS...14..619D |doi-access=free }}</ref> the other by [[George Paget Thomson]] and Alexander Reid;<ref>{{Cite journal |last1=Thomson |first1=G. P. |last2=Reid |first2=A. |date=1927 |title=Diffraction of Cathode Rays by a Thin Film |journal=Nature |language=en |volume=119 |issue=3007 |pages=890 |doi=10.1038/119890a0 |bibcode=1927Natur.119Q.890T |s2cid=4122313 |issn=0028-0836|doi-access=free }}</ref> see note{{efn|name=Wlength}} for more discussion. Alexander Reid, who was Thomson's graduate student, performed the first experiments,<ref>{{Cite journal |last=Reid |first=Alexander |date=1928 |title=The diffraction of cathode rays by thin celluloid films |journal=Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character |language=en |volume=119 |issue=783 |pages=663–667 |doi=10.1098/rspa.1928.0121 |bibcode=1928RSPSA.119..663R |s2cid=98311959 |issn=0950-1207|doi-access=free }}</ref> but he died soon after in a motorcycle accident<ref>{{Cite journal |last=Navarro |first=Jaume |date=2010 |title=Electron diffraction chez Thomson: early responses to quantum physics in Britain |url=https://www.cambridge.org/core/product/identifier/S0007087410000026/type/journal_article |journal=The British Journal for the History of Science |language=en |volume=43 |issue=2 |pages=245–275 |doi=10.1017/S0007087410000026 |s2cid=171025814 |issn=0007-0874|url-access=subscription }}</ref> and is rarely mentioned. These experiments were rapidly followed by the first non-relativistic diffraction model for electrons by [[Hans Bethe]]<ref name="Bethe" /> based upon the Schrödinger equation,<ref name="Schroedinger" /> which is very close to how electron diffraction is now described. Significantly, [[Clinton Davisson]] and [[Lester Germer]] noticed<ref name="DG2" /><ref name=":0" /> that their results could not be interpreted using a [[Bragg's law]] approach as the positions were systematically different; the approach of [[Hans Bethe]]<ref name="Bethe" /> which includes the refraction due to the average potential yielded more accurate results. These advances in understanding of electron wave mechanics were important for many developments of electron-based analytical techniques such as [[Seishi Kikuchi]]'s observations of lines due to combined elastic and inelastic scattering,<ref name=":17">{{Cite journal |last=Kikuchi |first=Seishi |date=1928 |title=Diffraction of cathode rays by mica |url=https://scholar.google.com/scholar?output=instlink&q=info:sxVYQV4VcTcJ:scholar.google.com/&hl=en&as_sdt=0,14&as_ylo=1927&as_yhi=1929&scillfp=7509118820046091375&oi=lle |journal=Proceedings of the Imperial Academy |volume=4 |issue=6 |pages=271–274 |doi=10.2183/pjab1912.4.271 |s2cid=4121059 |via=Google Scholar|doi-access=free }}</ref><ref name=":18" /> [[gas electron diffraction]] developed by [[Herman Francis Mark|Herman Mark]] and Raymond Weil,<ref>{{Cite journal |last1=Mark |first1=Herman |last2=Wierl |first2=Raymond |date=1930 |title=Neuere Ergebnisse der Elektronenbeugung |url=http://dx.doi.org/10.1007/bf01497860 |journal=Die Naturwissenschaften |volume=18 |issue=36 |pages=778–786 |doi=10.1007/bf01497860 |bibcode=1930NW.....18..778M |s2cid=9815364 |issn=0028-1042|url-access=subscription }}</ref><ref>{{Cite journal |last1=Mark |first1=Herman |last2=Wiel |first2=Raymond |date=1930 |title=Die ermittlung von molekülstrukturen durch beugung von elektronen an einem dampfstrahl |journal=Zeitschrift für Elektrochemie und angewandte physikalische Chemie |volume=36 |issue=9 |pages=675–676|doi=10.1002/bbpc.19300360921 |s2cid=178706417 }}</ref> diffraction in liquids by Louis Maxwell,<ref name=":20">{{Cite journal |last=Maxwell |first=Louis R. |date=1933 |title=Electron Diffraction by Liquids |url=https://link.aps.org/doi/10.1103/PhysRev.44.73 |journal=Physical Review |language=en |volume=44 |issue=2 |pages=73–76 |doi=10.1103/PhysRev.44.73 |bibcode=1933PhRv...44...73M |issn=0031-899X|url-access=subscription }}</ref> and the first electron microscopes developed by [[Max Knoll]] and [[Ernst Ruska]].<ref name="Knoll1">{{Cite journal |last1=Knoll |first1=M. |last2=Ruska |first2=E. |date=1932 |title=Beitrag zur geometrischen Elektronenoptik. I |url=http://dx.doi.org/10.1002/andp.19324040506 |journal=Annalen der Physik |volume=404 |issue=5 |pages=607–640 |doi=10.1002/andp.19324040506 |bibcode=1932AnP...404..607K |issn=0003-3804|url-access=subscription }}</ref><ref name="Knoll2">{{Cite journal |last1=Knoll |first1=M. |last2=Ruska |first2=E. |date=1932 |title=Das Elektronenmikroskop |url=http://link.springer.com/10.1007/BF01342199 |journal=Zeitschrift für Physik |language=de |volume=78 |issue=5–6 |pages=318–339 |doi=10.1007/BF01342199 |bibcode=1932ZPhy...78..318K |s2cid=186239132 |issn=1434-6001|url-access=subscription }}</ref>

=== Electron microscopes and early electron diffraction ===
{{See also|Transmission Electron Microscopy#History|label 1=History of transmission electron microscopy}}

In order to have a practical microscope or diffractometer, just having an electron beam was not enough, it needed to be controlled. Many developments laid the groundwork of [[electron optics]]; see the paper by Chester J. Calbick for an overview of the early work.<ref>{{Cite journal |last=Calbick |first=C. J. |date=1944 |title=Historical Background of Electron Optics |url=http://aip.scitation.org/doi/10.1063/1.1707371 |journal=Journal of Applied Physics |language=en |volume=15 |issue=10 |pages=685–690 |doi=10.1063/1.1707371 |bibcode=1944JAP....15..685C |issn=0021-8979|url-access=subscription }}</ref> One significant step was the work of [[Heinrich Hertz]] in 1883<ref>{{Citation |last=Hertz |first=Heinrich |title=Introduction to Heinrich Hertz's Miscellaneous Papers (1895) by Philipp Lenard |date=2019 |url=http://dx.doi.org/10.4324/9780429198960-4 |work=Heinrich Rudolf Hertz (1857–1894) |pages=87–88 |publisher=Routledge |doi=10.4324/9780429198960-4 |isbn=978-0-429-19896-0 |s2cid=195494352 |access-date=2023-02-24|url-access=subscription }}</ref> who made a cathode-ray tube with electrostatic and magnetic deflection, demonstrating manipulation of the direction of an electron beam. Others were focusing of electrons by an axial magnetic field by [[Emil Wiechert]] in 1899,<ref>{{Cite journal |last=Wiechert |first=E. |date=1899 |title=Experimentelle Untersuchungen über die Geschwindigkeit und die magnetische Ablenkbarkeit der Kathodenstrahlen |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.18993051203 |journal=Annalen der Physik und Chemie |language=de |volume=305 |issue=12 |pages=739–766 |doi=10.1002/andp.18993051203|bibcode=1899AnP...305..739W }}</ref> improved oxide-coated cathodes which produced more electrons by [[Arthur Wehnelt]] in 1905<ref>{{Cite journal |last=Wehnelt |first=A. |date=1905 |title=X. On the discharge of negative ions by glowing metallic oxides, and allied phenomena |url=https://www.tandfonline.com/doi/full/10.1080/14786440509463347 |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |language=en |volume=10 |issue=55 |pages=80–90 |doi=10.1080/14786440509463347 |issn=1941-5982}}</ref> and the development of the electromagnetic lens in 1926 by [[Hans Busch]].<ref>{{Cite journal |last=Busch |first=H. |date=1926 |title=Berechnung der Bahn von Kathodenstrahlen im axialsymmetrischen elektromagnetischen Felde |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.19263862507 |journal=Annalen der Physik |language=de |volume=386 |issue=25 |pages=974–993 |doi=10.1002/andp.19263862507|bibcode=1926AnP...386..974B |url-access=subscription }}</ref>

{{anchor|Figure 5}}[[File:Ernst Ruska Electron Microscope - Deutsches Museum - Munich-edit.jpg|Figure 5: Replica built in 1980 by Ernst Ruska of the original electron microscope, in the Deutsches Museum in Munich|thumb|alt=An images of a replica of one of the original electron microscopes which is now in a museum in Germany]]

Building an electron microscope involves combining these elements, similar to an [[optical microscope]] but with magnetic or electrostatic lenses instead of glass ones. To this day the issue of who invented the transmission electron microscope is controversial, as discussed by Thomas Mulvey<ref name=Mulvey/> and more recently by Yaping Tao.<ref>{{Cite book |last=Tao |first=Yaping |title=Proceedings of the 3rd International Conference on Contemporary Education, Social Sciences and Humanities (ICCESSH 2018) |date=2018 |publisher=Atlantis Press |isbn=978-94-6252-528-3 |series=Advances in Social Science, Education and Humanities Research |pages=1438–1441 |language=en |chapter=A Historical Investigation of the Debates on the Invention and Invention Rights of Electron Microscope |doi=10.2991/iccessh-18.2018.313 |chapter-url=https://www.atlantis-press.com/proceedings/iccessh-18/25898208 |doi-access=free}}</ref> Extensive additional information can be found in the articles by Martin Freundlich,<ref>{{Cite journal |last=Freundlich |first=Martin M. |date=1963 |title=Origin of the Electron Microscope: The history of a great invention, and of a misconception concerning the inventors, is reviewed. |url=https://www.science.org/doi/10.1126/science.142.3589.185 |journal=Science |language=en |volume=142 |issue=3589 |pages=185–188 |doi=10.1126/science.142.3589.185 |pmid=14057363 |issn=0036-8075|url-access=subscription }}</ref> [[Reinhold Rudenberg|Reinhold Rüdenberg]]<ref name="Rüdenberg">{{Citation |last=Rüdenberg |first=Reinhold |title=Origin and Background of the Invention of the Electron Microscope |date=2010 |url=http://dx.doi.org/10.1016/s1076-5670(10)60005-5 |series=Advances in Imaging and Electron Physics |volume=160 |pages=171–205 |publisher=Elsevier |doi=10.1016/s1076-5670(10)60005-5 |isbn=9780123810175 |access-date=2023-02-11|url-access=subscription }}.</ref> and Mulvey.<ref name=Mulvey>{{Cite journal |last=Mulvey |first=T |date=1962 |title=Origins and historical development of the electron microscope |url=https://iopscience.iop.org/article/10.1088/0508-3443/13/5/303 |journal=British Journal of Applied Physics |volume=13 |issue=5 |pages=197–207 |doi=10.1088/0508-3443/13/5/303 |issn=0508-3443|url-access=subscription }}</ref>

One effort was university based. In 1928, at the [[Technische Hochschule]] in Charlottenburg (now [[Technische Universität Berlin]]), {{ill|Adolf Matthias|de|Adolf Matthias (Elektrotechniker)}} (Professor of High Voltage Technology and Electrical Installations) appointed [[Max Knoll]] to lead a team of researchers to advance research on electron beams and cathode-ray oscilloscopes. The team consisted of several PhD students including [[Ernst Ruska]]. In 1931, Max Knoll and Ernst Ruska<ref name="Knoll1" /><ref name="Knoll2" /> successfully generated magnified images of mesh grids placed over an anode aperture. The device, a replicate of which is shown in [[#Figure 5|Figure 5]], used two  [[magnetic lens]]es to achieve higher magnifications, the first electron microscope. (Max Knoll died in 1969,<ref>{{Cite web |title=Max Knoll |url=https://www.ancientfaces.com/person/max-knoll-birth-1897-death-1969-europe/18955684 |access-date=2023-09-26 |website=AncientFaces |language=en}}</ref> so did not receive a share of the [[Nobel Prize in Physics]] in 1986.)

Apparently independent of this effort was work at [[Siemens-Schuckertwerke|Siemens-Schuckert]] by [[Reinhold Rudenberg]]. According to patent law (U.S. Patent No. 2058914<ref>{{Cite web |last=Rüdenberg |first=Reinhold |title=Apparatus for producing images of objects |url=https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/2058914 |access-date=24 February 2023 |website=Patent Public Search Basic}}</ref> and 2070318,<ref>{{Cite web |last=Rüdenberg |first=Reinhold |title=Apparatus for producing images of objects |url=https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/2070318 |access-date=24 February 2023 |website=Patent Public Search Basic}}</ref> both filed in 1932), he is the inventor of the electron microscope, but it is not clear when he had a working instrument. He stated in a very brief article in 1932<ref>{{Cite journal |last=Rodenberg |first=R. |date=1932 |title=Elektronenmikroskop |url=http://link.springer.com/10.1007/BF01505383 |journal=Die Naturwissenschaften |language=de |volume=20 |issue=28 |pages=522 |doi=10.1007/BF01505383 |bibcode=1932NW.....20..522R |s2cid=263996652 |issn=0028-1042|url-access=subscription }}</ref> that Siemens had been working on this for some years before the patents were filed in 1932, so his effort was parallel to the university effort. He died in 1961,<ref>{{Cite journal |date=April 1962 |title=Orbituary of Reinhold Rudenberg |url=https://pubs.aip.org/physicstoday/article/15/4/106/422766/Reinhold-Rudenberg |access-date=2023-09-26 |website=pubs.aip.org |doi=10.1063/1.3058109|doi-access=free |url-access=subscription }}</ref> so similar to Max Knoll, was not eligible for a share of the Nobel Prize.

These instruments could produce magnified images, but were not particularly useful for electron diffraction; indeed, the wave nature of electrons was not exploited during the development. Key for electron diffraction in microscopes was the advance in 1936 where {{ill|Hans Boersch|de}} showed that they could be used as micro-diffraction cameras with an aperture<ref>{{Cite journal |last=Boersch |first=H. |date=1936 |title=Über das primäre und sekundäre Bild im Elektronenmikroskop. II. Strukturuntersuchung mittels Elektronenbeugung |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.19364190107 |journal=Annalen der Physik |language=de |volume=419 |issue=1 |pages=75–80 |doi=10.1002/andp.19364190107|bibcode=1936AnP...419...75B |url-access=subscription }}</ref>—the birth of [[#Selected area electron diffraction|selected area electron diffraction]].<ref name="HirschEtAl" />{{Rp|location=Chpt 5-6}}

Less controversial was the development of [[#Low-energy electron diffraction|LEED]]—the early experiments of Davisson and Germer used this approach.<ref name=DG1/><ref name=DG2/> As early as 1929 Germer investigated gas adsorption,<ref>{{Cite journal |last=Germer |first=L. H. |date=1929 |title=Eine Anwendung der Elektronenbeugung auf die Untersuchung der Gasadsorption |url=http://link.springer.com/10.1007/BF01375462 |journal=Zeitschrift für Physik |language=de |volume=54 |issue=5–6 |pages=408–421 |doi=10.1007/BF01375462 |bibcode=1929ZPhy...54..408G |s2cid=121097655 |issn=1434-6001|url-access=subscription }}</ref> and in 1932 Harrison E. Farnsworth probed single crystals of copper and silver.<ref>{{Cite journal |last=Farnsworth |first=H. E. |date=1932 |title=Diffraction of Low-Speed Electrons by Single Crystals of Copper and Silver |url=https://link.aps.org/doi/10.1103/PhysRev.40.684 |journal=Physical Review |language=en |volume=40 |issue=5 |pages=684–712 |doi=10.1103/PhysRev.40.684 |bibcode=1932PhRv...40..684F |issn=0031-899X|url-access=subscription }}</ref> However, the vacuum systems available at that time were not good enough to properly control the surfaces, and it took almost forty years before these became available.<ref name="VanHove">{{cite book |last1=Van Hove |first1=Michel A. |url=https://www.springer.com/gp/book/9783642827235 |title=Low-Energy Electron Diffraction |last2=Weinberg |first2=William H. |last3=Chan |first3=Chi-Ming |date=1986 |publisher=Springer-Verlag, Berlin Heidelberg New York |isbn=978-3-540-16262-9 |pages=13–426}}</ref><ref>{{Cite book |url=https://www.worldcat.org/oclc/7276396 |title=Fifty years of electron diffraction : in recognition of fifty years of achievement by the crystallographers and gas diffractionists in the field of electron diffraction |date=1981 |publisher=Published for the International Union of Crystallography by D. Reidel |editor=Goodman, P. (Peter) |isbn=90-277-1246-8 |location=Dordrecht, Holland |oclc=7276396}}</ref> Similarly, it was not until about 1965 that Peter B. Sewell and M. Cohen demonstrated the power of [[Electron diffraction#Reflection high-energy electron diffraction (RHEED)|RHEED]] in a system with a very well controlled vacuum.<ref>{{Cite journal |last1=Sewell |first1=P. B. |last2=Cohen |first2=M. |date=1965 |title=The Observation Of Gas Adsorption Phenomena By Reflection High-Energy Electron Diffraction |url=http://aip.scitation.org/doi/10.1063/1.1754284 |journal=Applied Physics Letters |language=en |volume=7 |issue=2 |pages=32–34 |doi=10.1063/1.1754284 |bibcode=1965ApPhL...7...32S |issn=0003-6951|url-access=subscription }}</ref>

=== Subsequent developments in methods and modelling ===
Despite early successes such as the determination of the positions of hydrogen atoms in NH<sub>4</sub>Cl crystals by W. E. Laschkarew and I. D. Usykin in 1933,<ref>{{Cite journal |last1=Laschkarew |first1=W. E. |last2=Usyskin |first2=I. D. |date=1933 |title=Die Bestimmung der Lage der Wasserstoffionen im NH4Cl-Kristallgitter durch Elektronenbeugung |url=http://link.springer.com/10.1007/BF01331003 |journal=Zeitschrift für Physik |language=de |volume=85 |issue=9–10 |pages=618–630 |doi=10.1007/BF01331003 |bibcode=1933ZPhy...85..618L |s2cid=123199621 |issn=1434-6001|url-access=subscription }}</ref> boric acid by [[John M. Cowley]] in 1953<ref name="CowleyII">{{Cite journal |last=Cowley |first=J. M. |date=1953 |title=Structure analysis of single crystals by electron diffraction. II. Disordered boric acid structure |url=https://scripts.iucr.org/cgi-bin/paper?S0365110X53001423 |journal=Acta Crystallographica |volume=6 |issue=6 |pages=522–529 |doi=10.1107/S0365110X53001423 |bibcode=1953AcCry...6..522C |s2cid=94391285 |issn=0365-110X|doi-access=free |url-access=subscription }}</ref> and orthoboric acid by [[William Houlder Zachariasen]] in 1954,<ref>{{Cite journal |last=Zachariasen |first=W. H. |date=1954 |title=The precise structure of orthoboric acid |url=https://scripts.iucr.org/cgi-bin/paper?S0365110X54000886 |journal=Acta Crystallographica |volume=7 |issue=4 |pages=305–310 |doi=10.1107/S0365110X54000886 |bibcode=1954AcCry...7..305Z |issn=0365-110X|doi-access=free }}</ref> electron diffraction for many years was a qualitative technique used to check samples within electron microscopes. [[John M. Cowley|John M Cowley]] explains in a 1968 paper:<ref>{{Cite journal |last=Cowley |first=J.M. |date=1968 |title=Crystal structure determination by electron diffraction |url=https://linkinghub.elsevier.com/retrieve/pii/0079642568900236 |journal=Progress in Materials Science |language=en |volume=13 |pages=267–321 |doi=10.1016/0079-6425(68)90023-6|url-access=subscription }}</ref> <blockquote>''Thus was founded the belief, amounting in some cases almost to an article of faith, and persisting even to the present day, that it is impossible to interpret the intensities of electron diffraction patterns to gain structural information.''</blockquote>This has changed, in transmission, reflection and for low energies. Some of the key developments (some of which are also described later) from the early days to 2023 have been:
* Fast numerical methods based upon the Cowley–Moodie [[multislice]] algorithm,<ref name=MS1>{{Cite journal |last1=Cowley |first1=J. M. |last2=Moodie |first2=A. F. |date=1957 |title=The scattering of electrons by atoms and crystals. I. A new theoretical approach |url=https://scripts.iucr.org/cgi-bin/paper?S0365110X57002194 |journal=Acta Crystallographica |volume=10 |issue=10 |pages=609–619 |doi=10.1107/S0365110X57002194 |bibcode=1957AcCry..10..609C |issn=0365-110X|url-access=subscription }}</ref><ref>{{Cite journal |last=Ishizuka |first=Kazuo |date=2004 |title=FFT Multislice Method—The Silver Anniversary |url=https://academic.oup.com/mam/article/10/1/34/6912350 |journal=Microscopy and Microanalysis |language=en |volume=10 |issue=1 |pages=34–40 |doi=10.1017/S1431927604040292 |pmid=15306065 |bibcode=2004MiMic..10...34I |s2cid=8016041 |issn=1431-9276|url-access=subscription }}</ref> which only became possible<ref>{{Cite journal |last1=Goodman |first1=P. |last2=Moodie |first2=A. F. |date=1974 |title=Numerical evaluations of N -beam wave functions in electron scattering by the multi-slice method |url=https://scripts.iucr.org/cgi-bin/paper?S056773947400057X |journal=Acta Crystallographica Section A |volume=30 |issue=2 |pages=280–290 |doi=10.1107/S056773947400057X |bibcode=1974AcCrA..30..280G |issn=0567-7394|url-access=subscription }}</ref> once the fast Fourier transform ([[FFT]]) method was developed.<ref>{{Cite journal |last1=Cooley |first1=James W. |last2=Tukey |first2=John W. |date=1965 |title=An algorithm for the machine calculation of complex Fourier series |url=https://www.ams.org/mcom/1965-19-090/S0025-5718-1965-0178586-1/ |journal=Mathematics of Computation |language=en |volume=19 |issue=90 |pages=297–301 |doi=10.1090/S0025-5718-1965-0178586-1 |issn=0025-5718|doi-access=free }}</ref> With these and other numerical methods Fourier transforms are fast,<ref>{{Cite journal |title=The fast Fourier transform |url=https://ieeexplore.ieee.org/document/5217220 |access-date=2023-09-26 |journal=IEEE Spectrum |date=1967 |language=en-US |doi=10.1109/mspec.1967.5217220 |last1=Brigham |first1=E. O. |last2=Morrow |first2=R. E. |volume=4 |issue=12 |pages=63–70 |s2cid=20294294 |url-access=subscription }}</ref> and it became possible to calculate accurate, [[#Dynamical diffraction|dynamical]] diffraction in seconds to minutes with laptops using widely available [[Multislice#Available software|multislice programs]].
* Developments in the [[convergent-beam electron diffraction]] approach.  Building on the original work of [[Walther Kossel]] and [[Gottfried Möllenstedt]] in 1939,<ref name=KM/> it was extended by Peter Goodman and Gunter Lehmpfuhl,<ref name=":4">{{cite journal |last1=Goodman |first1=P. |last2=Lehmpfuhl |first2=G. |title=Observation of the breakdown of Friedel's law in electron diffraction and symmetry determination from zero-layer interactions |journal=Acta Crystallographica Section A |date=1968 |volume=24 |issue=3 |pages=339–347 |doi=10.1107/S0567739468000677|bibcode=1968AcCrA..24..339G }}</ref> then mainly by the groups of [[John Steeds (scientist)|John Steeds]]<ref name="Buxton1">{{cite journal |last1=Buxton |first1=B. F. |last2=Eades |first2=J. A. |last3=Steeds |first3=John Wickham |last4=Rackham |first4=G. M. |last5=Frank |first5=Frederick Charles |title=The symmetry of electron diffraction zone axis patterns |journal=Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences |date=1976 |volume=281 |issue=1301 |pages=171–194 |doi=10.1098/rsta.1976.0024 |bibcode=1976RSPTA.281..171B |s2cid=122890943 |url=https://doi.org/10.1098/rsta.1976.0024|url-access=subscription }}</ref><ref name=":5">{{Cite journal |last1=Steeds |first1=J. W. |last2=Vincent |first2=R. |date=1983 |title=Use of high-symmetry zone axes in electron diffraction in determining crystal point and space groups |url=https://scripts.iucr.org/cgi-bin/paper?S002188988301050X |journal=Journal of Applied Crystallography |volume=16 |issue=3 |pages=317–324 |doi=10.1107/S002188988301050X |bibcode=1983JApCr..16..317S |issn=0021-8898|url-access=subscription }}</ref><ref>{{Cite journal |last=Bird |first=D. M. |date=1989 |title=Theory of zone axis electron diffraction |url=https://onlinelibrary.wiley.com/doi/10.1002/jemt.1060130202 |journal=Journal of Electron Microscopy Technique |language=en |volume=13 |issue=2 |pages=77–97 |doi=10.1002/jemt.1060130202 |pmid=2681572 |issn=0741-0581|url-access=subscription }}</ref> and Michiyoshi Tanaka<ref name=":6">{{Cite journal |last1=Tanaka |first1=M. |last2=Saito |first2=R. |last3=Sekii |first3=H. |date=1983 |title=Point-group determination by convergent-beam electron diffraction |url=https://scripts.iucr.org/cgi-bin/paper?S010876738300080X |journal=Acta Crystallographica Section A |volume=39 |issue=3 |pages=357–368 |doi=10.1107/S010876738300080X |bibcode=1983AcCrA..39..357T |issn=0108-7673|url-access=subscription }}</ref><ref>{{Cite journal |last1=Tanaka |first1=M. |last2=Saito |first2=R. |last3=Watanabe |first3=D. |date=1980 |title=Symmetry determination of the room-temperature form of LnNbO 4 (Ln = La,Nd) by convergent-beam electron diffraction |url=https://scripts.iucr.org/cgi-bin/paper?S0567739480000800 |journal=Acta Crystallographica Section A |volume=36 |issue=3 |pages=350–352 |doi=10.1107/S0567739480000800 |bibcode=1980AcCrA..36..350T |s2cid=98184340 |issn=0567-7394|url-access=subscription }}</ref> who showed how to determine [[point group]]s and [[space group]]s. It can also be used for higher-level refinements of the electron density;<ref>{{Cite book |last1=Spence |first1=J. C. H. |url=http://link.springer.com/10.1007/978-1-4899-2353-0 |title=Electron Microdiffraction |last2=Zuo |first2=J. M. |date=1992 |publisher=Springer US |isbn=978-1-4899-2355-4 |location=Boston, MA |language=en |doi=10.1007/978-1-4899-2353-0|s2cid=45473741 }}</ref>{{Rp|location=Chpt 4}} for a brief history see [[Convergent-beam electron diffraction#History|CBED history]]. In many cases this is the best method to determine symmetry.<ref name="Buxton1" /><ref name="Atlas" />
* The development of new approaches to reduce dynamical effects such as [[precession electron diffraction]] and three-dimensional diffraction methods. Averaging over different directions has, empirically, been found to significantly reduce dynamical diffraction effects, e.g.,<ref name="LDMPD">{{Cite book |last=Marks |first=Laurence |url=https://link.springer.com/10.1007/978-94-007-5580-2 |title=Uniting Electron Crystallography and Powder Diffraction |date=2012 |publisher=Springer Netherlands |isbn=978-94-007-5579-6 |editor-last=Kolb |editor-first=Ute |series=NATO Science for Peace and Security Series B: Physics and Biophysics |location=Dordrecht |pages=281–291 |language=en |doi=10.1007/978-94-007-5580-2 |bibcode=2012uecp.book.....K |editor-last2=Shankland |editor-first2=Kenneth |editor-last3=Meshi |editor-first3=Louisa |editor-last4=Avilov |editor-first4=Anatoly |editor-last5=David |editor-first5=William I.F}}</ref> see [[Precession electron diffraction#Historical development|PED history]] for further details. Not only is it easier to identify known structures with this approach, it can also be used to solve unknown structures in some cases<ref name="White" /><ref name="LDMPD" /><ref name="Lukas1" /> – see [[precession electron diffraction]] for further information.
* The development of experimental methods exploiting [[ultra-high vacuum]] technologies (e.g. the approach described by {{ill|Daniel J. Alpert|de|Daniel Alpert}} in 1953<ref name="Alpert">{{Cite journal |last=Alpert |first=D. |date=1953 |title=New Developments in the Production and Measurement of Ultra High Vacuum |url=http://aip.scitation.org/doi/10.1063/1.1721395 |journal=Journal of Applied Physics |language=en |volume=24 |issue=7 |pages=860–876 |doi=10.1063/1.1721395 |bibcode=1953JAP....24..860A |issn=0021-8979|url-access=subscription }}</ref>) to better control surfaces, making [[Electron diffraction#Low-energy electron diffraction (LEED)|LEED]] and [[Electron diffraction#Reflection high-energy electron diffraction (RHEED)|RHEED]] more reliable and reproducible techniques. In the early days the surfaces were not well controlled; with these technologies they can both be cleaned and remain clean for hours to days, a key component of [[surface science]].<ref name="Alpert" /><ref name="Oura" /> 
* Fast and accurate methods to calculate intensities for [[Electron diffraction#Low-energy electron diffraction (LEED)|LEED]] so it could be used to determine atomic positions, for instance references.<ref>{{Cite journal |last=Kambe |first=Kyozaburo |date=1967 |title=Theory of Low-Energy Electron Diffraction |journal=Zeitschrift für Naturforschung A |volume=22 |issue=3 |pages=322–330 |doi=10.1515/zna-1967-0305 |s2cid=96851585 |issn=1865-7109|doi-access=free }}</ref><ref>{{Cite journal |last=McRae |first=E.G. |date=1968 |title=Electron diffraction at crystal surfaces |url=https://linkinghub.elsevier.com/retrieve/pii/0039602868900587 |journal=Surface Science |language=en |volume=11 |issue=3 |pages=479–491 |doi=10.1016/0039-6028(68)90058-7|url-access=subscription }}</ref><ref name="Pendry71" /> These have been extensively exploited to determine the structure of many surfaces, and the arrangement of foreign atoms on surfaces.<ref name="LEEDB" />
* Methods to simulate the intensities in [[Electron diffraction#Reflection high-energy electron diffraction (RHEED)|RHEED]], so it can be used semi-quantitatively to understand surfaces during growth and thereby to control the resulting materials.<ref name="Ichimiya" /> 
* The development of advanced [[detectors for transmission electron microscopy]] such as [[charge-coupled device]]<ref name="SpenceZuo">{{Cite journal |last1=Spence |first1=J. C. H. |last2=Zuo |first2=J. M. |date=1988 |title=Large dynamic range, parallel detection system for electron diffraction and imaging |url=http://aip.scitation.org/doi/10.1063/1.1140039 |journal=Review of Scientific Instruments |language=en |volume=59 |issue=9 |pages=2102–2105 |doi=10.1063/1.1140039 |bibcode=1988RScI...59.2102S |issn=0034-6748|url-access=subscription }}</ref> and direct electron detectors,<ref name="PDetect">{{Cite journal |last1=Faruqi |first1=A. R. |last2=Cattermole |first2=D. M. |last3=Henderson |first3=R. |last4=Mikulec |first4=B. |last5=Raeburn |first5=C. |date=2003 |title=Evaluation of a hybrid pixel detector for electron microscopy |url=https://www.sciencedirect.com/science/article/pii/S0304399102003364 |journal=Ultramicroscopy |language=en |volume=94 |issue=3 |pages=263–276 |doi=10.1016/S0304-3991(02)00336-4 |pmid=12524196 |issn=0304-3991|url-access=subscription }}</ref> which improve the accuracy and reliability of intensity measurements. These have efficiencies and accuracies that can be a thousand or more times that of the photographic film used in the earliest experiments,<ref name="SpenceZuo" /><ref name="PDetect" /> with the information available in real time rather than requiring [[photographic processing]] after the experiment.<ref name="SpenceZuo" /><ref name="PDetect" />