Editing Electron diffraction (section)

=== 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" />