electron crystallography

The general approach dates back to the work in 1924 of Louis de Broglie in his PhD thesis Recherches sur la théorie des quanta{{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.}} where he introduced the concept of electrons as matter waves. The wave nature was experimentally confirmed for electron beams in the work of two groups, the first the Davisson–Germer experiment,{{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 |bibcode=1927Natur.119..558D |doi=10.1038/119558a0 |issn=0028-0836 |s2cid=4104602|url-access=subscription }}{{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 |bibcode=1927PhRv...30..705D |doi=10.1103/physrev.30.705 |issn=0031-899X |doi-access=free}}{{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 |bibcode=1928PNAS...14..317D |doi=10.1073/pnas.14.4.317 |issn=0027-8424 |pmc=1085484 |pmid=16587341 |doi-access=free}}{{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 |bibcode=1928PNAS...14..619D |doi=10.1073/pnas.14.8.619 |issn=0027-8424 |pmc=1085652 |pmid=16587378 |doi-access=free}} the other by George Paget Thomson and Alexander Reid.{{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 |bibcode=1927Natur.119Q.890T |doi=10.1038/119890a0 |issn=0028-0836 |s2cid=4122313 |doi-access=free}} Alexander Reid, who was Thomson's graduate student, performed the first experiments,{{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 |bibcode=1928RSPSA.119..663R |doi=10.1098/rspa.1928.0121 |issn=0950-1207 |s2cid=98311959 |doi-access=free}} but he died soon after in a motorcycle accident.{{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 |issn=0007-0874 |s2cid=171025814|url-access=subscription }} These experiments were rapidly followed by the first non-relativistic diffraction model for electrons by Hans Bethe{{Cite journal |last=Bethe |first=H. |date=1928 |title=Theorie der Beugung von Elektronen an Kristallen |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.19283921704 |journal=Annalen der Physik |language=de |volume=392 |issue=17 |pages=55–129 |doi=10.1002/andp.19283921704|bibcode=1928AnP...392...55B |url-access=subscription }} based upon the Schrödinger equation,{{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 }} which is very close to how electron diffraction is now described. Significantly, Clinton Davisson and Lester Germer noticed that their results could not be interpreted using a Bragg's law approach as the positions were systematically different; the approach of Hans Bethe which includes both multiple scattering and the refraction due to the average potential yielded more accurate results. Very quickly there were multiple advances, for instance Seishi Kikuchi's observations of lines that can be used for crystallographic indexing due to combined elastic and inelastic scattering,{{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}} gas electron diffraction developed by Herman Mark and Raymond Weil,{{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 |bibcode=1930NW.....18..778M |doi=10.1007/bf01497860 |issn=0028-1042 |s2cid=9815364|url-access=subscription }}{{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}} diffraction in liquids by Louis Maxwell,{{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 |bibcode=1933PhRv...44...73M |doi=10.1103/PhysRev.44.73 |issn=0031-899X|url-access=subscription }} and the first electron microscopes developed by Max Knoll and Ernst Ruska.{{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 |bibcode=1932AnP...404..607K |doi=10.1002/andp.19324040506 |issn=0003-3804|url-access=subscription }}{{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 |bibcode=1932ZPhy...78..318K |doi=10.1007/BF01342199 |issn=1434-6001 |s2cid=186239132|url-access=subscription }}

Despite early successes such as the determination of the positions of hydrogen atoms in NH₄Cl crystals by W. E. Laschkarew and I. D. Usykin in 1933,{{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 |bibcode=1933ZPhy...85..618L |doi=10.1007/BF01331003 |issn=1434-6001 |s2cid=123199621|url-access=subscription }} boric acid by John M. Cowley in 1953{{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 |bibcode=1953AcCry...6..522C |doi=10.1107/S0365110X53001423 |issn=0365-110X |s2cid=94391285 |doi-access=free|url-access=subscription }} and orthoboric acid by William Houlder Zachariasen in 1954,{{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 |bibcode=1954AcCry...7..305Z |doi=10.1107/S0365110X54000886 |issn=0365-110X |doi-access=free}} electron diffraction for many years was a qualitative technique used to check samples within electron microscopes. John M Cowley explains in a 1968 paper:{{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 }}

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.

A second key set of work was that by the group of Boris Vainshtein who demonstrated solving the structure of many different materials such as clays and micas using powder diffraction patterns, a success attributed to the samples being relatively thin.{{Cite book |last=Vaĭnshteĭn |first=B. K. |url=https://www.worldcat.org/oclc/681437461 |title=Structure analysis by electron diffraction |date=1964 |publisher=Pergamon Press |isbn=978-0-08-010241-2 |location=Oxford |oclc=681437461}} (Since the advent of precession electron diffraction{{Cite journal |last1=Vincent |first1=R. |last2=Midgley |first2=P.A. |date=1994 |title=Double conical beam-rocking system for measurement of integrated electron diffraction intensities |url=https://doi.org/10.1016/0304-3991(94)90039-6 |journal=Ultramicroscopy |volume=53 |issue=3 |pages=271–282 |doi=10.1016/0304-3991(94)90039-6 |issn=0304-3991|url-access=subscription }} it has become clear that averaging over many different electron beam directions and thicknesses significantly reduces dynamical diffraction effects,Own, C. S.: PhD thesis, System Design and Verification of the Precession Electron Diffraction Technique, Northwestern University, 2005,http://www.numis.northwestern.edu/Research/Current/precession.shtml{{Cite journal |last1=Own |first1=C. S. |last2=Marks |first2=L. D. |last3=Sinkler |first3=W. |date=2006 |title=Precession electron diffraction 1: multislice simulation |url=https://scripts.iucr.org/cgi-bin/paper?S0108767306032892 |journal=Acta Crystallographica Section A |volume=62 |issue=6 |pages=434–443 |doi=10.1107/S0108767306032892 |pmid=17057352 |issn=0108-7673|url-access=subscription }} so was probably also important.)

More complete crystallographic analysis of intensity data was slow to develop. One of the key steps was the demonstration in 1976 by Douglas L. Dorset and Herbert A. Hauptman that conventional direct methods for x-ray crystallography could be used.{{Cite journal |last1=Dorset |first1=Douglas L. |last2=Hauptman |first2=Herbert A. |date=1976 |title=Direct phase determination for quasi-kinematical electron diffraction intensity data from organic microcrystals |url=https://doi.org/10.1016/0304-3991(76)90034-6 |journal=Ultramicroscopy |volume=1 |issue=3–4 |pages=195–201 |doi=10.1016/0304-3991(76)90034-6 |pmid=1028188 |issn=0304-3991|url-access=subscription }} Another was the demonstration in 1986 that a Patterson function could be powerful in the seminal solution of the silicon (111) 7x7 reconstructed surface by Kunio Takanayagi using ultra-high vacuum electron diffraction.{{Cite journal |last1=Takayanagi |first1=K. |last2=Tanishiro |first2=Y. |last3=Takahashi |first3=M. |last4=Takahashi |first4=S. |date=1985 |title=Structural analysis of Si(111)-7×7 by UHV-transmission electron diffraction and microscopy |url=http://dx.doi.org/10.1116/1.573160 |journal=Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films |volume=3 |issue=3 |pages=1502–1506 |bibcode=1985JVSTA...3.1502T |doi=10.1116/1.573160 |issn=0734-2101|url-access=subscription }}{{Cite journal |last1=Takayanagi |first1=Kunio |last2=Tanishiro |first2=Yasumasa |last3=Takahashi |first3=Shigeki |last4=Takahashi |first4=Masaetsu |date=1985 |title=Structure analysis of Si(111)-7 × 7 reconstructed surface by transmission electron diffraction |url=https://doi.org/10.1016/0039-6028(85)90753-8 |journal=Surface Science |volume=164 |issue=2–3 |pages=367–392 |doi=10.1016/0039-6028(85)90753-8 |bibcode=1985SurSc.164..367T |issn=0039-6028|url-access=subscription }} More complete analyses were the demonstration that classical inversion methods could be used for surfaces in 1997 by Dorset and Laurence D. Marks, and in 1998 the work by Jon Gjønnes who combined three-dimensional electron diffraction with precession electron diffraction and direct methods to solve an intermetallic, also using dynamical refinements.{{Cite journal |last1=Gjønnes |first1=J. |last2=Hansen |first2=V. |last3=Berg |first3=B. S. |last4=Runde |first4=P. |last5=Cheng |first5=Y. F. |last6=Gjønnes |first6=K. |last7=Dorset |first7=D. L. |last8=Gilmore |first8=C. J. |date=1998-05-01 |title=Structure Model for the Phase AlmFe Derived from Three-Dimensional Electron Diffraction Intensity Data Collected by a Precession Technique. Comparison with Convergent-Beam Diffraction |url=https://scripts.iucr.org/cgi-bin/paper?S0108767397017030 |journal=Acta Crystallographica Section A |volume=54 |issue=3 |pages=306–319 |doi=10.1107/S0108767397017030|bibcode=1998AcCrA..54..306G |url-access=subscription }}

At the same time as approaches to invert diffraction data using electrons were established, the resolution of electron microscopes became good enough that images could be combined with diffraction information. At first resolution was poor, with in 1956 James Menter publishing the first electron microscope images showing the lattice structure of a material at 1.2nm resolution.{{Cite journal |date=1956 |title=The direct study by electron microscopy of crystal lattices and their imperfections |url=https://royalsocietypublishing.org/doi/10.1098/rspa.1956.0117 |journal=Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences |language=en |volume=236 |issue=1204 |pages=119–135 |doi=10.1098/rspa.1956.0117 |bibcode=1956RSPSA.236..119M |issn=0080-4630 |last1=Menter |first1=J. W. |url-access=subscription }} In 1968 Aaron Klug and David DeRosier used electron microscopy to visualise the structure of the tail of bacteriophage T4, a common virus, a key step in the use of electrons for macromolecular structure determination.{{cite journal |last1=De Rosier |first1=D. J. |last2=Klug |first2=A. |date=1968 |title=Reconstruction of Three Dimensional Structures from Electron Micrographs |journal=Nature |volume=217 |issue=5124 |pages=130–134 |bibcode=1968Natur.217..130D |doi=10.1038/217130a0 |pmid=23610788}} The first quantitative matching of atomic scale images and dynamical simulations was published in 1972 by J. G. Allpress, E. A. Hewat, A. F. Moodie and J. V. Sanders.{{Cite journal |last1=Allpress |first1=J. G. |last2=Hewat |first2=E. A. |last3=Moodie |first3=A. F. |last4=Sanders |first4=J. V. |date=1972 |title=n -Beam lattice images. I. Experimental and computed images from W 4 Nb 26 O 77 |url=https://scripts.iucr.org/cgi-bin/paper?S0567739472001433 |journal=Acta Crystallographica Section A |volume=28 |issue=6 |pages=528–536 |doi=10.1107/S0567739472001433 |bibcode=1972AcCrA..28..528A |issn=0567-7394|url-access=subscription }} In the early 1980s the resolution of electron microscopes was now sufficient to resolve the atomic structure of materials, for instance with the 600 kV instrument led by Vernon Cosslett,{{Cite journal |date=1980-03-12 |title=Principles and performance of a 600 kV high resolution electron microscope |url=https://royalsocietypublishing.org/doi/10.1098/rspa.1980.0018 |journal=Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences |language=en |volume=370 |issue=1740 |pages=1–16 |doi=10.1098/rspa.1980.0018 |bibcode=1980RSPSA.370....1C |issn=0080-4630 |last1=Cosslett |first1=V. E. |url-access=subscription }} so combinations of high-resolution transmission electron microscopy and diffraction became standard across many areas of science.{{Cite book |last1=Buseck |first1=Peter |url=https://books.google.com/books?id=s-5OzwEACAAJ |title=High-resolution Transmission Electron Microscopy and Associated Techniques |last2=Cowley |first2=John M |last3=Eyring |first3=Leyroy |date=1992 |publisher=Oxford University Press |language=en}} Most of the research published using these approaches is described as electron microscopy, without the addition of the term electron crystallography.

It can complement X-ray crystallography for studies of very small crystals (<0.1 micrometers), both inorganic, organic, and proteins, such as membrane proteins, that cannot easily form the large 3-dimensional crystals required for that process. Protein structures are usually determined from either 2-dimensional crystals (sheets or helices), polyhedrons such as viral capsids, or dispersed individual proteins. Electrons can be used in these situations, whereas X-rays cannot, because electrons interact more strongly with atoms than X-rays do. Thus, X-rays will travel through a thin 2-dimensional crystal without diffracting significantly, whereas electrons can be used to form an image. Conversely, the strong interaction between electrons and protons makes thick (e.g. 3-dimensional > 1 micrometer) crystals impervious to electrons, which only penetrate short distances.

One of the main difficulties in X-ray crystallography is determining phases in the diffraction pattern. Because of the complexity of X-ray lenses, it is difficult to form an image of the crystal being diffracted, and hence phase information is lost. Fortunately, electron microscopes can resolve atomic structure in real space and the crystallographic structure factor phase information can be experimentally determined from an image's Fourier transform. The Fourier transform of an atomic resolution image is similar, but different, to a diffraction pattern—with reciprocal lattice spots reflecting the symmetry and spacing of a crystal.{{cite journal|author1=R Hovden |author2=Y Jiang |author3=HL Xin |author4=LF Kourkoutis |title= Periodic Artifact Reduction in Fourier Transforms of Full Field Atomic Resolution Images |journal= Microscopy and Microanalysis |volume=21|issue=2 |pages=436–441 |year=2015|doi =10.1017/S1431927614014639|pmid=25597865 |bibcode = 2015MiMic..21..436H |arxiv=2210.09024 |s2cid=22435248 }} Aaron Klug was the first to realize that the phase information could be read out directly from the Fourier transform of an electron microscopy image that had been scanned into a computer, already in 1968. For this, and his studies on virus structures and transfer-RNA, Klug received the Nobel Prize for chemistry in 1982.

A common problem to X-ray crystallography and electron crystallography is radiation damage, by which especially organic molecules and proteins are damaged as they are being imaged, limiting the resolution that can be obtained. This is especially troublesome in the setting of electron crystallography, where that radiation damage is focused on far fewer atoms. One technique used to limit radiation damage is electron cryomicroscopy, in which the samples undergo cryofixation and imaging takes place at liquid nitrogen or even liquid helium temperatures. Because of this problem, X-ray crystallography has been much more successful in determining the structure of proteins that are especially vulnerable to radiation damage. Radiation damage was recently investigated using MicroED{{Cite journal|last1=Nannenga|first1=Brent L|last2=Shi|first2=Dan|last3=Leslie|first3=Andrew G W|last4=Gonen|first4=Tamir|date=2014-08-03|title=High-resolution structure determination by continuous-rotation data collection in MicroED|journal=Nature Methods|volume=11|issue=9|pages=927–930|doi=10.1038/nmeth.3043|pmid=25086503|pmc=4149488|issn=1548-7091}}{{Cite journal|last1=Hattne|first1=Johan|last2=Shi|first2=Dan|last3=Glynn|first3=Calina|last4=Zee|first4=Chih-Te|last5=Gallagher-Jones|first5=Marcus|last6=Martynowycz|first6=Michael W.|last7=Rodriguez|first7=Jose A.|last8=Gonen|first8=Tamir|date=2018|title=Analysis of Global and Site-Specific Radiation Damage in Cryo-EM|journal=Structure|volume=26|issue=5|pages=759–766.e4|doi=10.1016/j.str.2018.03.021|pmid=29706530|issn=0969-2126|pmc=6333475}} of thin 3D crystals in a frozen hydrated state.

The first electron crystallographic protein structure to achieve atomic resolution was bacteriorhodopsin, determined by Richard Henderson and coworkers at the Medical Research Council Laboratory of Molecular Biology in 1990.{{cite journal|last1=Henderson|first1=R.|last2=Baldwin|first2=J.M.|last3=Ceska|first3=T.A.|last4=Zemlin|first4=F|last5=Beckmann|first5=E.|last6=Downing|first6=K.H.|title=Model for the structure of bacteriorhodopsin based on high-resolution electron cryo-microscopy|date=June 1990|volume=213|issue=4|pages=899–929|doi=10.1016/S0022-2836(05)80271-2|pmid=2359127|journal=J Mol Biol}} However, already in 1975 Unwin and Henderson had determined the first membrane protein structure at intermediate resolution (7 Ångström), showing for the first time the internal structure of a membrane protein, with its alpha-helices standing perpendicular to the plane of the membrane. Since then, several other high-resolution structures have been determined by electron crystallography, including the light-harvesting complex,{{cite journal | pmid = 8107845 | doi=10.1038/367614a0 | volume=367 | issue=6464 | title=Atomic model of plant light-harvesting complex by electron crystallography |date=February 1994 | journal=Nature | pages=614–21 | last1 = Kühlbrandt | first1 = Werner | last2 = Wang | first2 = Da Neng | last3 = Fujiyoshi | first3 = Yoshinori|bibcode = 1994Natur.367..614K | s2cid=4357116 }} the nicotinic acetylcholine receptor,{{cite journal | pmid = 12827192 | doi=10.1038/nature01748 | volume=423 | issue=6943 | title=Structure and gating mechanism of the acetylcholine receptor pore |date=June 2003 | journal=Nature | pages=949–55 | last1 = Miyazawa | first1 = Atsuo | last2 = Fujiyoshi | first2 = Yoshinori | last3 = Unwin | first3 = Nigel|bibcode = 2003Natur.423..949M | s2cid=205209809 }} and the bacterial flagellum.{{cite journal | pmid = 12904785 | doi=10.1038/nature01830 | volume=424 | issue=6949 | title=Complete atomic model of the bacterial flagellar filament by electron cryomicroscopy |date=August 2003 | journal=Nature | pages=643–50 | last1 = Yonekura | first1 = Koji | last2 = Maki-Yonekura | first2 = Saori | last3 = Namba | first3 = Keiichi|bibcode = 2003Natur.424..643Y | s2cid=4301660 }} The highest resolution protein structure solved by electron crystallography of 2D crystals is that of the water channel aquaporin-0.{{Cite journal|last1=Gonen|first1=Tamir|last2=Cheng|first2=Yifan|last3=Sliz|first3=Piotr|last4=Hiroaki|first4=Yoko|last5=Fujiyoshi|first5=Yoshinori|last6=Harrison|first6=Stephen C.|last7=Walz|first7=Thomas|date=2005|title=Lipid–protein interactions in double-layered two-dimensional AQP0 crystals|journal=Nature|volume=438|issue=7068|pages=633–638|doi=10.1038/nature04321|pmid=16319884|pmc=1350984|issn=0028-0836|bibcode=2005Natur.438..633G}} In 2012, Jan Pieter Abrahams and coworkers extended electron crystallography to 3D protein nanocrystals{{Cite journal |last1=Nederlof |first1=I. |last2=van Genderen |first2=E. |last3=Li |first3=Y.-W. |last4=Abrahams |first4=J. P. |date=2013-07-01 |title=A Medipix quantum area detector allows rotation electron diffraction data collection from submicrometre three-dimensional protein crystals |url=http://scripts.iucr.org/cgi-bin/paper?ba5186 |journal=Acta Crystallographica Section D |language=en |volume=69 |issue=7 |pages=1223–1230 |doi=10.1107/S0907444913009700 |issn=0907-4449 |pmc=3689525 |pmid=23793148|bibcode=2013AcCrD..69.1223N }} by rotation electron diffraction (RED).{{Cite journal |last1=Zhang |first1=Daliang |last2=Oleynikov |first2=Peter |last3=Hovmöller |first3=Sven |last4=Zou |first4=Xiaodong |date=March 2010 |title=Collecting 3D electron diffraction data by the rotation method |journal=Zeitschrift für Kristallographie |language=en |volume=225 |issue=2–3 |pages=94–102 |doi=10.1524/zkri.2010.1202 |bibcode=2010ZK....225...94Z |s2cid=55751260 |issn=0044-2968|doi-access=free }}

File:Tantalum oxide EM image.jpg

File:Tant-ED.jpg

Electron crystallographic studies on inorganic crystals using high-resolution electron microscopy (HREM) images were first performed by Aaron Klug in 1978Klug, A (1978/79) Image Analysis and Reconstruction in the Electron Microscopy of Biological Macromolecules Chemica Scripta vol 14, p. 245-256.

and by Sven Hovmöller and coworkers in 1984.{{cite journal|last1=Hovmöller|first1=Sven|last2=Sjögren|first2=Agneta|last3=Farrants|first3=George|last4=Sundberg|first4=Margareta|last5=Marinder|first5=Bengt-Olov|title=Accurate atomic positions from electron microscopy|journal=Nature|volume=311|issue=5983|pages=238|year=1984|doi=10.1038/311238a0|bibcode = 1984Natur.311..238H }} HREM images were used because they allow to select (by computer software) only the very thin regions close to the edge of the crystal for structure analysis (see also crystallographic image processing). This is of crucial importance since in the thicker parts of the crystal the exit-wave function (which carries the information about the intensity and position of the projected atom columns) is no longer linearly related to the projected crystal structure. Moreover, not only do the HREM images change their appearance with increasing crystal thickness, they are also very sensitive to the chosen setting of the defocus Δf of the objective lens (see the HREM images of GaN for example). To cope with this complexity methods based upon the Cowley-Moodie multislice algorithm{{Cite journal |last1=Cowley |first1=J. M. |last2=Moodie |first2=A. F. |date=1957-10-01 |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 }}{{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 }} and non-linear imaging theory{{Cite journal |last=Ishizuka |first=Kazuo |date=1980 |title=Contrast transfer of crystal images in TEM |url=https://linkinghub.elsevier.com/retrieve/pii/030439918090011X |journal=Ultramicroscopy |language=en |volume=5 |issue=1–3 |pages=55–65 |doi=10.1016/0304-3991(80)90011-X|url-access=subscription }} have been developed to simulate images; this only became possible{{Cite journal |last1=Goodman |first1=P. |last2=Moodie |first2=A. F. |date=1974-03-01 |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 A |volume=30 |issue=2 |pages=280–290 |doi=10.1107/S056773947400057X |bibcode=1974AcCrA..30..280G |issn=0567-7394|url-access=subscription }} once the FFT method was developed.{{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 }}

In addition to electron microscopy images, it is also possible to use electron diffraction (ED) patterns for crystal structure determination.B. K. Vainshtein (1964), Structure Analysis by Electron Diffraction, Pergamon Press OxfordD. L. Dorset (1995), [https://books.google.com/books?id=mWEB9WpktcUC Structural Electron Crystallography], Plenum Publishing Corporation {{ISBN|0-306-45049-6}} The utmost care must be taken to record such ED patterns from the thinnest areas in order to keep most of the structure related intensity differences between the reflections (quasi-kinematical diffraction conditions). Just as with X-ray diffraction patterns, the important crystallographic structure factor phases are lost in electron diffraction patterns and must be uncovered by special crystallographic methods such as direct methods, maximum likelihood or (more recently) by the charge-flipping method. On the other hand, ED patterns of inorganic crystals have often a high resolution (= interplanar spacings with high Miller indices) much below 1 Ångström. This is comparable to the point resolution of the best electron microscopes. Under favourable conditions it is possible to use ED patterns from a single orientation to determine the complete crystal structure.{{cite journal|doi=10.1107/S0108767399009605|last1=Weirich|first1=TE|last2=Zou|first2=X|last3=Ramlau|first3=R|last4=Simon|first4=A|last5=Cascarano|first5=GL|last6=Giacovazzo|first6=C|last7=Hovmöller|first7=S|title=Structures of nanometre-size crystals determined from selected-area electron diffraction data|journal=Acta Crystallographica A|volume=56|issue=Pt 1|pages=29–35|year=2000|pmid=10874414}} Alternatively a hybrid approach can be used which uses HRTEM images for solving and intensities from ED for refining the crystal structure.{{cite journal|last1=Zandbergen|first1=H. W.|title=Structure Determination of Mg5Si6 Particles in Al by Dynamic Electron Diffraction Studies|journal=Science|volume=277|issue=5330|pages=1221–1225|year=1997|doi=10.1126/science.277.5330.1221}}{{cite journal|last1=Weirich|first1=Thomas E.|last2=Ramlau|first2=Reiner|last3=Simon|first3=Arndt|last4=Hovmöller|first4=Sven|last5=Zou|first5=Xiaodong|title=A crystal structure determined with 0.02 Å accuracy by electron microscopy|journal=Nature|volume=382|issue=6587|pages=144|year=1996|doi=10.1038/382144a0|bibcode = 1996Natur.382..144W |s2cid=4327149 }}

Recent progress for structure analysis by ED was made by introducing the Vincent-Midgley{{Cite journal |last1=Vincent |first1=R. |last2=Midgley |first2=P. A. |date=1994-03-01 |title=Double conical beam-rocking system for measurement of integrated electron diffraction intensities |url=https://dx.doi.org/10.1016/0304-3991%2894%2990039-6 |journal=Ultramicroscopy |language=en |volume=53 |issue=3 |pages=271–282 |doi=10.1016/0304-3991(94)90039-6 |issn=0304-3991|url-access=subscription }} precession technique for recording electron diffraction patterns.[http://www.numis.northwestern.edu/Research/Current/precession.shtml Precession Electron Diffraction] The thereby obtained intensities are usually much closer to the kinematical intensities,{{Cite journal |last1=Marks |first1=L.D. |last2=Sinkler |first2=W. |date=2003 |title=Sufficient Conditions for Direct Methods with Swift Electrons |url=https://academic.oup.com/mam/article/9/5/399/6905535 |journal=Microscopy and Microanalysis |language=en |volume=9 |issue=5 |pages=399–410 |doi=10.1017/S1431927603030332 |pmid=19771696 |bibcode=2003MiMic...9..399M |s2cid=20112743 |issn=1431-9276|url-access=subscription }}{{Cite journal |last1=Own |first1=C. S. |last2=Marks |first2=L. D. |last3=Sinkler |first3=W. |date=2006-11-01 |title=Precession electron diffraction 1: multislice simulation |url=https://scripts.iucr.org/cgi-bin/paper?S0108767306032892 |journal=Acta Crystallographica A |volume=62 |issue=6 |pages=434–443 |doi=10.1107/S0108767306032892 |pmid=17057352 |issn=0108-7673|url-access=subscription }} so that even structures can be determined that are out of range when processing conventional (selected area) electron diffraction data.{{cite journal|doi=10.1107/S0108767302022559|last1=Gemmi|first1=M|last2=Zou|first2=X|last3=Hovmöller|first3=S|last4=Migliori|first4=A|last5=Vennström|first5=M|last6=Andersson|first6=Y|title=Structure of Ti2P solved by three-dimensional electron diffraction data collected with the precession technique and high-resolution electron microscopy|journal=Acta Crystallographica |volume=59|issue=Pt 2|pages=117–26|year=2003|pmid=12604849}}{{cite journal|last1=Weirich|first1=T|last2=Portillo|first2=J|last3=Cox|first3=G|last4=Hibst|first4=H|last5=Nicolopoulos|first5=S|title=Ab initio determination of the framework structure of the heavy-metal oxide CsxNb2.54W2.46O14 from 100kV precession electron diffraction data|journal=Ultramicroscopy|volume=106|issue=3|pages=164–75|year=2006|pmid=16137828|doi=10.1016/j.ultramic.2005.07.002}}

Crystal structures determined via electron crystallography can be checked for their quality by using first-principles calculations within density functional theory (DFT). This approach has been used to assist in solving surface structures{{Cite journal |last1=Erdman |first1=Natasha |last2=Poeppelmeier |first2=Kenneth R. |last3=Asta |first3=Mark |last4=Warschkow |first4=Oliver |last5=Ellis |first5=Donald E. |last6=Marks |first6=Laurence D. |date=2002 |title=The structure and chemistry of the TiO2-rich surface of SrTiO3 (001) |url=http://www.nature.com/articles/nature01010 |journal=Nature |language=en |volume=419 |issue=6902 |pages=55–58 |doi=10.1038/nature01010 |pmid=12214229 |bibcode=2002Natur.419...55E |s2cid=4384784 |issn=0028-0836|url-access=subscription }} and for the validation of several metal-rich structures which were only accessible by HRTEM and ED, respectively.{{cite journal|doi=10.1107/S0108767302018275|last1=Albe|first1=K|last2=Weirich|first2=TE|title=Structure and stability of alpha- and beta-Ti2Se. Electron diffraction versus density-functional theory calculations|journal=Acta Crystallographica A|volume=59|issue=Pt 1|pages=18–21|year=2003|pmid=12496457|bibcode=2003AcCrA..59...18A }}{{cite journal|doi=10.1107/S0108767303025042|last1=Weirich|first1=TE|title=First-principles calculations as a tool for structure validation in electron crystallography|journal=Acta Crystallographica A|volume=60|issue=Pt 1|pages=75–81|year=2004|pmid=14691330|bibcode = 2004AcCrA..60...75W }}

Recently, two very complicated zeolite structures have been determined by electron crystallography combined with X-ray powder diffraction.{{cite journal|last1=Gramm|first1=Fabian|last2=Baerlocher|first2=Christian|last3=McCusker|first3=Lynne B.|last4=Warrender|first4=Stewart J.|last5=Wright|first5=Paul A.|last6=Han|first6=Bada|last7=Hong|first7=Suk Bong|last8=Liu|first8=Zheng|last9=Ohsuna|first9=Tetsu|last10=Terasaki|first10=Osamu|title=Complex zeolite structure solved by combining powder diffraction and electron microscopy|journal=Nature|volume=444|issue=7115|pages=79–81|year=2006|pmid=17080087|doi=10.1038/nature05200|bibcode = 2006Natur.444...79G |s2cid=4396820 |display-authors=8}}{{cite journal|last1=Baerlocher|first1=C.|last2=Gramm|first2=F.|last3=Massuger|first3=L.|last4=McCusker|first4=L. B.|last5=He|first5=Z.|last6=Hovmoller|first6=S.|last7=Zou|first7=X.|title=Structure of the Polycrystalline Zeolite Catalyst IM-5 Solved by Enhanced Charge Flipping|journal=Science|volume=315|issue=5815|pages=1113–6|year=2007|pmid=17322057|doi=10.1126/science.1137920|bibcode = 2007Sci...315.1113B |s2cid=19509220 }} These are more complex than the most complex zeolite structures determined by X-ray crystallography.

{{reflist|30em}}

• Zou, XD, Hovmöller, S. and Oleynikov, P. "Electron Crystallography - Electron microscopy and Electron Diffraction". IUCr Texts on Crystallography 16, Oxford university press 2011. http://ukcatalogue.oup.com/product/9780199580200.do {{ISBN|978-0-19-958020-0}}
• {{cite journal | last1 = Downing | first1 = K. H. | last2 = Meisheng | first2 = H. | last3 = Wenk | first3 = H.-R. | last4 = O'Keefe | first4 = M. A. | year = 1990 | title = Resolution of oxygen atoms in staurolite by three-dimensional transmission electron microscopy | journal = Nature | volume = 348 | issue = 6301| pages = 525–528 | doi = 10.1038/348525a0 |bibcode = 1990Natur.348..525D | s2cid = 4340756 }}
• {{cite journal | last1 = Zou | first1 = X.D. | last2 = Hovmöller | first2 = S. | year = 2008 | title = Electron crystallography: Imaging and Single Crystal Diffraction from Powders | journal = Acta Crystallographica A | volume = 64 | issue = Pt 1 | pages = 149–160 | doi = 10.1107/S0108767307060084 | pmid = 18156680 |bibcode = 2008AcCrA..64..149Z | doi-access = free }}
• T.E. Weirich, X.D. Zou & J.L. Lábár (2006). Electron Crystallography: Novel Approaches for Structure Determination of Nanosized Materials. Springer Netherlands, {{ISBN|978-1-4020-3919-5}}

• [http://www.vega.org.uk/video/programme/122 Interview with Aaron Klug Nobel Laureate for work on crystallograph electron microscopy] Freeview video by the Vega Science Trust.
• {{cite journal |title=Electron Crystallography as a Technique to Study the Structure on Membrane Proteins in a Lipidic Environment |journal=Annual Review of Biophysics |volume=38 |issue=1 |year=2009 |doi=10.1146/annurev.biophys.050708.133649 |pmid=19416061 |last1=Raunser |first1=S |last2=Walz |first2=T |pages=89–105}}

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