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Electron crystallography

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advances from the 1950s in particular laid the foundation for more quantitative work, ranging from accurate methods to perform forward calculations to methods to invert to maps of the atomic structure. With the improvement of the imaging capabilities of electron microscopes crystallographic data is now commonly obtained by combining images with electron diffraction information, or in some cases by collecting three dimensional electron diffraction data by a number of different approaches.
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result from image processing, where the symmetry has been taken into account. The black dots show clearly all the tantalum atoms. The diffraction extends to 6 orders along the 15 Å direction and 10 orders in the perpendicular direction. Thus the resolution of the EM image is 2.5 Å (15/6 or 25/10). This calculated Fourier transform contain both amplitudes (as seen) and phases (not displayed).
484:) 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. Alternatively a hybrid approach can be used which uses HRTEM images for solving and intensities from ED for refining the crystal structure. 423: 349:, 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 456:(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 393:
in 1990. 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
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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
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In addition to electron microscopy images, it is also possible to use electron diffraction (ED) patterns for crystal structure determination. 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
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T4, a common virus, a key step in the use of electrons for macromolecular structure determination. 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. In the early 1980s the resolution
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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
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Electron microscopy image of an inorganic tantalum oxide, with its Fourier transform, inset. Notice how the appearance changes from the upper thin region to the thicker lower region. The unit cell of this compound is about 15 by 25 Ångström. It is outlined at the centre of the figure, inside the
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The technique date back to soon after the discovery of electron diffraction in 1927-28, and was used in many early works. However, for many years quantitative electron crystallography was not used, instead the diffraction information was combined qualitatively with imaging results. A number of
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Electron diffraction pattern of the same crystal of inorganic tantalum oxide shown above. Notice that there are many more diffraction spots here than in the diffractogram calculated from the EM image above. The diffraction extends to 12 orders along the 15 Å direction and 20 orders in the
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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.
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for recording electron diffraction patterns. The thereby obtained intensities are usually much closer to the kinematical intensities, so that even structures can be determined that are out of range when processing conventional (selected area) electron diffraction data.
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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
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and Alexander Reid. Alexander Reid, who was Thomson's graduate student, performed the first experiments, but he died soon after in a motorcycle accident. These experiments were rapidly followed by the first non-relativistic diffraction model for electrons by
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perpendicular direction. Thus the resolution of the ED pattern is 1.25 Å (15/12 or 25/20). ED patterns do not contain phase information, but the clear differences between intensities of the diffraction spots can be used in crystal structure determination.
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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
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Gramm, Fabian; Baerlocher, Christian; McCusker, Lynne B.; Warrender, Stewart J.; Wright, Paul A.; Han, Bada; Hong, Suk Bong; Liu, Zheng; et al. (2006). "Complex zeolite structure solved by combining powder diffraction and electron microscopy".
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Gemmi, M; Zou, X; Hovmöller, S; Migliori, A; Vennström, M; Andersson, Y (2003). "Structure of Ti2P solved by three-dimensional electron diffraction data collected with the precession technique and high-resolution electron microscopy".
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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
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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
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in 1978 and by Sven Hovmöller and coworkers in 1984. 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
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Weirich, T; Portillo, J; Cox, G; Hibst, H; Nicolopoulos, S (2006). "Ab initio determination of the framework structure of the heavy-metal oxide CsxNb2.54W2.46O14 from 100kV precession electron diffraction data".
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and diffraction became standard across many areas of science. Most of the research published using these approaches is described as electron microscopy, without the addition of the term electron crystallography.
327:, 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 198:
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. (Since the advent of
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structures have been determined by electron crystallography combined with X-ray powder diffraction. These are more complex than the most complex zeolite structures determined by X-ray crystallography.
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Henderson, R.; Baldwin, J.M.; Ceska, T.A.; Zemlin, F; Beckmann, E.; Downing, K.H. (June 1990). "Model for the structure of bacteriorhodopsin based on high-resolution electron cryo-microscopy".
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Baerlocher, C.; Gramm, F.; Massuger, L.; McCusker, L. B.; He, Z.; Hovmoller, S.; Zou, X. (2007). "Structure of the Polycrystalline Zeolite Catalyst IM-5 Solved by Enhanced Charge Flipping".
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Weirich, TE; Zou, X; Ramlau, R; Simon, A; Cascarano, GL; Giacovazzo, C; Hovmöller, S (2000). "Structures of nanometre-size crystals determined from selected-area electron diffraction data".
499:(DFT). This approach has been used to assist in solving surface structures and for the validation of several metal-rich structures which were only accessible by HRTEM and ED, respectively. 480:, 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 4887: 2233:"Structure Model for the Phase AlmFe Derived from Three-Dimensional Electron Diffraction Intensity Data Collected by a Precession Technique. Comparison with Convergent-Beam Diffraction" 457: 203:
it has become clear that averaging over many different electron beam directions and thicknesses significantly reduces dynamical diffraction effects, so was probably also important.)
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Zou, XD, Hovmöller, S. and Oleynikov, P. "Electron Crystallography - Electron microscopy and Electron Diffraction". IUCr Texts on Crystallography 16, Oxford university press 2011.
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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
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of electron microscopes was now sufficient to resolve the atomic structure of materials, for instance with the 600 kV instrument led by Vernon Cosslett, so combinations of
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Weirich, Thomas E.; Ramlau, Reiner; Simon, Arndt; Hovmöller, Sven; Zou, Xiaodong (1996). "A crystal structure determined with 0.02 Å accuracy by electron microscopy".
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Downing, K. H.; Meisheng, H.; Wenk, H.-R.; O'Keefe, M. A. (1990). "Resolution of oxygen atoms in staurolite by three-dimensional transmission electron microscopy".
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Goodman, P.; Lehmpfuhl, G. (1968). "Observation of the breakdown of Friedel's law in electron diffraction and symmetry determination from zero-layer interactions".
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Hovmöller, Sven; Sjögren, Agneta; Farrants, George; Sundberg, Margareta; Marinder, Bengt-Olov (1984). "Accurate atomic positions from electron microscopy".
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Yonekura, Koji; Maki-Yonekura, Saori; Namba, Keiichi (August 2003). "Complete atomic model of the bacterial flagellar filament by electron cryomicroscopy".
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Kühlbrandt, Werner; Wang, Da Neng; Fujiyoshi, Yoshinori (February 1994). "Atomic model of plant light-harvesting complex by electron crystallography".
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Albe, K; Weirich, TE (2003). "Structure and stability of alpha- and beta-Ti2Se. Electron diffraction versus density-functional theory calculations".
410:-0. In 2012, Jan Pieter Abrahams and coworkers extended electron crystallography to 3D protein nanocrystals by rotation electron diffraction (RED). 440: 267: 37: 4275: 4244: 4188: 4136: 2589:
Hattne, Johan; Shi, Dan; Glynn, Calina; Zee, Chih-Te; Gallagher-Jones, Marcus; Martynowycz, Michael W.; Rodriguez, Jose A.; Gonen, Tamir (2018).
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R Hovden; Y Jiang; HL Xin; LF Kourkoutis (2015). "Periodic Artifact Reduction in Fourier Transforms of Full Field Atomic Resolution Images".
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algorithm and non-linear imaging theory have been developed to simulate images; this only became possible once the FFT method was developed.
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Raunser, S; Walz, T (2009). "Electron Crystallography as a Technique to Study the Structure on Membrane Proteins in a Lipidic Environment".
2901:"A Medipix quantum area detector allows rotation electron diffraction data collection from submicrometre three-dimensional protein crystals" 5017: 48:
or combinations of these. It has been successful in determining some bulk structures, and also surface structures. Two related methods are
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Crystal structures determined via electron crystallography can be checked for their quality by using first-principles calculations within
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Own, C. S.: PhD thesis, System Design and Verification of the Precession Electron Diffraction Technique, Northwestern University, 2005,
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Miyazawa, Atsuo; Fujiyoshi, Yoshinori; Unwin, Nigel (June 2003). "Structure and gating mechanism of the acetylcholine receptor pore".
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More complete crystallographic analysis of intensity data was slow to develop. One of the key steps was the demonstration in 1976 by
233:. More complete analyses were the demonstration that classical inversion methods could be used for surfaces in 1997 by Dorset and 4172: 383: 5194: 5186: 1256:
Mark, Herman; Wiel, Raymond (1930). "Die ermittlung von molekülstrukturen durch beugung von elektronen an einem dampfstrahl".
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in 1954, electron diffraction for many years was a qualitative technique used to check samples within electron microscopes.
5240: 5090: 4756: 4621: 4470: 4089: 1025: 168: 45: 406:. The highest resolution protein structure solved by electron crystallography of 2D crystals is that of the water channel 113:'s observations of lines that can be used for crystallographic indexing due to combined elastic and inelastic scattering, 5230: 5128: 4824: 2834:
Gonen, Tamir; Cheng, Yifan; Sliz, Piotr; Hiroaki, Yoko; Fujiyoshi, Yoshinori; Harrison, Stephen C.; Walz, Thomas (2005).
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publishing the first electron microscope images showing the lattice structure of a material at 1.2nm resolution. In 1968
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Gjønnes, J.; Hansen, V.; Berg, B. S.; Runde, P.; Cheng, Y. F.; Gjønnes, K.; Dorset, D. L.; Gilmore, C. J. (1998-05-01).
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Erdman, Natasha; Poeppelmeier, Kenneth R.; Asta, Mark; Warschkow, Oliver; Ellis, Donald E.; Marks, Laurence D. (2002).
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Zandbergen, H. W. (1997). "Structure Determination of Mg5Si6 Particles in Al by Dynamic Electron Diffraction Studies".
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based upon the Schrödinger equation, which is very close to how electron diffraction is now described. Significantly,
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Weirich, TE (2004). "First-principles calculations as a tool for structure validation in electron crystallography".
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required for that process. Protein structures are usually determined from either 2-dimensional crystals (sheets or
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could be powerful in the seminal solution of the silicon (111) 7x7 reconstructed surface by Kunio Takanayagi using
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Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character
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De Rosier, D. J.; Klug, A. (1968). "Reconstruction of Three Dimensional Structures from Electron Micrographs".
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then, several other high-resolution structures have been determined by electron crystallography, including the
312:(e.g. 3-dimensional > 1 micrometer) crystals impervious to electrons, which only penetrate short distances. 81: 5085: 5075: 4380: 4234: 387: 350: 4229: 637: 5209: 4857: 4482: 4460: 4355: 4333: 121:
and Raymond Weil, diffraction in liquids by Louis Maxwell, and the first electron microscopes developed by
80:. The wave nature was experimentally confirmed for electron beams in the work of two groups, the first the 4761: 4515: 4410: 141: 5314: 5118: 4415: 4350: 1720:
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
171:(CBED), This approach was extended by Peter Goodman and Gunter Lehmpfuhl, then mainly by the groups of 3482: 2031: 1763:"Use of high-symmetry zone axes in electron diffraction in determining crystal point and space groups" 5133: 5062: 4520: 4510: 4296: 496: 1714:
Buxton, B. F.; Eades, J. A.; Steeds, John Wickham; Rackham, G. M.; Frank, Frederick Charles (1976).
1497:"Structure analysis of single crystals by electron diffraction. II. Disordered boric acid structure" 5309: 5275: 4999: 4768: 4731: 4646: 4525: 4505: 4373: 4239: 4126: 3446:"Double conical beam-rocking system for measurement of integrated electron diffraction intensities" 1994:"Double conical beam-rocking system for measurement of integrated electron diffraction intensities" 395: 114: 3258: 3212:"Numerical evaluations of N -beam wave functions in electron scattering by the multi-slice method" 164: 5123: 4967: 4912: 4661: 4626: 4260: 4213: 461: 172: 3180: 2408: 2271: 2186:"Structure analysis of Si(111)-7 × 7 reconstructed surface by transmission electron diffraction" 1602: 4877: 4819: 4636: 1633: 1075: 1809: 1442:"Die Bestimmung der Lage der Wasserstoffionen im NH4Cl-Kristallgitter durch Elektronenbeugung" 5176: 4972: 4934: 4741: 4693: 4317: 4301: 4270: 4131: 4027:
Electron Crystallography: Novel Approaches for Structure Determination of Nanosized Materials
280: 219: 2139:"Structural analysis of Si(111)-7×7 by UHV-transmission electron diffraction and microscopy" 524:"Structural analysis of Si(111)-7×7 by UHV-transmission electron diffraction and microscopy" 4900: 4773: 4609: 4500: 3996: 3955: 3886: 3835: 3791: 3748: 3689: 3558: 3507: 3410: 3223: 3211: 3129: 3082: 3070: 3043: 2977: 2912: 2847: 2792: 2741: 2690: 2534:"High-resolution structure determination by continuous-rotation data collection in MicroED" 2490: 2420: 2373: 2361: 2326: 2283: 2244: 2232: 2197: 2150: 2044: 1915: 1903: 1868: 1856: 1774: 1762: 1727: 1688: 1645: 1565: 1553: 1508: 1496: 1453: 1398: 1351: 1304: 1214: 1126: 1087: 980: 923: 856: 786: 734: 679: 586: 570: 535: 230: 85: 41: 29: 20: 4066: 132:
Despite early successes such as the determination of the positions of hydrogen atoms in NH
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Image Analysis and Reconstruction in the Electron Microscopy of Biological Macromolecules
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Recent progress for structure analysis by ED was made by introducing the Vincent-Midgley
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Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
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Takayanagi, Kunio; Tanishiro, Yasumasa; Takahashi, Shigeki; Takahashi, Masaetsu (1985).
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Interview with Aaron Klug Nobel Laureate for work on crystallograph electron microscopy
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The first electron crystallographic protein structure to achieve atomic resolution was
307:, or dispersed individual proteins. Electrons can be used in these situations, whereas 283:
for studies of very small crystals (<0.1 micrometers), both inorganic, organic, and
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and David DeRosier used electron microscopy to visualise the structure of the tail of
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Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
2362:"n -Beam lattice images. I. Experimental and computed images from W 4 Nb 26 O 77" 1292: 523: 358: 32:
focusing upon detailed determination of the positions of atoms in solids using a
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Zhang, Daliang; Oleynikov, Peter; Hovmöller, Sven; Zou, Xiaodong (March 2010).
2900: 2185: 2091: 1993: 481: 465: 452:). This is of crucial importance since in the thicker parts of the crystal the 188: 160: 145: 137: 110: 102: 4081: 4009: 3984: 3803: 3760: 3618: 3574: 3519: 3352: 3235: 3141: 3094: 2924: 2606: 2502: 2385: 2256: 2060: 1927: 1880: 1786: 1700: 1578: 1521: 1441: 1386: 1339: 1041: 573:; Asta, Mark; Warschkow, Oliver; Ellis, Donald E.; Marks, Laurence D. (2002). 238: 5303: 4982: 4795: 4594: 4046: 3709: 3677: 3582: 3527: 3469: 3284: 3243: 3149: 3102: 2999: 2932: 2867: 2614: 2557: 2440: 2393: 2303: 2217: 2170: 2115: 2068: 2017: 1978: 1935: 1888: 1833: 1794: 1665: 1657: 1587: 1530: 1473: 1418: 1371: 1363: 1324: 1269: 1234: 1146: 1099: 1049: 1002: 945: 878: 808: 756: 699: 606: 574: 555: 362: 324: 316: 262: 98: 3898: 2836:"Lipid–protein interactions in double-layered two-dimensional AQP0 crystals" 2532:
Nannenga, Brent L; Shi, Dan; Leslie, Andrew G W; Gonen, Tamir (2014-08-03).
2409:"Principles and performance of a 600 kV high resolution electron microscope" 1825: 1138: 373: 4688: 4678: 4572: 4455: 4208: 4074: 4018: 3906: 3855: 3811: 3768: 3717: 3662: 3626: 3590: 3535: 3360: 3157: 2990: 2965: 2950: 2885: 2812: 2761: 2632: 2575: 2510: 2432: 2346: 2295: 2076: 1739: 1178: 993: 968: 896: 826: 747: 722: 614: 354: 304: 254: 16:
Method to determine atomic positions in solids using an electron microscope
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High-resolution Transmission Electron Microscopy and Associated Techniques
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Takayanagi, K.; Tanishiro, Y.; Takahashi, M.; Takahashi, S. (1985-05-01).
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A common problem to X-ray crystallography and electron crystallography is
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Nederlof, I.; van Genderen, E.; Li, Y.-W.; Abrahams, J. P. (2013-07-01).
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Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films
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approach as the positions were systematically different; the approach of
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Cl crystals by W. E. Laschkarew and I. D. Usykin in 1933, boric acid by
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and Michiyoshi Tanaka who showed how to use CBED patterns to determine
106: 90: 3678:"The structure and chemistry of the TiO2-rich surface of SrTiO3 (001)" 2138: 667: 575:"The structure and chemistry of the TiO2-rich surface of SrTiO3 (001)" 4445: 3967: 3422: 3055: 2702: 2360:
Allpress, J. G.; Hewat, E. A.; Moodie, A. F.; Sanders, J. V. (1972).
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One of the main difficulties in X-ray crystallography is determining
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This has slowly changed. One key step was the development in 1936 by
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Takayanagi, K.; Tanishiro, Y.; Takahashi, M.; Takahashi, S. (1985).
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http://www.numis.northwestern.edu/Research/Current/precession.shtml
1857:"Point-group determination by convergent-beam electron diffraction" 4365: 2591:"Analysis of Global and Site-Specific Radiation Damage in Cryo-EM" 2470: 464:
for example). To cope with this complexity methods based upon the
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Zeitschrift für Elektrochemie und angewandte physikalische Chemie
503: 292: 284: 3824: 3033: 2966:"Collecting 3D electron diffraction data by the rotation method" 3876: 3675: 3496:"Sufficient Conditions for Direct Methods with Swift Electrons" 845:"Reflection and Refraction of Electrons by a Crystal of Nickel" 568: 3945: 2898: 1115:"An Undulatory Theory of the Mechanics of Atoms and Molecules" 5047: 308: 296: 249:
to solve an intermetallic, also using dynamical refinements.
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could be used. Another was the demonstration in 1986 that a
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noticed that their results could not be interpreted using a
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Zeitschrift für Kristallographie – New Crystal Structures
3603: 1716:"The symmetry of electron diffraction zone axis patterns" 1603:"Crystal structure determination by electron diffraction" 969:"The diffraction of cathode rays by thin celluloid films" 374:
Protein structures determined by electron crystallography
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who combined three-dimensional electron diffraction with
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Zeitschrift für Kristallographie – Crystalline Materials
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Electron crystallographic studies on inorganic crystals
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The general approach dates back to the work in 1924 of
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which is used to monitor surfaces often during growth.
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Buseck, Peter; Cowley, John M; Eyring, Leyroy (1992).
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which has solved the structure of many surfaces, and
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Own, C. S.; Marks, L. D.; Sinkler, W. (2006-11-01).
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http://ukcatalogue.oup.com/product/9780199580200.do
1901: 2453: 1076:"Theorie der Beugung von Elektronen an Kristallen" 291:, that cannot easily form the large 3-dimensional 194:A second key set of work was that by the group of 2588: 2090:Dorset, Douglas L.; Hauptman, Herbert A. (1976). 1631: 1439: 723:"Diffraction of Electrons by a Crystal of Nickel" 5301: 4025:T.E. Weirich, X.D. Zou & J.L. Lábár (2006). 1854: 1678: 1634:"Elektroneninterferenzen im konvergenten Bündel" 775:"Reflection of Electrons by a Crystal of Nickel" 370:of thin 3D crystals in a frozen hydrated state. 268:high-resolution transmission electron microscopy 76:where he introduced the concept of electrons as 38:high-resolution transmission electron microscopy 4111: 3556: 2042: 849:Proceedings of the National Academy of Sciences 779:Proceedings of the National Academy of Sciences 3443: 3118:"FFT Multislice Method—The Silver Anniversary" 2089: 2043:Own, C. S.; Marks, L. D.; Sinkler, W. (2006). 1991: 1340:"Beitrag zur geometrischen Elektronenoptik. I" 1030:The British Journal for the History of Science 842: 772: 720: 665: 4381: 4097: 3209: 2316: 1760: 3982: 3493: 3181:"Contrast transfer of crystal images in TEM" 3068: 1902:Tanaka, M.; Saito, R.; Watanabe, D. (1980). 1106: 912:"Diffraction of Cathode Rays by a Thin Film" 528:Journal of Vacuum Science & Technology A 5218: 4052: 3738: 3256: 3069:Cowley, J. M.; Moodie, A. F. (1957-10-01). 1551: 1112: 909: 54:reflection high-energy electron diffraction 4388: 4374: 4104: 4090: 3444:Vincent, R.; Midgley, P. A. (1994-03-01). 3373: 3302:Structure Analysis by Electron Diffraction 1960:Structure analysis by electron diffraction 1956: 1810:"Theory of zone axis electron diffraction" 1554:"The precise structure of orthoboric acid" 1440:Laschkarew, W. E.; Usyskin, I. D. (1933). 1384: 1337: 4049:Freeview video by the Vega Science Trust. 4008: 3274: 3257:Cooley, James W.; Tukey, John W. (1965). 3210:Goodman, P.; Moodie, A. F. (1974-03-01). 2989: 2940: 2875: 2622: 2565: 2484: 1855:Tanaka, M.; Saito, R.; Sekii, H. (1983). 1577: 1520: 1203:"Neuere Ergebnisse der Elektronenbeugung" 1200: 1177: 992: 935: 886: 868: 816: 798: 746: 3178: 3115: 3024:Chemica Scripta vol 14, p. 245-256. 2406: 1814:Journal of Electron Microscopy Technique 1488: 1255: 1069: 1067: 421: 412: 191:and atomic structure was of importance. 3781: 1707: 1290: 1159: 1023: 843:Davisson, C. J.; Germer, L. H. (1928). 773:Davisson, C. J.; Germer, L. H. (1928). 187:approaches, typically where both local 5302: 4491: 2269: 2024: 1600: 1494: 1378: 1331: 635: 629: 443:(HREM) images were first performed by 4369: 4085: 4067:10.1146/annurev.biophys.050708.133649 1201:Mark, Herman; Wierl, Raymond (1930). 1162:"Diffraction of cathode rays by mica" 1073: 1064: 838: 836: 768: 766: 323:. Because of the complexity of X-ray 275:Comparison with X-ray crystallography 5282: 4622:Phase transformation crystallography 1807: 1632:Kossel, W.; Möllenstedt, G. (1939). 966: 721:Davisson, C.; Germer, L. H. (1927). 666:Davisson, C.; Germer, L. H. (1927). 169:convergent beam electron diffraction 74:Recherches sur la théorie des quanta 46:convergent-beam electron diffraction 5129:Journal of Chemical Crystallography 4395: 3319:Structural Electron Crystallography 1992:Vincent, R.; Midgley, P.A. (1994). 1761:Steeds, J. W.; Vincent, R. (1983). 1284: 1166:Proceedings of the Imperial Academy 1153: 441:high-resolution electron microscopy 340: 13: 3924: 2525: 1848: 1767:Journal of Applied Crystallography 1754: 1672: 833: 763: 714: 659: 432:Application to inorganic materials 14: 5326: 4040: 3983:Zou, X.D.; Hovmöller, S. (2008). 3494:Marks, L.D.; Sinkler, W. (2003). 3276:10.1090/S0025-5718-1965-0178586-1 1293:"Electron Diffraction by Liquids" 910:Thomson, G. P.; Reid, A. (1927). 450:crystallographic image processing 36:(TEM). It can involve the use of 5281: 5270: 5269: 4876: 4199:Dual-polarization interferometry 3322:, Plenum Publishing Corporation 2970:Zeitschrift für Kristallographie 2905:Acta Crystallographica Section D 2366:Acta Crystallographica Section A 2237:Acta Crystallographica Section A 2049:Acta Crystallographica Section A 1908:Acta Crystallographica Section A 1861:Acta Crystallographica Section A 1681:Acta Crystallographica Section A 458:defocus Δf of the objective lens 400:nicotinic acetylcholine receptor 185:transmission electron microscopy 34:transmission electron microscope 3870: 3818: 3775: 3732: 3669: 3633: 3597: 3550: 3487: 3483:Precession Electron Diffraction 3476: 3437: 3394: 3367: 3332: 3307: 3291: 3250: 3203: 3172: 3109: 3062: 3027: 3014: 2957: 2892: 2827: 2776: 2725: 2674: 2582: 2464: 2447: 2400: 2353: 2310: 2263: 2224: 2177: 2130: 2083: 2036: 1985: 1950: 1895: 1801: 1625: 1594: 1545: 1433: 1249: 1194: 1017: 502:Recently, two very complicated 391:Laboratory of Molecular Biology 353:, in which the samples undergo 243:precession electron diffraction 201:precession electron diffraction 183:. This was combined with other 140:in 1953 and orthoboric acid by 50:low-energy electron diffraction 5071:Bilbao Crystallographic Server 4230:Analytical ultracentrifugation 3655:10.1016/j.ultramic.2005.07.002 2407:Cosslett, V. E. (1980-03-12). 960: 903: 645:Foundation of Louis de Broglie 562: 515: 1: 4235:Size exclusion chromatography 3388:10.1126/science.277.5330.1221 2660:10.1016/S0022-2836(05)80271-2 1607:Progress in Materials Science 1385:Knoll, M.; Ruska, E. (1932). 1338:Knoll, M.; Ruska, E. (1932). 509: 4334:Protein structure prediction 3500:Microscopy and Microanalysis 3462:10.1016/0304-3991(94)90039-6 3197:10.1016/0304-3991(80)90011-X 3122:Microscopy and Microanalysis 2473:Microscopy and Microanalysis 2210:10.1016/0039-6028(85)90753-8 2108:10.1016/0304-3991(76)90034-6 2010:10.1016/0304-3991(94)90039-6 1619:10.1016/0079-6425(68)90023-6 7: 5119:Crystal Growth & Design 4411:Timeline of crystallography 4292:Hydrogen–deuterium exchange 4113:Protein structural analysis 4055:Annual Review of Biophysics 1552:Zachariasen, W. H. (1954). 1190:– via Google Scholar. 357:and imaging takes place at 142:William Houlder Zachariasen 10: 5331: 4930:Nuclear magnetic resonance 3263:Mathematics of Computation 2460:. Oxford University Press. 1963:. Oxford: Pergamon Press. 1957:Vaĭnshteĭn, B. K. (1964). 1291:Maxwell, Louis R. (1933). 636:de Broglie, Louis Victor. 237:, and in 1998 the work by 82:Davisson–Germer experiment 63: 28:is a subset of methods in 18: 5265: 5185: 5157: 5134:Journal of Crystal Growth 5109: 5061: 5008: 4955: 4886: 4874: 4669: 4660: 4583: 4436: 4403: 4347: 4326: 4310: 4297:Site-directed mutagenesis 4284: 4253: 4222: 4181: 4155: 4119: 4010:10.1107/S0108767307060084 3804:10.1107/S0108767303025042 3761:10.1107/S0108767302018275 3619:10.1107/S0108767302022559 3575:10.1107/S0108767306032892 3520:10.1017/S1431927603030332 3353:10.1107/S0108767399009605 3236:10.1107/S056773947400057X 3142:10.1017/S1431927604040292 3095:10.1107/S0365110X57002194 2925:10.1107/S0907444913009700 2607:10.1016/j.str.2018.03.021 2503:10.1017/S1431927614014639 2386:10.1107/S0567739472001433 2257:10.1107/S0108767397017030 2061:10.1107/S0108767306032892 1928:10.1107/S0567739480000800 1881:10.1107/S010876738300080X 1787:10.1107/S002188988301050X 1701:10.1107/S0567739468000677 1579:10.1107/S0365110X54000886 1522:10.1107/S0365110X53001423 1387:"Das Elektronenmikroskop" 1042:10.1017/S0007087410000026 638:"On the Theory of Quanta" 497:density functional theory 148:explains in a 1968 paper: 5000:Single particle analysis 4858:Hermann–Mauguin notation 4142:Electron crystallography 4127:Cryo-electron microscopy 4029:. Springer Netherlands, 3989:Acta Crystallographica A 3784:Acta Crystallographica A 3741:Acta Crystallographica A 3563:Acta Crystallographica A 3341:Acta Crystallographica A 3216:Acta Crystallographica A 3179:Ishizuka, Kazuo (1980). 3116:Ishizuka, Kazuo (2004). 1658:10.1002/andp.19394280204 1364:10.1002/andp.19324040506 1270:10.1002/bbpc.19300360921 1160:Kikuchi, Seishi (1928). 1113:Schrödinger, E. (1926). 1100:10.1002/andp.19283921704 967:Reid, Alexander (1928). 571:Poeppelmeier, Kenneth R. 460:(see the HREM images of 396:light-harvesting complex 388:Medical Research Council 115:gas electron diffraction 26:Electron crystallography 5124:Crystallography Reviews 4968:Isomorphous replacement 4762:Lomer–Cottrell junction 4261:Fluorescence anisotropy 4223:Translational Diffusion 4214:Fluorescence anisotropy 3899:10.1126/science.1137920 3304:, Pergamon Press Oxford 1826:10.1002/jemt.1060130202 1207:Die Naturwissenschaften 1139:10.1103/PhysRev.28.1049 1024:Navarro, Jaume (2010). 351:electron cryomicroscopy 4637:Spinodal decomposition 3607:Acta Crystallographica 3075:Acta Crystallographica 2991:10.1524/zkri.2010.1202 2433:10.1098/rspa.1980.0018 2296:10.1098/rspa.1956.0117 2270:Menter, J. W. (1956). 1740:10.1098/rsta.1976.0024 1558:Acta Crystallographica 1501:Acta Crystallographica 1495:Cowley, J. M. (1953). 1446:Zeitschrift für Physik 1391:Zeitschrift für Physik 1179:10.2183/pjab1912.4.271 994:10.1098/rspa.1928.0121 748:10.1103/physrev.30.705 428: 419: 157: 5177:Gregori Aminoff Prize 4973:Molecular replacement 4356:Quaternary structure→ 4318:Equilibrium unfolding 4302:Chemical modification 4271:Dielectric relaxation 4132:X-ray crystallography 1601:Cowley, J.M. (1968). 1317:10.1103/PhysRev.44.73 870:10.1073/pnas.14.8.619 800:10.1073/pnas.14.4.317 425: 416: 386:and coworkers at the 281:X-ray crystallography 220:x-ray crystallography 165:Gottfried Möllenstedt 150: 4483:Structure prediction 4254:Rotational Diffusion 1808:Bird, D. M. (1989). 489:precession technique 402:, and the bacterial 231:electron diffraction 86:George Paget Thomson 42:electron diffraction 30:electron diffraction 21:Electron diffraction 4747:Cottrell atmosphere 4727:Partial dislocation 4471:Restriction theorem 4351:←Tertiary structure 4001:2008AcCrA..64..149Z 3960:1990Natur.348..525D 3891:2007Sci...315.1113B 3848:10.1038/nature05200 3840:2006Natur.444...79G 3796:2004AcCrA..60...75W 3753:2003AcCrA..59...18A 3702:10.1038/nature01010 3694:2002Natur.419...55E 3512:2003MiMic...9..399M 3415:1996Natur.382..144W 3382:(5330): 1221–1225. 3228:1974AcCrA..30..280G 3134:2004MiMic..10...34I 3087:1957AcCry..10..609C 3048:1984Natur.311..238H 2982:2010ZK....225...94Z 2917:2013AcCrD..69.1223N 2860:10.1038/nature04321 2852:2005Natur.438..633G 2805:10.1038/nature01830 2797:2003Natur.424..643Y 2754:10.1038/nature01748 2746:2003Natur.423..949M 2695:1994Natur.367..614K 2495:2015MiMic..21..436H 2425:1980RSPSA.370....1C 2378:1972AcCrA..28..528A 2331:1968Natur.217..130D 2288:1956RSPSA.236..119M 2249:1998AcCrA..54..306G 2202:1985SurSc.164..367T 2155:1985JVSTA...3.1502T 1920:1980AcCrA..36..350T 1873:1983AcCrA..39..357T 1779:1983JApCr..16..317S 1732:1976RSPTA.281..171B 1693:1968AcCrA..24..339G 1650:1939AnP...428..113K 1570:1954AcCry...7..305Z 1513:1953AcCry...6..522C 1458:1933ZPhy...85..618L 1403:1932ZPhy...78..318K 1356:1932AnP...404..607K 1309:1933PhRv...44...73M 1219:1930NW.....18..778M 1131:1926PhRv...28.1049S 1092:1928AnP...392...55B 985:1928RSPSA.119..663R 928:1927Natur.119Q.890T 861:1928PNAS...14..619D 791:1928PNAS...14..317D 739:1927PhRv...30..705D 684:1927Natur.119..558D 599:10.1038/nature01010 591:2002Natur.419...55E 540:1985JVSTA...3.1502T 321:diffraction pattern 212:Herbert A. Hauptman 44:patterns including 5167:Carl Hermann Medal 4978:Molecular dynamics 4825:Defects in diamond 4820:Stone–Wales defect 4466:Reciprocal lattice 4428:Biocrystallography 4266:Flow birefringence 4194:Circular dichroism 3020:Klug, A (1978/79) 2550:10.1038/nmeth.3043 1638:Annalen der Physik 1466:10.1007/BF01331003 1411:10.1007/BF01342199 1344:Annalen der Physik 1227:10.1007/bf01497860 1080:Annalen der Physik 1074:Bethe, H. (1928). 454:exit-wave function 429: 420: 279:It can complement 224:Patterson function 214:that conventional 72:in his PhD thesis 5315:Protein structure 5297: 5296: 5261: 5260: 4868:Thermal ellipsoid 4833: 4832: 4742:Frank–Read source 4702: 4701: 4568:Aperiodic crystal 4534: 4533: 4416:Crystallographers 4363: 4362: 4339:Molecular docking 4168:Mass spectrometry 4163:Fiber diffraction 4156:Medium resolution 4035:978-1-4020-3919-5 3995:(Pt 1): 149–160. 3954:(6301): 525–528. 3939:978-0-19-958020-0 2846:(7068): 633–638. 2601:(5): 759–766.e4. 2325:(5124): 130–134. 2282:(1204): 119–135. 1970:978-0-08-010241-2 1726:(1301): 171–194. 1452:(9–10): 618–630. 678:(2998): 558–560. 569:Erdman, Natasha; 384:Richard Henderson 380:bacteriorhodopsin 289:membrane proteins 235:Laurence D. Marks 228:ultra-high vacuum 208:Douglas L. Dorset 5322: 5285: 5284: 5273: 5272: 5216: 5215: 5139:Kristallografija 4993:Gerchberg–Saxton 4888:Characterisation 4880: 4863:Structure factor 4667: 4666: 4652:Ostwald ripening 4489: 4488: 4434: 4433: 4390: 4383: 4376: 4367: 4366: 4240:Light scattering 4106: 4099: 4092: 4083: 4082: 4078: 4022: 4012: 3979: 3968:10.1038/348525a0 3919: 3918: 3885:(5815): 1113–6. 3874: 3868: 3867: 3822: 3816: 3815: 3779: 3773: 3772: 3736: 3730: 3729: 3673: 3667: 3666: 3637: 3631: 3630: 3613:(Pt 2): 117–26. 3601: 3595: 3594: 3554: 3548: 3547: 3491: 3485: 3480: 3474: 3473: 3441: 3435: 3434: 3423:10.1038/382144a0 3398: 3392: 3391: 3371: 3365: 3364: 3336: 3330: 3311: 3305: 3298:B. K. Vainshtein 3295: 3289: 3288: 3278: 3254: 3248: 3247: 3207: 3201: 3200: 3176: 3170: 3169: 3113: 3107: 3106: 3066: 3060: 3059: 3056:10.1038/311238a0 3031: 3025: 3018: 3012: 3011: 2993: 2961: 2955: 2954: 2944: 2911:(7): 1223–1230. 2896: 2890: 2889: 2879: 2831: 2825: 2824: 2791:(6949): 643–50. 2780: 2774: 2773: 2740:(6943): 949–55. 2729: 2723: 2722: 2703:10.1038/367614a0 2689:(6464): 614–21. 2678: 2672: 2671: 2643: 2637: 2636: 2626: 2586: 2580: 2579: 2569: 2529: 2523: 2522: 2488: 2468: 2462: 2461: 2451: 2445: 2444: 2404: 2398: 2397: 2357: 2351: 2350: 2339:10.1038/217130a0 2314: 2308: 2307: 2267: 2261: 2260: 2228: 2222: 2221: 2196:(2–3): 367–392. 2181: 2175: 2174: 2163:10.1116/1.573160 2149:(3): 1502–1506. 2134: 2128: 2127: 2102:(3–4): 195–201. 2087: 2081: 2080: 2040: 2034: 2028: 2022: 2021: 1989: 1983: 1982: 1954: 1948: 1947: 1899: 1893: 1892: 1852: 1846: 1845: 1805: 1799: 1798: 1758: 1752: 1751: 1711: 1705: 1704: 1676: 1670: 1669: 1629: 1623: 1622: 1598: 1592: 1591: 1581: 1549: 1543: 1542: 1524: 1492: 1486: 1485: 1437: 1431: 1430: 1397:(5–6): 318–339. 1382: 1376: 1375: 1335: 1329: 1328: 1288: 1282: 1281: 1253: 1247: 1246: 1198: 1192: 1191: 1181: 1157: 1151: 1150: 1125:(6): 1049–1070. 1110: 1104: 1103: 1071: 1062: 1061: 1021: 1015: 1014: 996: 979:(783): 663–667. 964: 958: 957: 939: 937:10.1038/119890a0 907: 901: 900: 890: 872: 840: 831: 830: 820: 802: 770: 761: 760: 750: 718: 712: 711: 692:10.1038/119558a0 663: 657: 656: 654: 652: 642: 633: 627: 626: 566: 560: 559: 548:10.1116/1.573160 534:(3): 1502–1506. 519: 382:, determined by 347:radiation damage 341:Radiation damage 329:structure factor 196:Boris Vainshtein 95:Clinton Davisson 70:Louis de Broglie 5330: 5329: 5325: 5324: 5323: 5321: 5320: 5319: 5310:Crystallography 5300: 5299: 5298: 5293: 5257: 5214: 5181: 5153: 5105: 5057: 5028:CrystalExplorer 5004: 4988:Phase retrieval 4951: 4882: 4881: 4872: 4829: 4808:Schottky defect 4707:Perfect crystal 4698: 4694:Abnormal growth 4656: 4642:Supersaturation 4605:Miscibility gap 4586: 4579: 4530: 4487: 4451:Bravais lattice 4432: 4399: 4397:Crystallography 4394: 4364: 4359: 4358: 4353: 4343: 4322: 4306: 4280: 4249: 4218: 4177: 4151: 4120:High resolution 4115: 4110: 4043: 3927: 3925:Further reading 3922: 3875: 3871: 3834:(7115): 79–81. 3823: 3819: 3790:(Pt 1): 75–81. 3780: 3776: 3747:(Pt 1): 18–21. 3737: 3733: 3688:(6902): 55–58. 3674: 3670: 3643:Ultramicroscopy 3638: 3634: 3602: 3598: 3555: 3551: 3492: 3488: 3481: 3477: 3450:Ultramicroscopy 3442: 3438: 3399: 3395: 3372: 3368: 3347:(Pt 1): 29–35. 3337: 3333: 3312: 3308: 3296: 3292: 3269:(90): 297–301. 3255: 3251: 3208: 3204: 3185:Ultramicroscopy 3177: 3173: 3114: 3110: 3081:(10): 609–619. 3067: 3063: 3032: 3028: 3019: 3015: 2976:(2–3): 94–102. 2962: 2958: 2897: 2893: 2832: 2828: 2781: 2777: 2730: 2726: 2679: 2675: 2644: 2640: 2587: 2583: 2530: 2526: 2469: 2465: 2452: 2448: 2405: 2401: 2358: 2354: 2315: 2311: 2268: 2264: 2229: 2225: 2190:Surface Science 2182: 2178: 2135: 2131: 2096:Ultramicroscopy 2088: 2084: 2041: 2037: 2029: 2025: 1998:Ultramicroscopy 1990: 1986: 1971: 1955: 1951: 1900: 1896: 1853: 1849: 1806: 1802: 1759: 1755: 1712: 1708: 1677: 1673: 1630: 1626: 1599: 1595: 1550: 1546: 1493: 1489: 1438: 1434: 1383: 1379: 1336: 1332: 1297:Physical Review 1289: 1285: 1254: 1250: 1213:(36): 778–786. 1199: 1195: 1158: 1154: 1119:Physical Review 1111: 1107: 1072: 1065: 1022: 1018: 965: 961: 908: 904: 841: 834: 771: 764: 727:Physical Review 719: 715: 664: 660: 650: 648: 640: 634: 630: 585:(6902): 55–58. 567: 563: 520: 516: 512: 434: 376: 359:liquid nitrogen 343: 277: 135: 84:, the other by 66: 23: 17: 12: 11: 5: 5328: 5318: 5317: 5312: 5295: 5294: 5292: 5291: 5279: 5266: 5263: 5262: 5259: 5258: 5256: 5255: 5250: 5245: 5244: 5243: 5238: 5233: 5222: 5220: 5213: 5212: 5207: 5202: 5197: 5191: 5189: 5183: 5182: 5180: 5179: 5174: 5169: 5163: 5161: 5155: 5154: 5152: 5151: 5146: 5141: 5136: 5131: 5126: 5121: 5115: 5113: 5107: 5106: 5104: 5103: 5098: 5093: 5088: 5083: 5078: 5073: 5067: 5065: 5059: 5058: 5056: 5055: 5050: 5045: 5040: 5035: 5030: 5025: 5020: 5014: 5012: 5006: 5005: 5003: 5002: 4997: 4996: 4995: 4985: 4980: 4975: 4970: 4965: 4963:Direct methods 4959: 4957: 4953: 4952: 4950: 4949: 4948: 4947: 4942: 4932: 4927: 4926: 4925: 4920: 4910: 4909: 4908: 4903: 4892: 4890: 4884: 4883: 4875: 4873: 4871: 4870: 4865: 4860: 4855: 4850: 4848:Ewald's sphere 4845: 4840: 4834: 4831: 4830: 4828: 4827: 4822: 4817: 4816: 4815: 4810: 4800: 4799: 4798: 4793: 4791:Frenkel defect 4788: 4786:Bjerrum defect 4778: 4777: 4776: 4766: 4765: 4764: 4759: 4754: 4752:Peierls stress 4749: 4744: 4739: 4734: 4729: 4724: 4722:Burgers vector 4714: 4712:Stacking fault 4709: 4703: 4700: 4699: 4697: 4696: 4691: 4686: 4681: 4675: 4673: 4671:Grain boundary 4664: 4658: 4657: 4655: 4654: 4649: 4644: 4639: 4634: 4629: 4624: 4619: 4618: 4617: 4615:Liquid crystal 4612: 4607: 4602: 4591: 4589: 4581: 4580: 4578: 4577: 4576: 4575: 4565: 4564: 4563: 4553: 4552: 4551: 4546: 4535: 4532: 4531: 4529: 4528: 4523: 4518: 4513: 4508: 4503: 4497: 4495: 4486: 4485: 4480: 4478:Periodic table 4475: 4474: 4473: 4468: 4463: 4458: 4453: 4442: 4440: 4431: 4430: 4425: 4420: 4419: 4418: 4407: 4405: 4401: 4400: 4393: 4392: 4385: 4378: 4370: 4361: 4360: 4354: 4349: 4348: 4345: 4344: 4342: 4341: 4336: 4330: 4328: 4324: 4323: 4321: 4320: 4314: 4312: 4308: 4307: 4305: 4304: 4299: 4294: 4288: 4286: 4282: 4281: 4279: 4278: 4273: 4268: 4263: 4257: 4255: 4251: 4250: 4248: 4247: 4242: 4237: 4232: 4226: 4224: 4220: 4219: 4217: 4216: 4211: 4206: 4201: 4196: 4191: 4185: 4183: 4179: 4178: 4176: 4175: 4170: 4165: 4159: 4157: 4153: 4152: 4150: 4149: 4144: 4139: 4134: 4129: 4123: 4121: 4117: 4116: 4109: 4108: 4101: 4094: 4086: 4080: 4079: 4050: 4042: 4041:External links 4039: 4038: 4037: 4023: 3980: 3943: 3926: 3923: 3921: 3920: 3869: 3817: 3774: 3731: 3668: 3632: 3596: 3569:(6): 434–443. 3549: 3506:(5): 399–410. 3486: 3475: 3456:(3): 271–282. 3436: 3393: 3366: 3331: 3306: 3290: 3249: 3222:(2): 280–290. 3202: 3191:(1–3): 55–65. 3171: 3108: 3061: 3026: 3013: 2956: 2891: 2826: 2775: 2724: 2673: 2654:(4): 899–929. 2638: 2581: 2544:(9): 927–930. 2538:Nature Methods 2524: 2479:(2): 436–441. 2463: 2446: 2419:(1740): 1–16. 2399: 2372:(6): 528–536. 2352: 2309: 2262: 2243:(3): 306–319. 2223: 2176: 2129: 2082: 2055:(6): 434–443. 2035: 2023: 2004:(3): 271–282. 1984: 1969: 1949: 1914:(3): 350–352. 1894: 1867:(3): 357–368. 1847: 1800: 1773:(3): 317–324. 1753: 1706: 1687:(3): 339–347. 1671: 1644:(2): 113–140. 1624: 1593: 1564:(4): 305–310. 1544: 1507:(6): 522–529. 1487: 1432: 1377: 1350:(5): 607–640. 1330: 1283: 1264:(9): 675–676. 1248: 1193: 1172:(6): 271–274. 1152: 1105: 1086:(17): 55–129. 1063: 1036:(2): 245–275. 1016: 959: 902: 855:(8): 619–627. 832: 785:(4): 317–322. 762: 733:(6): 705–740. 713: 658: 628: 561: 513: 511: 508: 482:Miller indices 478:direct methods 433: 430: 375: 372: 342: 339: 276: 273: 247:direct methods 216:direct methods 189:microstructure 161:Walther Kossel 138:John M. Cowley 133: 111:Seishi Kikuchi 65: 62: 19:Main article: 15: 9: 6: 4: 3: 2: 5327: 5316: 5313: 5311: 5308: 5307: 5305: 5290: 5289: 5280: 5278: 5277: 5268: 5267: 5264: 5254: 5251: 5249: 5246: 5242: 5239: 5237: 5234: 5232: 5229: 5228: 5227: 5224: 5223: 5221: 5217: 5211: 5208: 5206: 5203: 5201: 5198: 5196: 5193: 5192: 5190: 5188: 5184: 5178: 5175: 5173: 5170: 5168: 5165: 5164: 5162: 5160: 5156: 5150: 5147: 5145: 5142: 5140: 5137: 5135: 5132: 5130: 5127: 5125: 5122: 5120: 5117: 5116: 5114: 5112: 5108: 5102: 5099: 5097: 5094: 5092: 5089: 5087: 5084: 5082: 5079: 5077: 5074: 5072: 5069: 5068: 5066: 5064: 5060: 5054: 5051: 5049: 5046: 5044: 5041: 5039: 5036: 5034: 5031: 5029: 5026: 5024: 5021: 5019: 5016: 5015: 5013: 5011: 5007: 5001: 4998: 4994: 4991: 4990: 4989: 4986: 4984: 4983:Patterson map 4981: 4979: 4976: 4974: 4971: 4969: 4966: 4964: 4961: 4960: 4958: 4954: 4946: 4943: 4941: 4938: 4937: 4936: 4933: 4931: 4928: 4924: 4921: 4919: 4916: 4915: 4914: 4911: 4907: 4904: 4902: 4899: 4898: 4897: 4894: 4893: 4891: 4889: 4885: 4879: 4869: 4866: 4864: 4861: 4859: 4856: 4854: 4853:Friedel's law 4851: 4849: 4846: 4844: 4841: 4839: 4836: 4835: 4826: 4823: 4821: 4818: 4814: 4811: 4809: 4806: 4805: 4804: 4801: 4797: 4796:Wigner effect 4794: 4792: 4789: 4787: 4784: 4783: 4782: 4781:Interstitials 4779: 4775: 4772: 4771: 4770: 4767: 4763: 4760: 4758: 4755: 4753: 4750: 4748: 4745: 4743: 4740: 4738: 4735: 4733: 4730: 4728: 4725: 4723: 4720: 4719: 4718: 4715: 4713: 4710: 4708: 4705: 4704: 4695: 4692: 4690: 4687: 4685: 4682: 4680: 4677: 4676: 4674: 4672: 4668: 4665: 4663: 4659: 4653: 4650: 4648: 4645: 4643: 4640: 4638: 4635: 4633: 4630: 4628: 4627:Precipitation 4625: 4623: 4620: 4616: 4613: 4611: 4608: 4606: 4603: 4601: 4598: 4597: 4596: 4595:Phase diagram 4593: 4592: 4590: 4588: 4582: 4574: 4571: 4570: 4569: 4566: 4562: 4559: 4558: 4557: 4554: 4550: 4547: 4545: 4542: 4541: 4540: 4537: 4536: 4527: 4524: 4522: 4519: 4517: 4514: 4512: 4509: 4507: 4504: 4502: 4499: 4498: 4496: 4494: 4490: 4484: 4481: 4479: 4476: 4472: 4469: 4467: 4464: 4462: 4459: 4457: 4454: 4452: 4449: 4448: 4447: 4444: 4443: 4441: 4439: 4435: 4429: 4426: 4424: 4421: 4417: 4414: 4413: 4412: 4409: 4408: 4406: 4402: 4398: 4391: 4386: 4384: 4379: 4377: 4372: 4371: 4368: 4357: 4352: 4346: 4340: 4337: 4335: 4332: 4331: 4329: 4327:Computational 4325: 4319: 4316: 4315: 4313: 4311:Thermodynamic 4309: 4303: 4300: 4298: 4295: 4293: 4290: 4289: 4287: 4283: 4277: 4274: 4272: 4269: 4267: 4264: 4262: 4259: 4258: 4256: 4252: 4246: 4243: 4241: 4238: 4236: 4233: 4231: 4228: 4227: 4225: 4221: 4215: 4212: 4210: 4207: 4205: 4202: 4200: 4197: 4195: 4192: 4190: 4187: 4186: 4184: 4182:Spectroscopic 4180: 4174: 4171: 4169: 4166: 4164: 4161: 4160: 4158: 4154: 4148: 4145: 4143: 4140: 4138: 4135: 4133: 4130: 4128: 4125: 4124: 4122: 4118: 4114: 4107: 4102: 4100: 4095: 4093: 4088: 4087: 4084: 4076: 4072: 4068: 4064: 4061:(1): 89–105. 4060: 4056: 4051: 4048: 4045: 4044: 4036: 4032: 4028: 4024: 4020: 4016: 4011: 4006: 4002: 3998: 3994: 3990: 3986: 3981: 3977: 3973: 3969: 3965: 3961: 3957: 3953: 3949: 3944: 3942: 3940: 3936: 3933: 3929: 3928: 3916: 3912: 3908: 3904: 3900: 3896: 3892: 3888: 3884: 3880: 3873: 3865: 3861: 3857: 3853: 3849: 3845: 3841: 3837: 3833: 3829: 3821: 3813: 3809: 3805: 3801: 3797: 3793: 3789: 3785: 3778: 3770: 3766: 3762: 3758: 3754: 3750: 3746: 3742: 3735: 3727: 3723: 3719: 3715: 3711: 3707: 3703: 3699: 3695: 3691: 3687: 3683: 3679: 3672: 3664: 3660: 3656: 3652: 3649:(3): 164–75. 3648: 3644: 3636: 3628: 3624: 3620: 3616: 3612: 3608: 3600: 3592: 3588: 3584: 3580: 3576: 3572: 3568: 3564: 3560: 3553: 3545: 3541: 3537: 3533: 3529: 3525: 3521: 3517: 3513: 3509: 3505: 3501: 3497: 3490: 3484: 3479: 3471: 3467: 3463: 3459: 3455: 3451: 3447: 3440: 3432: 3428: 3424: 3420: 3416: 3412: 3409:(6587): 144. 3408: 3404: 3397: 3389: 3385: 3381: 3377: 3370: 3362: 3358: 3354: 3350: 3346: 3342: 3335: 3329: 3328:0-306-45049-6 3325: 3321: 3320: 3315: 3310: 3303: 3299: 3294: 3286: 3282: 3277: 3272: 3268: 3264: 3260: 3253: 3245: 3241: 3237: 3233: 3229: 3225: 3221: 3217: 3213: 3206: 3198: 3194: 3190: 3186: 3182: 3175: 3167: 3163: 3159: 3155: 3151: 3147: 3143: 3139: 3135: 3131: 3127: 3123: 3119: 3112: 3104: 3100: 3096: 3092: 3088: 3084: 3080: 3076: 3072: 3065: 3057: 3053: 3049: 3045: 3042:(5983): 238. 3041: 3037: 3030: 3023: 3017: 3009: 3005: 3001: 2997: 2992: 2987: 2983: 2979: 2975: 2971: 2967: 2960: 2952: 2948: 2943: 2938: 2934: 2930: 2926: 2922: 2918: 2914: 2910: 2906: 2902: 2895: 2887: 2883: 2878: 2873: 2869: 2865: 2861: 2857: 2853: 2849: 2845: 2841: 2837: 2830: 2822: 2818: 2814: 2810: 2806: 2802: 2798: 2794: 2790: 2786: 2779: 2771: 2767: 2763: 2759: 2755: 2751: 2747: 2743: 2739: 2735: 2728: 2720: 2716: 2712: 2708: 2704: 2700: 2696: 2692: 2688: 2684: 2677: 2669: 2665: 2661: 2657: 2653: 2649: 2642: 2634: 2630: 2625: 2620: 2616: 2612: 2608: 2604: 2600: 2596: 2592: 2585: 2577: 2573: 2568: 2563: 2559: 2555: 2551: 2547: 2543: 2539: 2535: 2528: 2520: 2516: 2512: 2508: 2504: 2500: 2496: 2492: 2487: 2482: 2478: 2474: 2467: 2459: 2458: 2450: 2442: 2438: 2434: 2430: 2426: 2422: 2418: 2414: 2410: 2403: 2395: 2391: 2387: 2383: 2379: 2375: 2371: 2367: 2363: 2356: 2348: 2344: 2340: 2336: 2332: 2328: 2324: 2320: 2313: 2305: 2301: 2297: 2293: 2289: 2285: 2281: 2277: 2273: 2266: 2258: 2254: 2250: 2246: 2242: 2238: 2234: 2227: 2219: 2215: 2211: 2207: 2203: 2199: 2195: 2191: 2187: 2180: 2172: 2168: 2164: 2160: 2156: 2152: 2148: 2144: 2140: 2133: 2125: 2121: 2117: 2113: 2109: 2105: 2101: 2097: 2093: 2086: 2078: 2074: 2070: 2066: 2062: 2058: 2054: 2050: 2046: 2039: 2033: 2027: 2019: 2015: 2011: 2007: 2003: 1999: 1995: 1988: 1980: 1976: 1972: 1966: 1962: 1961: 1953: 1945: 1941: 1937: 1933: 1929: 1925: 1921: 1917: 1913: 1909: 1905: 1898: 1890: 1886: 1882: 1878: 1874: 1870: 1866: 1862: 1858: 1851: 1843: 1839: 1835: 1831: 1827: 1823: 1819: 1815: 1811: 1804: 1796: 1792: 1788: 1784: 1780: 1776: 1772: 1768: 1764: 1757: 1749: 1745: 1741: 1737: 1733: 1729: 1725: 1721: 1717: 1710: 1702: 1698: 1694: 1690: 1686: 1682: 1675: 1667: 1663: 1659: 1655: 1651: 1647: 1643: 1639: 1635: 1628: 1620: 1616: 1612: 1608: 1604: 1597: 1589: 1585: 1580: 1575: 1571: 1567: 1563: 1559: 1555: 1548: 1540: 1536: 1532: 1528: 1523: 1518: 1514: 1510: 1506: 1502: 1498: 1491: 1483: 1479: 1475: 1471: 1467: 1463: 1459: 1455: 1451: 1448:(in German). 1447: 1443: 1436: 1428: 1424: 1420: 1416: 1412: 1408: 1404: 1400: 1396: 1393:(in German). 1392: 1388: 1381: 1373: 1369: 1365: 1361: 1357: 1353: 1349: 1345: 1341: 1334: 1326: 1322: 1318: 1314: 1310: 1306: 1302: 1298: 1294: 1287: 1279: 1275: 1271: 1267: 1263: 1259: 1252: 1244: 1240: 1236: 1232: 1228: 1224: 1220: 1216: 1212: 1208: 1204: 1197: 1189: 1185: 1180: 1175: 1171: 1167: 1163: 1156: 1148: 1144: 1140: 1136: 1132: 1128: 1124: 1120: 1116: 1109: 1101: 1097: 1093: 1089: 1085: 1082:(in German). 1081: 1077: 1070: 1068: 1059: 1055: 1051: 1047: 1043: 1039: 1035: 1031: 1027: 1020: 1012: 1008: 1004: 1000: 995: 990: 986: 982: 978: 974: 970: 963: 955: 951: 947: 943: 938: 933: 929: 925: 922:(3007): 890. 921: 917: 913: 906: 898: 894: 889: 884: 880: 876: 871: 866: 862: 858: 854: 850: 846: 839: 837: 828: 824: 819: 814: 810: 806: 801: 796: 792: 788: 784: 780: 776: 769: 767: 758: 754: 749: 744: 740: 736: 732: 728: 724: 717: 709: 705: 701: 697: 693: 689: 685: 681: 677: 673: 669: 662: 646: 639: 632: 624: 620: 616: 612: 608: 604: 600: 596: 592: 588: 584: 580: 576: 572: 565: 557: 553: 549: 545: 541: 537: 533: 529: 525: 518: 514: 507: 505: 500: 498: 493: 490: 485: 483: 479: 473: 471: 467: 463: 459: 455: 451: 446: 442: 438: 424: 415: 411: 409: 405: 401: 397: 392: 389: 385: 381: 371: 369: 364: 363:liquid helium 360: 356: 352: 348: 338: 335: 330: 326: 322: 318: 313: 310: 306: 305:viral capsids 302: 298: 294: 290: 286: 282: 272: 269: 264: 263:bacteriophage 260: 256: 250: 248: 244: 240: 236: 232: 229: 225: 221: 217: 213: 209: 204: 202: 197: 192: 190: 186: 182: 178: 174: 170: 166: 162: 156: 155: 149: 147: 146:John M Cowley 143: 139: 130: 128: 124: 120: 117:developed by 116: 112: 108: 104: 100: 99:Lester Germer 96: 92: 87: 83: 79: 75: 71: 61: 57: 55: 51: 47: 43: 39: 35: 31: 27: 22: 5286: 5274: 5219:Associations 5187:Organisation 4895: 4679:Disclination 4610:Polymorphism 4573:Quasicrystal 4516:Orthorhombic 4456:Miller index 4404:Key concepts 4209:Fluorescence 4141: 4058: 4054: 4026: 3992: 3988: 3951: 3947: 3941: 3882: 3878: 3872: 3831: 3827: 3820: 3787: 3783: 3777: 3744: 3740: 3734: 3685: 3681: 3671: 3646: 3642: 3635: 3610: 3606: 3599: 3566: 3562: 3552: 3503: 3499: 3489: 3478: 3453: 3449: 3439: 3406: 3402: 3396: 3379: 3375: 3369: 3344: 3340: 3334: 3318: 3314:D. L. Dorset 3309: 3301: 3293: 3266: 3262: 3252: 3219: 3215: 3205: 3188: 3184: 3174: 3128:(1): 34–40. 3125: 3121: 3111: 3078: 3074: 3064: 3039: 3035: 3029: 3021: 3016: 2973: 2969: 2959: 2908: 2904: 2894: 2843: 2839: 2829: 2788: 2784: 2778: 2737: 2733: 2727: 2686: 2682: 2676: 2651: 2647: 2641: 2598: 2594: 2584: 2541: 2537: 2527: 2476: 2472: 2466: 2456: 2449: 2416: 2412: 2402: 2369: 2365: 2355: 2322: 2318: 2312: 2279: 2275: 2265: 2240: 2236: 2226: 2193: 2189: 2179: 2146: 2142: 2132: 2099: 2095: 2085: 2052: 2048: 2038: 2026: 2001: 1997: 1987: 1959: 1952: 1911: 1907: 1897: 1864: 1860: 1850: 1820:(2): 77–97. 1817: 1813: 1803: 1770: 1766: 1756: 1723: 1719: 1709: 1684: 1680: 1674: 1641: 1637: 1627: 1610: 1606: 1596: 1561: 1557: 1547: 1504: 1500: 1490: 1449: 1445: 1435: 1394: 1390: 1380: 1347: 1343: 1333: 1303:(2): 73–76. 1300: 1296: 1286: 1261: 1257: 1251: 1210: 1206: 1196: 1169: 1165: 1155: 1122: 1118: 1108: 1083: 1079: 1033: 1029: 1019: 976: 972: 962: 919: 915: 905: 852: 848: 782: 778: 730: 726: 716: 675: 671: 661: 649:. Retrieved 644: 631: 582: 578: 564: 531: 527: 517: 501: 494: 486: 474: 436: 435: 377: 355:cryofixation 344: 314: 278: 255:James Menter 251: 205: 193: 181:space groups 177:point groups 158: 154:information. 152: 151: 131: 78:matter waves 73: 67: 58: 25: 24: 5172:Ewald Prize 4940:Diffraction 4918:Diffraction 4901:Diffraction 4843:Bragg plane 4838:Bragg's law 4717:Dislocation 4632:Segregation 4544:Crystallite 4461:Point group 1613:: 267–321. 651:25 February 301:polyhedrons 239:Jon Gjønnes 173:John Steeds 127:Ernst Ruska 119:Herman Mark 103:Bragg's law 5304:Categories 4956:Algorithms 4945:Scattering 4923:Scattering 4906:Scattering 4774:Slip bands 4737:Cross slip 4587:transition 4521:Tetragonal 4511:Monoclinic 4423:Metallurgy 4204:Absorbance 2648:J Mol Biol 2486:2210.09024 510:References 470:multislice 445:Aaron Klug 334:Aaron Klug 287:, such as 259:Aaron Klug 107:Hans Bethe 91:Hans Bethe 5063:Databases 4526:Triclinic 4506:Hexagonal 4446:Unit cell 4438:Structure 3710:0028-0836 3583:0108-7673 3528:1431-9276 3470:0304-3991 3285:0025-5718 3244:0567-7394 3150:1431-9276 3103:0365-110X 3000:0044-2968 2933:0907-4449 2868:0028-0836 2770:205209809 2615:0969-2126 2595:Structure 2558:1548-7091 2441:0080-4630 2394:0567-7394 2304:0080-4630 2218:0039-6028 2171:0734-2101 2116:0304-3991 2069:0108-7673 2018:0304-3991 1979:681437461 1936:0567-7394 1889:0108-7673 1834:0741-0581 1795:0021-8898 1748:122890943 1666:0003-3804 1588:0365-110X 1531:0365-110X 1482:123199621 1474:1434-6001 1427:186239132 1419:1434-6001 1372:0003-3804 1325:0031-899X 1278:178706417 1235:0028-1042 1147:0031-899X 1058:171025814 1050:0007-0874 1003:0950-1207 946:0028-0836 879:0027-8424 809:0027-8424 757:0031-899X 700:0028-0836 607:0028-0836 556:0734-2101 408:aquaporin 404:flagellum 337:in 1982. 123:Max Knoll 5276:Category 5111:Journals 5043:OctaDist 5038:JANA2020 5010:Software 4896:Electron 4813:F-center 4600:Eutectic 4561:Fiveling 4556:Twinning 4549:Equiaxed 4285:Chemical 4075:19416061 4019:18156680 3915:19509220 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Index

Electron diffraction
electron diffraction
transmission electron microscope
high-resolution transmission electron microscopy
electron diffraction
convergent-beam electron diffraction
low-energy electron diffraction
reflection high-energy electron diffraction
Louis de Broglie
matter waves
Davisson–Germer experiment
George Paget Thomson
Hans Bethe
Clinton Davisson
Lester Germer
Bragg's law
Hans Bethe
Seishi Kikuchi
gas electron diffraction
Herman Mark
Max Knoll
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John M. Cowley
William Houlder Zachariasen
John M Cowley
Walther Kossel
Gottfried Möllenstedt
convergent beam electron diffraction
John Steeds
point groups

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