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potential over the whole field of view. The thereby reconstructed crystal potential is corrected for aberration and delocalisation and also not affected by possible transfer gaps since several images with different defocus are processed. CIP on the other side considers only one image and applies corrections on the averaged image amplitudes and phases. The result of the latter is a pseudo-potential map of one projected unit cell. The result can be further improved by crystal tilt compensation and search for the most likely projected symmetry. In conclusion one can say that the exit-wave function reconstruction method has most advantages for determining the (aperiodic) atomic structure of defects and small clusters and CIP is the method of choice if the periodic structure is in focus of the investigation or when defocus series of HREM images cannot be obtained, e.g. due to beam damage of the sample. However, a recent study on the catalyst related material Cs
438:
Medical
Research Council (MRC) image processing programs and possess additional functionality such as the "unbending" of the image. As the name suggests, unbending of the image is conceptually equivalent to "flattening out and relaxing to equilibrium positions" one building block thick samples so that all 2D periodic motifs are as similar as possible and all building blocks of the array possess the same crystallographic orientation with respect to a cartesian coordinate system that is fixed to the microscope. (The microscope's optical axis typically serves as the z-axis.) Unbending is often necessary when the 2D array of membrane proteins is
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201:
which is used to determine the defocus value (Îf = -650 Ă
). The reciprocal lattice is then indexed and amplitudes and phases are extracted. The amplitudes and phases can be used to calculate the averaged image for one unit cell via
Fourier synthesis. The pseudo-potential map (p2gg symmetry) for determining 2D atomic co-ordinates was obtained after correction of the phase-shifts imposed by the CTF. The average agreement of atomic co-ordinates determined from the pseudo-potential map and the superimposed model from X-ray diffraction is about 0.2 Ă
.
344:. Such inferences are deeply rooted in information theory, where one is not trying to model empirical data, but extracts and models the information content of the data. The key difference between geometric inference and all kinds of traditional statistical inferences is that the former merely states the co-existence of a set of definitive (and exact geometrical) constraints and noise, whereby noise is nothing else but an unknown characteristic of the measurement device and data processing operations. From this follows that
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the thickness of the crystal under investigation has also a significant influence on the image contrast. These two factors often mix and yield HREM images which cannot be straightforwardly interpreted as a projected structure. If the structure is unknown, so that image simulation techniques cannot be applied beforehand, image interpretation is even more complicated. Nowadays two approaches are available to overcome this problem: one method is the
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in the
Moorish/Arabic/Islamic tradition. The goals of these researchers are often related to the identification of point and translation symmetries by computational means and the subsequent classifications of patterns into groups. Since their patterns were artificially created, they do not need to obey all of the restrictions that nature typically imposes on long range periodic ordered arrays of atoms or molecules.
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304:, which has been inaccessible by X-ray crystallography. Since CIP on single HREM images works only smoothly for layer-structures with at least one short (3 to 5 Ă
) crystal axis, the method was extended to work also with data from different crystal orientations (= atomic resolution electron tomography). This approach was used in 1990 to reconstruct the 3D structure of the mineral
193:
22:
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3D crystals or along the layer normal of a membrane forming protein sample ensure the projection of 3D symmetry into 2D. (Along arbitrary high-index zone axes and inclined to the layer normal of membrane forming proteins, there will be no useful projected symmetry in transmission images.) The recovery of 3D structures and their symmetries relies on
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63:
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Structural biologists achieve resolutions of a few Ängströms (up from a to few nanometers in the past when samples used to be negatively stained) for membrane forming proteins in regular two-dimensional arrays, but prefer the usage of the programs 2dx, EMAN2, and IPLT. These programs are based on the
1472:
X.D. Zou, T.E. Weirich & S. Hovmöller (2001) "Electron
Crystallography - Structure determination by combining HREM, crystallographic image processing and electron diffraction." In: Progress in Transmission Electron Microscopy, I. Concepts and Techniques, X.F. Zhang, Z. Zhang Ed., Springer Series
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Inorganic crystals are much stiffer than 2D periodic protein membrane arrays so that there is no need for the unbending of images that were taken from suitably thinned parts of these crystals. Consequently, the CRISP program does not possess the unbending image processing feature but offers superior
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approximant phase Μ-AlCrFe and the structures of the complex zeolites TNU-9 and IM-5. As mentioned below in the section on crystallographic processing of images that were recorded from 2D periodic arrays with other types of microscopes, the CIP techniques were taken up since 2009 by members of the
2001:
Moeck, P., Toader, M., Abdel-Hafiez, M., Michael
Hietschold, M. (2009) "Quantifying and enforcing two-dimensional symmetries in scanning probe microscopy images", in: "Frontiers of Characterization and Metrology for Nanoelectronics", edited by D. G. Seiler, A. C. Diebold, R. McDonald, C. M. Garner,
510:
data organized in 2D arrays of pixels, core features of
Crystallographic Image Processing can be utilized independent of the type of microscope with which the images/data were recorded. The CIP technique has, accordingly been applied (on the basis of the 2dx program) to atomic resolution Z-contrast
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All individual transmission electron microscopy images are projections from the three-dimensional space of the samples into two dimensions (so that spatial distribution information along the projection direction is unavoidably lost). Projections along prominent (i.e. certain low-index) zone axes of
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name and without utilization of its full mathematical framework (e.g. ignorance to the proper choice of the origin of a unit cell and preference for direct space analyses). Frequently, they are working with artificially created 2D periodic patterns, e.g. wallpapers, textiles, or building decoration
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of the objective lens alter the image contrast as function of the defocus. Hence atom columns which appear at one defocus value as dark blobs can turn into white blobs at a different defocus and vice versa. In addition to the objective lens defocus (which can easily be changed by the TEM operator),
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group types (of which there are 46 in total and which are periodic only in 2D) due to the chiral nature of all (naturally occurring) proteins. Different crystallographic settings of four of these layer group types increase the number of possible layer group symmetries of regular arrays of membrane
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method, which requires several HREM images from the same area at different defocus and the other method is crystallographic image processing (CIP) which processes only a single HREM image. Exit-wave function reconstruction provides an amplitude and phase image of the (effective) projected crystal
224:
during the early 1980s and became rapidly a label for the "3D crystal structure from 2D transmission/projection images" approach. Since the late 1990s, analogous and complementary image processing techniques that are directed towards the achieving of goals with are either complementary or entirely
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Se recorded with a 300 kV TEM (JEOL 3010 UHR, point resolution 1.7 Ă
) along the zone axis. In the first step the
Fourier transform of the HREM image is calculated (only the amplitudes are shown). The position of the white ring marks the first crossover of the contrast transfer function (CTF)
359:
These kinds of ideas have, however, only been taken up by a tiny minority of researchers within the computational symmetry and scanning probe microscopy / applied crystallography communities. It is fair to say that the members of computational symmetry community are doing crystallographic image
433:
A few computer programs are available which assist to perform the necessary steps of processing. The most popular programs used by materials scientists (electron crystallographers) are CRISP, VEC, and the EDM package. There is also the recently developed crystallographic image processing program
526:
T. E. Weirich, From
Fourier series towards crystal structures - a survey of conventional methods for solving the phase problem; in: Electron Crystallography - Novel Approaches for Structure Determination of Nanosized Materials, T. E. Weirich, J. L. LĂĄbĂĄr, X. Zou, (Eds.), Springer 2006, 235 -
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heavy-metal oxide could be determined from single HREM images recorded at
Scherzer defocus. (Scherzer defocus ensures within the weak-phase object approximation a maximal contribution to the image of elastically scattered electrons that were scattered just once while contributions of doubly
478:
The origin refinement part of CIP relies on the definition of the plane symmetry group types as provided by the
International Tables of Crystallography, where all symmetry equivalent positions in the unit cell and their respective site symmetries are listed along with systematic absences in
511:
images of Si-clathrates, as recorded in an aberration-corrected scanning transmission electron microscope. Images of 2D periodic arrays of flat lying molecules on a substrate as recorded with scanning tunneling microscopes were also crystallographic processed utilizing the program CRISP.
2011:
Moeck, P. (2011) "Crystallographic Image Processing for Scanning Probe Microscopy" In: âMicroscopy: Science Technology, Applications and Educationâ, Microscopy Book Series No. 4, Vol. 3, pp. 1951-1962, A. MĂ©ndez-Vilas and J. Diaz (editors), Formatex Research Center, 2010,
946:
Gramm, Fabian; Baerlocher, Christian; McCusker, Lynne B.; Warrender, Stewart J.; Wright, Paul A.; Han, Bada; Hong, Suk Bong; Liu, Zheng; Ohsuna, Tetsu; Terasaki, Osamu (2006). "Complex zeolite structure solved by combining powder diffraction and electron microscopy".
241:. In that case the positions of the atom columns appear as black blobs in the image (when the spherical aberration coefficient of the objective lens is positive - as always the case for uncorrected TEMs). Difficulties for interpretation of HREM images arise for other
225:
beyond the scope of the original inception of CIP have been developed independently by members of the computational symmetry/geometry, scanning transmission electron microscopy, scanning probe microscopy communities, and applied crystallography communities.
453:
group out of the 230 possible groups types that exist in three dimensions. The regular arrays of membrane forming proteins that structural biologists deal with are, on the other hand, restricted to possess one out of only 17 (two-sided/black-white)
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All 3D space groups and their subperiodic 2D periodic layer groups (including the above-mentioned 46 two-sided groups) project to just 17 plane space group types, which are genuinely 2D periodic and are sometimes referred to as the
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In later years the methods became more sophisticated so that also non-Scherzer images could be processed. One of the most impressive applications at that time was the determination of the complete structure of the complex compound
356:. Because many of these approaches use linear approximations, the level of random noise needs to be low to moderate, or in other words, the measuring devices must be very well corrected for all kinds of known systematic errors.
1906:
Henderson, R.; Baldwin, J.M.; Downing, K.H.; Lepault, J.; Zemlin, F. (1986). "Structure of purple membrane from halobacterium halobium: Recording, measurement and evaluation of electron micrographs at 3.5 Ă
resolution".
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structures can also be used for structure determination of inorganic crystals. This idea was picked up by the research group of Sven Hovmöller which proved that the metal framework partial structure of the
2879:
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336:, but have so far failed to utilize the spatial distribution of site symmetries that result from crystallographic origin conventions. In addition, a well known statistician noted in his comments on
1351:"Double-tip effects on scanning tunneling microscopy imaging of 2D periodic objects: Unambiguous detection and limits of their removal by crystallographic averaging in the spatial frequency domain"
1050:, "Computational Symmetry" in: Symmetry 2000, Part I, eds. I. Hargittai and T. C. Laurent, chapter 21, p. 231â245, Portland Press, London, 2002, (Wenner-Gren International Series, vol. 80),
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When crystallographic image processing is utilized in scanning probe microscopy, the symmetry groups to be considered are just the 17 plane space group types in their possible 21 settings.
2930:
1236:
Burnham, Kenneth P.; Anderson, David R.; Huyvaert, Kathryn P. (2011). "AIC model selection and multimodel inference in behavioral ecology: Some background, observations, and comparisons".
495:, all other plane group symmetries are centrosymmetric so that the origin refinement simplifies to the determination of the correct signs of the amplitudes of the Fourier coefficients.
1181:
Hahn T. (2005) International Tables for Crystallography, Brief Teaching Edition of Volume A, Space-group symmetry. 5th revised edition, Chester: International Union of Crystallography
822:
Downing, Kenneth H.; Meisheng, Hu; Wenk, Hans-Rudolf; O'Keefe, Michael A. (1990). "Resolution of oxygen atoms in staurolite by three-dimensional transmission electron microscopy".
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that symmetry groups possess inclusion relations (are not disjoint in other words) so that conclusions about which symmetry is most likely present in an image need to be based on
1137:
Albert, F.; GĂłmis, J.M.; Blasco, J.; Valiente, J.M.; Aleixos, N. (2015). "A new method to analyse mosaics based on Symmetry Group theory applied to Islamic Geometric Patterns".
368:
Computational geometry takes a broader view on this issue and concluded already in 1991 that the problem of testing approximate point symmetries in noisy images is in general
35:
1463:
C. Dieckmann (2012) Symmetry Detection and Approximation, Dissertation zur Erlangung des Doktorgrades, Fachbereich Mathematik und Informatik der Freien UniversitÀt Berlin
1550:
Recent Progress in Mesostructured Materials - Proceedings of the 5th International Mesostructured Materials Symposium (IMMS2006), Shanghai, P.R. China, August 5-7, 2006
779:
Weirich, Thomas E.; Ramlau, Reiner; Simon, Arndt; Hovmöller, Sven; Zou, Xiaodong (1996). "A crystal structure determined with 0.02 Ă
accuracy by electron microscopy".
251:
238:
1967:
Morgan, D. G.; Ramasse, Q. M.; Browning, N. D. (2009). "Application of two-dimensional crystallography and image processing to atomic resolution Z-contrast images".
208:
is traditionally understood as being a set of key steps in the determination of the atomic structure of crystalline matter from high-resolution electron microscopy (
442:
rather than genuinely crystalline. It was estimated that unbending approximately doubles the spatial resolution with which the shape of molecules can be determined
865:
Wenk, H.-R.; Downing, K. H.; Hu, M.; O'Keefe, M. A. (1992). "3D structure determination from electron-microscope images: Electron crystallography of staurolite".
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415:
Imposing constrains of the most likely plane group symmetry on the amplitudes an phases. At this step the image phases are converted into the phases of the
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K. P. Burnham and D R Anderson (2002) Model selection and multimodel inference: a practical information-theoretic approach, 2nd edition. Springer, New York
2935:
2660:
2826:
2118:
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Philippsen, A.; Schenk, A. D.; Stahlberg, H.; Engel, A. (2003). "Iplt--image processing library and toolkit for the electron microscopy community".
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Hovmöller, Sven; Sukharev, Yuri I.; Zharov, Andrei G. (1991). "CRISP â A new system for crystallographic image processing on personal computers".
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376:. For restricted versions of this problem, there exist polynomial time algorithms that solve the corresponding optimization problems for a few
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2017:
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The principal steps for solving a structure of an inorganic crystal from HREM images by CIP are as follows (for a detailed discussion see ).
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143:
73:
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K. Kanatani, (1996) Statistical Optimization for Geometric Computation: Theory and Practice, Dover Books on Mathematics, Mineola, New York
84:
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Yanxi Liu; Collins, R.T.; Tsin, Y. (2004). "A computational model for periodic pattern perception based on frieze and wallpaper groups".
2961:
2859:
2555:
1069:, C. S. Kaplan, and L. V. Gool (2009) "Foundations and Trends in Computer Graphics and Vision" vol. 5, Nos. 1â2, p. 1â195, open access:
350:"geometric models we must take into account the fact that the noise is identical (but unknown) and has the same characteristic for both"
1624:
Xue-Ming, Li; Fang-Hua, Li; Hai-Fu, Fan (2009). "A revised version of the program VEC (Visual computing in electron crystallography)".
2208:
537:
Thust, A.; Overwijk, M.H.F.; Coene, W.M.J.; Lentzen, M. (1996). "Numerical correction of lens aberrations in phase-retrieval HRTEM".
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groups. (Although quite popular, this is a misnomer because wallpapers are not restricted to possess these symmetries by nature.)
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213:
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Gipson, Bryant; Zeng, Xiangyan; Zhang, Zi Yan; Stahlberg, Henning (2007). "2dxâUser-friendly image processing for 2D crystals".
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Sun, Junliang; He, Zhanbing; Hovmöller, Sven; Zou, Xiaodong; Gramm, Fabian; Baerlocher, Christian; McCusker, Lynne B. (2010).
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Determining the defocus value and compensating for the contrast changes imposed by the objective lens (done in Fourier space)
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2111:
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free for academic usages, particularly useful for the analysis of incommensurately modulated structures (for Windows PCs)
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2213:
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139:
135:
2246:
2141:
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Wan, Z.; Liu, Y.; Fu, Z.; Li, Y.; Cheng, T.; Li, F.; Fan, H. (2003). "Visual computing in electron crystallography".
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Crystallographic processing of images that were recorded from 2D periodic arrays with other types of microscopes
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2256:
2236:
2104:
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2414:
739:"Structure projection retrieval by image processing of HREM images taken under non-optimum defocus conditions"
638:
Klug, A. (1979). "Image Analysis and Reconstruction in the Electron Microscopy of Biological Macromolecules".
564:
Allen, L.J.; McBride, W.; O'Leary, N.L.; Oxley, M.P. (2004). "Exit wave reconstruction at atomic resolution".
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scanning transmission electron microscopy, scanning probe microscopy and applied crystallography communities.
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The latter feature is particularly important for electron crystallographers as their samples may possess any
2854:
2698:
2643:
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1548:: Software for determining 3D pore structures of ordered mesoporous materials by electron crystallography".
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1392:"Removal of multiple-tip artifacts from scanning tunneling microscope images by crystallographic averaging"
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2424:
2158:
599:
Barthel, Juri; Weirich, Thomas E.; Cox, Gerhard; Hibst, Hartmut; Thust, Andreas (2010). "Structure of Cs
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Many beam HREM images of extremely thin samples are only directly interpretable in terms of a projected
77:
that states a Knowledge (XXG) editor's personal feelings or presents an original argument about a topic.
2069:
1127:(2014) "Computational Symmetry", Computer Vision, A Reference Guide, Ikeuchi, K. (ed.), Springer, 2014
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Hovmöller, Sven; Sjögren, Agneta; Farrants, George; Sundberg, Margareta; Marinder, Bengt-Olov (1984).
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Crystallographic Image Processing (CIP) of a high-resolution electron microscopy (HREM) image of α-Ti
1871:
Gil, Debora; Carazo, Jose Maria; Marabini, Roberto (2006). "On the nature of 2D crystal unbending".
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open source, free for non-commercial purposes - a ready to go version of EDM is implemented on the
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suggested in 1979 that a technique that was originally developed for structure determination of
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may contain an excessive amount of intricate detail that may interest only a particular audience
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2042:, the classical standard for structural biology, free for academic usages (Fortran source code)
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Extracting amplitudes and phase values at the refined lattice positions (done in Fourier space)
216:) that is run in the parallel illumination mode. The term was created in the research group of
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2013:
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659:"Three-dimensional structure determination by electron microscopy of two-dimensional crystals"
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2002:
D. Herr, R. P. Khosla, and E. M. Secula, American Institute of Physics, 978-0-7354-0712-1/09.
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Zhang, H.; Yu, T.; Oleynikov, P.; Zhao, D.Y.; Hovmöller, S.; Zou, X.D. (2007). "Crisp and e
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Hovmöller, Sven (1992). "CRISP: Crystallographic image processing on a personal computer".
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Crowther, R.A.; Henderson, R.; Smith, J.M. (1996). "MRC Image Processing Programs".
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open source, structural biology (for Mac PCs, Linux, and a Windows PC demo version)
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1066:
984:
851:
808:
577:
325:
2066:, open source, structural biology including single particle reconstruction (Linux)
1934:
Braun, Thomas; Engel, Andreas (2005). "Twoâdimensional Electron Crystallography".
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332:
Contemporary robotics and computer vision researchers also deal with the topic of
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commercial, but superior for inorganic electron crystallography (for Windows PCs)
1602:
1271:
Kanatani, Kenichi (1998). "Geometric Information Criterion for Model Selection".
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Because digitized 2D periodic images are in the information theoretical approach
408:
Determining the origin of the projected unit cell and determining the projected (
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analysed by focal-series reconstruction and crystallographic image processing".
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450:
409:
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Kilaas, R.; Marks, L.D.; Own, C.S. (2005). "EDM 1.0: Electron direct methods".
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1552:. Studies in Surface Science and Catalysis. Vol. 165. pp. 109â112.
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1980:
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1000:"Structure determination of the zeolite IM-5 using electron crystallography"
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with corrected (structure factor) amplitudes and phases (done in real space)
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any relevant information, and removing excessive detail that may be against
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Zou, Xiaodong; Sundberg, Margareta; Larine, Maxim; Hovmöller, Sven (1996).
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EMIA, but so far there do not seem to be reports by users of this program.
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901:
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684:
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2075:
1073:, also published as a book by Now Publishers Inc., Boston and Delft, 2010
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elastically scattered electrons to the image are optimally suppressed.)
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if they have been recorded under special conditions, i.e. the so-called
2783:
1191:
Kanatani, K. (1997). "Comments on "Symmetry as a Continuous Feature"".
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techniques, which use sets of transmission electron microscopy images.
396:(= power spectrum consisting of a 2D periodic array of complex numbers)
369:
242:
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Straton, Jack C.; Moon, Bill; Bilyeu, Taylor T.; Moeck, Peter (2015).
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Straton, Jack C.; Bilyeu, Taylor T.; Moon, Bill; Moeck, Peter (2014).
1204:
1103:
843:
800:
723:
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Zou, X. D.; Mo, Z. M.; Hovmöller, S.; Li, X. Z.; Kuo, K. H. (2003).
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Determining 2D (projected) atomic co-ordinates (done in real space)
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191:
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HREM image contrasts and crystal potential reconstruction methods
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shows the advantages when both methods are linked in one study.
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open source, mainly for structural biology (for Mac PCs, Linux)
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Crystallographic image processing of high-resolution TEM images
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1308:
IEEE Transactions on Pattern Analysis and Machine Intelligence
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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https://www.cs.cmu.edu/~yanxi/images/computationalSymmetry.pdf
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15:
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personal reflection, personal essay, or argumentative essay
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and more recently to determine the structures of the huge
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Zeitschrift fĂŒr Kristallographie â New Crystal Structures
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http://vision.cse.psu.edu/publications/pdfs/liuCSinCV.pdf
402:
Indexing and refining the lattice (done in Fourier space)
212:) images obtained in a transmission electron microscope (
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Zeitschrift fĂŒr Kristallographie â Crystalline Materials
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Zeitschrift fĂŒr Kristallographie - Crystalline Materials
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in Surface Science. Vol. 38, Springer 2001, 191 â 222.
80:
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1433:"Testing approximate symmetry in the plane is NP-hard"
657:
Amos, L.A.; Henderson, Richard; Unwin, P.N.T. (1982).
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performance in the so-called phase origin refinement.
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Selecting the area of interest and calculation of the
700:"Accurate atomic positions from electron microscopy"
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263:Brief history of crystallographic image processing
902:"Three-dimensional reconstruction of the Μ-AlCr
479:reciprocal space. Besides plane symmetry groups
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8:
1083:Zabrodsky, H.; Peleg, S.; Avnir, D. (1995).
663:Progress in Biophysics and Molecular Biology
50:Learn how and when to remove these messages
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2105:
2097:
1448:
1407:
1366:
1158:
674:
180:Learn how and when to remove this message
162:Learn how and when to remove this message
103:Learn how and when to remove this message
1396:Advanced Structural and Chemical Imaging
1273:International Journal of Computer Vision
422:Calculating the pseudo-potential map by
1139:Computer Vision and Image Understanding
519:
206:Crystallographic image processing (CIP)
7:
3013:
2353:Phase transformation crystallography
2860:Journal of Chemical Crystallography
1238:Behavioral Ecology and Sociobiology
1085:"Symmetry as a continuous feature"
906:phase by electron crystallography"
338:"Symmetry as a continuous feature"
144:Knowledge (XXG)'s inclusion policy
14:
252:exit-wave function reconstruction
31:This article has multiple issues.
3012:
3001:
3000:
2607:
1007:Zeitschrift fĂŒr Kristallographie
913:Acta Crystallographica Section A
867:Acta Crystallographica Section A
119:
61:
20:
1355:Crystal Research and Technology
39:or discuss these issues on the
2802:Bilbao Crystallographic Server
1969:Journal of Electron Microscopy
1681:10.1016/j.ultramic.2004.10.004
578:10.1016/j.ultramic.2004.01.012
1:
2040:MRC Image Processing programs
1873:Journal of Structural Biology
1806:Journal of Structural Biology
1771:Journal of Structural Biology
1722:Journal of Structural Biology
1558:10.1016/S0167-2991(07)80277-1
1431:Iwanowski, Sebastian (1991).
625:10.1016/j.actamat.2010.03.016
459:forming proteins to just 21.
372:and later on that it is also
1921:10.1016/0304-3991(86)90203-2
1603:10.1524/zkri.218.4.308.20739
1531:10.1016/0739-6260(91)90130-R
1519:Micron and Microscopica Acta
1504:10.1016/0304-3991(92)90102-P
1450:10.1016/0304-3975(91)90389-J
1437:Theoretical Computer Science
758:10.1016/0304-3991(95)00090-9
676:10.1016/0079-6107(83)90017-2
551:10.1016/0304-3991(96)00022-8
2850:Crystal Growth & Design
2142:Timeline of crystallography
1840:"Image Processing Software"
3057:
2661:Nuclear magnetic resonance
1646:10.1088/1674-1056/18/6/056
1320:10.1109/TPAMI.2004.1262332
1151:10.1016/j.cviu.2014.09.002
2996:
2865:Journal of Crystal Growth
2605:
1885:10.1016/j.jsb.2006.07.012
1783:10.1016/j.jsb.2003.09.032
1734:10.1016/j.jsb.2006.07.020
1409:10.1186/s40679-015-0014-6
1250:10.1007/s00265-010-1029-6
925:10.1107/S0108767303018051
879:10.1107/s0108767392000850
2731:Single particle analysis
2589:HermannâMauguin notation
2093:Electron Crystallography
334:"computational symmetry"
2855:Crystallography Reviews
2699:Isomorphous replacement
2493:LomerâCottrell junction
1944:10.1038/npg.els.0003044
1285:10.1023/A:1007948927139
2368:Spinodal decomposition
1818:10.1006/jsbi.1996.0003
1368:10.1002/crat.201300240
1027:10.1524/zkri.2010.1204
342:"geometric inferences"
202:
83:by rewriting it in an
2908:Gregori Aminoff Prize
2704:Molecular replacement
2091:see also the Wiki on
1981:10.1093/jmicro/dfp007
195:
2214:Structure prediction
222:Stockholm University
2478:Cottrell atmosphere
2458:Partial dislocation
2202:Restriction theorem
1756:"EMAN2 - EMAN Wiki"
1638:2009ChPhB..18.2459L
1595:2003ZK....218..308W
1019:2010ZK....225...77S
969:10.1038/nature05200
961:2006Natur.444...79G
836:1990Natur.348..525D
793:1996Natur.382..144W
716:1984Natur.311..238H
617:2010AcMat..58.3764B
473:electron tomography
360:processing under a
247:transfer properties
245:values because the
2898:Carl Hermann Medal
2709:Molecular dynamics
2556:Defects in diamond
2551:StoneâWales defect
2197:Reciprocal lattice
2159:Biocrystallography
380:symmetries in 2D.
346:"in comparing two"
203:
85:encyclopedic style
72:is written like a
3028:
3027:
2992:
2991:
2599:Thermal ellipsoid
2564:
2563:
2473:FrankâRead source
2433:
2432:
2299:Aperiodic crystal
2265:
2264:
2147:Crystallographers
2018:978-84-614-6191-2
1626:Chinese Physics B
1479:978-3-540-67681-2
1205:10.1109/34.584101
1104:10.1109/34.476508
1098:(12): 1154â1166.
830:(6301): 525â528.
787:(6587): 144â146.
710:(5983): 238â241.
611:(10): 3764â3772.
424:Fourier synthesis
417:structure factors
394:Fourier transform
235:crystal structure
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2724:GerchbergâSaxton
2619:Characterisation
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2594:Structure factor
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272:membrane protein
239:Scherzer defocus
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2759:CrystalExplorer
2735:
2719:Phase retrieval
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2603:
2560:
2539:Schottky defect
2438:Perfect crystal
2429:
2425:Abnormal growth
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2373:Supersaturation
2336:Miscibility gap
2317:
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2182:Bravais lattice
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2130:
2128:Crystallography
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2087:Further reading
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1669:Ultramicroscopy
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640:Chemica Scripta
637:
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605:Acta Materialia
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572:(1â2): 91â104.
566:Ultramicroscopy
563:
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539:Ultramicroscopy
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440:paracrystalline
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81:help improve it
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2579:Ewald's sphere
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2522:Frenkel defect
2519:
2517:Bjerrum defect
2509:
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2497:
2496:
2495:
2490:
2485:
2483:Peierls stress
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2453:Burgers vector
2445:
2443:Stacking fault
2440:
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2402:Grain boundary
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2346:Liquid crystal
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2209:Periodic table
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2156:
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2034:External links
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2029:
2004:
1994:
1975:(3): 223â244.
1959:
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1915:(2): 147â178.
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1879:(3): 546â555.
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1443:(2): 227â262.
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1199:(3): 246â247.
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2950:Associations
2918:Organisation
2410:Disclination
2341:Polymorphism
2304:Quasicrystal
2247:Orthorhombic
2187:Miller index
2135:Key concepts
2090:
2064:EMAN Vers. 2
2007:
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136:spinning off
129:
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47:
40:
34:
33:Please help
30:
2903:Ewald Prize
2671:Diffraction
2649:Diffraction
2632:Diffraction
2574:Bragg plane
2569:Bragg's law
2448:Dislocation
2363:Segregation
2275:Crystallite
2192:Point group
1858:ccpem.ac.uk
1812:(1): 9â16.
1160:10251/51095
410:plane group
374:NP-complete
152:August 2016
93:August 2016
2687:Algorithms
2676:Scattering
2654:Scattering
2637:Scattering
2505:Slip bands
2468:Cross slip
2318:transition
2252:Tetragonal
2242:Monoclinic
2154:Metallurgy
2026:2011.13102
646:: 245â256.
515:References
412:) symmetry
348:(or more)
306:staurolite
268:Aaron Klug
140:relocating
36:improve it
2794:Databases
2257:Triclinic
2237:Hexagonal
2177:Unit cell
2169:Structure
1654:250873737
1244:: 23â35.
1169:207060370
1145:: 54â70.
1067:H. Hel-Or
465:wallpaper
362:different
42:talk page
3035:Category
3007:Category
2842:Journals
2774:OctaDist
2769:JANA2020
2741:Software
2627:Electron
2544:F-center
2331:Eutectic
2292:Fiveling
2287:Twinning
2280:Equiaxed
1989:19297343
1893:16997575
1791:14643205
1742:17055742
1689:15639355
1611:96860861
1418:51783244
1377:94543563
1328:15376882
1293:19248991
1112:13894016
1035:98380733
977:17080087
933:14581752
766:22666921
586:15219694
354:"models"
3019:Commons
2967:Germany
2644:Neutron
2534:Vacancy
2393:Defects
2378:GP-zone
2224:Systems
1826:8742717
1634:Bibcode
1591:Bibcode
1336:2394019
1258:3354490
1015:Bibcode
985:4396820
957:Bibcode
887:1445681
852:4340756
832:Bibcode
809:4327149
789:Bibcode
712:Bibcode
685:6289376
613:Bibcode
370:NP-hard
243:defocus
79:Please
2962:France
2957:Europe
2890:Awards
2420:Growth
2270:Growth
2016:
1987:
1950:
1891:
1854:"Home"
1824:
1789:
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1703:"Home"
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931:
885:
850:
824:Nature
807:
781:Nature
764:
704:Nature
683:
584:
352:(all)
2984:Japan
2931:IOBCr
2784:SHELX
2779:Olex2
2666:X-ray
2316:Phase
2232:Cubic
2080:elmiX
2046:CRISP
2022:arXiv
1650:S2CID
1607:S2CID
1414:S2CID
1373:S2CID
1332:S2CID
1289:S2CID
1254:S2CID
1165:S2CID
1108:S2CID
1088:(PDF)
1031:S2CID
1003:(PDF)
981:S2CID
909:(PDF)
848:S2CID
805:S2CID
742:(PDF)
456:layer
451:space
378:point
2926:IUCr
2827:ICDD
2822:ICSD
2807:CCDC
2754:Coot
2749:CCP4
2500:Slip
2463:Kink
2058:IPLT
2014:ISBN
1985:PMID
1948:ISBN
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1738:PMID
1685:PMID
1562:ISBN
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929:PMID
883:PMID
762:PMID
681:PMID
582:PMID
527:257.
508:just
493:p31m
491:and
489:p3m1
285:12+x
281:16âx
210:HREM
2941:DMG
2936:RAS
2832:PDB
2817:COD
2812:CIF
2764:DSR
2488:GND
2415:CSL
2076:EDM
2070:2dx
2052:VEC
1977:doi
1940:doi
1936:eLS
1917:doi
1881:doi
1877:156
1814:doi
1810:116
1779:doi
1775:144
1730:doi
1726:157
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1673:102
1642:doi
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1587:218
1554:doi
1546:Map
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708:311
671:doi
621:doi
601:0.5
574:doi
570:100
547:doi
308:HFe
277:8âx
257:0.5
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214:TEM
138:or
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2979:US
2972:UK
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