Convergent beam electron diffraction

Last updated November 08, 2023

Convergent beam electron diffraction (CBED) is an electron diffraction technique where a convergent or divergent beam (conical electron beam) of electrons is used to study materials.

History

CBED was first introduced in 1939 by Kossel and Möllenstedt.^[1] The development of the Field Emission Gun (FEG) in the 1970s,^[2] the Scanning Transmission Electron Microscopy (STEM), energy filtering devices and so on, made possible smaller probe diameters and larger convergence angles, and all this made CBED more popular. In the seventies, CBED was being used for the determination of the point group and space group symmetries by Goodman and Lehmpfuh,^[3] and Buxton, ^[4] and starting in 1985, CBED was used by Tanaka et al. for studying crystals structure.^[5]^[6]^[7]^[8]^[9]

Applications

By using CBED, the following information can be obtained:

parameters of the crystal lattice,^[10] sample thickness^[11]

strain distribution^[12]

defects such as stacking faults,^[13] dislocations,^[14] grain boundaries,^[15] three-dimensional deformations, lattice displacements^[16]

crystal symmetry information - by looking at the symmetries that appear in the CBED disks, point group^[17] and space group determination are performed.^[18]^[19]

Parameters

Positions of the CBED disks are the same as the positions of the Bragg peaks and are given approximately by the relation:

2d_{hkl}\sin \theta _{\rm {B}}=n\lambda ,

where $d_{hkl}$ is the distance between the crystallographic planes $(h,k,l)$ , $\theta _{\rm {B}}$ is the Bragg angle, $n$ is an integer, and $\lambda$ is the wavelength of the probing electrons.

The beam convergence semi-angle $\alpha$ - is controlled by the C2 aperture. The probing beam convergence semi-angle, $\alpha$ , is of the order of milliradians, ranging from 0.1˚ to 1˚.^[20] For small convergence semi-angle, the CBED disks do not overlap with each other, whereas for larger semi-convergence angles, the disks overlap.^[21]

The diameter of a CBED disk is given by the beam convergence semi-angle $\alpha$ :

D={\frac {4\pi }{\lambda }}\sin \alpha .

Defocus $\Delta f$ : The distance between the crossover of the probing beam and the $z$ position of the specimen is called the defocus distance $\Delta f$ . The sample can be moved along the $z$ axis. At a defocus distance, both the direct space and reciprocal space information are visible in the CBED pattern.^[22]

Related techniques

Conventional (C)TEM-CBED: In CTEM-CBED different shape condenser apertures are used to obtain the intensity distribution over the entire Brillouin zone.^[23]

Large Angle (LA)CBED: (LA)CBED is performed with a large incident angle, ranging from 1˚ to 10˚. LACBED makes it possible to obtain non-overlapping disks with a larger diameter than the one determined by the Bragg angle. With LACBED I one can obtain one selected CBED disk at a time on a detector.^[24] In LACBED II, with a slight change in the focusing conditions of the intermediate lens, bright field patterns and dark field patterns can be obtained simultaneously, without overlapping each other on the fluorescent screen.^[25] A disadvantage of LACBED is that it requires a large, flat specimen.

4D-STEM: In 4D-STEM a convergent probing beam is raster-scanned on a specimen in a 2D array and in each position of the array, a 2D diffraction pattern is obtained, thus generating a 4D data set. After acquisition, by using different phase techniques such as ptychography, one can recover the transmittion function and the induced phase shift.^[26] In some applications, 4D-STEM is called STEM-CBED.^[27]

Beam Rocking (BR)-CBED: With this technique, by rocking the incident beam with a rocking coil placed above the specimen, a virtual convergent beam is produced. Given that the diameter of the beam on the specimen is a few micrometers, this method has made CBED possible for materials that are susceptible to strong convergent beams. Furthermore, the large size of the illuminated specimen area and the low density current of the beam make specimen contamination insignificant.^[28]^[29]

BR-LACBED: In this technique, in addition to the rocking coil above the specimen, there is a rocking coil placed under the projector lens, which is used to bring the preferred beam to the STEM detector. Every time the incident beam is rocked, the second coil is simultaneously driven so that the beam always falls on the STEM detector.^[30]

Signal processing and BR-CBED: In order to enhance contrast in BR-CBED, a band-pass filter can be used that filters a certain frequency band in the CBED pattern. The combination of these two techniques makes the symmetries appearing in the patterns more clear.^[31]

CB-LEED (Low Energy Electron Diffraction): Rocking curves are analyzed at a single energy using a convergent probe.^[32] Advantages of this method are: mapping of LEED diffraction spots into CBLEED disks, the diffraction patterns originate from a localized region of the specimen which enables the extraction of localized structural information,^[33] mapping out of the surfaces, sensitivity enhancement of small atomic displacements etc.^[34]

Ptychography is a technique for recovering the phase of the exit electron wave. The reconstruction is done by applying an iterative phase retrieval algorithm which returns a real-space image with both phase and amplitude information. By using electron ptychography, in 2018, images of MoS₂ with an atomic resolution of 0.39 Å were reported by Jiang et al. which set the new world record for the highest resolution microscope.^[35]^[36]

Microdiffraction, nanodiffraction: In the literature, there are several terms used to refer to electron diffraction patterns that are acquired with a convergent beam. Such terms are CBED, microdiffraction, nanodiffraction etc. When the CBED technique is used for the acquisition of conventional diffraction information like lattice structure and interplanar spacing from very small areas, then the term microdiffraction is used.^[37] On the other hand, the term nanodiffraction is used when very small probes (< 1 nm or less in diameter) are used.^[38]^[39]

Advantages and disadvantages of CBED

Since the diameter of the probing convergent beam is smaller than in the case of a parallel beam, most of the information in the CBED pattern is obtained from very small regions, which other methods cannot reach. For example, in Selected Area Electron Diffraction (SAED), where a parallel beam illumination is used, the smallest area that can be selected is 0.5 µm at 100 kV, whereas in CBED, it is possible to go to areas smaller than 100 nm.^[40] Also, the amount of information that is obtained from a CBED pattern is larger than that from a SAED pattern. Nonetheless, CBED also has its disadvantages. The focused probe may generate contamination, which can cause localized stresses. But this was more of a problem in the past, and now, with the high vacuum conditions, one should be able to probe a clean region of the specimen in minutes to hours. Another disadvantage is that the convergent beam may heat or damage the chosen region of the specimen.^[41] Since 1939, CBED has been mainly used to study thicker materials.

CBED on 2D crystals

Recently, CBED was applied to study graphene^[42] and other 2D monolayer crystals and van der Waals structures. For 2D crystals, the analysis of CBED patterns is simplified, because the intensity distribution in a CBED disk is directly related to the atomic arrangement in the crystal. The deformations at a nanometer resolution have been retrieved, the interlayer distance of a bilayer crystal has been reconstructed, and so on, by using CBED.^[43]

Related Research Articles

An electron microscope is a microscope that uses a beam of electrons as a source of illumination. They use electron optics that are analogous to the glass lenses of an optical light microscope to control the electron beam, for instance focusing them to produce magnified images or electron diffraction patterns. As the wavelength of an electron can be up to 100,000 times smaller than that of visible light, electron microscopes have a much higher resolution of about 0.1 nm, which compares to about 200 nm for light microscopes. Electron microscope may refer to:

Microscopy is the technical field of using microscopes to view objects and areas of objects that cannot be seen with the naked eye. There are three well-known branches of microscopy: optical, electron, and scanning probe microscopy, along with the emerging field of X-ray microscopy.

$Transmission electron microscopy Imaging and diffraction using electrons that pass through samples$

Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a grid. An image is formed from the interaction of the electrons with the sample as the beam is transmitted through the specimen. The image is then magnified and focused onto an imaging device, such as a fluorescent screen, a layer of photographic film, or a sensor such as a scintillator attached to a charge-coupled device.

$Electron diffraction Bending of electron beams due to electrostatic interactions with matter$

Electron diffraction is a general term for phenomena associated with changes in the direction of electron beams due to elastic interactions with atoms. Close to the atoms the changes are described as Fresnel diffraction; far away they are called Fraunhofer diffraction. The resulting map of the directions of the electrons far from the sample is called a diffraction pattern, see for instance Figure 1. These patterns are similar to x-ray and neutron diffraction patterns, and are used to study the atomic structure of gases, liquids, surfaces and bulk solids. Electron diffraction also plays a major role in the contrast of images in electron microscopes.

$Electron backscatter diffraction Scanning electron microscopy technique$

Electron backscatter diffraction (EBSD) is a scanning electron microscopy (SEM) technique used to study the crystallographic structure of materials. EBSD is carried out in a scanning electron microscope equipped with an EBSD detector comprising at least a phosphorescent screen, a compact lens and a low-light camera. In this configuration, the SEM incident beam hits the tilted sample. As backscattered electrons leave the sample, they interact with the crystal's periodic atomic lattice planes and diffract according to Bragg's law at various scattering angles before reaching the phosphor screen forming Kikuchi patterns (EBSPs). EBSD spatial resolution depends on many factors, including the nature of the material under study and the sample preparation. Thus, EBSPs can be indexed to provide information about the material's grain structure, grain orientation, and phase at the micro-scale. EBSD is applied for impurities and defect studies, plastic deformation, and statistical analysis for average misorientation, grain size, and crystallographic texture. EBSD can also be combined with energy-dispersive X-ray spectroscopy (EDS), cathodoluminescence (CL), and wavelength-dispersive X-ray spectroscopy (WDS) for advanced phase identification and materials discovery.

Electron crystallography is a method to determine the arrangement of atoms in solids using a transmission electron microscope (TEM). It can involve the use of high-resolution transmission electron microscopy images, electron diffraction patterns including convergent-beam electron diffraction or combinations of these. It has been successful in determining some bulk structures, and also surface structures. Two related methods are low-energy electron diffraction which has solved the structure of many surfaces, and reflection high-energy electron diffraction which is used to monitor surfaces often during growth.

A scanning transmission electron microscope (STEM) is a type of transmission electron microscope (TEM). Pronunciation is [stɛm] or [ɛsti:i:ɛm]. As with a conventional transmission electron microscope (CTEM), images are formed by electrons passing through a sufficiently thin specimen. However, unlike CTEM, in STEM the electron beam is focused to a fine spot which is then scanned over the sample in a raster illumination system constructed so that the sample is illuminated at each point with the beam parallel to the optical axis. The rastering of the beam across the sample makes STEM suitable for analytical techniques such as Z-contrast annular dark-field imaging, and spectroscopic mapping by energy dispersive X-ray (EDX) spectroscopy, or electron energy loss spectroscopy (EELS). These signals can be obtained simultaneously, allowing direct correlation of images and spectroscopic data.

Phase-contrast imaging is a method of imaging that has a range of different applications. It measures differences in the refractive index of different materials to differentiate between structures under analysis. In conventional light microscopy, phase contrast can be employed to distinguish between structures of similar transparency, and to examine crystals on the basis of their double refraction. This has uses in biological, medical and geological science. In X-ray tomography, the same physical principles can be used to increase image contrast by highlighting small details of differing refractive index within structures that are otherwise uniform. In transmission electron microscopy (TEM), phase contrast enables very high resolution (HR) imaging, making it possible to distinguish features a few Angstrom apart.

$Selected area diffraction$

Selected area (electron) diffraction is a crystallographic experimental technique typically performed using a transmission electron microscope (TEM). It is a specific case of electron diffraction used primarily in material science and solid state physics as one of the most common experimental techniques. Especially with appropriate analytical software, SAD patterns (SADP) can be used to determine crystal orientation, measure lattice constants or examine its defects.

Low-energy electron microscopy, or LEEM, is an analytical surface science technique used to image atomically clean surfaces, atom-surface interactions, and thin (crystalline) films. In LEEM, high-energy electrons are emitted from an electron gun, focused using a set of condenser optics, and sent through a magnetic beam deflector. The “fast” electrons travel through an objective lens and begin decelerating to low energies near the sample surface because the sample is held at a potential near that of the gun. The low-energy electrons are now termed “surface-sensitive” and the near-surface sampling depth can be varied by tuning the energy of the incident electrons. The low-energy elastically backscattered electrons travel back through the objective lens, reaccelerate to the gun voltage, and pass through the beam separator again. However, now the electrons travel away from the condenser optics and into the projector lenses. Imaging of the back focal plane of the objective lens into the object plane of the projector lens produces a diffraction pattern at the imaging plane and recorded in a number of different ways. The intensity distribution of the diffraction pattern will depend on the periodicity at the sample surface and is a direct result of the wave nature of the electrons. One can produce individual images of the diffraction pattern spot intensities by turning off the intermediate lens and inserting a contrast aperture in the back focal plane of the objective lens, thus allowing for real-time observations of dynamic processes at surfaces. Such phenomena include : tomography, phase transitions, adsorption, reaction, segregation, thin film growth, etching, strain relief, sublimation, and magnetic microstructure. These investigations are only possible because of the accessibility of the sample; allowing for a wide variety of in situ studies over a wide temperature range. LEEM was invented by Ernst Bauer in 1962; however, not fully developed until 1985.

$Coherent diffraction imaging$

Coherent diffractive imaging (CDI) is a "lensless" technique for 2D or 3D reconstruction of the image of nanoscale structures such as nanotubes, nanocrystals, porous nanocrystalline layers, defects, potentially proteins, and more. In CDI, a highly coherent beam of X-rays, electrons or other wavelike particle or photon is incident on an object.

<span class="mw-page-title-main">Kikuchi lines (physics)</span> Patterns formed by scattering

Kikuchi lines are patterns of electrons formed by scattering. They pair up to form bands in electron diffraction from single crystal specimens, there to serve as "roads in orientation-space" for microscopists uncertain of what they are looking at. In transmission electron microscopes, they are easily seen in diffraction from regions of the specimen thick enough for multiple scattering. Unlike diffraction spots, which blink on and off as one tilts the crystal, Kikuchi bands mark orientation space with well-defined intersections as well as paths connecting one intersection to the next.

Ptychography is a computational method of microscopic imaging. It generates images by processing many coherent interference patterns that have been scattered from an object of interest. Its defining characteristic is translational invariance, which means that the interference patterns are generated by one constant function moving laterally by a known amount with respect to another constant function. The interference patterns occur some distance away from these two components, so that the scattered waves spread out and "fold" into one another as shown in the figure.

$Precession electron diffraction Averaging technique for electron diffraction$

Precession electron diffraction (PED) is a specialized method to collect electron diffraction patterns in a transmission electron microscope (TEM). By rotating (precessing) a tilted incident electron beam around the central axis of the microscope, a PED pattern is formed by integration over a collection of diffraction conditions. This produces a quasi-kinematical diffraction pattern that is more suitable as input into direct methods algorithms to determine the crystal structure of the sample.

John Charles Howorth Spence ForMemRS HonFRMS was Richard Snell Professor of Physics at Arizona State University and Director of Science at the National Science Foundation BioXFEL Science and Technology Center.

There are a variety of technologies available for detecting and recording the images, diffraction patterns, and electron energy loss spectra produced using transmission electron microscopy (TEM).

<span class="mw-page-title-main">CrysTBox</span> Free crystallographic software

CrysTBox is a suite of computer tools designed to accelerate material research based on transmission electron microscope images via highly accurate automated analysis and interactive visualization. Relying on artificial intelligence and computer vision, CrysTBox makes routine crystallographic analyses simpler, faster and more accurate compared to human evaluators. The high level of automation together with sub-pixel precision and interactive visualization makes the quantitative crystallographic analysis accessible even for non-crystallographers allowing for an interdisciplinary research. Simultaneously, experienced material scientists can take advantage of advanced functionalities for comprehensive analyses.

4D scanning transmission electron microscopy is a subset of scanning transmission electron microscopy (STEM) which utilizes a pixelated electron detector to capture a convergent beam electron diffraction (CBED) pattern at each scan location. This technique captures a 2 dimensional reciprocal space image associated with each scan point as the beam rasters across a 2 dimensional region in real space, hence the name 4D STEM. Its development was enabled by evolution in STEM detectors and improvements computational power. The technique has applications in visual diffraction imaging, phase orientation and strain mapping, phase contrast analysis, among others.

Transmission Kikuchi Diffraction (TKD), also sometimes called transmission-electron backscatter diffraction (t-EBSD), is a method for orientation mapping at the nanoscale. It’s used for analysing the microstructures of thin transmission electron microscopy (TEM) specimens in the scanning electron microscope (SEM). This technique has been widely utilised in the characterization of nano-crystalline materials, including oxides, superconductors, and metallic alloys.

Dark-field X-ray microscopy is an imaging technique used for multiscale structural characterisation. It is capable of mapping deeply embedded structural elements with nm-resolution using synchrotron X-ray diffraction-based imaging. The technique works by using scattered X-rays to create a high degree of contrast, and by measuring the intensity and spatial distribution of the diffracted beams, it is possible to obtain a three-dimensional map of the sample's structure, orientation, and local strain.

References

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↑ Crewe, A. V.; Isaacson, M.; Johnson, D. (February 1969). "A Simple Scanning Electron Microscope". Review of Scientific Instruments. 40 (2): 241–246. Bibcode:1969RScI...40..241C. doi:10.1063/1.1683910.
↑ Goodman, P.; Lehmpfuhl, G. (1 May 1968). "Observation of the breakdown of Friedel's law in electron diffraction and symmetry determination from zero-layer interactions". Acta Crystallographica Section A. 24 (3): 339–347. Bibcode:1968AcCrA..24..339G. doi:10.1107/S0567739468000677.
↑ Buxton, B. F.; Eades, J. A.; Steeds, John Wickham; Rackham, G. M.; Frank, Frederick Charles (11 March 1976). "The symmetry of electron diffraction zone axis patterns". Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences. 281 (1301): 171–194. Bibcode:1976RSPTA.281..171B. doi:10.1098/rsta.1976.0024. S2CID 122890943.
↑ Tanaka, Michiyoshi; Terauchi, Masami (1985). Convergent-Beam Electron Diffraction I. JEOL Ltd.
↑ Tanaka, Michiyoshi; Terauchi, Masami (1988). Convergent beam electron diffraction II. JEOL Ltd.
↑ Tanaka, Michiyoshi; Terauchi, Masami; Tsuda, Kenji (1994). Convergent beam electron diffraction III. JEOL Ltd.
↑ Tanaka, Michiyoshi (1994). "Convergent-beam electron diffraction". Acta Cryst. 2A50: 261–286. doi:10.1107/S0108767393010426.
↑ Tanaka, Michiyoshi; Terauchi, Masami; Tsuda, Kenji; Saitoh, Koh (2002). Convergent beam electron diffraction IV.
↑ Jones, P. M.; Rakham, G. M.; Steeds, John Wick (30 May 1977). "Higher order Laue zone effects in electron diffraction and their use in lattice parameter determination". Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences. 354 (1677): 197–222. Bibcode:1977RSPSA.354..197J. doi:10.1098/rspa.1977.0064. S2CID 98158162.
↑ Kelly, P. M.; Jostsons, A.; Blake, R. G.; Napier, J. G. (16 October 1975). "The determination of foil thickness by scanning transmission electron microscopy". Physica Status Solidi A. 31 (2): 771–780. Bibcode:1975PSSAR..31..771K. doi:10.1002/pssa.2210310251.
↑ Clément, L.; Pantel, R.; Kwakman, L. F. Tz.; Rouvière, J. L. (26 July 2004). "Strain measurements by convergent-beam electron diffraction: The importance of stress relaxation in lamella preparations". Applied Physics Letters. 85 (4): 651–653. Bibcode:2004ApPhL..85..651C. doi:10.1063/1.1774275.
↑ Morniroli, J. P. (September 2006). "CBED and LACBED characterization of crystal defects". Journal of Microscopy. 223 (3): 240–245. doi:10.1111/j.1365-2818.2006.01630.x. PMID 17059540. S2CID 21117117.
↑ Carpenter, R. W.; Spence, J. C. H. (1 January 1982). "Three-dimensional strain-field information in convergent-beam electron diffraction patterns". Acta Crystallographica Section A. 38 (1): 55–61. Bibcode:1982AcCrA..38...55C. doi:10.1107/S0567739482000102.
↑ Wu, Lijun; Zhu, Yimei; Tafto, J.; Welch, D. O.; Suenaga, M. (19 September 2002). "Quantitative analysis of twist boundaries and stacking faults in Bi-based superconductors by parallel recording of dark-field images with a coherent electron source". Physical Review B. 66 (10): 104517. Bibcode:2002PhRvB..66j4517W. doi:10.1103/PhysRevB.66.104517.
↑ Wu, Lijun; Zhu, Yimei; Tafto, J. (11 December 2000). "Picometer Accuracy in Measuring Lattice Displacements Across Planar Faults by Interferometry in Coherent Electron Diffraction". Physical Review Letters. 85 (24): 5126–5129. Bibcode:2000PhRvL..85.5126W. doi:10.1103/PhysRevLett.85.5126. PMID 11102202.
↑ Tanaka, M.; Saito, R.; Sekii, H. (1 May 1983). "Point-group determination by convergent-beam electron diffraction". Acta Crystallographica Section A: Foundations of Crystallography. 39 (3): 357–368. doi:10.1107/S010876738300080X.
↑ Goodman, P. (1 November 1975). "A practical method of three-dimensional space-group analysis using convergent-beam electron diffraction". Acta Crystallographica Section A. 31 (6): 804–810. Bibcode:1975AcCrA..31..804G. doi: 10.1107/S0567739475001738 . S2CID 98081846.
↑ Tanaka, M.; Sekii, H.; Nagasawa, T. (1 November 1983). "Space-group determination by dynamic extinction in convergent-beam electron diffraction". Acta Crystallographica Section A: Foundations of Crystallography. 39 (6): 825–837. doi:10.1107/S0108767383001695.
↑ Tanaka, Michiyoshi; Terauchi, Masami (1985). Convergent-Beam Electron Diffraction I.
↑ Morniroli, J. P. (2006). "CBED and LACBED characterization of crystal defects". Journal of Microscopy. 223 (3): 240–245. doi:10.1111/j.1365-2818.2006.01630.x. ISSN 1365-2818. PMID 17059540. S2CID 21117117.
↑ Cowley, J. M. (1987). Advances in electronics and electron physics.
↑ Tanaka, Michiyoshi (1986). "Conventional Transmission-Electron-Microscopy Techniques in Convergent-Beam Electron Diffraction". Journal of Electron Microscopy. doi:10.1093/oxfordjournals.jmicro.a050584.
↑ Tanaka, Michiyoshi; Saito, Ryuichi; Ueno, Katsuyoshi; Harada, Yoshiyasu (1980). "Large-Angle Convergent-Beam Electron Diffraction". Journal of Electron Microscopy. doi:10.1093/oxfordjournals.jmicro.a050262.
↑ Tanaka, Michiyoshi; Terauchi, Masami (1985). Convergent-Beam Electron Diffraction I.
↑ O'Leary, C. M.; Allen, C. S.; Huang, C.; Kim, J. S.; Liberti, E.; Nellist, P. D.; Kirkland, A. I. (23 March 2020). "Phase reconstruction using fast binary 4D STEM data". Applied Physics Letters. 116 (12): 124101. Bibcode:2020ApPhL.116l4101O. doi:10.1063/1.5143213. S2CID 216342216.
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↑ Tanaka, Michiyoshi; Terauchi, Masami (1985). Convergent-Beam Electron Diffraction I.
↑ Tanaka, Michiyoshi; Saito, Ryuichi; Ueno, Katsuyoshi; Harada, Yoshiyasu (1 January 1980). "Large-Angle Convergent-Beam Electron Diffraction". Journal of Electron Microscopy. 29 (4): 408–412. doi:10.1093/oxfordjournals.jmicro.a050262. ISSN 0022-0744.
↑ Tanaka, Michiyoshi; Ueno, Katsuyoshi; Hirata, Yoshihiro (April 1980). "Signal Processing of Convergent-Beam Electron Diffraction Patterns Obtained by the Beam-Rocking Method". Japanese Journal of Applied Physics. 19 (4): L201–L204. Bibcode:1980JaJAP..19L.201T. doi:10.1143/JJAP.19.L201. S2CID 122484061.
↑ Spence, J.C.H.; Poon, H.C.; Saldin, D.K. (February 2004). "Convergent-Beam Low Energy Electron Diffraction (CBLEED) and the Measurement of Surface Dipole Layers". Microscopy and Microanalysis. 10 (1): 128–133. Bibcode:2004MiMic..10..128S. doi:10.1017/S1431927604040346. PMID 15306076. S2CID 46584545.
↑ Ruben, G.; Jesson, D.E.; Paganin, D.M.; Smith, A.E. (May 2009). "Kinematic simulation of convergent beam low-energy electron diffraction patterns". Optik. 120 (9): 401–408. Bibcode:2009Optik.120..401R. doi:10.1016/j.ijleo.2007.10.006.
↑ Constantinou, Procopios C.; Jesson, David E. (September 2019). "On the sensitivity of convergent beam low energy electron diffraction patterns to small atomic displacements". Applied Surface Science. 489: 504–509. Bibcode:2019ApSS..489..504C. doi: 10.1016/j.apsusc.2019.05.274 . S2CID 182169602.
↑ Jiang, Yi; Chen, Zhen; Han, Yimo; Deb, Pratiti; Gao, Hui; Xie, Saien; Purohit, Prafull; Tate, Mark W.; Park, Jiwoong; Gruner, Sol M.; Elser, Veit; Muller, David A. (July 2018). "Electron ptychography of 2D materials to deep sub-ångström resolution". Nature. 559 (7714): 343–349. arXiv: 1801.04630 . Bibcode:2018Natur.559..343J. doi:10.1038/s41586-018-0298-5. PMID 30022131. S2CID 119359004.
↑ "Highest resolution microscope". Guinness World Records.
↑ Carpenter, R. W.; Spence, J. C. H. (November 1984). "Applications of modern microdiffraction to materials science". Journal of Microscopy. 136 (2): 165–178. doi:10.1111/j.1365-2818.1984.tb00526.x. S2CID 136906069.
↑ Williams, David B. (2009). Transmission electron microscopy: a textbook for materials science (2nd ed.). New York: Springer. ISBN 978-0-387-76501-3.
↑ Steeds, John Wickham; Hren, J. J.; Goldstein, J. I.; Joy, D. C. (1979). Introduction to Analytical Electron Microscopy. Plenum Press. p. 387.
↑ Champness, P. E. (March 1987). "Convergent beam electron diffraction". Mineralogical Magazine. 51 (359): 33–48. Bibcode:1987MinM...51...33C. doi:10.1180/minmag.1987.051.359.04. S2CID 30145465.
↑ Williams, David B. (2009). Transmission electron microscopy : a textbook for materials science (2nd ed.). New York: Springer. ISBN 978-0-387-76501-3.
↑ Meyer, Jannik; Geim, Andre K.; Katsnelson, M. I.; Novoselov, K. S.; Obergfell, D.; Roth, S.; Girit, C.; Zettl, A. (2007). "On the roughness of single- and bi-layer graphene membranes". Solid State Communications. 143: 101–109. arXiv: cond-mat/0703033 . doi:10.1016/j.ssc.2007.02.047.
↑ Latychevskaia, Tatiana; Woods, Colin Robert; Wang, Yi Bo; Holwill, Matthew; Prestat, Eric; Haigh, Sarah J.; Novoselov, Kostya S. (17 July 2018). "Convergent beam electron holography for analysis of van der Waals heterostructures". Proceedings of the National Academy of Sciences. 115 (29): 7473–7478. arXiv: 1807.01927 . Bibcode:2018PNAS..115.7473L. doi: 10.1073/pnas.1722523115 . PMC 6055151 . PMID 29970422.

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[1] Kossel, W.; Möllenstedt, G. (1939). "Elektroneninterferenzen im konvergenten Bündel". Annalen der Physik. 428 (2): 113–140. Bibcode:1939AnP...428..113K. doi:10.1002/andp.19394280204.

[2] Crewe, A. V.; Isaacson, M.; Johnson, D. (February 1969). "A Simple Scanning Electron Microscope". Review of Scientific Instruments. 40 (2): 241–246. Bibcode:1969RScI...40..241C. doi:10.1063/1.1683910.

[3] Goodman, P.; Lehmpfuhl, G. (1 May 1968). "Observation of the breakdown of Friedel's law in electron diffraction and symmetry determination from zero-layer interactions". Acta Crystallographica Section A. 24 (3): 339–347. Bibcode:1968AcCrA..24..339G. doi:10.1107/S0567739468000677.

[4] Buxton, B. F.; Eades, J. A.; Steeds, John Wickham; Rackham, G. M.; Frank, Frederick Charles (11 March 1976). "The symmetry of electron diffraction zone axis patterns". Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences. 281 (1301): 171–194. Bibcode:1976RSPTA.281..171B. doi:10.1098/rsta.1976.0024. S2CID 122890943.

[5] Tanaka, Michiyoshi; Terauchi, Masami (1985). Convergent-Beam Electron Diffraction I. JEOL Ltd.

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