Electron diffraction

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which case the electrons that go through the first are diffracted by the second. Electrons have no memory (like many of us), so after they have gone through the first grain and been diffracted, they traverse the second as if their current direction was that of the incident beam. This leads to diffraction spots which are the vector sum of those of the two (or even more) reciprocal lattices of the crystals, and can lead to complicated results. It can be difficult to know if this is real and due to some novel material, or just a case where multiple crystals and diffraction is leading to odd results.

4374:(CBED) pattern at each scan location; see the main page for further information. 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 better STEM detectors and improvements in computational power. The technique has applications in diffraction contrast imaging, phase orientation and identification, strain mapping, and atomic resolution imaging among others; it has become very popular and rapidly evolving from about 2020 onwards. 2176: 4560: 3507: 4273: 4617: 267: 3628: 3883: 24: 3757: 4471: 3942: 3696: 3780:; these act on the electrons similar to how glass lenses focus and control light. Optical elements above the sample are used to control the incident beam which can range from a wide and parallel beam to one which is a converging cone and can be smaller than an atom, 0.1 nm. As it interacts with the sample, part of the beam is diffracted and part is transmitted without changing its direction. This occurs simultaneously as electrons are everywhere until they are detected ( 4256: 5985: 3933: 803:—the early experiments of Davisson and Germer used this approach. As early as 1929 Germer investigated gas adsorption, and in 1932 Harrison E. Farnsworth probed single crystals of copper and silver. However, the vacuum systems available at that time were not good enough to properly control the surfaces, and it took almost forty years before these became available. Similarly, it was not until about 1965 that Peter B. Sewell and M. Cohen demonstrated the power of 777:. According to patent law (U.S. Patent No. 2058914 and 2070318, both filed in 1932), he is the inventor of the electron microscope, but it is not clear when he had a working instrument. He stated in a very brief article in 1932 that Siemens had been working on this for some years before the patents were filed in 1932, so his effort was parallel to the university effort. He died in 1961, so similar to Max Knoll, was not eligible for a share of the Nobel Prize. 15971: 15285: 258: 4600:(LEED) is also surface sensitive, and achieves surface sensitivity through the use of low energy electrons. The main uses of RHEED to date have been during thin film growth, as the geometry is amenable to simultaneous collection of the diffraction data and deposition. It can, for instance, be used to monitor surface roughness during growth by looking at both the shapes of the streaks in the diffraction pattern as well as variations in the intensities. 4381:, ND STEM (N- since the number of dimensions could be higher than 4), position resolved diffraction (PRD), spatial resolved diffractometry, momentum-resolved STEM, "nanobeam precision electron diffraction", scanning electron nano diffraction, nanobeam electron diffraction, or pixelated STEM. Most of these are the same, although there are instances such as momentum-resolved STEM where the emphasis can be very different. 6012:. Since the position of Kikuchi bands is highly sensitive to the crystal orientation, EBSD data can be used to determine the crystal orientation at particular locations of the sample. The data are processed by software yielding two-dimensional orientation maps. As the Kikuchi lines carry information about the interplanar angles and distances and, therefore, about the crystal structure, they can also be used for 15983: 15297: 6054:, and not consistent with the de Broglie wavelength. More importantly, the (non-relativistic) wavelength comes automatically from the Schrödinger equation, as do the equations for the amplitudes of electron diffraction; these cannot be derived from the de Broglie wavelength. As cited in the main text, Davisson and Germer were able to demonstrate that the diffraction angles were different from those of 4267:, although other methods exist. Unlike the parallel beam, the convergent beam is able to carry information from the sample volume, not just a two-dimensional projection available in SAED. With convergent beam there is also no need for the selected area aperture, as it is inherently site-selective since the beam crossover is positioned at the object plane where the sample is located. 3455:. If a diffraction spot is strong it could be because it has a larger structure factor, or it could be because the combination of thickness and excitation error is "right". Similarly the observed intensity can be small, even though the structure factor is large. This can complicate interpretation of the intensities. By comparison, these effects are much smaller in 3836:, the result is similar to a two-dimensional projection of the crystal reciprocal lattice. From this one can determine interplanar distances and angles and in some cases crystal symmetry, particularly when the electron beam is down a major zone axis, see for instance the database by Jean-Paul Morniroli. However, projector lens aberrations such as 4109:

sometimes they are quite large. Similar to a bulk superstructure there will be additional, weaker diffraction spots. One example is for the silicon (111) surface, where there is a supercell which is seven times larger than the simple bulk cell in two directions. This leads to diffraction patterns with additional spots some of which are marked in

221:. However, unlike x-ray and neutron diffraction where the simplest approximations are quite accurate, with electron diffraction this is not the case. Simple models give the geometry of the intensities in a diffraction pattern, but dynamical diffraction approaches are needed for accurate intensities and the positions of diffraction spots. 5822: 4500:; see the main page for more information and references. It has been used to solve a very large number of relatively simple surface structures of metals and semiconductors, plus cases with simple chemisorbants. For more complex cases transmission electron diffraction or surface x-ray diffraction have been used, often combined with 4336:(TEM). The technique involves rotating (precessing) a tilted incident electron beam around the central axis of the microscope, compensating for the tilt after the sample so a spot diffraction pattern is formed, similar to a SAED pattern. However, a PED pattern is an integration over a collection of diffraction conditions, see 6008:, captured with a camera inside the microscope. A depth from a few nanometers to a few microns, depending upon the electron energy used, is penetrated by the electrons, some of which are diffracted backwards and out of the sample. As result of combined inelastic and elastic scattering, typical features in an EBSD image are 3672:. The position of Kikuchi bands is fixed with respect to each other and the orientation of the sample, but not against the diffraction spots or the direction of the incident electron beam. As the crystal is tilted, the bands move on the diffraction pattern. Since the position of Kikuchi bands is quite sensitive to crystal 3823:

The simplest diffraction technique in TEM is selected area electron diffraction (SAED) where the incident beam is wide and close to parallel. An aperture is used to select a particular region of interest from which the diffraction is collected. These apertures are part of a thin foil of a heavy metal

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For all cases, when the reciprocal lattice points are close to the Ewald sphere (the excitation error is small) the intensity tends to be higher; when they are far away it tends to be smaller. The set of diffraction spots at right angles to the direction of the incident beam are called the zero-order

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which has a number of small holes in it. This way diffraction information can be limited to, for instance, individual crystallites. Unfortunately the method is limited by the spherical aberration of the objective lens, so is only accurate for large grains with tens of thousands of atoms or more; for

3676:, they can be used to fine-tune a zone-axis orientation or determine crystal orientation. They can also be used for navigation when changing the orientation between zone axes connected by some band, an example of such a map produced by combining many local sets of experimental Kikuchi patterns is in 6039:

Sometimes electron diffraction is defined similar to light or water wave diffraction, that is interference or bending of (electron) waves around the corners of an obstacle or through an aperture. With this definition the electrons are behaving as waves in a general sense, corresponding to a type of

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Textured materials yield a non-uniform distribution of intensity around the ring, which can be used to discriminate between nanocrystalline and amorphous phases. However, diffraction often cannot differentiate between very small grain polycrystalline materials and truly random order amorphous. Here

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and Alexander Reid; see note for more discussion. Alexander Reid, who was Thomson's graduate student, performed the first experiments, but he died soon after in a motorcycle accident and is rarely mentioned. These experiments were rapidly followed by the first non-relativistic diffraction model for

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and others were able to evacuate glass tubes below 10 atmospheres, and observed that the glow in the tube disappeared when the pressure was reduced but the glass behind the anode began to glow. Crookes was also able to show that the particles in the cathode rays were negatively charged and could be

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The disk diameter can be controlled using the microscope optics and apertures. The larger is the angle, the broader the disks are with more features. If the angle is increased to significantly, the disks begin to overlap. This is avoided in large angle convergent electron beam diffraction (LACBED)

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were zero for every reciprocal lattice vector, this grid would be at exactly the spacings of the reciprocal lattice vectors. This would be equivalent to a Bragg's law condition for all of them. In TEM the wavelength is small and this is close to correct, but not exact. In practice the deviation of

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In addition to those which occur in the bulk, superstructures can also occur at surfaces. When half the material is (nominally) removed to create a surface, some of the atoms will be under coordinated. To reduce their energy they can rearrange. Sometimes these rearrangements are relatively small;

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In simple cases there is only one grain or one type of material in the area used for collecting a diffraction pattern. However, often there is more than one. If they are in different areas then the diffraction pattern will be a combination. In addition there can be one grain on top of another, in

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While kinematical diffraction is adequate to understand the geometry of the diffraction spots, it does not correctly give the intensities and has a number of other limitations. For a more complete approach one has to include multiple scattering of the electrons using methods that date back to the

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and direct electron detectors, which improve the accuracy and reliability of intensity measurements. These have efficiencies and accuracies that can be a thousand or more times that of the photographic film used in the earliest experiments, with the information available in real time rather than

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but with magnetic or electrostatic lenses instead of glass ones. To this day the issue of who invented the transmission electron microscope is controversial, as discussed by Thomas Mulvey and more recently by Yaping Tao. Extensive additional information can be found in the articles by Martin

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In their first, shorter paper in Nature Davisson and Germer stated that their results were consistent with the de Broglie wavelength. Similarly Thomson and Reid used the de Broglie wavelength to explain their results. However, in their subsequently, more detailed papers Davisson and Germer

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Modelling at least semi-empirically the role of inelastic scattering by an imaginary component of the potential, also called an "optical potential". There is always inelastic scattering, and often it can have a major effect on both the background and sometimes the details, see

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later. By comparison, with both x-ray and neutron diffraction the scattering is significantly weaker, so typically requires much larger crystals, in which case the shape function shrinks to just around the reciprocal lattice points, leading to simpler Bragg's law diffraction.

4292:, the details within the disk change with sample thickness, as does the inelastic background. With appropriate analysis CBED patterns can be used for indexation of the crystal point group, space group identification, measurement of lattice parameters, thickness or strain. 12560: 4188:

for an Al-Cu-Fe-Cr decagonal quasicrystal grown by magnetron sputtering on a sodium chloride substrate and then lifted off by dissolving the substrate with water. In the pattern there are pentagons which are a characteristic of the aperiodic nature of these materials.

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What is seen in an electron diffraction pattern depends upon the sample and also the energy of the electrons. The electrons need to be considered as waves, which involves describing the electron via a wavefunction, written in crystallographic notation (see notes and)

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These instruments could produce magnified images, but were not particularly useful for electron diffraction; indeed, the wave nature of electrons was not exploited during the development. Key for electron diffraction in microscopes was the advance in 1936 where

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Quantitatively, where the intensities of diffracted beams are recorded as a function of incident electron beam energy to generate the so-called I–V curves. By comparison with theoretical curves, these may provide accurate information on atomic positions on the

4288:. Even though the zone axis and lattice parameter analysis based on disk positions does not significantly differ from SAED, the analysis of disks content is more complex and simulations based on dynamical diffraction theory is often required. As illustrated in 4476:

Figure 21: LEED pattern of a Si(100) reconstructed surface. The underlying lattice is a square lattice, while the surface reconstruction has a 2x1 periodicity. Also seen is the electron gun that generates the primary electron beam; it covers up parts of the

233:, from small particles such as electrons up to macroscopic objects – although it is impossible to measure any of the "wave-like" behavior of macroscopic objects. Waves can move around objects and create interference patterns, and a classic example is the 6592:, normally two-dimensional real and reciprocal lattice vectors in the surface are used, defined in terms of a matrix multiplier of the simple surface unit cell when there are reconstructions. To make things slightly more complicated, frequently four 1572: 1405:, which acts as if it is a particle with a positive charge and a mass similar to that of an electron, although it can be several times lighter or heavier. For electron diffraction the electrons behave as if they are non-relativistic particles of mass 3521:

Taking into account the scattering back into the incident beam both from diffracted beams and between all others, not just single scattering from the incident beam to diffracted beams. This is important even for samples which are only a few atoms

10738: 3807:; a map of these directions, often an array of spots, is the diffraction pattern. Alternatively the lenses can form a magnified image of the sample. Herein the focus is on collecting a diffraction pattern; for other information see the pages on 3195: 13628:"I. Hargittai, M. Hargittai (Eds.): The Electron Diffraction Technique, Part A von: Stereochemical Applications of Gas-Phase Electron Diffraction, VCH Verlagsgesellschaft, Weinheim, Basel. Cambridge, New York 1988. 206 Seiten, Preis: DM 210,-" 6058:, needing a proper treatment which includes the average potential inside the material. Since all theoretical models start from the Schrödinger equation (with relativistic terms included) this is really the key to electron diffraction, not the 3864:. This can be used to determine the crystal orientation, which in turn can be used to set the orientation needed for a particular experiment. Furthermore, a series of diffraction patterns varying in tilt can be acquired and processed using a 61:

when they interact with both the positively charged atomic core and the negatively charged electrons around the atoms. The resulting map of the directions of the electrons far from the sample is called a diffraction pattern, see for instance

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If the sample is tilted relative to the electron beam, different sets of crystallographic planes contribute to the pattern yielding different types of diffraction patterns, approximately different projections of the reciprocal lattice, see

2272:. One can also have intensities further out from reciprocal lattice points which are in a higher layer. The first of these is called the first order Laue zone (FOLZ); the series is called by the generic name higher order Laue zone (HOLZ). 3466:

This form is a reasonable first approximation which is qualitatively correct in many cases, but more accurate forms including multiple scattering (dynamical diffraction) of the electrons are needed to properly understand the intensities.

245:. If instead of two slits there are a number of small points then similar phenomena can occur as shown in the second image where the wave (red and blue) is coming in from the bottom right corner. This is comparable to diffraction of an 317:

that dominated early television and electronics; the second is how these led to the development of electron microscopes; the last is work on the nature of electron beams and the fundamentals of how electrons behave, a key component of

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which includes the refraction due to the average potential yielded more accurate results. These advances in understanding of electron wave mechanics were important for many developments of electron-based analytical techniques such as

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observed that the radiation emitted from the negatively charged cathode caused phosphorescent light to appear on the tube wall near it, and the region of the phosphorescent light could be moved by application of a magnetic field.

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Kikuchi lines come in pairs forming Kikuchi bands, and are indexed in terms of the crystallographic planes they are connected to, with the angular width of the band equal to the magnitude of the corresponding diffraction vector

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in gases. A gas carrying the molecules is exposed to the electron beam, which is diffracted by the molecules. Since the molecules are randomly oriented, the resulting diffraction pattern consists of broad concentric rings, see

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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

3451:. The intensity in transmission electron diffraction oscillates as a function of thickness, which can be confusing; there can similarly be intensity changes due to variations in orientation and also structural defects such as 5180: 4239:. Because of the vacancies at the niobium sites, there is diffuse intensity with snake-like structure due to correlations of the distances between vacancies and also the relaxation of Co and Sb atoms around these vacancies. 2632:

For a crystal these will be near the reciprocal lattice points typically forming a two dimensional grid. Different samples and modes of diffraction give different results, as do different approximations for the amplitudes

1596: 1050: 542:, and that electrons and all matter could be considered as waves. He merged the idea of thinking about them as particles (or corpuscles), and of thinking of them as waves. He proposed that particles are bundles of waves ( 5964:

is negligible in most cases. If the molecular intensity is extracted from an experimental pattern by subtracting other contributions, it can be used to match and refine a structural model against the experimental data.

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or by a number of differently oriented crystallites, for instance in a polycrystalline material. If there are many contributing crystallites, the diffraction image is a superposition of individual crystal patterns, see

2562: 11936:"Fine Structure due to Refraction Effect in Electron Diffraction Pattern of Powder Sample Part II. Multiple Structures due to Double Refraction given by Randomly Oriented Smoke Particles of Magnesium and Cadmium Oxide" 3361: 4867: 2050: 2630: 2832: 1746:

While the wavevector increases as the energy increases, the change in the effective mass compensates this so even at the very high energies used in electron diffraction there are still significant interactions.

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in 1883 who made a cathode-ray tube with electrostatic and magnetic deflection, demonstrating manipulation of the direction of an electron beam. Others were focusing of electrons by an axial magnetic field by

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so it could be used to determine atomic positions, for instance references. These have been extensively exploited to determine the structure of many surfaces, and the arrangement of foreign atoms on surfaces.

241:, where a wave impinges upon two slits in the first of the two images (blue waves). After going through the slits there are directions where the wave is stronger, ones where it is weaker – the wave has been 2278: 4173:), similar to supercells above, but in addition there is some additional periodicity (one to three) which cannot be described as a multiple of the three; it is a genuine additional periodicity which is an 934:

more reliable and reproducible techniques. In the early days the surfaces were not well controlled; with these technologies they can both be cleaned and remain clean for hours to days, a key component of

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for the distances between point defects or what type of substitutional atom there is, which leads to distinct three-dimensional intensity features in diffraction patterns. An example of this is for a Nb

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in electron diffraction patterns due to disorder, which is also known for x-ray or neutron scattering. This can occur from inelastic processes, for instance, in bulk silicon the atomic vibrations (

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described earlier. Even at very high energies dynamical diffraction is needed as the relativistic mass and wavelength partially cancel, so the role of the potential is larger than might be thought.

1963: 6520: 6118: 5817:{\displaystyle I_{m}(s)={\frac {K^{2}}{R^{2}}}I_{0}\sum _{i=1}^{N}\sum _{\stackrel {j=1}{i\neq j}}^{N}\left|f_{i}(s)\right|\left|f_{j}(s)\right|{\frac {\sin}{sr_{ij}}}e^{-(1/2l_{ij}s^{2})}\cos,} 1458: 1130:

of the plane wave. For most cases the electrons are travelling at a respectable fraction of the speed of light, so rigorously need to be considered using relativistic quantum mechanics via the

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This article provides an overview of electron diffraction and electron diffraction patterns, collective referred to by the generic name electron diffraction. This includes aspects of how in a

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of the shape of the object. If, for instance, the object is small in one dimension then the shape function extends far in that direction in the Fourier transform—a reciprocal relationship.

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as well as dynamical diffraction effects (e.g.) cannot be ignored. For instance, certain diffraction spots which are not present in x-ray diffraction can appear, for instance those due to

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and shows both rings from the higher-order Laue zones and streaky spots. RHEED systems gather information only from the surface layers of the sample, which distinguishes RHEED from other

14901: 13152:"Structure Model for the Phase AlmFe Derived from Three-Dimensional Electron Diffraction Intensity Data Collected by a Precession Technique. Comparison with Convergent-Beam Diffraction" 5250: 4280:

A CBED pattern consists of disks arranged similar to the spots in SAED. Intensity within the disks represents dynamical diffraction effects and symmetries of the sample structure, see

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Figure 2: Young's double slit experiment, showing the wave in blue and the two slits in yellow; the other Figure with red and blue waves is similar from a small array of white atoms.

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Hage, Fredrik S.; Nicholls, Rebecca J.; Yates, Jonathan R.; McCulloch, Dougal G.; Lovejoy, Tracy C.; Dellby, Niklas; Krivanek, Ondrej L.; Refson, Keith; Ramasse, Quentin M. (2018).

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Figure 9: Diffraction patterns (below, black background) with different crystallinity (above, diagrams) and beam convergence. From left: spot diffraction (parallel illumination),

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Both the wave nature and the undulatory mechanics approach were experimentally confirmed for electron beams by experiments from two groups performed independently, the first the

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measured the mass of these cathode rays, proving they were made of particles. These particles, however, were 1800 times lighter than the lightest particle known at that time – a

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This has changed, in transmission, reflection and for low energies. Some of the key developments (some of which are also described later) from the early days to 2023 have been:

15157: 4184:, which can be described similarly by a higher number of Miller indices in reciprocal space—but not by any translational symmetry in real space. An example of this is shown in 2464: 6564: 3449: 3390: 2493: 2226: 2137: 2108: 2079: 6040:

Fresnel diffraction. However, in every case where electron diffraction is used in practice the obstacles of relevance are atoms, so the general definition is not used herein.

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Qualitatively, where the diffraction pattern is recorded and analysis of the spot positions gives information on the symmetry of the surface structure. In the presence of an

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In Kinematical theory an approximation is made that the electrons are only scattered once. For transmission electron diffraction it is common to assume a constant thickness

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Fifty years of electron diffraction : in recognition of fifty years of achievement by the crystallographers and gas diffractionists in the field of electron diffraction

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in 1928, are linear features created by electrons scattered both inelastically and elastically. As the electron beam interacts with matter, the electrons are diffracted via

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and three-dimensional diffraction methods. Averaging over different directions has, empirically, been found to significantly reduce dynamical diffraction effects, e.g., see

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In order to have a practical microscope or diffractometer, just having an electron beam was not enough, it needed to be controlled. Many developments laid the groundwork of

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through a thin sample, from 1 nm to 100 nm (10 atoms to 1000 thick), where the results depending upon how the atoms are arranged in the material, for instance a

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In convergent beam electron diffraction (CBED), the incident electrons are normally focused in a converging cone-shaped beam with a crossover located at the sample, e.g.

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The historical background is divided into several subsections. The first is the general background to electrons in vacuum and the technological developments that led to

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of quantum mechanics, only the probabilities of electrons at detectors can be measured. These electrons form Kikuchi lines which provide information on the orientation.

14697: 5962: 5452: 5389: 5333: 5047: 5011: 4975: 4939: 4903: 2466:.) For a crystalline sample these wavevectors have to be of the same magnitude for elastic scattering (no change in energy), and are related to the incident direction 1453: 754:. In 1931, Max Knoll and Ernst Ruska successfully generated magnified images of mesh grids placed over an anode aperture. The device, a replicate of which is shown in 5906: 4665: 4135:

the structure can no longer be simply described by three different vectors in real or reciprocal space. In general there is a substructure describable by three (e.g.

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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".

6475: 6141: 5926: 5297: 4460: 4433: 3501: 3275: 3222: 3064: 2994: 2776: 2164: 1995: 1925: 1890: 1430: 1391: 1320: 987: 289:, whereas electron diffraction patterns are measured far from the sample, which is described as far-field or Fraunhofer diffraction. A map of the directions of the 249:

where the small dots would be atoms in a small crystal, see also note. Note the strong dependence on the relative orientation of the crystal and the incoming wave.

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Around each reciprocal lattice point one has this shape function. How much intensity there will be in the diffraction pattern depends upon the intersection of the

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a phase factor which is important for atomic pairs with very different nuclear charges. The summation is performed over all atom pairs. Atomic triplet intensity

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for further details. Not only is it easier to identify known structures with this approach, it can also be used to solve unknown structures in some cases – see

455:. Hittorf inferred that there are straight rays emitted from the cathode and that the phosphorescence was caused by the rays striking the tube walls. In 1876 15615: 4113:. Here the (220) are stronger bulk diffraction spots, and the weaker ones due to the surface reconstruction are marked 7x7—see note for convention comments. 4028:(see also note). There are many others where the repeat is some larger multiple of the smaller unit cell (subcell) along one or more direction, for instance 4745: 2000: 14441: 4519:

the qualitative analysis may reveal information about the size and rotational alignment of the adsorbate unit cell with respect to the substrate unit cell.

2567: 1138:. Fortunately one can side-step many complications and use a non-relativistic approach based around the Schrödinger equation. Following Kunio Fujiwara and 6000:

the region near the surface can be mapped using an electron beam that is scanned in a grid across the sample. A diffraction pattern can be recorded using

7452: 3746:, TEM analysis is significantly more localized and can be used to obtain information from tens of thousands of atoms to just a few or even single atoms. 593:

who developed the propagation equations of a new theory and who in searching for its solutions has established what has become known as “Wave Mechanics”.

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simulated using CrysTBox for various crystal orientations. Note how the diffraction pattern (white/black) changes with the crystal orientation (yellow).

2807:, and also what is called the Column Approximation (e.g. references and further reading). For a perfect crystal the intensity for each diffraction spot 750:

to lead a team of researchers to advance research on electron beams and cathode-ray oscilloscopes. The team consisted of several PhD students including

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Figure 19: Geometry of electron beam in precession electron diffraction. Original diffraction patterns collected by C.S. Own at Northwestern University

916: 12088:""Ab initio" structure solution from electron diffraction data obtained by a combination of automated diffraction tomography and precession technique" 3910:. With a large number of grains this superposition yields diffraction spots of all possible reciprocal lattice vectors. This results in a pattern of 2231:

For transmission electron diffraction the samples used are thin, so most of the shape function is along the direction of the electron beam. For both

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Colliex, C.; Cowley, J. M.; Dudarev, S. L.; Fink, M.; Gjønnes, J.; Hilderbrandt, R.; Howie, A.; Lynch, D. F.; Peng, L. M. (2006), Prince, E. (ed.),

15598: 15593: 11854: 11805: 3966: 3727: 736: 606:, as well as many other phenomena. Electron waves as hypothesized by de Broglie were automatically part of the solutions to his equation, see also 293:

leaving the sample will show high intensity (white) for favored directions, such as the three prominent ones in the Young's two-slit experiment of

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Independent of the developments for electrons in vacuum, at about the same time the components of quantum mechanics were being assembled. In 1924

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The control of electron beams that this work led to resulted in significant technology advances in electronic amplifiers and television displays.

4300:. It is a CBED pattern, often but not always of an amorphous material, with many intentionally overlapping disks providing information about the 4296:

where the sample is moved upwards or downwards. There are applications, however, where the overlapping disks are beneficial, for instance with a

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across the sample which produce information that is often easier to interpret. There are also many other types of instruments. For instance, in

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can be used to determine crystal orientation across the sample. Electron diffraction patterns can also be used to characterize molecules using

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corresponds to the background which, unlike the previous contributions, must be determined experimentally. The intensity of atomic scattering

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have their own characteristic patterns. There are many different ways of collecting diffraction information, from parallel illumination to a

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Figure 10: Imaging scheme of magnetic lens (center, colored ray diagram) with image (left) and diffraction pattern (right, black background)

15635: 15608: 15031: 4361: 854:) method was developed. With these and other numerical methods Fourier transforms are fast, and it became possible to calculate accurate, 13906: 13106:

Own, C. S.: PhD thesis, System Design and Verification of the Precession Electron Diffraction Technique, Northwestern University, 2005,

6358: 6299: 6240: 4596:. Transmission electron microscopy samples mainly the bulk of the sample, although in special cases it can provide surface information. 3510:

Figure 7: CBED patterns using all the electrons, with just those which have not lost any energy and those which have excited one or two

1739:{\displaystyle 2\pi {\frac {m^{*}}{h^{2}k}}=2\pi {\frac {m^{*}\lambda }{h^{2}}}={\frac {\pi }{hc}}{\sqrt {{\frac {2m_{0}c^{2}}{E}}+1}}.} 901: 15543: 15218: 14943: 4219:) are more prevalent along specific directions, which leads to streaks in diffraction patterns. Sometimes it is due to arrangements of 3872:

algorithms using electrons and other methods such as charge flipping, or automated diffraction tomography to solve crystal structures.

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the positions from a simple Bragg's law interpretation is often neglected, particularly if a column approximation is made (see below).

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Enterkin, James A.; Subramanian, Arun K.; Russell, Bruce C.; Castell, Martin R.; Poeppelmeier, Kenneth R.; Marks, Laurence D. (2010).

6588:.) Similar notation differences can occur with aperiodic materials and superstructures. Furthermore, when dealing with surfaces as in 6017: 4402: 15603: 15109: 14401: 4367: 3812: 3476:

early work of Hans Bethe in 1928. These are based around solutions of the Schrödinger equation using the relativistic effective mass

1209: 1145: 15747: 8703:"Origin of the Electron Microscope: The history of a great invention, and of a misconception concerning the inventors, is reviewed" 4545: 890: 2671:

is a grid of high intensity spots (white) on a dark background, approximating a projection of the reciprocal lattice vectors, see

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at either end of a glass tube that had been partially evacuated of air, and noticed a strange light arc with its beginning at the

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Below the sample, the beam is controlled by another set of magnetic lneses and apertures. Each set of initially parallel rays (a

2179:

Figure 6: Ewald sphere construction for transmission electron diffraction, showing two of the Laue zones and the excitation error

66:. Beyond patterns showing the directions of electrons, electron diffraction also plays a major role in the contrast of images in 13251:"Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM): From Scanning Nanodiffraction to Ptychography and Beyond" 11292: 4584:, it uses mainly the higher-order Laue zones which have a reflection component. An experimental diffraction pattern is shown in 93:, giving birth to electron microscopy and diffraction in 1920–1935. While this was the birth, there have been a large number of 15563: 15208: 15200: 459:

showed that the rays were emitted perpendicular to the cathode surface, which differentiated them from the incandescent light.

8216:

Mark, Herman; Wiel, Raymond (1930). "Die ermittlung von molekülstrukturen durch beugung von elektronen an einem dampfstrahl".

4031: 3954:

as recorded (left) and processed with CrysTBox ringGUI (right, with indexing). Corresponding simulated pattern can be seen in

297:, while the other directions will be low intensity (dark). Often there will be an array of spots (preferred directions) as in 15687: 15553: 15500: 15261: 15239: 14349: 14321: 14288: 14220: 14151: 12643: 12445: 11830: 11756: 11729: 11637: 10986: 10601: 10403: 10097: 10005: 9113: 8685: 8474: 7237: 7204: 6993: 6893: 6767: 6711: 4492:

of low-energy electrons (30–200 eV). In this case the Ewald sphere leads to approximately back-reflection, as illustrated in

2962:{\displaystyle I_{g}=\left|\phi (\mathbf {k} )\right|^{2}\propto \left|F_{g}{\frac {\sin(\pi ts_{z})}{\pi s_{z}}}\right|^{2}} 381: 81:

behind modern electron diffraction, how the combination of developments in the 19th century in understanding and controlling

6202: 4138: 4080:

Larger unit cells due to electronic ordering which leads to small displacements of the atoms in the subcell. One example is

3993: 1930: 953:, so it can be used semi-quantitatively to understand surfaces during growth and thereby to control the resulting materials. 827:

in 1954, electron diffraction for many years was a qualitative technique used to check samples within electron microscopes.

762:

to achieve higher magnifications, the first electron microscope. (Max Knoll died in 1969, so did not receive a share of the

15987: 15942: 15670: 15655: 15581: 15254: 15104: 14770: 14635: 14484: 14092:"Progressive steps in the development of electron backscatter diffraction and orientation imaging microscopy: EBSD AND OIM" 11977: 11229: 11117:"Diffraction contrast of electron microscope images of crystal lattice defects – II. The development of a dynamical theory" 11009:"A kinematical theory of diffraction contrast of electron transmission microscope images of dislocations and other defects" 10076:. NATO Science for Peace and Security Series B: Physics and Biophysics. Dordrecht: Springer Netherlands. pp. 281–291. 7999: 6480: 6078: 4371: 4248: 3731: 2275:

The result is that the electron wave after it has been diffracted can be written as an integral over different plane waves:

1323: 866: 741: 676: 551: 13191:"Precession electron diffraction and its advantages for structural fingerprinting in the transmission electron microscope" 15244: 15142: 14838: 281:

Close to an aperture or atoms, often called the "sample", the electron wave would be described in terms of near field or

13730:"Least-squares refinements and error analysis based on correlated electron diffraction intensities of gaseous molecules" 11501:"n -Beam dynamical diffraction of high-energy electrons at glancing incidence. General theory and computational methods" 8668:

Proceedings of the 3rd International Conference on Contemporary Education, Social Sciences and Humanities (ICCESSH 2018)

4644:. The diffraction intensity is a sum of several components such as background, atomic intensity or molecular intensity. 4352:

of the sample. Because it avoids many dynamical effects it can also be used to better identify crystallographic phases.

2371:{\displaystyle \psi (\mathbf {r} )=\int \phi (\mathbf {k} )\exp(2\pi i\mathbf {k} \cdot \mathbf {r} )d^{3}\mathbf {k} ,} 14491: 1892:

the corresponding Fourier coefficient of the potential. The reciprocal lattice vector is often referred to in terms of

8789: 630:

based upon the Schrödinger equation, which is very close to how electron diffraction is now described. Significantly,

451:

found that a solid body placed between the cathode and the phosphorescence would cast a shadow on the tube wall, e.g.

186:

The first level of more accuracy where it is approximated that the electrons are only scattered once, which is called

15692: 15525: 15378: 15328: 15266: 15124: 15094: 15023: 14250: 14190: 13772:"Procedure and Computer Programs for the Structure Determination of Gaseous Molecules from Electron Diffraction Data" 13597: 12920: 11693: 10784: 10461: 10287: 9933:"Symmetry determination of the room-temperature form of LnNbO 4 (Ln = La,Nd) by convergent-beam electron diffraction" 9140: 8767: 7415: 6945: 6665: 4073: 3735: 711:

Figure 5: Replica built in 1980 by Ernst Ruska of the original electron microscope, in the Deutsches Museum in Munich

607: 503: 13907:"Determining the radial distribution function of water using electron scattering: A key to solution phase chemistry" 1126:

is what is used when drawing ray diagrams, and in vacuum is parallel to the direction or, better, group velocity or

15680: 15675: 15573: 15548: 15515: 15301: 14976: 6001: 5977: 4345: 4333: 3869: 3808: 3711:

exploits controlled electron beams using electron optics. Different types of diffraction experiments, for instance

3708: 3564: 1750:

The high-energy electrons interact with the Coulomb potential, which for a crystal can be considered in terms of a

707: 514: 149: 13150:

Gjønnes, J.; Hansen, V.; Berg, B. S.; Runde, P.; Cheng, Y. F.; Gjønnes, K.; Dorset, D. L.; Gilmore, C. J. (1998).

12468:"Antiferroelectrics: History, fundamentals, crystal chemistry, crystal structures, size effects, and applications" 10070:

Marks, Laurence (2012). Kolb, Ute; Shankland, Kenneth; Meshi, Louisa; Avilov, Anatoly; David, William I.F (eds.).

2255:

the electrons reflect off the surface at a small angle and typically yield diffraction patterns with streaks, see

732: 598:

The Schrödinger equation combines the kinetic energy of waves and the potential energy due to, for electrons, the

15752: 15737: 15717: 15249: 15172: 15046: 14645: 11719: 4597: 4390: 4313: 3970: 1582:(eV), the voltage used to accelerate the electrons; the actual energy of each electron is this voltage times the 1578:, roughly the size of an atom, down to a thousandth of that. Typically the energy of the electrons is written in 905: 897: 11910: 10889:

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

8956:"Über das primäre und sekundäre Bild im Elektronenmikroskop. II. Strukturuntersuchung mittels Elektronenbeugung" 7947:

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

4177:

relative to the subcell lattice. The diffraction pattern can then only be described by more than three indices.

57:, when there is no change in the energy of the electrons. The negatively charged electrons are scattered due to 15947: 15520: 15455: 15363: 15084: 15006: 8920: 8505:"Experimentelle Untersuchungen über die Geschwindigkeit und die magnetische Ablenkbarkeit der Kathodenstrahlen" 5185: 4501: 618: 584:

on September 8, 1927, in the preface to the German translation of his theses (in turn translated into English):

234: 15937: 685:; see the paper by Chester J. Calbick for an overview of the early work. One significant step was the work of 602:. He was able to explain earlier work such as the quantization of the energy of electrons around atoms in the 15697: 15660: 15505: 15099: 15089: 14394: 7258:"A life of its own: The tenuous connection between Thales of Miletus and the study of electrostatic charging" 367:

Figure 3: A Crookes tube – without emission (top, grey background) and with emission and a shadow due to the

7406:

Martin, Andre (1986), "Cathode Ray Tubes for Industrial and Military Applications", in Hawkes, Peter (ed.),

6848: 4100: 1567:{\displaystyle \lambda ={\frac {1}{k}}={\frac {h}{\sqrt {2m^{*}E}}}={\frac {hc}{\sqrt {E(2m_{0}c^{2}+E)}}},} 201:

methods, and track the electrons through the sample, being accurate both near and far from the sample (both

16029: 15975: 15535: 15321: 15223: 14871: 14496: 14474: 8840: 8814: 5997: 659:

and Raymond Weil, diffraction in liquids by Louis Maxwell, and the first electron microscopes developed by

5454:, as it contains information about the distance between all pairs of atoms in the molecule. It is given by 4090:

Magnetic order of the spins. These may be in opposite directions on some atoms, leading to what is called

14775: 14529: 14424: 4123: 3545:

approaches. With these diffraction spots which are not present in kinematical theory can be present, e.g.

2636: 2381: 1393:

the rest mass of the electron. The concept of effective mass occurs throughout physics (see for instance

824: 12432:, vol. C (1 ed.), Chester, England: International Union of Crystallography, pp. 907–955, 10596:. International series in pure and applied physics (3. ed., 24. print ed.). New York: McGraw-Hill. 8664:"A Historical Investigation of the Debates on the Invention and Invention Rights of Electron Microscope" 6754:, vol. C (1 ed.), Chester, England: International Union of Crystallography, pp. 259–429, 6199:

Notations differ depending upon whether the source is crystallography, physics or other. In addition to

4484:

Low-energy electron diffraction (LEED) is a technique for the determination of the surface structure of

4276:

Figure 18: Variations in CBED due to dynamical diffraction, with thickness increasing from a)-d) for Si

2999: 16039: 16034: 15722: 15640: 15132: 14429: 14091: 11013:

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences

9743:

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences

7196: 3035:

along z, the distance along the beam direction (z-axis by convention) from the diffraction spot to the

2437: 13107: 10543: 9789:"Use of high-symmetry zone axes in electron diffraction in determining crystal point and space groups" 7257: 6547: 5968:

Similar methods of analysis have also been applied to analyze electron diffraction data from liquids.

3425: 3366: 3190:{\displaystyle F_{g}=\sum _{j=1}^{N}f_{j}\exp {(2\pi i\mathbf {g} \cdot \mathbf {r} _{j}-T_{j}g^{2})}} 2469: 2202: 2113: 2084: 2055: 15147: 15076: 14534: 14524: 11591: 8670:. Advances in Social Science, Education and Humanities Research. Atlantis Press. pp. 1438–1441. 7229: 4589: 4580:

materials by reflecting electrons off a surface. As illustrated for the Ewald sphere construction in

4505: 3785: 3726:

It is common to combine it with other methods, for instance images using selected diffraction beams,

3621: 3620:

losing part of their energy. These occur simultaneously, and cannot be separated – according to the

1135: 9737:

Buxton, B. F.; Eades, J. A.; Steeds, John Wickham; Rackham, G. M.; Frank, Frederick Charles (1976).

9271:"Structure analysis of single crystals by electron diffraction. II. Disordered boric acid structure" 3643: 889:. It can also be used for higher-level refinements of the electron density; for a brief history see 16014: 15901: 15727: 15289: 15013: 14909: 14782: 14745: 14660: 14539: 14519: 14387: 13121:"Double conical beam-rocking system for measurement of integrated electron diffraction intensities" 11175:"Inelastic scattering of electrons by crystals. I. The theory of small-angle in elastic scattering" 4628: 4609: 4228: 3542: 2412: 652: 13770:

Andersen, B.; Seip, H. M.; Strand, T. G.; Stølevik, R.; Borch, Gunner; Craig, J. Cymerman (1969).

12467: 12466:

Randall, Clive A.; Fan, Zhongming; Reaney, Ian; Chen, Long-Qing; Trolier-McKinstry, Susan (2021).

10279: 9567: 9521:"Numerical evaluations of N -beam wave functions in electron scattering by the multi-slice method" 6569: 6525: 4223:. Completely disordered substitutional point defects lead to a general background which is called 3403: 3284: 3227: 2810: 1842: 1107: 1081: 1055: 874: 358: 347: 77:

electrons can act as waves, and diffract and interact with matter. It also involves the extensive

15650: 15586: 15460: 15419: 15137: 14981: 14926: 14675: 14640: 13867: 13404: 13020: 12816: 12514: 12275: 10119: 8663: 8543: 7597: 6786: 5885: 4104:

Figure 14: Electron diffraction from a thin silicon (111) sample with a 7x7 reconstructed surface

3553: 3278: 966: 878: 488: 13729: 13120: 11406: 11008: 10884: 10353: 9376: 8624: 7471: 7077: 2199:. The vector from a reciprocal lattice point to the Ewald sphere is called the excitation error 577: 198: 15840: 14891: 14833: 14650: 14235:

Large coverage of many different areas of electron microscopy with large numbers of references.

12134: 11309: 9658: 8955: 8582: 8504: 8057: 3865: 3781: 3673: 3579: 2187:, that is energy conservation, and the shape function around each reciprocal lattice point—see 770: 763: 448: 206: 180: 12634:

Oura, Kenjiro; Lifšic, Viktor G.; Saranin, A. A.; Zotov, A. V.; Katayama, Masao, eds. (2003).

9835: 9213:"Die Bestimmung der Lage der Wasserstoffionen im NH4Cl-Kristallgitter durch Elektronenbeugung" 7431: 7342: 7222: 6414:

for reciprocal space. Also, sometimes reciprocal lattice vectors are written with capitals as

5931: 5421: 5358: 5302: 5016: 4980: 4944: 4908: 4872: 1438: 1142:, the relationship between the total energy of the electrons and the wavevector is written as: 193:

More complete and accurate explanations where multiple scattering is included, what is called

15845: 15665: 15190: 14986: 14948: 14755: 14707: 13671: 9135:. Dordrecht, Holland: Published for the International Union of Crystallography by D. Reidel. 5891: 5391:

is the main contribution and easily obtained for known gas composition. Note that the vector

4650: 3743: 961: 877:

in 1939, it was extended by Peter Goodman and Gunter Lehmpfuhl, then mainly by the groups of

728: 214: 12664:"Structural analysis of Si(111)-7×7 by UHV-transmission electron diffraction and microscopy" 10271: 9166:"The Observation Of Gas Adsorption Phenomena By Reflection High-Energy Electron Diffraction" 6146: 5857: 5827: 518:

Figure 4: Propagation of a wave packet demonstrating the movement of a bundle of waves; see

16019: 15850: 14787: 14623: 14514: 14048: 13993: 13918: 13824: 13741: 13683: 13502: 13455: 13416: 13351: 13262: 13202: 13163: 13151: 12967: 12867: 12828: 12779: 12732: 12675: 12598: 12526: 12345: 12287: 12240: 12193: 12146: 11989: 11559: 11547: 11512: 11500: 11460: 11418: 11371: 11359: 11321: 11241: 11186: 11128: 11078: 11020: 10896: 10818: 10686: 10630: 10618: 10503: 10233: 10173: 10161: 10077: 9944: 9932: 9897: 9885: 9800: 9788: 9750: 9708: 9670: 9532: 9520: 9469: 9422: 9410: 9339: 9327: 9282: 9270: 9224: 9177: 9061: 9006: 8967: 8878: 8702: 8594: 8516: 8419: 8364: 8314: 8264: 8174: 8069: 7954: 7897: 7830: 7760: 7706: 7648: 7191: 7141: 7089: 7037: 6457: 6123: 5911: 5275: 4573: 4438: 4411: 4408:

Figure 20: Ewald sphere construction for LEED, with the shape function streaks indicated,

4081: 3617: 3590: 3549: 3479: 3253: 3200: 3042: 2972: 2754: 2142: 1968: 1898: 1868: 1408: 1369: 1298: 622: 179:

is invoked. This approach only considers the electrons far from the sample, a far-field or

8583:"Berechnung der Bahn von Kathodenstrahlen im axialsymmetrischen elektromagnetischen Felde" 6075:

Herein crystallographic conventions are used. Often in physics a plane wave is defined as

5411:

used here is not the same as the excitation error used in other areas of diffraction, see

4320: 2378:

that is a sum of plane waves going in different directions, each with a complex amplitude

2243:

this results in (a simplification) back-reflection of the electrons leading to spots, see

1100:

is called the wavevector, has units of inverse nanometers, and the form above is called a

859: 815:

Despite early successes such as the determination of the positions of hydrogen atoms in NH

792:

showed that they could be used as micro-diffraction cameras with an aperture—the birth of

590: 570: 8: 16044: 15815: 15800: 15707: 15702: 15645: 15510: 15492: 15424: 15414: 15358: 15344: 14931: 14919: 14794: 14760: 14740: 10272: 4341: 4301: 3886:

Figure 12: Relation between spot and ring diffraction illustrated on 1 to 1000 grains of

3739: 3632: 3582:

and other atoms at the surface. Often these change the diffraction details significantly.

3460: 2695:

later. There are also cases which will be mentioned later where diffraction patterns are

1755: 1394: 1127: 656: 380:

Experiments involving electron beams occurred long before the discovery of the electron;

286: 282: 218: 202: 171:

The simplest approximation using the de Broglie wavelength for electrons, where only the

67: 14052: 13997: 13922: 13828: 13745: 13687: 13506: 13459: 13420: 13403:

Gilmore, C.J.; Marks, L.D.; Grozea, D.; Collazo, C.; Landree, E.; Twesten, R.D. (1997).

13355: 13266: 13206: 13167: 12971: 12945: 12871: 12832: 12783: 12736: 12679: 12602: 12530: 12349: 12291: 12244: 12197: 12150: 12135:"Interpretation of electron micrographs and diffraction patterns of amorphous materials" 11993: 11563: 11516: 11464: 11422: 11375: 11325: 11245: 11190: 11179:

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences

11132: 11121:

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences

11082: 11024: 10900: 10854: 10822: 10764: 10690: 10634: 10507: 10237: 10177: 10081: 9948: 9901: 9804: 9754: 9712: 9674: 9536: 9473: 9426: 9343: 9286: 9228: 9181: 9065: 9010: 8971: 8882: 8598: 8520: 8423: 8368: 8318: 8268: 8178: 8073: 7958: 7901: 7834: 7764: 7710: 7652: 7580: 7472:"I. On the illumination of lines of molecular pressure, and the trajectory of molecules" 7145: 7093: 7041: 15886: 15465: 15429: 15180: 14991: 14936: 14479: 14294: 14119: 14072: 14017: 13962: 13848: 13707: 13443: 13380: 13339: 13296: 13228: 13089: 12996: 12957: 12891: 12722: 12616: 12495: 12311: 12228: 12188:. Proceedings of the Topical Conference on Atomic Scale Structure of Amorphous Solids. 12021: 11848: 11799: 11651: 11643: 11273: 11210: 11152: 11044: 10920: 10776: 10421: 10334: 10166:

Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials

10047: 10037: 10011: 9968: 9766: 9628: 9501: 9457: 9308: 9248: 9030: 8902: 8754:, Advances in Imaging and Electron Physics, vol. 160, Elsevier, pp. 171–205, 8544:"X. On the discharge of negative ions by glowing metallic oxides, and allied phenomena" 8480: 8388: 8233: 8198: 8121: 8027: 7980: 7923: 7861: 7818: 7791: 7748: 7672: 7499: 6814: 6437: 6417: 6166: 5394: 5338: 5255: 4632: 4091: 3796: 3764:

In TEM, the electron beam passes through a thin film of the material as illustrated in

3613: 3567:

effects due to variations in the thickness of the sample and the normal to the surface.

3247: 2790: 1862: 1349: 1329: 1274: 774: 721: 716: 54: 13589:

Applied RHEED : reflection high-energy electron diffraction during crystal growth

13428: 12840: 12710: 12538: 12424:

Janssen, T.; Janner, A.; Looijenga-Vos, A.; de Wolff, P. M. (2006), Prince, E. (ed.),

12299: 12181: 11869: 10559: 10071: 9584: 8759: 6802: 4377:

The name 4D STEM is common in literature, however it is known by other names: 4D STEM

4087:

Chemical ordering, that is different atom types at different locations of the subcell.

3847: 16024: 15830: 15825: 15114: 14953: 14881: 14861: 14581: 14451: 14367: 14345: 14327: 14317: 14284: 14270: 14256: 14246: 14226: 14216: 14196: 14186: 14157: 14147: 14111: 14107: 14076: 14064: 14021: 14009: 13966: 13954: 13946: 13941: 13887: 13840: 13793: 13753: 13711: 13699: 13647: 13603: 13593: 13565: 13526: 13518: 13471: 13385: 13367: 13300: 13288: 13280: 13220: 13136: 13093: 13081: 13040: 13001: 12983: 12926: 12916: 12895: 12883: 12855: 12797: 12748: 12691: 12639: 12542: 12499: 12487: 12441: 12403: 12399: 12361: 12303: 12256: 12209: 12205: 12162: 12115: 12107: 12068: 12060: 12013: 12005: 11955: 11889: 11885: 11836: 11826: 11787: 11762: 11752: 11725: 11689: 11655: 11633: 11528: 11478: 11430: 11387: 11337: 11265: 11257: 11214: 11202: 11156: 11144: 11094: 11048: 11036: 10982: 10912: 10836: 10780: 10702: 10646: 10597: 10571: 10563: 10519: 10492:"Large dynamic range, parallel detection system for electron diffraction and imaging" 10467: 10457: 10409: 10399: 10369: 10326: 10283: 10249: 10199: 10191: 10139: 10093: 10001: 9987: 9960: 9913: 9863: 9855: 9816: 9770: 9589: 9548: 9493: 9485: 9438: 9392: 9357: 9300: 9252: 9240: 9193: 9146: 9136: 9109: 9077: 9034: 9022: 8906: 8894: 8763: 8730: 8722: 8681: 8644: 8640: 8563: 8484: 8470: 8435: 8392: 8380: 8330: 8280: 8237: 8190: 8031: 8019: 7972: 7915: 7866: 7848: 7796: 7778: 7724: 7664: 7617: 7538: 7503: 7491: 7411: 7383: 7324: 7316: 7277: 7233: 7200: 7157: 7101: 7053: 7049: 6999: 6989: 6951: 6941: 6889: 6818: 6806: 6763: 6717: 6707: 6671: 6661: 4349: 4174: 4132: 3837: 3720: 3716: 3456: 3036: 2167: 1104:

as the term inside the exponential is constant on the surface of a plane. The vector

1075: 912: 599: 428: 424: 396: 389: 319: 46: 15917: 14298: 14212:

Transmission Electron Microscopy : Physics of Image Formation and Microanalysis

14123: 13788: 13771: 13232: 12620: 12315: 12087: 12040: 12025: 11333: 10924: 10338: 10015: 9972: 9632: 9312: 7984: 6703:

Transmission Electron Microscopy : Physics of Image Formation and Microanalysis

4735:{\displaystyle |s|={\frac {4\pi }{\lambda }}\sin \left({\frac {\theta }{2}}\right).} 4199: 3990:

Many materials have relatively simple structures based upon small unit cell vectors

1832:{\displaystyle V(\mathbf {r} )=\sum V_{g}\exp(2\pi i\mathbf {g} \cdot \mathbf {r} )} 440: 15780: 15712: 15152: 14958: 14876: 14866: 14665: 14598: 14569: 14562: 14276: 14103: 14056: 14001: 13936: 13926: 13879: 13852: 13832: 13783: 13749: 13691: 13639: 13557: 13510: 13463: 13424: 13375: 13359: 13270: 13210: 13171: 13132: 13071: 13036: 13032: 12991: 12975: 12875: 12836: 12787: 12740: 12683: 12606: 12534: 12479: 12433: 12395: 12353: 12295: 12248: 12201: 12154: 12103: 12099: 12056: 12052: 11997: 11947: 11881: 11681: 11625: 11567: 11520: 11468: 11426: 11379: 11329: 11277: 11249: 11194: 11136: 11086: 11028: 10974: 10967:"Column Approximation and Howie-Whelan's Method for Dynamical Electron Diffraction" 10904: 10826: 10772: 10694: 10674: 10638: 10555: 10511: 10365: 10316: 10241: 10181: 10135: 10131: 10085: 9993: 9952: 9905: 9847: 9808: 9758: 9716: 9678: 9620: 9579: 9540: 9505: 9477: 9430: 9388: 9347: 9290: 9232: 9185: 9069: 9014: 8975: 8928: 8886: 8755: 8749: 8714: 8671: 8636: 8602: 8555: 8524: 8462: 8427: 8372: 8322: 8272: 8225: 8202: 8182: 8125: 8111: 8077: 8011: 7962: 7927: 7905: 7856: 7838: 7786: 7768: 7714: 7676: 7656: 7609: 7530: 7483: 7375: 7308: 7269: 7149: 7129: 7097: 7045: 6798: 6755: 4207:

CoSb sample showing diffuse intensity (snake-like) due to vacancies at the Nb sites

3800: 3067: 921: 631: 581: 527: 310: 58: 14239:

Hirsch, P. B.; Howie, A.; Nicholson, R. B.; Pashley, D. W.; Whelan, M. J. (1965).

13021:"On the peculiarities of CBED pattern formation revealed by multislice simulation" 12768:"Metallic Phase with Long-Range Orientational Order and No Translational Symmetry" 12611: 12586: 11407:"Motion of swift charged particles, as influenced by strings of atoms in crystals" 11066: 10966: 10542:

Faruqi, A. R.; Cattermole, D. M.; Henderson, R.; Mikulec, B.; Raeburn, C. (2003).

9411:"The scattering of electrons by atoms and crystals. I. A new theoretical approach" 9049: 8000:"Electron diffraction chez Thomson: early responses to quantum physics in Britain" 6934:

Hirsch, P. B.; Howie, A.; Nicholson, R. B.; Pashley, D. W.; Whelan, M. J. (1965).

5418:

The most valuable information is carried by the intensity of molecular scattering

5175:{\displaystyle I_{a}(s)={\frac {K^{2}}{R^{2}}}I_{0}\sum _{i=1}^{N}|f_{i}(s)|^{2},} 4259:

Figure 17: Schematic of CBED technique. Adapted from W. Kossel and G. Möllenstedt.

3593:

terms can be important. Without these the calculations may not be accurate enough.

403:

allowing for the study of the effects of high voltage electricity passing through

197:(e.g. refs). These involve more general analyses using relativistically corrected 15835: 15041: 15036: 15001: 14821: 14720: 14655: 14618: 14613: 14464: 14410: 12944:

Roth, N.; Beyer, J.; Fischer, K. F. F.; Xia, K.; Zhu, T.; Iversen, B. B. (2021).

12437: 10978: 10491: 10221: 9165: 9103: 8718: 8407: 8252: 7557: 7447: 7273: 6759: 4489: 3769: 2166:

needs to be combined with what is called the shape function (e.g.), which is the

1583: 1292: 1139: 936: 787: 715:

Building an electron microscope involves combining these elements, similar to an

682: 563: 468: 460: 456: 408: 13467: 13444:"Direct Determination of the Au(110) Reconstructed Surface by X-Ray Diffraction" 12792: 12767: 12383: 12252: 11678:

Large-Angle Convergent-Beam Electron Diffraction Applications to Crystal Defects

8676: 8455:"Introduction to Heinrich Hertz's Miscellaneous Papers (1895) by Philipp Lenard" 7025: 4211:

A further step beyond superstructures and aperiodic materials is what is called

3973:

can be more powerful, although this is still a topic of continuing development.

15790: 15404: 14851: 14816: 14804: 14799: 14765: 14735: 14725: 14684: 14628: 14552: 14506: 13695: 12744: 9624: 9608: 8548:

The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science

7602:

The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science

7523:

The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science

7433:

Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin

7368:

The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science

6593: 6055: 6013: 4485: 3902: 3833: 3609: 1893: 1751: 1398: 1131: 870: 828: 820: 695: 686: 648: 639: 547: 519: 176: 42: 14280: 14230: 14036: 13981: 13883: 13627: 13275: 13250: 13175: 13076: 13059: 12979: 12879: 12711:"Diffraction refinement of localized antibonding at the Si(111) 7 × 7 surface" 12158: 12001: 11766: 11572: 11524: 11449:"Multiple-Scattering Treatment of Low-Energy Electron-Diffraction Intensities" 11383: 11253: 10831: 10806: 10642: 10413: 10269: 10186: 10089: 9997: 9956: 9909: 9812: 9720: 9544: 9481: 9434: 9352: 9295: 9212: 8994: 8866: 8559: 8352: 8302: 8015: 7613: 7534: 7379: 6721: 5884:

is the mean square amplitude of vibration between the two atoms, similar to a

4565:

Figure 23: RHEED pattern of a silicon (111) surface with a 7x7 reconstruction.

3841: 3463:

because they interact with matter far less and often Bragg's law is adequate.

1045:{\displaystyle \psi (\mathbf {r} )=\exp(2\pi i\mathbf {k} \cdot \mathbf {r} )} 746:(Professor of High Voltage Technology and Electrical Installations) appointed 16003: 15866: 15810: 15470: 14996: 14809: 14608: 14331: 14200: 14161: 14068: 14013: 13950: 13891: 13844: 13797: 13703: 13651: 13643: 13569: 13522: 13475: 13371: 13284: 13224: 13085: 12987: 12887: 12801: 12752: 12695: 12546: 12491: 12407: 12365: 12333: 12307: 12260: 12213: 12166: 12111: 12064: 12009: 11959: 11893: 11840: 11791: 11532: 11482: 11391: 11341: 11261: 11206: 11148: 11098: 11040: 10916: 10840: 10706: 10650: 10567: 10523: 10330: 10253: 10195: 9964: 9917: 9859: 9820: 9682: 9593: 9552: 9489: 9442: 9361: 9304: 9244: 9197: 9081: 9026: 8995:"Eine Anwendung der Elektronenbeugung auf die Untersuchung der Gasadsorption" 8979: 8898: 8726: 8648: 8606: 8567: 8528: 8454: 8439: 8384: 8334: 8326: 8284: 8229: 8194: 8081: 8023: 7976: 7919: 7852: 7782: 7728: 7668: 7621: 7542: 7495: 7387: 7320: 7281: 7161: 7057: 7003: 6810: 6675: 6522:

is used for plane waves. (Different notations also exist for the wavevectors

6009: 4181: 3773: 3603: 3557: 1587: 1402: 759: 691: 635: 539: 538:

waves. He suggested that an electron around a nucleus could be thought of as

476: 432: 368: 14371: 13607: 12930: 12357: 11174: 11116: 10471: 9851: 9050:"Diffraction of Low-Speed Electrons by Single Crystals of Copper and Silver" 8466: 7518: 7363: 7296: 7153: 4559: 2557:{\displaystyle \mathbf {k} =\mathbf {k} _{0}+\mathbf {g} +\mathbf {s} _{g}.} 41:

is a generic term for phenomena associated with changes in the direction of

15927: 15891: 15785: 15775: 15450: 15399: 14702: 14692: 14586: 14469: 14260: 14115: 13958: 13812: 13530: 13490: 13389: 13363: 13314: 13292: 13215: 13190: 13044: 13005: 12119: 12072: 12017: 11647: 11629: 11619: 11269: 11198: 11140: 11032: 10908: 10575: 10393: 10203: 10143: 9762: 9497: 9150: 9073: 8734: 8116: 7967: 7942: 7870: 7800: 7719: 7694: 7487: 7328: 7312: 6955: 6883: 6063: 4329: 4220: 3517:

The main components of current dynamical diffraction of electrons include:

3452: 3356:{\displaystyle \mathbf {k} =\mathbf {k} _{0}+\mathbf {g} +\mathbf {s} _{z}} 2184: 1593:

The magnitude of the interaction of the electrons with a material scales as

1579: 651:'s observations of lines due to combined elastic and inelastic scattering, 611: 404: 335: 167:

There are also many levels of analysis of electron diffraction, including:

14311: 11685: 10321: 10304: 10270:

K. Oura; V. G. Lifshifts; A. A. Saranin; A. V. Zotov; M. Katayama (2003).

9867: 8276: 7843: 7773: 6983: 15871: 15805: 15795: 15185: 14856: 14730: 14557: 13905:

de Kock, M. B.; Azim, S.; Kassier, G. H.; Miller, R. J. D. (2020-11-21).

13587: 12910: 12668:

Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films

10698: 10451: 10222:"New Developments in the Production and Measurement of Ultra High Vacuum" 9738: 4577: 1590:

is a few eV; electron diffraction involves electrons up to 5,000,000 eV.

886: 882: 751: 694:

in 1899, improved oxide-coated cathodes which produced more electrons by

664: 642:

approach as the positions were systematically different; the approach of

589:

M. Einstein from the beginning has supported my thesis, but it was M. E.

559: 543: 507: 464: 400: 372: 331: 314: 242: 230: 104:

of electron diffraction. The most common approach is where the electrons

14342:

Transmission electron microscopy: diffraction, imaging, and spectrometry

14240: 13060:"Introduction to the Ronchigram and its Calculation with Ronchigram.com" 12229:"Diminished Medium-Range Order Observed in Annealed Amorphous Germanium" 11935: 11090: 9130: 8162: 6935: 4616: 4496:, and diffracted electrons as spots on a fluorescent screen as shown in 3882: 3589:, use more careful analyses of the potential because contributions from 3575: 2236: 950: 931: 819:

Cl crystals by W. E. Laschkarew and I. D. Usykin in 1933, boric acid by

804: 371:

blocking part of the electron beam (bottom, black background); see also

161: 90: 15952: 15932: 15373: 15368: 14750: 14436: 14356:, a recent textbook with many images, stronger on experimental aspects. 14140:

Schwartz, Adam J; Kumar, Mukul; Adams, Brent L; Field, David P (2009).

14060: 14005: 13561: 13545: 12483: 11951: 10619:"A Relativistic n -Beam Dynamical Theory for Fast Electron Diffraction" 9236: 9018: 8890: 8376: 8186: 7364:"XLVI. Observations on the electrical discharge through rarefied gases" 4551:

Figure 22: Ewald sphere in_RHEED, where higher-order Laue zones matter.

4297: 3911: 3538: 3537:

Higher-order numerical approaches to calculate the intensities such as

1575: 1101: 850:

algorithm, which only became possible once the fast Fourier transform (

847: 699: 643: 627: 603: 16:

Bending of electron beams due to electrostatic interactions with matter

15313: 14210: 13931: 12663: 12384:"Commensurate phases, incommensurate phases and the devil's staircase" 12274:

Treacy, M M J; Gibson, J M; Fan, L; Paterson, D J; McNulty, I (2005).

11746: 11473: 11448: 10723:

Howie, A (1962). "Discussion of K. Fujiwara's paper by M. J. Whelan".

10515: 10245: 9189: 8933: 8431: 7636: 7343:"VIII. Experimental researches in electricity. — Thirteenth series.," 6701: 4862:{\displaystyle I_{\text{tot}}(s)=I_{a}(s)+I_{m}(s)+I_{t}(s)+I_{b}(s),} 4527: 4366:

4D scanning transmission electron microscopy (4D STEM) is a subset of

3422:

has to have the same modulus (i.e. energy) as the incoming wavevector

2045:{\displaystyle \mathbf {g} =h\mathbf {A} +k\mathbf {B} +l\mathbf {C} } 896:

The development of new approaches to reduce dynamical effects such as

858:

diffraction in seconds to minutes with laptops using widely available

670: 558:. Both of these depend upon the energy, which in turn connects to the 15820: 15475: 14459: 14180: 14141: 13836: 13514: 12687: 12661: 11820: 11781: 11598:(Winter 2019 ed.), Metaphysics Research Lab, Stanford University 11360:"Extinction conditions in the dynamic theory of electron diffraction" 7910: 7885: 7660: 7186: 6655: 4647:

In GED the diffraction intensities at a particular diffraction angle

4593: 4516: 4470: 4370:(STEM) methods which uses a pixelated electron detector to capture a 4328:

Precession electron diffraction (PED), invented by Roger Vincent and

3901:

Diffraction patterns depend on whether the beam is diffracted by one

3852: 3777: 2625:{\displaystyle I(\mathbf {k} )=\left|\phi (\mathbf {k} )\right|^{2}.} 2239:

the shape function is mainly normal to the surface of the sample. In

747: 660: 412: 156:, liquids, surfaces using lower energy electrons, a technique called 94: 28: 14361: 14340:

Carter, C. Barry; Williams, David B.; Thomas, John M., eds. (2016).

12662:

Takayanagi, K.; Tanishiro, Y.; Takahashi, M.; Takahashi, S. (1985).

9568:"An algorithm for the machine calculation of complex Fourier series" 7297:"Otto von Gericke (1602–1686) and his pioneering vacuum experiments" 4742:

The total intensity is then given as a sum of partial contributions:

3397: 290: 266: 172: 15922: 15388: 15056: 14826: 14574: 14205:. Contains extensive coverage of kinematical and other diffraction. 13108:

http://www.numis.northwestern.edu/Research/Current/precession.shtml

12962: 12817:"Microstructural evolution in Al–Cu–Fe quasicrystalline thin films" 12709:

Ciston, J.; Subramanian, A.; Robinson, I. K.; Marks, L. D. (2009).

12041:"Towards automated diffraction tomography: Part I—Data acquisition" 10456:. Cambridge, U.K.: Cambridge University Press. pp. Chpt 4–19. 9886:"Point-group determination by convergent-beam electron diffraction" 8142:

Kikuchi, Seishi (1928). "Electron diffraction in single crystals".

7182: 4636: 4332:

in 1994, is a method to collect electron diffraction patterns in a

4127:

Figure 15: Electron diffraction pattern of a decagonal quasicrystal

3941: 3891: 3832:

If a parallel beam is used to acquire a diffraction pattern from a

3825: 3511: 2409:. (This is a three dimensional integral, which is often written as 810: 698:

in 1905 and the development of the electromagnetic lens in 1926 by

535: 480: 436: 388:, which is connected to the recording of electrostatic charging by 14379: 12727: 12423: 12039:

Kolb, U.; Gorelik, T.; Kübel, C.; Otten, M.T.; Hubert, D. (2007).

11721:

Principles of Electron Optics Volume Two: Applied Geometric Optics

9102:

Van Hove, Michel A.; Weinberg, William H.; Chan, Chi-Ming (1986).

6407:{\displaystyle \mathbf {b} _{1},\mathbf {b} _{2},\mathbf {b} _{3}} 6348:{\displaystyle \mathbf {a} _{1},\mathbf {a} _{2},\mathbf {a} _{3}} 6289:{\displaystyle \mathbf {a} ^{*},\mathbf {b} ^{*},\mathbf {c} ^{*}} 3756: 1326:

used to cancel out the relativistic terms for electrons of energy

978: 15876: 15558: 15066: 14303:, a large coverage of topic related to dynamical diffraction and 13982:"Microtexture determination by electron back-scatter diffraction" 13491:"A homologous series of structures on the surface of SrTiO3(110)" 13488: 12585:

Andersen, Tassie K.; Fong, Dillon D.; Marks, Laurence D. (2018).

12515:"Magnetic, chemical and structural ordering in transition metals" 11724:(2nd ed.). Elsevier. pp. Chpts 36, 40, 41, 43, 49, 50. 8751:

Origin and Background of the Invention of the Electron Microscope

8218:

Zeitschrift für Elektrochemie und angewandte physikalische Chemie

6596:

are used for hexagonal systems even though only three are needed.

5989: 4621: 3506: 416: 23: 14376:, an older source for experimental details, albeit hard to find. 10939:"higher-order Laue zone (HOLZ) reflection | Glossary | JEOL Ltd" 10541: 9108:. Springer-Verlag, Berlin Heidelberg New York. pp. 13–426. 6888:(Repr ed.). South Melbourne: Brooks/Cole Thomson Learning. 4272: 3932: 2252: 15896: 13546:"Surface transmission electron diffraction for SrTiO3 surfaces" 11978:"Sufficient Conditions for Direct Methods with Swift Electrons" 10807:"The shape transform in electron diffraction by small crystals" 10544:"Evaluation of a hybrid pixel detector for electron microscopy" 8625:"Origins and historical development of the electron microscope" 7819:"Reflection and Refraction of Electrons by a Crystal of Nickel" 4216: 3703:(converging), and ring diffraction (parallel with many grains). 1134:, which as spin does not normally matter can be reduced to the 435:. Using these tubes, while studying electrical conductivity in 160:, and by reflecting electrons off surfaces, a technique called 12708: 10943:

higher-order Laue zone (HOLZ) reflection | Glossary | JEOL Ltd

7130:"An Undulatory Theory of the Mechanics of Atoms and Molecules" 4255: 3570:

Both in the geometry of scattering and calculations, for both

893:. In many cases this is the best method to determine symmetry. 117: 15061: 12182:"High resolution electron microscopy of amorphous thin films" 6237:

for the reciprocal lattice vectors as used herein, sometimes

4533: 3768:. Before and after the sample the beam is manipulated by the 3734:, investigations of electronic structure and bonding through 2740: 1078:

description; one cannot use a classical approach. The vector

420: 385: 257: 246: 86: 50: 32: 11822:

Electron energy-loss spectroscopy in the electron microscope

10765:"Experimental Electron Diffraction Structure Investigations" 7026:"Ion core scattering and low energy electron diffraction. I" 3976: 638:

noticed that their results could not be interpreted using a

15881: 14304: 14238: 14035:

Adams, Brent L.; Wright, Stuart I.; Kunze, Karsten (1993).

12766:

Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J. W. (1984).

11297:. Commission of the European Communities. pp. 397–552. 7637:"The Scattering of Electrons by a Single Crystal of Nickel" 6933: 4378: 3700: 3695: 3586: 3571: 3541:, matrix methods which are called Bloch-wave approaches or 3400:. The excitation error comes in as the outgoing wavevector 2668: 2232: 943: 927: 497: 157: 14336:. Very extensive coverage of modern dynamical diffraction. 13769: 13337: 12638:. Advanced texts in physics. Berlin Heidelberg: Springer. 5984: 4572:

Reflection high energy electron diffraction (RHEED), is a

3627: 2175: 105: 15163:

Zeitschrift für Kristallographie – New Crystal Structures

13402: 12765: 9739:"The symmetry of electron diffraction zone axis patterns" 9377:"Crystal structure determination by electron diffraction" 7943:"The diffraction of cathode rays by thin celluloid films" 7346:

Philosophical Transactions of the Royal Society of London

4384: 3951: 3887: 2724: 851: 133: 27:

Figure 1: Selected area diffraction pattern of a twinned

15158:

Zeitschrift für Kristallographie – Crystalline Materials

14037:"Orientation imaging: The emergence of a new microscopy" 13904: 13672:"Electron Diffraction as a Tool of Structural Chemistry" 13632:

Berichte der Bunsengesellschaft für physikalische Chemie

13058:

Schnitzer, Noah; Sung, Suk Hyun; Hovden, Robert (2019).

10938: 10855:"Kevin Cowtan's Book of Fourier, University of York, UK" 10278:. Springer-Verlag, Berlin Heidelberg New York. pp. 10120:"Is precession electron diffraction kinematical? Part I" 9736: 6858:(English translation by A.F. Kracklauer, 2004. ed.) 6745: 6050:

specifically stated that their work was consistent with

5272:

is the distance between the scattering object detector,

4065:{\displaystyle N\mathbf {a} ,M\mathbf {b} ,\mathbf {c} } 3730:

showing the atomic structure, chemical analysis through

3688: 973: 14139: 12276:"Fluctuation microscopy: a probe of medium range order" 12273: 10675:"Relativistic Dynamical Theory of Electron Diffraction" 10073:

Uniting Electron Crystallography and Powder Diffraction

7562:

The Scientific Transactions of the Royal Dublin Society

7408:

Advances in Electronics and Electron Physics, Volume 67

4242: 4072:. which has larger dimensions in two directions. These 3197:

the sum being over all the atoms in the unit cell with

942:

Fast and accurate methods to calculate intensities for

793: 109: 15051: 13340:"Nanoscale momentum-resolved vibrational spectroscopy" 13149: 12633: 12426:"Incommensurate and commensurate modulated structures" 6230:{\displaystyle \mathbf {A} ,\mathbf {B} ,\mathbf {C} } 4203:

Figure 16: Single frame extracted from a video of a Nb

4166:{\displaystyle \mathbf {a} ,\mathbf {b} ,\mathbf {c} } 4021:{\displaystyle \mathbf {a} ,\mathbf {b} ,\mathbf {c} } 1958:{\displaystyle \mathbf {A} ,\mathbf {B} ,\mathbf {C} } 423:(positive electrode). Building on this, in the 1850s, 145: 14143:

Electron backscatter diffraction in materials science

12912:

Diffuse neutron scattering from crystalline materials

12038: 10616: 6572: 6550: 6528: 6515:{\displaystyle \exp(i\mathbf {k} \cdot \mathbf {r} )} 6483: 6460: 6440: 6420: 6361: 6302: 6296:

are used. Less common, but still sometimes used, are

6243: 6205: 6169: 6149: 6126: 6113:{\displaystyle \exp(i\mathbf {k} \cdot \mathbf {r} )} 6081: 5934: 5914: 5894: 5860: 5830: 5460: 5424: 5397: 5361: 5341: 5305: 5278: 5258: 5188: 5055: 5019: 4983: 4947: 4911: 4875: 4748: 4673: 4653: 4441: 4414: 4141: 4034: 3996: 3894:. Corresponding experimental patterns can be seen in 3818: 3749: 3738:, and studies of the electrostatic potential through 3646: 3482: 3428: 3406: 3369: 3309: 3287: 3256: 3230: 3203: 3076: 3045: 3002: 2975: 2835: 2813: 2793: 2757: 2639: 2570: 2507: 2472: 2440: 2415: 2384: 2281: 2205: 2145: 2116: 2087: 2058: 2052:(Sometimes reciprocal lattice vectors are written as 2003: 1971: 1933: 1927:, a sum of the individual reciprocal lattice vectors 1901: 1871: 1845: 1764: 1599: 1461: 1441: 1411: 1372: 1352: 1332: 1301: 1277: 1212: 1148: 1110: 1084: 1058: 990: 121: 74: 14339: 13865: 12465: 12085: 10039:

The atlas of electron diffraction zone axis patterns

9101: 6589: 6120:. This changes some of the equations by a factor of 5971: 3303:

is the wavevector for the diffraction beam which is:

2240: 846:

Fast numerical methods based upon the Cowley-Moodie

800: 137: 14310:Peng, L.-M.; Dudarev, S. L.; Whelan, M. J. (2011). 13057: 12943: 11067:"Effect of Inelastic Waves on Electron Diffraction" 10117: 9930: 9128: 7453:

A History of the Theories of Aether and Electricity

7436:(in German). The Academy. pp. 279–295, pp 286. 6982:Peng, L.-M.; Dudarev, S. L.; Whelan, M. J. (2011). 4528:

Reflection high-energy electron diffraction (RHEED)

4235:CoSb sample, with the diffraction pattern shown in 3985: 911:The development of experimental methods exploiting 671:

Electron microscopes and early electron diffraction

224: 14363:Practical electron microscopy in materials science 13727: 12132: 11671: 11669: 11667: 11665: 10395:Surface structure determination by LEED and X-rays 10162:"The charge-flipping algorithm in crystallography" 10118:White, T.A.; Eggeman, A.S.; Midgley, P.A. (2010). 8058:"Theorie der Beugung von Elektronen an Kristallen" 7221: 7177: 7175: 7173: 7171: 6580: 6558: 6536: 6514: 6469: 6446: 6426: 6406: 6347: 6288: 6229: 6175: 6155: 6135: 6112: 5956: 5920: 5900: 5876: 5846: 5816: 5446: 5403: 5383: 5347: 5327: 5299:is the intensity of the primary electron beam and 5291: 5264: 5244: 5174: 5041: 5005: 4969: 4933: 4897: 4861: 4734: 4659: 4454: 4427: 4307: 4165: 4064: 4020: 3664: 3495: 3443: 3414: 3384: 3355: 3295: 3269: 3238: 3216: 3189: 3058: 3027: 2988: 2961: 2821: 2799: 2770: 2667:A typical electron diffraction pattern in TEM and 2656: 2624: 2556: 2487: 2458: 2426: 2401: 2370: 2220: 2158: 2131: 2102: 2073: 2044: 1989: 1957: 1919: 1884: 1853: 1831: 1738: 1566: 1447: 1424: 1385: 1358: 1338: 1314: 1283: 1263: 1198: 1118: 1092: 1066: 1044: 881:and Michiyoshi Tanaka who showed how to determine 769:Apparently independent of this effort was work at 392:around 585 BCE, and possibly others even earlier. 14309: 13544:Kienzle, Danielle M.; Marks, Laurence D. (2012). 13405:"Direct solutions of the Si(111) 7 × 7 structure" 12946:"Tuneable local order in thermoelectric crystals" 12584: 12133:Howie, A.; Krivanek, O. L.; Rudee, M. L. (1973). 11353: 11351: 11294:Electron Microscopy in Materials Science: Part II 9656: 9210: 7695:"Diffraction of Electrons by a Crystal of Nickel" 6981: 4667:is described via a scattering variable defined as 3680:; Kikuchi maps are available for many materials. 727:One effort was university based. In 1928, at the 16001: 14265:, often called the bible of electron microscopy. 14034: 12636:Surface science: an introduction; with 16 tables 11592:"Copenhagen Interpretation of Quantum Mechanics" 10398:. Cambridge, United Kingdom. pp. Chpt 3–5. 9883: 9698: 9659:"Elektroneninterferenzen im konvergenten Bündel" 7749:"Reflection of Electrons by a Crystal of Nickel" 4340:. This integration produces a quasi-kinematical 3967:high-resolution transmission electron microscopy 3719:, symmetries, and sometimes to solve an unknown 3578:, effects due to the presence of surface steps, 811:Subsequent developments in methods and modelling 807:in a system with a very well controlled vacuum. 14313:High energy electron diffraction and microscopy 13728:Seip, H.M.; Strand, T.G.; Stølevik, R. (1969). 12856:"One Hundred Years of Diffuse X-ray Scattering" 12419: 12417: 11662: 7823:Proceedings of the National Academy of Sciences 7753:Proceedings of the National Academy of Sciences 7168: 7123: 7121: 7119: 7117: 7115: 7113: 7111: 6985:High energy electron diffraction and microscopy 5988:Figure 25: Kikuchi lines in an EBSD pattern of 5412: 4620:Figure 24: Gas electron diffraction pattern of 3792: 1264:{\displaystyle m^{*}=m_{0}+{\frac {E}{2c^{2}}}} 979:Plane waves, wavevectors and reciprocal lattice 569:This rapidly became part of what was called by 190:and is also a far-field or Fraunhofer approach. 15743:Serial block-face scanning electron microscopy 15446:Detectors for transmission electron microscopy 13118: 13018: 11971: 11969: 11348: 11230:"FFT Multislice Method—The Silver Anniversary" 10617:Watanabe, K.; Hara, S.; Hashimoto, I. (1996). 10391: 9458:"FFT Multislice Method—The Silver Anniversary" 8303:"Beitrag zur geometrischen Elektronenoptik. I" 8004:The British Journal for the History of Science 7816: 7746: 7692: 7634: 7401: 7399: 7397: 6881: 6787:"The scattering of fast electrons by crystals" 5355:of the molecular structure in the experiment. 3868:approach. There are ways to combine this with 1432:in terms of how they interact with the atoms. 1199:{\displaystyle E={\frac {h^{2}k^{2}}{2m^{*}}}} 958:detectors for transmission electron microscopy 15329: 14395: 13979: 13866:Kálmán, E.; Pálinkás, G.; Kovács, P. (1977). 13810: 13188: 12334:"Symmetry of periodically distorted crystals" 12331: 12086:Mugnaioli, E.; Gorelik, T.; Kolb, U. (2009). 11357: 10449: 9786: 9606: 9518: 6929: 6927: 6925: 4905:results from scattering by individual atoms, 2564:A diffraction pattern detects the intensities 915:technologies (e.g. the approach described by 322:and the explanation of electron diffraction. 153: 85:and the early 20th century developments with 13765: 13763: 13543: 12814: 12561:"6.8: Ferro-, Ferri- and Antiferromagnetism" 12414: 12327: 12325: 12226: 11975: 11853:: CS1 maint: multiple names: authors list ( 11804:: CS1 maint: multiple names: authors list ( 11717: 11172: 11060: 11058: 11006: 10485: 10483: 10481: 9931:Tanaka, M.; Saito, R.; Watanabe, D. (1980). 9408: 7886:"Diffraction of Cathode Rays by a Thin Film" 7598:"On the constitution of atoms and molecules" 7255: 7108: 6923: 6921: 6919: 6917: 6915: 6913: 6911: 6909: 6907: 6905: 6882:Ashcroft, Neil W.; Mermin, N. David (2012). 4362:4D scanning transmission electron microscopy 4348:algorithms using electrons to determine the 926:in 1953) to better control surfaces, making 869:approach. Building on the original work of 427:was able to achieve a pressure of around 10 187: 113: 15232: 13592:. Berlin: Springer. pp. Chpts 2–4, 7. 12512: 11966: 11933: 11624:. Yale University Press. pp. 243–263. 11494: 11492: 11114: 11110: 11108: 10973:, Tokyo: Springer Japan, pp. 293–296, 10668: 10666: 10664: 10662: 10660: 10453:Reflection high-energy electron diffraction 10445: 10443: 10441: 10439: 10437: 10392:Moritz, Wolfgang; Van Hove, Michel (2022). 10305:"Theory of Low-Energy Electron Diffraction" 9565: 9325: 9264: 9262: 9163: 8841:"Apparatus for producing images of objects" 8815:"Apparatus for producing images of objects" 7883: 7394: 7301:Aviation, Space, and Environmental Medicine 7288: 7213: 7127: 7075: 7019: 7017: 7015: 7013: 6649: 6647: 6645: 6643: 6641: 6639: 6637: 6635: 6633: 6454:, and the length can differ by a factor of 4603: 3829:smaller regions a focused probe is needed. 3742:; this list is not exhaustive. Compared to 3635:material, within the stereographic triangle 677:History of transmission electron microscopy 15336: 15322: 14402: 14388: 13625: 12915:. David A. Keen. Oxford: Clarendon Press. 12860:Metallurgical and Materials Transactions A 11911:"Apertures, Electron Microscope Apertures" 11786:. National Technical Information Service. 11310:"Diffraction in crystals at high energies" 11168: 11166: 11115:Howie, Archibald; Whelan, Michael (1961). 10960: 10958: 10882: 10769:Structure Analysis by Electron Diffraction 10537: 10535: 10533: 10426:: CS1 maint: location missing publisher ( 10354:"Electron diffraction at crystal surfaces" 10052:: CS1 maint: location missing publisher ( 9836:"Theory of zone axis electron diffraction" 9732: 9730: 9328:"The precise structure of orthoboric acid" 9211:Laschkarew, W. E.; Usyskin, I. D. (1933). 9097: 9095: 9093: 9091: 9047: 8700: 8408:"Historical Background of Electron Optics" 8350: 8300: 7582:Relativity: The Special and General Theory 7476:Proceedings of the Royal Society of London 6631: 6629: 6627: 6625: 6623: 6621: 6619: 6617: 6615: 6613: 3875: 2782: 855: 799:Less controversial was the development of 194: 14268: 13940: 13930: 13787: 13760: 13379: 13274: 13214: 13075: 12995: 12961: 12791: 12726: 12610: 12322: 11905: 11903: 11675: 11571: 11472: 11442: 11440: 11314:Journal of Physics C: Solid State Physics 11290: 11055: 10878: 10876: 10874: 10830: 10804: 10762: 10718: 10716: 10489: 10478: 10450:Ichimiya, Ayahiko; Cohen, Philip (2004). 10320: 10215: 10213: 10185: 10159: 10155: 10153: 10035: 9985: 9884:Tanaka, M.; Saito, R.; Sekii, H. (1983). 9583: 9566:Cooley, James W.; Tukey, John W. (1965). 9351: 9294: 8932: 8864: 8747: 8741: 8675: 8618: 8616: 8346: 8344: 8296: 8294: 8163:"Neuere Ergebnisse der Elektronenbeugung" 8160: 8115: 7966: 7909: 7860: 7842: 7790: 7772: 7718: 7446: 7440: 7429: 7071: 7069: 7067: 7030:Journal of Physics C: Solid State Physics 6902: 6842: 6840: 6838: 6836: 6834: 6832: 6830: 6828: 6784: 5245:{\displaystyle K=(8\pi ^{2}me^{2})/h^{2}} 4592:methods that also rely on diffraction of 4368:scanning transmission electron microscopy 3977:Multiple materials and double diffraction 3813:scanning transmission electron microscopy 2996:is the magnitude of the excitation error 2139:and see note.) The contribution from the 411:applied a high voltage between two metal 101: 14359: 13723: 13721: 13441: 12853: 12430:International Tables for Crystallography 12227:Gibson, J. M.; Treacy, M. M. J. (1997). 11940:Journal of the Physical Society of Japan 11489: 11404: 11227: 11105: 11071:Journal of the Physical Society of Japan 11064: 10725:Journal of the Physical Society of Japan 10679:Journal of the Physical Society of Japan 10672: 10657: 10434: 10387: 10385: 10383: 10381: 10379: 10113: 10111: 10109: 10065: 10063: 10031: 10029: 10027: 10025: 9840:Journal of Electron Microscopy Technique 9455: 9259: 8502: 8215: 8051: 8049: 8047: 8045: 8043: 8041: 7256:Iversen, Paul; Lacks, Daniel J. (2012). 7251: 7249: 7181: 7010: 6752:International Tables for Crystallography 6695: 6693: 6691: 6689: 6687: 6685: 5983: 5335:is the scattering amplitude of the atom 4615: 4319: 4271: 4254: 4198: 4122: 4099: 3881: 3846: 3755: 3694: 3626: 3505: 3470: 2696: 2174: 706: 513: 498:Waves, diffraction and quantum mechanics 419:(negative electrode) and its end at the 285:. This has relevance for imaging within 125: 82: 22: 15343: 14178: 14135: 14133: 14089: 13811:Lengyel, SáNdor; KáLmáN, Erika (1974). 13669: 13665: 13663: 13661: 13621: 13619: 13617: 13581: 13579: 13189:Moeck, Peter; Rouvimov, Sergei (2010). 13100: 12657: 12655: 12472:Journal of the American Ceramic Society 12377: 12375: 11621:Falling Felines and Fundamental Physics 11613: 11611: 11596:The Stanford Encyclopedia of Philosophy 11585: 11583: 11545: 11498: 11173:Hirsch, Peter; Whelan, Michael (1963). 11163: 11007:Hirsch, Peter; Whelan, Michael (1960). 10955: 10530: 10265: 10263: 9727: 9088: 8953: 8541: 8405: 8250: 8141: 8097: 7997: 7817:Davisson, C. J.; Germer, L. H. (1928). 7747:Davisson, C. J.; Germer, L. H. (1928). 7516: 7469: 7361: 7219: 6653: 6610: 6195: 6193: 6191: 6189: 6043: 3683: 2704: 1586:. For context, the typical energy of a 949:Methods to simulate the intensities in 472:deflected by an electromagnetic field. 129: 16002: 14505: 14208: 13868:"Liquid water: I. Electron scattering" 13813:"Electron diffraction on liquid water" 13244: 13242: 11934:Honjo, Goro; Mihama, Kazuhiro (1954). 11900: 11867: 11744: 11713: 11711: 11709: 11707: 11705: 11437: 10964: 10885:"The reflection of X-rays by crystals" 10871: 10713: 10591: 10587: 10585: 10219: 10210: 10150: 9607:Brigham, E. O.; Morrow, R. E. (1967). 9404: 9402: 9374: 9268: 8992: 8622: 8613: 8341: 8291: 8137: 8135: 8093: 8091: 7742: 7740: 7738: 7688: 7686: 7555: 7405: 7294: 7064: 7023: 6977: 6975: 6973: 6971: 6969: 6967: 6965: 6846: 6825: 6741: 6739: 6737: 6735: 6733: 6731: 6699: 6035: 6033: 4385:Low-energy electron diffraction (LEED) 4116: 3548:Contributions to the diffraction from 2727:they can also be a grid of discs, see 325: 16010:Applied and interdisciplinary physics 15317: 14383: 14269:Spence, J. C. H.; Zuo, J. M. (1992). 13718: 13585: 13248: 12908: 12179: 11870:"Twenty forms of electron holography" 11718:Hawkes, Peter; Kasper, Erwin (2018). 11446: 11307: 10805:Rees, A. L. G.; Spink, J. A. (1950). 10722: 10490:Spence, J. C. H.; Zuo, J. M. (1988). 10376: 10351: 10302: 10106: 10069: 10060: 10022: 9986:Spence, J. C. H.; Zuo, J. M. (1992). 9879: 9877: 9782: 9780: 9694: 9692: 9652: 9650: 9648: 9409:Cowley, J. M.; Moodie, A. F. (1957). 8838: 8812: 8580: 8452: 8161:Mark, Herman; Wierl, Raymond (1930). 8100:"Diffraction of cathode rays by mica" 8055: 8038: 7812: 7810: 7465: 7463: 7246: 6780: 6778: 6682: 4511:LEED may be used in one of two ways: 4192: 3950:Figure 13: Ring diffraction image of 3689:In a transmission electron microscope 1455:in vacuum is from the above equations 974:Core elements of electron diffraction 15982: 15296: 14636:Phase transformation crystallography 14242:Electron microscopy of thin crystals 14130: 13658: 13614: 13576: 12652: 12587:"Pauling's rules for oxide surfaces" 12372: 11783:Energy dispersive x-ray spectrometry 11617: 11608: 11589: 11580: 10260: 9833: 9657:Kossel, W.; Möllenstedt, G. (1939). 7940: 7693:Davisson, C.; Germer, L. H. (1927). 7635:Davisson, C.; Germer, L. H. (1927). 7595: 7578: 7410:, Academic Press, pp. 183–186, 6937:Electron microscopy of thin crystals 6877: 6875: 6873: 6186: 4576:used to characterize the surface of 4372:convergent beam electron diffraction 4344:that is more suitable as input into 4249:Convergent-beam electron diffraction 4243:Convergent beam electron diffraction 3732:energy-dispersive x-ray spectroscopy 2268:Laue zone (ZOLZ) spots, as shown in 867:convergent-beam electron diffraction 562:and the relativistic formulation of 532:Recherches sur la théorie des quanta 15143:Journal of Chemical Crystallography 14409: 14316:. Oxford: Oxford University Press. 13980:Dingley, D. J.; Randle, V. (1992). 13239: 13119:Vincent, R.; Midgley, P.A. (1994). 12815:Widjaja, E.J.; Marks, L.D. (2003). 12519:Journal of Physics F: Metal Physics 12381: 11748:High-resolution electron microscopy 11702: 11358:Gjønnes, J.; Moodie, A. F. (1965). 10582: 9787:Steeds, J. W.; Vincent, R. (1983). 9519:Goodman, P.; Moodie, A. F. (1974). 9399: 8661: 8244: 8132: 8104:Proceedings of the Imperial Academy 8088: 7735: 7683: 7628: 6988:. Oxford: Oxford University Press. 6962: 6728: 6030: 5854:is the distance between two atoms, 4631:(GED) can be used to determine the 2657:{\displaystyle \phi (\mathbf {k} )} 2402:{\displaystyle \phi (\mathbf {k} )} 1397:), and comes up in the behavior of 483:atom. These were originally called 301:and the other figures shown later. 213:Electron diffraction is similar to 13: 14360:Edington, Jeffrey William (1977). 14172: 11818: 11779: 10777:10.1016/b978-0-08-010241-2.50010-9 9874: 9793:Journal of Applied Crystallography 9777: 9689: 9645: 8629:British Journal of Applied Physics 7807: 7558:"Cause of Double Lines in Spectra" 7460: 7355: 7335: 7076:Maksym, P.A.; Beeby, J.L. (1981). 6775: 6069: 5908:is the anharmonicity constant and 4180:An extreme example of this is for 3851:Figure 11: Diffraction pattern of 3819:Selected area electron diffraction 3803:of this lens, forming a spot on a 3750:Formation of a diffraction pattern 3028:{\displaystyle |\mathbf {s} _{z}|} 2723:. With conical illumination as in 794:selected area electron diffraction 136:of electrons or where the beam is 14: 16056: 15379:Timeline of microscope technology 13019:Chuvilin, A.; Kaiser, U. (2005). 12186:Journal of Non-Crystalline Solids 11976:Marks, L.D.; Sinkler, W. (2003). 10883:Bragg, W.H.; Bragg, W.L. (1913). 9585:10.1090/S0025-5718-1965-0178586-1 9164:Sewell, P. B.; Cohen, M. (1965). 9129:Goodman, P. (Peter), ed. (1981). 8921:"Orbituary of Reinhold Rudenberg" 8459:Heinrich Rudolf Hertz (1857–1894) 8253:"Electron Diffraction by Liquids" 7884:Thomson, G. P.; Reid, A. (1927). 7556:Stoney, George Johnstone (1891). 6870: 5972:In a scanning electron microscope 3736:electron energy loss spectroscopy 3608:Kikuchi lines, first observed by 3565:transmission electron microscopes 2459:{\displaystyle d^{3}\mathbf {k} } 608:introduction to quantum mechanics 504:Introduction to quantum mechanics 431:, inventing what became known as 384:(ἤλεκτρον) is the Greek word for 15981: 15970: 15969: 15295: 15284: 15283: 14890: 14215:. Springer Berlin / Heidelberg. 14108:10.1111/j.0022-2720.2004.01321.x 14083: 14028: 13973: 13898: 13859: 13804: 13537: 13482: 13435: 13396: 13331: 13307: 13195:Zeitschrift für Kristallographie 13182: 13156:Acta Crystallographica Section A 13143: 13112: 13051: 13012: 12937: 12902: 12847: 12808: 12759: 12702: 12627: 12578: 12553: 12506: 12459: 12332:Janner, A.; Janssen, T. (1977). 12267: 12220: 12173: 12126: 12079: 12032: 11927: 11861: 11812: 11773: 11738: 11548:"The Theory of Kikuchi patterns" 11539: 11505:Acta Crystallographica Section A 11398: 11301: 11284: 11221: 11000: 10931: 10847: 10798: 10623:Acta Crystallographica Section A 10496:Review of Scientific Instruments 10309:Zeitschrift für Naturforschung A 9937:Acta Crystallographica Section A 9890:Acta Crystallographica Section A 9701:Acta Crystallographica Section A 9525:Acta Crystallographica Section A 6706:. Springer Berlin / Heidelberg. 6574: 6559:{\displaystyle \mathbf {\chi } } 6530: 6505: 6497: 6394: 6379: 6364: 6335: 6320: 6305: 6276: 6261: 6246: 6223: 6215: 6207: 6103: 6095: 6002:electron backscatter diffraction 5978:Electron backscatter diffraction 4558: 4544: 4488:materials by bombardment with a 4469: 4401: 4334:transmission electron microscope 4304:of the electron optical system. 4159: 4151: 4143: 4058: 4050: 4039: 4014: 4006: 3998: 3986:Bulk and surface superstructures 3940: 3931: 3795:) is focused by the first lens ( 3653: 3597: 3444:{\displaystyle \mathbf {k} _{0}} 3431: 3408: 3385:{\displaystyle \mathbf {k} _{0}} 3372: 3343: 3334: 3320: 3311: 3289: 3232: 3150: 3141: 3010: 2862: 2815: 2647: 2601: 2578: 2541: 2532: 2518: 2509: 2488:{\displaystyle \mathbf {k} _{0}} 2475: 2452: 2420: 2392: 2361: 2343: 2335: 2309: 2289: 2221:{\displaystyle \mathbf {s} _{g}} 2208: 2132:{\displaystyle \mathbf {c} ^{*}} 2119: 2103:{\displaystyle \mathbf {b} ^{*}} 2090: 2074:{\displaystyle \mathbf {a} ^{*}} 2061: 2038: 2027: 2016: 2005: 1951: 1943: 1935: 1847: 1822: 1814: 1772: 1435:The wavelength of the electrons 1112: 1086: 1060: 1035: 1027: 998: 580:or wave mechanics. As stated by 357: 346: 265: 256: 229:All matter can be thought of as 225:A primer on electron diffraction 150:electron backscatter diffraction 15738:Precession electron diffraction 14344:. Cham, Switzerland: Springer. 13911:The Journal of Chemical Physics 13789:10.3891/acta.chem.scand.23-3224 11453:The Journal of Chemical Physics 10756: 10731: 10610: 10345: 10296: 9979: 9924: 9827: 9600: 9559: 9512: 9449: 9368: 9319: 9204: 9157: 9122: 9105:Low-Energy Electron Diffraction 9041: 8986: 8947: 8913: 8858: 8832: 8806: 8782: 8694: 8655: 8574: 8535: 8496: 8446: 8399: 8209: 8154: 7991: 7934: 7877: 7589: 7572: 7549: 7510: 7423: 4598:Low-energy electron diffraction 4391:Low-energy electron diffraction 4314:Precession electron diffraction 4308:Precession electron diffraction 3971:fluctuation electron microscopy 3844:-Moodie extinction conditions. 906:precession electron diffraction 898:precession electron diffraction 823:in 1953 and orthoboric acid by 120:of solids. Other cases such as 15085:Bilbao Crystallographic Server 13037:10.1016/j.ultramic.2005.03.003 12513:Heine, V; Samson, J H (1983). 12388:Reports on Progress in Physics 12280:Reports on Progress in Physics 12104:10.1016/j.ultramic.2009.01.011 12057:10.1016/j.ultramic.2006.10.007 10771:, Elsevier, pp. 295–390, 10136:10.1016/j.ultramic.2009.10.013 8701:Freundlich, Martin M. (1963). 7456:. Vol. 1. London: Nelson. 6856:Foundation of Louis de Broglie 6791:Reports on Progress in Physics 6509: 6490: 6107: 6088: 6005: 5951: 5945: 5808: 5805: 5799: 5783: 5777: 5764: 5753: 5716: 5684: 5681: 5649: 5643: 5626: 5620: 5597: 5591: 5477: 5471: 5441: 5435: 5378: 5372: 5322: 5316: 5224: 5195: 5159: 5154: 5148: 5134: 5072: 5066: 5036: 5030: 5000: 4994: 4964: 4958: 4928: 4922: 4892: 4886: 4853: 4847: 4831: 4825: 4809: 4803: 4787: 4781: 4765: 4759: 4683: 4675: 4641: 4585: 4581: 4497: 4493: 4337: 4289: 4285: 4264: 4236: 4185: 4110: 3919: 3915: 3907: 3861: 3765: 3715:, provide information such as 3665:{\displaystyle |\mathbf {g} |} 3658: 3648: 3531: 3363:for an incident wavevector of 3183: 3128: 3021: 3004: 2927: 2908: 2866: 2858: 2748: 2744: 2736: 2720: 2716: 2712: 2708: 2700: 2692: 2688: 2684: 2680: 2651: 2643: 2605: 2597: 2582: 2574: 2396: 2388: 2347: 2322: 2313: 2305: 2293: 2285: 2260: 2256: 2248: 2244: 2196: 2192: 1914: 1902: 1826: 1801: 1776: 1768: 1555: 1523: 1039: 1014: 1002: 994: 146:a scanning electron microscope 1: 13429:10.1016/S0039-6028(97)00062-9 12841:10.1016/S0040-6090(03)00903-9 12612:10.1016/j.surfrep.2018.08.001 11676:Morniroli, Jean Paul (2004). 11594:, in Zalta, Edward N. (ed.), 10560:10.1016/S0304-3991(02)00336-4 10036:Morniroli, Jean-Paul (2015). 9381:Progress in Materials Science 8760:10.1016/s1076-5670(10)60005-5 8509:Annalen der Physik und Chemie 8461:, Routledge, pp. 87–88, 8351:Knoll, M.; Ruska, E. (1932). 8301:Knoll, M.; Ruska, E. (1932). 6603: 4502:scanning tunneling microscopy 4281: 4076:can arise from many reasons: 3712: 3677: 3527: 3393: 2732: 2728: 2676: 2672: 2496: 2427:{\displaystyle d\mathbf {k} } 2269: 2188: 1574:and can range from about 0.1 755: 733:Technische Universität Berlin 555: 487:and later named electrons by 452: 298: 294: 238: 63: 14041:Metallurgical Transactions A 13986:Journal of Materials Science 13754:10.1016/0009-2614(69)85125-0 13255:Microscopy and Microanalysis 13137:10.1016/0304-3991(94)90039-6 12438:10.1107/97809553602060000624 12206:10.1016/0022-3093(78)90098-4 11982:Microscopy and Microanalysis 11886:10.1016/0304-3991(92)90213-4 11780:J., Heinrich, K. F. (1981). 11431:10.1016/0031-9163(64)91133-3 11234:Microscopy and Microanalysis 10979:10.1007/978-4-431-56502-4_27 10370:10.1016/0039-6028(68)90058-7 9609:"The fast Fourier transform" 9462:Microscopy and Microanalysis 9393:10.1016/0079-6425(68)90023-6 8748:Rüdenberg, Reinhold (2010), 8719:10.1126/science.142.3589.185 7274:10.1016/j.elstat.2012.03.002 7102:10.1016/0039-6028(81)90649-X 6760:10.1107/97809553602060000593 6581:{\displaystyle \mathbf {q} } 6537:{\displaystyle \mathbf {k} } 5998:scanning electron microscope 4977:by atom triplets. Intensity 4462:one of the diffracted beams. 3631:Figure 8: Kikuchi map for a 3560:called the string potential. 3415:{\displaystyle \mathbf {k} } 3296:{\displaystyle \mathbf {k} } 3277:is a simplified form of the 3239:{\displaystyle \mathbf {g} } 2822:{\displaystyle \mathbf {g} } 1854:{\displaystyle \mathbf {g} } 1119:{\displaystyle \mathbf {k} } 1093:{\displaystyle \mathbf {k} } 1067:{\displaystyle \mathbf {r} } 956:The development of advanced 141: 78: 7: 15133:Crystal Growth & Design 14425:Timeline of crystallography 14275:. Boston, MA: Springer US. 13468:10.1103/PhysRevLett.50.1145 12909:Nield, Victoria M. (2001). 12793:10.1103/PhysRevLett.53.1951 12539:10.1088/0305-4608/13/10/025 12300:10.1088/0034-4885/68/12/R06 12253:10.1103/PhysRevLett.78.1074 11751:. Oxford University Press. 11745:Spence, John C. H. (2017). 10592:Schiff, Leonard I. (1987). 9992:. Boston, MA: Springer US. 9326:Zachariasen, W. H. (1954). 8677:10.2991/iccessh-18.2018.313 8144:Japanese Journal of Physics 8128:– via Google Scholar. 6803:10.1088/0034-4885/42/11/002 3890:using simulation engine of 2751:. If the excitation errors 2743:is slightly different, see 825:William Houlder Zachariasen 447:In 1869, Plücker's student 235:Young's two-slit experiment 10: 16061: 15723:Immune electron microscopy 15641:Annular dark-field imaging 15456:Everhart–Thornley detector 14944:Nuclear magnetic resonance 13696:10.1366/000370276774456381 12745:10.1103/PhysRevB.79.193302 12400:10.1088/0034-4885/45/6/001 10727:. 17(Supplement BII): 118. 10226:Journal of Applied Physics 9625:10.1109/mspec.1967.5217220 9572:Mathematics of Computation 9048:Farnsworth, H. E. (1932). 8845:Patent Public Search Basic 8819:Patent Public Search Basic 8641:10.1088/0508-3443/13/5/303 8412:Journal of Applied Physics 8251:Maxwell, Louis R. (1933). 7224:Dictionary of Word Origins 7197:Cambridge University Press 7050:10.1088/0022-3719/4/16/015 6847:de Broglie, Louis Victor. 6183:, but nothing significant. 6004:(EBSD), as illustrated in 5975: 4607: 4590:materials characterization 4531: 4388: 4359: 4355: 4311: 4246: 4225:Laue monotonic scattering. 3707:Electron diffraction in a 3601: 831:explains in a 1968 paper: 674: 619:Davisson–Germer experiment 501: 329: 304: 15965: 15910: 15877:Hitachi High-Technologies 15859: 15768: 15761: 15628: 15572: 15534: 15491: 15484: 15438: 15387: 15351: 15279: 15199: 15171: 15148:Journal of Crystal Growth 15123: 15075: 15022: 14969: 14900: 14888: 14683: 14674: 14597: 14450: 14417: 14281:10.1007/978-1-4899-2353-0 14272:Electron Microdiffraction 13942:21.11116/0000-0007-6FBC-A 13884:10.1080/00268977700101871 13776:Acta Chemica Scandinavica 13276:10.1017/S1431927619000497 13176:10.1107/S0108767397017030 13077:10.1017/s1551929519000427 12980:10.1107/S2052252521005479 12880:10.1007/s11661-013-1889-2 12159:10.1080/14786437308228927 12002:10.1017/S1431927603030332 11618:Gbur, Gregory J. (2019). 11573:10.1107/S0365110X55000832 11525:10.1107/S0567739472000026 11384:10.1107/S0365110X65002773 11334:10.1088/0022-3719/4/6/006 11291:Metherell, A. J. (1975). 11254:10.1017/S1431927604040292 10832:10.1107/s0365110x50000823 10643:10.1107/S0108767395015893 10303:Kambe, Kyozaburo (1967). 10187:10.1107/S2052519212051366 10160:Palatinus, Lukáš (2013). 10090:10.1007/978-94-007-5580-2 9998:10.1007/978-1-4899-2353-0 9989:Electron Microdiffraction 9957:10.1107/S0567739480000800 9910:10.1107/S010876738300080X 9813:10.1107/S002188988301050X 9721:10.1107/S0567739468000677 9545:10.1107/S056773947400057X 9482:10.1017/S1431927604040292 9435:10.1107/S0365110X57002194 9353:10.1107/S0365110X54000886 9296:10.1107/S0365110X53001423 8560:10.1080/14786440509463347 8353:"Das Elektronenmikroskop" 8016:10.1017/S0007087410000026 7614:10.1080/14786441308634955 7535:10.1080/14786449708621070 7470:Crookes, William (1878). 7430:Goldstein, Eugen (1876). 7380:10.1080/14786445808642591 7262:Journal of Electrostatics 7230:The Philosophical Library 6849:"On the Theory of Quanta" 4506:density functional theory 3786:Copenhagen interpretation 3622:Copenhagen interpretation 534:introduced his theory of 89:were combined with early 15902:Thermo Fisher Scientific 15728:Geometric phase analysis 15616:Aberration-Corrected TEM 15014:Single particle analysis 14872:Hermann–Mauguin notation 14245:. London: Butterworths. 14179:John M., Cowley (1995). 13734:Chemical Physics Letters 13670:Schåfer, Lothar (1976). 13644:10.1002/bbpc.19890931027 13586:Braun, Wolfgang (1999). 13442:Robinson, I. K. (1983). 12854:Welberry, T. R. (2014). 11819:F., Egerton, R. (2011). 11680:. Taylor & Francis. 11228:Ishizuka, Kazuo (2004). 10763:Vainstein, B.K. (1964), 10673:Fujiwara, Kunio (1961). 9683:10.1002/andp.19394280204 9456:Ishizuka, Kazuo (2004). 8980:10.1002/andp.19364190107 8607:10.1002/andp.19263862507 8529:10.1002/andp.18993051203 8453:Hertz, Heinrich (2019), 8327:10.1002/andp.19324040506 8230:10.1002/bbpc.19300360921 8098:Kikuchi, Seishi (1928). 8082:10.1002/andp.19283921704 7941:Reid, Alexander (1928). 7128:Schrödinger, E. (1926). 6940:. London: Butterworths. 6654:John M., Cowley (1995). 6023: 5957:{\displaystyle I_{t}(s)} 5447:{\displaystyle I_{a}(s)} 5384:{\displaystyle I_{a}(s)} 5328:{\displaystyle f_{i}(s)} 5042:{\displaystyle I_{a}(s)} 5006:{\displaystyle I_{b}(s)} 4970:{\displaystyle I_{t}(s)} 4934:{\displaystyle I_{m}(s)} 4898:{\displaystyle I_{a}(s)} 4629:Gas electron diffraction 4610:Gas electron diffraction 4604:Gas electron diffraction 4229:probability distribution 3554:crystallographic defects 1448:{\displaystyle \lambda } 908:for further information. 653:gas electron diffraction 175:is considered and often 154:gas electron diffraction 15651:Charge contrast imaging 15461:Field electron emission 15138:Crystallography Reviews 14982:Isomorphous replacement 14776:Lomer–Cottrell junction 14209:Reimer, Ludwig (2013). 13626:Oberhammer, H. (1989). 13448:Physical Review Letters 12772:Physical Review Letters 12591:Surface Science Reports 12358:10.1103/physrevb.15.643 12233:Physical Review Letters 11065:Yoshioka, Hide (1957). 10042:. Webpage and hardcopy. 9852:10.1002/jemt.1060130202 9170:Applied Physics Letters 8871:Die Naturwissenschaften 8467:10.4324/9780429198960-4 8406:Calbick, C. J. (1944). 8167:Die Naturwissenschaften 7998:Navarro, Jaume (2010). 7517:Thomson, J. J. (1897). 7341:Michael Faraday (1838) 7295:Harsch, Viktor (2007). 7154:10.1103/PhysRev.28.1049 6785:Humphreys, C J (1979). 6700:Reimer, Ludwig (2013). 5901:{\displaystyle \kappa } 4660:{\displaystyle \theta } 3876:Polycrystalline pattern 3580:surface reconstructions 2783:Kinematical diffraction 1366:the speed of light and 967:photographic processing 731:in Charlottenburg (now 489:George Johnstone Stoney 336:History of the electron 188:kinematical diffraction 15841:Thomas Eugene Everhart 14651:Spinodal decomposition 13364:10.1126/sciadv.aar7495 13315:"4D STEM | Gatan, Inc" 13216:10.1524/zkri.2010.1162 12139:Philosophical Magazine 11868:Cowley, J. M. (1992). 11630:10.2307/j.ctvqc6g7s.17 11552:Acta Crystallographica 11364:Acta Crystallographica 11199:10.1098/rspa.1963.0017 11141:10.1098/rspa.1961.0157 11033:10.1098/rsta.1960.0013 10965:Tanaka, Nobuo (2017), 10909:10.1098/rspa.1913.0040 10811:Acta Crystallographica 9763:10.1098/rsta.1976.0024 9415:Acta Crystallographica 9332:Acta Crystallographica 9275:Acta Crystallographica 9269:Cowley, J. M. (1953). 9217:Zeitschrift für Physik 9074:10.1103/PhysRev.40.684 8999:Zeitschrift für Physik 8993:Germer, L. H. (1929). 8865:Rodenberg, R. (1932). 8357:Zeitschrift für Physik 8117:10.2183/pjab1912.4.271 7968:10.1098/rspa.1928.0121 7720:10.1103/physrev.30.705 7568:. Dublin: 563, pp 583. 7488:10.1098/rspl.1878.0098 7313:10.3357/asem.2159.2007 7220:Shipley, J.T. (1945). 6748:"Electron diffraction" 6582: 6560: 6538: 6516: 6477:as mentioned above if 6471: 6448: 6428: 6408: 6349: 6290: 6231: 6177: 6157: 6156:{\displaystyle \hbar } 6137: 6114: 5993: 5958: 5922: 5902: 5878: 5877:{\displaystyle l_{ij}} 5848: 5847:{\displaystyle r_{ij}} 5818: 5575: 5537: 5448: 5405: 5385: 5349: 5329: 5293: 5266: 5246: 5176: 5132: 5043: 5007: 4971: 4941:by pairs of atoms and 4935: 4899: 4863: 4736: 4661: 4625: 4456: 4435:the incident beam and 4429: 4325: 4277: 4260: 4208: 4167: 4128: 4105: 4066: 4022: 3898: 3866:diffraction tomography 3856: 3761: 3728:high-resolution images 3704: 3666: 3636: 3514: 3497: 3445: 3416: 3386: 3357: 3297: 3271: 3240: 3218: 3191: 3110: 3060: 3029: 2990: 2963: 2823: 2801: 2772: 2711:, or have rings as in 2658: 2626: 2558: 2489: 2460: 2428: 2403: 2372: 2222: 2180: 2160: 2133: 2104: 2075: 2046: 1991: 1959: 1921: 1886: 1855: 1833: 1740: 1568: 1449: 1426: 1401:. A common one is the 1387: 1360: 1340: 1316: 1285: 1265: 1200: 1120: 1094: 1068: 1046: 840: 764:Nobel Prize in Physics 712: 596: 523: 449:Johann Wilhelm Hittorf 35: 31:crystal in a piece of 15846:Vernon Ellis Cosslett 15666:Dark-field microscopy 15191:Gregori Aminoff Prize 14987:Molecular replacement 14146:. Springer New York. 14096:Journal of Microscopy 13249:Ophus, Colin (2019). 11686:10.1201/9781420034073 11447:McRae, E. G. (1966). 11405:Lindhard, J. (1964). 10971:Electron Nano-Imaging 10322:10.1515/zna-1967-0305 9375:Cowley, J.M. (1968). 8867:"Elektronenmikroskop" 8839:Rüdenberg, Reinhold. 8813:Rüdenberg, Reinhold. 8503:Wiechert, E. (1899). 8277:10.1103/PhysRev.44.73 7844:10.1073/pnas.14.8.619 7774:10.1073/pnas.14.4.317 6583: 6561: 6539: 6517: 6472: 6470:{\displaystyle 2\pi } 6449: 6429: 6409: 6350: 6291: 6232: 6178: 6158: 6138: 6136:{\displaystyle 2\pi } 6115: 6060:de Broglie wavelength 5987: 5959: 5923: 5921:{\displaystyle \eta } 5903: 5879: 5849: 5819: 5538: 5517: 5449: 5406: 5386: 5350: 5330: 5294: 5292:{\displaystyle I_{0}} 5267: 5247: 5177: 5112: 5044: 5008: 4972: 4936: 4900: 4864: 4737: 4662: 4619: 4457: 4455:{\displaystyle k_{f}} 4430: 4428:{\displaystyle k_{i}} 4323: 4275: 4258: 4202: 4168: 4126: 4103: 4067: 4023: 3885: 3850: 3782:wavefunction collapse 3759: 3744:x-ray crystallography 3698: 3667: 3630: 3616:, and also scattered 3509: 3498: 3496:{\displaystyle m^{*}} 3471:Dynamical diffraction 3446: 3417: 3387: 3358: 3298: 3272: 3270:{\displaystyle T_{j}} 3241: 3219: 3217:{\displaystyle f_{j}} 3192: 3090: 3061: 3059:{\displaystyle F_{g}} 3030: 2991: 2989:{\displaystyle s_{z}} 2964: 2824: 2802: 2773: 2771:{\displaystyle s_{g}} 2659: 2627: 2559: 2490: 2461: 2429: 2404: 2373: 2223: 2178: 2161: 2159:{\displaystyle V_{g}} 2134: 2105: 2076: 2047: 1992: 1990:{\displaystyle h,k,l} 1960: 1922: 1920:{\displaystyle (hkl)} 1887: 1885:{\displaystyle V_{g}} 1856: 1834: 1741: 1569: 1450: 1427: 1425:{\displaystyle m^{*}} 1388: 1386:{\displaystyle m_{0}} 1361: 1341: 1317: 1315:{\displaystyle m^{*}} 1286: 1266: 1201: 1136:Klein–Gordon equation 1121: 1095: 1069: 1047: 969:after the experiment. 962:charge-coupled device 875:Gottfried Möllenstedt 833: 729:Technische Hochschule 710: 586: 517: 195:dynamical diffraction 26: 15851:Vladimir K. Zworykin 15501:Correlative light EM 15410:Electron diffraction 14497:Structure prediction 14090:Dingley, D. (2004). 13676:Applied Spectroscopy 12565:Chemistry LibreTexts 11546:Kainuma, Y. (1955). 11499:Colella, R. (1972). 10743:Chemistry LibreTexts 10699:10.1143/JPSJ.16.2226 10352:McRae, E.G. (1968). 9834:Bird, D. M. (1989). 8954:Boersch, H. (1936). 8662:Tao, Yaping (2018). 8542:Wehnelt, A. (1905). 7482:(190–195): 103–111. 7362:Plücker, M. (1858). 7192:Principles of Optics 7024:Pendry, J B (1971). 6570: 6548: 6526: 6481: 6458: 6438: 6418: 6359: 6355:for real space, and 6300: 6241: 6203: 6167: 6147: 6124: 6079: 6066:for more discussion. 6052:undulatory mechanics 5932: 5912: 5892: 5858: 5828: 5458: 5422: 5395: 5359: 5339: 5303: 5276: 5256: 5186: 5053: 5017: 4981: 4945: 4909: 4873: 4746: 4671: 4651: 4439: 4412: 4139: 4082:antiferroelectricity 4032: 3994: 3799:) to a point in the 3684:Types and techniques 3644: 3480: 3426: 3404: 3367: 3307: 3285: 3254: 3228: 3201: 3074: 3043: 3000: 2973: 2833: 2811: 2791: 2755: 2637: 2568: 2505: 2470: 2438: 2413: 2382: 2279: 2203: 2143: 2114: 2085: 2056: 2001: 1969: 1931: 1899: 1869: 1843: 1762: 1597: 1459: 1439: 1409: 1370: 1350: 1330: 1299: 1275: 1210: 1146: 1108: 1082: 1056: 988: 865:Developments in the 623:George Paget Thomson 578:Schrödinger equation 574:undulatory mechanics 566:a few years before. 287:electron microscopes 199:Schrödinger equation 102:types and techniques 95:further developments 68:electron microscopes 39:Electron diffraction 16030:Electron microscopy 15816:Manfred von Ardenne 15801:Gerasimos Danilatos 15708:Electron tomography 15703:Electron holography 15646:Cathodoluminescence 15425:Secondary electrons 15415:Electron scattering 15359:Electron microscopy 15345:Electron microscopy 14761:Cottrell atmosphere 14741:Partial dislocation 14485:Restriction theorem 14182:Diffraction physics 14053:1993MTA....24..819A 13998:1992JMatS..27.4545D 13923:2020JChPh.153s4504D 13829:1974Natur.248..405L 13746:1969CPL.....3..617S 13688:1976ApSpe..30..123S 13507:2010NatMa...9..245E 13460:1983PhRvL..50.1145R 13421:1997SurSc.381...77G 13356:2018SciA....4.7495H 13267:2019MiMic..25..563O 13207:2010ZK....225..110M 13168:1998AcCrA..54..306G 12972:2021IUCrJ...8..695R 12872:2014MMTA...45...75W 12833:2003TSF...441...63W 12784:1984PhRvL..53.1951S 12737:2009PhRvB..79s3302C 12680:1985JVSTA...3.1502T 12603:2018SurSR..73..213A 12531:1983JPhF...13.2155H 12350:1977PhRvB..15..643J 12292:2005RPPh...68.2899T 12245:1997PhRvL..78.1074G 12198:1978JNCS...31...41H 12151:1973PMag...27..235H 11994:2003MiMic...9..399M 11564:1955AcCry...8..247K 11517:1972AcCrA..28...11C 11465:1966JChPh..45.3258M 11423:1964PhL....12..126L 11376:1965AcCry..19...65G 11326:1971JPhC....4..697B 11308:Berry, M V (1971). 11246:2004MiMic..10...34I 11191:1963RSPSA.271..268H 11133:1961RSPSA.263..217H 11091:10.1143/JPSJ.12.618 11083:1957JPSJ...12..618Y 11025:1960RSPTA.252..499H 10901:1913RSPSA..88..428B 10859:www.ysbl.york.ac.uk 10823:1950AcCry...3..316R 10691:1961JPSJ...16.2226F 10635:1996AcCrA..52..379W 10508:1988RScI...59.2102S 10238:1953JAP....24..860A 10220:Alpert, D. (1953). 10178:2013AcCrB..69....1P 10082:2012uecp.book.....K 9949:1980AcCrA..36..350T 9902:1983AcCrA..39..357T 9805:1983JApCr..16..317S 9755:1976RSPTA.281..171B 9713:1968AcCrA..24..339G 9675:1939AnP...428..113K 9537:1974AcCrA..30..280G 9474:2004MiMic..10...34I 9427:1957AcCry..10..609C 9344:1954AcCry...7..305Z 9287:1953AcCry...6..522C 9229:1933ZPhy...85..618L 9182:1965ApPhL...7...32S 9066:1932PhRv...40..684F 9011:1929ZPhy...54..408G 8972:1936AnP...419...75B 8883:1932NW.....20..522R 8599:1926AnP...386..974B 8521:1899AnP...305..739W 8424:1944JAP....15..685C 8369:1932ZPhy...78..318K 8319:1932AnP...404..607K 8269:1933PhRv...44...73M 8179:1930NW.....18..778M 8074:1928AnP...392...55B 7959:1928RSPSA.119..663R 7902:1927Natur.119Q.890T 7835:1928PNAS...14..619D 7765:1928PNAS...14..317D 7711:1927PhRv...30..705D 7653:1927Natur.119..558D 7146:1926PhRv...28.1049S 7094:1981SurSc.110..423M 7078:"A theory of RHEED" 7042:1971JPhC....4.2501P 6885:Solid state physics 6657:Diffraction physics 6163:appears instead of 5886:Debye–Waller factor 4342:diffraction pattern 4302:optical aberrations 4117:Aperiodic materials 3784:) according to the 3740:electron holography 3633:face centered cubic 3461:neutron diffraction 3279:Debye–Waller factor 1756:Ashcroft and Mermin 1395:Ashcroft and Mermin 1128:probability current 860:multislice programs 554:, see for instance 546:) that move with a 326:Electrons in vacuum 283:Fresnel diffraction 219:neutron diffraction 83:electrons in vacuum 53:. It occurs due to 15938:Digital Micrograph 15544:Environmental SEM 15466:Field emission gun 15430:X-ray fluorescence 15181:Carl Hermann Medal 14992:Molecular dynamics 14839:Defects in diamond 14834:Stone–Wales defect 14480:Reciprocal lattice 14442:Biocrystallography 14061:10.1007/BF02656503 14006:10.1007/BF01165988 13562:10.1039/c2ce25204j 12484:10.1111/jace.17834 12180:Howie, A. (1978). 11952:10.1143/jpsj.9.184 11590:Faye, Jan (2019), 9663:Annalen der Physik 9237:10.1007/BF01331003 9019:10.1007/BF01375462 8960:Annalen der Physik 8891:10.1007/BF01505383 8623:Mulvey, T (1962). 8587:Annalen der Physik 8581:Busch, H. (1926). 8377:10.1007/BF01342199 8307:Annalen der Physik 8187:10.1007/bf01497860 8062:Annalen der Physik 8056:Bethe, H. (1928). 7579:Einstein, Albert. 7519:"XL. Cathode Rays" 6578: 6556: 6534: 6512: 6467: 6444: 6424: 6404: 6345: 6286: 6227: 6173: 6153: 6133: 6110: 6016:identification or 5994: 5954: 5918: 5898: 5874: 5844: 5814: 5444: 5401: 5381: 5345: 5325: 5289: 5262: 5242: 5172: 5039: 5003: 4967: 4931: 4895: 4859: 4732: 4657: 4626: 4486:single-crystalline 4452: 4425: 4326: 4278: 4261: 4213:diffuse scattering 4209: 4193:Diffuse scattering 4163: 4129: 4106: 4092:antiferromagnetism 4062: 4018: 3914:rings as shown in 3899: 3857: 3762: 3705: 3662: 3637: 3614:elastic scattering 3515: 3493: 3441: 3412: 3382: 3353: 3293: 3267: 3248:reciprocal lattice 3236: 3224:the form factors, 3214: 3187: 3056: 3025: 2986: 2959: 2819: 2797: 2768: 2703:, have additional 2654: 2622: 2554: 2485: 2456: 2424: 2399: 2368: 2251:later, whereas in 2218: 2181: 2156: 2129: 2100: 2071: 2042: 1987: 1955: 1917: 1882: 1863:reciprocal lattice 1851: 1829: 1754:(see for instance 1736: 1564: 1445: 1422: 1383: 1356: 1336: 1322:is a relativistic 1312: 1281: 1261: 1196: 1116: 1090: 1064: 1042: 775:Reinhold Rudenberg 722:Reinhold Rüdenberg 717:optical microscope 713: 530:in his PhD thesis 524: 55:elastic scattering 49:interactions with 36: 16040:Quantum mechanics 16035:Materials science 15997: 15996: 15961: 15960: 15831:Nestor J. Zaluzec 15826:Maximilian Haider 15624: 15623: 15311: 15310: 15275: 15274: 14882:Thermal ellipsoid 14847: 14846: 14756:Frank–Read source 14716: 14715: 14582:Aperiodic crystal 14548: 14547: 14430:Crystallographers 14351:978-3-319-26649-7 14323:978-0-19-960224-7 14290:978-1-4899-2355-4 14222:978-3-662-13553-2 14153:978-1-4899-9334-2 13992:(17): 4545–4566. 13932:10.1063/5.0024127 13872:Molecular Physics 13823:(5447): 405–406. 13638:(10): 1151–1152. 13454:(15): 1145–1148. 12778:(20): 1951–1953. 12715:Physical Review B 12645:978-3-540-00545-2 12525:(10): 2155–2168. 12447:978-1-4020-1900-5 12338:Physical Review B 12286:(12): 2899–2944. 11832:978-1-4419-9582-7 11758:978-0-19-879583-4 11731:978-0-12-813369-9 11639:978-0-300-23129-8 11474:10.1063/1.1728101 11185:(1345): 268–287. 11127:(1313): 217–237. 11019:(1017): 499–529. 10988:978-4-431-56500-0 10685:(11): 2226–2238. 10603:978-0-07-085643-1 10594:Quantum mechanics 10516:10.1063/1.1140039 10405:978-1-108-28457-8 10246:10.1063/1.1721395 10099:978-94-007-5579-6 10007:978-1-4899-2355-4 9749:(1301): 171–194. 9223:(9–10): 618–630. 9190:10.1063/1.1754284 9115:978-3-540-16262-9 8934:10.1063/1.3058109 8713:(3589): 185–188. 8687:978-94-6252-528-3 8476:978-0-429-19896-0 8432:10.1063/1.1707371 7647:(2998): 558–560. 7596:Bohr, N. (1913). 7352: : 125–168. 7307:(11): 1075–1077. 7239:978-0-88029-751-6 7206:978-0-521-64222-4 7036:(16): 2501–2513. 6995:978-0-19-960224-7 6895:978-0-03-083993-1 6797:(11): 1825–1887. 6769:978-1-4020-1900-5 6713:978-3-662-13553-2 6447:{\displaystyle g} 6427:{\displaystyle G} 6176:{\displaystyle h} 5706: 5567: 5505: 5404:{\displaystyle s} 5348:{\displaystyle i} 5265:{\displaystyle R} 5100: 4756: 4723: 4703: 4350:crystal structure 4227:Often there is a 4175:irrational number 4133:aperiodic crystal 3838:barrel distortion 3776:, deflectors and 3721:crystal structure 3717:lattice constants 3457:x-ray diffraction 2946: 2800:{\displaystyle t} 2168:Fourier transform 1731: 1723: 1689: 1671: 1633: 1559: 1558: 1504: 1503: 1476: 1359:{\displaystyle c} 1339:{\displaystyle E} 1293:Planck's constant 1284:{\displaystyle h} 1259: 1194: 1076:quantum mechanics 913:ultra-high vacuum 771:Siemens-Schuckert 600:Coulomb potential 576:, now called the 571:Erwin Schrödinger 522:for more details. 425:Heinrich Geissler 397:Otto von Guericke 390:Thales of Miletus 320:quantum mechanics 311:cathode-ray tubes 16052: 15985: 15984: 15973: 15972: 15781:Bodo von Borries 15766: 15765: 15526:Photoemission EM 15489: 15488: 15338: 15331: 15324: 15315: 15314: 15299: 15298: 15287: 15286: 15230: 15229: 15153:Kristallografija 15007:Gerchberg–Saxton 14902:Characterisation 14894: 14877:Structure factor 14681: 14680: 14666:Ostwald ripening 14503: 14502: 14448: 14447: 14404: 14397: 14390: 14381: 14380: 14375: 14355: 14335: 14302: 14264: 14234: 14204: 14166: 14165: 14137: 14128: 14127: 14087: 14081: 14080: 14032: 14026: 14025: 13977: 13971: 13970: 13944: 13934: 13902: 13896: 13895: 13863: 13857: 13856: 13837:10.1038/248405a0 13808: 13802: 13801: 13791: 13767: 13758: 13757: 13725: 13716: 13715: 13667: 13656: 13655: 13623: 13612: 13611: 13583: 13574: 13573: 13541: 13535: 13534: 13515:10.1038/nmat2636 13495:Nature Materials 13486: 13480: 13479: 13439: 13433: 13432: 13400: 13394: 13393: 13383: 13344:Science Advances 13335: 13329: 13328: 13326: 13325: 13311: 13305: 13304: 13278: 13246: 13237: 13236: 13218: 13201:(2–3): 110–124. 13186: 13180: 13179: 13147: 13141: 13140: 13116: 13110: 13104: 13098: 13097: 13079: 13064:Microscopy Today 13055: 13049: 13048: 13016: 13010: 13009: 12999: 12965: 12941: 12935: 12934: 12906: 12900: 12899: 12851: 12845: 12844: 12821:Thin Solid Films 12812: 12806: 12805: 12795: 12763: 12757: 12756: 12730: 12706: 12700: 12699: 12688:10.1116/1.573160 12674:(3): 1502–1506. 12659: 12650: 12649: 12631: 12625: 12624: 12614: 12582: 12576: 12575: 12573: 12572: 12557: 12551: 12550: 12510: 12504: 12503: 12478:(8): 3775–3810. 12463: 12457: 12456: 12455: 12454: 12421: 12412: 12411: 12379: 12370: 12369: 12329: 12320: 12319: 12271: 12265: 12264: 12239:(6): 1074–1077. 12224: 12218: 12217: 12177: 12171: 12170: 12130: 12124: 12123: 12083: 12077: 12076: 12051:(6–7): 507–513. 12036: 12030: 12029: 11973: 11964: 11963: 11931: 11925: 11924: 11922: 11921: 11915:www.tedpella.com 11907: 11898: 11897: 11865: 11859: 11858: 11852: 11844: 11816: 11810: 11809: 11803: 11795: 11777: 11771: 11770: 11742: 11736: 11735: 11715: 11700: 11699: 11673: 11660: 11659: 11615: 11606: 11605: 11604: 11603: 11587: 11578: 11577: 11575: 11543: 11537: 11536: 11496: 11487: 11486: 11476: 11459:(9): 3258–3276. 11444: 11435: 11434: 11402: 11396: 11395: 11355: 11346: 11345: 11305: 11299: 11298: 11288: 11282: 11281: 11225: 11219: 11218: 11170: 11161: 11160: 11112: 11103: 11102: 11062: 11053: 11052: 11004: 10998: 10997: 10996: 10995: 10962: 10953: 10952: 10950: 10949: 10935: 10929: 10928: 10895:(605): 428–438. 10880: 10869: 10868: 10866: 10865: 10851: 10845: 10844: 10834: 10802: 10796: 10795: 10794: 10793: 10760: 10754: 10753: 10751: 10750: 10735: 10729: 10728: 10720: 10711: 10710: 10670: 10655: 10654: 10614: 10608: 10607: 10589: 10580: 10579: 10539: 10528: 10527: 10502:(9): 2102–2105. 10487: 10476: 10475: 10447: 10432: 10431: 10425: 10417: 10389: 10374: 10373: 10349: 10343: 10342: 10324: 10300: 10294: 10293: 10277: 10267: 10258: 10257: 10217: 10208: 10207: 10189: 10157: 10148: 10147: 10115: 10104: 10103: 10067: 10058: 10057: 10051: 10043: 10033: 10020: 10019: 9983: 9977: 9976: 9928: 9922: 9921: 9881: 9872: 9871: 9831: 9825: 9824: 9784: 9775: 9774: 9734: 9725: 9724: 9696: 9687: 9686: 9654: 9643: 9642: 9640: 9639: 9604: 9598: 9597: 9587: 9563: 9557: 9556: 9516: 9510: 9509: 9453: 9447: 9446: 9406: 9397: 9396: 9372: 9366: 9365: 9355: 9323: 9317: 9316: 9298: 9266: 9257: 9256: 9208: 9202: 9201: 9161: 9155: 9154: 9126: 9120: 9119: 9099: 9086: 9085: 9045: 9039: 9038: 9005:(5–6): 408–421. 8990: 8984: 8983: 8951: 8945: 8944: 8942: 8941: 8936: 8917: 8911: 8910: 8862: 8856: 8855: 8853: 8851: 8836: 8830: 8829: 8827: 8825: 8810: 8804: 8803: 8801: 8800: 8786: 8780: 8778: 8777: 8776: 8745: 8739: 8738: 8698: 8692: 8691: 8679: 8659: 8653: 8652: 8620: 8611: 8610: 8578: 8572: 8571: 8539: 8533: 8532: 8500: 8494: 8493: 8492: 8491: 8450: 8444: 8443: 8403: 8397: 8396: 8363:(5–6): 318–339. 8348: 8339: 8338: 8298: 8289: 8288: 8248: 8242: 8241: 8213: 8207: 8206: 8158: 8152: 8151: 8139: 8130: 8129: 8119: 8095: 8086: 8085: 8053: 8036: 8035: 7995: 7989: 7988: 7970: 7953:(783): 663–667. 7938: 7932: 7931: 7913: 7911:10.1038/119890a0 7881: 7875: 7874: 7864: 7846: 7814: 7805: 7804: 7794: 7776: 7744: 7733: 7732: 7722: 7690: 7681: 7680: 7661:10.1038/119558a0 7632: 7626: 7625: 7593: 7587: 7586: 7576: 7570: 7569: 7553: 7547: 7546: 7529:(269): 293–316. 7514: 7508: 7507: 7467: 7458: 7457: 7444: 7438: 7437: 7427: 7421: 7420: 7403: 7392: 7391: 7374:(109): 408–418. 7359: 7353: 7339: 7333: 7332: 7292: 7286: 7285: 7253: 7244: 7243: 7227: 7217: 7211: 7210: 7179: 7166: 7165: 7140:(6): 1049–1070. 7125: 7106: 7105: 7073: 7062: 7061: 7021: 7008: 7007: 6979: 6960: 6959: 6931: 6900: 6899: 6879: 6868: 6867: 6865: 6863: 6853: 6844: 6823: 6822: 6782: 6773: 6772: 6743: 6726: 6725: 6697: 6680: 6679: 6651: 6597: 6587: 6585: 6584: 6579: 6577: 6565: 6563: 6562: 6557: 6555: 6543: 6541: 6540: 6535: 6533: 6521: 6519: 6518: 6513: 6508: 6500: 6476: 6474: 6473: 6468: 6453: 6451: 6450: 6445: 6433: 6431: 6430: 6425: 6413: 6411: 6410: 6405: 6403: 6402: 6397: 6388: 6387: 6382: 6373: 6372: 6367: 6354: 6352: 6351: 6346: 6344: 6343: 6338: 6329: 6328: 6323: 6314: 6313: 6308: 6295: 6293: 6292: 6287: 6285: 6284: 6279: 6270: 6269: 6264: 6255: 6254: 6249: 6236: 6234: 6233: 6228: 6226: 6218: 6210: 6197: 6184: 6182: 6180: 6179: 6174: 6162: 6160: 6159: 6154: 6142: 6140: 6139: 6134: 6119: 6117: 6116: 6111: 6106: 6098: 6073: 6067: 6047: 6041: 6037: 5963: 5961: 5960: 5955: 5944: 5943: 5927: 5925: 5924: 5919: 5907: 5905: 5904: 5899: 5883: 5881: 5880: 5875: 5873: 5872: 5853: 5851: 5850: 5845: 5843: 5842: 5823: 5821: 5820: 5815: 5798: 5797: 5776: 5775: 5757: 5756: 5752: 5751: 5742: 5741: 5726: 5707: 5705: 5704: 5703: 5687: 5680: 5679: 5664: 5663: 5635: 5633: 5629: 5619: 5618: 5604: 5600: 5590: 5589: 5574: 5569: 5568: 5566: 5555: 5544: 5536: 5531: 5516: 5515: 5506: 5504: 5503: 5494: 5493: 5484: 5470: 5469: 5453: 5451: 5450: 5445: 5434: 5433: 5410: 5408: 5407: 5402: 5390: 5388: 5387: 5382: 5371: 5370: 5354: 5352: 5351: 5346: 5334: 5332: 5331: 5326: 5315: 5314: 5298: 5296: 5295: 5290: 5288: 5287: 5271: 5269: 5268: 5263: 5251: 5249: 5248: 5243: 5241: 5240: 5231: 5223: 5222: 5210: 5209: 5181: 5179: 5178: 5173: 5168: 5167: 5162: 5147: 5146: 5137: 5131: 5126: 5111: 5110: 5101: 5099: 5098: 5089: 5088: 5079: 5065: 5064: 5048: 5046: 5045: 5040: 5029: 5028: 5012: 5010: 5009: 5004: 4993: 4992: 4976: 4974: 4973: 4968: 4957: 4956: 4940: 4938: 4937: 4932: 4921: 4920: 4904: 4902: 4901: 4896: 4885: 4884: 4868: 4866: 4865: 4860: 4846: 4845: 4824: 4823: 4802: 4801: 4780: 4779: 4758: 4757: 4754: 4741: 4739: 4738: 4733: 4728: 4724: 4716: 4704: 4699: 4691: 4686: 4678: 4666: 4664: 4663: 4658: 4562: 4548: 4473: 4461: 4459: 4458: 4453: 4451: 4450: 4434: 4432: 4431: 4426: 4424: 4423: 4405: 4172: 4170: 4169: 4164: 4162: 4154: 4146: 4071: 4069: 4068: 4063: 4061: 4053: 4042: 4027: 4025: 4024: 4019: 4017: 4009: 4001: 3944: 3935: 3801:back focal plane 3671: 3669: 3668: 3663: 3661: 3656: 3651: 3556:, and also what 3502: 3500: 3499: 3494: 3492: 3491: 3450: 3448: 3447: 3442: 3440: 3439: 3434: 3421: 3419: 3418: 3413: 3411: 3391: 3389: 3388: 3383: 3381: 3380: 3375: 3362: 3360: 3359: 3354: 3352: 3351: 3346: 3337: 3329: 3328: 3323: 3314: 3302: 3300: 3299: 3294: 3292: 3276: 3274: 3273: 3268: 3266: 3265: 3245: 3243: 3242: 3237: 3235: 3223: 3221: 3220: 3215: 3213: 3212: 3196: 3194: 3193: 3188: 3186: 3182: 3181: 3172: 3171: 3159: 3158: 3153: 3144: 3120: 3119: 3109: 3104: 3086: 3085: 3068:structure factor 3065: 3063: 3062: 3057: 3055: 3054: 3034: 3032: 3031: 3026: 3024: 3019: 3018: 3013: 3007: 2995: 2993: 2992: 2987: 2985: 2984: 2968: 2966: 2965: 2960: 2958: 2957: 2952: 2948: 2947: 2945: 2944: 2943: 2930: 2926: 2925: 2900: 2898: 2897: 2879: 2878: 2873: 2869: 2865: 2845: 2844: 2828: 2826: 2825: 2820: 2818: 2806: 2804: 2803: 2798: 2777: 2775: 2774: 2769: 2767: 2766: 2707:structure as in 2663: 2661: 2660: 2655: 2650: 2631: 2629: 2628: 2623: 2618: 2617: 2612: 2608: 2604: 2581: 2563: 2561: 2560: 2555: 2550: 2549: 2544: 2535: 2527: 2526: 2521: 2512: 2494: 2492: 2491: 2486: 2484: 2483: 2478: 2465: 2463: 2462: 2457: 2455: 2450: 2449: 2433: 2431: 2430: 2425: 2423: 2408: 2406: 2405: 2400: 2395: 2377: 2375: 2374: 2369: 2364: 2359: 2358: 2346: 2338: 2312: 2292: 2227: 2225: 2224: 2219: 2217: 2216: 2211: 2165: 2163: 2162: 2157: 2155: 2154: 2138: 2136: 2135: 2130: 2128: 2127: 2122: 2109: 2107: 2106: 2101: 2099: 2098: 2093: 2080: 2078: 2077: 2072: 2070: 2069: 2064: 2051: 2049: 2048: 2043: 2041: 2030: 2019: 2008: 1996: 1994: 1993: 1988: 1964: 1962: 1961: 1956: 1954: 1946: 1938: 1926: 1924: 1923: 1918: 1891: 1889: 1888: 1883: 1881: 1880: 1860: 1858: 1857: 1852: 1850: 1838: 1836: 1835: 1830: 1825: 1817: 1794: 1793: 1775: 1745: 1743: 1742: 1737: 1732: 1724: 1719: 1718: 1717: 1708: 1707: 1694: 1692: 1690: 1688: 1677: 1672: 1670: 1669: 1660: 1656: 1655: 1645: 1634: 1632: 1628: 1627: 1617: 1616: 1607: 1573: 1571: 1570: 1565: 1560: 1548: 1547: 1538: 1537: 1519: 1518: 1510: 1505: 1499: 1498: 1486: 1482: 1477: 1469: 1454: 1452: 1451: 1446: 1431: 1429: 1428: 1423: 1421: 1420: 1392: 1390: 1389: 1384: 1382: 1381: 1365: 1363: 1362: 1357: 1345: 1343: 1342: 1337: 1321: 1319: 1318: 1313: 1311: 1310: 1290: 1288: 1287: 1282: 1270: 1268: 1267: 1262: 1260: 1258: 1257: 1256: 1240: 1235: 1234: 1222: 1221: 1205: 1203: 1202: 1197: 1195: 1193: 1192: 1191: 1178: 1177: 1176: 1167: 1166: 1156: 1125: 1123: 1122: 1117: 1115: 1099: 1097: 1096: 1091: 1089: 1073: 1071: 1070: 1065: 1063: 1051: 1049: 1048: 1043: 1038: 1030: 1001: 925: 917:Daniel J. Alpert 791: 745: 632:Clinton Davisson 582:Louis de Broglie 528:Louis de Broglie 373:cathode ray tube 361: 350: 269: 260: 16060: 16059: 16055: 16054: 16053: 16051: 16050: 16049: 16015:Crystallography 16000: 15999: 15998: 15993: 15957: 15906: 15855: 15836:Ondrej Krivanek 15757: 15620: 15568: 15530: 15516:Liquid-Phase EM 15480: 15439:Instrumentation 15434: 15392: 15383: 15347: 15342: 15312: 15307: 15271: 15228: 15195: 15167: 15119: 15071: 15042:CrystalExplorer 15018: 15002:Phase retrieval 14965: 14896: 14895: 14886: 14843: 14822:Schottky defect 14721:Perfect crystal 14712: 14708:Abnormal growth 14670: 14656:Supersaturation 14619:Miscibility gap 14600: 14593: 14544: 14501: 14465:Bravais lattice 14446: 14413: 14411:Crystallography 14408: 14352: 14324: 14291: 14253: 14223: 14193: 14175: 14173:Further reading 14170: 14169: 14154: 14138: 14131: 14088: 14084: 14033: 14029: 13978: 13974: 13903: 13899: 13864: 13860: 13809: 13805: 13768: 13761: 13726: 13719: 13668: 13659: 13624: 13615: 13600: 13584: 13577: 13542: 13538: 13487: 13483: 13440: 13436: 13409:Surface Science 13401: 13397: 13350:(6): eaar7495. 13336: 13332: 13323: 13321: 13313: 13312: 13308: 13247: 13240: 13187: 13183: 13148: 13144: 13125:Ultramicroscopy 13117: 13113: 13105: 13101: 13056: 13052: 13025:Ultramicroscopy 13017: 13013: 12942: 12938: 12923: 12907: 12903: 12852: 12848: 12813: 12809: 12764: 12760: 12707: 12703: 12660: 12653: 12646: 12632: 12628: 12583: 12579: 12570: 12568: 12559: 12558: 12554: 12511: 12507: 12464: 12460: 12452: 12450: 12448: 12422: 12415: 12382:Bak, P (1982). 12380: 12373: 12330: 12323: 12272: 12268: 12225: 12221: 12178: 12174: 12131: 12127: 12092:Ultramicroscopy 12084: 12080: 12045:Ultramicroscopy 12037: 12033: 11974: 11967: 11932: 11928: 11919: 11917: 11909: 11908: 11901: 11874:Ultramicroscopy 11866: 11862: 11846: 11845: 11833: 11817: 11813: 11797: 11796: 11778: 11774: 11759: 11743: 11739: 11732: 11716: 11703: 11696: 11674: 11663: 11640: 11616: 11609: 11601: 11599: 11588: 11581: 11544: 11540: 11497: 11490: 11445: 11438: 11411:Physics Letters 11403: 11399: 11356: 11349: 11306: 11302: 11289: 11285: 11226: 11222: 11171: 11164: 11113: 11106: 11063: 11056: 11005: 11001: 10993: 10991: 10989: 10963: 10956: 10947: 10945: 10937: 10936: 10932: 10881: 10872: 10863: 10861: 10853: 10852: 10848: 10803: 10799: 10791: 10789: 10787: 10761: 10757: 10748: 10746: 10739:"Bond Energies" 10737: 10736: 10732: 10721: 10714: 10671: 10658: 10615: 10611: 10604: 10590: 10583: 10548:Ultramicroscopy 10540: 10531: 10488: 10479: 10464: 10448: 10435: 10419: 10418: 10406: 10390: 10377: 10358:Surface Science 10350: 10346: 10301: 10297: 10290: 10274:Surface Science 10268: 10261: 10218: 10211: 10158: 10151: 10124:Ultramicroscopy 10116: 10107: 10100: 10068: 10061: 10045: 10044: 10034: 10023: 10008: 9984: 9980: 9929: 9925: 9882: 9875: 9832: 9828: 9785: 9778: 9735: 9728: 9697: 9690: 9655: 9646: 9637: 9635: 9605: 9601: 9578:(90): 297–301. 9564: 9560: 9517: 9513: 9454: 9450: 9421:(10): 609–619. 9407: 9400: 9373: 9369: 9324: 9320: 9267: 9260: 9209: 9205: 9162: 9158: 9143: 9127: 9123: 9116: 9100: 9089: 9054:Physical Review 9046: 9042: 8991: 8987: 8952: 8948: 8939: 8937: 8919: 8918: 8914: 8863: 8859: 8849: 8847: 8837: 8833: 8823: 8821: 8811: 8807: 8798: 8796: 8788: 8787: 8783: 8774: 8772: 8770: 8746: 8742: 8699: 8695: 8688: 8660: 8656: 8621: 8614: 8593:(25): 974–993. 8579: 8575: 8540: 8536: 8515:(12): 739–766. 8501: 8497: 8489: 8487: 8477: 8451: 8447: 8418:(10): 685–690. 8404: 8400: 8349: 8342: 8299: 8292: 8257:Physical Review 8249: 8245: 8214: 8210: 8173:(36): 778–786. 8159: 8155: 8140: 8133: 8096: 8089: 8054: 8039: 7996: 7992: 7939: 7935: 7882: 7878: 7815: 7808: 7745: 7736: 7699:Physical Review 7691: 7684: 7633: 7629: 7594: 7590: 7577: 7573: 7554: 7550: 7515: 7511: 7468: 7461: 7448:Whittaker, E.T. 7445: 7441: 7428: 7424: 7418: 7404: 7395: 7360: 7356: 7340: 7336: 7293: 7289: 7254: 7247: 7240: 7232:. p. 133. 7218: 7214: 7207: 7180: 7169: 7134:Physical Review 7126: 7109: 7082:Surface Science 7074: 7065: 7022: 7011: 6996: 6980: 6963: 6948: 6932: 6903: 6896: 6880: 6871: 6861: 6859: 6851: 6845: 6826: 6783: 6776: 6770: 6744: 6729: 6714: 6698: 6683: 6668: 6652: 6611: 6606: 6601: 6600: 6573: 6571: 6568: 6567: 6551: 6549: 6546: 6545: 6529: 6527: 6524: 6523: 6504: 6496: 6482: 6479: 6478: 6459: 6456: 6455: 6439: 6436: 6435: 6419: 6416: 6415: 6398: 6393: 6392: 6383: 6378: 6377: 6368: 6363: 6362: 6360: 6357: 6356: 6339: 6334: 6333: 6324: 6319: 6318: 6309: 6304: 6303: 6301: 6298: 6297: 6280: 6275: 6274: 6265: 6260: 6259: 6250: 6245: 6244: 6242: 6239: 6238: 6222: 6214: 6206: 6204: 6201: 6200: 6198: 6187: 6168: 6165: 6164: 6148: 6145: 6144: 6143:, for instance 6125: 6122: 6121: 6102: 6094: 6080: 6077: 6076: 6074: 6070: 6048: 6044: 6038: 6031: 6026: 6018:strain analysis 5980: 5974: 5939: 5935: 5933: 5930: 5929: 5913: 5910: 5909: 5893: 5890: 5889: 5865: 5861: 5859: 5856: 5855: 5835: 5831: 5829: 5826: 5825: 5793: 5789: 5771: 5767: 5747: 5743: 5734: 5730: 5722: 5712: 5708: 5696: 5692: 5688: 5675: 5671: 5656: 5652: 5636: 5634: 5614: 5610: 5609: 5605: 5585: 5581: 5580: 5576: 5570: 5556: 5545: 5543: 5542: 5532: 5521: 5511: 5507: 5499: 5495: 5489: 5485: 5483: 5465: 5461: 5459: 5456: 5455: 5429: 5425: 5423: 5420: 5419: 5396: 5393: 5392: 5366: 5362: 5360: 5357: 5356: 5340: 5337: 5336: 5310: 5306: 5304: 5301: 5300: 5283: 5279: 5277: 5274: 5273: 5257: 5254: 5253: 5236: 5232: 5227: 5218: 5214: 5205: 5201: 5187: 5184: 5183: 5163: 5158: 5157: 5142: 5138: 5133: 5127: 5116: 5106: 5102: 5094: 5090: 5084: 5080: 5078: 5060: 5056: 5054: 5051: 5050: 5024: 5020: 5018: 5015: 5014: 4988: 4984: 4982: 4979: 4978: 4952: 4948: 4946: 4943: 4942: 4916: 4912: 4910: 4907: 4906: 4880: 4876: 4874: 4871: 4870: 4841: 4837: 4819: 4815: 4797: 4793: 4775: 4771: 4753: 4749: 4747: 4744: 4743: 4715: 4711: 4692: 4690: 4682: 4674: 4672: 4669: 4668: 4652: 4649: 4648: 4612: 4606: 4570: 4569: 4568: 4567: 4566: 4563: 4554: 4553: 4552: 4549: 4536: 4530: 4490:collimated beam 4482: 4481: 4480: 4479: 4478: 4474: 4465: 4464: 4463: 4446: 4442: 4440: 4437: 4436: 4419: 4415: 4413: 4410: 4409: 4406: 4393: 4387: 4364: 4358: 4316: 4310: 4251: 4245: 4234: 4206: 4195: 4158: 4150: 4142: 4140: 4137: 4136: 4119: 4074:superstructures 4057: 4049: 4038: 4033: 4030: 4029: 4013: 4005: 3997: 3995: 3992: 3991: 3988: 3979: 3962: 3961: 3960: 3959: 3947: 3946: 3945: 3937: 3936: 3878: 3821: 3774:magnetic lenses 3770:electron optics 3752: 3691: 3686: 3657: 3652: 3647: 3645: 3642: 3641: 3606: 3600: 3487: 3483: 3481: 3478: 3477: 3473: 3435: 3430: 3429: 3427: 3424: 3423: 3407: 3405: 3402: 3401: 3376: 3371: 3370: 3368: 3365: 3364: 3347: 3342: 3341: 3333: 3324: 3319: 3318: 3310: 3308: 3305: 3304: 3288: 3286: 3283: 3282: 3261: 3257: 3255: 3252: 3251: 3231: 3229: 3226: 3225: 3208: 3204: 3202: 3199: 3198: 3177: 3173: 3167: 3163: 3154: 3149: 3148: 3140: 3127: 3115: 3111: 3105: 3094: 3081: 3077: 3075: 3072: 3071: 3050: 3046: 3044: 3041: 3040: 3020: 3014: 3009: 3008: 3003: 3001: 2998: 2997: 2980: 2976: 2974: 2971: 2970: 2953: 2939: 2935: 2931: 2921: 2917: 2901: 2899: 2893: 2889: 2888: 2884: 2883: 2874: 2861: 2854: 2850: 2849: 2840: 2836: 2834: 2831: 2830: 2814: 2812: 2809: 2808: 2792: 2789: 2788: 2785: 2762: 2758: 2756: 2753: 2752: 2646: 2638: 2635: 2634: 2613: 2600: 2593: 2589: 2588: 2577: 2569: 2566: 2565: 2545: 2540: 2539: 2531: 2522: 2517: 2516: 2508: 2506: 2503: 2502: 2479: 2474: 2473: 2471: 2468: 2467: 2451: 2445: 2441: 2439: 2436: 2435: 2419: 2414: 2411: 2410: 2391: 2383: 2380: 2379: 2360: 2354: 2350: 2342: 2334: 2308: 2288: 2280: 2277: 2276: 2212: 2207: 2206: 2204: 2201: 2200: 2150: 2146: 2144: 2141: 2140: 2123: 2118: 2117: 2115: 2112: 2111: 2094: 2089: 2088: 2086: 2083: 2082: 2065: 2060: 2059: 2057: 2054: 2053: 2037: 2026: 2015: 2004: 2002: 1999: 1998: 1970: 1967: 1966: 1950: 1942: 1934: 1932: 1929: 1928: 1900: 1897: 1896: 1876: 1872: 1870: 1867: 1866: 1846: 1844: 1841: 1840: 1821: 1813: 1789: 1785: 1771: 1763: 1760: 1759: 1713: 1709: 1703: 1699: 1695: 1693: 1691: 1681: 1676: 1665: 1661: 1651: 1647: 1646: 1644: 1623: 1619: 1618: 1612: 1608: 1606: 1598: 1595: 1594: 1584:electron charge 1543: 1539: 1533: 1529: 1511: 1509: 1494: 1490: 1481: 1468: 1460: 1457: 1456: 1440: 1437: 1436: 1416: 1412: 1410: 1407: 1406: 1377: 1373: 1371: 1368: 1367: 1351: 1348: 1347: 1331: 1328: 1327: 1306: 1302: 1300: 1297: 1296: 1276: 1273: 1272: 1252: 1248: 1244: 1239: 1230: 1226: 1217: 1213: 1211: 1208: 1207: 1187: 1183: 1179: 1172: 1168: 1162: 1158: 1157: 1155: 1147: 1144: 1143: 1140:Archibald Howie 1111: 1109: 1106: 1105: 1085: 1083: 1080: 1079: 1059: 1057: 1054: 1053: 1052:for a position 1034: 1026: 997: 989: 986: 985: 981: 976: 937:surface science 919: 818: 813: 785: 760:magnetic lenses 739: 683:electron optics 679: 673: 621:, the other by 564:Albert Einstein 510: 500: 469:William Crookes 467:. By the 1870s 461:Eugen Goldstein 457:Eugen Goldstein 439:gases in 1859, 409:Michael Faraday 378: 377: 376: 375: 364: 363: 362: 353: 352: 351: 338: 328: 307: 279: 278: 277: 276: 272: 271: 270: 262: 261: 227: 134:converging beam 118:different types 100:There are many 17: 12: 11: 5: 16058: 16048: 16047: 16042: 16037: 16032: 16027: 16022: 16017: 16012: 15995: 15994: 15992: 15991: 15979: 15966: 15963: 15962: 15959: 15958: 15956: 15955: 15950: 15945: 15943:Direct methods 15940: 15935: 15930: 15925: 15920: 15914: 15912: 15908: 15907: 15905: 15904: 15899: 15894: 15889: 15884: 15879: 15874: 15869: 15863: 15861: 15857: 15856: 15854: 15853: 15848: 15843: 15838: 15833: 15828: 15823: 15818: 15813: 15808: 15803: 15798: 15793: 15791:Ernst G. Bauer 15788: 15783: 15778: 15772: 15770: 15763: 15759: 15758: 15756: 15755: 15750: 15745: 15740: 15735: 15730: 15725: 15720: 15715: 15710: 15705: 15700: 15695: 15690: 15685: 15684: 15683: 15673: 15668: 15663: 15658: 15653: 15648: 15643: 15638: 15632: 15630: 15626: 15625: 15622: 15621: 15619: 15618: 15613: 15612: 15611: 15601: 15596: 15591: 15590: 15589: 15578: 15576: 15570: 15569: 15567: 15566: 15561: 15556: 15551: 15546: 15540: 15538: 15532: 15531: 15529: 15528: 15523: 15518: 15513: 15508: 15503: 15497: 15495: 15486: 15482: 15481: 15479: 15478: 15473: 15468: 15463: 15458: 15453: 15448: 15442: 15440: 15436: 15435: 15433: 15432: 15427: 15422: 15417: 15412: 15407: 15405:Bremsstrahlung 15402: 15396: 15394: 15385: 15384: 15382: 15381: 15376: 15371: 15366: 15361: 15355: 15353: 15349: 15348: 15341: 15340: 15333: 15326: 15318: 15309: 15308: 15306: 15305: 15293: 15280: 15277: 15276: 15273: 15272: 15270: 15269: 15264: 15259: 15258: 15257: 15252: 15247: 15236: 15234: 15227: 15226: 15221: 15216: 15211: 15205: 15203: 15197: 15196: 15194: 15193: 15188: 15183: 15177: 15175: 15169: 15168: 15166: 15165: 15160: 15155: 15150: 15145: 15140: 15135: 15129: 15127: 15121: 15120: 15118: 15117: 15112: 15107: 15102: 15097: 15092: 15087: 15081: 15079: 15073: 15072: 15070: 15069: 15064: 15059: 15054: 15049: 15044: 15039: 15034: 15028: 15026: 15020: 15019: 15017: 15016: 15011: 15010: 15009: 14999: 14994: 14989: 14984: 14979: 14977:Direct methods 14973: 14971: 14967: 14966: 14964: 14963: 14962: 14961: 14956: 14946: 14941: 14940: 14939: 14934: 14924: 14923: 14922: 14917: 14906: 14904: 14898: 14897: 14889: 14887: 14885: 14884: 14879: 14874: 14869: 14864: 14862:Ewald's sphere 14859: 14854: 14848: 14845: 14844: 14842: 14841: 14836: 14831: 14830: 14829: 14824: 14814: 14813: 14812: 14807: 14805:Frenkel defect 14802: 14800:Bjerrum defect 14792: 14791: 14790: 14780: 14779: 14778: 14773: 14768: 14766:Peierls stress 14763: 14758: 14753: 14748: 14743: 14738: 14736:Burgers vector 14728: 14726:Stacking fault 14723: 14717: 14714: 14713: 14711: 14710: 14705: 14700: 14695: 14689: 14687: 14685:Grain boundary 14678: 14672: 14671: 14669: 14668: 14663: 14658: 14653: 14648: 14643: 14638: 14633: 14632: 14631: 14629:Liquid crystal 14626: 14621: 14616: 14605: 14603: 14595: 14594: 14592: 14591: 14590: 14589: 14579: 14578: 14577: 14567: 14566: 14565: 14560: 14549: 14546: 14545: 14543: 14542: 14537: 14532: 14527: 14522: 14517: 14511: 14509: 14500: 14499: 14494: 14492:Periodic table 14489: 14488: 14487: 14482: 14477: 14472: 14467: 14456: 14454: 14445: 14444: 14439: 14434: 14433: 14432: 14421: 14419: 14415: 14414: 14407: 14406: 14399: 14392: 14384: 14378: 14377: 14357: 14350: 14337: 14322: 14307: 14289: 14266: 14251: 14236: 14221: 14206: 14191: 14174: 14171: 14168: 14167: 14152: 14129: 14102:(3): 214–224. 14082: 14047:(4): 819–831. 14027: 13972: 13897: 13878:(2): 505–524. 13858: 13803: 13759: 13740:(8): 617–623. 13717: 13682:(2): 123–149. 13657: 13613: 13598: 13575: 13536: 13501:(3): 245–248. 13481: 13434: 13415:(2–3): 77–91. 13395: 13330: 13306: 13261:(3): 563–582. 13238: 13181: 13162:(3): 306–319. 13142: 13131:(3): 271–282. 13111: 13099: 13050: 13011: 12956:(4): 695–702. 12936: 12921: 12901: 12846: 12827:(1–2): 63–71. 12807: 12758: 12721:(19): 193302. 12701: 12651: 12644: 12626: 12597:(5): 213–232. 12577: 12552: 12505: 12458: 12446: 12413: 12394:(6): 587–629. 12371: 12344:(2): 643–658. 12321: 12266: 12219: 12172: 12145:(1): 235–255. 12125: 12098:(6): 758–765. 12078: 12031: 11988:(5): 399–410. 11965: 11946:(2): 184–198. 11926: 11899: 11880:(4): 335–348. 11860: 11831: 11811: 11772: 11757: 11737: 11730: 11701: 11694: 11661: 11638: 11607: 11579: 11558:(5): 247–257. 11538: 11488: 11436: 11417:(2): 126–128. 11397: 11347: 11320:(6): 697–722. 11300: 11283: 11220: 11162: 11104: 11077:(6): 618–628. 11054: 10999: 10987: 10954: 10930: 10870: 10846: 10817:(4): 316–317. 10797: 10785: 10755: 10730: 10712: 10656: 10629:(3): 379–384. 10609: 10602: 10581: 10554:(3): 263–276. 10529: 10477: 10462: 10433: 10404: 10375: 10364:(3): 479–491. 10344: 10315:(3): 322–330. 10295: 10288: 10259: 10232:(7): 860–876. 10209: 10149: 10130:(7): 763–770. 10105: 10098: 10059: 10021: 10006: 9978: 9943:(3): 350–352. 9923: 9896:(3): 357–368. 9873: 9826: 9799:(3): 317–324. 9776: 9726: 9707:(3): 339–347. 9688: 9669:(2): 113–140. 9644: 9599: 9558: 9531:(2): 280–290. 9511: 9448: 9398: 9367: 9338:(4): 305–310. 9318: 9281:(6): 522–529. 9258: 9203: 9156: 9141: 9121: 9114: 9087: 9060:(5): 684–712. 9040: 8985: 8946: 8927:. April 1962. 8912: 8857: 8831: 8805: 8781: 8768: 8740: 8693: 8686: 8654: 8635:(5): 197–207. 8612: 8573: 8534: 8495: 8475: 8445: 8398: 8340: 8313:(5): 607–640. 8290: 8243: 8224:(9): 675–676. 8208: 8153: 8150:(3061): 83–96. 8131: 8110:(6): 271–274. 8087: 8068:(17): 55–129. 8037: 8010:(2): 245–275. 7990: 7933: 7876: 7829:(8): 619–627. 7806: 7759:(4): 317–322. 7734: 7705:(6): 705–740. 7682: 7627: 7588: 7571: 7548: 7509: 7459: 7439: 7422: 7416: 7393: 7354: 7334: 7287: 7268:(3): 309–311. 7245: 7238: 7212: 7205: 7167: 7107: 7088:(2): 423–438. 7063: 7009: 6994: 6961: 6946: 6901: 6894: 6869: 6824: 6774: 6768: 6727: 6712: 6681: 6666: 6608: 6607: 6605: 6602: 6599: 6598: 6594:Miller indices 6576: 6554: 6532: 6511: 6507: 6503: 6499: 6495: 6492: 6489: 6486: 6466: 6463: 6443: 6423: 6401: 6396: 6391: 6386: 6381: 6376: 6371: 6366: 6342: 6337: 6332: 6327: 6322: 6317: 6312: 6307: 6283: 6278: 6273: 6268: 6263: 6258: 6253: 6248: 6225: 6221: 6217: 6213: 6209: 6185: 6172: 6152: 6132: 6129: 6109: 6105: 6101: 6097: 6093: 6090: 6087: 6084: 6068: 6042: 6028: 6027: 6025: 6022: 5976:Main article: 5973: 5970: 5953: 5950: 5947: 5942: 5938: 5917: 5897: 5871: 5868: 5864: 5841: 5838: 5834: 5813: 5810: 5807: 5804: 5801: 5796: 5792: 5788: 5785: 5782: 5779: 5774: 5770: 5766: 5763: 5760: 5755: 5750: 5746: 5740: 5737: 5733: 5729: 5725: 5721: 5718: 5715: 5711: 5702: 5699: 5695: 5691: 5686: 5683: 5678: 5674: 5670: 5667: 5662: 5659: 5655: 5651: 5648: 5645: 5642: 5639: 5632: 5628: 5625: 5622: 5617: 5613: 5608: 5603: 5599: 5596: 5593: 5588: 5584: 5579: 5573: 5565: 5562: 5559: 5554: 5551: 5548: 5541: 5535: 5530: 5527: 5524: 5520: 5514: 5510: 5502: 5498: 5492: 5488: 5482: 5479: 5476: 5473: 5468: 5464: 5443: 5440: 5437: 5432: 5428: 5400: 5380: 5377: 5374: 5369: 5365: 5344: 5324: 5321: 5318: 5313: 5309: 5286: 5282: 5261: 5239: 5235: 5230: 5226: 5221: 5217: 5213: 5208: 5204: 5200: 5197: 5194: 5191: 5171: 5166: 5161: 5156: 5153: 5150: 5145: 5141: 5136: 5130: 5125: 5122: 5119: 5115: 5109: 5105: 5097: 5093: 5087: 5083: 5077: 5074: 5071: 5068: 5063: 5059: 5038: 5035: 5032: 5027: 5023: 5002: 4999: 4996: 4991: 4987: 4966: 4963: 4960: 4955: 4951: 4930: 4927: 4924: 4919: 4915: 4894: 4891: 4888: 4883: 4879: 4858: 4855: 4852: 4849: 4844: 4840: 4836: 4833: 4830: 4827: 4822: 4818: 4814: 4811: 4808: 4805: 4800: 4796: 4792: 4789: 4786: 4783: 4778: 4774: 4770: 4767: 4764: 4761: 4752: 4731: 4727: 4722: 4719: 4714: 4710: 4707: 4702: 4698: 4695: 4689: 4685: 4681: 4677: 4656: 4608:Main article: 4605: 4602: 4564: 4557: 4556: 4555: 4550: 4543: 4542: 4541: 4540: 4539: 4532:Main article: 4529: 4526: 4525: 4524: 4520: 4508:calculations. 4475: 4468: 4467: 4466: 4449: 4445: 4422: 4418: 4407: 4400: 4399: 4398: 4397: 4396: 4389:Main article: 4386: 4383: 4360:Main article: 4357: 4354: 4346:direct methods 4312:Main article: 4309: 4306: 4247:Main article: 4244: 4241: 4232: 4204: 4194: 4191: 4161: 4157: 4153: 4149: 4145: 4118: 4115: 4096: 4095: 4088: 4085: 4060: 4056: 4052: 4048: 4045: 4041: 4037: 4016: 4012: 4008: 4004: 4000: 3987: 3984: 3978: 3975: 3949: 3948: 3939: 3938: 3930: 3929: 3928: 3927: 3926: 3903:single crystal 3877: 3874: 3870:direct methods 3834:single-crystal 3820: 3817: 3751: 3748: 3690: 3687: 3685: 3682: 3660: 3655: 3650: 3610:Seishi Kikuchi 3602:Main article: 3599: 3596: 3595: 3594: 3583: 3568: 3561: 3550:elastic strain 3546: 3535: 3523: 3490: 3486: 3472: 3469: 3438: 3433: 3410: 3379: 3374: 3350: 3345: 3340: 3336: 3332: 3327: 3322: 3317: 3313: 3291: 3264: 3260: 3234: 3211: 3207: 3185: 3180: 3176: 3170: 3166: 3162: 3157: 3152: 3147: 3143: 3139: 3136: 3133: 3130: 3126: 3123: 3118: 3114: 3108: 3103: 3100: 3097: 3093: 3089: 3084: 3080: 3053: 3049: 3023: 3017: 3012: 3006: 2983: 2979: 2956: 2951: 2942: 2938: 2934: 2929: 2924: 2920: 2916: 2913: 2910: 2907: 2904: 2896: 2892: 2887: 2882: 2877: 2872: 2868: 2864: 2860: 2857: 2853: 2848: 2843: 2839: 2817: 2796: 2784: 2781: 2765: 2761: 2653: 2649: 2645: 2642: 2621: 2616: 2611: 2607: 2603: 2599: 2596: 2592: 2587: 2584: 2580: 2576: 2573: 2553: 2548: 2543: 2538: 2534: 2530: 2525: 2520: 2515: 2511: 2482: 2477: 2454: 2448: 2444: 2422: 2418: 2398: 2394: 2390: 2387: 2367: 2363: 2357: 2353: 2349: 2345: 2341: 2337: 2333: 2330: 2327: 2324: 2321: 2318: 2315: 2311: 2307: 2304: 2301: 2298: 2295: 2291: 2287: 2284: 2215: 2210: 2153: 2149: 2126: 2121: 2097: 2092: 2068: 2063: 2040: 2036: 2033: 2029: 2025: 2022: 2018: 2014: 2011: 2007: 1986: 1983: 1980: 1977: 1974: 1965:with integers 1953: 1949: 1945: 1941: 1937: 1916: 1913: 1910: 1907: 1904: 1894:Miller indices 1879: 1875: 1849: 1828: 1824: 1820: 1816: 1812: 1809: 1806: 1803: 1800: 1797: 1792: 1788: 1784: 1781: 1778: 1774: 1770: 1767: 1752:Fourier series 1735: 1730: 1727: 1722: 1716: 1712: 1706: 1702: 1698: 1687: 1684: 1680: 1675: 1668: 1664: 1659: 1654: 1650: 1643: 1640: 1637: 1631: 1626: 1622: 1615: 1611: 1605: 1602: 1563: 1557: 1554: 1551: 1546: 1542: 1536: 1532: 1528: 1525: 1522: 1517: 1514: 1508: 1502: 1497: 1493: 1489: 1485: 1480: 1475: 1472: 1467: 1464: 1444: 1419: 1415: 1399:quasiparticles 1380: 1376: 1355: 1335: 1324:effective mass 1309: 1305: 1280: 1255: 1251: 1247: 1243: 1238: 1233: 1229: 1225: 1220: 1216: 1190: 1186: 1182: 1175: 1171: 1165: 1161: 1154: 1151: 1132:Dirac equation 1114: 1088: 1062: 1041: 1037: 1033: 1029: 1025: 1022: 1019: 1016: 1013: 1010: 1007: 1004: 1000: 996: 993: 980: 977: 975: 972: 971: 970: 954: 947: 940: 909: 894: 871:Walther Kossel 863: 821:John M. Cowley 816: 812: 809: 737:Adolf Matthias 696:Arthur Wehnelt 687:Heinrich Hertz 672: 669: 649:Seishi Kikuchi 552:effective mass 548:group velocity 540:standing waves 520:group velocity 499: 496: 477:Joseph Thomson 441:Julius Plücker 433:Geissler tubes 366: 365: 356: 355: 354: 345: 344: 343: 342: 341: 327: 324: 306: 303: 291:electron waves 274: 273: 264: 263: 255: 254: 253: 252: 251: 226: 223: 211: 210: 191: 184: 126:no periodicity 122:larger repeats 110:single crystal 87:electron waves 59:Coulomb forces 43:electron beams 15: 9: 6: 4: 3: 2: 16057: 16046: 16043: 16041: 16038: 16036: 16033: 16031: 16028: 16026: 16023: 16021: 16018: 16016: 16013: 16011: 16008: 16007: 16005: 15990: 15989: 15980: 15978: 15977: 15968: 15967: 15964: 15954: 15951: 15949: 15946: 15944: 15941: 15939: 15936: 15934: 15931: 15929: 15926: 15924: 15921: 15919: 15916: 15915: 15913: 15909: 15903: 15900: 15898: 15895: 15893: 15890: 15888: 15885: 15883: 15880: 15878: 15875: 15873: 15870: 15868: 15867:Carl Zeiss AG 15865: 15864: 15862: 15860:Manufacturers 15858: 15852: 15849: 15847: 15844: 15842: 15839: 15837: 15834: 15832: 15829: 15827: 15824: 15822: 15819: 15817: 15814: 15812: 15811:James Hillier 15809: 15807: 15804: 15802: 15799: 15797: 15794: 15792: 15789: 15787: 15784: 15782: 15779: 15777: 15774: 15773: 15771: 15767: 15764: 15760: 15754: 15751: 15749: 15746: 15744: 15741: 15739: 15736: 15734: 15731: 15729: 15726: 15724: 15721: 15719: 15716: 15714: 15711: 15709: 15706: 15704: 15701: 15699: 15696: 15694: 15691: 15689: 15686: 15682: 15679: 15678: 15677: 15674: 15672: 15669: 15667: 15664: 15662: 15659: 15657: 15654: 15652: 15649: 15647: 15644: 15642: 15639: 15637: 15634: 15633: 15631: 15627: 15617: 15614: 15610: 15607: 15606: 15605: 15602: 15600: 15597: 15595: 15592: 15588: 15585: 15584: 15583: 15580: 15579: 15577: 15575: 15571: 15565: 15564:Ultrafast SEM 15562: 15560: 15557: 15555: 15552: 15550: 15547: 15545: 15542: 15541: 15539: 15537: 15533: 15527: 15524: 15522: 15521:Low-energy EM 15519: 15517: 15514: 15512: 15509: 15507: 15504: 15502: 15499: 15498: 15496: 15494: 15490: 15487: 15483: 15477: 15474: 15472: 15471:Magnetic lens 15469: 15467: 15464: 15462: 15459: 15457: 15454: 15452: 15449: 15447: 15444: 15443: 15441: 15437: 15431: 15428: 15426: 15423: 15421: 15420:Kikuchi lines 15418: 15416: 15413: 15411: 15408: 15406: 15403: 15401: 15398: 15397: 15395: 15390: 15386: 15380: 15377: 15375: 15372: 15370: 15367: 15365: 15362: 15360: 15357: 15356: 15354: 15350: 15346: 15339: 15334: 15332: 15327: 15325: 15320: 15319: 15316: 15304: 15303: 15294: 15292: 15291: 15282: 15281: 15278: 15268: 15265: 15263: 15260: 15256: 15253: 15251: 15248: 15246: 15243: 15242: 15241: 15238: 15237: 15235: 15231: 15225: 15222: 15220: 15217: 15215: 15212: 15210: 15207: 15206: 15204: 15202: 15198: 15192: 15189: 15187: 15184: 15182: 15179: 15178: 15176: 15174: 15170: 15164: 15161: 15159: 15156: 15154: 15151: 15149: 15146: 15144: 15141: 15139: 15136: 15134: 15131: 15130: 15128: 15126: 15122: 15116: 15113: 15111: 15108: 15106: 15103: 15101: 15098: 15096: 15093: 15091: 15088: 15086: 15083: 15082: 15080: 15078: 15074: 15068: 15065: 15063: 15060: 15058: 15055: 15053: 15050: 15048: 15045: 15043: 15040: 15038: 15035: 15033: 15030: 15029: 15027: 15025: 15021: 15015: 15012: 15008: 15005: 15004: 15003: 15000: 14998: 14997:Patterson map 14995: 14993: 14990: 14988: 14985: 14983: 14980: 14978: 14975: 14974: 14972: 14968: 14960: 14957: 14955: 14952: 14951: 14950: 14947: 14945: 14942: 14938: 14935: 14933: 14930: 14929: 14928: 14925: 14921: 14918: 14916: 14913: 14912: 14911: 14908: 14907: 14905: 14903: 14899: 14893: 14883: 14880: 14878: 14875: 14873: 14870: 14868: 14867:Friedel's law 14865: 14863: 14860: 14858: 14855: 14853: 14850: 14849: 14840: 14837: 14835: 14832: 14828: 14825: 14823: 14820: 14819: 14818: 14815: 14811: 14810:Wigner effect 14808: 14806: 14803: 14801: 14798: 14797: 14796: 14795:Interstitials 14793: 14789: 14786: 14785: 14784: 14781: 14777: 14774: 14772: 14769: 14767: 14764: 14762: 14759: 14757: 14754: 14752: 14749: 14747: 14744: 14742: 14739: 14737: 14734: 14733: 14732: 14729: 14727: 14724: 14722: 14719: 14718: 14709: 14706: 14704: 14701: 14699: 14696: 14694: 14691: 14690: 14688: 14686: 14682: 14679: 14677: 14673: 14667: 14664: 14662: 14659: 14657: 14654: 14652: 14649: 14647: 14644: 14642: 14641:Precipitation 14639: 14637: 14634: 14630: 14627: 14625: 14622: 14620: 14617: 14615: 14612: 14611: 14610: 14609:Phase diagram 14607: 14606: 14604: 14602: 14596: 14588: 14585: 14584: 14583: 14580: 14576: 14573: 14572: 14571: 14568: 14564: 14561: 14559: 14556: 14555: 14554: 14551: 14550: 14541: 14538: 14536: 14533: 14531: 14528: 14526: 14523: 14521: 14518: 14516: 14513: 14512: 14510: 14508: 14504: 14498: 14495: 14493: 14490: 14486: 14483: 14481: 14478: 14476: 14473: 14471: 14468: 14466: 14463: 14462: 14461: 14458: 14457: 14455: 14453: 14449: 14443: 14440: 14438: 14435: 14431: 14428: 14427: 14426: 14423: 14422: 14420: 14416: 14412: 14405: 14400: 14398: 14393: 14391: 14386: 14385: 14382: 14373: 14369: 14366:. Techbooks. 14365: 14364: 14358: 14353: 14347: 14343: 14338: 14333: 14329: 14325: 14319: 14315: 14314: 14308: 14306: 14300: 14296: 14292: 14286: 14282: 14278: 14274: 14273: 14267: 14262: 14258: 14254: 14252:0-408-18550-3 14248: 14244: 14243: 14237: 14232: 14228: 14224: 14218: 14214: 14213: 14207: 14202: 14198: 14194: 14192:0-444-82218-6 14188: 14184: 14183: 14177: 14176: 14163: 14159: 14155: 14149: 14145: 14144: 14136: 14134: 14125: 14121: 14117: 14113: 14109: 14105: 14101: 14097: 14093: 14086: 14078: 14074: 14070: 14066: 14062: 14058: 14054: 14050: 14046: 14042: 14038: 14031: 14023: 14019: 14015: 14011: 14007: 14003: 13999: 13995: 13991: 13987: 13983: 13976: 13968: 13964: 13960: 13956: 13952: 13948: 13943: 13938: 13933: 13928: 13924: 13920: 13916: 13912: 13908: 13901: 13893: 13889: 13885: 13881: 13877: 13873: 13869: 13862: 13854: 13850: 13846: 13842: 13838: 13834: 13830: 13826: 13822: 13818: 13814: 13807: 13799: 13795: 13790: 13785: 13782:: 3224–3234. 13781: 13777: 13773: 13766: 13764: 13755: 13751: 13747: 13743: 13739: 13735: 13731: 13724: 13722: 13713: 13709: 13705: 13701: 13697: 13693: 13689: 13685: 13681: 13677: 13673: 13666: 13664: 13662: 13653: 13649: 13645: 13641: 13637: 13633: 13629: 13622: 13620: 13618: 13609: 13605: 13601: 13599:3-540-65199-3 13595: 13591: 13590: 13582: 13580: 13571: 13567: 13563: 13559: 13555: 13551: 13547: 13540: 13532: 13528: 13524: 13520: 13516: 13512: 13508: 13504: 13500: 13496: 13492: 13485: 13477: 13473: 13469: 13465: 13461: 13457: 13453: 13449: 13445: 13438: 13430: 13426: 13422: 13418: 13414: 13410: 13406: 13399: 13391: 13387: 13382: 13377: 13373: 13369: 13365: 13361: 13357: 13353: 13349: 13345: 13341: 13334: 13320: 13319:www.gatan.com 13316: 13310: 13302: 13298: 13294: 13290: 13286: 13282: 13277: 13272: 13268: 13264: 13260: 13256: 13252: 13245: 13243: 13234: 13230: 13226: 13222: 13217: 13212: 13208: 13204: 13200: 13196: 13192: 13185: 13177: 13173: 13169: 13165: 13161: 13157: 13153: 13146: 13138: 13134: 13130: 13126: 13122: 13115: 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9714: 9710: 9706: 9702: 9695: 9693: 9684: 9680: 9676: 9672: 9668: 9665:(in German). 9664: 9660: 9653: 9651: 9649: 9634: 9630: 9626: 9622: 9619:(12): 63–70. 9618: 9614: 9613:IEEE Spectrum 9610: 9603: 9595: 9591: 9586: 9581: 9577: 9573: 9569: 9562: 9554: 9550: 9546: 9542: 9538: 9534: 9530: 9526: 9522: 9515: 9507: 9503: 9499: 9495: 9491: 9487: 9483: 9479: 9475: 9471: 9467: 9463: 9459: 9452: 9444: 9440: 9436: 9432: 9428: 9424: 9420: 9416: 9412: 9405: 9403: 9394: 9390: 9386: 9382: 9378: 9371: 9363: 9359: 9354: 9349: 9345: 9341: 9337: 9333: 9329: 9322: 9314: 9310: 9306: 9302: 9297: 9292: 9288: 9284: 9280: 9276: 9272: 9265: 9263: 9254: 9250: 9246: 9242: 9238: 9234: 9230: 9226: 9222: 9219:(in German). 9218: 9214: 9207: 9199: 9195: 9191: 9187: 9183: 9179: 9175: 9171: 9167: 9160: 9152: 9148: 9144: 9142:90-277-1246-8 9138: 9134: 9133: 9125: 9117: 9111: 9107: 9106: 9098: 9096: 9094: 9092: 9083: 9079: 9075: 9071: 9067: 9063: 9059: 9055: 9051: 9044: 9036: 9032: 9028: 9024: 9020: 9016: 9012: 9008: 9004: 9001:(in German). 9000: 8996: 8989: 8981: 8977: 8973: 8969: 8965: 8962:(in German). 8961: 8957: 8950: 8935: 8930: 8926: 8922: 8916: 8908: 8904: 8900: 8896: 8892: 8888: 8884: 8880: 8876: 8873:(in German). 8872: 8868: 8861: 8846: 8842: 8835: 8820: 8816: 8809: 8795: 8791: 8785: 8771: 8769:9780123810175 8765: 8761: 8757: 8753: 8752: 8744: 8736: 8732: 8728: 8724: 8720: 8716: 8712: 8708: 8704: 8697: 8689: 8683: 8678: 8673: 8669: 8665: 8658: 8650: 8646: 8642: 8638: 8634: 8630: 8626: 8619: 8617: 8608: 8604: 8600: 8596: 8592: 8589:(in German). 8588: 8584: 8577: 8569: 8565: 8561: 8557: 8554:(55): 80–90. 8553: 8549: 8545: 8538: 8530: 8526: 8522: 8518: 8514: 8511:(in German). 8510: 8506: 8499: 8486: 8482: 8478: 8472: 8468: 8464: 8460: 8456: 8449: 8441: 8437: 8433: 8429: 8425: 8421: 8417: 8413: 8409: 8402: 8394: 8390: 8386: 8382: 8378: 8374: 8370: 8366: 8362: 8359:(in German). 8358: 8354: 8347: 8345: 8336: 8332: 8328: 8324: 8320: 8316: 8312: 8308: 8304: 8297: 8295: 8286: 8282: 8278: 8274: 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3611: 3605: 3604:Kikuchi lines 3598:Kikuchi lines 3592: 3588: 3584: 3581: 3577: 3573: 3569: 3566: 3562: 3559: 3558:Jens Lindhard 3555: 3551: 3547: 3544: 3540: 3536: 3533: 3529: 3524: 3520: 3519: 3518: 3513: 3508: 3504: 3488: 3484: 3468: 3464: 3462: 3458: 3454: 3436: 3399: 3395: 3377: 3348: 3338: 3330: 3325: 3315: 3280: 3262: 3258: 3249: 3209: 3205: 3178: 3174: 3168: 3164: 3160: 3155: 3145: 3137: 3134: 3131: 3124: 3121: 3116: 3112: 3106: 3101: 3098: 3095: 3091: 3087: 3082: 3078: 3069: 3051: 3047: 3038: 3015: 2981: 2977: 2954: 2949: 2940: 2936: 2932: 2922: 2918: 2914: 2911: 2905: 2902: 2894: 2890: 2885: 2880: 2875: 2870: 2855: 2851: 2846: 2841: 2837: 2794: 2780: 2763: 2759: 2750: 2746: 2742: 2738: 2734: 2730: 2726: 2722: 2718: 2714: 2710: 2706: 2702: 2698: 2694: 2690: 2686: 2682: 2678: 2674: 2670: 2665: 2640: 2619: 2614: 2609: 2594: 2590: 2585: 2571: 2551: 2546: 2536: 2528: 2523: 2513: 2500: 2498: 2480: 2446: 2442: 2416: 2385: 2365: 2355: 2351: 2339: 2331: 2328: 2325: 2319: 2316: 2302: 2299: 2296: 2282: 2273: 2271: 2265: 2262: 2258: 2254: 2250: 2246: 2242: 2238: 2234: 2229: 2213: 2198: 2194: 2190: 2186: 2177: 2173: 2171: 2169: 2151: 2147: 2124: 2095: 2066: 2034: 2031: 2023: 2020: 2012: 2009: 1984: 1981: 1978: 1975: 1972: 1947: 1939: 1911: 1908: 1905: 1895: 1877: 1873: 1864: 1818: 1810: 1807: 1804: 1798: 1795: 1790: 1786: 1782: 1779: 1765: 1757: 1753: 1748: 1733: 1728: 1725: 1720: 1714: 1710: 1704: 1700: 1696: 1685: 1682: 1678: 1673: 1666: 1662: 1657: 1652: 1648: 1641: 1638: 1635: 1629: 1624: 1620: 1613: 1609: 1603: 1600: 1591: 1589: 1588:chemical bond 1585: 1581: 1580:electronvolts 1577: 1561: 1552: 1549: 1544: 1540: 1534: 1530: 1526: 1520: 1515: 1512: 1506: 1500: 1495: 1491: 1487: 1483: 1478: 1473: 1470: 1465: 1462: 1442: 1433: 1417: 1413: 1404: 1403:electron hole 1400: 1396: 1378: 1374: 1353: 1333: 1325: 1307: 1303: 1294: 1278: 1253: 1249: 1245: 1241: 1236: 1231: 1227: 1223: 1218: 1214: 1188: 1184: 1180: 1173: 1169: 1163: 1159: 1152: 1149: 1141: 1137: 1133: 1129: 1103: 1077: 1031: 1023: 1020: 1017: 1011: 1008: 1005: 991: 968: 963: 959: 955: 952: 948: 945: 941: 938: 933: 929: 923: 918: 914: 910: 907: 903: 899: 895: 892: 888: 884: 880: 876: 872: 868: 864: 861: 857: 853: 849: 845: 844: 843: 839: 838: 832: 830: 829:John M Cowley 826: 822: 808: 806: 802: 797: 795: 789: 784: 778: 776: 772: 767: 765: 761: 757: 753: 749: 743: 738: 734: 730: 725: 723: 718: 709: 705: 703: 701: 697: 693: 692:Emil Wiechert 688: 684: 678: 668: 666: 662: 658: 655:developed by 654: 650: 645: 641: 637: 636:Lester Germer 633: 629: 626:electrons by 624: 620: 615: 613: 609: 605: 601: 595: 594: 592: 585: 583: 579: 575: 572: 567: 565: 561: 557: 553: 549: 545: 541: 537: 533: 529: 521: 516: 512: 509: 505: 495: 492: 490: 486: 482: 478: 473: 470: 466: 462: 458: 454: 450: 445: 442: 438: 434: 430: 426: 422: 418: 414: 410: 406: 402: 399:invented the 398: 393: 391: 387: 383: 374: 370: 369:maltese cross 360: 349: 340: 337: 333: 323: 321: 316: 312: 302: 300: 296: 292: 288: 284: 268: 259: 250: 248: 247:electron wave 244: 240: 236: 232: 222: 220: 216: 209:diffraction). 208: 204: 200: 196: 192: 189: 185: 182: 178: 174: 170: 169: 168: 165: 163: 159: 155: 151: 147: 143: 139: 135: 131: 127: 123: 119: 115: 114:many crystals 111: 107: 103: 98: 96: 92: 88: 84: 80: 76: 71: 69: 65: 60: 56: 52: 48: 44: 40: 34: 30: 25: 21: 19: 15986: 15974: 15928:EM Data Bank 15892:Nion Company 15786:Dennis Gabor 15776:Albert Crewe 15554:Confocal SEM 15451:Electron gun 15409: 15400:Auger effect 15300: 15288: 15233:Associations 15201:Organisation 14914: 14693:Disclination 14624:Polymorphism 14587:Quasicrystal 14530:Orthorhombic 14470:Miller index 14418:Key concepts 14362: 14341: 14312: 14271: 14241: 14211: 14185:. Elsevier. 14181: 14142: 14099: 14095: 14085: 14044: 14040: 14030: 13989: 13985: 13975: 13914: 13910: 13900: 13875: 13871: 13861: 13820: 13816: 13806: 13779: 13775: 13737: 13733: 13679: 13675: 13635: 13631: 13588: 13556:(23): 7833. 13553: 13550:CrystEngComm 13549: 13539: 13498: 13494: 13484: 13451: 13447: 13437: 13412: 13408: 13398: 13347: 13343: 13333: 13322:. Retrieved 13318: 13309: 13258: 13254: 13198: 13194: 13184: 13159: 13155: 13145: 13128: 13124: 13114: 13102: 13070:(3): 12–15. 13067: 13063: 13053: 13031:(1): 73–82. 13028: 13024: 13014: 12953: 12949: 12939: 12911: 12904: 12866:(1): 75–84. 12863: 12859: 12849: 12824: 12820: 12810: 12775: 12771: 12761: 12718: 12714: 12704: 12671: 12667: 12635: 12629: 12594: 12590: 12580: 12569:. Retrieved 12567:. 2019-09-13 12564: 12555: 12522: 12518: 12508: 12475: 12471: 12461: 12451:, retrieved 12429: 12391: 12387: 12341: 12337: 12283: 12279: 12269: 12236: 12232: 12222: 12192:(1): 41–55. 12189: 12185: 12175: 12142: 12138: 12128: 12095: 12091: 12081: 12048: 12044: 12034: 11985: 11981: 11943: 11939: 11929: 11918:. Retrieved 11914: 11877: 11873: 11863: 11825:. Springer. 11821: 11814: 11782: 11775: 11747: 11740: 11720: 11677: 11620: 11600:, retrieved 11595: 11555: 11551: 11541: 11511:(1): 11–15. 11508: 11504: 11456: 11452: 11414: 11410: 11400: 11370:(1): 65–67. 11367: 11363: 11317: 11313: 11303: 11293: 11286: 11240:(1): 34–40. 11237: 11233: 11223: 11182: 11178: 11124: 11120: 11074: 11070: 11016: 11012: 11002: 10992:, retrieved 10970: 10946:. Retrieved 10942: 10933: 10892: 10888: 10862:. Retrieved 10858: 10849: 10814: 10810: 10800: 10790:, retrieved 10768: 10758: 10747:. Retrieved 10745:. 2013-10-02 10742: 10733: 10724: 10682: 10678: 10626: 10622: 10612: 10593: 10551: 10547: 10499: 10495: 10452: 10394: 10361: 10357: 10347: 10312: 10308: 10298: 10273: 10229: 10225: 10169: 10165: 10127: 10123: 10072: 10038: 9988: 9981: 9940: 9936: 9926: 9893: 9889: 9846:(2): 77–97. 9843: 9839: 9829: 9796: 9792: 9746: 9742: 9704: 9700: 9666: 9662: 9636:. Retrieved 9616: 9612: 9602: 9575: 9571: 9561: 9528: 9524: 9514: 9468:(1): 34–40. 9465: 9461: 9451: 9418: 9414: 9384: 9380: 9370: 9335: 9331: 9321: 9278: 9274: 9220: 9216: 9206: 9176:(2): 32–34. 9173: 9169: 9159: 9131: 9124: 9104: 9057: 9053: 9043: 9002: 8998: 8988: 8966:(1): 75–80. 8963: 8959: 8949: 8938:. Retrieved 8925:pubs.aip.org 8924: 8915: 8874: 8870: 8860: 8848:. Retrieved 8844: 8834: 8822:. Retrieved 8818: 8808: 8797:. Retrieved 8794:AncientFaces 8793: 8784: 8773:, retrieved 8750: 8743: 8710: 8706: 8696: 8667: 8657: 8632: 8628: 8590: 8586: 8576: 8551: 8547: 8537: 8512: 8508: 8498: 8488:, retrieved 8458: 8448: 8415: 8411: 8401: 8360: 8356: 8310: 8306: 8263:(2): 73–76. 8260: 8256: 8246: 8221: 8217: 8211: 8170: 8166: 8156: 8147: 8143: 8107: 8103: 8065: 8061: 8007: 8003: 7993: 7950: 7946: 7936: 7893: 7889: 7879: 7826: 7822: 7756: 7752: 7702: 7698: 7644: 7640: 7630: 7605: 7601: 7591: 7581: 7574: 7565: 7561: 7551: 7526: 7522: 7512: 7479: 7475: 7451: 7442: 7432: 7425: 7407: 7371: 7367: 7357: 7349: 7345: 7337: 7304: 7300: 7290: 7265: 7261: 7223: 7215: 7190: 7137: 7133: 7085: 7081: 7033: 7029: 6984: 6936: 6884: 6860:. Retrieved 6855: 6794: 6790: 6751: 6702: 6660:. Elsevier. 6656: 6071: 6064:matter waves 6059: 6051: 6045: 5995: 5981: 5967: 5417: 4646: 4627: 4613: 4571: 4537: 4510: 4483: 4394: 4376: 4365: 4330:Paul Midgley 4327: 4317: 4294: 4279: 4269: 4262: 4252: 4224: 4212: 4210: 4196: 4179: 4130: 4120: 4107: 4097: 3989: 3980: 3963: 3955: 3924: 3900: 3895: 3879: 3858: 3831: 3822: 3790: 3763: 3753: 3725: 3706: 3692: 3638: 3607: 3516: 3474: 3465: 3453:dislocations 3037:Ewald sphere 2786: 2697:not periodic 2666: 2501: 2434:rather than 2274: 2266: 2230: 2185:Ewald sphere 2182: 2172: 1997:in the form: 1749: 1592: 1434: 1074:. This is a 982: 891:CBED history 887:space groups 883:point groups 841: 837:information. 835: 834: 814: 798: 783:Hans Boersch 779: 768: 758:, used two 726: 724:and Mulvey. 720:Freundlich, 714: 704: 680: 616: 612:matter waves 597: 588: 587: 573: 568: 550:and have an 544:wave packets 531: 525: 511: 493: 484: 474: 465:cathode rays 463:dubbed them 446: 405:rarefied air 394: 379: 339: 315:vacuum tubes 308: 280: 231:matter waves 228: 212: 166: 99: 97:since then. 72: 38: 37: 20: 18: 16020:Diffraction 15872:FEI Company 15806:Harald Rose 15796:Ernst Ruska 15485:Microscopes 15393:with matter 15391:interaction 15186:Ewald Prize 14954:Diffraction 14932:Diffraction 14915:Diffraction 14857:Bragg plane 14852:Bragg's law 14731:Dislocation 14646:Segregation 14558:Crystallite 14475:Point group 11648:j.ctvqc6g7s 10172:(1): 1–16. 9387:: 267–321. 8877:(28): 522. 8850:24 February 8824:24 February 8790:"Max Knoll" 6862:25 February 6056:Bragg's Law 4578:crystalline 3674:orientation 1865:vector and 920: [ 902:PED history 879:John Steeds 786: [ 752:Ernst Ruska 740: [ 665:Ernst Ruska 657:Herman Mark 640:Bragg's law 591:Schrödinger 508:matter wave 429:atmospheres 407:. In 1838, 401:vacuum pump 332:Cathode ray 313:as well as 177:Bragg's law 91:instruments 75:general way 16045:Scattering 16004:Categories 15953:Multislice 15769:Developers 15629:Techniques 15374:Microscope 15369:Micrograph 14970:Algorithms 14959:Scattering 14937:Scattering 14920:Scattering 14788:Slip bands 14751:Cross slip 14601:transition 14535:Tetragonal 14525:Monoclinic 14437:Metallurgy 14231:1066178493 13324:2022-03-13 12963:2103.08543 12571:2023-09-26 12453:2023-03-24 11920:2023-02-11 11767:1001251352 11602:2023-09-26 10994:2023-02-11 10948:2023-10-02 10864:2023-09-26 10792:2023-02-11 10749:2023-09-26 10414:1293917727 9638:2023-09-26 8940:2023-09-26 8799:2023-09-26 8775:2023-02-11 8490:2023-02-24 6722:1066178493 6604:References 4298:ronchigram 3912:concentric 3896:Figure 13. 3793:plane wave 3772:including 3543:muffin-tin 3539:multislice 1758:), that is 1576:nanometers 1102:plane wave 965:requiring 848:multislice 766:in 1986.) 700:Hans Busch 675:See also: 644:Hans Bethe 628:Hans Bethe 604:Bohr model 560:wavevector 502:See also: 485:corpuscles 413:electrodes 330:See also: 243:diffracted 207:Fraunhofer 181:Fraunhofer 15821:Max Knoll 15476:Stigmator 15077:Databases 14540:Triclinic 14520:Hexagonal 14460:Unit cell 14452:Structure 14332:656767858 14201:247191522 14162:902763902 14077:137379846 14069:0360-2133 14022:137281137 14014:0022-2461 13967:227100401 13951:0021-9606 13892:0026-8976 13845:0028-0836 13798:0904-213X 13712:208256341 13704:0003-7028 13652:0005-9021 13570:1466-8033 13523:1476-4660 13476:0031-9007 13372:2375-2548 13301:263414171 13285:1431-9276 13225:0044-2968 13094:155224415 13086:1551-9295 12988:2052-2525 12896:137476417 12888:1073-5623 12802:0031-9007 12753:1098-0121 12728:0901.3135 12696:0734-2101 12547:0305-4608 12500:233534909 12492:0002-7820 12408:0034-4885 12366:0556-2805 12308:0034-4885 12261:0031-9007 12214:0022-3093 12167:0031-8086 12112:0304-3991 12065:0304-3991 12010:1431-9276 11960:0031-9015 11894:0304-3991 11849:cite book 11841:706920411 11800:cite book 11792:801808484 11656:243353224 11533:0567-7394 11483:0021-9606 11392:0365-110X 11342:0022-3719 11262:1431-9276 11215:123122726 11207:0080-4630 11157:121465295 11149:0080-4630 11099:0031-9015 11049:123349515 11041:0080-4614 10917:0950-1207 10841:0365-110X 10707:0031-9015 10651:0108-7673 10568:0304-3991 10524:0034-6748 10422:cite book 10331:1865-7109 10254:0021-8979 10196:2052-5192 10048:cite book 9965:0567-7394 9918:0108-7673 9860:0741-0581 9821:0021-8898 9771:122890943 9594:0025-5718 9553:0567-7394 9490:1431-9276 9443:0365-110X 9362:0365-110X 9305:0365-110X 9253:123199621 9245:1434-6001 9198:0003-6951 9082:0031-899X 9035:121097655 9027:1434-6001 8907:263996652 8899:0028-1042 8727:0036-8075 8649:0508-3443 8568:1941-5982 8485:195494352 8440:0021-8979 8393:186239132 8385:1434-6001 8335:0003-3804 8285:0031-899X 8238:178706417 8195:0028-1042 8032:171025814 8024:0007-0874 7977:0950-1207 7920:0028-0836 7853:0027-8424 7783:0027-8424 7729:0031-899X 7669:0028-0836 7622:1941-5982 7543:1941-5982 7504:122006529 7496:0370-1662 7388:1941-5982 7321:0095-6562 7282:0304-3886 7162:0031-899X 7058:0022-3719 7004:656767858 6819:250876999 6811:0034-4885 6676:247191522 6553:χ 6502:⋅ 6488:⁡ 6465:π 6282:∗ 6267:∗ 6252:∗ 6151:ℏ 6131:π 6100:⋅ 6086:⁡ 6006:Figure 25 5916:η 5896:κ 5791:η 5787:− 5769:η 5762:⁡ 5714:− 5669:κ 5666:− 5641:⁡ 5550:≠ 5540:∑ 5519:∑ 5203:π 5114:∑ 4718:θ 4709:⁡ 4701:λ 4697:π 4655:θ 4642:Figure 24 4637:molecules 4594:electrons 4586:Figure 23 4582:Figure 22 4574:technique 4517:adsorbate 4498:Figure 21 4494:Figure 20 4338:Figure 19 4290:Figure 18 4265:Figure 17 4237:Figure 16 4186:Figure 15 4111:Figure 14 4084:ordering. 3956:Figure 12 3916:Figure 12 3908:Figure 12 3862:Figure 11 3853:magnesium 3797:objective 3778:apertures 3766:Figure 10 3489:∗ 3161:− 3146:⋅ 3135:π 3125:⁡ 3092:∑ 2933:π 2912:π 2906:⁡ 2881:∝ 2856:ϕ 2745:Figure 22 2713:Figure 12 2709:Figure 16 2701:Figure 15 2641:ϕ 2595:ϕ 2386:ϕ 2340:⋅ 2329:π 2320:⁡ 2303:ϕ 2300:∫ 2283:ψ 2257:Figure 22 2245:Figure 20 2125:∗ 2096:∗ 2067:∗ 1819:⋅ 1808:π 1799:⁡ 1783:∑ 1679:π 1658:λ 1653:∗ 1642:π 1614:∗ 1604:π 1496:∗ 1463:λ 1443:λ 1418:∗ 1308:∗ 1219:∗ 1189:∗ 1032:⋅ 1021:π 1012:⁡ 992:ψ 856:dynamical 748:Max Knoll 661:Max Knoll 475:In 1897, 395:In 1650, 237:shown in 183:approach. 29:austenite 16025:Electron 15976:Category 15923:CrysTBox 15911:Software 15582:Cryo-TEM 15389:Electron 15290:Category 15125:Journals 15057:OctaDist 15052:JANA2020 15024:Software 14910:Electron 14827:F-center 14614:Eutectic 14575:Fiveling 14570:Twinning 14563:Equiaxed 14372:27997701 14299:45473741 14124:41385346 14116:15009688 13959:33218233 13608:40857022 13531:20154691 13390:29951584 13293:31084643 13233:52059939 13045:15935917 13006:34258017 12931:45485010 12621:53137808 12316:16316238 12120:19269095 12073:17234347 12026:20112743 12018:19771696 11270:15306065 10925:13112732 10576:12524196 10472:54529276 10339:96851585 10204:23364455 10144:19910121 10016:45473741 9973:98184340 9633:20294294 9498:15306065 9313:94391285 8735:14057363 7985:98311959 7871:16587378 7801:16587341 7450:(1951). 7329:18018443 7189:(1999). 7187:Wolf, E. 7183:Born, M. 4633:geometry 4523:surface. 4282:Figure 7 3892:CrysTBox 3826:tungsten 3824:such as 3805:detector 3713:Figure 9 3678:Figure 8 3591:exchange 3528:Figure 7 3512:plasmons 3394:Figure 6 3392:, as in 3250:vector, 2829:is then: 2729:Figure 7 2673:Figure 1 2497:Figure 6 2495:by (see 2270:Figure 6 2189:Figure 6 960:such as 756:Figure 5 556:Figure 4 536:electron 481:hydrogen 453:Figure 3 437:rarefied 382:ēlektron 299:Figure 1 295:Figure 2 239:Figure 2 173:geometry 130:disorder 106:transmit 64:Figure 1 15988:Commons 15636:4D STEM 15609:4D STEM 15587:Cryo-ET 15559:SEM-XRF 15549:CryoSEM 15506:Cryo-EM 15364:History 15302:Commons 15250:Germany 14927:Neutron 14817:Vacancy 14676:Defects 14661:GP-zone 14507:Systems 14261:2365578 14049:Bibcode 13994:Bibcode 13919:Bibcode 13853:4201332 13825:Bibcode 13742:Bibcode 13684:Bibcode 13503:Bibcode 13456:Bibcode 13417:Bibcode 13381:6018998 13352:Bibcode 13263:Bibcode 13203:Bibcode 13164:Bibcode 12997:8256708 12968:Bibcode 12868:Bibcode 12829:Bibcode 12780:Bibcode 12733:Bibcode 12676:Bibcode 12599:Bibcode 12527:Bibcode 12346:Bibcode 12288:Bibcode 12241:Bibcode 12194:Bibcode 12147:Bibcode 11990:Bibcode 11560:Bibcode 11513:Bibcode 11461:Bibcode 11419:Bibcode 11372:Bibcode 11322:Bibcode 11278:8016041 11242:Bibcode 11187:Bibcode 11129:Bibcode 11079:Bibcode 11021:Bibcode 10897:Bibcode 10819:Bibcode 10687:Bibcode 10631:Bibcode 10504:Bibcode 10234:Bibcode 10174:Bibcode 10078:Bibcode 9945:Bibcode 9898:Bibcode 9868:2681572 9801:Bibcode 9751:Bibcode 9709:Bibcode 9671:Bibcode 9533:Bibcode 9506:8016041 9470:Bibcode 9423:Bibcode 9340:Bibcode 9283:Bibcode 9225:Bibcode 9178:Bibcode 9151:7276396 9062:Bibcode 9007:Bibcode 8968:Bibcode 8879:Bibcode 8707:Science 8595:Bibcode 8517:Bibcode 8420:Bibcode 8365:Bibcode 8315:Bibcode 8265:Bibcode 8203:9815364 8175:Bibcode 8126:4121059 8070:Bibcode 7955:Bibcode 7928:4122313 7898:Bibcode 7862:1085652 7831:Bibcode 7792:1085484 7761:Bibcode 7707:Bibcode 7677:4104602 7649:Bibcode 7142:Bibcode 7090:Bibcode 7038:Bibcode 6956:2365578 5990:silicon 5413:earlier 4622:benzene 4477:screen. 4356:4D STEM 4217:phonons 3842:Gjønnes 3066:is the 2705:diffuse 417:cathode 305:History 203:Fresnel 148:(SEM), 142:scanned 138:rotated 79:history 47:elastic 45:due to 15933:EMsoft 15918:CASINO 15897:TESCAN 15762:Others 15661:cryoEM 15352:Basics 15245:France 15240:Europe 15173:Awards 14703:Growth 14553:Growth 14370: 14348: 14330: 14320: 14297: 14287: 14259: 14249: 14229: 14219: 14199: 14189: 14160: 14150: 14122: 14114: 14075: 14067: 14020: 14012: 13965: 13957: 13949: 13917:(19). 13890: 13851: 13843: 13817:Nature 13796: 13710: 13702: 13650: 13606: 13596: 13568: 13529: 13521: 13474: 13388: 13378: 13370: 13299: 13291: 13283: 13231: 13223: 13092: 13084: 13043: 13004: 12994: 12986: 12929: 12919: 12894: 12886: 12800: 12751: 12694: 12642: 12619: 12545: 12498: 12490: 12444: 12406: 12364: 12314: 12306: 12259: 12212: 12165: 12118: 12110: 12071: 12063: 12024: 12016: 12008: 11958: 11892: 11839: 11829: 11790: 11765: 11755: 11728: 11692: 11654: 11646: 11636: 11531: 11481: 11390: 11340: 11276: 11268: 11260: 11213: 11205: 11155: 11147: 11097: 11047: 11039: 10985: 10923: 10915: 10839: 10783: 10705: 10649: 10600: 10574: 10566: 10522: 10470: 10460: 10412: 10402: 10337: 10329: 10286: 10252: 10202: 10194: 10142: 10096: 10014: 10004: 9971: 9963: 9916: 9866: 9858: 9819: 9769: 9631: 9592: 9551: 9504: 9496: 9488: 9441: 9360: 9311: 9303: 9251: 9243: 9196: 9149: 9139: 9112: 9080: 9033: 9025: 8905: 8897: 8766: 8733: 8725: 8684: 8647: 8566: 8483: 8473: 8438: 8391: 8383: 8333: 8283: 8236: 8201: 8193: 8124: 8030: 8022: 7983: 7975: 7926: 7918: 7890:Nature 7869: 7859: 7851: 7799: 7789: 7781: 7727: 7675: 7667: 7641:Nature 7620: 7541: 7502: 7494: 7414: 7386: 7327: 7319: 7280: 7236: 7203: 7160: 7056: 7002: 6992: 6954: 6944: 6892: 6817: 6809: 6766: 6720: 6710: 6674: 6664: 6062:. 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