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Multislice
The multislice algorithm is a method for the simulation of the elastic scattering of an electron beam with matter, including all multiple scattering effects. The method is reviewed in the book by John M. Cowley, and also the work by Ishizuka. The algorithm is used in the simulation of high resolution transmission electron microscopy (HREM) micrographs, and serves as a useful tool for analyzing experimental images. This article describes some relevant background information, the theoretical basis of the technique, approximations used, and several software packages that implement this technique. Some of the advantages and limitations of the technique and important considerations that need to be taken into account are described. Background The multislice method has found wide application in Electron microscope, electron microscopy and Electron crystallography, crystallography. The mapping from a crystal structure to its image or electron diffraction pattern is relatively well unders ...
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Electron Diffraction
Electron diffraction is a generic term for phenomena associated with changes in the direction of electron beams due to elastic interactions with atoms. It occurs due to elastic scattering, when there is no change in the energy of the electrons. The negatively charged electrons are scattered due to Coulomb forces 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 Figure 1. Beyond patterns showing the directions of electrons, electron diffraction also plays a major role in the contrast of images in electron microscopes. 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 general way electrons can act as waves, and diffract and interact with matter. It a ...
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Electron Crystallography
Electron crystallography is a subset of methods in electron diffraction focusing upon detailed determination of the positions of atoms in solids using a transmission electron microscope (TEM). It can involve the use of high-resolution transmission electron microscopy images, electron diffraction patterns including convergent-beam electron diffraction or combinations of these. It has been successful in determining some bulk structures, and also surface structures. Two related methods are low-energy electron diffraction which has solved the structure of many surfaces, and reflection high-energy electron diffraction which is used to monitor surfaces often during growth. The technique date back to soon after the discovery of electron diffraction in 1927-28, and was used in many early works. However, for many years quantitative electron crystallography was not used, instead the diffraction information was combined qualitatively with imaging results. A number of advances from the 195 ...
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Transmission Electron Microscopy
Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a grid. An image is formed from the interaction of the electrons with the sample as the beam is transmitted through the specimen. The image is then magnified and focused onto an imaging device, such as a fluorescent screen, a layer of photographic film, or a detector such as a scintillator attached to a charge-coupled device or a direct electron detector. Transmission electron microscopes are capable of imaging at a significantly higher resolution than light microscopes, owing to the smaller de Broglie wavelength of electrons. This enables the instrument to capture fine detail—even as small as a single column of atoms, which is thousands of times smaller than a resolvable object seen in a light microscope. Transmission electron micr ...
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Spin (physics)
Spin is an Intrinsic and extrinsic properties, intrinsic form of angular momentum carried by elementary particles, and thus by List of particles#Composite particles, composite particles such as hadrons, atomic nucleus, atomic nuclei, and atoms. Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory. The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The relativistic spin–statistics theorem connects electron spin quantization to the Pauli exclusion principle: observations of exclusion imply half-integer spin, and observations of half-integer spin imply exclusion. Spin is described mathematically as a vector for some particles such as photons, and as a spinor or bispinor for other particles such as electrons. Sp ...
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Pauli Equation
In quantum mechanics, the Pauli equation or Schrödinger–Pauli equation is the formulation of the Schrödinger equation for spin-1/2 particles, which takes into account the interaction of the particle's spin with an external electromagnetic field. It is the non- relativistic limit of the Dirac equation and can be used where particles are moving at speeds much less than the speed of light, so that relativistic effects can be neglected. It was formulated by Wolfgang Pauli in 1927. In its linearized form it is known as Lévy-Leblond equation. Equation For a particle of mass m and electric charge q, in an electromagnetic field described by the magnetic vector potential \mathbf and the electric scalar potential \phi, the Pauli equation reads: Here \boldsymbol = (\sigma_x, \sigma_y, \sigma_z) are the Pauli operators collected into a vector for convenience, and \mathbf = -i\hbar \nabla is the momentum operator in position representation. The state of the system, , \psi\ran ...
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CUDA
In computing, CUDA (Compute Unified Device Architecture) is a proprietary parallel computing platform and application programming interface (API) that allows software to use certain types of graphics processing units (GPUs) for accelerated general-purpose processing, an approach called general-purpose computing on GPUs. CUDA was created by Nvidia in 2006. When it was first introduced, the name was an acronym for ''Compute Unified Device Architecture'', but Nvidia later dropped the common use of the acronym and now rarely expands it. CUDA is a software layer that gives direct access to the GPU's virtual instruction set and parallel computational elements for the execution of compute kernels. In addition to drivers and runtime kernels, the CUDA platform includes compilers, libraries and developer tools to help programmers accelerate their applications. CUDA is designed to work with programming languages such as C, C++, Fortran, Python and Julia. This accessibility makes ...
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University Of Warwick
The University of Warwick ( ; abbreviated as ''Warw.'' in post-nominal letters) is a public research university on the outskirts of Coventry between the West Midlands and Warwickshire, England. The university was founded in 1965 as part of a government initiative to expand higher education. The Warwick Business School was established in 1967, the Warwick Law School in 1968, Warwick Manufacturing Group (WMG) in 1980, and Warwick Medical School in 2000. Warwick incorporated Coventry College of Education in 1979 and Horticulture Research International in 2004. Warwick is primarily based on a campus on the outskirts of Coventry, with a satellite campus in Wellesbourne and a central London base at the Shard. It is organised into three faculties—Arts; Science, Engineering and Medicine, and Social Sciences—within which there are thirty-two departments. Warwick has around 29,534 full-time students and 2,691 academic and research staff, with an average intake of 4,950 ...
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Fast Fourier Transform
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). A Fourier transform converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical. An FFT rapidly computes such transformations by Matrix decomposition, factorizing the DFT matrix into a product of Sparse matrix, sparse (mostly zero) factors. As a result, it manages to reduce the Computational complexity theory, complexity of computing the DFT from O(n^2), which arises if one simply applies the definition of DFT, to O(n \log n), where is the data size. The difference in speed can be enormous, especially for long data sets where may be in the thousands or millions. ...
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Jülich Research Centre
Jülich (; in old spellings also known as ''Guelich'' or ''Gülich'', , , Ripuarian: ''Jöllesch'') is a town in the district of Düren, in the federal state of North Rhine-Westphalia, in western Germany. As a border region between the competing powers in the Lower Rhine and Meuse areas, the town and the Duchy of Jülich played a historic role from the Middle Ages up to the 17th century. The town is well known in the state for being home to Forschungszentrum Jülich, one of the largest national research institutions in Europe. Geography Jülich stands in the Rur valley on the banks of the river Rur. The town is bordered by the town of Linnich in the north, the municipality of Titz in the northeast, the municipality of Niederzier in the southeast, the municipality of Inden in the south, and by the municipality of Aldenhoven in the west. Its maximum size is 13.3 km from east to west and 10.9 km from north to south. The highest point in Jülich is in Bourheim, 110 m ...
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Ernst Ruska-Centre
The Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons (ER-C) is an institute located on the campus of Forschungszentrum Jülich belonging to the Helmholtz Association of German Research Centres. It comprises three divisions: “''Physics of Nanoscale systems''”,  “''Materials Science and Technology''” and “''Structural Biology''”. The ER-C's main purposes are fundamental research in electron microscopy, focusing on method development and applications of high-resolution transmission electron microscopy (HRTEM) and scanning-transmission electron microscopy (STEM) in physics, chemistry and biology. History As a competence platform, the ER-C was founded on 27 January 2004 through a contract signed by the chairman of Forschungszentrum Jülich Joachim Treusch and the rector of RWTH Aachen University Burkhard Rauhut. It was inaugurated on 18 May 2006 in the presence of members of the Ernst Ruska Ernst August Friedrich Ruska (; 25 December 1906 – 27 M ...
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