Pendellösung
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Pendellösung
The Pendellösung effect or phenomenon is seen in diffraction in which there is a beating in the intensity of electromagnetic waves travelling within a crystal lattice. It was predicted by P. P. Ewald in 1916 and first observed in electron diffraction of magnesium oxide in 1942 by Robert D. Heidenreich and in X-ray diffraction by Norio Kato and Andrew Richard Lang in 1959. At the exit surface of a photonic crystal (PhC), the intensity of the diffracted wave can be periodically modulated, showing a maximum in the "positive" (forward diffracted) or in the "negative" (diffracted) direction, depending on the crystal slab thickness. The Pendellösung effect in photonic crystal A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of Crystal structure, natural crystals gives rise to X-ray crystallograp ...s can be understood as a beating phenomenon due to the phas ...
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Norio Kato
Norio Kato (Japanese: 加藤 範夫, ''Kato Norio'', March 10, 1923 – April 5, 2002) was a Japanese physicist and crystallographer. He was known for his contributions in diffraction topography and the dynamical theory of diffraction, including the validation of the Pendellösung effect and extensions to account for realistic scattering conditions. Education and career Kato was born in Shanghai, China but received his education in Japan. He studied at Seikei Gakuen, where he was taught haiku by Nakamura Kusatao, which would become one of Kato's lifelong hobby. Kato entered University of Tokyo to study physics, where he obtained a BSc degree in 1944. He went on to study under the electron microscopist Ryoji Uyeda at Nagoya University, where he received a MSc in 1946 and a doctoral degree in physics in 1954. In 1950, Kato worked at the Kobayasi Institute of Physical Research (now part of RIKEN) under Shoji Nishikawa. After his PhD, Kato continued working at the Kobayasi institu ...
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Paul Peter Ewald
Paul Peter Ewald, FRS (January23, 1888August22, 1985) was a German crystallographer and physicist, a pioneer of X-ray diffraction methods. Education Ewald received his early education in the classics at the Gymnasium in Berlin and Potsdam, where he learned to speak Greek, French, and English, in addition to his native German.Ewald
– Memorial
Ewald began his higher education in , , and at
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Diffraction
Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the Wave propagation, propagating wave. Diffraction is the same physical effect as Wave interference, interference, but interference is typically applied to superposition of a few waves and the term diffraction is used when many waves are superposed. Italian scientist Francesco Maria Grimaldi coined the word ''diffraction'' and was the first to record accurate observations of the phenomenon in 1660 in science, 1660. In classical physics, the diffraction phenomenon is described by the Huygens–Fresnel principle that treats each point in a propagating wavefront as a collection of individual spherical wavelets. The characteristic pattern is most pronounced when a wave from a Coherence (physics), coherent source (such as a laser) encounters a slit/aperture tha ...
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Beat (acoustics)
In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, ''perceived'' as a periodic variation in volume whose rate is the difference of the two frequencies. With tuning instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a unison will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies as in a tremolo as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. As the two tones get further apart, their beat frequency starts to approach the range of human pitch perception, the beating starts to sound like a note, and a combination tone is produced. Mathematics and physics of beat tones This phenomenon is best known in acoustics or music, though it can be found in ...
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Electromagnetic Radiation
In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ranging from radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. All forms of EMR travel at the speed of light in a vacuum and exhibit wave–particle duality, behaving both as waves and as discrete particles called photons. Electromagnetic radiation is produced by accelerating charged particles such as from the Sun and other celestial bodies or artificially generated for various applications. Its interaction with matter depends on wavelength, influencing its uses in communication, medicine, industry, and scientific research. Radio waves enable broadcasting and wireless communication, infrared is used in thermal imaging, visible light is essential for vision, and higher-energy radiation, such ...
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Crystal Lattice
In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystal, crystalline material. Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that repeat along the principal directions of Three-dimensional space (mathematics), three-dimensional space in matter. The smallest group of particles in a material that constitutes this repeating pattern is the unit cell of the structure. The unit cell completely reflects the symmetry and structure of the entire crystal, which is built up by repetitive Translation (geometry), translation of the unit cell along its principal axes. The translation vectors define the nodes of the Bravais lattice. The lengths of principal axes/edges, of the unit cell and angles between them are lattice constants, also called ''lattice parameters'' or ''cell parameters''. The symmetry properties of a crystal are described by the concept of space groups. All possi ...
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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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Magnesium Oxide
Magnesium oxide (MgO), or magnesia, is a white hygroscopic solid mineral that occurs naturally as periclase and is a source of magnesium (see also oxide). It has an empirical formula of MgO and consists of a lattice of Mg2+ ions and O2− ions held together by ionic bonding. Magnesium hydroxide forms in the presence of water (MgO + H2O → Mg(OH)2), but it can be reversed by heating it to remove moisture. Magnesium oxide was historically known as magnesia alba (literally, the white mineral from Magnesia), to differentiate it from '' magnesia nigra'', a black mineral containing what is now known as manganese. Related oxides While "magnesium oxide" normally refers to MgO, the compound magnesium peroxide MgO2 is also known. According to evolutionary crystal structure prediction, MgO2 is thermodynamically stable at pressures above 116 GPa (gigapascals), and a semiconducting suboxide Mg3O2 is thermodynamically stable above 500 GPa. Because of its stability, MgO is used as a mod ...
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Andrew Richard Lang
Andrew Richard Lang FRS CBE (9 September 1924 – 30 June 2008) was a British scientist and crystallographer. Biography Andrew Lang was the son of Ernest Frederick Stephen Lang, technical engineer with Beyer, Peacock & Company and Susannah C E A Guterbock, a naturalized German citizen. As a child, he suffered from repeated respiratory infections. Although he was accepted for entry to Trinity College, Cambridge, ill health postponed his start, and he went instead to the University College of the South West, now the University of Exeter, in 1942. He graduated two years later with a first class honours external BSc in physics. In February 1945 he started his war-time ‘essential work’ at Unilever Research Laboratories in Cheshire, where he carried out X-ray crystallography on crystals of pure soaps. In addition, part-time study earned him a London University external MSc in 1947. Later that year he took a one-year position at the Cavendish Laboratory and in 1948 started on ...
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Photonic Crystal
A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of Crystal structure, natural crystals gives rise to X-ray crystallography, X-ray diffraction and that the atomic lattices (crystal structure) of semiconductors affect their conductivity of electrons. Photonic crystals occur in nature in the form of structural coloration and animal reflectors, and, as artificially produced, promise to be useful in a range of applications. Photonic crystals can be fabricated for one, two, or three dimensions. One-dimensional photonic crystals can be made of thin film layers deposited on each other. Two-dimensional ones can be made by photolithography, or by drilling holes in a suitable substrate. Fabrication methods for three-dimensional ones include drilling under different angles, stacking multiple 2-D layers on top of each other, direct laser writing, or, for example, instig ...
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Condensed Matter Physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconductivity, superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of Spin (physics), spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theoretical physics, physic ...
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Metamaterials
A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is a type of material engineered to have a property, typically rarely observed in naturally occurring materials, that is derived not from the properties of the base materials but from their newly designed structures. Metamaterials are usually fashioned from multiple materials, such as metals and plastics, and are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Their precise shape, geometry, size, orientation, and arrangement give them their "smart" properties of manipulating electromagnetic, acoustic, or even seismic waves: by blocking, absorbing, enhancing, or bending waves, to achieve benefits that go beyond what is possible with conventional materials. Appropriately designed metamaterials can affect waves of electromagnetic radiation or sound in a manner not ...
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