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Magic Angle (EELS)
The magic angle is a particular value of the collection angle of an electron microscope at which the measured energy-loss spectrum "magically" becomes independent of the tilt angle of the sample with respect to the beam direction. The magic angle is not uniquely defined for isotropic samples, but the definition is unique in the (typical) case of small angle scattering on materials with a "c-axis", such as graphite. The "magic" angle depends on both the incoming electron energy (which is typically fixed) and the energy loss suffered by the electron. The ratio of the magic angle \theta_M to the characteristic angle \theta_E is roughly independent of the energy loss and roughly independent of the particular type of sample considered. Mathematical definition For the case of a relativistic incident electron, the "magic" angle is defined by the equality of two different functions (denoted below by A and C) of the collection angle \alpha: A(\alpha)=\frac\int_0^dx\frac and C(\al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Microscope
An electron microscope is a microscope that uses a beam of accelerated electrons as a source of illumination. As the wavelength of an electron can be up to 100,000 times shorter than that of visible light photons, electron microscopes have a higher resolving power than light microscopes and can reveal the structure of smaller objects. A scanning transmission electron microscope has achieved better than 50 pm resolution in annular dark-field imaging mode and magnifications of up to about 10,000,000× whereas most light microscopes are limited by diffraction to about 200 nm resolution and useful magnifications below 2000×. Electron microscopes use shaped magnetic fields to form electron optical lens systems that are analogous to the glass lenses of an optical light microscope. Electron microscopes are used to investigate the ultrastructure of a wide range of biological and inorganic specimens including microorganisms, cells, large molecules, biopsy samples, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Beam
Cathode rays or electron beam (e-beam) are streams of electrons observed in discharge tubes. If an evacuated glass tube is equipped with two electrodes and a voltage is applied, glass behind the positive electrode is observed to glow, due to electrons emitted from the cathode (the electrode connected to the negative terminal of the voltage supply). They were first observed in 1859 by German physicist Julius Plücker and Johann Wilhelm Hittorf, and were named in 1876 by Eugen Goldstein ''Kathodenstrahlen'', or cathode rays. In 1897, British physicist J. J. Thomson showed that cathode rays were composed of a previously unknown negatively charged particle, which was later named the ''electron''. Cathode-ray tubes (CRTs) use a focused beam of electrons deflected by electric or magnetic fields to render an image on a screen. Description Cathode rays are so named because they are emitted by the negative electrode, or cathode, in a vacuum tube. To release electrons into the tube, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isotrope
Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence '' anisotropy''. ''Anisotropy'' is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. Mathematics Within mathematics, ''isotropy'' has a few different meanings: ; Isotropic manifolds: A manifold is isotropic if the geometry on the manifold is the same regardless of direction. A similar concept is homogeneity. ; Isotropic quadratic form: A quadratic form ''q'' is said to be isotropic if there is a non-zero vector ''v'' such that ; such a ''v'' is an isotropic vector or null vector. In complex geometry, a line through the origin in the direction of an isotropic vector is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphite
Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on large scale (300 kton/year, in 1989) for uses in pencils, lubricants, and electrodes. Under high pressures and temperatures it converts to diamond. It is a weak conductor of heat and electricity. Types and varieties Natural graphite The principal types of natural graphite, each occurring in different types of ore deposits, are * Crystalline small flakes of graphite (or flake graphite) occurs as isolated, flat, plate-like particles with hexagonal edges if unbroken. When broken the edges can be irregular or angular; * Amorphous graphite: very fine flake graphite is sometimes called amorphous; * Lump graphite (or vein graphite) occurs in fissure veins or fractures and appears as massive platy intergrowths of fibrous or acicular crystalline ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum ( spin) of a half-integer value, expressed in units of the reduced Planck constant, . Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: They can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7). The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be Positive integer, positive. A ratio may be specified either by giving both constituting numbers, written as "''a'' to ''b''" or "''a'':''b''", or by giving just the value of their quotient Equal quotients correspond to equal ratios. Consequently, a ratio may be considered as an ordered pair of numbers, a Fraction (mathematics), fraction with the first number in the numerator and the second in the denom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Relativity
The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. It applies to the cosmological and astrophysical realm, including astronomy. The theory transformed theoretical physics and astronomy during the 20th century, superseding a 200-year-old Classical mechanics, theory of mechanics created primarily by Isaac Newton. It introduced concepts including 4-dimensional spacetime as a unified entity of space and time in physics, time, relativity of simultaneity, kinematics, kinematic and gravity, gravitational time dilation, and length contraction. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, along with ushering in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speed Of Light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space. All forms of electromagnetic radiation, including visible light, travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects. Starlight viewed on Earth left the stars many years ago, allowing humans to study the history of the universe by viewing distant objects. When communicating with distant space probes, it can take minutes to hours for signals to travel from Earth to the spacecraft and vice versa. In computing, the speed of light fixes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., an integral assigns numbers to functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with Derivative, differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Function
In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, including possibly their inverse functions (e.g., arcsin, log, or ''x''1/''n''). All elementary functions are continuous on their domains. Elementary functions were introduced by Joseph Liouville in a series of papers from 1833 to 1841. An algebraic treatment of elementary functions was started by Joseph Fels Ritt in the 1930s. Examples Basic examples Elementary functions of a single variable include: * Constant functions: 2,\ \pi,\ e, etc. * Rational powers of : x,\ x^2,\ \sqrt\ (x^\frac),\ x^\frac, etc. * more general algebraic functions: f(x) satisfying f(x)^5+f(x)+x=0, which is not expressible through n-th roots or rational powers of alone * Exponential functions: e^x, \ a^x * Logarithms: \ln x, \ \log_a x ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Momentum Transfer
In particle physics, wave mechanics and optics, momentum transfer is the amount of momentum that one particle gives to another particle. It is also called the scattering vector as it describes the transfer of wavevector in wave mechanics. In the simplest example of scattering of two colliding particles with initial momenta \vec_,\vec_, resulting in final momenta \vec_,\vec_, the momentum transfer is given by : \vec q = \vec_ - \vec_ = \vec_ - \vec_ where the last identity expresses momentum conservation. Momentum transfer is an important quantity because \Delta x = \hbar / , q, is a better measure for the typical distance resolution of the reaction than the momenta themselves. Wave mechanics and optics A wave has a momentum p = \hbar k and is a vectorial quantity. The difference of the momentum of the scattered wave to the incident wave is called ''momentum transfer''. The wave number k is the absolute of the wave vector k = p / \hbar and is related to the wavelength k = 2\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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