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Direct Methods (electron Microscopy)
In crystallography, direct methods is a set of techniques used for structure determination using diffraction data and ''a priori'' information. It is a solution to the crystallographic phase problem, where phase information is lost during a diffraction measurement. Direct methods provides a method of estimating the phase information by establishing statistical relationships between the recorded amplitude information and phases of strong reflections. Background Phase Problem In electron diffraction, a diffraction pattern is produced by the interaction of the electron beam and the crystal potential. The real space and reciprocal space information about a crystal structure can be related through the Fourier transform relationships shown below, where f(\textbf) is in real space and corresponds to the crystal potential, and F(\textbf) is its Fourier transform in reciprocal space. The vectors \textbf and \textbf are position vectors in real and reciprocal space, respectively. : f( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Crystallography
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The word "crystallography" is derived from the Greek word κρύσταλλος (''krystallos'') "clear ice, rock-crystal", with its meaning extending to all solids with some degree of transparency, and γράφειν (''graphein'') "to write". In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming that 2014 would be the International Year of Crystallography. denote a direction vector (in real space). * Coordinates in ''angle brackets'' or ''chevrons'' such as <100> denote a ''family'' of directions which are related by symmetry operations. In the cubic crystal system for example, would mean 00 10 01/nowiki> or the negative of any of those directions. * Miller indices in ''parentheses ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Intensity (physics)
In physics, the intensity or flux of radiant energy is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy. In the SI system, it has units watts per square metre (W/m2), or kg⋅ s−3 in base units. Intensity is used most frequently with waves such as acoustic waves (sound) or electromagnetic waves such as light or radio waves, in which case the ''average'' power transfer over one period of the wave is used. ''Intensity'' can be applied to other circumstances where energy is transferred. For example, one could calculate the intensity of the kinetic energy carried by drops of water from a garden sprinkler. The word "intensity" as used here is not synonymous with " strength", "amplitude", " magnitude", or " level", as it sometimes is in colloquial speech. Intensity can be found by taking the energy density (energy per unit volume) at a point in space and multiplying it by the velocity at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Herbert A
Herbert may refer to: People Individuals * Herbert (musician), a pseudonym of Matthew Herbert Name * Herbert (given name) * Herbert (surname) Places Antarctica * Herbert Mountains, Coats Land * Herbert Sound, Graham Land Australia * Herbert, Northern Territory, a rural locality * Herbert, South Australia. former government town * Division of Herbert, an electoral district in Queensland * Herbert River, a river in Queensland * County of Herbert, a cadastral unit in South Australia Canada * Herbert, Saskatchewan, Canada, a town * Herbert Road, St. Albert, Canada New Zealand * Herbert, New Zealand, a town * Mount Herbert (New Zealand) United States * Herbert, Illinois, an unincorporated community * Herbert, Michigan, a former settlement * Herbert Creek, a stream in South Dakota * Herbert Island, Alaska Arts, entertainment, and media Fictional entities * Herbert (Disney character) * Herbert Pocket (''Great Expectations'' character), Pip's close friend and roommat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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William Houlder Zachariasen
William Houlder Zachariasen (5 February 1906 – 24 December 1979), more often known as W. H. Zachariasen, was a Norwegian-American physicist, specializing in X-ray crystallography and famous for his work on the structure of glass. Background Zachariasen was born in Langesund at Bamble in Telemark, Norway. He entered the University of Oslo in 1923, where he studied in the Mineralogical Institute. Zachariasen published his first article in 1925 when he was 19 years old, after having presented the contents of the article to the Norwegian Academy of Sciences in the preceding year. Over a span of 55 years he published over 200 scientific papers, many of which he was the sole author. In 1928 at the age of 22 he earned his PhD from the University of Oslo, becoming the youngest person ever to receive a PhD in Norway. His thesis advisor was the famous geochemist Victor Moritz Goldschmidt. In the years 1928–1929, as a postdoctoral fellow at Manchester University in the laboratory of Si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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William Gemmell Cochran
William Gemmell Cochran (15 July 1909 – 29 March 1980) was a prominent statistician. He was born in Scotland but spent most of his life in the United States. Cochran studied mathematics at the University of Glasgow and the University of Cambridge. He worked at Rothamsted Experimental Station from 1934 to 1939, when he moved to the United States. There he helped establish several departments of statistics. His longest spell in any one university was at Harvard, which he joined in 1957 and from which he retired in 1976. Writings Cochran wrote many articles and books. His books became standard texts: * ''Experimental Designs'' (with Gertrude Mary Cox Gertrude Mary Cox (January 13, 1900 – October 17, 1978) was an American statistician and founder of the department of Experimental Statistics at North Carolina State University. She was later appointed director of both the Institute of Statistic ...) 1950 * * ''Statistical Methods Applied to Experiments in Agriculture and Bio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Acta Crystallographica
''Acta Crystallographica'' is a series of peer-reviewed scientific journals, with articles centred on crystallography, published by the International Union of Crystallography (IUCr). Originally established in 1948 as a single journal called ''Acta Crystallographica'', there are now six independent ''Acta Crystallographica'' titles: *'' Acta Crystallographica Section A: Foundations and Advances'' *'' Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials'' *'' Acta Crystallographica Section C: Structural Chemistry'' *'' Acta Crystallographica Section D: Structural Biology'' *'' Acta Crystallographica Section E: Crystallographic Communications'' *'' Acta Crystallographica Section F: Structural Biology Communications'' ''Acta Crystallographica'' has been noted for the high quality of the papers that it produces, as well as the large impact that its papers have had on the field of crystallography. The current six journals form part of the journal port ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Sayre Equation
In crystallography, the Sayre equation, named after David Sayre who introduced it in 1952, is a mathematical relationship that allows one to calculate probable values for the phases of some diffracted beams. It is used when employing direct methods to solve a structure. Its formulation is the following: F_ = \sum_ F_F_ which states how the structure factor for a beam can be calculated as the sum of the products of pairs of structure factors whose indices sum to the desired values of h,k,l. Since weak diffracted beams will contribute a little to the sum, this method can be a powerful way of finding the phase of related beams, if some of the initial phases are already known by other methods. In particular, for three such related beams in a centrosymmetric structure, the phases can only be 0 or \pi and the Sayre equation reduces to the triplet relationship: S_ \approx S_ S_ where the S indicates the sign of the structure factor (positive if the phase is 0 and negative if it i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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David Sayre
David Sayre (March 2, 1924 – February 23, 2012) was an American scientist, credited with the early development of direct methods for protein crystallography and of diffraction microscopy (also called coherent diffraction imaging). While working at IBM he was part of the initial team of ten programmers who created FORTRAN, and later suggested the use of electron beam lithography for the fabrication of X-ray Fresnel zone plates. The International Union of Crystallography awarded Sayre the Ewald Prize in 2008 for the "unique breadth of his contributions to crystallography, which range from seminal contributions to the solving of the phase problem to the complex physics of imaging generic objects by X-ray diffraction and microscopy(...)". Life and career Sayre was born in New York City. He completed his bachelor's degree in physics at Yale University at the age of 19. After working at the MIT Radiation Laboratory, he earned his MS degree at Auburn University in 1948. In 194 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Absolute Value
In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), and For example, the absolute value of 3 and the absolute value of −3 is The absolute value of a number may be thought of as its distance from zero. Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts. Terminology and notation In 1806, Jean-Robert Argand introduced the term ''module'', meaning ''unit of measure'' in French, specifically for the ''complex'' absolute value, Oxford English Dictionary, Draft Revision, Ju ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Average
In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, and 9 (summing to 25) is 5. Depending on the context, an average might be another statistic such as the median, or mode. For example, the average personal income is often given as the median—the number below which are 50% of personal incomes and above which are 50% of personal incomes—because the mean would be higher by including personal incomes from a few billionaires. For this reason, it is recommended to avoid using the word "average" when discussing measures of central tendency. General properties If all numbers in a list are the same number, then their average is also equal to this number. This property is shared by each of the many types of average. Another universal property is monotonicity: if two lists of numbers ''A'' a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Exponential Function
The exponential function is a mathematical function denoted by f(x)=\exp(x) or e^x (where the argument is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all real arguments, including irrational numbers. Its ubiquitous occurrence in pure and applied mathematics led mathematician Walter Rudin to opine that the exponential function is "the most important function in mathematics". The exponential function satisfies the exponentiation identity e^ = e^x e^y \text x,y\in\mathbb, which, along with the definition e = \exp(1), shows that e^n=\underbrace_ for posi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Wave Function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi, respectively). The wave function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. Once such a representation is chosen, the wave function can be derived from the quantum state. For a given system, the choice of which commuting degrees of freedom to use is not unique, and correspondingly the domain of the wave function is also not unique. For instance, it may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space; the two are related by a Fourier ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |