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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 (waves), 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 reflection (physics), 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 coordinate space, 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 Euclidean vector, vectors \textbf and \text ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Crystallography
Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the Ancient Greek word (; "clear ice, rock-crystal"), and (; "to write"). In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming 2014 the International Year of Crystallography.UN announcement "International Year of Crystallography" iycr2014.org. 12 July 2012 Crystallography is a broad topic, and many of its subareas, such as X-ray crystallography, are themselves important scientific topics. Crystallography ranges from the fundamentals of crystal structure to the mathematics of Crystal system, crystal geometry, including those that are Aperiodic crystal, not periodic or quasi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Intensity (physics)
In physics and many other areas of science and engineering the intensity or flux of radiant energy is the Power (physics), 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 kilogram, kg⋅second, s−3 in SI base unit, base units. Intensity is used most frequently with waves such as acoustic waves (sound), matter waves such as electrons in electron microscopes, and electromagnetic waves such as light or radio waves, in which case the time averaging, ''average'' power transfer over one Period (physics), 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 "wikt:strength, strength", "wikt:amplitude, amplitude ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Herbert A
Herbert may refer to: People * Herbert (musician), a pseudonym of Matthew Herbert * 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, a character in the Charles Dickens novel ''Great Expectations'' * Herbert West ... [...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 ... [...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) 1950 * * ''Statistical Methods Applied to Experiments in Agriculture and Biology'' by George W. Snedecor (Cochran contributed from the fifth (1956) edition) * ''Planning and Analysis of Observational Studies'' (edited by Lincoln E. Moses and Frederick Mosteller Charles Frederick Mosteller (December 24, 1916 – July 23, 2 ... [...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 po ... [...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 is ... [...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 ... [...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 x 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 colloquial, ordinary language, an average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean the sum of the numbers divided by how many numbers are in the list. For example, the mean or average of the numbers 2, 3, 4, 7, and 9 (summing to 25) is 5. Depending on the context, the most representative statistics, statistic to be taken as the average might be another measure of central tendency, such as the mid-range, median, Mode (statistics), mode or geometric mean. For example, the average income, 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. 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 o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Wave Function
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter), psi, respectively). Wave functions are complex number, complex-valued. For example, a wave function might assign a complex number to each point in a region of space. The Born rule provides the means to turn these complex probability amplitudes into actual probabilities. In one common form, it says that the squared modulus of a wave function that depends upon position is the probability density function, probability density of measurement in quantum mechanics, measuring a particle as being at a given place. The integral of a wavefunction's squared modulus over all the system's degrees of freedom must be equal to 1, a condition called ''normalization''. Since the wave function is complex-valued, only its relative phase and relative magnitud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |