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Homometric Structures
In chemistry and crystallography, crystal structures that have the same set of interatomic distances are called homometric structures. Homometric structures need not be congruent (that is, related by a rigid motion or reflection). Homometric crystal structures produce identical diffraction patterns; therefore, they cannot be distinguished by a diffraction experiment. Recently, a Monte Carlo algorithm was proposed to calculate the number of homometric structures corresponding to any given set of interatomic distances. Image:homometric1.png, Example of two homometric structures (top) formed by the convolution between two non-centrosymmetric structures (bottom) with different orientations. See also * Patterson function * Arthur Lindo Patterson Notes [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemistry
Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a Chemical reaction, reaction with other Chemical substance, substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology. It is sometimes called the central science because it provides a foundation for understanding both Basic research, basic and Applied science, applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth (botany), the formation of igneous rocks (geology), how atmospheric ozone is formed and how environmental pollutants are degraded (ecology), the properties ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Patterson Function
The Patterson function is used to solve the phase problem in X-ray crystallography. It was introduced in 1935 by Arthur Lindo Patterson while he was a visiting researcher in the laboratory of Bertram Eugene Warren at MIT. The Patterson function is defined as :P(u,v,w) = \sum\limits_ \left, F_\^2 \;e^. It is essentially the Fourier transform of the intensities rather than the structure factors. The Patterson function is also equivalent to the electron density convolved with its inverse: :P\left(\vec\right) = \rho\left(\vec\right) * \rho\left(-\vec\right). Furthermore, a Patterson map of ''N'' points will have peaks, excluding the central (origin) peak and any overlap. The peaks' positions in the Patterson function are the interatomic distance vectors and the peak heights are proportional to the product of the number of electrons in the atoms concerned. Because for each vector between atoms ''i'' and ''j'' there is an oppositely oriented vector of the same length (between atoms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Lindo Patterson
Arthur Lindo Patterson (23 July 1902, Nelson, New Zealand - 6 November 1966, Philadelphia, Pennsylvania) was a pioneering British X-ray crystallographer. Patterson was born to British parents in New Zealand in 1902. Shortly afterwards the family moved to Montreal, Canada and later to London, England. In 1920 Patterson moved to Canada for college at McGill University, Montreal. Firstly he concentrated on Mathematics and but then changed his major to Physics. He received his bachelor's degree in 1923 and a master's in 1924. His master's thesis was on the production of hard X-rays by interaction of radium β rays with solids. From 1924 to 1926 he worked in London in the laboratory of W. H. Bragg, where he learnt the art of crystal structure analysis. In 1926 Patterson moved to the Kaiser Wilhelm Institute for Fibrous Materials Chemistry (later the Fritz Haber Institute) in the Dahlem neighbourhood of Berlin, where he worked on the X-ray crystallography of cellulose fibres. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
