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Coordination Sequence
In crystallography and the theory of infinite vertex-transitive graphs, the coordination sequence of a vertex v is an integer sequence that counts how many vertices are at each possible distance from v. That is, it is a sequence n_0, n_1, n_2,\dots where each n_i is the number of vertices that are i steps away from v. If the graph is vertex-transitive, then the sequence is an Graph property, invariant of the graph that does not depend on the specific choice of v. Coordination sequences can also be defined for sphere packings, by using either the contact graph of the spheres or the Delaunay triangulation of their centers, but these two choices may give rise to different sequences. As an example, in a square grid, for each positive integer i, there are 4i grid points that are i steps away from the origin. Therefore, the coordination sequence of the square grid is the sequence 1,4,8,12,16,20,\dots\ . in which, except for the initial value of one, each number is a multiple of four. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Michael O'Keeffe (chemist)
Michael O’Keeffe (born April 3, 1934) is a British-American chemist. He is currently Regents’ Professor Emeritus in the School of Molecular Sciences at Arizona State University. As a scientist, he is particularly known for his contributions to the field of reticular chemistry. In 2019, he received the Gregori Aminoff Prize in Crystallography from the Royal Swedish Academy of Sciences. Early life and education Michael O’Keeffe was born in Bury St Edmunds, Suffolk, England, on the 3rd April, 1934. He was one of four children born to Dr. E. Joseph O’Keeffe, an immigrant from Ireland, and his mother Marjorie G. O’Keeffe (née Marten). From 1942 to 1951 he attended Prior Park College (Bath) and then from 1951 to 1957 the University of Bristol: B.Sc. in chemistry (1954), Ph.D. (1958, mentor Frank S. Stone). He spent 1958-1959 at Philips Natuurkundig Laboratorium (group of Evert W. Gorter) then did postdoctoral research at Indiana University (mentor Walter J. Moore). 1960 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Zeitschrift Für Kristallographie – Crystalline Materials
''Zeitschrift für Kristallographie – Crystalline Materials'' is a monthly peer-reviewed scientific journal published in English. The journal publishes theoretical and experimental studies in crystallography of both organic and inorganic substances. The editor-in-chief of the journal is from the University of Münster. The journal was founded in 1877 under the title ''Zeitschrift für Krystallographie und Mineralogie'' by crystallographer and mineralogist Paul Heinrich von Groth, who served as the editor for 44 years. It has used several titles over its history, with the present title having been adopted in 2010. The journal is indexed in a variety of databases and has a 2020 impact factor of 1.616. History The journal was established in 1877 by Paul von Groth as a German-language publication under the title ''Zeitschrift für Krystallographie und Mineralogie'', and he served as its editor until the end of 1920. Groth was appointed as the inaugural Professor of Mineralogy at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acta Crystallographica Section A
''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 portf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The Royal Society A
''Proceedings of the Royal Society'' is the main research journal of the Royal Society. The journal began in 1831 and was split into two series in 1905: * Series A: for papers in physical sciences and mathematics. * Series B: for papers in life sciences. Many landmark scientific discoveries are published in the Proceedings, making it one of the most historically significant science journals. The journal contains several articles written by the most celebrated names in science, such as Paul Dirac, Werner Heisenberg, Ernest Rutherford, Erwin Schrödinger, William Lawrence Bragg, Lord Kelvin, J.J. Thomson, James Clerk Maxwell, Dorothy Hodgkin and Stephen Hawking. In 2004, the Royal Society began ''The Journal of the Royal Society Interface'' for papers at the interface of physical sciences and life sciences. History The journal began in 1831 as a compilation of abstracts of papers in the ''Philosophical Transactions of the Royal Society'', the older Royal Society publication, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Solid State Chemistry
The ''Journal of Solid State Chemistry'' is a monthly peer-reviewed scientific journal published by Elsevier. The journal covers the chemical, structural, thermodynamic, electronic, and electromagnetic characteristics and properties of solids, including ceramics and amorphous materials. The editor-in-chief is M.G. Kanatzidis ( Northwestern University). Abstracting and indexing This journal is abstracted and indexed by: * BioEngineering Abstracts * Chemical Abstracts Service * Coal Abstracts - International Energy Agency * Current Contents/Physics, Chemical, & Earth Sciences * Engineering Index Ei Compendex is an engineering bibliographic database published by Elsevier. The name "Compendex" stands for COMPuterized ENgineering inDEX. It covers scientific literature pertaining to engineering materials. It started in 1884 under the ... * Science Abstracts * Science Citation Index According to the '' Journal Citation Reports'', the journal has a 2020 impact fac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Tiling
In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive. Uniform tilings can exist in both the Euclidean plane and hyperbolic plane. Uniform tilings are related to the finite uniform polyhedra which can be considered uniform tilings of the sphere. Most uniform tilings can be made from a Wythoff construction starting with a symmetry group and a singular generator point inside of the fundamental domain. A planar symmetry group has a polygonal fundamental domain and can be represented by the group name represented by the order of the mirrors in sequential vertices. A fundamental domain triangle is (''p'' ''q'' ''r''), and a right triangle (''p'' ''q'' 2), where ''p'', ''q'', ''r'' are whole numbers greater than 1. The triangle may exist as a spherical triangle, a Euclidean plane triangle, or a hyperbolic plane triangle, depending on the values of ''p'', ''q'' and ''r''. There are a number of symbolic sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fritz Laves
Fritz Henning Emil Paul Berndt Laves (27 February 1906 – 12 August 1978) was a German crystallographer who served as the president of the German Mineralogical Society from 1956 to 1958. He is the namesake of Laves phases and the Laves tilings; the Laves graph, a highly-symmetrical three-dimensional crystal structure that he studied, was named after him by H. S. M. Coxeter. Education and career Laves was born in Hanover, the son of a judge and the great-grandson of architect Georg Ludwig Friedrich Laves. He grew up in Göttingen, where his interests included piano music as well as collecting rocks and minerals. He began his university studies in geology in 1924 at the University of Innsbruck, and continued at the University of Göttingen before moving to ETH Zurich for doctoral studies under Paul Niggli. In 1929 he took a faculty position under Victor Goldschmidt at Göttingen. He tried unsuccessfully to prevent Goldschmidt from being dismissed in 1933, and later had difficul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertex-transitive Graph
In the mathematical field of graph theory, a vertex-transitive graph is a graph in which, given any two vertices and of , there is some automorphism :f : G \to G\ such that :f(v_1) = v_2.\ In other words, a graph is vertex-transitive if its automorphism group acts transitively on its vertices.. A graph is vertex-transitive if and only if its graph complement is, since the group actions are identical. Every symmetric graph without isolated vertices is vertex-transitive, and every vertex-transitive graph is regular. However, not all vertex-transitive graphs are symmetric (for example, the edges of the truncated tetrahedron), and not all regular graphs are vertex-transitive (for example, the Frucht graph and Tietze's graph). Finite examples Finite vertex-transitive graphs include the symmetric graphs (such as the Petersen graph, the Heawood graph and the vertices and edges of the Platonic solids). The finite Cayley graphs (such as cube-connected cycles) are also ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Grid
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of meaning it has 4 squares around every vertex. Conway called it a quadrille. The internal angle of the square is 90 degrees so four squares at a point make a full 360 degrees. It is one of three regular tilings of the plane. The other two are the triangular tiling and the hexagonal tiling. Uniform colorings There are 9 distinct uniform colorings of a square tiling. Naming the colors by indices on the 4 squares around a vertex: 1111, 1112(i), 1112(ii), 1122, 1123(i), 1123(ii), 1212, 1213, 1234. (i) cases have simple reflection symmetry, and (ii) glide reflection symmetry. Three can be seen in the same symmetry domain as reduced colorings: 1112i from 1213, 1123i from 1234, and 1112ii reduced from 1123ii. Related polyhedra and tilings This tiling is topologically related as a part of sequence of regular polyhedra and tilings, extending ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distance Countours In A Square Grid
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). Since spatial cognition is a rich source of conceptual metaphors in human thought, the term is also frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation (as exemplified by distance between people in a social network). Most such notions of distance, both physical and metaphorical, are formalized in mathematics using the notion of a metric space. In the social sciences, distance can refer to a qualitative measurement of separation, such as social distance or psychological distance. Distances in physics and geometry The distance between physica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
