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Cation-anion Radius Ratio
Anions are larger than cations. Large sized anions occupy lattice sites, while small sized cations are found in voids. The ratio of radius of cation to anion is called radius ratio. In condensed matter physics and inorganic chemistry the cation-anion radius ratio (also: radius ratio rule) is the ratio of the ionic radius of the cation to the ionic radius of the anion in a cation-anion compound. This is simply given by r_ / r_. According to Pauling's rules for crystal structures, the allowed size of the cation for a given structure is determined by the critical radius ratio. If the cation is too small, then it will attract the anions into each other and they will collide hence the compound will be unstable due to anion-anion repulsion; this occurs when the radius ratio drops below 0.155. At the stability limit the cation is touching all the anions and the anions are just touching at their edges (radius ratio = 0.155). For radius ratios greater than 0.155, the compound may be sta ...
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Boron Trioxide
Boron trioxide or diboron trioxide is the oxide of boron with the formula . It is a colorless transparent solid, almost always glassy (amorphous), which can be crystallized only with great difficulty. It is also called boric oxide or boria. It has many important industrial applications, chiefly in ceramics as a flux for glazes and enamels and in the production of glasses. Structure Boron trioxide has three known forms, one amorphous and two crystalline. Amorphous form The amorphous form (g-) is by far the most common. It is thought to be composed of boroxol rings which are six-membered rings composed of alternating 3-coordinate boron and 2-coordinate oxygen. Because of the difficulty of building disordered models at the correct density with many boroxol rings, this view was initially controversial, but such models have recently been constructed and exhibit properties in excellent agreement with experiment. It is now recognized, from experimental and theoretical studies, that ...
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Inorganic Chemistry
Inorganic chemistry deals with synthesis and behavior of inorganic and organometallic compounds. This field covers chemical compounds that are not carbon-based, which are the subjects of organic chemistry. The distinction between the two disciplines is far from absolute, as there is much overlap in the subdiscipline of organometallic chemistry. It has applications in every aspect of the chemical industry, including catalysis, materials science, pigments, surfactants, coatings, medications, fuels, and agriculture. Key concepts Many inorganic compounds are ionic compounds, consisting of cations and anions joined by ionic bonding. Examples of salts (which are ionic compounds) are magnesium chloride MgCl2, which consists of magnesium cations Mg2+ and chloride anions Cl−; or sodium oxide Na2O, which consists of sodium cations Na+ and oxide anions O2−. In any salt, the proportions of the ions are such that the electric charges cancel out, so that the bulk compound is e ...
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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'' ...
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Face-centered Cubic
In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of these crystals: *Primitive cubic (abbreviated ''cP'' and alternatively called simple cubic) *Body-centered cubic (abbreviated ''cI'' or bcc) *Face-centered cubic (abbreviated ''cF'' or fcc, and alternatively called ''cubic close-packed'' or ccp) Each is subdivided into other variants listed below. Although the ''unit cells'' in these crystals are conventionally taken to be cubes, the primitive unit cells often are not. Bravais lattices The three Bravais lattices in the cubic crystal system are: The primitive cubic lattice (cP) consists of one lattice point on each corner of the cube; this means each simple cubic unit cell has in total one lattice point. Each atom at a lattice point is then shared equally between eight adjacent cubes, ...
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Victor Goldschmidt
Victor Moritz Goldschmidt (27 January 1888 in Zürich – 20 March 1947 in Oslo) was a Norwegian mineralogist considered (together with Vladimir Vernadsky) to be the founder of modern geochemistry and crystal chemistry, developer of the Goldschmidt Classification of elements. Early life and education Goldschmidt was born in Zürich, Switzerland on 27 January 1888. His father, Heinrich Jacob Goldschmidt, (1857–1937) was a physical chemist at the Eidgenössisches Polytechnikum and his mother, Amelie Koehne (1864–1929), was the daughter of a lumber merchant. They named him Viktor after a colleague of Heinrich, Victor Meyer. His father's family was Jewish back to at least 1600 and mostly highly educated, with rabbis, judges, lawyers and military officers among their numbers. As his father's career progressed, the family moved first to Amsterdam in 1893, to Heidelberg in 1896, and finally to Kristiania (later Oslo), Norway in 1901, where he took over the physical chemis ...
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Cubic Crystal System
In crystallography, the cubic (or isometric) crystal system is a crystal system where the Crystal_structure#Unit_cell, unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of these crystals: *Primitive cubic (abbreviated ''cP'' and alternatively called simple cubic) *Body-centered cubic (abbreviated ''cI'' or bcc) *Face-centered cubic (abbreviated ''cF'' or fcc, and alternatively called Close-packing_of_equal_spheres, ''cubic close-packed'' or ccp) Each is subdivided into other variants listed below. Although the ''unit cells'' in these crystals are conventionally taken to be cubes, the primitive_cell, primitive unit cells often are not. Bravais lattices The three Bravais lattices in the cubic crystal system are: The primitive cubic lattice (cP) consists of one Lattice_(group), lattice point on each corner of the cube; this means each simple cubic unit cell has in total one latt ...
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Octahedron
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. A regular octahedron is the dual polyhedron of a cube. It is a rectified tetrahedron. It is a square bipyramid in any of three orthogonal orientations. It is also a triangular antiprism in any of four orientations. An octahedron is the three-dimensional case of the more general concept of a cross polytope. A regular octahedron is a 3-ball in the Manhattan () metric. Regular octahedron Dimensions If the edge length of a regular octahedron is ''a'', the radius of a circumscribed sphere (one that touches the octahedron at all vertices) is :r_u = \frac a \approx 0.707 \cdot a and the radius of an inscribed sphere (tangent to each of the octahedron's faces) is :r_i = \frac a \approx 0.408\cdot a while the midradius, which ...
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Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces. The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid". Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. It has two such nets. For any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and another sphere ...
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Journal Of Chemical Education
The ''Journal of Chemical Education'' is a monthly peer-reviewed academic journal available in both print and electronic versions. It is published by the Division of Chemical Education of the American Chemical Society and was established in 1924 by Neil Gordon. The journal covers research on chemical education Chemistry education (or chemical education) is the study of teaching and learning chemistry. It is one subset of STEM education or discipline-based education research (DBER). Topics in chemistry education include understanding how students learn ..., and its target audience includes instructors of chemistry from middle school through graduate school and some scientists in commerce, industry, and government. References External links * Chemical education journals American Chemical Society academic journals Monthly journals Publications established in 1924 English-language journals {{chemistry-journal-stub ...
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Condensed Matter Physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the subject deals with "condensed" phases of matter: systems of many constituents with strong interactions between them. More exotic condensed phases include the superconducting phase exhibited by certain materials at low temperature, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, and the Bose–Einstein condensate found in ultracold atomic systems. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theories to develop mathematical models. The diversity of systems and phenomena available for study makes condensed matter phy ...
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Coordination Number
In chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central ion/molecule/atom is called a ligand. This number is determined somewhat differently for molecules than for crystals. For molecules and polyatomic ions the coordination number of an atom is determined by simply counting the other atoms to which it is bonded (by either single or multiple bonds). For example, r(NH3)2Cl2Br2sup>− has Cr3+ as its central cation, which has a coordination number of 6 and is described as ''hexacoordinate''. The common coordination numbers are 4, 6 and 8. Molecules, polyatomic ions and coordination complexes In chemistry, coordination number, defined originally in 1893 by Alfred Werner, is the total number of neighbors of a central atom in a molecule or ion. The concept is most commonly applied to coordin ...
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