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Magnetic Space Group
In solid state physics, the magnetic space groups, or Shubnikov groups, are the symmetry groups which classify the symmetries of a crystal both in space, and in a two-valued property such as electron spin. To represent such a property, each lattice point is colored black or white, and in addition to the usual three-dimensional symmetry operations, there is a so-called "antisymmetry" operation which turns all black lattice points white and all white lattice points black. Thus, the magnetic space groups serve as an extension to the crystallographic space groups which describe spatial symmetry alone. The application of magnetic space groups to crystal structures is motivated by Curie's Principle. Compatibility with a material's symmetries, as described by the magnetic space group, is a necessary condition for a variety of material properties, including ferromagnetism, ferroelectricity, topological insulation. History A major step was the work of Heinrich Heesch, who first rigorousl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid State Physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale properties. Thus, solid-state physics forms a theoretical basis of materials science. It also has direct applications, for example in the technology of transistors and semiconductors. Background Solid materials are formed from densely packed atoms, which interact intensely. These interactions produce the mechanical (e.g. hardness and elasticity), thermal, electrical, magnetic and optical properties of solids. Depending on the material involved and the conditions in which it was formed, the atoms may be arranged in a regular, geometric pattern ( crystalline solids, which include metals and ordinary water ice) or irregularly (an amorphous solid such as common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Index Of A Subgroup
In mathematics, specifically group theory, the index of a subgroup ''H'' in a group ''G'' is the number of left cosets of ''H'' in ''G'', or equivalently, the number of right cosets of ''H'' in ''G''. The index is denoted , G:H, or :H/math> or (G:H). Because ''G'' is the disjoint union of the left cosets and because each left coset has the same size as ''H'', the index is related to the orders of the two groups by the formula :, G, = , G:H, , H, (interpret the quantities as cardinal numbers if some of them are infinite). Thus the index , G:H, measures the "relative sizes" of ''G'' and ''H''. For example, let G = \Z be the group of integers under addition, and let H = 2\Z be the subgroup consisting of the even integers. Then 2\Z has two cosets in \Z, namely the set of even integers and the set of odd integers, so the index , \Z:2\Z, is 2. More generally, , \Z:n\Z, = n for any positive integer ''n''. When ''G'' is finite, the formula may be written as , G:H, = , G, /, H, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PG C2'
PG or P.G. may refer to: *Parental Guidance (PG), a content rating in motion picture content rating systems and television content rating systems *Paying Guest (PG), also called homestay, a type of accommodation Businesses and organisations * P.G. Cigars, a cigar brand named after Paul Garmirian * PG Tips, a British brand of tea * Bangkok Airways, a Thai regional airline, IATA airline designator PG * Procter & Gamble (P&G), an American multi-national consumer goods corporation * Left Party (France) (''Parti de gauche''), a French democratic socialist political party * Partido Galeguista (1931), a Galician nationalist political party in Galicia, Spain * Partido Galeguista (1978), a Galician nationalist political party in Galicia, Spain *Peoples Gazette, a Nigerian online newspaper * PlatinumGames, a Japanese video game developer * Porter-Gaud School, Charleston, South Carolina, U.S. People * PG, student in a postgraduate year after high school (secondary school) * P.G., Brazili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PG C2
PG or P.G. may refer to: *Parental Guidance (PG), a content rating in motion picture content rating systems and television content rating systems *Paying Guest (PG), also called homestay, a type of accommodation Businesses and organisations * P.G. Cigars, a cigar brand named after Paul Garmirian * PG Tips, a British brand of tea * Bangkok Airways, a Thai regional airline, IATA airline designator PG * Procter & Gamble (P&G), an American multi-national consumer goods corporation * Left Party (France) (''Parti de gauche''), a French democratic socialist political party * Partido Galeguista (1931), a Galician nationalist political party in Galicia, Spain * Partido Galeguista (1978), a Galician nationalist political party in Galicia, Spain *Peoples Gazette, a Nigerian online newspaper * PlatinumGames, a Japanese video game developer * Porter-Gaud School, Charleston, South Carolina, U.S. People * PG, student in a postgraduate year after high school (secondary school) * P.G., Bra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PG Ci'
PG or P.G. may refer to: *Parental Guidance (PG), a content rating in motion picture content rating systems and television content rating systems *Paying Guest (PG), also called homestay, a type of accommodation Businesses and organisations * P.G. Cigars, a cigar brand named after Paul Garmirian * PG Tips, a British brand of tea * Bangkok Airways, a Thai regional airline, IATA airline designator PG * Procter & Gamble (P&G), an American multi-national consumer goods corporation * Left Party (France) (''Parti de gauche''), a French democratic socialist political party * Partido Galeguista (1931), a Galician nationalist political party in Galicia, Spain * Partido Galeguista (1978), a Galician nationalist political party in Galicia, Spain *Peoples Gazette, a Nigerian online newspaper * PlatinumGames, a Japanese video game developer * Porter-Gaud School, Charleston, South Carolina, U.S. People * PG, student in a postgraduate year after high school (secondary school) * P.G., Bra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PG C1
PG or P.G. may refer to: *Parental Guidance (PG), a content rating in motion picture content rating systems and television content rating systems *Paying Guest (PG), also called homestay, a type of accommodation Businesses and organisations * P.G. Cigars, a cigar brand named after Paul Garmirian * PG Tips, a British brand of tea * Bangkok Airways, a Thai regional airline, IATA airline designator PG * Procter & Gamble (P&G), an American multi-national consumer goods corporation * Left Party (France) (''Parti de gauche''), a French democratic socialist political party * Partido Galeguista (1931), a Galician nationalist political party in Galicia, Spain * Partido Galeguista (1978), a Galician nationalist political party in Galicia, Spain *Peoples Gazette, a Nigerian online newspaper * PlatinumGames, a Japanese video game developer * Porter-Gaud School, Charleston, South Carolina, U.S. People * PG, student in a postgraduate year after high school (secondary school) * P.G., Bra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stereographic Projection
In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the ''pole'' or ''center of projection''), onto a plane (geometry), plane (the ''projection plane'') perpendicular to the diameter through the point. It is a smooth function, smooth, bijection, bijective function (mathematics), function from the entire sphere except the center of projection to the entire plane. It maps circle of a sphere, circles on the sphere to generalised circle, circles or lines on the plane, and is conformal map, conformal, meaning that it preserves angles at which curves meet and thus Local property, locally approximately preserves similarity (geometry), shapes. It is neither isometry, isometric (distance preserving) nor Equiareal map, equiareal (area preserving). The stereographic projection gives a way to representation (mathematics), represent a sphere by a plane. The metric tensor, metric induced metric, induced by the inverse s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Piezoelectricity
Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word ''piezoelectricity'' means electricity resulting from pressure and latent heat. It is derived from the Greek word ; ''piezein'', which means to squeeze or press, and ''ēlektron'', which means amber, an ancient source of electric charge. The piezoelectric effect results from the linear electromechanical interaction between the mechanical and electrical states in crystalline materials with no inversion symmetry. The piezoelectric effect is a reversible process: materials exhibiting the piezoelectric effect also exhibit the reverse piezoelectric effect, the internal generation of a mechanical strain resulting from an applied electrical field. For example, lead zirconate titanate crystals will generate measurable piezoelectricity when their ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetoelectric Effect
In its most general form, the magnetoelectric effect (ME) denotes any coupling between the magnetic and the electric properties of a material. The first example of such an effect was described by Wilhelm Röntgen in 1888, who found that a dielectric material moving through an electric field would become magnetized. A material where such a coupling is intrinsically present is called a magnetoelectric. Historically, the first and most studied example of this effect is the linear magnetoelectric effect. Mathematically, while the electric susceptibility \chi^e and magnetic susceptibility \chi^v describe the electric and magnetic polarization responses to an electric, resp. a magnetic field, there is also the possibility of a magnetoelectric susceptibility \alpha_ which describes a linear response of the electric polarization to a magnetic field, and vice versa: :P_i= \sum_j \epsilon_0\chi^e_ E_ + \sum_j \alpha_H_j :\mu_0 M_i= \sum_j \mu_0\chi^v_H_ + \sum_j \alpha_E_j, The tensor \alpha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toroidal Moment
A toroidal moment is an independent term in the multipole expansion of electromagnetic fields besides magnetic and electric multipoles. In the electrostatic multipole expansion, all charge and current distributions can be expanded into a complete set of electric and magnetic multipole coefficients. However, additional terms arise in an electrodynamic multipole expansion. The coefficients of these terms are given by the toroidal multipole moments as well as time derivatives of the electric and magnetic multipole moments. While electric dipoles can be understood as separated charges and magnetic dipoles as circular currents, axial (or electric) toroidal dipoles describes toroidal charge arrangements whereas polar (or magnetic) toroidal dipole (also called anapole) correspond to the field of a solenoid bent into a torus. Classical toroidal dipole moment A complex expression allows the current density J to be written as a sum of electric, magnetic, and toroidal moments using Cart ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polar Point Group
In geometry, a polar point group is a point group in which there is more than one point that every symmetry operation leaves unmoved. The unmoved points will constitute a line, a plane, or all of space. While the simplest point group, C1, leaves all points invariant, most polar point groups will move some, but not all points. To describe the points which are unmoved by the symmetry operations of the point group, we draw a straight line joining two unmoved points. This line is called a polar direction. The electric polarization must be parallel to a polar direction. In polar point groups of high symmetry, the polar direction can be a unique axis of rotation, but if the symmetry operations do not allow any rotation at all, such as mirror symmetry, there can be an infinite number of such axes: in that case the only restriction on the polar direction is that it must be parallel to any mirror planes. A point group with more than one axis of rotation or with a mirror plane perpendicular ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystallographic Point Group
In crystallography, a crystallographic point group is a set of symmetry operations, corresponding to one of the point groups in three dimensions, such that each operation (perhaps followed by a translation) would leave the structure of a crystal unchanged i.e. the same kinds of atoms would be placed in similar positions as before the transformation. For example, in many crystals in the cubic crystal system, a rotation of the unit cell by 90 degrees around an axis that is perpendicular to one of the faces of the cube is a symmetry operation that moves each atom to the location of another atom of the same kind, leaving the overall structure of the crystal unaffected. In the classification of crystals, each point group defines a so-called (geometric) crystal class. There are infinitely many three-dimensional point groups. However, the crystallographic restriction on the general point groups results in there being only 32 crystallographic point groups. These 32 point groups are one-and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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