Polytypism
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Polytypism
Many compound materials exhibit polymorphism, that is they can exist in different structures called polymorphs. Silicon carbide (SiC) is unique in this regard as more than 250 polymorphs of silicon carbide had been identified by 2006, with some of them having a lattice constant as long as 301.5 nm, about one thousand times the usual SiC lattice spacings. The polymorphs of SiC include various amorphous phases observed in thin films and fibers, as well as a large family of similar crystalline structures called polytypes. They are variations of the same chemical compound that are identical in two dimensions and differ in the third. Thus, they can be viewed as layers stacked in a certain sequence. The atoms of those layers can be arranged in three configurations, A, B or C, to achieve closest packing. The stacking sequence of those configurations defines the crystal structure, where the unit cell is the shortest periodically repeated sequence of the stacking sequence. This descrip ...
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Polymorphism (materials Science)
In materials science, polymorphism describes the existence of a solid material in more than one form or crystal structure. Polymorphism is a form of isomerism. Any crystalline material can exhibit the phenomenon. Allotropy refers to polymorphism for chemical elements. Polymorphism is of practical relevance to pharmaceuticals, agrochemicals, pigments, dyestuffs, foods, and explosives. According to IUPAC, a polymorphic transition is "A reversible transition of a solid crystalline phase at a certain temperature and pressure (the inversion point) to another phase of the same chemical composition with a different crystal structure." According to McCrone, polymorphs are "different in crystal structure but identical in the liquid or vapor states." Materials with two polymorphs are called dimorphic, with three polymorphs, trimorphic, etc. Examples Many compounds exhibit polymorphism. It has been claimed that "every compound has different polymorphic forms, and that, in general, the n ...
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Band Gap
In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference (in electron volts) between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. It is the energy required to promote a valence electron bound to an atom to become a conduction electron, which is free to move within the crystal lattice and serve as a charge carrier to conduct electric current. It is closely related to the HOMO/LUMO gap in chemistry. If the valence band is completely full and the conduction band is completely empty, then electrons cannot move within the solid because there are no available states. If the electrons are not free to move within the crystal lattice, then there is no generated current due to no net charge carrier mobility. However, if some electrons transfer from th ...
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Silicon Carbide Fibers
Silicon carbide fibers are fibers ranging from 5 to 150 micrometres in diameter and composed primarily of silicon carbide molecules. Depending on manufacturing process, they may have some excess silicon or carbon, or have a small amount of oxygen. Relative to organic fibers and some ceramic fibers, silicon carbide fibers have high stiffness, high tensile strength, low weight, high chemical resistance, high temperature tolerance and low thermal expansion. (refs) These properties have made silicon carbide fiber the choice for hot section components in the next generation of gas turbines, e.g. the LEAP engine from GE (General Electric). Manufacture There are several manufacturing approaches to making silicon carbide fibers. The one with the longest historical experience, invented in 1975 and called the Yajima process, uses a pre-ceramic liquid polymer that is injected through a spinneret to produce solidified green (unfired) fibers that go through a series of processing steps, inc ...
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Electron Volt
In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. When used as a unit of energy, the numerical value of 1 eV in joules (symbol J) is equivalent to the numerical value of the charge of an electron in coulombs (symbol C). Under the 2019 redefinition of the SI base units, this sets 1 eV equal to the exact value Historically, the electronvolt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences, because a particle with electric charge ''q'' gains an energy after passing through a voltage of ''V.'' Since ''q'' must be an integer multiple of the elementary charge ''e'' for any isolated particle, the gained energy in units of electronvolts conveniently equals that integer times the voltage. It is a common unit of energy within p ...
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Bandgap
In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference (in electron volts) between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. It is the energy required to promote a valence electron bound to an atom to become a conduction electron, which is free to move within the crystal lattice and serve as a charge carrier to conduct electric current. It is closely related to the HOMO/LUMO gap in chemistry. If the valence band is completely full and the conduction band is completely empty, then electrons cannot move within the solid because there are no available states. If the electrons are not free to move within the crystal lattice, then there is no generated current due to no net charge carrier mobility. However, if some electrons transfer from the ...
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Angstrom
The angstromEntry "angstrom" in the Oxford online dictionary. Retrieved on 2019-03-02 from https://en.oxforddictionaries.com/definition/angstrom.Entry "angstrom" in the Merriam-Webster online dictionary. Retrieved on 2019-03-02 from https://www.merriam-webster.com/dictionary/angstrom. (, ; , ) or ångström is a metric unit of length equal to m; that is, one ten-billionth ( US) of a metre, a hundred-millionth of a centimetre,Entry "angstrom" in the Oxford English Dictionary, 2nd edition (1986). Retrieved on 2021-11-22 from https://www.oed.com/oed2/00008552. 0.1 nanometre, or 100 picometres. Its symbol is Å, a letter of the Swedish alphabet. The unit is named after the Swedish physicist Anders Jonas Ångström (1814–1874). The angstrom is often used in the natural sciences and technology to express sizes of atoms, molecules, microscopic biological structures, and lengths of chemical bonds, arrangement of atoms in crystals,Arturas Vailionis (2015):Geometry of Crystals Lect ...
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Pearson Symbol
The Pearson symbol, or Pearson notation, is used in crystallography as a means of describing a crystal structure, and was originated by W. B. Pearson. The symbol is made up of two letters followed by a number. For example: * Diamond structure, ''cF''8 * Rutile structure, ''tP''6 The two (italicised) letters specify the Bravais lattice. The lower-case letter specifies the crystal family, and the upper-case letter the centering type. The number at the end of the Pearson symbol gives the number of the atoms in the conventional unit cell.Nomenclature of Inorganic Chemistry IUPAC Recommendations 2005
IR-3.4.4, pp. 49–51; IR-11.5, pp. 241–242.

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Space Group
In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it unchanged. In three dimensions, space groups are classified into 219 distinct types, or 230 types if chiral copies are considered distinct. Space groups are discrete cocompact groups of isometries of an oriented Euclidean space in any number of dimensions. In dimensions other than 3, they are sometimes called Bieberbach groups. In crystallography, space groups are also called the crystallographic or Fedorov groups, and represent a description of the symmetry of the crystal. A definitive source regarding 3-dimensional space groups is the ''International Tables for Crystallography'' . History Space groups in 2 dimensions are the 17 wallpaper groups which have been known for several centuries, though the proof that the list was complete was only ...
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Lattice Constants
A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal. A simple cubic crystal has only one lattice constant, the distance between atoms, but in general lattices in three dimensions have six lattice constants: the lengths ''a'', ''b'', and ''c'' of the three cell edges meeting at a vertex, and the angles ''α'', ''β'', and ''γ'' between those edges. The crystal lattice parameters ''a'', ''b'', and ''c'' have the dimension of length. The three numbers represent the size of the unit cell, that is, the distance from a given atom to an identical atom in the same position and orientation in a neighboring cell (except for very simple crystal structures, this will not necessarily be disance to the nearest neighbor). Their SI unit is the meter, and they are traditionally specified in angstroms (Å); an angstrom being 0.1 nano ...
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Eicke Weber
Eicke Richard Weber (born 28 October 1949 in Münnerstadt) is a German physicist. Life Scientific activity Weber grew up from 1955 in Cologne, where he also took his Abitur. He studied mathematics and physics at the University of Cologne from 1967. After graduating in 1972, he took on an assistant position at the RWTH Aachen and finished his doctorate in physics in 1976 with the topic ''Point Defects in Deformed Silicon'' and received his Ph.D. His habilitation followed in 1983 with the topic ''Transition Metals in Silicon''. Weber joined the faculty of the Department of Materials Science and Engineering, University of California, Berkeley, first as Assistant in 1983, than Associate and since 2001 as Full Professor, and stayed there for 23 years, until he accepted in 2006 a call from the Fraunhofer society. He spent one research semester each as a visiting professor at Tōhoku-Gakuin University in Sendai, and Kyoto University in Japan. In Berkeley, he served 2004–06 as fou ...
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Rhombohedral
In geometry, a rhombohedron (also called a rhombic hexahedron or, inaccurately, a rhomboid) is a three-dimensional figure with six faces which are rhombus, rhombi. It is a special case of a parallelepiped where all edges are the same length. It can be used to define the rhombohedral lattice system, a Honeycomb (geometry), honeycomb with rhombohedral cells. A cube is a special case of a rhombohedron with all sides square. In general a ''rhombohedron'' can have up to three types of rhombic faces in congruent opposite pairs, ''C''''i'' symmetry, Order (group theory), order 2. Four points forming non-adjacent vertices of a rhombohedron necessarily form the four vertices of an orthocentric tetrahedron, and all orthocentric tetrahedra can be formed in this way. Rhombohedral lattice system The rhombohedral lattice system has rhombohedral cells, with 6 congruent rhombic faces forming a trigonal trapezohedron: : Special cases by symmetry * Cube: with Octahedral symmetry, Oh symm ...
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Hexagonal
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A '' regular hexagon'' has Schläfli symbol and can also be constructed as a truncated equilateral triangle, t, which alternates two types of edges. A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals \tfrac times the apothem (radius of the inscribed circle). All internal angles are 120 degrees. A regular hexagon has six rotational symmetries (''rotational symmetry of order six'') and six reflection symmetries (''six lines of symmetry''), making up the dihedral group D6. The longest diagonals of a regular ...
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