Allotropes Of Boron
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Allotropes Of Boron
Boron can be prepared in several crystalline and amorphous forms. Well known crystalline forms are α-rhombohedral (α-R), β-rhombohedral (β-R), and β-tetragonal (β-T). In special circumstances, boron can also be synthesized in the form of its α-tetragonal (α-T) and γ-orthorhombic (γ) allotropes. Two amorphous forms, one a finely divided powder and the other a glassy solid, are also known. Although at least 14 more allotropes have been reported, these other forms are based on tenuous evidence or have not been experimentally confirmed, or are thought to represent mixed allotropes, or boron frameworks stabilized by impurities. Whereas the β-rhombohedral phase is the most stable and the others are metastable, the transformation rate is negligible at room temperature, and thus all five phases can exist at ambient conditions. Amorphous powder boron and polycrystalline β-rhombohedral boron are the most common forms. The latter allotrope is a very hardVickers hardness comparab ...
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Crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification. The word ''crystal'' derives from the Ancient Greek word (), meaning both "ice" and "rock crystal", from (), "icy cold, frost". Examples of large crystals include snowflakes, diamonds, and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Polycrystals include most metals, rocks, ceramics, and ice. A third category of ...
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Tungsten
Tungsten, or wolfram, is a chemical element with the symbol W and atomic number 74. Tungsten is a rare metal found naturally on Earth almost exclusively as compounds with other elements. It was identified as a new element in 1781 and first isolated as a metal in 1783. Its important ores include scheelite and wolframite, the latter lending the element its alternate name. The free element is remarkable for its robustness, especially the fact that it has the highest melting point of all known elements barring carbon (which sublimes at normal pressure), melting at . It also has the highest boiling point, at . Its density is , comparable with that of uranium and gold, and much higher (about 1.7 times) than that of lead. Polycrystalline tungsten is an intrinsically brittle and hard material (under standard conditions, when uncombined), making it difficult to work. However, pure single-crystalline tungsten is more ductile and can be cut with a hard-steel hacksaw. Tungsten occurs in many ...
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Boron Carbides
Boron carbides are boron–carbon compounds. Boron carbide (B4C) B13C2 α-tetragonal boron α-tetragonal boron is a boron-rich isotropic boron carbide (B50C2). Borafullerenes Borafullerenes are a class of heterofullerenes in which the element substituting for carbon is boron. See also * Crystal structure of boron-rich metal borides Metals, and specifically rare-earth elements, form numerous chemical complexes with boron. Their crystal structure and chemical bonding depend strongly on the metal element M and on its atomic ratio to boron. When B/M ratio exceeds 12, boron atom ... References Sources * * * * {{boron compounds Inorganic carbon compounds Boron compounds ...
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Cubic Honeycomb
The cubic honeycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb) in Euclidean 3-space made up of cubic cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its vertex figure is a regular octahedron. It is a self-dual tessellation with Schläfli symbol . John Horton Conway called this honeycomb a cubille. Related honeycombs It is part of a multidimensional family of hypercube honeycombs, with Schläfli symbols of the form , starting with the square tiling, in the plane. It is one of 28 uniform honeycombs using convex uniform polyhedral cells. Isometries of simple cubic lattices Simple cubic lattices can be distorted into lower symmetries, represented by lower crystal systems: Uniform colorings There is a large number of uniform colorings, derived from different symmetries. These include: Projections The ''cubic honeycomb'' can be orthogonally projected into the euclidean plane with various symmetr ...
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Covalent
A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding. For many molecules, the sharing of electrons allows each atom to attain the equivalent of a full valence shell, corresponding to a stable electronic configuration. In organic chemistry, covalent bonding is much more common than ionic bonding. Covalent bonding also includes many kinds of interactions, including σ-bonding, π-bonding, metal-to-metal bonding, agostic interactions, bent bonds, three-center two-electron bonds and three-center four-electron bonds. The term ''covalent bond'' dates from 1939. The prefix ''co-'' means ''jointly, associated in action, partnered to a lesser degree, '' etc.; thus a "co-valent bond", in essence, means that the atoms share " valence", such a ...
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Carbonado
Carbonado, commonly known as black diamond, is one of the toughest forms of natural diamond. It is an impure, high-density, micro-porous form of polycrystalline diamond consisting of diamond, graphite, and amorphous carbon, with minor crystalline precipitates filling pores and occasional reduced metal inclusions. It is found primarily in alluvial deposits where it is most prominent in mid-elevation equatorial regions such as Central African Republic and in Brazil, where the vast majority of carbonado diamondites have been found. Its natural colour is black or dark grey, and it is more porous than other diamonds. Unusual properties Carbonado diamonds are typically pea-sized or larger porous aggregates of many tiny black crystals. The most characteristic carbonados are mined in the Central African Republic and in Brazil, in neither place associated with kimberlite, the source of typical gem diamonds. Lead isotope analyses have been interpreted as documenting crystallization of c ...
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Conchoidal Fracture
Conchoidal fracture describes the way that brittle materials break or fracture when they do not follow any natural planes of separation. Mindat.org defines conchoidal fracture as follows: "a fracture with smooth, curved surfaces, typically slightly concave, showing concentric undulations resembling the lines of growth of a shell".Conchoidal fracture
at Mindat.org
Materials that break in this way include , ,

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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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Bulk Modulus
The bulk modulus (K or B) of a substance is a measure of how resistant to compression the substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting ''relative'' decrease of the volume. Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear stress, and Young's modulus describes the response to normal (lengthwise stretching) stress. For a fluid, only the bulk modulus is meaningful. For a complex anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law. The reciprocal of the bulk modulus at fixed temperature is called the isothermal compressibility. Definition The bulk modulus K (which is usually positive) can be formally defined by the equation :K=-V\frac , where P is pressure, V is the initial volume of the substance, and dP/dV denotes the derivative of ...
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Tetragonal
In crystallography, the tetragonal crystal system is one of the 7 crystal systems. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (''a'' by ''a'') and height (''c'', which is different from ''a''). Bravais lattices There are two tetragonal Bravais lattices: the primitive tetragonal and the body-centered tetragonal. The base-centered tetragonal lattice is equivalent to the primitive tetragonal lattice with a smaller unit cell, while the face-centered tetragonal lattice is equivalent to the body-centered tetragonal lattice with a smaller unit cell. Crystal classes The point groups that fall under this crystal system are listed below, followed by their representations in international notation, Schoenflies notation, orbifold notation, Coxeter notation and mineral examples.Hurlbut, Cornelius S.; Klein, Cornelis, 1985, ''Manual of Mineralogy'', 20th ed., p ...
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Orthorhombic
In crystallography, the orthorhombic crystal system is one of the 7 crystal systems. Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with a rectangular base (''a'' by ''b'') and height (''c''), such that ''a'', ''b'', and ''c'' are distinct. All three bases intersect at 90° angles, so the three lattice vectors remain mutually orthogonal. Bravais lattices There are four orthorhombic Bravais lattices: primitive orthorhombic, base-centered orthorhombic, body-centered orthorhombic, and face-centered orthorhombic. For the base-centered orthorhombic lattice, the primitive cell has the shape of a right rhombic prism;See , row oC, column Primitive, where the cell parameters are given as a1 = a2, α = β = 90° it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. Note that the length a of the primit ...
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