1.
Fullerene
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A fullerene is a molecule of carbon in the form of a hollow sphere, ellipsoid, tube, and many other shapes. Spherical fullerenes, also referred to as Buckminsterfullerenes, resemble the balls used in football, cylindrical fullerenes are also called carbon nanotubes. Fullerenes are similar in structure to graphite, which is composed of stacked sheets of linked hexagonal rings. The name was an homage to Buckminster Fuller, whose geodesic domes it resembles, the structure was also identified some five years earlier by Sumio Iijima, from an electron microscope image, where it formed the core of a bucky onion. Fullerenes have since found to occur in nature. More recently, fullerenes have been detected in outer space, according to astronomer Letizia Stanghellini, It’s possible that buckyballs from outer space provided seeds for life on Earth. The discovery of fullerenes greatly expanded the number of carbon allotropes, which until recently were limited to graphite, graphene, diamond. The icosahedral C60H60 cage was mentioned in 1965 as a topological structure. Eiji Osawa of Toyohashi University of Technology predicted the existence of C60 in 1970 and he noticed that the structure of a corannulene molecule was a subset of an Association football shape, and he hypothesised that a full ball shape could also exist. Japanese scientific journals reported his idea, but neither it nor any translations of it reached Europe or the Americas, also in 1970, R. W. Henson proposed the structure and made a model of C60. Unfortunately, the evidence for new form of carbon was very weak and was not accepted. The results were never published but were acknowledged in Carbon in 1999, in 1973 independently from Henson, a group of scientists from the USSR, directed by Prof. Bochvar, made a quantum-chemical analysis of the stability of C60 and calculated its electronic structure. As in the cases, the scientific community did not accept the theoretical prediction. The paper was published in 1973 in Proceedings of the USSR Academy of Sciences, in mass spectrometry discrete peaks appeared corresponding to molecules with the exact mass of sixty or seventy or more carbon atoms. Kroto, Curl, and Smalley were awarded the 1996 Nobel Prize in Chemistry for their roles in the discovery of this class of molecules, C60 and other fullerenes were later noticed occurring outside the laboratory. By 1990 it was easy to produce gram-sized samples of fullerene powder using the techniques of Donald Huffman, Wolfgang Krätschmer, Lowell D. Lamb. Fullerene purification remains a challenge to chemists and to a large extent determines fullerene prices, so-called endohedral fullerenes have ions or small molecules incorporated inside the cage atoms. Fullerene is a reactant in many organic reactions such as the Bingel reaction discovered in 1993
2.
Carbon
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Carbon is a chemical element with symbol C and atomic number 6. It is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds, three isotopes occur naturally, 12C and 13C being stable, while 14C is a radioactive isotope, decaying with a half-life of about 5,730 years. Carbon is one of the few elements known since antiquity, Carbon is the 15th most abundant element in the Earths crust, and the fourth most abundant element in the universe by mass after hydrogen, helium, and oxygen. It is the second most abundant element in the body by mass after oxygen. The atoms of carbon can bond together in different ways, termed allotropes of carbon, the best known are graphite, diamond, and amorphous carbon. The physical properties of carbon vary widely with the allotropic form, for example, graphite is opaque and black while diamond is highly transparent. Graphite is soft enough to form a streak on paper, while diamond is the hardest naturally occurring material known, graphite is a good electrical conductor while diamond has a low electrical conductivity. Under normal conditions, diamond, carbon nanotubes, and graphene have the highest thermal conductivities of all known materials, all carbon allotropes are solids under normal conditions, with graphite being the most thermodynamically stable form. They are chemically resistant and require high temperature to react even with oxygen, the most common oxidation state of carbon in inorganic compounds is +4, while +2 is found in carbon monoxide and transition metal carbonyl complexes. The largest sources of carbon are limestones, dolomites and carbon dioxide, but significant quantities occur in organic deposits of coal, peat, oil. For this reason, carbon has often referred to as the king of the elements. The allotropes of carbon graphite, one of the softest known substances, and diamond. It bonds readily with other small atoms including other carbon atoms, Carbon is known to form almost ten million different compounds, a large majority of all chemical compounds. Carbon also has the highest sublimation point of all elements, although thermodynamically prone to oxidation, carbon resists oxidation more effectively than elements such as iron and copper that are weaker reducing agents at room temperature. Carbon is the element, with a ground-state electron configuration of 1s22s22p2. Its first four ionisation energies,1086.5,2352.6,4620.5 and 6222.7 kJ/mol, are higher than those of the heavier group 14 elements. Carbons covalent radii are normally taken as 77.2 pm,66.7 pm and 60.3 pm, although these may vary depending on coordination number, in general, covalent radius decreases with lower coordination number and higher bond order. Carbon compounds form the basis of all life on Earth
3.
Hexagon
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In geometry, a hexagon is a six sided polygon or 6-gon. The total of the angles of any hexagon is 720°. A regular hexagon has Schläfli symbol and can also be constructed as an equilateral triangle, t. A regular hexagon is defined as a hexagon that is both equilateral and equiangular and it is bicentric, meaning that it is both cyclic and tangential. The common length of the sides equals the radius of the circumscribed circle, all internal angles are 120 degrees. A regular hexagon has 6 rotational symmetries and 6 reflection symmetries, the longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side. Like squares and equilateral triangles, regular hexagons fit together without any gaps to tile the plane, the cells of a beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of space and building materials. The Voronoi diagram of a triangular lattice is the honeycomb tessellation of hexagons. It is not usually considered a triambus, although it is equilateral, the maximal diameter, D is twice the maximal radius or circumradius, R, which equals the side length, t. The minimal diameter or the diameter of the circle, d, is twice the minimal radius or inradius. If a regular hexagon has successive vertices A, B, C, D, E, F, the regular hexagon has Dih6 symmetry, order 12. There are 3 dihedral subgroups, Dih3, Dih2, and Dih1, and 4 cyclic subgroups, Z6, Z3, Z2 and these symmetries express 9 distinct symmetries of a regular hexagon. John Conway labels these by a letter and group order, r12 is full symmetry, and a1 is no symmetry. These two forms are duals of each other and have half the order of the regular hexagon. The i4 forms are regular hexagons flattened or stretched along one symmetry direction and it can be seen as an elongated rhombus, while d2 and p2 can be seen as horizontally and vertically elongated kites. G2 hexagons, with sides parallel are also called hexagonal parallelogons. Each subgroup symmetry allows one or more degrees of freedom for irregular forms, only the g6 subgroup has no degrees of freedom but can seen as directed edges. Hexagons of symmetry g2, i4, and r12, as parallelogons can tessellate the Euclidean plane by translation, other hexagon shapes can tile the plane with different orientations
4.
Pentagon
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In geometry, a pentagon is any five-sided polygon or 5-gon. The sum of the angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting, a self-intersecting regular pentagon is called a pentagram. A regular pentagon has Schläfli symbol and interior angles are 108°, a regular pentagon has five lines of reflectional symmetry, and rotational symmetry of order 5. The diagonals of a regular pentagon are in the golden ratio to its sides. The area of a regular convex pentagon with side length t is given by A = t 225 +1054 =5 t 2 tan 4 ≈1.720 t 2. A pentagram or pentangle is a regular star pentagon and its sides form the diagonals of a regular convex pentagon – in this arrangement the sides of the two pentagons are in the golden ratio. The area of any polygon is, A =12 P r where P is the perimeter of the polygon. Substituting the regular pentagons values for P and r gives the formula A =12 ×5 t × t tan 2 =5 t 2 tan 4 with side length t, like every regular convex polygon, the regular convex pentagon has an inscribed circle. The apothem, which is the r of the inscribed circle. Like every regular polygon, the regular convex pentagon has a circumscribed circle. For a regular pentagon with successive vertices A, B, C, D, E, the regular pentagon is constructible with compass and straightedge, as 5 is a Fermat prime. A variety of methods are known for constructing a regular pentagon, one method to construct a regular pentagon in a given circle is described by Richmond and further discussed in Cromwells Polyhedra. The top panel shows the construction used in Richmonds method to create the side of the inscribed pentagon, the circle defining the pentagon has unit radius. Its center is located at point C and a midpoint M is marked halfway along its radius and this point is joined to the periphery vertically above the center at point D. Angle CMD is bisected, and the bisector intersects the axis at point Q. A horizontal line through Q intersects the circle at point P, to determine the length of this side, the two right triangles DCM and QCM are depicted below the circle. Using Pythagoras theorem and two sides, the hypotenuse of the triangle is found as 5 /2
5.
Graphite
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Graphite, archaically referred to as plumbago, is a crystalline form of carbon, a semimetal, a native element mineral, and one of the allotropes of carbon. Graphite is the most stable form of carbon under standard conditions, therefore, it is used in thermochemistry as the standard state for defining the heat of formation of carbon compounds. Highly ordered pyrolytic graphite or more correctly highly oriented pyrolytic graphite refers to graphite with a spread between the graphite sheets of less than 1°. The name graphite fiber is sometimes used to refer to carbon fibers or carbon fiber-reinforced polymer. Graphite occurs in rocks as a result of the reduction of sedimentary carbon compounds during metamorphism. It also occurs in rocks and in meteorites. Minerals associated with graphite include quartz, calcite, micas and tourmaline, in meteorites it occurs with troilite and silicate minerals. Small graphitic crystals in meteoritic iron are called cliftonite, Graphite is not mined in the United States, but U. S. production of synthetic graphite in 2010 was 134 kt valued at $1.07 billion. Graphite has a layered, planar structure, the individual layers are called graphene. In each layer, the atoms are arranged in a honeycomb lattice with separation of 0.142 nm. Atoms in the plane are bonded covalently, with three of the four potential bonding sites satisfied. The fourth electron is free to migrate in the plane, making graphite electrically conductive, however, it does not conduct in a direction at right angles to the plane. Bonding between layers is via weak van der Waals bonds, which allows layers of graphite to be easily separated, the two known forms of graphite, alpha and beta, have very similar physical properties, except for that the graphene layers stack slightly differently. The alpha graphite may be flat or buckled. The alpha form can be converted to the form through mechanical treatment. The acoustic and thermal properties of graphite are highly anisotropic, since phonons propagate quickly along the tightly-bound planes, graphites high thermal stability and electrical and thermal conductivity facilitate its widespread use as electrodes and refractories in high temperature material processing applications. However, in oxygen containing atmospheres graphite readily oxidizes to form CO2 at temperatures of 700 °C, Graphite is an electric conductor, consequently, useful in such applications as arc lamp electrodes. It can conduct electricity due to the vast electron delocalization within the carbon layers and these valence electrons are free to move, so are able to conduct electricity
6.
Carbon nanotube
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Carbon nanotubes are allotropes of carbon with a cylindrical nanostructure. These cylindrical carbon molecules have unusual properties, which are valuable for nanotechnology, electronics, optics and other fields of materials science and technology. Owing to the exceptional strength and stiffness, nanotubes have been constructed with length-to-diameter ratio of up to 132,000,000,1. In addition, owing to their thermal conductivity, mechanical. For instance, nanotubes form a portion of the material in some baseball bats, golf clubs. Nanotubes are members of the fullerene structural family and their name is derived from their long, hollow structure with the walls formed by one-atom-thick sheets of carbon, called graphene. Nanotubes are categorized as single-walled nanotubes and multi-walled nanotubes, individual nanotubes naturally align themselves into ropes held together by van der Waals forces, more specifically, pi-stacking. Applied quantum chemistry, specifically, orbital hybridization best describes chemical bonding in nanotubes, the chemical bonding of nanotubes is composed entirely of sp2 bonds, similar to those of graphite. These bonds, which are stronger than the sp3 bonds found in alkanes and diamond, most single-walled nanotubes have a diameter of close to 1 nanometer, and can be many millions of times longer. The structure of a SWNT can be conceptualized by wrapping a one-atom-thick layer of graphite called graphene into a seamless cylinder, the way the graphene sheet is wrapped is represented by a pair of indices. The integers n and m denote the number of unit vectors along two directions in the crystal lattice of graphene. If m =0, the nanotubes are called zigzag nanotubes, and if n = m, the diameter of an ideal nanotube can be calculated from its indices as follows d = a π =78.3 p m, where a =0.246 nm. SWNTs are an important variety of carbon nanotube because most of their properties change significantly with the values, in particular, their band gap can vary from zero to about 2 eV and their electrical conductivity can show metallic or semiconducting behavior. Single-walled nanotubes are likely candidates for miniaturizing electronics, the most basic building block of these systems is the electric wire, and SWNTs with diameters of an order of a nanometer can be excellent conductors. One useful application of SWNTs is in the development of the first intermolecular field-effect transistors, the first intermolecular logic gate using SWCNT FETs was made in 2001. A logic gate requires both a p-FET and an n-FET, because SWNTs are p-FETs when exposed to oxygen and n-FETs otherwise, it is possible to expose half of an SWNT to oxygen and protect the other half from it. The resulting SWNT acts as a not logic gate with both p and n-type FETs in the same molecule, prices for single-walled nanotubes declined from around $1500 per gram as of 2000 to retail prices of around $50 per gram of as-produced 40–60% by weight SWNTs as of March 2010. As of 2016 the retail price of as-produced 75% by weight SWNTs were $2 per gram, SWNTs are forecast to make a large impact in electronics applications by 2020 according to the The Global Market for Carbon Nanotubes report
7.
Carbide-derived carbon
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Carbide-derived carbon, also known as tunable nanoporous carbon, is the common term for carbon materials derived from carbide precursors, such as binary, or ternary carbides, also known as MAX phases. CDCs have also derived from polymer-derived ceramics such as Si-O-C or Ti-C. CDCs can occur in structures, ranging from amorphous to crystalline carbon, from sp2- to sp3-bonded. Among carbon materials, microporous CDCs exhibit some of the highest reported specific surface areas, by varying the type of the precursor and the CDC synthesis conditions, microporous and mesoporous structures with controllable average pore size and pore size distributions can be produced. Depending on the precursor and the conditions, the average pore size control can be applied at sub-Angstrom accuracy. The production of SiCl4 by high temperature reaction of Chlorine gas with Silicon Carbide was first patented in 1918 by Otis Hutchins, the solid porous carbon product was initially regarded as a waste byproduct until its properties and potential applications were investigated in more detail in 1959 by Walter Mohun. Most recently, research activities have centered on optimized CDC synthesis, historically, various terms have been used for CDC, such as mineral carbon or nanoporous carbon. Later, a more adequate nomenclature introduced by Yury Gogotsi was adopted that clearly denotes the precursor, for example, CDC derived from silicon carbide has been referred to as SiC-CDC, Si-CDC, or SiCDC. Recently, it was recommended to adhere to a unified precursor-CDC-nomenclature to reflect the composition of the precursor. CDCs have been synthesized using several chemical and physical synthesis methods, most commonly, dry chlorine treatment is used to selectively etch metal or metalloid atoms from the carbide precursor lattice. The term chlorine treatment is to be preferred over chlorination as the product, metal chloride, is the discarded byproduct. This method is implemented for commercial production of CDC by Skeleton in Estonia, hydrothermal etching has also been used for synthesis of SiC-CDC which yielded a route for porous carbon films and nanodiamond synthesis. The most common method for producing porous carbide-derived carbons involves high-temperature etching with halogens, temperatures above 1000 °C result in predominantly graphitic carbon and an observed shrinkage of the material due to graphitization. The linear growth rate of the carbon product phase suggests a reaction-driven kinetic mechanism. A high mass transport condition facilitates the removal of the chloride, most produced CDCs exhibit a prevalence of micropores and mesopores, with specific distributions affected by carbide precursor and synthesis conditions. Hierarchic porosity can be achieved by using polymer-derived ceramics with or without utilizing a templating method, templating yields an ordered array of mesopores in addition to the disordered network of micropores. It has been shown that the crystal structure of the carbide is the primary factor affecting the CDC porosity. In general, a spacing between carbon atoms in the lattice correlates with an increase in the average pore diameter
8.
Activated carbon
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Activated carbon, also called activated charcoal, is a form of carbon processed to have small, low-volume pores that increase the surface area available for adsorption or chemical reactions. Activated is sometimes substituted with active, due to its high degree of microporosity, just one gram of activated carbon has a surface area in excess of 3,000 m2, as determined by gas adsorption. An activation level sufficient for useful application may be attained solely from high surface area, activated carbon is usually derived from charcoal and is sometimes utilized as biochar. Those derived from coal and coke are referred as activated coal, one major industrial application involves use of activated carbon in the metal finishing field. It is very widely employed for purification of electroplating solutions, for example, it is a main purification technique for removing organic impurities from bright nickel plating solutions. A variety of chemicals are added to plating solutions for improving their deposit qualities and for enhancing properties like brightness, smoothness, ductility. Due to passage of current and electrolytic reactions of anodic oxidation and cathodic reduction. Their excessive build up can adversely affect the quality and physical properties of deposited metal. Activated carbon treatment removes such impurities and restores plating performance to the desired level, activated carbon is used to treat poisonings and overdoses following oral ingestion. Tablets or capsules of activated carbon are used in countries as an over-the-counter drug to treat diarrhea, indigestion. However, it is ineffective for a number of poisonings including strong acids or alkali, cyanide, iron, lithium, arsenic, incorrect application results in pulmonary aspiration, which can sometimes be fatal if immediate medical treatment is not initiated. During early implementation of the 1974 Safe Drinking Water Act in the USA, activated carbon is also used for the measurement of radon concentration in air. Activated carbon is a substance used by organic farmers in both livestock production and wine making. In livestock production it is used as a pesticide, animal feed additive, processing aid, benefits in case of animal feed additive are questionable. In organic winemaking, activated carbon is allowed for use as an agent to absorb brown color pigments from white grape concentrates. Activated carbon filters can be used to filter vodka and whiskey of organic impurities which can affect color, taste, research is being done testing various activated carbons ability to store natural gas and hydrogen gas. The porous material acts like a sponge for different types of gases, the gas is attracted to the carbon material via Van der Waals forces. Some carbons have been able to achieve bonding energies of 5–10 kJ per mol, the gas may then be desorbed when subjected to higher temperatures and either combusted to do work or in the case of hydrogen gas extracted for use in a hydrogen fuel cell
9.
Chromatography
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Chromatography is a laboratory technique for the separation of a mixture. The mixture is dissolved in a called the mobile phase. The various constituents of the mixture travel at different speeds, causing them to separate, the separation is based on differential partitioning between the mobile and stationary phases. Subtle differences in a partition coefficient result in differential retention on the stationary phase. Chromatography may be preparative or analytical, the purpose of preparative chromatography is to separate the components of a mixture for later use, and is thus a form of purification. Analytical chromatography is done normally with smaller amounts of material and is for establishing the presence or measuring the proportions of analytes in a mixture. The two are not mutually exclusive, Chromatography was first employed in Russia by the Italian-born scientist Mikhail Tsvet in 1900. He continued to work with chromatography in the first decade of the 20th century, primarily for the separation of plant pigments such as chlorophyll, carotenes, since these components have different colors they gave the technique its name. New types of chromatography developed during the 1930s and 1940s made the technique useful for separation processes. Since then, the technology has advanced rapidly, researchers found that the main principles of Tsvets chromatography could be applied in many different ways, resulting in the different varieties of chromatography described below. Advances are continually improving the performance of chromatography, allowing the separation of increasingly similar molecules. The analyte is the substance to be separated during chromatography and it is also normally what is needed from the mixture. Analytical chromatography is used to determine the existence and possibly also the concentration of analyte in a sample, a bonded phase is a stationary phase that is covalently bonded to the support particles or to the inside wall of the column tubing. A chromatogram is the output of the chromatograph. In the case of a separation, different peaks or patterns on the chromatogram correspond to different components of the separated mixture. Plotted on the x-axis is the time and plotted on the y-axis a signal corresponding to the response created by the analytes exiting the system. In the case of a system the signal is proportional to the concentration of the specific analyte separated. A chromatograph is equipment that enables a sophisticated separation, e. g. gas chromatographic or liquid chromatographic separation, Chromatography is a physical method of separation that distributes components to separate between two phases, one stationary, the other moving in a definite direction
10.
Allotropes of carbon
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Carbon is capable of forming many allotropes due to its valency. Well-known forms of carbon include diamond and graphite, in recent decades many more allotropes and forms of carbon have been discovered and researched including ball shapes such as buckminsterfullerene and sheets such as graphene. Larger scale structures of carbon nanotubes, nanobuds and nanoribbons. Other unusual forms of carbon exist at high temperatures or extreme pressures. Around 350 hypotetical 3-periodic allotropes of carbon are known at the present time according to SACADA database, Diamond is a well known allotrope of carbon. The hardness and high dispersion of light of diamond make it useful for industrial applications and jewelry. Diamond is the hardest known natural mineral and this makes it an excellent abrasive and makes it hold polish and luster extremely well. No known naturally occurring substance can cut a diamond, except another diamond, the market for industrial-grade diamonds operates much differently from its gem-grade counterpart. Industrial diamonds are valued mostly for their hardness and heat conductivity, making many of the characteristics of diamond, including clarity and color. This helps explain why 80% of mined diamonds are unsuitable for use as gemstones, the dominant industrial use of diamond is in cutting, drilling, grinding, and polishing. Most uses of diamonds in these technologies do not require large diamonds, in fact, diamonds are embedded in drill tips or saw blades, or ground into a powder for use in grinding and polishing applications. Specialized applications include use in laboratories as containment for high pressure experiments, high-performance bearings, with the continuing advances being made in the production of synthetic diamond, future applications are beginning to become feasible. Garnering much excitement is the use of diamond as a semiconductor suitable to build microchips from. Each carbon atom in a diamond is covalently bonded to four other carbons in a tetrahedron and these tetrahedrons together form a 3-dimensional network of six-membered carbon rings, in the chair conformation, allowing for zero bond angle strain. This stable network of covalent bonds and hexagonal rings, is the reason that diamond is so strong.1 kJ/mol compared to graphite, graphite, named by Abraham Gottlob Werner in 1789, from the Greek γράφειν is one of the most common allotropes of carbon. Unlike diamond, graphite is an electrical conductor, thus, it can be used in, for instance, electrical arc lamp electrodes. Likewise, under conditions, graphite is the most stable form of carbon. Therefore, it is used in thermochemistry as the state for defining the heat of formation of carbon compounds
11.
Graphene
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Graphene is an allotrope of carbon in the form of a two-dimensional, atomic-scale, hexagonal lattice in which one atom forms each vertex. It is the structural element of other allotropes, including graphite, charcoal. It can be considered as a large aromatic molecule, the ultimate case of the family of flat polycyclic aromatic hydrocarbons. It is about 200 times stronger than the strongest steel and it efficiently conducts heat and electricity and is nearly transparent. Graphene shows a large and nonlinear diamagnetism, greater than graphite, scientists have theorized about graphene for years. It has unintentionally been produced in small quantities for centuries, through the use of pencils and it was originally observed in electron microscopes in 1962, but it was studied only while supported on metal surfaces. The material was later rediscovered, isolated, and characterized in 2004 by Andre Geim, research was informed by existing theoretical descriptions of its composition, structure, and properties. This work resulted in the two winning the Nobel Prize in Physics in 2010 for groundbreaking experiments regarding the material graphene. The global market for graphene reached $9 million by 2012 with most sales in the semiconductor, electronics, battery energy, Graphene is a combination of graphite and the suffix -ene, named by Hanns-Peter Boehm, who described single-layer carbon foils in 1962. The term was used in early descriptions of carbon nanotubes, as well as for epitaxial graphene. Graphene can be considered an infinite alternant polycyclic aromatic hydrocarbon, the IUPAC compendium of technology states, previously, descriptions such as graphite layers, carbon layers, or carbon sheets have been used for the term graphene. It is incorrect to use for a single layer a term includes the term graphite. The term graphene should be used only when the reactions, structural relations or other properties of individual layers are discussed and this definition is narrower than the IUPAC definition and refers to cloven, transferred and suspended graphene. Other forms such as graphene grown on various metals, can become free-standing if, for example, in 1859 Benjamin Collins Brodie became aware of the highly lamellar structure of thermally reduced graphite oxide. The structure of graphite was identified in 1916 by the method of powder diffraction. It was studied in detail by Kohlschütter and Haenni in 1918 and its structure was determined from single-crystal diffraction in 1924. The theory of graphene was first explored by Wallace in 1947 as a point for understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was first pointed out by Semenoff, DiVincenzo, Semenoff emphasized the occurrence in a magnetic field of an electronic Landau level precisely at the Dirac point
12.
Cubic crystal system
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In crystallography, the cubic 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 Body-centered cubic, Face-centered cubic Each is subdivided into other variants listed below. Note that although the cell in these crystals is conventionally taken to be a cube. This is related to the fact that in most cubic crystal systems, a classic isometric crystal has square or pentagonal faces. The three Bravais lattices in the crystal system are, The primitive cubic system consists of one lattice point on each corner of the cube. Each atom at a point is then shared equally between eight adjacent cubes, and the unit cell therefore contains in total one atom. The body-centered cubic system has one point in the center of the unit cell in addition to the eight corner points. It has a net total of 2 lattice points per unit cell, Each sphere in a cF lattice has coordination number 12. The face-centered cubic system is related to the hexagonal close packed system. The plane of a cubic system is a hexagonal grid. Attempting to create a C-centered cubic crystal system would result in a simple tetragonal Bravais lattice, there are a total 36 cubic space groups. Other terms for hexoctahedral are, normal class, holohedral, ditesseral central class, a simple cubic unit cell has a single cubic void in the center. Additionally, there are 24 tetrahedral voids located in a square spacing around each octahedral void and these tetrahedral voids are not local maxima and are not technically voids, but they do occasionally appear in multi-atom unit cells. A face-centered cubic unit cell has eight tetrahedral voids located midway between each corner and the center of the cell, for a total of eight net tetrahedral voids. One important characteristic of a structure is its atomic packing factor. This is calculated by assuming all the atoms are identical spheres. The atomic packing factor is the proportion of space filled by these spheres, assuming one atom per lattice point, in a primitive cubic lattice with cube side length a, the sphere radius would be a⁄2 and the atomic packing factor turns out to be about 0.524. Similarly, in a bcc lattice, the atomic packing factor is 0.680, as a rule, since atoms in a solid attract each other, the more tightly packed arrangements of atoms tend to be more common
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