Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Sometimes the term chromatic dispersion is used to refer to optics specifically, as opposed to wave propagation in general. A medium having this common property may be termed a dispersive medium .
135-420: Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic . Diamond as a form of carbon is a tasteless, odourless, strong, brittle solid, colourless in pure form, a poor conductor of electricity, and insoluble in water. Another solid form of carbon known as graphite is the chemically stable form of carbon at room temperature and pressure , but diamond
270-578: A semiconductor suitable to build microchips from, or the use of diamond as a heat sink in electronics . Significant research efforts in Japan , Europe , and the United States are under way to capitalize on the potential offered by diamond's unique material properties, combined with increased quality and quantity of supply starting to become available from synthetic diamond manufacturers. Graphite , named by Abraham Gottlob Werner in 1789, from
405-656: A subduction zone . Allotropes of carbon Carbon is capable of forming many allotropes (structurally different forms of the same element) due to its valency ( tetravalent ). Well-known forms of carbon include diamond and graphite . In recent decades, many more allotropes have been discovered and researched, including ball shapes such as buckminsterfullerene and sheets such as graphene . Larger-scale structures of carbon include nanotubes , nanobuds and nanoribbons . Other unusual forms of carbon exist at very high temperatures or extreme pressures. Around 500 hypothetical 3‑periodic allotropes of carbon are known at
540-549: A C-C bond length of 154 pm . This network of unstrained covalent bonds makes diamond extremely strong. Diamond is thermodynamically less stable than graphite at pressures below 1.7 GPa . The dominant industrial use of diamond is cutting , drilling ( drill bits ), grinding (diamond edged cutters), and polishing. Most uses of diamonds in these technologies do not require large diamonds, and most diamonds that are not gem-quality can find an industrial use. Diamonds are embedded in drill tips and saw blades or ground into
675-488: A Christie's auction. In May 2009, a 7.03-carat (1.406 g) blue diamond fetched the highest price per carat ever paid for a diamond when it was sold at auction for 10.5 million Swiss francs (6.97 million euros, or US$ 9.5 million at the time). That record was, however, beaten the same year: a 5-carat (1.0 g) vivid pink diamond was sold for US$ 10.8 million in Hong Kong on December 1, 2009. Clarity
810-451: A cigarette lighter, but house fires and blow torches are hot enough. Jewelers must be careful when molding the metal in a diamond ring. Diamond powder of an appropriate grain size (around 50 microns) burns with a shower of sparks after ignition from a flame. Consequently, pyrotechnic compositions based on synthetic diamond powder can be prepared. The resulting sparks are of the usual red-orange color, comparable to charcoal, but show
945-413: A communications signal, for instance, and its information only travels at the group velocity rate, even though it consists of wavefronts advancing at a faster rate (the phase velocity). It is possible to calculate the group velocity from the refractive-index curve n ( ω ) or more directly from the wavenumber k = ωn / c , where ω is the radian frequency ω = 2 πf . Whereas one expression for
1080-450: A component of some prosthetic devices. It was first produced by Bernard Redfern in the mid-1950s at the laboratories of The Carborundum Company, Manchester, UK. He had set out to develop a polymer matrix to mirror a diamond structure and discovered a resole (phenolic) resin that would, with special preparation, set without a catalyst. Using this resin, the first glassy carbon was produced. The preparation of glassy carbon involves subjecting
1215-726: A continuum with carbonatites , but the latter have too much oxygen for carbon to exist in a pure form. Instead, it is locked up in the mineral calcite ( Ca C O 3 ). All three of the diamond-bearing rocks (kimberlite, lamproite and lamprophyre) lack certain minerals ( melilite and kalsilite ) that are incompatible with diamond formation. In kimberlite , olivine is large and conspicuous, while lamproite has Ti- phlogopite and lamprophyre has biotite and amphibole . They are all derived from magma types that erupt rapidly from small amounts of melt, are rich in volatiles and magnesium oxide , and are less oxidizing than more common mantle melts such as basalt . These characteristics allow
1350-449: A diamond to fluoresce. Diamonds can fluoresce in a variety of colors including blue (most common), orange, yellow, white, green and very rarely red and purple. Although the causes are not well understood, variations in the atomic structure, such as the number of nitrogen atoms present are thought to contribute to the phenomenon. Diamonds can be identified by their high thermal conductivity (900– 2320 W·m·K ). Their high refractive index
1485-404: A function of frequency, leading to attenuation distortion ; this is not dispersion, although sometimes reflections at closely spaced impedance boundaries (e.g. crimped segments in a cable) can produce signal distortion which further aggravates inconsistent transit time as observed across signal bandwidth. The most familiar example of dispersion is probably a rainbow , in which dispersion causes
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#17327755316161620-480: A gemstone. Because it can only be scratched by other diamonds, it maintains its polish extremely well. Unlike many other gems, it is well-suited to daily wear because of its resistance to scratching—perhaps contributing to its popularity as the preferred gem in engagement or wedding rings , which are often worn every day. The hardest natural diamonds mostly originate from the Copeton and Bingara fields located in
1755-451: A given gemstone is a function of the gemstone's facet angles, the polish quality, the lighting environment, the material's refractive index, the saturation of color, and the orientation of the viewer relative to the gemstone. In photographic and microscopic lenses, dispersion causes chromatic aberration , which causes the different colors in the image not to overlap properly. Various techniques have been developed to counteract this, such as
1890-468: A higher refractive index, will be bent more strongly than red light, resulting in the well-known rainbow pattern. Beyond simply describing a change in the phase velocity over wavelength, a more serious consequence of dispersion in many applications is termed group-velocity dispersion (GVD). While phase velocity v is defined as v = c / n , this describes only one frequency component. When different frequency components are combined, as when considering
2025-471: A loose three-dimensional web. Each cluster is about 6 nanometers wide and consists of about 4000 carbon atoms linked in graphite -like sheets that are given negative curvature by the inclusion of heptagons among the regular hexagonal pattern. This is the opposite of what happens in the case of buckminsterfullerenes , in which carbon sheets are given positive curvature by the inclusion of pentagons . The large-scale structure of carbon nanofoam
2160-473: A metallic fluid. The extreme conditions required for this to occur are present in the ice giants Neptune and Uranus . Both planets are made up of approximately 10 percent carbon and could hypothetically contain oceans of liquid carbon. Since large quantities of metallic fluid can affect the magnetic field, this could serve as an explanation as to why the geographic and magnetic poles of the two planets are unaligned. The most common crystal structure of diamond
2295-482: A nanotube is cylindrical , with at least one end typically capped with a hemisphere of the buckyball structure. Their name is derived from their size, since the diameter of a nanotube is on the order of a few nanometers (approximately 50,000 times smaller than the width of a human hair), while they can be up to several centimeters in length. There are two main types of nanotubes: single-walled nanotubes (SWNTs) and multi-walled nanotubes (MWNTs). Carbon nanobuds are
2430-415: A negatively chirped signal in the acoustic domain is that of an approaching train hitting deformities on a welded track. The sound caused by the train itself is impulsive and travels much faster in the metal tracks than in air, so that the train can be heard well before it arrives. However, from afar it is not heard as causing impulses, but leads to a distinctive descending chirp, amidst reverberation caused by
2565-418: A net negative dispersion. Waveguides are highly dispersive due to their geometry (rather than just to their material composition). Optical fibers are a sort of waveguide for optical frequencies (light) widely used in modern telecommunications systems. The rate at which data can be transported on a single fiber is limited by pulse broadening due to chromatic dispersion among other phenomena. In general, for
2700-477: A newly discovered allotrope of carbon in which fullerene like "buds" are covalently attached to the outer sidewalls of the carbon nanotubes . This hybrid material has useful properties of both fullerenes and carbon nanotubes. For instance, they have been found to be exceptionally good field emitters . Schwarzites are negatively curved carbon surfaces originally proposed by decorating triply periodic minimal surfaces with carbon atoms. The geometric topology of
2835-401: A pale blue flame, and continues to burn after the source of heat is removed. By contrast, in air the combustion will cease as soon as the heat is removed because the oxygen is diluted with nitrogen. A clear, flawless, transparent diamond is completely converted to carbon dioxide; any impurities will be left as ash. Heat generated from cutting a diamond will not ignite the diamond, and neither will
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#17327755316162970-490: A powder for use in grinding and polishing applications (due to its extraordinary hardness). Specialized applications include use in laboratories as containment for high pressure experiments (see diamond anvil ), high-performance bearings , and specialized windows of technical apparatuses. 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
3105-458: A result of polarization mode dispersion (since there are still two polarization modes). These are not examples of chromatic dispersion, as they are not dependent on the wavelength or bandwidth of the pulses propagated. When a broad range of frequencies (a broad bandwidth) is present in a single wavepacket, such as in an ultrashort pulse or a chirped pulse or other forms of spread spectrum transmission, it may not be accurate to approximate
3240-405: A signal or a pulse, one is often more interested in the group velocity , which describes the speed at which a pulse or information superimposed on a wave (modulation) propagates. In the accompanying animation, it can be seen that the wave itself (orange-brown) travels at a phase velocity much faster than the speed of the envelope (black), which corresponds to the group velocity. This pulse might be
3375-437: A static press or using explosives. It can also be produced by the thermal decomposition of a polymer, poly(hydridocarbyne) , at atmospheric pressure, under inert gas atmosphere (e.g. argon, nitrogen), starting at temperature 110 °C (230 °F). Graphenylene is a single layer carbon material with biphenylene -like subunits as basis in its hexagonal lattice structure. It is also known as biphenylene-carbon. Carbophene
3510-578: A team of scientists from Rice University and the University of Sussex, three of whom were awarded the 1996 Nobel Prize in Chemistry. They are named for the resemblance to the geodesic structures devised by Richard Buckminster "Bucky" Fuller . Fullerenes are positively curved molecules of varying sizes composed entirely of carbon, which take the form of a hollow sphere, ellipsoid, or tube (the C60 version has
3645-461: A transition between graphite and diamond are well established theoretically and experimentally. The equilibrium pressure varies linearly with temperature, between 1.7 GPa at 0 K and 12 GPa at 5000 K (the diamond/graphite/liquid triple point ). However, the phases have a wide region about this line where they can coexist. At standard temperature and pressure , 20 °C (293 K) and 1 standard atmosphere (0.10 MPa),
3780-1018: A useful material in blood-contacting implants such as prosthetic heart valves . Graphite is the most stable allotrope of carbon. Contrary to popular belief, high-purity graphite does not readily burn, even at elevated temperatures. For this reason, it is used in nuclear reactors and for high-temperature crucibles for melting metals. At very high temperatures and pressures (roughly 2000 °C and 5 GPa), it can be transformed into diamond. Natural and crystalline graphites are not often used in pure form as structural materials due to their shear-planes, brittleness and inconsistent mechanical properties. In its pure glassy (isotropic) synthetic forms, pyrolytic graphite and carbon fiber graphite are extremely strong, heat-resistant (to 3000 °C) materials, used in reentry shields for missile nosecones, solid rocket engines, high temperature reactors , brake shoes and electric motor brushes . Intumescent or expandable graphites are used in fire seals, fitted around
3915-466: A very linear trajectory which is explained by their high density. Diamond also reacts with fluorine gas above about 700 °C (1,292 °F). Diamond has a wide band gap of 5.5 eV corresponding to the deep ultraviolet wavelength of 225 nanometers. This means that pure diamond should transmit visible light and appear as a clear colorless crystal. Colors in diamond originate from lattice defects and impurities. The diamond crystal lattice
4050-422: A volcanic rock. There are many theories for its origin, including formation in a star, but no consensus. Diamond is the hardest material on the qualitative Mohs scale . To conduct the quantitative Vickers hardness test , samples of materials are struck with a pyramid of standardized dimensions using a known force – a diamond crystal is used for the pyramid to permit a wide range of materials to be tested. From
4185-402: A waveguide mode with an angular frequency ω ( β ) at a propagation constant β (so that the electromagnetic fields in the propagation direction z oscillate proportional to e ), the group-velocity dispersion parameter D is defined as where λ = 2 π c / ω is the vacuum wavelength, and v g = dω / dβ is the group velocity. This formula generalizes the one in
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4320-406: A wide variety of applications (e.g., nano-electronics, optics , materials applications, etc.). They exhibit extraordinary strength, unique electrical properties, and are efficient conductors of heat . Non-carbon nanotubes have also been synthesized. Carbon nanotubes are a members of the fullerene structural family, which also includes buckyballs . Whereas buckyballs are spherical in shape,
4455-471: Is metastable and converts to it at a negligible rate under those conditions. Diamond has the highest hardness and thermal conductivity of any natural material, properties that are used in major industrial applications such as cutting and polishing tools. They are also the reason that diamond anvil cells can subject materials to pressures found deep in the Earth. Because the arrangement of atoms in diamond
4590-446: Is 0.01% for nickel and even less for cobalt. Virtually any element can be introduced to diamond by ion implantation. Nitrogen is by far the most common impurity found in gem diamonds and is responsible for the yellow and brown color in diamonds. Boron is responsible for the blue color. Color in diamond has two additional sources: irradiation (usually by alpha particles), that causes the color in green diamonds, and plastic deformation of
4725-408: Is a 2 dimensional covalent organic framework . 4-6 carbophene has been synthesized from 1-3-5 trihydroxybenzene . It consists of 4-carbon and 6-carbon rings in 1:1 ratio. The angles between the three σ-bonds of the orbitals are approximately 120°, 90°, and 150°. AA'-graphite is an allotrope of carbon similar to graphite, but where the layers are positioned differently to each other as compared to
4860-413: Is a solid form of pure carbon with its atoms arranged in a crystal. Solid carbon comes in different forms known as allotropes depending on the type of chemical bond. The two most common allotropes of pure carbon are diamond and graphite . In graphite, the bonds are sp orbital hybrids and the atoms form in planes, with each bound to three nearest neighbors, 120 degrees apart. In diamond, they are sp and
4995-870: Is accomplished using chlorine treatment, hydrothermal synthesis, or high-temperature selective metal desorption under vacuum. Depending on the synthesis method, carbide precursor, and reaction parameters, multiple carbon allotropes can be achieved, including endohedral particles composed of predominantly amorphous carbon, carbon nanotubes, epitaxial graphene, nanocrystalline diamond, onion-like carbon, and graphitic ribbons, barrels, and horns. These structures exhibit high porosity and specific surface areas, with highly tunable pore diameters, making them promising materials for supercapacitor-based energy storage, water filtration and capacitive desalinization, catalyst support, and cytokine removal. Other metastable carbon phases, some diamondlike, have been produced from reactions of SiC or CH3SiCl3 with CF4. A one-dimensional carbon polymer with
5130-420: Is aided by isotopic dating and modeling of the geological history. Then surveyors must go to the area and collect samples, looking for kimberlite fragments or indicator minerals . The latter have compositions that reflect the conditions where diamonds form, such as extreme melt depletion or high pressures in eclogites . However, indicator minerals can be misleading; a better approach is geothermobarometry , where
5265-722: Is also indicative, but other materials have similar refractivity. Diamonds are extremely rare, with concentrations of at most parts per billion in source rock. Before the 20th century, most diamonds were found in alluvial deposits . Loose diamonds are also found along existing and ancient shorelines , where they tend to accumulate because of their size and density. Rarely, they have been found in glacial till (notably in Wisconsin and Indiana ), but these deposits are not of commercial quality. These types of deposit were derived from localized igneous intrusions through weathering and transport by wind or water . Most diamonds come from
5400-403: Is an allotrope sometimes called " hexagonal diamond", formed from graphite present in meteorites upon their impact on the earth. The great heat and pressure of the impact transforms the graphite into a denser form similar to diamond but retaining graphite's hexagonal crystal lattice . "Hexagonal diamond" has also been synthesized in the laboratory, by compressing and heating graphite either in
5535-400: Is another mechanical property toughness , which is a material's ability to resist breakage from forceful impact. The toughness of natural diamond has been measured as 50–65 MPa ·m. This value is good compared to other ceramic materials, but poor compared to most engineering materials such as engineering alloys, which typically exhibit toughness over 80 MPa·m. As with any material,
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5670-412: Is called diamond cubic . It is formed of unit cells (see the figure) stacked together. Although there are 18 atoms in the figure, each corner atom is shared by eight unit cells and each atom in the center of a face is shared by two, so there are a total of eight atoms per unit cell. The length of each side of the unit cell is denoted by a and is 3.567 angstroms . The nearest neighbor distance in
5805-402: Is exceptionally strong, and only atoms of nitrogen , boron , and hydrogen can be introduced into diamond during the growth at significant concentrations (up to atomic percents). Transition metals nickel and cobalt , which are commonly used for growth of synthetic diamond by high-pressure high-temperature techniques, have been detected in diamond as individual atoms; the maximum concentration
5940-574: Is extremely rigid, few types of impurity can contaminate it (two exceptions are boron and nitrogen ). Small numbers of defects or impurities (about one per million of lattice atoms) can color a diamond blue (boron), yellow (nitrogen), brown (defects), green (radiation exposure), purple, pink, orange, or red. Diamond also has a very high refractive index and a relatively high optical dispersion . Most natural diamonds have ages between 1 billion and 3.5 billion years. Most were formed at depths between 150 and 250 kilometres (93 and 155 mi) in
6075-418: Is formed of layers stacked in a repeating ABCABC ... pattern. Diamonds can also form an ABAB ... structure, which is known as hexagonal diamond or lonsdaleite , but this is far less common and is formed under different conditions from cubic carbon. Diamonds occur most often as euhedral or rounded octahedra and twinned octahedra known as macles . As diamond's crystal structure has a cubic arrangement of
6210-411: Is higher for flawless, pure crystals oriented to the <111> direction (along the longest diagonal of the cubic diamond lattice). Therefore, whereas it might be possible to scratch some diamonds with other materials, such as boron nitride , the hardest diamonds can only be scratched by other diamonds and nanocrystalline diamond aggregates . The hardness of diamond contributes to its suitability as
6345-404: Is hybrid rock with a chaotic mixture of small minerals and rock fragments ( clasts ) up to the size of watermelons. They are a mixture of xenocrysts and xenoliths (minerals and rocks carried up from the lower crust and mantle), pieces of surface rock, altered minerals such as serpentine , and new minerals that crystallized during the eruption. The texture varies with depth. The composition forms
6480-644: Is in the form of micro/nanoscale wires or needles (~100–300 nanometers in diameter, micrometers long), they can be elastically stretched by as much as 9–10 percent tensile strain without failure, with a maximum local tensile stress of about 89–98 GPa , very close to the theoretical limit for this material. Other specialized applications also exist or are being developed, including use as semiconductors : some blue diamonds are natural semiconductors, in contrast to most diamonds, which are excellent electrical insulators . The conductivity and blue color originate from boron impurity. Boron substitutes for carbon atoms in
6615-510: Is injected into the zeolite, where the carbon gathers on the pores' walls, creating the negative curve. Dissolving the zeolite leaves the carbon. A team generated structures by decorating the pores of a zeolite with carbon through a Monte Carlo method . Some of the resulting models resemble schwarzite-like structures. Glassy carbon or vitreous carbon is a class of non-graphitizing carbon widely used as an electrode material in electrochemistry , as well as for high-temperature crucibles and as
6750-441: Is much larger than atomic dimensions, because the dielectric kernel dies out at macroscopic distances. Nevertheless, it can result in non-negligible macroscopic effects, particularly in conducting media such as metals , electrolytes and plasmas . Spatial dispersion also plays role in optical activity and Doppler broadening , as well as in the theory of metamaterials . In the technical terminology of gemology , dispersion
6885-567: Is no long-range pattern of atomic positions. While entirely amorphous carbon can be produced, most amorphous carbon contains microscopic crystals of graphite -like, or even diamond -like carbon. Coal and soot or carbon black are informally called amorphous carbon. However, they are products of pyrolysis (the process of decomposing a substance by the action of heat), which does not produce true amorphous carbon under normal conditions. The buckminsterfullerenes , or usually just fullerenes or buckyballs for short, were discovered in 1985 by
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#17327755316167020-553: Is often detected via spectroscopy in extraterrestrial bodies, including comets and certain stars . Diamond is a well-known allotrope of carbon. The hardness , extremely high refractive index , and high dispersion of light make diamond useful for industrial applications and for jewelry. Diamond is the hardest known natural mineral . This makes it an excellent abrasive and makes it hold polish and luster extremely well. No known naturally occurring substance can cut or scratch diamond, except another diamond. In diamond form, carbon
7155-477: Is one of the 4C's (color, clarity, cut and carat weight) that helps in identifying the quality of diamonds. The Gemological Institute of America (GIA) developed 11 clarity scales to decide the quality of a diamond for its sale value. The GIA clarity scale spans from Flawless (FL) to included (I) having internally flawless (IF), very, very slightly included (VVS), very slightly included (VS) and slightly included (SI) in between. Impurities in natural diamonds are due to
7290-479: Is one of the costliest elements. The crystal structure of diamond is a face-centered cubic lattice having eight atoms per unit cell to form a diamond cubic structure. Each carbon atom is covalently bonded to four other carbons in a tetrahedral geometry . These tetrahedrons together form a 3-dimensional network of six-membered carbon rings in the chair conformation , allowing for zero bond angle strain. The bonding occurs through sp hybridized orbitals to give
7425-794: Is partially oxidized. The oxidized surface can be reduced by heat treatment under hydrogen flow. That is to say, this heat treatment partially removes oxygen-containing functional groups. But diamonds (spC) are unstable against high temperature (above about 400 °C (752 °F)) under atmospheric pressure. The structure gradually changes into spC above this temperature. Thus, diamonds should be reduced below this temperature. At room temperature, diamonds do not react with any chemical reagents including strong acids and bases. In an atmosphere of pure oxygen, diamond has an ignition point that ranges from 690 °C (1,274 °F) to 840 °C (1,540 °F); smaller crystals tend to burn more easily. It increases in temperature from red to white heat and burns with
7560-767: Is possible to treat regular diamonds under a combination of high pressure and high temperature to produce diamonds that are harder than the diamonds used in hardness gauges. Diamonds cut glass, but this does not positively identify a diamond because other materials, such as quartz, also lie above glass on the Mohs scale and can also cut it. Diamonds can scratch other diamonds, but this can result in damage to one or both stones. Hardness tests are infrequently used in practical gemology because of their potentially destructive nature. The extreme hardness and high value of diamond means that gems are typically polished slowly, using painstaking traditional techniques and greater attention to detail than
7695-561: Is reduced to a powder by a mixture of concentrated sulfuric and nitric acids at room temperature, glassy carbon is unaffected by such treatment, even after several months. Carbon nanofoam is the fifth known allotrope of carbon, discovered in 1997 by Andrei V. Rode and co-workers at the Australian National University in Canberra . It consists of a low-density cluster-assembly of carbon atoms strung together in
7830-503: Is similar to that of an aerogel , but with 1% of the density of previously produced carbon aerogels – only a few times the density of air at sea level . Unlike carbon aerogels, carbon nanofoam is a poor electrical conductor . Carbide-derived carbon (CDC) is a family of carbon materials with different surface geometries and carbon ordering that are produced via selective removal of metals from metal carbide precursors, such as TiC, SiC, Ti 3 AlC 2 , Mo 2 C , etc. This synthesis
7965-452: Is the case with most other gemstones; these tend to result in extremely flat, highly polished facets with exceptionally sharp facet edges. Diamonds also possess an extremely high refractive index and fairly high dispersion. Taken together, these factors affect the overall appearance of a polished diamond and most diamantaires still rely upon skilled use of a loupe (magnifying glass) to identify diamonds "by eye". Somewhat related to hardness
8100-480: Is the column density of free electrons ( total electron content ) – i.e. the number density of electrons n e integrated along the path traveled by the photon from the pulsar to the Earth ;– and is given by with units of parsecs per cubic centimetre (1 pc/cm = 30.857 × 10 m ). Typically for astronomical observations, this delay cannot be measured directly, since
8235-451: Is the difference in the refractive index of a material at the B and G (686.7 nm and 430.8 nm) or C and F (656.3 nm and 486.1 nm) Fraunhofer wavelengths , and is meant to express the degree to which a prism cut from the gemstone demonstrates "fire". Fire is a colloquial term used by gemologists to describe a gemstone's dispersive nature or lack thereof. Dispersion is a material property. The amount of fire demonstrated by
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#17327755316168370-596: Is the separation of white light into a color spectrum by a prism . From Snell's law it can be seen that the angle of refraction of light in a prism depends on the refractive index of the prism material. Since that refractive index varies with wavelength, it follows that the angle that the light is refracted by will also vary with wavelength, causing an angular separation of the colors known as angular dispersion . For visible light, refraction indices n of most transparent materials (e.g., air, glasses) decrease with increasing wavelength λ : or generally, In this case,
8505-446: Is to use soliton pulses in the regime of negative dispersion, a form of optical pulse which uses a nonlinear optical effect to self-maintain its shape. Solitons have the practical problem, however, that they require a certain power level to be maintained in the pulse for the nonlinear effect to be of the correct strength. Instead, the solution that is currently used in practice is to perform dispersion compensation, typically by matching
8640-692: Is too high, a group of pulses representing a bit-stream will spread in time and merge, rendering the bit-stream unintelligible. This limits the length of fiber that a signal can be sent down without regeneration. One possible answer to this problem is to send signals down the optical fibre at a wavelength where the GVD is zero (e.g., around 1.3–1.5 μm in silica fibres ), so pulses at this wavelength suffer minimal spreading from dispersion. In practice, however, this approach causes more problems than it solves because zero GVD unacceptably amplifies other nonlinear effects (such as four-wave mixing ). Another possible option
8775-412: Is used to construct spectrometers and spectroradiometers . However, in lenses, dispersion causes chromatic aberration , an undesired effect that may degrade images in microscopes, telescopes, and photographic objectives. The phase velocity v of a wave in a given uniform medium is given by where c is the speed of light in vacuum, and n is the refractive index of the medium. In general,
8910-737: The Earth's mantle , and most of this section discusses those diamonds. However, there are other sources. Some blocks of the crust, or terranes , have been buried deep enough as the crust thickened so they experienced ultra-high-pressure metamorphism . These have evenly distributed microdiamonds that show no sign of transport by magma. In addition, when meteorites strike the ground, the shock wave can produce high enough temperatures and pressures for microdiamonds and nanodiamonds to form. Impact-type microdiamonds can be used as an indicator of ancient impact craters. Popigai impact structure in Russia may have
9045-566: The New England area in New South Wales , Australia. These diamonds are generally small, perfect to semiperfect octahedra, and are used to polish other diamonds. Their hardness is associated with the crystal growth form, which is single-stage crystal growth. Most other diamonds show more evidence of multiple growth stages, which produce inclusions, flaws, and defect planes in the crystal lattice, all of which affect their hardness. It
9180-557: The Wawa belt of the Superior province in Canada and microdiamonds in the island arc of Japan are found in a type of rock called lamprophyre . Kimberlites can be found in narrow (1 to 4 meters) dikes and sills, and in pipes with diameters that range from about 75 m to 1.5 km. Fresh rock is dark bluish green to greenish gray, but after exposure rapidly turns brown and crumbles. It
9315-428: The gemological characteristics of diamond, including clarity and color, mostly irrelevant. This helps explain why 80% of mined diamonds (equal to about 100 million carats or 20 tonnes annually) are unsuitable for use as gemstones and known as bort , are destined for industrial use. In addition to mined diamonds, synthetic diamonds found industrial applications almost immediately after their invention in
9450-405: The heat of formation of carbon compounds. Graphite conducts electricity , due to delocalization of the pi bond electrons above and below the planes of the carbon atoms. These electrons are free to move, so are able to conduct electricity. However, the electricity is only conducted along the plane of the layers. In diamond, all four outer electrons of each carbon atom are 'localized' between
9585-435: The kernel f i k {\displaystyle f_{ik}} is dielectric response (susceptibility); its indices make it in general a tensor to account for the anisotropy of the medium. Spatial dispersion is negligible in most macroscopic cases, where the scale of variation of E k ( t − τ , r ′ ) {\displaystyle E_{k}(t-\tau ,r')}
9720-435: The lithosphere . Such depths occur below cratons in mantle keels , the thickest part of the lithosphere. These regions have high enough pressure and temperature to allow diamonds to form and they are not convecting, so diamonds can be stored for billions of years until a kimberlite eruption samples them. Host rocks in a mantle keel include harzburgite and lherzolite , two type of peridotite . The most dominant rock type in
9855-535: The normal color range , and applies a grading scale from "D" (colorless) to "Z" (light yellow). Yellow diamonds of high color saturation or a different color, such as pink or blue, are called fancy colored diamonds and fall under a different grading scale. In 2008, the Wittelsbach Diamond , a 35.56-carat (7.112 g) blue diamond once belonging to the King of Spain, fetched over US$ 24 million at
9990-516: The pulses of light in optical fiber . In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light, as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses. Design of compound achromatic lenses , in which chromatic aberration is largely cancelled, uses a quantification of a glass's dispersion given by its Abbe number V , where lower Abbe numbers correspond to greater dispersion over
10125-401: The upper mantle , peridotite is an igneous rock consisting mostly of the minerals olivine and pyroxene ; it is low in silica and high in magnesium . However, diamonds in peridotite rarely survive the trip to the surface. Another common source that does keep diamonds intact is eclogite , a metamorphic rock that typically forms from basalt as an oceanic plate plunges into the mantle at
10260-405: The visible spectrum . In some applications such as telecommunications, the absolute phase of a wave is often not important but only the propagation of wave packets or "pulses"; in that case one is interested only in variations of group velocity with frequency, so-called group-velocity dispersion . All common transmission media also vary in attenuation (normalized to transmission length) as
10395-403: The 1950s; another 400 million carats (80 tonnes) of synthetic diamonds are produced annually for industrial use, which is nearly four times the mass of natural diamonds mined over the same period. With the continuing advances being made in the production of synthetic diamond, future applications are beginning to become feasible. Garnering much excitement is the possible use of diamond as
10530-820: The Earth's mantle , although a few have come from as deep as 800 kilometres (500 mi). Under high pressure and temperature, carbon-containing fluids dissolved various minerals and replaced them with diamonds. Much more recently (hundreds to tens of million years ago), they were carried to the surface in volcanic eruptions and deposited in igneous rocks known as kimberlites and lamproites . Synthetic diamonds can be grown from high-purity carbon under high pressures and temperatures or from hydrocarbon gases by chemical vapor deposition (CVD). Imitation diamonds can also be made out of materials such as cubic zirconia and silicon carbide . Natural, synthetic, and imitation diamonds are most commonly distinguished using optical techniques or thermal conductivity measurements. Diamond
10665-459: The Greek γράφειν ( graphein , "to draw/write", for its use in pencils) 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 standard conditions , graphite is the most stable form of carbon. Therefore, it is used in thermochemistry as the standard state for defining
10800-456: The atoms form tetrahedra, with each bound to four nearest neighbors. Tetrahedra are rigid, the bonds are strong, and, of all known substances, diamond has the greatest number of atoms per unit volume, which is why it is both the hardest and the least compressible . It also has a high density, ranging from 3150 to 3530 kilograms per cubic metre (over three times the density of water) in natural diamonds and 3520 kg/m in pure diamond. In graphite,
10935-445: The atoms in covalent bonding. The movement of electrons is restricted and diamond does not conduct an electric current. In graphite, each carbon atom uses only 3 of its 4 outer energy level electrons in covalently bonding to three other carbon atoms in a plane. Each carbon atom contributes one electron to a delocalized system of electrons that is also a part of the chemical bonding. The delocalized electrons are free to move throughout
11070-419: The atoms, they have many facets that belong to a cube , octahedron, rhombicosidodecahedron , tetrakis hexahedron , or disdyakis dodecahedron . The crystals can have rounded-off and unexpressive edges and can be elongated. Diamonds (especially those with rounded crystal faces) are commonly found coated in nyf , an opaque gum-like skin. Some diamonds contain opaque fibers. They are referred to as opaque if
11205-409: The bonds between nearest neighbors are even stronger, but the bonds between parallel adjacent planes are weak, so the planes easily slip past each other. Thus, graphite is much softer than diamond. However, the stronger bonds make graphite less flammable. Diamonds have been adopted for many uses because of the material's exceptional physical characteristics. It has the highest thermal conductivity and
11340-507: The carbon source is more likely carbonate rocks and organic carbon in sediments, rather than coal. Diamonds are far from evenly distributed over the Earth. A rule of thumb known as Clifford's rule states that they are almost always found in kimberlites on the oldest part of cratons , the stable cores of continents with typical ages of 2.5 billion years or more. However, there are exceptions. The Argyle diamond mine in Australia ,
11475-410: The change in refractive index with optical frequency. However, in a waveguide there is also the phenomenon of waveguide dispersion , in which case a wave's phase velocity in a structure depends on its frequency simply due to the structure's geometry. More generally, "waveguide" dispersion can occur for waves propagating through any inhomogeneous structure (e.g., a photonic crystal ), whether or not
11610-435: The coloration, while pure or nearly pure diamonds are transparent and colorless. Most diamond impurities replace a carbon atom in the crystal lattice , known as a carbon flaw . The most common impurity, nitrogen, causes a slight to intense yellow coloration depending upon the type and concentration of nitrogen present. The Gemological Institute of America (GIA) classifies low saturation yellow and brown diamonds as diamonds in
11745-421: The complexity of the vibrational modes of the track. Group-velocity dispersion can be heard in that the volume of the sounds stays audible for a surprisingly long time, up to several seconds. The result of GVD, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on optical fiber, since if dispersion
11880-413: The components of each pulse emitted at higher radio frequencies arrive before those emitted at lower frequencies. This dispersion occurs because of the ionized component of the interstellar medium , mainly the free electrons, which make the group velocity frequency-dependent. The extra delay added at a frequency ν is where the dispersion constant k DM is given by and the dispersion measure (DM)
12015-499: The compositions of minerals are analyzed as if they were in equilibrium with mantle minerals. Finding kimberlites requires persistence, and only a small fraction contain diamonds that are commercially viable. The only major discoveries since about 1980 have been in Canada. Since existing mines have lifetimes of as little as 25 years, there could be a shortage of new diamonds in the future. Diamonds are dated by analyzing inclusions using
12150-598: The decay of radioactive isotopes. Depending on the elemental abundances, one can look at the decay of rubidium to strontium , samarium to neodymium , uranium to lead , argon-40 to argon-39 , or rhenium to osmium . Those found in kimberlites have ages ranging from 1 to 3.5 billion years , and there can be multiple ages in the same kimberlite, indicating multiple episodes of diamond formation. The kimberlites themselves are much younger. Most of them have ages between tens of millions and 300 million years old, although there are some older exceptions (Argyle, Premier and Wawa). Thus,
12285-467: The diamond crystal lattice. Plastic deformation is the cause of color in some brown and perhaps pink and red diamonds. In order of increasing rarity, yellow diamond is followed by brown, colorless, then by blue, green, black, pink, orange, purple, and red. "Black", or carbonado , diamonds are not truly black, but rather contain numerous dark inclusions that give the gems their dark appearance. Colored diamonds contain impurities or structural defects that cause
12420-505: The diamond lattice is 1.732 a /4 where a is the lattice constant, usually given in Angstrøms as a = 3.567 Å, which is 0.3567 nm. A diamond cubic lattice can be thought of as two interpenetrating face-centered cubic lattices with one displaced by 1 ⁄ 4 of the diagonal along a cubic cell, or as one lattice with two atoms associated with each lattice point. Viewed from a <1 1 1> crystallographic direction , it
12555-412: The diamond lattice, donating a hole into the valence band . Substantial conductivity is commonly observed in nominally undoped diamond grown by chemical vapor deposition . This conductivity is associated with hydrogen -related species adsorbed at the surface, and it can be removed by annealing or other surface treatments. Thin needles of diamond can be made to vary their electronic band gap from
12690-406: The diamonds' surface cannot be wet by water, but can be easily wet and stuck by oil. This property can be utilized to extract diamonds using oil when making synthetic diamonds. However, when diamond surfaces are chemically modified with certain ions, they are expected to become so hydrophilic that they can stabilize multiple layers of water ice at human body temperature . The surface of diamonds
12825-443: The different-frequency components within the pulse travel at different velocities. Group-velocity dispersion is quantified as the derivative of the reciprocal of the group velocity with respect to angular frequency , which results in group-velocity dispersion = d k / dω . If a light pulse is propagated through a material with positive group-velocity dispersion, then the shorter-wavelength components travel slower than
12960-415: The dispersion by a constant over the entire bandwidth, and more complex calculations are required to compute effects such as pulse spreading. In particular, the dispersion parameter D defined above is obtained from only one derivative of the group velocity. Higher derivatives are known as higher-order dispersion . These terms are simply a Taylor series expansion of the dispersion relation β ( ω ) of
13095-605: The duration of the pulses emitted by the laser. A pair of prisms can be arranged to produce net negative dispersion, which can be used to balance the usually positive dispersion of the laser medium. Diffraction gratings can also be used to produce dispersive effects; these are often used in high-power laser amplifier systems. Recently, an alternative to prisms and gratings has been developed: chirped mirrors . These dielectric mirrors are coated so that different wavelengths have different penetration lengths, and therefore different group delays. The coating layers can be tailored to achieve
13230-418: The fiber with another fiber of opposite-sign dispersion so that the dispersion effects cancel; such compensation is ultimately limited by nonlinear effects such as self-phase modulation , which interact with dispersion to make it very difficult to undo. Dispersion control is also important in lasers that produce short pulses . The overall dispersion of the optical resonator is a major factor in determining
13365-449: The fibers grow from a clear substrate or fibrous if they occupy the entire crystal. Their colors range from yellow to green or gray, sometimes with cloud-like white to gray impurities. Their most common shape is cuboidal, but they can also form octahedra, dodecahedra, macles, or combined shapes. The structure is the result of numerous impurities with sizes between 1 and 5 microns. These diamonds probably formed in kimberlite magma and sampled
13500-404: The hardness and transparency of diamond, are the reasons that diamond anvil cells are the main tool for high pressure experiments. These anvils have reached pressures of 600 GPa . Much higher pressures may be possible with nanocrystalline diamonds. Usually, attempting to deform bulk diamond crystal by tension or bending results in brittle fracture. However, when single crystalline diamond
13635-409: The hardness of diamonds, the chemical bonds that hold the carbon atoms in diamonds together are actually weaker than those that hold together graphite. The difference is that in diamond, the bonds form an inflexible three-dimensional lattice. In graphite, the atoms are tightly bonded into sheets, but the sheets can slide easily over each other, making graphite soft. Optical dispersion Although
13770-612: The hexagonal layers of carbon atoms in graphite. It is unaffected by ordinary solvents, dilute acids, or fused alkalis. However, chromic acid oxidizes it to carbon dioxide. A single layer of graphite is called graphene and has extraordinary electrical, thermal, and physical properties. It can be produced by epitaxy on an insulating or conducting substrate or by mechanical exfoliation (repeated peeling) from graphite. Its applications may include replacing silicon in high-performance electronic devices. With two layers stacked, bilayer graphene results with different properties. Lonsdaleite
13905-454: The highest sound velocity. It has low adhesion and friction, and its coefficient of thermal expansion is extremely low. Its optical transparency extends from the far infrared to the deep ultraviolet and it has high optical dispersion . It also has high electrical resistance. It is chemically inert, not reacting with most corrosive substances, and has excellent biological compatibility. The equilibrium pressure and temperature conditions for
14040-420: The kimberlites formed independently of the diamonds and served only to transport them to the surface. Kimberlites are also much younger than the cratons they have erupted through. The reason for the lack of older kimberlites is unknown, but it suggests there was some change in mantle chemistry or tectonics. No kimberlite has erupted in human history. Most gem-quality diamonds come from depths of 150–250 km in
14175-472: The largest producer of diamonds by weight in the world, is located in a mobile belt , also known as an orogenic belt , a weaker zone surrounding the central craton that has undergone compressional tectonics. Instead of kimberlite , the host rock is lamproite . Lamproites with diamonds that are not economically viable are also found in the United States, India, and Australia. In addition, diamonds in
14310-424: The longer-wavelength components. The pulse therefore becomes positively chirped , or up-chirped , increasing in frequency with time. On the other hand, if a pulse travels through a material with negative group-velocity dispersion, shorter-wavelength components travel faster than the longer ones, and the pulse becomes negatively chirped , or down-chirped , decreasing in frequency with time. An everyday example of
14445-465: The macroscopic geometry of a diamond contributes to its resistance to breakage. Diamond has a cleavage plane and is therefore more fragile in some orientations than others. Diamond cutters use this attribute to cleave some stones before faceting them. "Impact toughness" is one of the main indexes to measure the quality of synthetic industrial diamonds. Diamond has compressive yield strength of 130–140 GPa. This exceptionally high value, along with
14580-450: The medium is said to have normal dispersion . Whereas if the index increases with increasing wavelength (which is typically the case in the ultraviolet ), the medium is said to have anomalous dispersion . At the interface of such a material with air or vacuum (index of ~1), Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle arcsin( sin θ / n ). Thus, blue light, with
14715-465: The medium or waveguide around some particular frequency. Their effects can be computed via numerical evaluation of Fourier transforms of the waveform, via integration of higher-order slowly varying envelope approximations , by a split-step method (which can use the exact dispersion relation rather than a Taylor series), or by direct simulation of the full Maxwell's equations rather than an approximate envelope equation. In electromagnetics and optics,
14850-589: The melting point of diamond increases slowly with increasing pressure; but at pressures of hundreds of GPa, it decreases. At high pressures, silicon and germanium have a BC8 body-centered cubic crystal structure, and a similar structure is predicted for carbon at high pressures. At 0 K , the transition is predicted to occur at 1100 GPa . Results published in an article in the scientific journal Nature Physics in 2010 suggest that, at ultra-high pressures and temperatures (about 10 million atmospheres or 1 TPa and 50,000 °C), diamond melts into
14985-578: The melts to carry diamonds to the surface before they dissolve. Kimberlite pipes can be difficult to find. They weather quickly (within a few years after exposure) and tend to have lower topographic relief than surrounding rock. If they are visible in outcrops, the diamonds are never visible because they are so rare. In any case, kimberlites are often covered with vegetation, sediments, soils, or lakes. In modern searches, geophysical methods such as aeromagnetic surveys , electrical resistivity , and gravimetry , help identify promising regions to explore. This
15120-467: The normal 5.6 eV to near zero by selective mechanical deformation. High-purity diamond wafers 5 cm in diameter exhibit perfect resistance in one direction and perfect conductance in the other, creating the possibility of using them for quantum data storage. The material contains only 3 parts per million of nitrogen. The diamond was grown on a stepped substrate, which eliminated cracking. Diamonds are naturally lipophilic and hydrophobic , which means
15255-533: The order in graphite. Diamane is a 2D form of diamond. It can be made via high pressures, but without that pressure, the material reverts to graphene. Another technique is to add hydrogen atoms, but those bonds are weak. Using fluorine (xenon-difluoride) instead brings the layers closer together, strengthening the bonds. This is called f-diamane. Amorphous carbon is the name used for carbon that does not have any crystalline structure. As with all glassy materials, some short-range order can be observed, but there
15390-488: The organic precursors to a series of heat treatments at temperatures up to 3000 °C. Unlike many non-graphitizing carbons, they are impermeable to gases and are chemically extremely inert, especially those prepared at very high temperatures. It has been demonstrated that the rates of oxidation of certain glassy carbons in oxygen, carbon dioxide or water vapor are lower than those of any other carbon. They are also highly resistant to attack by acids. Thus, while normal graphite
15525-414: The perimeter of a fire door. During a fire the graphite intumesces (expands and chars) to resist fire penetration and prevent the spread of fumes. A typical start expansion temperature (SET) is between 150 and 300 °C. Graphite's specific gravity is 2.3, which makes it less dense than diamond. Graphite is slightly more reactive than diamond. This is because the reactants are able to penetrate between
15660-426: The phase velocity is v p = ω / k , the group velocity can be expressed using the derivative : v g = dω / dk . Or in terms of the phase velocity v p , When dispersion is present, not only the group velocity is not equal to the phase velocity, but generally it itself varies with wavelength. This is known as group-velocity dispersion and causes a short pulse of light to be broadened, as
15795-464: The plane. For this reason, graphite conducts electricity along the planes of carbon atoms, but does not conduct electricity in a direction at right angles to the plane. Graphite powder is used as a dry lubricant . Although it might be thought that this industrially important property is due entirely to the loose interlamellar coupling between sheets in the structure, in fact in a vacuum environment (such as in technologies for use in space ), graphite
15930-617: The presence of natural minerals and oxides. The clarity scale grades the diamond based on the color, size, location of impurity and quantity of clarity visible under 10x magnification. Inclusions in diamond can be extracted by optical methods. The process is to take pre-enhancement images, identifying the inclusion removal part and finally removing the diamond facets and noises. Between 25% and 35% of natural diamonds exhibit some degree of fluorescence when examined under invisible long-wave ultraviolet light or higher energy radiation sources such as X-rays and lasers. Incandescent lighting will not cause
16065-522: The present time, according to the Samara Carbon Allotrope Database (SACADA). Under certain conditions, carbon can be found in its atomic form. It can be formed by vaporizing graphite, by passing large electric currents to form a carbon arc under very low pressure. It is extremely reactive, but it is an intermediate product used in the creation of carbenes . Diatomic carbon can also be found under certain conditions. It
16200-504: The previous section for homogeneous media and includes both waveguide dispersion and material dispersion. The reason for defining the dispersion in this way is that | D | is the (asymptotic) temporal pulse spreading Δ t per unit bandwidth Δ λ per unit distance travelled, commonly reported in ps /( nm ⋅ km ) for optical fibers. In the case of multi-mode optical fibers , so-called modal dispersion will also lead to pulse broadening. Even in single-mode fibers , pulse broadening can occur as
16335-531: The refractive index is some function of the frequency f of the light, thus n = n ( f ), or alternatively, with respect to the wave's wavelength n = n ( λ ). The wavelength dependence of a material's refractive index is usually quantified by its Abbe number or its coefficients in an empirical formula such as the Cauchy or Sellmeier equations . Because of the Kramers–Kronig relations ,
16470-561: The same form as a traditional stitched soccer ball). As of the early twenty-first century, the chemical and physical properties of fullerenes are still under heavy study, in both pure and applied research labs. In April 2003, fullerenes were under study for potential medicinal use — binding specific antibiotics to the structure to target resistant bacteria and even target certain cancer cells such as melanoma. Carbon nanotubes, also called buckytubes, are cylindrical carbon molecules with novel properties that make them potentially useful in
16605-526: The size of the resulting indentation, a Vickers hardness value for the material can be determined. Diamond's great hardness relative to other materials has been known since antiquity, and is the source of its name. This does not mean that it is infinitely hard, indestructible, or unscratchable. Indeed, diamonds can be scratched by other diamonds and worn down over time even by softer materials, such as vinyl phonograph records . Diamond hardness depends on its purity, crystalline perfection, and orientation: hardness
16740-486: The spatial separation of a white light into components of different wavelengths (different colors ). However, dispersion also has an effect in many other circumstances: for example, group-velocity dispersion causes pulses to spread in optical fibers , degrading signals over long distances; also, a cancellation between group-velocity dispersion and nonlinear effects leads to soliton waves. Most often, chromatic dispersion refers to bulk material dispersion, that is,
16875-417: The stable phase of carbon is graphite, but diamond is metastable and its rate of conversion to graphite is negligible. However, at temperatures above about 4500 K , diamond rapidly converts to graphite. Rapid conversion of graphite to diamond requires pressures well above the equilibrium line: at 2000 K , a pressure of 35 GPa is needed. Above the graphite–diamond–liquid carbon triple point,
17010-464: The structure is determined by the presence of ring defects, such as heptagons and octagons, to graphene 's hexagonal lattice. (Negative curvature bends surfaces outwards like a saddle rather than bending inwards like a sphere.) Recent work has proposed zeolite-templated carbons (ZTCs) may be schwarzites. The name, ZTC, derives from their origin inside the pores of zeolites , crystalline silicon dioxide minerals. A vapor of carbon-containing molecules
17145-416: The structure —(C≡C) n —. Its structure is relatively like that of Amorphous carbon. Cyclo[18]carbon (C 18 ) was synthesized in 2019. Many other allotropes have been hypothesized but have yet to be synthesized. The system of carbon allotropes spans an astounding range of extremes, considering that they are all merely structural formations of the same element. Between diamond and graphite: Despite
17280-400: The term dispersion generally refers to aforementioned temporal or frequency dispersion. Spatial dispersion refers to the non-local response of the medium to the space; this can be reworded as the wavevector dependence of the permittivity. For an exemplary anisotropic medium, the spatial relation between electric and electric displacement field can be expressed as a convolution : where
17415-409: The term is used in the field of optics to describe light and other electromagnetic waves , dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, and in gravity waves (ocean waves). Within optics, dispersion is a property of telecommunication signals along transmission lines (such as microwaves in coaxial cable ) or
17550-432: The use of achromats , multielement lenses with glasses of different dispersion. They are constructed in such a way that the chromatic aberrations of the different parts cancel out. Pulsars are spinning neutron stars that emit pulses at very regular intervals ranging from milliseconds to seconds. Astronomers believe that the pulses are emitted simultaneously over a wide range of frequencies. However, as observed on Earth,
17685-451: The volatiles. Diamonds can also form polycrystalline aggregates. There have been attempts to classify them into groups with names such as boart , ballas , stewartite, and framesite, but there is no widely accepted set of criteria. Carbonado, a type in which the diamond grains were sintered (fused without melting by the application of heat and pressure), is black in color and tougher than single crystal diamond. It has never been observed in
17820-543: The wavelength dependence of the real part of the refractive index is related to the material absorption , described by the imaginary part of the refractive index (also called the extinction coefficient ). In particular, for non-magnetic materials ( μ = μ 0 ), the susceptibility χ that appears in the Kramers–Kronig relations is the electric susceptibility χ e = n − 1. The most commonly seen consequence of dispersion in optics
17955-475: The waves are confined to some region. In a waveguide, both types of dispersion will generally be present, although they are not strictly additive. For example, in fiber optics the material and waveguide dispersion can effectively cancel each other out to produce a zero-dispersion wavelength , important for fast fiber-optic communication . Material dispersion can be a desirable or undesirable effect in optical applications. The dispersion of light by glass prisms
18090-429: The world's largest diamond deposit, estimated at trillions of carats, and formed by an asteroid impact. A common misconception is that diamonds form from highly compressed coal . Coal is formed from buried prehistoric plants, and most diamonds that have been dated are far older than the first land plants . It is possible that diamonds can form from coal in subduction zones , but diamonds formed in this way are rare, and
18225-477: Was found to be a very poor lubricant. This fact led to the discovery that graphite's lubricity is due to adsorbed air and water between the layers, unlike other layered dry lubricants such as molybdenum disulfide . Recent studies suggest that an effect called superlubricity can also account for this effect. When a large number of crystallographic defects (physical) bind these planes together, graphite loses its lubrication properties and becomes pyrolytic carbon ,
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