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106-480: A crew is a body or a group of people who work at a common activity, generally in a structured or hierarchical organization. A location in which a crew works is called a crewyard or a workyard . The word has nautical resonances: the tasks involved in operating a ship, particularly a sailing ship, providing numerous specialities within a ship's crew, often organised with a chain of command . Traditional nautical usage strongly distinguishes officers from crew, though

212-505: A 3D model of a human for example, the chest is a parent of the upper left arm, which is a parent of the lower left arm, which is a parent of the hand . This pattern is used in modeling and animation for almost everything built as a 3D digital model. Many grammatical theories, such as phrase-structure grammar , involve hierarchy. Direct–inverse languages such as Cree and Mapudungun distinguish subject and object on verbs not by different subject and object markers, but via

318-411: A branching hierarchy , one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher). For many people, the word "hierarchy" automatically evokes an image of a branching hierarchy. Branching hierarchies are present within numerous systems, including organizations and classification schemes . The broad category of branching hierarchies can be further subdivided based on

424-436: 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 is metastable and converts to it at a negligible rate under those conditions. Diamond has

530-514: A family tree ) and inheritance ( succession and heirship ). All the requisites of a well-rounded life and lifestyle can be organized using Maslow's hierarchy of human needs - according to Maslow's hierarchy of human needs. Learning steps often follow a hierarchical scheme—to master differential equations one must first learn calculus ; to learn calculus one must first learn elementary algebra ; and so on. Nature offers hierarchical structures, as numerous schemes such as Linnaean taxonomy ,

636-475: A reverse hierarchy , the conceptual pyramid of authority is turned upside-down, so that the apex is at the bottom and the base is at the top. This mode represents the idea that members of the higher rankings are responsible for the members of the lower rankings. Empirically, when we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure. On theoretical grounds we could expect complex systems to be hierarchies in

742-491: 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

848-400: A business setting, a superior is a supervisor/boss and a peer is a colleague . Degree of branching refers to the number of direct subordinates or children an object has (in graph theory, equivalent to the number of other vertices connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the "maximum degree", the highest degree present in

954-453: 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

1060-446: A containment hierarchy is demonstrated in class inheritance in object-oriented programming . Two types of containment hierarchies are the subsumptive containment hierarchy and the compositional containment hierarchy. A subsumptive hierarchy " subsumes " its children, and a compositional hierarchy is " composed " of its children. A hierarchy can also be both subsumptive and compositional . A subsumptive containment hierarchy

1166-727: 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

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1272-459: 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 the Earth's mantle , although

1378-452: 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

1484-789: 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

1590-402: A file on a computer desktop, one may first direct them towards the main folder, then the subfolders within the main folder. They will keep opening files within the folders until the designated file is located. For more complicated hierarchies, the stair structure represents hierarchical relationships through the use of visual stacking. Visually imagine the top of a downward staircase beginning at

1696-480: 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

1802-428: A generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example: A square can always also be referred to as a quadrilateral, polygon or shape. In this way, it is a hierarchy. However, consider the set of polygons using this classification. A square can only be

1908-511: A hierarchy of persons. In this system, the three (or four with Algonquian languages ) persons occur in a hierarchy of salience . To distinguish which is subject and which object, inverse markers are used if the object outranks the subject. On the other hand, languages include a variety of phenomena that are not hierarchical. For example, the relationship between a pronoun and a prior noun-phrase to which it refers commonly crosses grammatical boundaries in non-hierarchical ways. The structure of

2014-406: A higher-level entity can have on x' s properties and interactions. Furthermore, the entities found at each level are autonomous . Kulish (2002) suggests that almost every system of organization which humans apply to the world is arranged hierarchically. Some conventional definitions of the terms "nation" and "government" suggest that every nation has a government and that every government

2120-475: 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

2226-529: A musical composition is often understood hierarchically (for example by Heinrich Schenker (1768–1835, see Schenkerian analysis ), and in the (1985) Generative Theory of Tonal Music , by composer Fred Lerdahl and linguist Ray Jackendoff ). The sum of all notes in a piece is understood to be an all-inclusive surface, which can be reduced to successively more sparse and more fundamental types of motion. The levels of structure that operate in Schenker's theory are

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2332-403: 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

2438-410: A problem. The use of parentheses is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example: (2 + 5) × (7 - 4). In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with

2544-439: A quadrilateral; it can never be a triangle , hexagon , etc. Nested hierarchies are the organizational schemes behind taxonomies and systematic classifications. For example, using the original Linnaean taxonomy (the version he laid out in the 10th edition of Systema Naturae ), a human can be formulated as: Taxonomies may change frequently (as seen in biological taxonomy ), but the underlying concept of nested hierarchies

2650-404: A required general property. These level hierarchies are characterized by bi-directional causation . Upward causation involves lower-level entities causing some property of a higher level entity; children entities may interact to yield parent entities, and parents are composed at least partly by their children. Downward causation refers to the effect that the incorporation of entity x into

2756-441: A system that is largely hierarchical can also incorporate alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a path . All parts of the hierarchy that are not linked vertically to one another nevertheless can be "horizontally" linked through a path by traveling up the hierarchy to find a common direct or indirect superior, and then down again. This

2862-463: 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),

2968-467: 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

3074-425: 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

3180-466: A world in which complexity had to evolve from simplicity. System hierarchies analysis performed in the 1950s, laid the empirical foundations for a field that would become, from the 1980s, hierarchical ecology . The theoretical foundations are summarized by thermodynamics . When biological systems are modeled as physical systems , in the most general abstraction, they are thermodynamic open systems that exhibit self-organised behavior, and

3286-449: 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

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3392-555: Is a branching hierarchy in which at least one object has two parent objects. For example, a graduate student can have two co-supervisors to whom the student reports directly and equally, and who have the same level of authority within the university hierarchy (i.e., they have the same position or tenure status). Possibly the first use of the English word hierarchy cited by the Oxford English Dictionary

3498-441: Is a classification of object classes from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and " IS-A hierarchy". The last term describes the relationship between each level—a lower-level object "is a" member of the higher class. The taxonomical structure outlined above is a subsumptive containment hierarchy. Using again the example of Linnaean taxonomy, it can be seen that an object that

3604-404: Is a direct extrapolation of the nested hierarchy concept. All of the ordered sets are still nested, but every set must be " strict "—no two sets can be identical. The shapes example above can be modified to demonstrate this: The notation x ⊊ y {\displaystyle x\subsetneq y\,} means x is a subset of y but is not equal to  y . A general example of

3710-485: Is a hierarchical ordering of nested sets . The concept of nesting is exemplified in Russian matryoshka dolls . Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll;

3816-508: Is a member of the level Mammalia "is a" member of the level Animalia ; more specifically, a human "is a" primate, a primate "is a" mammal, and so on. A subsumptive hierarchy can also be defined abstractly as a hierarchy of " concepts ". For example, with the Linnaean hierarchy outlined above, an entity name like Animalia is a way to group all the species that fit the conceptualization of an animal. A compositional containment hierarchy

3922-415: 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

4028-420: 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

4134-413: Is akin to two co-workers or colleagues ; each reports to a common superior, but they have the same relative amount of authority. Organizational forms exist that are both alternative and complementary to hierarchy. Heterarchy is one such form. Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see below ). In an organizational context,

4240-728: 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

4346-405: Is always transitive . The second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects. Mathematically, in its most general form, a hierarchy is a partially ordered set or poset . The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with

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4452-420: Is always the same. In many programming taxonomies and syntax models (as well as fractals in mathematics), nested hierarchies, including Russian dolls, are also used to illustrate the properties of self-similarity and recursion . Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic. A containment hierarchy

4558-507: Is an ordering of the parts that make up a system—the system is "composed" of these parts. Most engineered structures, whether natural or artificial, can be broken down in this manner. The compositional hierarchy that every person encounters at every moment is the hierarchy of life . Every person can be reduced to organ systems , which are composed of organs , which are composed of tissues , which are composed of cells , which are composed of molecules , which are composed of atoms . In fact,

4664-405: 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,

4770-414: 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

4876-490: Is credited with first use of it as an abstract noun. Since hierarchical churches, such as the Roman Catholic (see Catholic Church hierarchy ) and Eastern Orthodox churches, had tables of organization that were "hierarchical" in the modern sense of the word (traditionally with God as the pinnacle or head of the hierarchy), the term came to refer to similar organizational methods in secular settings. A hierarchy

4982-402: 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

5088-419: 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

5194-631: Is hierarchical. Sociologists can analyse socioeconomic systems in terms of stratification into a social hierarchy (the social stratification of societies), and all systematic classification schemes ( taxonomies ) are hierarchical. Most organized religions , regardless of their internal governance structures, operate as a hierarchy under deities and priesthoods . Many Christian denominations have an autocephalous ecclesiastical hierarchy of leadership . Families can be viewed as hierarchical structures in terms of cousinship (e.g., first cousin once removed, second cousin, etc.), ancestry (as depicted in

5300-412: 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

5406-404: 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

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5512-647: 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

5618-598: Is infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point. Organizations can be structured as a dominance hierarchy . In an organizational hierarchy, there is a single person or group with the most power or authority , and each subsequent level represents a lesser authority. Most organizations are structured in this manner, including governments , companies , armed forces , militia and organized religions . The units or persons within an organization may be depicted hierarchically in an organizational chart . In

5724-477: 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

5830-797: 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 (sp C) are unstable against high temperature (above about 400 °C (752 °F)) under atmospheric pressure. The structure gradually changes into sp C 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

5936-769: 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

6042-454: 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

6148-420: Is typically depicted as a pyramid , where the height of a level represents that level's status and width of a level represents the quantity of items at that level relative to the whole. For example, the few Directors of a company could be at the apex , and the base could be thousands of people who have no subordinates. These pyramids are often diagrammed with a triangle diagram which serves to emphasize

6254-484: The "postal district" , consists of 18 objects (letters). The next level down is the "zone", where the objects are the digits 0–9. This is an example of an overlapping hierarchy , because each of these 10 objects has 18 parents. The hierarchy continues downward to generate, in theory, 7,200,000 unique codes of the format A0A 0A0 (the second and third letter positions allow 20 objects each). Most library classification systems are also hierarchical. The Dewey Decimal System

6360-739: 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

6466-566: 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

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6572-559: 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

6678-436: 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

6784-536: 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

6890-477: The organization of life , and biomass pyramids attempt to document. While the above examples are often clearly depicted in a hierarchical form and are classic examples, hierarchies exist in numerous systems where this branching structure is not immediately apparent. For example, most postal-code systems are hierarchical. Using the Canadian postal code system as an example, the top level's binding concept,

6996-579: The set/subset relations between dissipative structures can be characterized in a hierarchy. Other hierarchical representations related to biology include ecological pyramids which illustrate energy flow or trophic levels in ecosystems , and taxonomic hierarchies, including the Linnean classification scheme and phylogenetic trees that reflect inferred patterns of evolutionary relationship among living and extinct species. CGI and computer-animation programs mostly use hierarchies for models. On

7102-402: 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

7208-462: 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,

7314-420: 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

7420-410: 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

7526-512: 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 ,

7632-436: 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

7738-501: 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

7844-598: 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,

7950-515: The degree. A flat hierarchy (also known for companies as flat organization ) is a branching hierarchy in which the maximum degree approaches infinity, i.e., that has a wide span. Most often, systems intuitively regarded as hierarchical have at most a moderate span. Therefore, a flat hierarchy is often not viewed as a hierarchy at all. For example, diamonds and graphite are flat hierarchies of numerous carbon atoms that can be further decomposed into subatomic particles. An overlapping hierarchy

8056-470: 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

8162-506: 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

8268-415: 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

8374-407: 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

8480-449: 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

8586-412: The following terms are often used related to hierarchies: In a mathematical context (in graph theory ), the general terminology used is different. Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, with data structures , objects are known as nodes , superiors are called parents and subordinates are called children . In

8692-433: The foreground, which is seen in all the details of the musical score; the middle ground, which is roughly a summary of an essential contrapuntal progression and voice-leading; and the background or Ursatz , which is one of only a few basic "long-range counterpoint" structures that are shared in the gamut of tonal music literature. Diamond Diamond is a solid form of the element carbon with its atoms arranged in

8798-408: 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

8904-525: 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 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

9010-455: 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

9116-423: 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

9222-474: 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

9328-527: The last two levels apply to all matter , at least at the macroscopic scale . Moreover, each of these levels inherit all the properties of their children . In this particular example, there are also emergent properties —functions that are not seen at the lower level (e.g., cognition is not a property of neurons but is of the brain )—and a scalar quality (molecules are bigger than atoms, cells are bigger than molecules, etc.). Both of these concepts commonly exist in compositional hierarchies, but they are not

9434-429: The left and descending on the right. Child elements are towards the bottom of the stairs and parent elements are at the top. This structure represents hierarchical relationships through the use of visual stacking. In plain English, a hierarchy can be thought of as a set in which: The first requirement is also interpreted to mean that a hierarchy can have no circular relationships ; the association between two objects

9540-467: 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

9646-591: 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

9752-579: 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

9858-469: 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

9964-620: 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

10070-407: The problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations. A nested hierarchy or inclusion hierarchy

10176-477: The rules of visual hierarchy . Visual hierarchy is also important for proper organization of files on computers. An example of visually representing hierarchy is through nested clusters. Nested clusters represent hierarchical relationships using layers of information. The child element is within the parent element, such as in a Venn diagram . This structure is most effective in representing simple hierarchical relationships. For example, when directing someone to open

10282-469: The same property value are grouped together, and each of those resulting levels is referred to as a class . "Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to

10388-470: The size differences between the levels (but not all triangle/pyramid diagrams are hierarchical; for example, the 1992 USDA food guide pyramid ). An example of a triangle diagram appears to the right. Another common representation of a hierarchical scheme is as a tree diagram . Phylogenetic trees , charts showing the structure of § Organizations , and playoff brackets in sports are often illustrated this way. More recently, as computers have allowed

10494-529: 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

10600-419: 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,

10706-399: The storage and navigation of ever larger data sets, various methods have been developed to represent hierarchies in a manner that makes more efficient use of the available space on a computer's screen. Examples include fractal maps, TreeMaps and Radial Trees . In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on

10812-517: The system as a whole. Categorization in this way yields two broad classes: linear and branching . In a linear hierarchy , the maximum degree is 1. In other words, all of the objects can be visualized in a line-up, and each object (excluding the top and bottom ones) has exactly one direct subordinate and one direct superior. This is referring to the objects and not the levels ; every hierarchy has this property with respect to levels, but normally each level can have an infinite number of objects. In

10918-496: The two groups combined form the ship's company . Members of a crew are often referred to by the title crewman or crew-member . Crew also refers to the sport of rowing , where teams row competitively in racing shells. Hierarchy A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates , although

11024-454: 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

11130-430: 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

11236-606: Was in 1881, when it was used in reference to the three orders of three angels as depicted by Pseudo-Dionysius the Areopagite (5th–6th centuries). Pseudo-Dionysius used the related Greek word (ἱεραρχία, hierarchia ) both in reference to the celestial hierarchy and the ecclesiastical hierarchy . The Greek term hierarchia means 'rule of a high priest', from hierarches (ἱεράρχης, 'president of sacred rites, high-priest') and that from hiereus (ἱερεύς, 'priest') and arche (ἀρχή, 'first place or power, rule'). Dionysius

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