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Tetragonal
In crystallography, the tetragonal crystal system is one of the 7 crystal systems. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (''a'' by ''a'') and height (''c'', which is different from ''a''). Bravais lattices There are two tetragonal Bravais lattices: the primitive tetragonal and the body-centered tetragonal. The base-centered tetragonal lattice is equivalent to the primitive tetragonal lattice with a smaller unit cell, while the face-centered tetragonal lattice is equivalent to the body-centered tetragonal lattice with a smaller unit cell. Crystal classes The point groups that fall under this crystal system are listed below, followed by their representations in international notation, Schoenflies notation, orbifold notation, Coxeter notation and mineral examples.Hurlbut, Cornelius S.; Klein, Cornelis, 1985, ''Manual of Mineralogy'', 20th ed., ...
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Crystal System
In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their point groups, and into lattice systems according to their Bravais lattices. Crystal systems that have space groups assigned to a common lattice system are combined into a crystal family. The seven crystal systems are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. Informally, two crystals are in the same crystal system if they have similar symmetries (albeit there are many exceptions). Classifications Crystals can be classified in three ways: lattice systems, crystal systems and crystal families. The various classifications are often confused: in particular the trigonal crystal system is often confused with the rhombohedral lattice system, and the term "crystal system" is sometimes used to mean "lattic ...
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Tetragonal
In crystallography, the tetragonal crystal system is one of the 7 crystal systems. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (''a'' by ''a'') and height (''c'', which is different from ''a''). Bravais lattices There are two tetragonal Bravais lattices: the primitive tetragonal and the body-centered tetragonal. The base-centered tetragonal lattice is equivalent to the primitive tetragonal lattice with a smaller unit cell, while the face-centered tetragonal lattice is equivalent to the body-centered tetragonal lattice with a smaller unit cell. Crystal classes The point groups that fall under this crystal system are listed below, followed by their representations in international notation, Schoenflies notation, orbifold notation, Coxeter notation and mineral examples.Hurlbut, Cornelius S.; Klein, Cornelis, 1985, ''Manual of Mineralogy'', 20th ed., ...
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Body-centered Tetragonal
In crystallography, the tetragonal crystal system is one of the 7 crystal systems. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (''a'' by ''a'') and height (''c'', which is different from ''a''). Bravais lattices There are two tetragonal Bravais lattices: the primitive tetragonal and the body-centered tetragonal. The base-centered tetragonal lattice is equivalent to the primitive tetragonal lattice with a smaller unit cell, while the face-centered tetragonal lattice is equivalent to the body-centered tetragonal lattice with a smaller unit cell. Crystal classes The point groups that fall under this crystal system are listed below, followed by their representations in international notation, Schoenflies notation, orbifold notation, Coxeter notation and mineral examples.Hurlbut, Cornelius S.; Klein, Cornelis, 1985, ''Manual of Mineralogy'', 20th ed ...
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Cristobalite
Cristobalite is a mineral polymorph of silica that is formed at very high temperatures. It has the same chemical formula as quartz, SiO2, but a distinct crystal structure. Both quartz and cristobalite are polymorphs with all the members of the quartz group, which also include coesite, tridymite and stishovite. It is named after Cerro San Cristóbal in Pachuca Municipality, Hidalgo, Mexico. It is used in dentistry as a component of alginate impression materials as well as for making models of teeth. Properties Metastability Cristobalite is stable only above 1470 °C, but can crystallize and persist metastably at lower temperatures. The persistence of cristobalite outside its thermodynamic stability range occurs because the transition from cristobalite to quartz or tridymite is "reconstructive", requiring the breaking up and reforming of the silica framework. These frameworks are composed of Si O4 tetrahedra in which every oxygen atom is shared with a neighbouring te ...
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Wulfenite
Wulfenite is a lead molybdate mineral with the formula Pb Mo O4. It can be most often found as thin tabular crystals with a bright orange-red to yellow-orange color, sometimes brown, although the color can be highly variable. In its yellow form it is sometimes called "yellow lead ore". It crystallizes in the tetragonal system, often occurring as stubby, pyramidal or tabular crystals. It also occurs as earthy, granular masses. It is found in many localities, associated with lead ores as a secondary mineral associated with the oxidized zone of lead deposits. It is also a secondary ore of molybdenum, and is sought by collectors. Discovery and occurrence Wulfenite was first described in 1845 for an occurrence in Bad Bleiberg, Carinthia, Austria. It was named for Franz Xavier von Wulfen (1728–1805), an Austrian mineralogist. It occurs as a secondary mineral in oxidized hydrothermal lead deposits. It occurs with cerussite, anglesite, smithsonite, hemimorphite, vanadinite, ...
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Coxeter Notation
In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups. The notation is named after H. S. M. Coxeter, and has been more comprehensively defined by Norman Johnson. Reflectional groups For Coxeter groups, defined by pure reflections, there is a direct correspondence between the bracket notation and Coxeter-Dynkin diagram. The numbers in the bracket notation represent the mirror reflection orders in the branches of the Coxeter diagram. It uses the same simplification, suppressing 2s between orthogonal mirrors. The Coxeter notation is simplified with exponents to represent the number of branches in a row for linear diagram. So the ''A''''n'' group is represented by ''n''−1 to imply ''n'' nodes connected by ''n−1'' order-3 branches. Examp ...
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Chalcopyrite
Chalcopyrite ( ) is a copper iron sulfide mineral and the most abundant copper ore mineral. It has the chemical formula CuFeS2 and crystallizes in the tetragonal system. It has a brassy to golden yellow color and a hardness of 3.5 to 4 on the Mohs scale. Its streak is diagnostic as green-tinged black. On exposure to air, chalcopyrite tarnishes to a variety of oxides, hydroxides, and sulfates. Associated copper minerals include the sulfides bornite (Cu5FeS4), chalcocite (Cu2S), covellite (CuS), digenite (Cu9S5); carbonates such as malachite and azurite, and rarely oxides such as cuprite (Cu2O). Is rarely found in association with native copper. Chalcopyrite is a conductor of electricity. Etymology The name chalcopyrite comes from the Greek words , which means copper, and ', which means striking fire. It was sometimes historically referred to as "yellow copper". Identification Chalcopyrite is often confused with pyrite and gold since all three of these minerals have a yell ...
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Space Group
In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it unchanged. In three dimensions, space groups are classified into 219 distinct types, or 230 types if chiral copies are considered distinct. Space groups are discrete cocompact groups of isometries of an oriented Euclidean space in any number of dimensions. In dimensions other than 3, they are sometimes called Bieberbach groups. In crystallography, space groups are also called the crystallographic or Fedorov groups, and represent a description of the symmetry of the crystal. A definitive source regarding 3-dimensional space groups is the ''International Tables for Crystallography'' . History Space groups in 2 dimensions are the 17 wallpaper groups which have been known for several centuries, though the proof that the list was complete was ...
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Hermann–Mauguin Notation
In geometry, Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups. It is named after the German crystallographer Carl Hermann (who introduced it in 1928) and the French mineralogist Charles-Victor Mauguin (who modified it in 1931). This notation is sometimes called international notation, because it was adopted as standard by the ''International Tables For Crystallography'' since their first edition in 1935. The Hermann–Mauguin notation, compared with the Schoenflies notation, is preferred in crystallography because it can easily be used to include translational symmetry elements, and it specifies the directions of the symmetry axes. Point groups Rotation axes are denoted by a number ''n'' — 1, 2, 3, 4, 5, 6, 7, 8 ... (angle of rotation ''φ'' = ). For improper rotations, Hermann–Mauguin symbols show rotoinversion axes, unlike Schoenflies and Shubnikov notations, that shows rotation-reflection a ...
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Pinnoite
Pinnoite is a magnesium borate mineral with formula: MgB2O(OH)6 or MgB2O4·3(H2O). It crystallizes in the tetragonal crystal system and occurs as colorless to yellow or light green radial fibrous clusters and rarely as short prismatic crystals. Pinnoite was first described in 1884 for an occurrence in the Stassfurt potash deposit, Saxony-Anhalt, Germany and named for the mine counselor Oberbergrat Pinno of Halle, Germany. It occurs in marine evaporite deposits and as efflorescence associated with mineral springs. It occurs with boracite and kaliborite. It also occurs in the borax mines of Death Valley in California, the Da Quidam saline lake of the Qinghai-Xizang Plateau in Tibet and in Socacastro, Salta Province, Argentina Argentina (), officially the Argentine Republic ( es, link=no, República Argentina), is a country in the southern half of South America. Argentina covers an area of , making it the second-largest country in South America after Brazil, th .... R ...
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Piypite
Piypite is a rare potassium, copper sulfate mineral with formula: K2Cu2O(SO4)2. It crystallizes in the tetragonal system and occurs as needlelike crystals and masses. Individual crystals are square in cross-section and often hollow. It is emerald green to black in color with a vitreous to greasy luster. It was first described in 1982 for an occurrence in the Main Fracture of the Tolbachik volcano, Kamchatka Oblast, Russia. It has also been reported from Mount Vesuvius, Italy, and in a slag deposit in the Bad Ems District in the Rhineland-Palatinate, Germany. Piypite occurs as a sublimate phase in a fumarole environment. Associated minerals include halite, sylvite, langbeinite, tenorite, hematite, tolbachite, dolerophanite, urusovite, aphthitalite Aphthitalite is a potassium sulfate mineral with the chemical formula: (K,Na)3Na(SO4)2. It was first described in 1835 for an occurrence on Mount Vesuvius, Italy. The name is from the Greek άφθητος, "unalterable", ...
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Diaboleite
Diaboleite is a blue-colored mineral with formula Pb2CuCl2(OH)4. It was discovered in England in 1923 and named ''diaboleite'', from the Greek word διά and boleite, meaning "distinct from boleite". The mineral has since been found in a number of countries. Description Diaboleite is deep blue in color and pale blue in transmitted light. The mineral occurs as tabular crystals up to in size, as subparallel aggregates, or it has massive habit. Vicinal forms of the tabular crystals have a square or octagonal outline and rarely exhibit pyramidal hemihedralism. Formation Diaboleite occurs in manganese oxide ores, as a secondary mineral in lead and copper oxide ores, and in seawater-exposed slag. Diaboleite has been found in association with atacamite, boleite, caledonite, cerussite, chloroxiphite, hydrocerussite, leadhillite, mendipite, paratacamite, phosgenite, and wherryite. A study in 1986 synthesized diaboleite crystals up to in size using two different methods. The stu ...
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