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46-412: Like many monoxides, MnO adopts the rock salt structure , where cations and anions are both octahedrally coordinated. Also like many oxides, manganese(II) oxide is often nonstoichiometric : its composition can vary from MnO to MnO 1.045 . Below 118 K MnO is antiferromagnetic . MnO has the distinction of being one of the first compounds to have its magnetic structure determined by neutron diffraction ,

92-537: A cF lattice 12. Atomic packing factor (APF) is the fraction of volume that is occupied by atoms. The cP lattice has an APF of about 0.524, the cI lattice an APF of about 0.680, and the cF lattice an APF of about 0.740. The isometric crystal system class names, point groups (in Schönflies notation , Hermann–Mauguin notation , orbifold , and Coxeter notation ), type, examples, international tables for crystallography space group number, and space groups are listed in

138-600: A description is rarely used. The hexagonal crystal family consists of two crystal systems : trigonal and hexagonal. A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to a lattice system (see table in Crystal system#Crystal classes ). The trigonal crystal system consists of the 5 point groups that have a single three-fold rotation axis, which includes space groups 143 to 167. These 5 point groups have 7 corresponding space groups (denoted by R) assigned to

184-414: A face-centered cubic lattice is a hexagonal grid. Attempting to create a base-centered cubic lattice (i.e., putting an extra lattice point in the center of each horizontal face) results in a simple tetragonal Bravais lattice . Coordination number (CN) is the number of nearest neighbors of a central atom in the structure. Each sphere in a cP lattice has coordination number 6, in a cI lattice 8, and in

230-439: A motif is set onto the lattice points. E.g. the diamond and the zincblende lattices are fcc but not close-packed. Each is subdivided into other variants listed below. Although the unit cells in these crystals are conventionally taken to be cubes, the primitive unit cells often are not. The three Bravais latices in the cubic crystal system are: The primitive cubic lattice (cP) consists of one lattice point on each corner of

276-459: A primitive hexagonal nickel sublattice and a hexagonal close-packed arsenic sublattice. Each nickel atom is octahedrally coordinated to six arsenic atoms, while each arsenic atom is trigonal prismatically coordinated to six nickel atoms. The structure can also be described as an HCP lattice of arsenic with nickel occupying each octahedral void . Compounds adopting the NiAs structure are generally

322-510: A right rhombic prism unit cell with two equal axes ( a by a ), an included angle of 120° ( γ ) and a height ( c , which can be different from a ) perpendicular to the two base axes. The hexagonal unit cell for the rhombohedral Bravais lattice is the R-centered cell, consisting of two additional lattice points which occupy one body diagonal of the unit cell. There are two ways to do this, which can be thought of as two notations which represent

368-512: A structure in which water molecules lie at the nodes of the Weaire–Phelan structure and are hydrogen bonded together, and the larger gas molecules are trapped in the polyhedral cages. Hexagonal crystal system In crystallography , the hexagonal crystal family is one of the six crystal families , which includes two crystal systems (hexagonal and trigonal ) and two lattice systems (hexagonal and rhombohedral ). While commonly confused,

414-484: Is "B3". The Zincblende structure (also written "zinc blende") is named after the mineral zincblende ( sphalerite ), one form of zinc sulfide (β-ZnS). As in the rock-salt structure, the two atom types form two interpenetrating face-centered cubic lattices. However, it differs from rock-salt structure in how the two lattices are positioned relative to one another. The zincblende structure has tetrahedral coordination : Each atom's nearest neighbors consist of four atoms of

460-457: Is L2 1 . Together with the closely related half-Heusler and inverse-Huesler compounds, there are hundreds of examples. The space group of the iron monosilicide structure is P2 1 3 (No. 198), and the Strukturbericht designation is B20. This is a chiral structure, and is sometimes associated with helimagnetic properties. There are four atoms of each element for a total of eight atoms in

506-408: Is a component of fertilizers and food additives. Many thousands of tons are consumed annually for this purpose. Other uses include: a catalyst in the manufacture of allyl alcohol , ceramics, paints, colored glass, bleaching tallow and textile printing. Cubic crystal system#Rock-salt structure In crystallography , the cubic (or isometric ) crystal system is a crystal system where

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552-540: Is also an Fm 3 m structure but has 1:2 ratio of ions. The anti-fluorite structure is nearly identical, except the positions of the anions and cations are switched in the structure. They are designated Wyckoff positions 4a and 8c whereas the rock-salt structure positions are 4a and 4b. The space group of the Zincblende structure is called F 4 3m (in Hermann–Mauguin notation ), or 216. The Strukturbericht designation

598-514: Is also known as the II-VI family of compounds, most of which can be made in both the zincblende (cubic) or wurtzite (hexagonal) form. This group is also known as the III-V family of compounds. The Heusler structure, based on the structure of Cu 2 MnAl, is a common structure for ternary compounds involving transition metals . It has the space group Fm 3 m (No. 225), and the Strukturbericht designation

644-630: Is given by a c •sin(60°) Hexagonal close packed (hcp) is one of the two simple types of atomic packing with the highest density, the other being the face-centered cubic (fcc). However, unlike the fcc, it is not a Bravais lattice, as there are two nonequivalent sets of lattice points. Instead, it can be constructed from the hexagonal Bravais lattice by using a two-atom motif (the additional atom at about ( 2 ⁄ 3 ,  1 ⁄ 3 ,  1 ⁄ 2 )) associated with each lattice point. Compounds that consist of more than one element (e.g. binary compounds ) often have crystal structures based on

690-551: Is not a lattice, since it contains multiple atoms in its primitive cell . Other cubic elemental structures include the A15 structure found in tungsten , and the extremely complicated structure of manganese . Compounds that consist of more than one element (e.g. binary compounds ) often have crystal structures based on the cubic crystal system. Some of the more common ones are listed here. These structures can be viewed as two or more interpenetrating sublattices where each sublattice occupies

736-428: Is the union of the hexagonal crystal system and the trigonal crystal system. There are 52 space groups associated with it, which are exactly those whose Bravais lattice is either hexagonal or rhombohedral. The hexagonal crystal family consists of two lattice systems : hexagonal and rhombohedral. Each lattice system consists of one Bravais lattice . In the hexagonal family, the crystal is conventionally described by

782-426: The alkali metal hydrides and halides have the rock salt structure, though a few have the caesium chloride structure instead. Many transition metal monoxides also have the rock salt structure ( TiO , VO , CrO , MnO , FeO , CoO , NiO , CdO ). The early actinoid monocarbides also have this structure ( ThC , PaC , UC , NpC , PuC ). Much like the rock salt structure, the fluorite structure (AB 2 )

828-694: The caesium chloride (CsCl) structure is called Pm 3 m (in Hermann–Mauguin notation ), or "221" (in the International Tables for Crystallography). The Strukturbericht designation is "B2". There are nearly a hundred rare earth intermetallic compounds that crystallize in the CsCl structure, including many binary compounds of rare earths with magnesium , and with elements in groups 11 , 12 , and 13 . Other compounds showing caesium chloride like structure are CsBr , CsI , high-temperature RbCl , AlCo, AgZn, BeCu, MgCe, RuAl and SrTl. The space group of

874-447: The interstitial sites of the others. One structure is the "interpenetrating primitive cubic" structure, also called a "caesium chloride" or B2 structure. This structure is often confused for a body-centered cubic structure because the arrangement of atoms is the same. However, the caesium chloride structure has a basis composed of two different atomic species. In a body-centered cubic structure, there would be translational symmetry along

920-411: The radius ratio rule , this structure is more likely to be formed if the cation is somewhat smaller than the anion (a cation/anion radius ratio of 0.414 to 0.732). The interatomic distance (distance between cation and anion, or half the unit cell length a ) in some rock-salt-structure crystals are: 2.3 Å (2.3 × 10  m) for NaF, 2.8 Å for NaCl, and 3.2 Å for SnTe. Most of

966-472: The tetrahedral voids or vice versa. Examples of compounds with this structure include zincblende itself, lead(II) nitrate , many compound semiconductors (such as gallium arsenide and cadmium telluride ), and a wide array of other binary compounds. The boron group pnictogenides usually have a zincblende structure, though the nitrides are more common in the wurtzite structure , and their zincblende forms are less well known polymorphs . This group

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1012-410: The unit cell is in the shape of a cube . This is one of the most common and simplest shapes found in crystals and minerals . There are three main varieties of these crystals: Note: the term fcc is often used in synonym for the cubic close-packed or ccp structure occurring in metals. However, fcc stands for a face-centered-cubic Bravais lattice, which is not necessarily close-packed when

1058-457: The [111] direction. In the caesium chloride structure, translation along the [111] direction results in a change of species. The structure can also be thought of as two separate simple cubic structures, one of each species, that are superimposed within each other. The corner of the chloride cube is the center of the caesium cube, and vice versa. It works the same way for the NaCl structure described in

1104-420: The bulk crystal, but the structure can be favored in some nanocrystal forms of the material. In materials with more than one crystal structure, the prefix "w-" is sometimes added to the empirical formula to denote the wurtzite crystal structure, as in w-BN . Each of the two individual atom types forms a sublattice which is hexagonal close-packed (HCP-type). When viewed all together, the atomic positions are

1150-401: The carbonate: This calcining process is conducted anaerobically, lest Mn 2 O 3 form. An alternative route, mostly for demonstration purposes, is the oxalate method, which also applicable to the synthesis of ferrous oxide and stannous oxide . Upon heating in an oxygen-free atmosphere (usually CO 2 ), manganese(II) oxalate decomposes into MnO: Together with manganese sulfate, MnO

1196-410: The compounds that can take the wurtzite structure are wurtzite itself ( ZnS with up to 8% iron instead of zinc ), silver iodide (AgI), zinc oxide (ZnO), cadmium sulfide (CdS), cadmium selenide (CdSe), silicon carbide (α-SiC), gallium nitride (GaN), aluminium nitride (AlN), boron nitride (w-BN) and other semiconductors . In most of these compounds, wurtzite is not the favored form of

1242-489: The corners of a cube. Alternately, one could view this lattice as a simple cubic structure with a secondary atom in its cubic void . In addition to caesium chloride itself, the structure also appears in certain other alkali halides when prepared at low temperatures or high pressures. Generally, this structure is more likely to be formed from two elements whose ions are of roughly the same size (for example, ionic radius of Cs = 167 pm, and Cl = 181 pm). The space group of

1288-543: The cube; this means each simple cubic unit cell has in total one lattice point. Each atom at a lattice point is then shared equally between eight adjacent cubes, and the unit cell therefore contains in total one atom ( 1 ⁄ 8  × 8). The body-centered cubic lattice (cI) has one lattice point in the center of the unit cell in addition to the eight corner points. It has a net total of two lattice points per unit cell ( 1 ⁄ 8  × 8 + 1). The face-centered cubic lattice (cF) has lattice points on

1334-469: The faces of the cube, that each gives exactly one half contribution, in addition to the corner lattice points, giving a total of four lattice points per unit cell ( 1 ⁄ 8  × 8 from the corners plus 1 ⁄ 2  × 6 from the faces). The face-centered cubic lattice is closely related to the hexagonal close packed (hcp) system, where two systems differ only in the relative placements of their hexagonal layers. The [111] plane of

1380-723: The hexagonal crystal family. Some of the more common ones are listed here. These structures can be viewed as two or more interpenetrating sublattices where each sublattice occupies the interstitial sites of the others. The wurtzite crystal structure is referred to by the Strukturbericht designation B4 and the Pearson symbol hP4. The corresponding space group is No. 186 (in International Union of Crystallography classification) or P6 3 mc (in Hermann–Mauguin notation ). The Hermann-Mauguin symbols in P6 3 mc can be read as follows: Among

1426-446: The hexagonal lattice system. The 5 point groups in this crystal system are listed below, with their international number and notation, their space groups in name and example crystals. The 7 point groups ( crystal classes ) in this crystal system are listed below, followed by their representations in Hermann–Mauguin or international notation and Schoenflies notation , and mineral examples, if they exist. The unit cell volume

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1472-438: The lattice is non-primitive. The Bravais lattices in the hexagonal crystal family can also be described by rhombohedral axes. The unit cell is a rhombohedron (which gives the name for the rhombohedral lattice). This is a unit cell with parameters a = b = c ; α = β = γ ≠ 90°. In practice, the hexagonal description is more commonly used because it is easier to deal with a coordinate system with two 90° angles. However,

1518-457: The next section.  If you take out the Cl atoms, the leftover Na atoms still form an FCC structure, not a simple cubic structure. In the unit cell of CsCl, each ion is at the center of a cube of ions of the opposite kind, so the coordination number is eight. The central cation is coordinated to 8 anions on the corners of a cube as shown, and similarly, the central anion is coordinated to 8 cations on

1564-402: The opposite type, positioned like the four vertices of a regular tetrahedron . In zinc sulfide the ratio of zinc to sulfur is 1:1. Altogether, the arrangement of atoms in zincblende structure is the same as diamond cubic structure, but with alternating types of atoms at the different lattice sites. The structure can also be described as an FCC lattice of zinc with sulfur atoms occupying half of

1610-485: The opposite type, positioned like the six vertices of a regular octahedron . In sodium chloride there is a 1:1 ratio of sodium to chlorine atoms.  The structure can also be described as an FCC lattice of sodium with chlorine occupying each octahedral void or vice versa. Examples of compounds with this structure include sodium chloride itself, along with almost all other alkali halides, and "many divalent metal oxides, sulfides, selenides, and tellurides". According to

1656-526: The primitive cubic structure, with especially low atomic packing factor, is rare in nature, but is found in polonium . The bcc and fcc , with their higher densities, are both quite common in nature. Examples of bcc include iron , chromium , tungsten , and niobium . Examples of fcc include aluminium , copper , gold and silver . Another important cubic crystal structure is the diamond cubic structure, which can appear in carbon , silicon , germanium , and tin . Unlike fcc and bcc, this structure

1702-401: The rare mineral manganosite . It is prepared commercially by reduction of MnO 2 with hydrogen , carbon monoxide or methane , e.g.: Upon heating to 450   °C, manganese(II) nitrate gives a mixture of oxides, MnO 2-x , which can be reduced to the monoxide with hydrogen at ≥750   °C. MnO is particularly stable and resists further reduction. MnO can also be prepared by heating

1748-517: The report appearing in 1951. This study showed that the Mn ions form a face centered cubic magnetic sub-lattice where there are ferromagnetically coupled sheets that are anti-parallel with adjacent sheets. Manganese(II) oxide undergoes the chemical reactions typical of an ionic oxide. Upon treatment with acids, it converts to the corresponding manganese(II) salt and water . Oxidation of manganese(II) oxide gives manganese(III) oxide . MnO occurs in nature as

1794-530: The rhombohedral axes are often shown (for the rhombohedral lattice) in textbooks because this cell reveals the 3 m symmetry of the crystal lattice. The rhombohedral unit cell for the hexagonal Bravais lattice is the D-centered cell, consisting of two additional lattice points which occupy one body diagonal of the unit cell with coordinates ( 1 ⁄ 3 , 1 ⁄ 3 , 1 ⁄ 3 ) and ( 2 ⁄ 3 , 2 ⁄ 3 , 2 ⁄ 3 ). However, such

1840-463: The rhombohedral lattice system and 18 corresponding space groups (denoted by P) assigned to the hexagonal lattice system. Hence, the trigonal crystal system is the only crystal system whose point groups have more than one lattice system associated with their space groups. The hexagonal crystal system consists of the 7 point groups that have a single six-fold rotation axis. These 7 point groups have 27 space groups (168 to 194), all of which are assigned to

1886-506: The rock-salt or halite (sodium chloride) structure is denoted as Fm 3 m (in Hermann–Mauguin notation ), or "225" (in the International Tables for Crystallography). The Strukturbericht designation is "B1". In the rock-salt structure, each of the two atom types forms a separate face-centered cubic lattice, with the two lattices interpenetrating so as to form a 3D checkerboard pattern. The rock-salt structure has octahedral coordination : Each atom's nearest neighbors consist of six atoms of

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1932-552: The same as in lonsdaleite (hexagonal diamond ). Each atom is tetrahedrally coordinated. The structure can also be described as an HCP lattice of zinc with sulfur atoms occupying half of the tetrahedral voids or vice versa. The wurtzite structure is non-centrosymmetric (i.e., lacks inversion symmetry ). Due to this, wurtzite crystals can (and generally do) have properties such as piezoelectricity and pyroelectricity , which centrosymmetric crystals lack. The nickel arsenide structure consists of two interpenetrating sublattices:

1978-475: The same structure. In the usual so-called obverse setting, the additional lattice points are at coordinates ( 2 ⁄ 3 , 1 ⁄ 3 , 1 ⁄ 3 ) and ( 1 ⁄ 3 , 2 ⁄ 3 , 2 ⁄ 3 ), whereas in the alternative reverse setting they are at the coordinates ( 1 ⁄ 3 , 2 ⁄ 3 , 1 ⁄ 3 ) and ( 2 ⁄ 3 , 1 ⁄ 3 , 2 ⁄ 3 ). In either case, there are 3 lattice points per unit cell in total and

2024-424: The table below. There are a total 36 cubic space groups. Other terms for hexoctahedral are: normal class, holohedral , ditesseral central class, galena type. As a rule, since atoms in a solid attract each other, the more tightly packed arrangements of atoms tend to be more common. (Loosely packed arrangements do occur, though, for example if the orbital hybridization demands certain bond angles .) Accordingly,

2070-403: The trigonal crystal system and the rhombohedral lattice system are not equivalent (see section crystal systems below). In particular, there are crystals that have trigonal symmetry but belong to the hexagonal lattice (such as α- quartz ). The hexagonal crystal family consists of the 12 point groups such that at least one of their space groups has the hexagonal lattice as underlying lattice, and

2116-502: The unit cell. Examples occur among the transition metal silicides and germanides, as well as a few other compounds such as gallium palladide . A Weaire–Phelan structure has Pm 3 n (223) symmetry. It has three orientations of stacked tetradecahedrons with pyritohedral cells in the gaps. It is found as a crystal structure in chemistry where it is usually known as a "type I clathrate structure". Gas hydrates formed by methane, propane, and carbon dioxide at low temperatures have

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