1.
Germany
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Germany, officially the Federal Republic of Germany, is a federal parliamentary republic in central-western Europe. It includes 16 constituent states, covers an area of 357,021 square kilometres, with about 82 million inhabitants, Germany is the most populous member state of the European Union. After the United States, it is the second most popular destination in the world. Germanys capital and largest metropolis is Berlin, while its largest conurbation is the Ruhr, other major cities include Hamburg, Munich, Cologne, Frankfurt, Stuttgart, Düsseldorf and Leipzig. Various Germanic tribes have inhabited the northern parts of modern Germany since classical antiquity, a region named Germania was documented before 100 AD. During the Migration Period the Germanic tribes expanded southward, beginning in the 10th century, German territories formed a central part of the Holy Roman Empire. During the 16th century, northern German regions became the centre of the Protestant Reformation, in 1871, Germany became a nation state when most of the German states unified into the Prussian-dominated German Empire. After World War I and the German Revolution of 1918–1919, the Empire was replaced by the parliamentary Weimar Republic, the establishment of the national socialist dictatorship in 1933 led to World War II and the Holocaust. After a period of Allied occupation, two German states were founded, the Federal Republic of Germany and the German Democratic Republic, in 1990, the country was reunified. In the 21st century, Germany is a power and has the worlds fourth-largest economy by nominal GDP. As a global leader in industrial and technological sectors, it is both the worlds third-largest exporter and importer of goods. Germany is a country with a very high standard of living sustained by a skilled. It upholds a social security and universal health system, environmental protection. Germany was a member of the European Economic Community in 1957. It is part of the Schengen Area, and became a co-founder of the Eurozone in 1999, Germany is a member of the United Nations, NATO, the G8, the G20, and the OECD. The national military expenditure is the 9th highest in the world, the English word Germany derives from the Latin Germania, which came into use after Julius Caesar adopted it for the peoples east of the Rhine. This in turn descends from Proto-Germanic *þiudiskaz popular, derived from *þeudō, descended from Proto-Indo-European *tewtéh₂- people, the discovery of the Mauer 1 mandible shows that ancient humans were present in Germany at least 600,000 years ago. The oldest complete hunting weapons found anywhere in the world were discovered in a mine in Schöningen where three 380, 000-year-old wooden javelins were unearthed
2.
Oxide minerals
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The oxide mineral class includes those minerals in which the oxide anion is bonded to one or more metal ions. The hydroxide bearing minerals are typically included in the oxide class, the minerals with complex anion groups such as the silicates, sulfates, carbonates and phosphates are classed separately. This list uses it to modify the Classification of Nickel–Strunz,00 Clinobirnessite*,00 Kleberite*,00 Chubutite*,00 Struverite
3.
Chemical formula
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These are limited to a single typographic line of symbols, which may include subscripts and superscripts. A chemical formula is not a name, and it contains no words. Although a chemical formula may imply certain simple chemical structures, it is not the same as a full chemical structural formula. Chemical formulas can fully specify the structure of only the simplest of molecules and chemical substances, the simplest types of chemical formulas are called empirical formulas, which use letters and numbers indicating the numerical proportions of atoms of each type. Molecular formulas indicate the numbers of each type of atom in a molecule. For example, the formula for glucose is CH2O, while its molecular formula is C6H12O6. This is possible if the relevant bonding is easy to show in one dimension, an example is the condensed molecular/chemical formula for ethanol, which is CH3-CH2-OH or CH3CH2OH. For reasons of structural complexity, there is no condensed chemical formula that specifies glucose, chemical formulas may be used in chemical equations to describe chemical reactions and other chemical transformations, such as the dissolving of ionic compounds into solution. A chemical formula identifies each constituent element by its chemical symbol, in empirical formulas, these proportions begin with a key element and then assign numbers of atoms of the other elements in the compound, as ratios to the key element. For molecular compounds, these numbers can all be expressed as whole numbers. For example, the formula of ethanol may be written C2H6O because the molecules of ethanol all contain two carbon atoms, six hydrogen atoms, and one oxygen atom. Some types of compounds, however, cannot be written with entirely whole-number empirical formulas. An example is boron carbide, whose formula of CBn is a variable non-whole number ratio with n ranging from over 4 to more than 6.5. When the chemical compound of the consists of simple molecules. These types of formulas are known as molecular formulas and condensed formulas. A molecular formula enumerates the number of atoms to reflect those in the molecule, so that the formula for glucose is C6H12O6 rather than the glucose empirical formula. However, except for very simple substances, molecular chemical formulas lack needed structural information, for simple molecules, a condensed formula is a type of chemical formula that may fully imply a correct structural formula. For example, ethanol may be represented by the chemical formula CH3CH2OH
4.
Uranium dioxide
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Uranium dioxide or uranium oxide, also known as urania or uranous oxide, is an oxide of uranium, and is a black, radioactive, crystalline powder that naturally occurs in the mineral uraninite. It is used in fuel rods in nuclear reactors. A mixture of uranium and plutonium dioxides is used as MOX fuel, prior to 1960, it was used as yellow and black color in ceramic glazes and glass. Uranium dioxide is produced by reducing uranium trioxide with hydrogen, uO3 + H2 → UO2 + H2O at 700 °C This reaction plays an important part in the creation of nuclear fuel through nuclear reprocessing and uranium enrichment. The solid is isostructural with fluorite, where each U is surrounded by eight O nearest neighbors in a cubic arrangement, in addition, the dioxides of cerium, plutonium and neptunium have the same structures. No other elemental dioxides have the fluorite structure, upon melting, the measured average U-O coordination reduces from 8 in the crystalline solid, down to 6. 7±0.5 in the melt. Uranium dioxide is oxidized in contact with oxygen to the triuranium octaoxide, see the spent nuclear fuel page for further details. Water increases the rate of plutonium and uranium metals. Uranium dioxide is carbonized in contact with carbon, forming uranium carbide, UO2 +4 C → UC2 +2 CO This process must be done under an inert gas as uranium carbide is easily oxidized back into uranium oxide. UO2 is used mainly as fuel, specifically as UO2 or as a mixture of UO2 and PuO2 called a mixed oxide. Note that the conductivity of uranium dioxide is very low when compared with uranium, uranium nitride, uranium carbide. This low thermal conductivity can result in localised overheating in the centres of fuel pellets, the graph below shows the different temperature gradients in different fuel compounds. For these fuels the power density is the same and the diameter of all the pellets are the same. Uranium oxide was used to color glass and ceramics prior to World War II, in 1958 the military in both the USA and Europe allowed its commercial use again as depleted uranium, and its use began again on a more limited scale. Urania-based ceramic glazes are dark green or black when fired in a reduction or when UO2 is used, more commonly it is used in oxidation to produce yellow, orange. Orange-colored Fiestaware is an example of a product with a urania-colored glaze. Uranium glass is green to yellow, and often has strong fluorescent properties. Urania has also used in formulations of enamel and porcelain
5.
Crystal system
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In crystallography, the terms crystal system, crystal family and lattice system each refer to one of several classes of space groups, lattices, point groups or crystals. Informally, two crystals are in the crystal system if they have similar symmetries, though there are many exceptions to this. Space groups and crystals are divided into seven crystal systems according to their point groups, five of the crystal systems are essentially the same as five of the lattice systems, but the hexagonal and trigonal crystal systems differ from the hexagonal and rhombohedral lattice systems. The six crystal families are formed by combining the hexagonal and trigonal crystal systems into one hexagonal family, a lattice system is a class of lattices with the same set of lattice point groups, which are subgroups of the arithmetic crystal classes. The 14 Bravais lattices are grouped into seven lattice systems, triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, in a crystal system, a set of point groups and their corresponding space groups are assigned to a lattice system. Of the 32 point groups that exist in three dimensions, most are assigned to only one system, in which case both the crystal and lattice systems have the same name. However, five point groups are assigned to two systems, rhombohedral and hexagonal, because both exhibit threefold rotational symmetry. These point groups are assigned to the crystal system. In total there are seven crystal systems, triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, a crystal family is determined by lattices and point groups. It is formed by combining crystal systems which have space groups assigned to a lattice system. In three dimensions, the families and systems are identical, except the hexagonal and trigonal crystal systems. In total there are six families, triclinic, monoclinic, orthorhombic, tetragonal, hexagonal. Spaces with less than three dimensions have the number of crystal systems, crystal families and lattice systems. In one-dimensional space, there is one crystal system, in 2D space, there are four crystal systems, oblique, rectangular, square and hexagonal. The relation between three-dimensional crystal families, crystal systems and lattice systems is shown in the table, Note. To avoid confusion of terminology, the term trigonal lattice is not used, if the original structure and inverted structure are identical, then the structure is centrosymmetric. Still, even for non-centrosymmetric case, inverted structure in some cases can be rotated to align with the original structure and this is the case of non-centrosymmetric achiral structure. If the inverted structure cannot be rotated to align with the structure, then the structure is chiral
6.
Cubic crystal system
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In crystallography, the cubic crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals, there are three main varieties of these crystals, Primitive cubic Body-centered cubic, Face-centered cubic Each is subdivided into other variants listed below. Note that although the cell in these crystals is conventionally taken to be a cube. This is related to the fact that in most cubic crystal systems, a classic isometric crystal has square or pentagonal faces. The three Bravais lattices in the crystal system are, The primitive cubic system consists of one lattice point on each corner of the cube. Each atom at a point is then shared equally between eight adjacent cubes, and the unit cell therefore contains in total one atom. The body-centered cubic system has one point in the center of the unit cell in addition to the eight corner points. It has a net total of 2 lattice points per unit cell, Each sphere in a cF lattice has coordination number 12. The face-centered cubic system is related to the hexagonal close packed system. The plane of a cubic system is a hexagonal grid. Attempting to create a C-centered cubic crystal system would result in a simple tetragonal Bravais lattice, there are a total 36 cubic space groups. Other terms for hexoctahedral are, normal class, holohedral, ditesseral central class, a simple cubic unit cell has a single cubic void in the center. Additionally, there are 24 tetrahedral voids located in a square spacing around each octahedral void and these tetrahedral voids are not local maxima and are not technically voids, but they do occasionally appear in multi-atom unit cells. A face-centered cubic unit cell has eight tetrahedral voids located midway between each corner and the center of the cell, for a total of eight net tetrahedral voids. One important characteristic of a structure is its atomic packing factor. This is calculated by assuming all the atoms are identical spheres. The atomic packing factor is the proportion of space filled by these spheres, assuming one atom per lattice point, in a primitive cubic lattice with cube side length a, the sphere radius would be a⁄2 and the atomic packing factor turns out to be about 0.524. Similarly, in a bcc lattice, the atomic packing factor is 0.680, as a rule, since atoms in a solid attract each other, the more tightly packed arrangements of atoms tend to be more common
7.
Crystallographic point group
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For a periodic crystal, the group must also be consistent with maintenance of the three-dimensional translational symmetry that defines crystallinity. The macroscopic properties of a crystal would look exactly the same before, in the classification of crystals, each point group is also known as a crystal class. There are infinitely many three-dimensional point groups, however, the crystallographic restriction of the infinite families of general point groups results in there being only 32 crystallographic point groups. These 32 point groups are one-and-the same as the 32 types of morphological crystalline symmetries derived in 1830 by Johann Friedrich Christian Hessel from a consideration of observed crystal forms, the point groups are denoted by their component symmetries. There are a few standard notations used by crystallographers, mineralogists, for the correspondence of the two systems below, see crystal system. In Schoenflies notation, point groups are denoted by a symbol with a subscript. The symbols used in crystallography mean the following, Cn indicates that the group has a rotation axis. Cnh is Cn with the addition of a plane perpendicular to the axis of rotation. Cnv is Cn with the addition of n mirror planes parallel to the axis of rotation, s2n denotes a group that contains only a 2n-fold rotation-reflection axis. Dn indicates that the group has a rotation axis plus n twofold axes perpendicular to that axis. Dnh has, in addition, a plane perpendicular to the n-fold axis. Dnd has, in addition to the elements of Dn, mirror planes parallel to the n-fold axis, the letter T indicates that the group has the symmetry of a tetrahedron. Td includes improper rotation operations, T excludes improper rotation operations, the letter O indicates that the group has the symmetry of an octahedron, with or without improper operations. Due to the crystallographic restriction theorem, n =1,2,3,4, d4d and D6d are actually forbidden because they contain improper rotations with n=8 and 12 respectively. The 27 point groups in the table plus T, Td, Th, O, an abbreviated form of the Hermann–Mauguin notation commonly used for space groups also serves to describe crystallographic point groups. Group names are Molecular symmetry Point group Space group Point groups in three dimensions Crystal system Point-group symbols in International Tables for Crystallography,12.1, pp. 818-820 Names and symbols of the 32 crystal classes in International Tables for Crystallography. 10.1, p.794 Pictorial overview of the 32 groups Point Groups - Flow Chart Inorganic Chemistry Group Theory Practice Problems
8.
H-M symbol
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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 and the French mineralogist Charles-Victor Mauguin and 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. Rotation axes are denoted by a number n —1,2,3,4,5,6,7,8, for improper rotations, Hermann–Mauguin symbols show rotoinversion axes, unlike Schoenflies and Shubnikov notations, where the preference is given to rotation-reflection axes. The rotoinversion axes are represented by the number with a macron. The symbol for a plane is m. The direction of the plane is defined as the direction of perpendicular to the face. Hermann–Mauguin symbols show symmetrically non-equivalent axes and planes, the direction of a symmetry element is represented by its position in the Hermann–Mauguin symbol. If a rotation axis n and a mirror plane m have the same direction, if two or more axes have the same direction, the axis with higher symmetry is shown. Higher symmetry means that the axis generates a pattern with more points, for example, rotation axes 3,4,5,6,7,8 generate 3-, 4-, 5-, 6-, 7-, 8-point patterns, respectively. Improper rotation axes 3,4,5,6,7,8 generate 6-, 4-, 10-, 6-, 14-, 8-point patterns, if both, the rotation and rotoinversion axes satisfy the previous rule, the rotation axis should be chosen. For example, 3/m combination is equivalent to 6, since 6 generates 6 points, and 3 generates only 3,6 should be written instead of 3/m. Analogously, in the case when both 3 and 3 axes are present,3 should be written, however we write 4/m, not 4/m, because both 4 and 4 generate four points. Finally, the Hermann–Mauguin symbol depends on the type of the group and these groups may contain only two-fold axes, mirror planes, and inversion center. These are the point groups 1 and 1,2, m, and 2/m, and 222, 2/m2/m2/m. If the symbol contains three positions, then they denote symmetry elements in the x, y, z direction, First position — primary direction — z direction, assigned to the higher-order axis. Second position — symmetrically equivalent secondary directions, which are perpendicular to the z-axis and these can be 2, m, or 2/m. Third position — symmetrically equivalent tertiary directions, passing between secondary directions and these can be 2, m, or 2/m. These are the crystallographic groups 3,32, 3m,3, and 32/m,4,422, 4mm,4, 42m, 4/m, and 4/m2/m2/m, and 6,622, 6mm,6, 6m2, 6/m, and 6/m2/m2/m
