1.
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
2.
Aluminium oxide
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Aluminium oxide or aluminum oxide is a chemical compound of aluminium and oxygen with the chemical formula Al2O3. It is the most commonly occurring of several aluminium oxides, and it is commonly called alumina, and may also be called aloxide, aloxite, or alundum depending on particular forms or applications. It occurs naturally in its crystalline polymorphic phase α-Al2O3 as the mineral corundum, varieties of form the precious gemstones ruby. Al2O3 is significant in its use to produce metal, as an abrasive owing to its hardness. Corundum is the most common naturally occurring form of aluminium oxide. Rubies and sapphires are gem-quality forms of corundum, which owe their characteristic colors to trace impurities, rubies are given their characteristic deep red color and their laser qualities by traces of chromium. Sapphires come in different colors given by various other impurities, such as iron, Al2O3 is an electrical insulator but has a relatively high thermal conductivity for a ceramic material. Aluminium oxide is insoluble in water, in its most commonly occurring crystalline form, called corundum or α-aluminium oxide, its hardness makes it suitable for use as an abrasive and as a component in cutting tools. Aluminium oxide is responsible for the resistance of aluminium to weathering. Metallic aluminium is very reactive with oxygen, and a thin passivation layer of aluminium oxide forms on any exposed aluminium surface. This layer protects the metal from further oxidation, the thickness and properties of this oxide layer can be enhanced using a process called anodising. A number of alloys, such as bronzes, exploit this property by including a proportion of aluminium in the alloy to enhance corrosion resistance. Aluminium oxide was taken off the United States Environmental Protection Agencys chemicals lists in 1988, aluminium oxide is on EPAs Toxics Release Inventory list if it is a fibrous form. Al2O3 +6 HF →2 AlF3 +3 H2O Al2O3 +2 NaOH +3 H2O →2 NaAl4 The most common form of aluminium oxide is known as corundum. The oxygen ions form a hexagonal close-packed structure with aluminium ions filling two-thirds of the octahedral interstices. In terms of its crystallography, corundum adopts a trigonal Bravais lattice with a group of R-3c. The primitive cell contains two units of aluminium oxide. Each has a crystal structure and properties
3.
Aluminium
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Aluminium or aluminum is a chemical element in the boron group with symbol Al and atomic number 13. It is a silvery-white, soft, nonmagnetic, ductile metal, Aluminium metal is so chemically reactive that native specimens are rare and limited to extreme reducing environments. Instead, it is combined in over 270 different minerals. The chief ore of aluminium is bauxite, Aluminium is remarkable for the metals low density and its ability to resist corrosion through the phenomenon of passivation. Aluminium and its alloys are vital to the industry and important in transportation and structures, such as building facades. The oxides and sulfates are the most useful compounds of aluminium, despite its prevalence in the environment, no known form of life uses aluminium salts metabolically, but aluminium is well tolerated by plants and animals. Because of these salts abundance, the potential for a role for them is of continuing interest. Aluminium is a soft, durable, lightweight, ductile. It is nonmagnetic and does not easily ignite, a fresh film of aluminium serves as a good reflector of visible light and an excellent reflector of medium and far infrared radiation. The yield strength of aluminium is 7–11 MPa, while aluminium alloys have yield strengths ranging from 200 MPa to 600 MPa. Aluminium has about one-third the density and stiffness of steel and it is easily machined, cast, drawn and extruded. Aluminium atoms are arranged in a cubic structure. Aluminium has an energy of approximately 200 mJ/m2. Aluminium is a thermal and electrical conductor, having 59% the conductivity of copper. Aluminium is capable of superconductivity, with a critical temperature of 1.2 kelvin. Aluminium is the most common material for the fabrication of superconducting qubits, the strongest aluminium alloys are less corrosion resistant due to galvanic reactions with alloyed copper. This corrosion resistance is reduced by aqueous salts, particularly in the presence of dissimilar metals. In highly acidic solutions, aluminium reacts with water to form hydrogen, primarily because it is corroded by dissolved chlorides, such as common sodium chloride, household plumbing is never made from aluminium
4.
Oxygen
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Oxygen is a chemical element with symbol O and atomic number 8. It is a member of the group on the periodic table and is a highly reactive nonmetal. By mass, oxygen is the third-most abundant element in the universe, after hydrogen, at standard temperature and pressure, two atoms of the element bind to form dioxygen, a colorless and odorless diatomic gas with the formula O2. This is an important part of the atmosphere and diatomic oxygen gas constitutes 20. 8% of the Earths atmosphere, additionally, as oxides the element makes up almost half of the Earths crust. Most of the mass of living organisms is oxygen as a component of water, conversely, oxygen is continuously replenished by photosynthesis, which uses the energy of sunlight to produce oxygen from water and carbon dioxide. Oxygen is too reactive to remain a free element in air without being continuously replenished by the photosynthetic action of living organisms. Another form of oxygen, ozone, strongly absorbs ultraviolet UVB radiation, but ozone is a pollutant near the surface where it is a by-product of smog. At low earth orbit altitudes, sufficient atomic oxygen is present to cause corrosion of spacecraft, the name oxygen was coined in 1777 by Antoine Lavoisier, whose experiments with oxygen helped to discredit the then-popular phlogiston theory of combustion and corrosion. One of the first known experiments on the relationship between combustion and air was conducted by the 2nd century BCE Greek writer on mechanics, Philo of Byzantium. In his work Pneumatica, Philo observed that inverting a vessel over a burning candle, Philo incorrectly surmised that parts of the air in the vessel were converted into the classical element fire and thus were able to escape through pores in the glass. Many centuries later Leonardo da Vinci built on Philos work by observing that a portion of air is consumed during combustion and respiration, Oxygen was discovered by the Polish alchemist Sendivogius, who considered it the philosophers stone. In the late 17th century, Robert Boyle proved that air is necessary for combustion, English chemist John Mayow refined this work by showing that fire requires only a part of air that he called spiritus nitroaereus. From this he surmised that nitroaereus is consumed in both respiration and combustion, Mayow observed that antimony increased in weight when heated, and inferred that the nitroaereus must have combined with it. Accounts of these and other experiments and ideas were published in 1668 in his work Tractatus duo in the tract De respiratione. Robert Hooke, Ole Borch, Mikhail Lomonosov, and Pierre Bayen all produced oxygen in experiments in the 17th and the 18th century but none of them recognized it as a chemical element. This may have been in part due to the prevalence of the philosophy of combustion and corrosion called the phlogiston theory, which was then the favored explanation of those processes. Established in 1667 by the German alchemist J. J. Becher, one part, called phlogiston, was given off when the substance containing it was burned, while the dephlogisticated part was thought to be its true form, or calx. The fact that a substance like wood gains overall weight in burning was hidden by the buoyancy of the combustion products
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.
Hexagonal crystal family
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In crystallography, the hexagonal crystal family is one of the 6 crystal families. In the hexagonal family, the crystal is described by a right rhombic prism unit cell with two equal axes, an included angle of 120° and a height perpendicular to the two base axes. 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, hence, there are 3 lattice points per unit cell in total and 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. This is a cell with parameters a = b = c, α = β = γ ≠ 90°. In practice, the description is more commonly used because it is easier to deal with a coordinate system with two 90° angles. However, the axes are often shown in textbooks because this cell reveals 3m symmetry of crystal lattice. However, such 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, the trigonal crystal system consists of the 5 point groups that have a single three-fold rotation axis. The crystal structures of alpha-quartz in the example are described by two of those 18 space groups associated with the hexagonal lattice system. The hexagonal crystal system consists of the seven point groups such that all their groups have the hexagonal lattice as underlying lattice. Graphite is an example of a crystal that crystallizes in the crystal system. Note that the atom in the center of the HCP unit cell in the hexagonal lattice system does not appear in the unit cell of the hexagonal lattice. It is part of the two atom motif associated with each point in the underlying lattice. The trigonal crystal system is the crystal system whose point groups have more than one lattice system associated with their space groups. The 5 point groups in this system are listed below, with their international number and notation, their space groups in name. The point groups in this system are listed below, followed by their representations in Hermann–Mauguin or international notation and Schoenflies notation
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
