1.
Mineral
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A mineral is a naturally occurring chemical compound, usually of crystalline form and abiogenic in origin. A mineral has one specific chemical composition, whereas a rock can be an aggregate of different minerals or mineraloids, the study of minerals is called mineralogy. There are over 5,300 known mineral species, over 5,070 of these have been approved by the International Mineralogical Association, the silicate minerals compose over 90% of the Earths crust. The diversity and abundance of species is controlled by the Earths chemistry. Silicon and oxygen constitute approximately 75% of the Earths crust, which translates directly into the predominance of silicate minerals, minerals are distinguished by various chemical and physical properties. Differences in chemical composition and crystal structure distinguish the various species, changes in the temperature, pressure, or bulk composition of a rock mass cause changes in its minerals. Minerals can be described by their various properties, which are related to their chemical structure. Common distinguishing characteristics include crystal structure and habit, hardness, lustre, diaphaneity, colour, streak, tenacity, cleavage, fracture, parting, more specific tests for describing minerals include magnetism, taste or smell, radioactivity and reaction to acid. Minerals are classified by key chemical constituents, the two dominant systems are the Dana classification and the Strunz classification, the silicate class of minerals is subdivided into six subclasses by the degree of polymerization in the chemical structure. All silicate minerals have a unit of a 4− silica tetrahedron—that is, a silicon cation coordinated by four oxygen anions. These tetrahedra can be polymerized to give the subclasses, orthosilicates, disilicates, cyclosilicates, inosilicates, phyllosilicates, other important mineral groups include the native elements, sulfides, oxides, halides, carbonates, sulfates, and phosphates. The first criterion means that a mineral has to form by a natural process, stability at room temperature, in the simplest sense, is synonymous to the mineral being solid. More specifically, a compound has to be stable or metastable at 25 °C, modern advances have included extensive study of liquid crystals, which also extensively involve mineralogy. Minerals are chemical compounds, and as such they can be described by fixed or a variable formula, many mineral groups and species are composed of a solid solution, pure substances are not usually found because of contamination or chemical substitution. Finally, the requirement of an ordered atomic arrangement is usually synonymous with crystallinity, however, crystals are also periodic, an ordered atomic arrangement gives rise to a variety of macroscopic physical properties, such as crystal form, hardness, and cleavage. There have been recent proposals to amend the definition to consider biogenic or amorphous substances as minerals. The formal definition of an approved by the IMA in 1995, A mineral is an element or chemical compound that is normally crystalline. However, if geological processes were involved in the genesis of the compound, Mineral classification schemes and their definitions are evolving to match recent advances in mineral science

2.
Space group
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In mathematics, physics and chemistry, a space group is the symmetry group of a configuration in space, usually in three dimensions. In three dimensions, there are 219 distinct types, or 230 if chiral copies are considered distinct, Space groups are also studied in dimensions other than 3 where they are sometimes called Bieberbach groups, and are discrete cocompact groups of isometries of an oriented Euclidean space. In crystallography, space groups are called the crystallographic or Fedorov groups. A definitive source regarding 3-dimensional space groups is the International Tables for Crystallography, in 1879 Leonhard Sohncke listed the 65 space groups whose elements preserve the orientation. More accurately, he listed 66 groups, but Fedorov and Schönflies both noticed that two of them were really the same, the space groups in 3 dimensions were first enumerated by Fedorov, and shortly afterwards were independently enumerated by Schönflies. The correct list of 230 space groups was found by 1892 during correspondence between Fedorov and Schönflies, burckhardt describes the history of the discovery of the space groups in detail. The space groups in three dimensions are made from combinations of the 32 crystallographic point groups with the 14 Bravais lattices, the combination of all these symmetry operations results in a total of 230 different space groups describing all possible crystal symmetries. The elements of the space group fixing a point of space are rotations, reflections, the identity element, the translations form a normal abelian subgroup of rank 3, called the Bravais lattice. There are 14 possible types of Bravais lattice, the quotient of the space group by the Bravais lattice is a finite group which is one of the 32 possible point groups. Translation is defined as the moves from one point to another point. A glide plane is a reflection in a plane, followed by a parallel with that plane. This is noted by a, b or c, depending on which axis the glide is along. There is also the n glide, which is a glide along the half of a diagonal of a face, and the d glide, the latter is called the diamond glide plane as it features in the diamond structure. In 17 space groups, due to the centering of the cell, the glides occur in two directions simultaneously, i. e. the same glide plane can be called b or c, a or b. For example, group Abm2 could be also called Acm2, group Ccca could be called Cccb, in 1992, it was suggested to use symbol e for such planes. The symbols for five groups have been modified, A screw axis is a rotation about an axis. These are noted by a number, n, to describe the degree of rotation, the degree of translation is then added as a subscript showing how far along the axis the translation is, as a portion of the parallel lattice vector. So,21 is a rotation followed by a translation of 1/2 of the lattice vector

3.
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

4.
Specific gravity
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This page is about the measurement using water as a reference. For a general use of gravity, see relative density. See intensive property for the property implied by specific, Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance. The reference substance is always water at its densest for liquids. Nonetheless, the temperature and pressure must be specified for both the sample and the reference, pressure is nearly always 1 atm. Temperatures for both sample and reference vary from industry to industry, in British beer brewing, the practice for specific gravity as specified above is to multiply it by 1000. Being a ratio of densities, specific gravity is a dimensionless quantity, Specific gravity varies with temperature and pressure, reference and sample must be compared at the same temperature and pressure or be corrected to a standard reference temperature and pressure. Substances with a gravity of 1 are neutrally buoyant in water. Those with SG greater than 1 are denser than water and will, disregarding surface tension effects and those with an SG less than 1 are less dense than water and will float on it. In scientific work, the relationship of mass to volume is expressed directly in terms of the density of the substance under study. It is in industry where specific gravity finds wide application, often for historical reasons. True specific gravity can be expressed mathematically as, S G true = ρ sample ρ H2 O where ρ sample is the density of the sample, the density of water varies with temperature and pressure as does the density of the sample. So it is necessary to specify the temperatures and pressures at which the densities or weights were determined and it is nearly always the case that measurements are made at 1 nominal atmosphere. For true specific gravity calculations, air pressure must be considered, temperatures are specified by the notation with T s representing the temperature at which the samples density was determined and T r the temperature at which the reference density is specified. For example, SG would be understood to mean that the density of the sample was determined at 20°C and of the water at 4°C. Taking into account different sample and reference temperatures, we note that, while S G H2 O =1.000000, it is also the case that S G H2 O =0.998203 /0.999840 =0.998363. Here, temperature is being specified using the current ITS-90 scale, on the previous IPTS-68 scale, the densities at 20 °C and 4 °C are 0.9982071 and 0.9999720 respectively, resulting in an SG value for water of 0.9982343. For example, in the industry, the Plato table lists sucrose concentration by weight against true SG

5.
Kornerupine
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Kornerupine is a rare boro-silicate mineral with the formula 4652. It crystallizes in the orthorhombic - dipyramidal crystal system as brown, green and it has a Mohs hardness of 7 and a specific gravity of 3.3 to 3.34. Its indices of refraction are nα=1.660 -1.671, nβ=1.673 -1.683 and it occurs in boron-rich volcanic and sedimentary rocks which have undergone high grade metamorphism. It is also found in metamorphosed anorthosite complexes, kornerupine is valued as a gemstone when it is found in translucent green to yellow shades. The emerald green varieties are especially sought after and it forms a solid solution series with prismatine. It was first described in 1884 for an occurrence in Fiskernaes in SW Greenland and it was named in honor of the Danish geologist, Andreas Nikolaus Kornerup

6.
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

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.
Orthorhombic crystal system
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In crystallography, the orthorhombic crystal system is one of the 7 crystal systems. All three bases intersect at 90° angles, so the three lattice vectors remain mutually orthogonal, there are two orthorhombic Bravais lattices in two dimensions, Primitive rectangular and centered rectangular. The primitive rectangular lattice can also be described by a centered rhombic unit cell, there are four orthorhombic Bravais lattices, primitive orthorhombic, base-centered orthorhombic, body-centered orthorhombic, and face-centered orthorhombic. In this axis setting, the primitive and base-centered lattices interchange in centering type, crystal structure Overview of all space groups Hurlbut, Cornelius S. Klein, Cornelis. Hahn, Theo, ed. International Tables for Crystallography, Volume A, Space Group Symmetry