1.
Beryl
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Beryl is a mineral composed of beryllium aluminium cyclosilicate with the chemical formula Be3Al26. Well-known varieties of beryl include emerald and aquamarine, naturally occurring, hexagonal crystals of beryl can be up to several meters in size, but terminated crystals are relatively rare. Pure beryl is colorless, but it is tinted by impurities, possible colors are green, blue, yellow, red. The name beryl is derived from Greek βήρυλλος beryllos which referred to a precious blue-green color-of-sea-water stone, akin to Prakrit verulia, the term was later adopted for the mineral beryl more exclusively. When the first eyeglasses were constructed in 13th century Italy, the lenses were made of beryl as glass could not be clear enough. Consequently glasses were named Brillen in German, beryl of various colors is found most commonly in granitic pegmatites, but also occurs in mica schists in the Ural Mountains, and limestone in Colombia. Beryl is often associated with tin and tungsten ore bodies, beryl is found in Europe in Norway, Austria, Germany, Sweden, Ireland and Russia, as well as Brazil, Colombia, Madagascar, Mozambique, Pakistan, South Africa, the United States, and Zambia. US beryl locations are in California, Colorado, Connecticut, Georgia, Idaho, Maine, New Hampshire, North Carolina, South Dakota and Utah. As of 1999, the worlds largest known naturally occurring crystal of any mineral is a crystal of beryl from Malakialina, Madagascar,18 m long and 3.5 m in diameter, aquamarine is a blue or cyan variety of beryl. It occurs at most localities which yield ordinary beryl, the gem-gravel placer deposits of Sri Lanka contain aquamarine. Clear yellow beryl, such as occurring in Brazil, is sometimes called aquamarine chrysolite. The deep blue version of aquamarine is called maxixe, maxixe is commonly found in the country of Madagascar. Its color fades to white when exposed to sunlight or is subjected to heat treatment, the pale blue color of aquamarine is attributed to Fe2+. Fe3+ ions produce golden-yellow color, and when both Fe2+ and Fe3+ are present, the color is a darker blue as in maxixe, decoloration of maxixe by light or heat thus may be due to the charge transfer between Fe3+ and Fe2+. Dark-blue maxixe color can be produced in green, pink or yellow beryl by irradiating it with high-energy particles, in the United States, aquamarines can be found at the summit of Mt. Antero in the Sawatch Range in central Colorado. In Wyoming, aquamarine has been discovered in the Big Horn Mountains, another location within the United States is the Sawtooth Range near Stanley, Idaho, although the minerals are within a wilderness area which prevents collecting. In Brazil, there are mines in the states of Minas Gerais, Espírito Santo, and Bahia, the mines of Colombia, Zambia, Madagascar, Malawi, Tanzania and Kenya also produce aquamarine. The largest aquamarine of gemstone quality ever mined was found in Marambaia, Minas Gerais, Brazil and it weighed over 110 kg, and its dimensions were 48.5 cm long and 42 cm in diameter

2.
Tectosilicate
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Silicate minerals are rock-forming minerals made up of silicate groups. They are the largest and most important class of rock-forming minerals and they are classified based on the structure of their silicate groups, which contain different ratios of silicon and oxygen. Nesosilicates, or orthosilicates, have the orthosilicate ion, which constitute isolated 4− tetrahedra that are connected only by interstitial cations and these exist as 3-member 6− and 6-member 12− rings, where T stands for a tetrahedrally coordinated cation. Inosilicates, or chain silicates, have interlocking chains of silicate tetrahedra with either SiO3,1,3 ratio, for single chains or Si4O11,4,11 ratio, for double chains. Nickel–Strunz classification,09. D Pyroxene group Enstatite – orthoferrosilite series Enstatite – MgSiO3 Ferrosilite – FeSiO3 Pigeonite – Ca0.251, all phyllosilicate minerals are hydrated, with either water or hydroxyl groups attached. Serpentine subgroup Antigorite – Mg3Si2O54 Chrysotile – Mg3Si2O54 Lizardite – Mg3Si2O54 Clay minerals group Halloysite – Al2Si2O54 Kaolinite – Al2Si2O54 Illite – 24O10 Montmorillonite –0 and this group comprises nearly 75% of the crust of the Earth. Tectosilicates, with the exception of the group, are aluminosilicates. Nickel–Strunz classification,09. F and 09. G,04. A, an introduction to the rock-forming minerals. Wise, W. S. Zussman, J. Rock-forming minerals, P.982 pp. Hurlbut, Cornelius S. Danas Manual of Mineralogy. Mindat. org, Dana classification Webmineral, Danas New Silicate Classification Media related to Silicates at Wikimedia Commons

3.
Quartz
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Quartz is the second most abundant mineral in Earths continental crust, behind feldspar. There are many different varieties of quartz, several of which are semi-precious gemstones, since antiquity, varieties of quartz have been the most commonly used minerals in the making of jewelry and hardstone carvings, especially in Eurasia. The word quartz is derived from the German word Quarz and its Middle High German ancestor twarc, the Ancient Greeks referred to quartz as κρύσταλλος derived from the Ancient Greek κρύος meaning icy cold, because some philosophers apparently believed the mineral to be a form of supercooled ice. Today, the rock crystal is sometimes used as an alternative name for the purest form of quartz. Quartz belongs to the crystal system. The ideal crystal shape is a six-sided prism terminating with six-sided pyramids at each end, well-formed crystals typically form in a bed that has unconstrained growth into a void, usually the crystals are attached at the other end to a matrix and only one termination pyramid is present. However, doubly terminated crystals do occur where they develop freely without attachment, a quartz geode is such a situation where the void is approximately spherical in shape, lined with a bed of crystals pointing inward. α-quartz crystallizes in the crystal system, space group P3121 and P3221 respectively. β-quartz belongs to the system, space group P6222 and P6422. These space groups are truly chiral, both α-quartz and β-quartz are examples of chiral crystal structures composed of achiral building blocks. The transformation between α- and β-quartz only involves a comparatively minor rotation of the tetrahedra with respect to one another, although many of the varietal names historically arose from the color of the mineral, current scientific naming schemes refer primarily to the microstructure of the mineral. Color is an identifier for the cryptocrystalline minerals, although it is a primary identifier for the macrocrystalline varieties. Pure quartz, traditionally called rock crystal or clear quartz, is colorless and transparent or translucent, common colored varieties include citrine, rose quartz, amethyst, smoky quartz, milky quartz, and others. The most important distinction between types of quartz is that of macrocrystalline and the microcrystalline or cryptocrystalline varieties, the cryptocrystalline varieties are either translucent or mostly opaque, while the transparent varieties tend to be macrocrystalline. Chalcedony is a form of silica consisting of fine intergrowths of both quartz, and its monoclinic polymorph moganite. Other opaque gemstone varieties of quartz, or mixed rocks including quartz, often including contrasting bands or patterns of color, are agate, carnelian or sard, onyx, heliotrope, amethyst is a form of quartz that ranges from a bright to dark or dull purple color. The worlds largest deposits of amethysts can be found in Brazil, Mexico, Uruguay, Russia, France, Namibia, sometimes amethyst and citrine are found growing in the same crystal. It is then referred to as ametrine, an amethyst is formed when there is iron in the area where it was formed

4.
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

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.
Monoclinic crystal system
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In crystallography, the monoclinic crystal system is one of the 7 crystal systems. A crystal system is described by three vectors, in the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic system. They form a rectangular prism with a parallelogram as its base, hence two vectors are perpendicular, while the third vector meets the other two at an angle other than 90°. There is only one monoclinic Bravais lattice in two dimensions, the oblique lattice, two monoclinic Bravais lattices exist, the primitive monoclinic and the centered monoclinic lattices. In this axis setting, the primitive and base-centered lattices interchange in centering type, sphenoidal is also monoclinic hemimorphic, Domatic is also monoclinic hemihedral, Prismatic is also monoclinic normal. Crystal structure Hurlbut, Cornelius S. Klein, Cornelis, hahn, Theo, ed. International Tables for Crystallography, Volume A, Space Group Symmetry

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

9.
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