1.
Sorosilicate
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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

2.
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

3.
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

4.
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

5.
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

6.
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

7.
Silicate minerals
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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

8.
Mohs scale of mineral hardness
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The Mohs scale of mineral hardness is a qualitative ordinal scale characterizing scratch resistance of various minerals through the ability of harder material to scratch softer material. Created in 1812 by German geologist and mineralogist Friedrich Mohs, it is one of several definitions of hardness in materials science, while greatly facilitating the identification of minerals in the field, the Mohs scale does not show how well hard materials perform in an industrial setting. Despite its lack of precision, the Mohs scale is highly relevant for field geologists, the Mohs scale hardness of minerals can be commonly found in reference sheets. Reference materials may be expected to have a uniform Mohs hardness, the Mohs scale of mineral hardness is based on the ability of one natural sample of mineral to scratch another mineral visibly. The samples of matter used by Mohs are all different minerals, Minerals are pure substances found in nature. Rocks are made up of one or more minerals, as the hardest known naturally occurring substance when the scale was designed, diamonds are at the top of the scale. The hardness of a material is measured against the scale by finding the hardest material that the material can scratch. For example, if material is scratched by apatite but not by fluorite. Scratching a material for the purposes of the Mohs scale means creating non-elastic dislocations visible to the naked eye, frequently, materials that are lower on the Mohs scale can create microscopic, non-elastic dislocations on materials that have a higher Mohs number. The Mohs scale is an ordinal scale. For example, corundum is twice as hard as topaz, the table below shows the comparison with the absolute hardness measured by a sclerometer, with pictorial examples. On the Mohs scale, a streak plate has a hardness of 7.0, using these ordinary materials of known hardness can be a simple way to approximate the position of a mineral on the scale. The table below incorporates additional substances that may fall between levels, Comparison between Hardness and Hardness, Mohs hardness of elements is taken from G. V, samsonov in Handbook of the physicochemical properties of the elements, IFI-Plenum, New York, USA,1968. The Hardness of Minerals and Rocks

9.
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