Cubic crystal system
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 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 unit cell in these crystals is conventionally taken to be a cube, the primitive unit cell is not; the three Bravais lattices in the cubic crystal system are: The primitive cubic system consists of one lattice point on each corner of the cube. Each atom at a lattice point is shared between eight adjacent cubes, the unit cell therefore contains in total one atom; the body-centered cubic system has one lattice 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; the face-centered cubic system has lattice points on the faces of the cube, that each gives one half contribution, in addition to the corner lattice points, giving a total of 4 lattice points per unit cell.
Each sphere in a cF lattice has coordination number 12. Coordination number is the number of nearest neighbours of a central atom in the structure; the face-centered cubic system is related to the hexagonal close packed system, where two systems differ only in the relative placements of their hexagonal layers. The plane of a face-centered cubic system is a hexagonal grid. Attempting to create a C-centered cubic crystal system would result in a simple tetragonal Bravais lattice; the isometric crystal system class names, point groups, examples, International Tables for Crystallography space group number, space groups are listed in the table below. There are a total 36 cubic space groups. Other terms for hexoctahedral are: normal class, ditesseral central class, galena type. A simple cubic unit cell has a single cubic void in the center. A body-centered cubic unit cell has six octahedral voids located at the center of each face of the unit cell, twelve further ones located at the midpoint of each edge of the same cell, for a total of six net octahedral voids.
Additionally, there are 24 tetrahedral voids located in a square spacing around each octahedral void, for a total of twelve net tetrahedral voids. These tetrahedral voids are not local maxima and are not technically voids, but they do 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 unit cell, for a total of eight net tetrahedral voids. Additionally, there are twelve octahedral voids located at the midpoints of the edges of the unit cell as well as one octahedral hole in the center of the cell, for a total of four net octahedral voids. One important characteristic of a crystalline structure is its atomic packing factor; this is calculated by assuming that all the atoms are identical spheres, with a radius large enough that each sphere abuts on the next. 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.
In a bcc lattice, the atomic packing factor is 0.680, in fcc it is 0.740. The fcc value is the highest theoretically possible value for any lattice, although there are other lattices which achieve the same value, such as hexagonal close packed and one version of tetrahedral bcc; as a rule, since atoms in a solid attract each other, the more packed arrangements of atoms tend to be more common. Accordingly, the primitive cubic structure, with low atomic packing factor, is rare in nature, but is found in polonium; the bcc and fcc, with their higher densities, are both quite common in nature. Examples of bcc include iron, chromium and niobium. Examples of fcc include aluminium, copper and silver. Compounds that consist of more than one element have crystal structures based on a cubic crystal system; some of the more common ones are listed here. The space group of the caesium chloride structure is called Pm3m, or "221"; the Strukturbericht designation is "B2". One structure is the "interpenetrating primitive cubic" structure called the "caesium chloride" structure.
Each of the two atom types forms a separate primitive cubic lattice, with an atom of one type at the center of each cube of the other type. Altogether, the arrangement of atoms is the same as body-centered cubic, but with alternating types of atoms at the different lattice sites. Alternately, one could view this lattice as a simple cubic structure with a secondary atom in its cubic void. In addition to caesium chloride itself, the structure appears in certain other alkali halides when prepared at low temperatures or high pressures; this structure is more to be formed from two elements whose ions are of the same size. The coordination
Carbonate minerals are those minerals containing the carbonate ion, CO32−. Calcite group: trigonal Calcite CaCO3 Gaspeite CO3 Magnesite MgCO3 Otavite CdCO3 Rhodochrosite MnCO3 Siderite FeCO3 Smithsonite ZnCO3 Spherocobaltite CoCO3 Aragonite group: orthorhombic Aragonite CaCO3 Cerussite PbCO3 Strontianite SrCO3 Witherite BaCO3 Rutherfordine UO2CO3 Natrite Na2CO3 Dolomite group: trigonal Ankerite CaFe2 Dolomite CaMg2 Huntite Mg3Ca4 Minrecordite CaZn2 Barytocite BaCa2 Carbonate with hydroxide: monoclinic Azurite Cu322 Hydrocerussite Pb322 Malachite Cu2CO32 Rosasite 2CO32 Phosgenite Pb2Cl2 Hydrozincite Zn526 Aurichalcite 526 Hydromagnesite Mg542.4H2O Ikaite CaCO3·6 Lansfordite MgCO3·5 Monohydrocalcite CaCO3·H2O Natron Na2CO3·10 Zellerite Ca2·5The carbonate class in both the Dana and the Strunz classification systems include the nitrates. IMA-CNMNC proposes a new hierarchical scheme; this list uses the classification of Nickel–Strunz. Abbreviations: "*" – discredited. "?" – questionable/doubtful.
"REE" – Rare-earth element "PGE" – Platinum-group element 03. C Aluminofluorides, 06 Borates, 08 Vanadates, 09 Silicates: Neso: insular Soro: grouping Cyclo: ring Ino: chain Phyllo: sheet Tekto: three-dimensional framework Nickel–Strunz code scheme: NN. XY.##x NN: Nickel–Strunz mineral class number X: Nickel–Strunz mineral division letter Y: Nickel–Strunz mineral family letter ##x: Nickel–Strunz mineral/group number, x add-on letter 05. A Carbonates without additional anions, without H2O 05. AA Alkali carbonates: 05 Zabuyelite. AB Alkali-earth carbonates: 05 Calcite, 05 Gaspeite, 05 Magnesite, 05 Rhodochrosite, 05 Otavite, 05 Spherocobaltite, 05 Siderite, 05 Smithsonite. AC Alkali and alkali-earth carbonates: 05 Eitelite, 10 Nyerereite, 10 Natrofairchildite, 10 Zemkorite. AD With rare-earth elements: 05 Sahamalite-. B Carbonates with additional anions, without H2O 05. BA With Cu, Co, Ni, Zn, Mg, Mn: 05 Azurite, 10 Chukanovite, 10 Malachite, 10 Georgeite, 10 Pokrovskite, 10 Nullaginite, 10 Glaukosphaerite, 10 Mcguinnessite, 10 Kolwezite, 10 Rosasite, 10 Zincrosasite.
BB With alkalies, etc.: 05 Barentsite, 10 Dawsonite, 15 Tunisite, 20 Sabinaite 05. BC With alkali-earth cations: 05 Brenkite, 10 Rouvilleite, 15 Podlesnoite 05. BD With rare-earth elements: 05 Cordylite-, 05 Lukechangite-. BE With Pb, Bi: 05 Shannonite, 10 Hydrocerussite, 15 Plumbonacrite, 20 Phosgenite, 25 Bismutite, 30 Kettnerite, 35 Beyerite 05. BF With, SO4, PO4, TeO3: 05 Northupite, 05 Ferrotychite, 05 Manganotychite, 05 Tychite. C Carbonates without additional anions, with H2O 05. CA With medium-sized cations: 05 Nesquehonite, 10 Lansfordite, 15 Barringtonite, 20 Hellyerite 05. CB With large cations: 05 Thermonatrite, 10 Natron, 15 Trona, 20 Monohydrocalcite, 25 Ikaite, 30 Pirssonite, 35 Gaylussite, 40 Chalconatronite, 45 Baylissite, 50 Tuliokite 05. CC With rare-earth elements: 05 Donnayite-, 05 Mckelveyite-*, 05 Mckelveyite-, 05 Weloganite. D Carbonates with additional anions, with H2O 05. DA With medium-sized cations: 05 Dypingite, 05 Giorgiosite, 05 Hydromagnesite, 05 Widgiemoolthalite.
DB With large and medium-sized cations: 05 Alumohydrocalcite, 05 Para-alumohydrocalcite, 05 Nasledovite.
Rhodochrosite is a manganese carbonate mineral with chemical composition MnCO3. In its pure form, it is a rose-red color, but impure specimens can be shades of pink to pale brown, it streaks white, its Mohs hardness varies between 3.5 and 4. Its specific gravity is between 3.5 and 3.7. It crystallizes in the trigonal system, cleaves with rhombohedral carbonate cleavage in three directions. Crystal twinning is present, it is transparent to translucent with refractive indices of nω=1.814 to 1.816, nε=1.596 to 1.598. It is confused with the manganese silicate, but is distinctly softer. Rhodochrosite forms a complete solid solution series with iron carbonate. Calcium substitutes for manganese in the structure, leading to lighter shades of red and pink, depending on the degree of substitution, it is for this reason. Rhodochrosite occurs as a hydrothermal vein mineral along with other manganese minerals in low temperature ore deposits as in the silver mines of Romania where it was first found. Banded rhodochrosite is mined in Argentina.
It was first described in 1813 in reference to a sample from Maramureş, present-day Romania. According to Dimitrescu and Radulescu, 1966 and to Papp, 1997, this mineral was described for the first time in Sacaramb, not in Cavnic, Romania; the name is derived from the Greek word ῥοδόχρως meaning rose-colored. Its main use is as an ore of manganese, a key component of low-cost stainless steel formulations and certain aluminum alloys. Quality banded specimens are used for decorative stones and jewelry. Due to its being soft, having perfect cleavage, it is difficult to cut, therefore found faceted in jewelry, it is typically used to make other desirable gems. Manganese carbonate is destructive to the amalgamation process used in the concentration of silver ores, so until quality mineral specimens became sought after by collectors, they were discarded on the mine dump! Rhodochrosite is Argentina's "national gemstone". Colorado named rhodochrosite as its state mineral in 2002. Large specimens have been found in the Sweet Home Mine near Colorado.
It is sometimes called "Rosa del Inca", "Inca Rose" or Rosinca. Manganoan Calcite Hurlbut, Cornelius S..
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group on the periodic table, a reactive nonmetal, an oxidizing agent that forms oxides with most elements as well as with other compounds. By mass, oxygen is the third-most abundant element in the universe, after helium. At standard temperature and pressure, two atoms of the element bind to form dioxygen, a colorless and odorless diatomic gas with the formula O2. Diatomic oxygen gas constitutes 20.8% of the Earth's atmosphere. As compounds including oxides, the element makes up half of the Earth's crust. Dioxygen is used in cellular respiration and many major classes of organic molecules in living organisms contain oxygen, such as proteins, nucleic acids and fats, as do the major constituent inorganic compounds of animal shells and bone. Most of the mass of living organisms is oxygen as a component of water, the major constituent of lifeforms. Oxygen is continuously replenished in Earth's atmosphere by photosynthesis, which uses the energy of sunlight to produce oxygen from water and carbon dioxide.
Oxygen is too chemically reactive to remain a free element in air without being continuously replenished by the photosynthetic action of living organisms. Another form of oxygen, ozone absorbs ultraviolet UVB radiation and the high-altitude ozone layer helps protect the biosphere from ultraviolet radiation. However, ozone present at the surface is a byproduct of thus a pollutant. Oxygen was isolated by Michael Sendivogius before 1604, but it is believed that the element was discovered independently by Carl Wilhelm Scheele, in Uppsala, in 1773 or earlier, Joseph Priestley in Wiltshire, in 1774. Priority is given for Priestley because his work was published first. Priestley, called oxygen "dephlogisticated air", did not recognize it as a chemical element; the name oxygen was coined in 1777 by Antoine Lavoisier, who first recognized oxygen as a chemical element and characterized the role it plays in combustion. Common uses of oxygen include production of steel and textiles, brazing and cutting of steels and other metals, rocket propellant, oxygen therapy, life support systems in aircraft, submarines and diving.
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 and surrounding the vessel's neck with water resulted in some water rising into the neck. 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 Leonardo da Vinci built on Philo's work by observing that a portion of air is consumed during combustion and respiration. In the late 17th century, Robert Boyle proved. English chemist John Mayow refined this work by showing that fire requires only a part of air that he called spiritus nitroaereus. In one experiment, he found that placing either a mouse or a lit candle in a closed container over water caused the water to rise and replace one-fourteenth of the air's volume before extinguishing the subjects.
From this he surmised that nitroaereus is consumed in both combustion. Mayow observed that antimony increased in weight when heated, inferred that the nitroaereus must have combined with it, he thought that the lungs separate nitroaereus from air and pass it into the blood and that animal heat and muscle movement result from the reaction of nitroaereus with certain substances in the body. 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, 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, the favored explanation of those processes. Established in 1667 by the German alchemist J. J. Becher, modified by the chemist Georg Ernst Stahl by 1731, phlogiston theory stated that all combustible materials were made of two parts.
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. Combustible materials that leave little residue, such as wood or coal, were thought to be made of phlogiston. Air did not play a role in phlogiston theory, nor were any initial quantitative experiments conducted to test the idea. Polish alchemist and physician Michael Sendivogius in his work De Lapide Philosophorum Tractatus duodecim e naturae fonte et manuali experientia depromti described a substance contained in air, referring to it as'cibus vitae', this substance is identical with oxygen. Sendivogius, during his experiments performed between 1598 and 1604, properly recognized that the substance is equivalent to the gaseous byproduct released by the thermal decomposition of potassium nitrate. In Bugaj’s view, the isolation of oxygen and the proper association of the substance to that part of air, required for life, lends sufficient weight to the discovery of oxygen by Sendivogius.
Hausmannite is a complex oxide of manganese containing both di- and tri-valent manganese. The formula can be represented as Mn2+Mn3+2O4, it forms tetragonal crystals. Hausmannite is a brown to black metallic mineral with Mohs hardness of 5.5 and a specific gravity of 4.8. The type locality is Oehrenstock, Thuringian Forest, Germany, where it was first described in 1813. Locations include Batesville, Arkansas, US. High quality samples have been found in South Africa and Namibia where it is associated with other manganese oxides and psilomelane and the iron-manganese mineral bixbyite. Wilhelm Haidinger named it in honour of Johann Friedrich Ludwig Hausmann, Professor of Mineralogy, University of Göttingen, Germany
A mineral is, broadly speaking, a solid chemical compound that occurs in pure form. A rock may consist of a single mineral, or may be an aggregate of two or more different minerals, spacially segregated into distinct phases. Compounds that occur only in living beings are excluded, but some minerals are biogenic and/or are organic compounds in the sense of chemistry. Moreover, living beings synthesize inorganic minerals that occur in rocks. In geology and mineralogy, the term "mineral" is reserved for mineral species: crystalline compounds with a well-defined chemical composition and a specific crystal structure. Minerals without a definite crystalline structure, such as opal or obsidian, are more properly called mineraloids. If a chemical compound may occur with different crystal structures, each structure is considered different mineral species. Thus, for example and stishovite are two different minerals consisting of the same compound, silicon dioxide; the International Mineralogical Association is the world's premier standard body for the definition and nomenclature of mineral species.
As of November 2018, the IMA recognizes 5,413 official mineral species. Out of more than 5,500 proposed or traditional ones; the chemical composition of a named mineral species may vary somewhat by the inclusion of small amounts of impurities. Specific varieties of a species sometimes have official names of their own. For example, amethyst is a purple variety of the mineral species quartz; some mineral species can have variable proportions of two or more chemical elements that occupy equivalent positions in the mineral's structure. Sometimes a mineral with variable composition is split into separate species, more or less arbitrarily, forming a mineral group. Besides the essential chemical composition and crystal structure, the description of a mineral species includes its common physical properties such as habit, lustre, colour, tenacity, fracture, specific gravity, fluorescence, radioactivity, as well as its taste or smell and its reaction to acid. Minerals are classified by key chemical constituents.
Silicate minerals comprise 90% of the Earth's crust. Other important mineral groups include the native elements, oxides, carbonates and phosphates. One definition of a mineral encompasses the following criteria: Formed by a natural process. Stable or metastable at room temperature. In the simplest sense, this means. Classical examples of exceptions to this rule include native mercury, which crystallizes at −39 °C, water ice, solid only below 0 °C. Modern advances have included extensive study of liquid crystals, which extensively involve mineralogy. Represented by a chemical formula. Minerals are chemical compounds, as such they can be described by fixed or a variable formula. Many mineral groups and species are composed of a solid solution. For example, the olivine group is described by the variable formula 2SiO4, a solid solution of two end-member species, magnesium-rich forsterite and iron-rich fayalite, which are described by a fixed chemical formula. Mineral species themselves could have a variable composition, such as the sulfide mackinawite, 9S8, a ferrous sulfide, but has a significant nickel impurity, reflected in its formula.
Ordered atomic arrangement. This means crystalline. An ordered atomic arrangement gives rise to a variety of macroscopic physical properties, such as crystal form and cleavage. There have been several recent proposals to classify amorphous substances as minerals; the formal definition of a mineral approved by the IMA in 1995: "A mineral is an element or chemical compound, crystalline and, formed as a result of geological processes." Abiogenic. Biogenic substances are explicitly excluded by the IMA: "Biogenic substances are chemical compounds produced by biological processes without a geological component and are not regarded as minerals. However, if geological processes were involved in the genesis of the compound the product can be accepted as a mineral."The first three general characteristics are less debated than the last two. Mineral classification schemes and their definitions are evolving to match recent advances in mineral science. Recent changes have included the addition of an organic class, in both the new Dana and the Strunz classification schemes.
The organic class includes a rare group of minerals with hydrocarbons. The IMA Commission on New Minerals and Mineral Names adopted in 2009 a hierarchical scheme for the naming and classification of mineral groups and group names and established seven commissions and four working groups to review and classify minerals into an official listing of their published names. According to these new r
In mathematics and chemistry, a space group is the symmetry group of a configuration in space in three dimensions. In three dimensions, there are 230 if chiral copies are considered distinct. Space groups are studied in dimensions other than 3 where they are sometimes called Bieberbach groups, are discrete cocompact groups of isometries of an oriented Euclidean space. In crystallography, space groups are called the crystallographic or Fedorov groups, represent a description of the symmetry of the crystal. A definitive source regarding 3-dimensional space groups is the International Tables for Crystallography. Space groups in 2 dimensions are the 17 wallpaper groups which have been known for several centuries, though the proof that the list was complete was only given in 1891, after the much more difficult classification of space groups had been completed. In 1879 Leonhard Sohncke listed the 65 space groups. More he listed 66 groups, but Fedorov and Schönflies both noticed that two of them were the same.
The space groups in three dimensions were first enumerated by Fedorov, shortly afterwards were independently enumerated by Schönflies. The correct list of 230 space groups was found by 1892 during correspondence between Fedorov and Schönflies. Barlow enumerated the groups with a different method, but omitted four groups though he had the correct list of 230 groups from 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, each of the latter belonging to one of 7 lattice systems. This results in a space group being some combination of the translational symmetry of a unit cell including lattice centering, the point group symmetry operations of reflection and improper rotation, the screw axis and glide plane symmetry operations; 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 the identity element, reflections and improper rotations. 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, one of the 32 possible point groups. Translation is defined as the face moves from one point to another point. A glide plane is a reflection in a plane, followed by a translation parallel with that plane; this is noted depending on which axis the glide is along. There is the n glide, a glide along the half of a diagonal of a face, the d glide, a fourth of the way along either a face or space diagonal of the unit cell; the latter is called the diamond glide plane. In 17 space groups, due to the centering of the cell, the glides occur in two perpendicular directions i.e. the same glide plane can be called b or c, a or b, a or c. For example, group Abm2 could be called Acm2, group Ccca could be called Cccb.
In 1992, it was suggested to use symbol e for such planes. The symbols for five space groups have been modified: A screw axis is a rotation about an axis, followed by a translation along the direction of the axis; these are noted by a number, n, to describe the degree of rotation, where the number is how many operations must be applied to complete a full rotation. The degree of translation is 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 twofold rotation followed by a translation of 1/2 of the lattice vector; the general formula for the action of an element of a space group is y = M.x + D where M is its matrix, D is its vector, where the element transforms point x into point y. In general, D = D + D, where D is a unique function of M, zero for M being the identity; the matrices M form a point group, a basis of the space group. The lattice dimension can be less than the overall dimension, resulting in a "subperiodic" space group.
For:: One-dimensional line groups: Two-dimensional line groups: frieze groups: Wallpaper groups: Three-dimensional line groups. Some of these methods can assign several different names to the same space group, so altogether there are many thousands of different names. Number; the International Union of Crystallography publishes tables of all space group types, assigns each a unique number from 1 to 230. The numbering is arbitrary, except that groups with the same crystal system or point group are given consecutive numbers. International symbol or Hermann–Mauguin notation; the Hermann–Mauguin notation describes the lattice and some generators for the group. It has a shortened form called the international short symbol, the one most used in crystallography