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
Siderite is the name of a type of iron meteorite. Siderite is a mineral composed of iron carbonate, it takes its name from the Greek word σίδηρος sideros, “iron”. It is a valuable iron mineral, since it contains no sulfur or phosphorus. Zinc and manganese substitute for the iron resulting in the siderite-smithsonite, siderite-magnesite and siderite-rhodochrosite solid solution series. Siderite has Mohs hardness of 3.75-4.25, a specific gravity of 3.96, a white streak and a vitreous lustre or pearly luster. It crystallizes in the trigonal crystal system, are rhombohedral in shape with curved and striated faces, it occurs in masses. Color ranges from black, the latter being due to the presence of manganese. Siderite is found in hydrothermal veins, is associated with barite, fluorite and others, it is a common diagenetic mineral in shales and sandstones, where it sometimes forms concretions, which can encase three-dimensionally preserved fossils. In sedimentary rocks, siderite forms at shallow burial depths and its elemental composition is related to the depositional environment of the enclosing sediments.
In addition, a number of recent studies have used the oxygen isotopic composition of sphaerosiderite as a proxy for the isotopic composition of meteoric water shortly after deposition. Although spathic iron ores, such as siderite, have been economically important for steel production, they are far from ideal as an ore, their hydrothermal mineralisation tends to form them as small ore lenses following steeply dipping bedding planes. This makes them not amenable to opencast working, increases the cost of working them by mining with horizontal stopes; as the individual ore bodies are small, it may be necessary to duplicate or relocate the pit head machinery, winding engine and pumping engine, between these bodies as each is worked out. This makes mining the ore an expensive proposition compared to typical ironstone or haematite opencasts; the recovered ore has drawbacks. The carbonate ore is more difficult to smelt than other oxide ore. Driving off the carbonate as carbon dioxide requires more energy and so the ore'kills' the blast furnace if added directly.
Instead the ore must be given a preliminary roasting step. Developments of specific techniques to deal with these ores began in the early 19th century with the work of Sir Thomas Lethbridge in Somerset. His'Iron Mill' of 1838 used a three-chambered concentric roasting furnace, before passing the ore to a separate reducing furnace for smelting. Details of this Mill were the invention of Charles Sanderson, a steel maker of Sheffield, who held the patent for it; these differences between spathic ore and haematite have led to the failure of a number of mining concerns, notably the Brendon Hills Iron Ore Company. Spathic iron ores have negligible phosphorus; this led to their one major benefit. Although the first demonstrations by Bessemer in 1856 had been successful attempts to reproduce this were infamously failures. Work by the metallurgist Robert Forester Mushet discovered that the reason for this was the nature of the Swedish ores that Bessemer had innocently used, being low in phosphorus. Using a typical European high-phosphorus ore in Bessemer's converter gave a poor quality steel.
To produce high quality steel from a high-phosphorus ore, Mushet realised that he could operate the Bessemer converter for longer, burning off all the steel's impurities including the unwanted phosphorus and the essential carbon, but re-adding carbon, with manganese, in the form of a obscure ferromanganese ore with no phosphorus, spiegeleisen. This created a sudden demand for spiegeleisen. Although it was not available in sufficient quantity as a mineral, steelworks such as that at Ebbw Vale in South Wales soon learned to make it from the spathic siderite ores. For a few decades, spathic ores were now in demand and this encouraged their mining. In time though, the original'acidic' liner, made from siliceous sandstone or ganister, of the Bessemer converter was replaced by a'basic' liner in the developed Gilchrist Thomas process; this removed the phosphorus impurities as slag, produced by chemical reaction with the liner, no longer required spiegeleisen. From the 1880s demand for the ores fell once again and many of their mines, including those of the Brendon Hills, closed soon after
Freibergite is a complex sulfosalt mineral of silver, iron and arsenic with formula 124S13. It is formed in hydrothermal deposits, it forms another with argentotennantite. Freibergite leaves a reddish-black streak, it has a Mohs hardness of 3.5 to 4.0 and a specific gravity of 4.85 - 5. It is massive to granular in habit with no cleavage and an irregular fracture; the mineral was first described in 1853 from an occurrence in the silver mines of the type locality at Freiberg, Saxony. Mineral handbook Webmineral Mindat
Encyclopædia Britannica, Eleventh Edition
The Encyclopædia Britannica, Eleventh Edition is a 29-volume reference work, an edition of the Encyclopædia Britannica. It was developed during the encyclopaedia's transition from a British to an American publication; some of its articles were written by the best-known scholars of the time. This edition of the encyclopedia, containing 40,000 entries, is now in the public domain, many of its articles have been used as a basis for articles in Wikipedia. However, the outdated nature of some of its content makes its use as a source for modern scholarship problematic; some articles have special value and interest to modern scholars as cultural artifacts of the 19th and early 20th centuries. The 1911 eleventh edition was assembled with the management of American publisher Horace Everett Hooper. Hugh Chisholm, who had edited the previous edition, was appointed editor in chief, with Walter Alison Phillips as his principal assistant editor. Hooper bought the rights to the 25-volume 9th edition and persuaded the British newspaper The Times to issue its reprint, with eleven additional volumes as the tenth edition, published in 1902.
Hooper's association with The Times ceased in 1909, he negotiated with the Cambridge University Press to publish the 29-volume eleventh edition. Though it is perceived as a quintessentially British work, the eleventh edition had substantial American influences, not only in the increased amount of American and Canadian content, but in the efforts made to make it more popular. American marketing methods assisted sales; some 14% of the contributors were from North America, a New York office was established to coordinate their work. The initials of the encyclopedia's contributors appear at the end of selected articles or at the end of a section in the case of longer articles, such as that on China, a key is given in each volume to these initials; some articles were written by the best-known scholars of the time, such as Edmund Gosse, J. B. Bury, Algernon Charles Swinburne, John Muir, Peter Kropotkin, T. H. Huxley, James Hopwood Jeans and William Michael Rossetti. Among the lesser-known contributors were some who would become distinguished, such as Ernest Rutherford and Bertrand Russell.
Many articles were carried over from some with minimal updating. Some of the book-length articles were divided into smaller parts for easier reference, yet others much abridged; the best-known authors contributed only a single article or part of an article. Most of the work was done by British Museum scholars and other scholars; the 1911 edition was the first edition of the encyclopædia to include more than just a handful of female contributors, with 34 women contributing articles to the edition. The eleventh edition introduced a number of changes of the format of the Britannica, it was the first to be published complete, instead of the previous method of volumes being released as they were ready. The print type was subject to continual updating until publication, it was the first edition of Britannica to be issued with a comprehensive index volume in, added a categorical index, where like topics were listed. It was the first not to include long treatise-length articles. Though the overall length of the work was about the same as that of its predecessor, the number of articles had increased from 17,000 to 40,000.
It was the first edition of Britannica to include biographies of living people. Sixteen maps of the famous 9th edition of Stielers Handatlas were translated to English, converted to Imperial units, printed in Gotha, Germany by Justus Perthes and became part this edition. Editions only included Perthes' great maps as low quality reproductions. According to Coleman and Simmons, the content of the encyclopedia was distributed as follows: Hooper sold the rights to Sears Roebuck of Chicago in 1920, completing the Britannica's transition to becoming a American publication. In 1922, an additional three volumes, were published, covering the events of the intervening years, including World War I. These, together with a reprint of the eleventh edition, formed the twelfth edition of the work. A similar thirteenth edition, consisting of three volumes plus a reprint of the twelfth edition, was published in 1926, so the twelfth and thirteenth editions were related to the eleventh edition and shared much of the same content.
However, it became apparent that a more thorough update of the work was required. The fourteenth edition, published in 1929, was revised, with much text eliminated or abridged to make room for new topics; the eleventh edition was the basis of every version of the Encyclopædia Britannica until the new fifteenth edition was published in 1974, using modern information presentation. The eleventh edition's articles are still of value and interest to modern readers and scholars as a cultural artifact: the British Empire was at its maximum, imperialism was unchallenged, much of the world was still ruled by monarchs, the tragedy of the modern world wars was still in the future, they are an invaluable resource for topics omitted from modern encyclopedias for biography and the history of science and technology. As a literary text, the encyclopedia has value as an example of early 20th-century prose. For example, it employs literary devices, such as pathetic fallacy, which are not as common in modern reference texts.
In 1917, using the pseudonym of S. S. Van Dine, the US art critic and author Willard Huntington Wright published Misinforming a Nation, a 200+
Transparency and translucency
In the field of optics, transparency is the physical property of allowing light to pass through the material without being scattered. On a macroscopic scale, the photons can be said to follow Snell's Law. Translucency is a superset of transparency: it allows light to pass through, but does not follow Snell's law. In other words, a translucent medium allows the transport of light while a transparent medium not only allows the transport of light but allows for image formation. Transparent materials appear clear, with the overall appearance of one color, or any combination leading up to a brilliant spectrum of every color; the opposite property of translucency is opacity. When light encounters a material, it can interact with it in several different ways; these interactions depend on the nature of the material. Photons interact with an object by some combination of reflection and transmission; some materials, such as plate glass and clean water, transmit much of the light that falls on them and reflect little of it.
Many liquids and aqueous solutions are transparent. Absence of structural defects and molecular structure of most liquids are responsible for excellent optical transmission. Materials which do not transmit light are called opaque. Many such substances have a chemical composition which includes what are referred to as absorption centers. Many substances are selective in their absorption of white light frequencies, they absorb certain portions of the visible spectrum while reflecting others. The frequencies of the spectrum which are not absorbed are either reflected or transmitted for our physical observation; this is. The attenuation of light of all frequencies and wavelengths is due to the combined mechanisms of absorption and scattering. Transparency can provide perfect camouflage for animals able to achieve it; this is easier in turbid seawater than in good illumination. Many marine animals such as jellyfish are transparent. With regard to the absorption of light, primary material considerations include: At the electronic level, absorption in the ultraviolet and visible portions of the spectrum depends on whether the electron orbitals are spaced such that they can absorb a quantum of light of a specific frequency, does not violate selection rules.
For example, in most glasses, electrons have no available energy levels above them in range of that associated with visible light, or if they do, they violate selection rules, meaning there is no appreciable absorption in pure glasses, making them ideal transparent materials for windows in buildings. At the atomic or molecular level, physical absorption in the infrared portion of the spectrum depends on the frequencies of atomic or molecular vibrations or chemical bonds, on selection rules. Nitrogen and oxygen are not greenhouse gases because there is no absorption, but because there is no molecular dipole moment. With regard to the scattering of light, the most critical factor is the length scale of any or all of these structural features relative to the wavelength of the light being scattered. Primary material considerations include: Crystalline structure: whether or not the atoms or molecules exhibit the'long-range order' evidenced in crystalline solids. Glassy structure: scattering centers include fluctuations in density or composition.
Microstructure: scattering centers include internal surfaces such as grain boundaries, crystallographic defects and microscopic pores. Organic materials: scattering centers include fiber and cell structures and boundaries. Diffuse reflection - Generally, when light strikes the surface of a solid material, it bounces off in all directions due to multiple reflections by the microscopic irregularities inside the material, by its surface, if it is rough. Diffuse reflection is characterized by omni-directional reflection angles. Most of the objects visible to the naked eye are identified via diffuse reflection. Another term used for this type of reflection is "light scattering". Light scattering from the surfaces of objects is our primary mechanism of physical observation. Light scattering in liquids and solids depends on the wavelength of the light being scattered. Limits to spatial scales of visibility therefore arise, depending on the frequency of the light wave and the physical dimension of the scattering center.
Visible light has a wavelength scale on the order of a half a micrometer. Scattering centers as small. Optical transparency in polycrystalline materials is limited by the amount of light, scattered by their microstructural features. Light scattering depends on the wavelength of the light. Limits to spatial scales of visibility therefore arise, depending on the frequency of the light wave and the physical dimension of the scattering center. For example, since visible light has a wavelength scale on the order of a micrometer, scattering centers will have dimensions on a similar spatial scale. Primary scattering centers in polycrystalline materi
Silver is a chemical element with symbol Ag and atomic number 47. A soft, lustrous transition metal, it exhibits the highest electrical conductivity, thermal conductivity, reflectivity of any metal; the metal is found in the Earth's crust in the pure, free elemental form, as an alloy with gold and other metals, in minerals such as argentite and chlorargyrite. Most silver is produced as a byproduct of copper, gold and zinc refining. Silver has long been valued as a precious metal. Silver metal is used in many bullion coins, sometimes alongside gold: while it is more abundant than gold, it is much less abundant as a native metal, its purity is measured on a per-mille basis. As one of the seven metals of antiquity, silver has had an enduring role in most human cultures. Other than in currency and as an investment medium, silver is used in solar panels, water filtration, ornaments, high-value tableware and utensils, in electrical contacts and conductors, in specialized mirrors, window coatings, in catalysis of chemical reactions, as a colorant in stained glass and in specialised confectionery.
Its compounds are used in X-ray film. Dilute solutions of silver nitrate and other silver compounds are used as disinfectants and microbiocides, added to bandages and wound-dressings and other medical instruments. Silver is similar in its physical and chemical properties to its two vertical neighbours in group 11 of the periodic table and gold, its 47 electrons are arranged in the configuration 4d105s1 to copper and gold. This distinctive electron configuration, with a single electron in the highest occupied s subshell over a filled d subshell, accounts for many of the singular properties of metallic silver. Silver is an soft and malleable transition metal, though it is less malleable than gold. Silver crystallizes in a face-centered cubic lattice with bulk coordination number 12, where only the single 5s electron is delocalized to copper and gold. Unlike metals with incomplete d-shells, metallic bonds in silver are lacking a covalent character and are weak; this observation explains the low high ductility of single crystals of silver.
Silver has a brilliant white metallic luster that can take a high polish, and, so characteristic that the name of the metal itself has become a colour name. Unlike copper and gold, the energy required to excite an electron from the filled d band to the s-p conduction band in silver is large enough that it no longer corresponds to absorption in the visible region of the spectrum, but rather in the ultraviolet. Protected silver has greater optical reflectivity than aluminium at all wavelengths longer than ~450 nm. At wavelengths shorter than 450 nm, silver's reflectivity is inferior to that of aluminium and drops to zero near 310 nm. High electrical and thermal conductivity is common to the elements in group 11, because their single s electron is free and does not interact with the filled d subshell, as such interactions lower electron mobility; the electrical conductivity of silver is the greatest of all metals, greater than copper, but it is not used for this property because of the higher cost.
An exception is in radio-frequency engineering at VHF and higher frequencies where silver plating improves electrical conductivity because those currents tend to flow on the surface of conductors rather than through the interior. During World War II in the US, 13540 tons of silver were used in electromagnets for enriching uranium because of the wartime shortage of copper. Pure silver has the highest thermal conductivity of any metal, although the conductivity of carbon and superfluid helium-4 are higher. Silver has the lowest contact resistance of any metal. Silver forms alloys with copper and gold, as well as zinc. Zinc-silver alloys with low zinc concentration may be considered as face-centred cubic solid solutions of zinc in silver, as the structure of the silver is unchanged while the electron concentration rises as more zinc is added. Increasing the electron concentration further leads to body-centred cubic, complex cubic, hexagonal close-packed phases. Occurring silver is composed of two stable isotopes, 107Ag and 109Ag, with 107Ag being more abundant.
This equal abundance is rare in the periodic table. The atomic weight is 107.8682 u. Both isotopes of silver are produced in stars via the s-process, as well as in supernovas via the r-process. Twenty-eight radioisotopes have been characterized, the most stable being 105Ag with a half-life of 41.29 days, 111Ag with a half-life of 7.45 days, 112Ag with a half-life of 3.13 hours. Silver has numerous nuclear isomers, the most stable being 108mAg, 110mAg and 106mAg. All of the remaining radioactive isotopes have half-lives of less than an hour, the majority of these have half-lives of less than three minutes. Isotopes of silver range in relative atomic mass from 92.950 u
Crystal twinning occurs when two separate crystals share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals in a variety of specific configurations; the surface along which the lattice points are shared in twinned crystals is called a composition surface or twin plane. Crystallographers classify twinned crystals by a number of twin laws; these twin laws are specific to the crystal system. The type of twinning can be a diagnostic tool in mineral identification. Twinning is an important mechanism for permanent shape changes in a crystal. Twinning can be a problem in X-ray crystallography, as a twinned crystal does not produce a simple diffraction pattern. Twin laws are either defined by the direction of the twin axes. If the twin law can be defined by a simple planar composition surface, the twin plane is always parallel to a possible crystal face and never parallel to an existing plane of symmetry. If the twin law is a rotation axis, the composition surface will be irregular, the twin axis will be perpendicular to a lattice plane, but will never be an even-fold rotation axis of the existing symmetry.
For example twinning cannot occur on a new 2 fold axis, parallel to an existing 4-fold axis. In the isometric system, the most common types of twins are the Spinel Law, where the twin axis is perpendicular to an octahedral face, the Iron Cross, the interpenetration of two pyritohedrons a subtype of dodecahedron. In the hexagonal system, calcite shows the contact. Quartz shows the Brazil Law, Dauphiné Law which are penetration twins caused by transformation and Japanese Law, caused by accidents during growth. In the tetragonal system, cyclical contact twins are the most observed type of twin, such as in rutile titanium dioxide and cassiterite tin oxide. In the orthorhombic system, crystals twin on planes parallel to the prism face, where the most common is a twin which produces cyclical twins, such as in aragonite and cerussite. In the monoclinic system, twin occur most on the planes and by the Manebach Law, Carlsbad Law, Braveno Law in orthoclase, the Swallow Tail Twins in gypsum. In the triclinic system, the most twinned crystals are the feldspar minerals plagioclase and microcline.
These minerals show the Pericline Laws. Simple twinned crystals may be contact twins or penetration twins. Contact twins share a single composition surface appearing as mirror images across the boundary. Plagioclase, quartz and spinel exhibit contact twinning. Merohedral twinning occurs when the lattices of the contact twins superimpose in three dimensions, such as by relative rotation of one twin from the other. An example is metazeunerite. In penetration twins the individual crystals have the appearance of passing through each other in a symmetrical manner. Orthoclase, staurolite and fluorite show penetration twinning. If several twin crystal parts are aligned by the same twin law they are referred to as multiple or repeated twins. If these multiple twins are aligned in parallel they are called polysynthetic twins; when the multiple twins are not parallel they are cyclic twins. Albite and pyrite show polysynthetic twinning. Spaced polysynthetic twinning is observed as striations or fine parallel lines on the crystal face.
Rutile, aragonite and chrysoberyl exhibit cyclic twinning in a radiating pattern. But in general, based on the relationship between the twin axis and twin plane, there are 3 types of twinning: 1-parallel twinning, when the twin axis and compositional plane lie parallel to each other, 2-normal twining, when the twin plane and compositional plane lie and 3-complex twining, a combination of parallel twinning and normal twinning on one compositional plane. There are three modes of formation of twinned crystals. Growth twins are the result of an interruption or change in the lattice during formation or growth due to a possible deformation from a larger substituting ion. Annealing or transformation twins are the result of a change in crystal system during cooling as one form becomes unstable and the crystal structure must re-organize or transform into another more stable form. Deformation or gliding twins are the result of stress on the crystal. If a metal with face-centered cubic structure, like Al, Cu, Ag, Au, etc. is subjected to stress, it will experience twinning.
The formation and migration of twin boundaries is responsible for ductility and malleability of fcc metals. Deformation twinning is a common result of regional metamorphism. Crystal twinning is used as an indicator of force direction in mountain building processes in orogeny research. Crystals that grow adjacent to each other may be aligned to resemble twinning; this parallel growth reduces system energy and is not twinning. Twinning can occur by cooperative displacement of atoms along the face of the twin boundary; this displacement of a large quantity of atoms requires significant energy to perform. Therefore, the theoretical stress required to form a twin is quite high, it is believed that twinning is associated with dislocation motion on a coordinated scale, in contrast to slip, caused by independent glide at several locations in the crystal. Twinning and slip are competitive mechanisms for crystal deformation; each mechanism is dominant under certain conditions. In fcc metals, slip is always dominant because the stres