In geometry and crystallography, a Bravais lattice, named after Auguste Bravais, is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by: R = n 1 a 1 + n 2 a 2 + n 3 a 3 where ni are any integers and ai are primitive vectors which lie in different directions and span the lattice. This discrete set of vectors must be closed under vector subtraction. For any choice of position vector R, the lattice looks the same; when the discrete points are atoms, ions, or polymer strings of solid matter, the Bravais lattice concept is used to formally define a crystalline arrangement and its frontiers. A crystal is made up of a periodic arrangement of one or more atoms repeated at each lattice point; the crystal looks the same when viewed from any equivalent lattice point, namely those separated by the translation of one unit cell. Two Bravais lattices are considered equivalent if they have isomorphic symmetry groups. In this sense, there are 14 possible Bravais lattices in three-dimensional space.
The 14 possible symmetry groups of Bravais lattices are 14 of the 230 space groups. In two-dimensional space, there are 5 Bravais lattices, grouped into four crystal families; the unit cells are specified according to the relative lengths of the cell edges and the angle between them. The area of the unit cell can be calculated by evaluating the norm ||a × b||, where a and b are the lattice vectors; the properties of the crystal families are given below: In three-dimensional space, there are 14 Bravais lattices. These are obtained by combining one of the seven lattice systems with one of the centering types; the centering types identify the locations of the lattice points in the unit cell as follows: Primitive: lattice points on the cell corners only Base-centered: lattice points on the cell corners with one additional point at the center of each face of one pair of parallel faces of the cell Body-centered: lattice points on the cell corners, with one additional point at the center of the cell Face-centered: lattice points on the cell corners, with one additional point at the center of each of the faces of the cellNot all combinations of lattice systems and centering types are needed to describe all of the possible lattices, as it can be shown that several of these are in fact equivalent to each other.
For example, the monoclinic I lattice can be described by a monoclinic C lattice by different choice of crystal axes. All A- or B-centred lattices can be described either by a C- or P-centering; this reduces the number of combinations to 14 conventional Bravais lattices, shown in the table below. The unit cells are specified according to the relative lengths of the cell edges and the angles between them; the volume of the unit cell can be calculated by evaluating the triple product a ·, where a, b, c are the lattice vectors. The properties of the lattice systems are given below: In four dimensions, there are 64 Bravais lattices. Of these, 23 are primitive and 41 are centered. Ten Bravais lattices split into enantiomorphic pairs. Bravais, A.. "Mémoire sur les systèmes formés par les points distribués régulièrement sur un plan ou dans l'espace". J. Ecole Polytech. 19: 1–128. Hahn, Theo, ed.. International Tables for Crystallography, Volume A: Space Group Symmetry. International Tables for Crystallography.
A. Berlin, New York: Springer-Verlag. Doi:10.1107/97809553602060000100. ISBN 978-0-7923-6590-7. Catalogue of Lattices Smith, Walter Fox. "The Bravais Lattices Song"
Lead oxide called red lead is the inorganic compound with the formula Pb3O4. A bright red or orange solid, it is used as pigment, in the manufacture of batteries, lead glass, rustproof primer paints, it is an example of a mixed valence compound, being composed of both Pb. Lead oxide has a tetragonal crystal structure at room temperature, which transforms to an orthorhombic form at temperature 170 K; this phase transition only changes the symmetry of the crystal and modifies the interatomic distances and angles. Lead oxide is prepared by calcination of lead oxide in air at about 450-480 °C: 6 PbO + O2 → 2 Pb3O4The resulting material is contaminated with PbO. If a pure compound is desired, PbO can be removed by a potassium hydroxide solution: PbO + KOH + H2O → KAnother method of preparation relies on annealing of lead carbonate in air: 6 PbCO3 + O2 → 2 Pb3O4 + 6 CO2Yet another method is oxidative annealing of white lead: 3 Pb2CO32 + O2 → 2 Pb3O4 + 3 CO2 + 3 H2OIn solution, lead oxide can be prepared by reaction of potassium plumbate with lead acetate, yielding yellow insoluble lead oxide monohydrate, Pb3O4·H2O, which can be turned into the anhydrous form by gentle heating: K2PbO3 + 2 Pb2 + H2O → Pb3O4 + 2 KOCOCH3 + 2 CH3COOHNatural minium is uncommon, forming only in extreme oxidizing conditions of lead ore bodies.
The best known natural specimens come from Broken Hill, New South Wales, where they formed as the result of a mine fire. Red lead is insoluble in water and in ethanol. However, it is soluble in hydrochloric acid present in the stomach, is therefore toxic when ingested, it dissolves in glacial acetic acid and a diluted mixture of nitric acid and hydrogen peroxide. When heated to 500 °C, it decomposes to lead oxygen. At 580 °C, the reaction is complete. 2Pb3O4 → 6 PbO + O2Nitric acid dissolves the lead oxide component, leaving behind the insoluble lead oxide: Pb3O4 + 4 HNO3 → PbO2 + 2 Pb2 + 2 H2OWith iron oxides and with elemental iron, lead oxide forms insoluble iron and iron plumbates, the basis of the anti-corrosive properties of lead-based paints applied to iron objects. Lead tetroxide is most used as a pigment for primer paints for iron objects. Due to its toxicity, its use is being limited. In the past, it was used in combination with linseed oil as a thick, long-lasting anti-corrosive paint.
The combination of minium and linen fibres was used for plumbing, now replaced with PTFE tape. It is used for manufacture of glass lead crystal glass, it finds limited use in some amateur pyrotechnics as a delay charge and was used in the past in the manufacture of dragon's egg pyrotechnic stars. Red lead is used as a curing agent in some polychloroprene rubber compounds, it is used in place of magnesium oxide to provide better water resistance properties. Red lead was used before being supplanted by engineer's blue, it is used as an adultering agent in turmeric powder. When inhaled, lead oxide irritates lungs. In case of high dose, the victim experiences a metallic taste, chest pain, abdominal pain; when ingested, it is absorbed, leading to lead poisoning. High concentrations can be absorbed through skin as well, it is important to follow safety precautions when working with lead-based paint. Long-term contact with lead oxide may lead to accumulation of lead compounds in organisms, with development of symptoms of acute lead poisoning.
Chronic poisoning displays as agitation, vision disorders, a grayish facial hue. Lead oxide was shown to be carcinogenic for laboratory animals, its carcinogenicity for humans was not proven. This compound's Latin name minium originates from the Minius, a river in northwest Iberia where it was first mined. Lead oxide was used as a red pigment in ancient Rome, where it was prepared by calcination of white lead. In the ancient and medieval periods it was used as a pigment in the production of illuminated manuscripts, gave its name to the minium or miniature, a style of picture painted with the colour; as a finely divided powder, it was sprinkled on dielectric surfaces to study Lichtenberg figures. In traditional Chinese medicine, red lead is used to treat ringworms and ulcerations, though the practice is limited due to its toxicity. Azarcón, a Mexican folk remedy for gastrointestinal disorders, contains up to 95% lead oxide, it was used before the 18th century as medicine. Lead paint Lead oxide, PbO Lead oxide, PbO2 List of inorganic pigments Minium Minium National Pollutant Inventory - Lead and Lead Compounds Fact Sheet Minium mineral data
A hot spring is a spring produced by the emergence of geothermally heated groundwater that rises from the Earth's crust. While some of these springs contain water, a safe temperature for bathing, others are so hot that immersion can result in injury or death. There is no universally accepted definition of a hot spring. For example, one can find the phrase hot spring defined as any geothermal spring a spring with water temperatures above its surroundings a natural spring with water temperature above human body temperature –, between 36.5 and 37.5 °C a natural spring with warm water above body temperature a thermal spring with water warmer than 36.7 °C a natural spring of water greater than 21.1 °C a natural discharge of groundwater with elevated temperatures a type of thermal spring in which hot water is brought to the surface. The water temperature of a hot spring is 6.5 °C or more above mean air temperature. Note that by this definition, "thermal spring" is not synonymous with the term "hot spring" a spring whose hot water is brought to the surface.
The water temperature of the spring is 8.3 °C or more above the mean air temperature. A spring with water above the core human body temperature – 36.7 °C. a spring with water above average ambient ground temperature. A spring with water temperatures above 50 °C The related term "warm spring" is defined as a spring with water temperature less than a hot spring by many sources, although Pentecost et al. suggest that the phrase "warm spring" is not useful and should be avoided. The US NOAA Geophysical Data Center defines a "warm spring" as a spring with water between 20 and 50 °C Much of the heat is created by decay of radioactive elements. An estimated 45 to 90 percent of the heat escaping from the Earth originates from radioactive decay of elements located in the mantle; the major heat-producing isotopes in the Earth are potassium-40, uranium-238, uranium-235, thorium-232. Water issuing from a hot spring is heated geothermally, that is, with heat produced from the Earth's mantle. In general, the temperature of rocks within the earth increases with depth.
The rate of temperature increase with depth is known as the geothermal gradient. If water percolates enough into the crust, it will be heated as it comes into contact with hot rocks; the water from hot springs in non-volcanic areas is heated in this manner. In active volcanic zones such as Yellowstone National Park, water may be heated by coming into contact with magma; the high temperature gradient near magma may cause water to be heated enough that it boils or becomes superheated. If the water becomes so hot that it builds steam pressure and erupts in a jet above the surface of the Earth, it is called a geyser. If the water only reaches the surface in the form of steam, it is called a fumarole. If the water is mixed with mud and clay, it is called a mud pot. Note that hot springs in volcanic areas are at or near the boiling point. People have been scalded and killed by accidentally or intentionally entering these springs. Warm springs are sometimes the result of cold springs mixing, they may occur within a volcanic outside of one.
One example of a non-volcanic warm spring is Georgia. Hot springs range in flow rate from the tiniest "seeps" to veritable rivers of hot water. Sometimes there is fountain. There are many claims in the literature about the flow rates of hot springs. There are many more high flow non-thermal springs than geothermal springs. For example, there are 33 recognized "magnitude one springs" (having a flow in excess of 2,800 L/s in Florida alone. Silver Springs, Florida has a flow of more than 21,000 L/s. Springs with high flow rates include: The Excelsior Geyser Crater in Yellowstone National Park yields about 4,000 U. S. gal/min. Evans Plunge in Hot Springs, South Dakota has a flow rate of 5,000 U. S. gal/min of 87 °F spring water. The Plunge, built in 1890, is the world's largest natural warm water indoor swimming pool; the combined flow of the 47 hot springs in Hot Springs, Arkansas is 35 L/s. The hot spring of Saturnia, Italy with around 500 liters a second The combined flow of the hot springs complex in Truth or Consequences, New Mexico is estimated at 99 liters/second.
Lava Hot Springs in Idaho has a flow of 130 liters/second. Glenwood Springs in Colorado has a flow of 143 liters/second. Elizabeth Springs in western Queensland, Australia might have had a flow of 158 liters/second in the late 19th century, but now has a flow of about 5 liters/second. Deildartunguhver in Iceland has a flow of 180 liters/second; the hot springs of Brazil's Caldas Novas are tapped by 86 wells, from which 333 liters/second are pumped for 14 hours per day. This corresponds to a peak average flow rate of 3.89 liters/second per well. The 2,850 hot springs of Beppu in Japan are the highest flow hot spring complex in Japan. Together the Beppu hot springs produce about 1,592 liters/second, or corresponding to an average hot spring flow of 0.56 liters/second. The 303 hot springs of Kokonoe in Japan produce 1,028 liters/second, which gives the average hot spring a flow of 3.39 liters/second. Ōita Prefecture has 4,762 hot springs, with a total flow of 4,437 liters/second, so the average hot spring flow is 0.93 liters/second.
The highest flow rate hot spring in Japan is the Tamagawa Hot Spring in Akita Prefecture, w
Solubility is the property of a solid, liquid or gaseous chemical substance called solute to dissolve in a solid, liquid or gaseous solvent. The solubility of a substance fundamentally depends on the physical and chemical properties of the solute and solvent as well as on temperature and presence of other chemicals of the solution; the extent of the solubility of a substance in a specific solvent is measured as the saturation concentration, where adding more solute does not increase the concentration of the solution and begins to precipitate the excess amount of solute. Insolubility is the inability to dissolve in a liquid or gaseous solvent. Most the solvent is a liquid, which can be a pure substance or a mixture. One may speak of solid solution, but of solution in a gas. Under certain conditions, the equilibrium solubility can be exceeded to give a so-called supersaturated solution, metastable. Metastability of crystals can lead to apparent differences in the amount of a chemical that dissolves depending on its crystalline form or particle size.
A supersaturated solution crystallises when'seed' crystals are introduced and rapid equilibration occurs. Phenylsalicylate is one such simple observable substance when melted and cooled below its fusion point. Solubility is not to be confused with the ability to'dissolve' a substance, because the solution might occur because of a chemical reaction. For example, zinc'dissolves' in hydrochloric acid as a result of a chemical reaction releasing hydrogen gas in a displacement reaction; the zinc ions are soluble in the acid. The solubility of a substance is an different property from the rate of solution, how fast it dissolves; the smaller a particle is, the faster it dissolves although there are many factors to add to this generalization. Crucially solubility applies to all areas of chemistry, inorganic, physical and biochemistry. In all cases it will depend on the physical conditions and the enthalpy and entropy directly relating to the solvents and solutes concerned. By far the most common solvent in chemistry is water, a solvent for most ionic compounds as well as a wide range of organic substances.
This is a crucial factor in much environmental and geochemical work. According to the IUPAC definition, solubility is the analytical composition of a saturated solution expressed as a proportion of a designated solute in a designated solvent. Solubility may be stated in various units of concentration such as molarity, mole fraction, mole ratio, mass per volume and other units; the extent of solubility ranges from infinitely soluble such as ethanol in water, to poorly soluble, such as silver chloride in water. The term insoluble is applied to poorly or poorly soluble compounds. A number of other descriptive terms are used to qualify the extent of solubility for a given application. For example, U. S. Pharmacopoeia gives the following terms: The thresholds to describe something as insoluble, or similar terms, may depend on the application. For example, one source states that substances are described as "insoluble" when their solubility is less than 0.1 g per 100 mL of solvent. Solubility occurs under dynamic equilibrium, which means that solubility results from the simultaneous and opposing processes of dissolution and phase joining.
The solubility equilibrium occurs. The term solubility is used in some fields where the solute is altered by solvolysis. For example, many metals and their oxides are said to be "soluble in hydrochloric acid", although in fact the aqueous acid irreversibly degrades the solid to give soluble products, it is true that most ionic solids are dissolved by polar solvents, but such processes are reversible. In those cases where the solute is not recovered upon evaporation of the solvent, the process is referred to as solvolysis; the thermodynamic concept of solubility does not apply straightforwardly to solvolysis. When a solute dissolves, it may form several species in the solution. For example, an aqueous suspension of ferrous hydroxide, Fe2, will contain the series + as well as other species. Furthermore, the solubility of ferrous hydroxide and the composition of its soluble components depend on pH. In general, solubility in the solvent phase can be given only for a specific solute, thermodynamically stable, the value of the solubility will include all the species in the solution.
Solubility is defined for specific phases. For example, the solubility of aragonite and calcite in water are expected to differ though they are both polymorphs of calcium carbonate and have the same chemical formula; the solubility of one substance in another is determined by the balance of intermolecular forces between the solvent and solute, the entropy change that accompanies the solvation. Factors such as temperature and pressure will alter this balance. Solubility may strongly depend on the presence of other species dissolved in the solvent, for example, complex-forming anions in liquids. Solubility will depend on the excess or deficiency of a common ion in the solution, a phenomenon known as the common-ion effect. To a lesser extent, solubility will depend on the ionic strength of solutions; the last two effects can be quantified using the equation for solubility equilibrium. For a solid that dissolves in a redox reaction, solubility is expe
Stoneware is a rather broad term for pottery or other ceramics fired at a high temperature. A modern technical definition is a vitreous or semi-vitreous ceramic made from stoneware clay or non-refractory fire clay. Whether vitrified or not, it is nonporous. Across the world, it has been developed after earthenware and before porcelain, has been used for high-quality as well as utilitarian wares; as a rough guide, modern earthenwares are fired in a kiln at temperatures in the range of about 1,000°C to 1,200 °C. Reaching high temperatures was a long-lasting challenge, temperatures somewhat below these were used for a long time. Earthenware can be fired as low as 600°C, achievable in primitive pit firing, but 800 °C to 1,100 °C was more typical. Stoneware needs certain types of clays, more specific than those able to make earthenware, but can be made from a much wider range than porcelain. Stoneware is not recognised as a category in traditional East Asian terminology, much Asian stoneware, such as Chinese Ding ware for example, is counted as porcelain by local definitions.
Terms such as "porcellaneous" or "near-porcelain" may be used in such cases. One definition of stoneware is from the Combined Nomenclature of the European Communities, a European industry standard, it states: Stoneware, though dense and hard enough to resist scratching by a steel point, differs from porcelain because it is more opaque, only vitrified. It may be semi-vitreous, it is coloured grey or brownish because of impurities in the clay used for its manufacture, is glazed. In industrial ceramics, five basic categories of stoneware have been suggested: Traditional stoneware – a dense and inexpensive body, it can be of any colour and breaks with a conchoidal or stony fracture. Traditionally made of fine-grained secondary, plastic clays which can be used to shape large pieces. Fine stoneware – made from more selected and blended raw materials, it is used to produce art ware. Chemical stoneware – used in the chemical industry, when resistance to chemical attack is needed. Purer raw materials are used than for other stoneware bodies.
Ali Baba is a popular name for a large chemical stoneware jars of up to 5,000 litres capacity used to store acids. Thermal shock resistant stoneware – has additions of certain materials to enhance the thermal shock resistance of the fired body. Electrical stoneware – used for electrical insulators, although it has been replaced by electrical porcelain; the key raw material in stoneware is either occurring stoneware clay or non-refractory fire clay. The mineral kaolinite is present but disordered, although mica and quartz are present their particle size is small. Stoneware clay is accompanied by impurities such as iron or carbon, giving it a "dirty" look, its plasticity can vary widely. Non-refractory fire clay may be another key raw material. Fire clays are considered refractory, because they withstand high temperatures before melting or crumbling. Refractory fire clays have a high concentration of kaolinite, with lesser amounts of mica and quartz. Non-refractory fire clays, have larger amounts of mica and feldspar.
Formulations for stoneware vary although the vast majority will conform to: plastic fire clays, 0 to 100 percent. Stoneware can be twice-fired. Maximum firing temperatures can vary from 1100 °C to 1300 °C depending on the flux content. Temperatures will be between 1180 °C and 1280 °C, the higher end of which equate to Bullers Rings 38 to 40 or Seger cones 4 to 8. To produce a better quality fired glaze finish, twice-firing can be used; this can be important for formulations composed of carbonaceous clays. For these, biscuit firing is around 900 °C, glost firing 1180–1280 °C. Water absorption of stoneware products is less than 1 percent. Another type, Flintless Stoneware, has been identified, it is defined in the UK Pottery Special Regulations of 1950 as: "Stoneware, the body of which consists of natural clay to which no flint or quartz or other form of free silica has been added."Traditional East Asian thinking classifies pottery only into "low-fired" and "high-fired" wares, equating to earthenware and porcelain, without the intermediate European class of stoneware, the many local types of stoneware were classed as porcelain, though not white and translucent.
Methods of forming stoneware bodies include moulding and wheel throwing. Underglaze and overglaze decoration of many types can be used. Much tableware in stoneware is white-glazed and decorated, it is visually similar to porcelain or faience earthenware; the Indus Valley Civilization produced stoneware, with an industry of a nearly industrial-scale mass-production of stoneware bangles throughout the civilization's Mature Period. Early examples of stoneware have been found in China as an extension of higher temperatures achieved from early development of reduction firing, with large quantities produced from the Han dynasty onwards. In both medieval China and Japan, stoneware was common, several types became admired for their simple forms and subtle glaze effects. Japan
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