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Clathrate hydrate

Clathrate hydrates, or gas hydrates, clathrates, or hydrates, are crystalline water-based solids physically resembling ice, in which small non-polar molecules (typically gases) or polar molecules with large hydrophobic moieties are trapped inside "cages" of hydrogen bonded, frozen water molecules. In other words, clathrate hydrates are clathrate compounds in which the host molecule is water and the guest molecule is typically a gas or liquid. Without the support of the trapped molecules, the lattice structure of hydrate clathrates would collapse into conventional ice crystal structure or liquid water. Most low molecular weight gases, including O2, H2, N2, CO2, CH4, H2S, Ar, Kr, and Xe, as well as some higher hydrocarbons and freons, will form hydrates at suitable temperatures and pressures. Clathrate hydrates are not officially chemical compounds, as the enclathrated guest molecules are never bonded to the lattice. The formation and decomposition of clathrate hydrates are first order phase transitions, not chemical reactions. Their detailed formation and decomposition mechanisms on a molecular level are still not well understood. Clathrate hydrates were first documented in 1810 by Sir Humphry Davy who found that water was a primary component of what was earlier thought to be solidified chlorine.

Clathrates have been found to occur naturally in large quantities. Around 6.4 trillion ($6.4$) tonnes of methane is trapped in deposits of methane clathrate on the deep ocean floor. Such deposits can be found on the Norwegian continental shelf in the northern headwall flank of the Storegga Slide. Clathrates can also exist as permafrost, as at the Mallik gas hydrate site in the Mackenzie Delta of northwestern Canadian Arctic. These natural gas hydrates are seen as a potentially vast energy resource and several countries have dedicated national programs to develop this energy resource. Clathrate hydrate has also been of great interest as technology enabler for many applications like seawater desalination, gas storage, carbon dioxide capture & storage, cooling medium for data centre and district cooling etc. Hydrocarbon clathrates cause problems for the petroleum industry, because they can form inside gas pipelines, often resulting in obstructions. Deep sea deposition of carbon dioxide clathrate has been proposed as a method to remove this greenhouse gas from the atmosphere and control climate change. Clathrates are suspected to occur in large quantities on some outer planets, moons and trans-Neptunian objects, binding gas at fairly high temperatures.

Structure

Gas hydrates usually form two crystallographic cubic structures: structure (Type) I (named sI) and structure (Type) II (named sII) of space groups $$Pm\overline{3}n$$ and $$Fd\overline{3}m$$ respectively. A third hexagonal structure of space group $$P6/mmm$$ may also be observed (Type H).

The unit cell of Type I consists of 46 water molecules, forming two types of cages – small and large. The unit cell contains two small cages and six large ones. The small cage has the shape of a pentagonal dodecahedron (512) (which is not a regular dodecahedron) and the large one that of a tetradecahedron, specifically a hexagonal truncated trapezohedron (51262). Together, they form a version of the Weaire–Phelan structure. Typical guests forming Type I hydrates are CO2 in carbon dioxide clathrate and CH4 in methane clathrate.

The unit cell of Type II consists of 136 water molecules, again forming two types of cages – small and large. In this case there are sixteen small cages and eight large ones in the unit cell. The small cage again has the shape of a pentagonal dodecahedron (512), but the large one is a hexadecahedron (51264). Type II hydrates are formed by gases like O2 and N2.

The unit cell of Type H consists of 34 water molecules, forming three types of cages – two small ones of different types, and one "huge". In this case, the unit cell consists of three small cages of type 512, two small ones of type 435663 and one huge of type 51268. The formation of Type H requires the cooperation of two guest gases (large and small) to be stable. It is the large cavity that allows structure H hydrates to fit in large molecules (e.g. butane, hydrocarbons), given the presence of other smaller help gases to fill and support the remaining cavities. Structure H hydrates were suggested to exist in the Gulf of Mexico. Thermogenically produced supplies of heavy hydrocarbons are common there.

Hydrates in the universe
Iro et al., trying to interpret the nitrogen deficiency in comets, stated most of the conditions for hydrate formation in the protoplanetary nebulae, surrounding the pre-main and main sequence stars were fulfilled, despite the rapid grain growth to metre-scale. The key was to provide enough microscopic ice particles exposed to a gaseous environment. Observations of the radiometric continuum of circumstellar discs around $$\tau$$-Tauri and Herbig Ae/Be stars suggest massive dust disks consisting of millimetre-sized grains, which disappear after several million years (e.g., ). A lot of work on detecting water ices in the Universe was done on the Infrared Space Observatory (ISO). For instance, broad emission bands of water ice at 43 and 60 μm were found in the disk of the isolated Herbig Ae/Be star HD 100546 in Musca. The one at 43 μm is much weaker than the one at 60 μm, which means the water ice, is located in the outer parts of the disk at temperatures below 50 K. There is also another broad ice feature between 87 and 90 μm, which is very similar to the one in NGC 6302 (the Bug or Butterfly nebula in Scorpius). Crystalline ices were also detected in the proto-planetary disks of ε-Eridani and the isolated Fe star HD 142527 in Lupus. 90% of the ice in the latter was found crystalline at temperature around 50 K. HST demonstrated that relatively old circumstellar disks, as the one around the 5-million-year-old B9.5Ve Herbig Ae/Be star HD 141569A, are dusty. Li & Lunine found water ice there. Knowing the ices usually exist at the outer parts of the proto-planetary nebulae, Hersant et al. proposed an interpretation of the volatile enrichment, observed in the four giant planets of the Solar System, with respect to the Solar abundances. They assumed the volatiles had been trapped in the form of hydrates and incorporated in the planetesimals flying in the protoplanets' feeding zones.

Kieffer et al. (2006) hypothesized that the geyser activity in the south polar region of Saturn's moon Enceladus originates from clathrate hydrates, where carbon dioxide, methane, and nitrogen are released when exposed to the vacuum of space through the "Tiger Stripe" fractures found in that area. However, subsequent analysis of plume material makes it more likely that the geysers on Enceladus derive from a salty subsurface ocean.

Carbon dioxide clathrate is believed to play a major role in different processes on Mars. Hydrogen clathrate is likely to form in condensation nebulae for gas giants.

Kamata et al. (2019) of the University of Hokkaido have proposed that a thin layer of clathrate hydrates thermally insulates the subsurface ocean of liquid water of Pluto, the existence of which is suggested by data from the New Horizons probe.

Natural gas hydrates
Naturally on Earth gas hydrates can be found on the seabed, in ocean sediments, in deep lake sediments (e.g. Lake Baikal), as well as in the permafrost regions. The amount of methane potentially trapped in natural methane hydrate deposits may be significant (1015 to 1017 cubic metres), which makes them of major interest as a potential energy resource. Catastrophic release of methane from the decomposition of such deposits may lead to a global climate change, referred to as the "clathrate gun hypothesis", because CH4 is a more potent greenhouse gas than CO2 (see Atmospheric methane). The fast decomposition of such deposits is considered a geohazard, due to its potential to trigger landslides, earthquakes and tsunamis. However, natural gas hydrates do not contain only methane but also other hydrocarbon gases, as well as H2S and CO2. Air hydrates are frequently observed in polar ice samples.

Pingos are common structures in permafrost regions. Similar structures are found in deep water related to methane vents. Significantly, gas hydrates can even be formed in the absence of a liquid phase. Under that situation, water is dissolved in gas or in liquid hydrocarbon phase.

In 2017, both Japan and China announced that attempts at large-scale resource extraction of methane hydrates from under the seafloor were successful. However, commercial-scale production remains years away.

The 2020 Research Fronts report identified gas hydrate accumulation and mining technology as one of the top 10 research fronts in the geosciences.

Gas hydrates in pipelines
Thermodynamic conditions favouring hydrate formation are often found in pipelines. This is highly undesirable, because the clathrate crystals might agglomerate and plug the line and cause flow assurance failure and damage valves and instrumentation. The results can range from flow reduction to equipment damage.

Hydrate formation, prevention and mitigation philosophy
Hydrates have a strong tendency to agglomerate and to adhere to the pipe wall and thereby plug the pipeline. Once formed, they can be decomposed by increasing the temperature and/or decreasing the pressure. Even under these conditions, the clathrate dissociation is a slow process.

Therefore, preventing hydrate formation appears to be the key to the problem. A hydrate prevention philosophy could typically be based on three levels of security, listed in order of priority:
 * 1) Avoid operational conditions that might cause formation of hydrates by depressing the hydrate formation temperature using glycol dehydration;
 * 2) Temporarily change operating conditions in order to avoid hydrate formation;
 * 3) Prevent formation of hydrates by addition of chemicals that (a) shift the hydrate equilibrium conditions towards lower temperatures and higher pressures or (b) increase hydrate formation time (inhibitors)

The actual philosophy would depend on operational circumstances such as pressure, temperature, type of flow (gas, liquid, presences of water etc.).

Hydrate inhibitors
When operating within a set of parameters where hydrates could be formed, there are still ways to avoid their formation. Altering the gas composition by adding chemicals can lower the hydrate formation temperature and/or delay their formation. Two options generally exist:
 * Thermodynamic inhibitors
 * Kinetic inhibitors and anti-agglomerants

The most common thermodynamic inhibitors are methanol, monoethylene glycol (MEG), and diethylene glycol (DEG), commonly referred to as glycol. All may be recovered and recirculated, but the economics of methanol recovery is not favourable in most cases. MEG is preferred over DEG for applications where the temperature is expected to be −10 °C or lower due to high viscosity at low temperatures. Triethylene glycol (TEG) has too low vapour pressure to be suited as an inhibitor injected into a gas stream. More methanol is lost in the gas phase when compared to MEG or DEG.

The use of kinetic inhibitors and anti-agglomerants in actual field operations is a new and evolving technology. It requires extensive tests and optimisation to the actual system. While kinetic inhibitors work by slowing down the kinetics of the nucleation, anti-agglomerants do not stop the nucleation, but stop the agglomeration (sticking together) of gas hydrate crystals. These two kinds of inhibitors are also known as low dosage hydrate inhibitors, because they require much smaller concentrations than the conventional thermodynamic inhibitors. Kinetic inhibitors, which do not require water and hydrocarbon mixture to be effective, are usually polymers or copolymers and anti-agglomerants (requires water and hydrocarbon mixture) are polymers or zwitterionic – usually ammonium and COOH – surfactants being both attracted to hydrates and hydrocarbons.

Empty clathrate hydrates
Empty clathrate hydrates are thermodynamically unstable (guest molecules are of paramount importance to stabilize these structures) with respect to ice, and as such their study using experimental techniques is greatly limited to very specific formation conditions; however, their mechanical stability renders theoretical and computer simulation methods the ideal choice to address their thermodynamic properties. Starting from very cold samples (110–145 K), Falenty et al. degassed Ne–sII clathrates for several hours using vacuum pumping to obtain a so-called ice XVI, while employing neutron diffraction to observe that (i) the empty sII hydrate structure decomposes at T ≥ 145 K and, furthermore, (ii) the empty hydrate shows a negative thermal expansion at T < 55 K, and it is mechanically more stable and has a larger lattice constant at low temperatures than the Ne-filled analogue. The existence of such a porous ice had been theoretically predicted before. From a theoretical perspective, empty hydrates can be probed using Molecular Dynamics or Monte Carlo techniques. Conde et al. used empty hydrates and a fully atomic description of the solid lattice to estimate the phase diagram of H2O at negative pressures and T ≤ 300 K, and obtain the differences in chemical potentials between ice Ih and the empty hydrates, central to the van der Waals−Platteeuw theory. Jacobson et al. performed simulations using a monoatomic (coarse-grained) model developed for H2O that is capable of capturing the tetrahedral symmetry of hydrates. Their calculations revealed that, under 1 atm pressure, sI and sII empty hydrates are metastable regarding the ice phases up to their melting temperatures, T = 245 ± 2 K and T = 252 ± 2 K, respectively. Matsui et al. employed molecular dynamics to perform a thorough and systematic study of several ice polymorphs, namely space fullerene ices, zeolitic ices, and aeroices, and interpreted their relative stability in terms of geometrical considerations.

The thermodynamics of metastable empty sI clathrate hydrates have been probed over broad temperature and pressure ranges, 100 K ≤ T ≤ 220 K and 100 kPa ≤ p ≤ 500 MPa, by Cruz et al. using large-scale simulations and compared with experimental data at 100 kPa. The whole p–V–T surface obtained was fitted by the universal form of the Parsafar and Mason equation of state with an accuracy of 99.7–99.9%. Framework deformation caused by applied temperature followed a parabolic law, and there is a critical temperature above which the isobaric thermal expansion becomes negative, ranging from 194.7 K at 100 kPa to 166.2 K at 500 MPa. Response to the applied (p, T) field was analyzed in terms of angle and distance descriptors of a classical tetrahedral structure and observed to occur essentially by means of angular alteration for (p, T) > (200 MPa, 200 K). The length of the hydrogen bonds responsible for framework integrity was insensitive to the thermodynamic conditions and its average value is r(̅O H) = 0.25 nm.

CO2 hydrate
Clathrate hydrate, which encaged CO2 as guest molecule is termed as CO2 hydrate. The term CO2 hydrates are more commonly used these days with its relevance in anthropogenic CO2 capture and sequestration. A nonstoichiometric compound, carbon dioxide hydrate, is composed of hydrogen-bonded water molecules arranged in ice-like frameworks that are occupied by molecules with appropriate sizes and regions. In structure I, the CO2 hydrate crystallizes as one of two cubic hydrates composed of 46 H2O molecules (or D2O) and eight CO2 molecules occupying both large cavities (tetrakaidecahedral) and small cavities (pentagonal dodecahedral). Researchers believed that oceans and permafrost have immense potential to capture anthropogenic CO2 in the form CO2 hydrates. The utilization of additives to shift the CO2 hydrate equilibrium curve in phase diagram towards higher temperature and lower pressures is still under scrutiny to make extensive large-scale storage of CO2 viable in shallower subsea depths.

title: Clathrate hydrate


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Talk:Grooved Ware culture

How do we know they co-existed? How do we know they didn't capture each others' potters and enslave them? I'm sorry, just a crabby historian complaining about the deductions of archaeologists... ;) I like this neolithic material!  It should be linked, I guess, from the archaeology page (with a subheader for 'sites'?) and neolithic. --MichaelTinkler

 * Well, we still don't know what one of the rooms at Skara Brae was for... maybe it was a Pottery Research & Development facility. Still, I'll get onto fleshing the others out in good time -- Dweir

Another thing occurred to me - this is the wrong place to put it, but shouldn't Neolithic/Bronze Age/Iron Age etc. for regions be on the Timeline?

There is now new evidence that the grooved ware people, a venus worshiping group of prehistory, were the first peoples to have developed the technology for the building in stone creating structures such as stone henge, and skara brae hundereds of years before the Egiptions built the pyrimids. All Megalythic sites across briton are related to each other in two very importaint ways, first all are alined to observe vairous astronomical events, and second by a unit of measurement known as the megalythic yard. These people were great traders and sailers, traveling as far as Israil and Irak to trade in stone and copper axe heads and tin. With these exports however, other things were passed on to those peoples that they made contact with, these were the venus worshiping traditons and the knoledge of astrology and building in stone. These Groved ware people once they had left the british iles are known in history as the Sumarians, whos name litteraly means those who arrived. They have been discribed in history as having arrived with their culture already intact, already possesting vast knowledge in building, astrology and navigation. It is now believed that Sumer begain as a trading out post of the grooved ware people, arising at the hight of the grooved ware civilisation in Briton. As with all groups in history, when they reach a peak in productivity and success they expanded and set up trade routes and ports. There is several bits of evidance to support this such as the fact that a vast amount of grooved ware pottery and tools have been found right accross europe and the middle east, where as not much material from other cultures has been found in and around the British Iles suggesting that the trafic was moving to the east rather than from it. Other proof includes the fact that stone circles or henges have been found in Israil and Irak, and also in Africa. In fact a particualy importaint and large stone circle has been found in Africa which is at a point on the planet where the sun shines directly down on the earth, which would have been a significant site for the astronomicaly minded Grooved ware people/sumerians. Also interesting to note is a heaving duty pontoon for a port is still standing created from megalythic uprignt stones put there almost 4500 years ago right on the edge of one of the powerful trade currents flowing around africa. This would have been an essential stop off station for trade traffic moving around affrica. Several sites around the mediterainian have evidence of being once a trade port for these people, for example in Crete. It is quite possible that the infulx of ideas and skills brought with these people kick started a whole host of civilisations, for example Abraham of the bible who is the traditional farther of the Jews came from land infulenced by the Sumerians, and Egipt has tablets discribing giant builder gods who showed them the scinece of astrology and building, baring in mind that the arverage hight of grooved ware person was 6'6" where as the average egiption was only around 5' at the time!. for more information check out Robert lomas and Chriss Knight.

Knight and Lomas in their book "The Book ofHiram" provide some archeological evidence to support the grooved ware people trading and travelling. Wickham-Jones, CR Scotland's First Settlers, Historic Scotland, 1994 Renfrew C Before Civilisation Jonathon Cape 1973 Mackie, E "The Megolithic Builders" Phaidon Press, 1977 Mccallanjam (talk) 01:18, 20 November 2013 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Grooved Ware culture


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Breadfruit

Breadfruit (Artocarpus altilis) is a species of flowering tree in the mulberry and jackfruit family (Moraceae) believed to be a domesticated descendant of Artocarpus camansi originating in New Guinea, the Maluku Islands, and the Philippines. It was initially spread to Oceania via the Austronesian expansion. It was further spread to other tropical regions of the world during the Colonial Era. British and French navigators introduced a few Polynesian seedless varieties to Caribbean islands during the late 18th century. Today it is grown in some 90 countries throughout South and Southeast Asia, the Pacific Ocean, the Caribbean, Central America and Africa. Its name is derived from the texture of the moderately ripe fruit when cooked, similar to freshly baked bread and having a potato-like flavor.

The trees have been widely planted in tropical regions, including lowland Central America, northern South America, and the Caribbean. In addition to the fruit serving as a staple food in many cultures, the light, sturdy timber of breadfruit has been used for outriggers, ships, and houses in the tropics.

Breadfruit is closely related to Artocarpus camansi (breadnut or seeded breadfruit) of New Guinea, the Maluku Islands, and the Philippines, Artocarpus blancoi (tipolo or antipolo) of the Philippines, and Artocarpus mariannensis (dugdug) of Micronesia, all of which are sometimes also referred to as "breadfruit". It is also closely related to the jackfruit.

Description
Breadfruit trees grow to a height of 26 m. The large and thick leaves are deeply cut into pinnate lobes. All parts of the tree yield latex, which is useful for boat caulking.

The trees are monoecious, with male and female flowers growing on the same tree. The male flowers emerge first, followed shortly afterward by the female flowers. The latter grow into capitula, which are capable of pollination just three days later. Pollination occurs mainly by fruit bats, but cultivated varieties produce fruit without pollination. The compound, false fruit develops from the swollen perianth, and originates from 1,500 to 2,000 flowers visible on the skin of the fruit as hexagon-like disks.

Breadfruit is one of the highest-yielding food plants, with a single tree producing up to 200 or more grapefruit-sized fruits per season, requiring limited care. In the South Pacific, the trees yield 50 to 150 fruits per year, usually round, oval or oblong weighing 0.25 to 6 kg. Productivity varies between wet and dry areas. Studies in Barbados indicate a reasonable potential of 6.7 to 13.4 ST/acre. The ovoid fruit has a rough surface, and each fruit is divided into many achenes, each achene surrounded by a fleshy perianth and growing on a fleshy receptacle. Most selectively bred cultivars have seedless fruit, whereas seeded varieties are grown mainly for their edible seeds. Breadfruit is usually propagated using root cuttings.

Breadfruit is closely related to the breadnut. It is similar in appearance to its relative of the same genus, the jackfruit (Artocarpus heterophyllus). The closely related Artocarpus camansi can be distinguished from A. altilis by having spinier fruits with numerous seeds. Artocarpus mariannensis can be distinguished by having dark green elongated fruits with darker yellow flesh, as well as entire or shallowly lobed leaves.

Propagation
Breadfruit is propagated mainly by seeds, though seedless breadfruit can be propagated by transplanting suckers that grow off the surface roots of the tree. The roots can be purposefully injured to induce the growth of suckers, which are then separated from the root and planted in a pot or directly transplanted into the ground. Pruning also induces sucker growth. Sucker cuttings are placed in plastic bags containing a mixture of soil, peat and sand, and kept in the shade while moistened with liquid fertilizer. When roots are developed, the transplant is put in full sun until time for planting in the orchard.

For large-scale propagation, root cuttings are preferred, using segments about 2 in thick and 9 in long. Rooting may take up to 5 months to develop, with the young trees ready for planting when they are 2 ft high.

Etymology and common names
The term breadfruit was first used in the 17th century to describe the bread-like texture of the fruit when baked. Breadfruit has hundreds of varieties and numerous common names varying by its geographic distribution.

Taxonomy
According to DNA fingerprinting studies, the wild seeded ancestor of breadfruit is the breadnut (Artocarpus camansi) which is native to New Guinea, the Maluku Islands, and the Philippines. It was one of the canoe plants spread by Austronesian voyagers around 3,000 years ago into Micronesia, Melanesia, and Polynesia, where it was not native.

A. camansi was domesticated and selectively bred in Polynesia, giving rise to the mostly seedless Artocarpus altilis. Micronesian breadfruit also show evidence of hybridization with the native Artocarpus mariannensis, while most Polynesian and Melanesian cultivars do not. This indicates that Micronesia was initially colonized separately from Polynesia and Melanesia through two different migration events which later came into contact with each other in eastern Micronesia.

Distribution and habitat

Breadfruit is an equatorial lowland species. It has been spread from its Pacific source to many tropical regions.

In 1769, Joseph Banks was stationed in Tahiti as part of the HMS Endeavour expedition commanded by Captain James Cook. The late-18th-century quest for cheap, high-energy food sources for slaves in British colonies prompted colonial administrators and plantation owners to call for breadfruit to be brought to the Caribbean. As president of the Royal Society, Banks provided a cash bounty and gold medal for success in this endeavor, and successfully lobbied for a British Naval expedition. After an unsuccessful voyage to the South Pacific to collect the plants as commander of HMS Bounty, in 1791, William Bligh commanded a second expedition with HMS Providence (1791) and HMS Assistant, which collected seedless breadfruit plants in Tahiti and transported these to St. Helena in the Atlantic and St. Vincent and Jamaica in the West Indies.

The plant grows best below elevations of 650 m, but is found at elevations of 1550 m. Preferred soils are neutral to alkaline (pH of 6.1–7.4) and either sand, sandy loam, loam or sandy clay loam. Breadfruit is able to grow in coral sands and saline soils. The breadfruit is ultra-tropical, requiring a temperature range of 16 - 38 C and an annual rainfall of 2000-2500 mm.

Nutrition
Breadfruit is 71% water, 27% carbohydrates, 1% protein and contains negligible fat (table). In a reference amount of 100 g, raw breadfruit supplies 103 calories, is a rich source of vitamin C (32% of the Daily Value, DV), and provides a moderate source of potassium (16% DV), with no other nutrients in significant content.

Food
Breadfruit is a staple food in many tropical regions. Most breadfruit varieties produce fruit throughout the year. Both ripe and unripe fruit have culinary uses; unripe breadfruit is cooked before consumption. Before being eaten, the fruit are roasted, baked, fried or boiled. When cooked, the taste of moderately ripe breadfruit is described as potato-like, or similar to freshly baked bread.

One breadfruit tree can produce 450 lb each season. Because breadfruit trees usually produce large crops at certain times of the year, the preservation of harvested fruit is an issue. One traditional preservation technique is to bury peeled and washed fruits in a leaf-lined pit where they ferment over several weeks and produce a sour, sticky paste. So stored, the product may endure a year or more, and some pits are reported to have produced edible contents more than 20 years later.

In addition to being edible raw, breadfruit can be ground into flour and the seeds can be cooked for consumption.

Southeast Asia, Pacific Islands and Madagascar

The seedless breadfruit is found in Brunei, Indonesia and Malaysia, where it is called sukun. It is commonly made into fritters and eaten as snacks. Breadfruit fritters are sold as local street food.

In the Philippines, breadfruit is known as rimas in Tagalog and kolo in the Visayan languages. It is also called kamansi (also spelled camansi), along with the closely related Artocarpus camansi, and the endemic Artocarpus blancoi (tipolo or antipolo). All three species, as well as the closely related jackfruit, are commonly used much in the same way in savory dishes. The immature fruits are most commonly eaten as ginataang rimas (cooked with coconut milk).

In the Hawaiian staple food called poi, the traditional ingredient of mashed taro root can be replaced by, or augmented with, mashed breadfruit (ulu in Hawaiian). The resulting "breadfruit poi" is called poi ulu.

South Asia
In Sri Lanka, it is cooked as a curry using coconut milk and spices (which becomes a side dish) or boiled. Boiled breadfruit is a famous main meal. It is often consumed with scraped coconut or coconut sambol, made of scraped coconut, red chili powder and salt mixed with a dash of lime juice. A traditional sweet snack made of finely sliced, sun-dried breadfruit chips deep-fried in coconut oil and dipped in heated treacle or sugar syrup is known as rata del petti. In India, fritters of breadfruit, called jeev kadge phodi in Konkani or kadachakka varuthath in Malayalam, are a local delicacy in coastal Karnataka and Kerala. In Seychelles, it was traditionally eaten as a substitute for rice, as an accompaniment to the mains. It would either be consumed boiled (friyapen bwi) or grilled (friyapen griye), where it would be put whole in the wood fire used for cooking the main meal and then taken out when ready. It is also eaten as a dessert, called ladob friyapen, where it is boiled in coconut milk, sugar, vanilla, cinnamon and a pinch of salt.

Caribbean and Latin America
In Belize, the Mayan people call it masapan.

In Puerto Rico, breadfruit is called panapén or pana, for short, although the name pana is often used to refer to breadnut, seeds of which have traditionally been boiled, peeled and eaten whole. In some inland regions it is also called mapén and used to make pasteles and alcapurrias. Breadfruit is often served boiled with a mixture of sauteed bacalao (salted cod fish), olive oil and onions. Mostly as tostones where about 1 inch chunks are fried, lighty flattened and fried again. Mofongo de panapén fried breadfruit mashed with olive oil, garlic, broth, and chicharrón. Rellenos de panapén the breadfruit version of papa rellena. Dipping sauce made from boiled ripe breadfruit similar to chutney using spices, sesame seeds, herbs, lentil, coconut milk, and fruit. Both ripe and unripe are boiled together and mashed with milk and butter to make pastelón de panapén, a dish similar to lasagna. Ripe breadfruit is used in desserts: flan de pana (breadfruit custard). Cazuela, a crustless pie with ripe breadfruit, spices, raisins, coconut milk, and sweet potatoes. Breadfruit flour is sold all over Puerto Rico and used for making bread, pastries, cookies, pancakes, waffles, crepes, and almojábana.

In the Dominican Republic, it is called buen pan or "good bread". Breadfruit is not popular in Dominican cookery and is used mainly for feeding pigs.

In Barbados, breadfruit is boiled with salted meat and mashed with butter to make breadfruit coucou. It is usually eaten with saucy meat dishes.

In Haiti, steamed breadfruit is mashed to make a dish called tonmtonm which is eaten with a sauce made with okra and other ingredients, such as fish and crab.

In Trinidad and Tobago, breadfruit is boiled, then fried and eaten with saucy meat dishes like curried duck.

In Jamaica, breadfruit is boiled in soups or roasted on stove top, in the oven or on wood coal. It is eaten with the national dish ackee and salt fish. The ripe fruit is used in salads or fried as a side dish.

In St. Vincent and the Grenadines it is eaten boiled in soups, roasted and fried. When roasted and served with fried jackfish, it is the country's national dish. The ripe fruit is used as a base to make drinks, cakes and ice cream.

Timber and other uses
Breadfruit was widely used in a variety of ways among Pacific Islanders. Its lightweight wood (specific gravity of 0.27) is resistant to termites and shipworms, so it is used as timber for structures and outrigger canoes. Its wood pulp can also be used to make paper, called breadfruit tapa. Native Hawaiians used its sticky latex to trap birds, whose feathers were made into cloaks. The wood of the breadfruit tree was one of the most valuable timbers in the construction of traditional houses in Samoan architecture.

Breadfruit contains phytochemicals having potential as an insect repellent. The parts of the fruits that are discarded can be used to feed livestock. The leaves of breadfruit trees can also be browsed by cattle.

In culture
On Puluwat in the Caroline Islands, in the context of sacred yitang lore, breadfruit (poi) is a figure of speech for knowledge. This lore is organized into five categories: war, magic, meetings, navigation, and breadfruit.

According to an etiological Hawaiian myth, the breadfruit originated from the sacrifice of the war god Kū. After deciding to live secretly among mortals as a farmer, Kū married and had children. He and his family lived happily until a famine seized their island. When he could no longer bear to watch his children suffer, Kū told his wife that he could deliver them from starvation, but to do so he would have to leave them. Reluctantly she agreed, and at her word, Kū descended into the ground right where he had stood until only the top of his head was visible. His family waited around the spot he had last been, day and night, watering it with their tears until suddenly, a small green shoot appeared where Kū had stood. Quickly, the shoot grew into a tall and leafy tree that was laden with heavy breadfruits that Kū's family and neighbors gratefully ate, joyfully saved from starvation.

Though they are widely distributed throughout the Pacific, many breadfruit hybrids and cultivars are seedless or otherwise biologically incapable of naturally dispersing long distances. Therefore, it is clear that humans aided distribution of the plant in the Pacific, specifically prehistoric groups who colonized the Pacific Islands. To investigate the patterns of human migration throughout the Pacific, scientists have used molecular dating of breadfruit hybrids and cultivars in concert with anthropological data. Results support the west-to-east migration hypothesis, in which the Lapita people are thought to have traveled from Melanesia to numerous Polynesian islands.

The world's largest collection of breadfruit varieties was established by botanist Diane Ragone, from over 20 years' travel to 50 Pacific islands, on a 10 acre plot outside of Hana, on the isolated east coast of Maui (Hawaii).

title: Breadfruit


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Bremsstrahlung

In particle physics, bremsstrahlung  is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation (i.e., photons), thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases.

Broadly speaking, bremsstrahlung or braking radiation is any radiation produced due to the acceleration (positive or negative) of a charged particle, which includes synchrotron radiation (i.e., photon emission by a relativistic particle), cyclotron radiation (i.e. photon emission by a non-relativistic particle), and the emission of electrons and positrons during beta decay. However, the term is frequently used in the more narrow sense of radiation from electrons (from whatever source) slowing in matter.

Bremsstrahlung emitted from plasma is sometimes referred to as free–free radiation. This refers to the fact that the radiation in this case is created by electrons that are free (i.e., not in an atomic or molecular bound state) before, and remain free after, the emission of a photon. In the same parlance, bound–bound radiation refers to discrete spectral lines (an electron "jumps" between two bound states), while free–bound radiation refers to the radiative combination process, in which a free electron recombines with an ion.

This article uses SI units, along with the scaled single-particle charge $$\bar q \equiv q / (4\pi \epsilon_0)^{1/2}$$.

Classical description

If quantum effects are negligible, an accelerating charged particle radiates power as described by the Larmor formula and its relativistic generalization.

Total radiated power
The total radiated power is $$P = \frac{2 \bar q^2 \gamma^4}{3 c}    \left( \dot{\beta}^2 + \frac{\left(\boldsymbol{\beta} \cdot \dot{\boldsymbol{\beta}}\right)^2}{1 - \beta^2}\right),$$ where $\boldsymbol\beta = \frac{\mathbf v}{c}$ (the velocity of the particle divided by the speed of light), $\gamma = {1}/{\sqrt{1-\beta^2}}$  is the Lorentz factor, $$\varepsilon_0$$ is the vacuum permittivity, $$\dot{\boldsymbol\beta}$$ signifies a time derivative of $\boldsymbol\beta$, and $q$ is the charge of the particle. In the case where velocity is parallel to acceleration (i.e., linear motion), the expression reduces to $$P_{a \parallel v} = \frac{2 \bar q^2 a^2 \gamma^6}{3 c^3},$$ where $$a \equiv \dot{v} = \dot{\beta}c$$ is the acceleration. For the case of acceleration perpendicular to the velocity ($$\boldsymbol{\beta} \cdot \dot{\boldsymbol{\beta}} = 0$$), for example in synchrotrons, the total power is $$P_{a \perp v} = \frac{2 \bar q^2 a^2 \gamma^4 }{3c^3}.$$

Power radiated in the two limiting cases is proportional to $$\gamma^4$$ $$\left(a \perp v\right)$$ or $$\gamma^6$$ $$\left(a \parallel v\right)$$. Since $$E = \gamma m c^2$$, we see that for particles with the same energy $$E$$ the total radiated power goes as $$m^{-4}$$ or $$m^{-6}$$, which accounts for why electrons lose energy to bremsstrahlung radiation much more rapidly than heavier charged particles (e.g., muons, protons, alpha particles). This is the reason a TeV energy electron-positron collider (such as the proposed International Linear Collider) cannot use a circular tunnel (requiring constant acceleration), while a proton-proton collider (such as the Large Hadron Collider) can utilize a circular tunnel. The electrons lose energy due to bremsstrahlung at a rate $$(m_\text{p}/m_\text{e})^4 \approx 10^{13}$$ times higher than protons do.

Angular distribution
The most general formula for radiated power as a function of angle is: $$\frac{d P}{d\Omega} = \frac{\bar q^2}{4\pi c} \frac{\left|\hat{\mathbf n} \times \left(\left(\hat{\mathbf n} - \boldsymbol{\beta}\right) \times \dot{\boldsymbol{\beta}}\right)\right|^2}{\left(1 - \hat{\mathbf n}\cdot\boldsymbol{\beta}\right)^5}$$ where $$\hat{\mathbf n}$$ is a unit vector pointing from the particle towards the observer, and $$d\Omega$$ is an infinitesimal solid angle.

In the case where velocity is parallel to acceleration (for example, linear motion), this simplifies to $$\frac{dP_{a \parallel v}}{d\Omega} = \frac{\bar q^2a^2}{4\pi c^3}\frac{\sin^2 \theta}{(1 - \beta \cos\theta)^5}$$ where $$\theta$$ is the angle between $$\boldsymbol{\beta}$$ and the direction of observation $$ \hat{\mathbf n}$$.

Simplified quantum-mechanical description
The full quantum-mechanical treatment of bremsstrahlung is very involved. The "vacuum case" of the interaction of one electron, one ion, and one photon, using the pure Coulomb potential, has an exact solution that was probably first published by A. Sommerfeld in 1931. This analytical solution involves complicated mathematics, and several numerical calculations have been published, such as by Karzas and Latter. Other approximate formulas have been presented, such as in recent work by Weinberg and Pradler and Semmelrock.

This section gives a quantum-mechanical analog of the prior section, but with some simplifications to illustrate the important physics. We give a non-relativistic treatment of the special case of an electron of mass $$m_\text{e}$$, charge $$-e$$, and initial speed $$v$$ decelerating in the Coulomb field of a gas of heavy ions of charge $$Ze$$ and number density $$n_i$$. The emitted radiation is a photon of frequency $$\nu=c/\lambda$$ and energy $$h\nu$$. We wish to find the emissivity $$j(v,\nu)$$ which is the power emitted per (solid angle in photon velocity space * photon frequency), summed over both transverse photon polarizations. We express it as an approximate classical result times the free−free emission Gaunt factor gff accounting for quantum and other corrections: $$j(v,\nu) = {8\pi\over 3\sqrt3} {Z^2\bar e^6 n_i \over c^3m_\text{e}^2v}g_{\rm ff}(v,\nu)$$ $$j(\nu,v) = 0$$ if $$h\nu > mv^2/2$$, that is, the electron does not have enough kinetic energy to emit the photon. A general, quantum-mechanical formula for $$g_{\rm ff}$$ exists but is very complicated, and usually is found by numerical calculations. We present some approximate results with the following additional assumptions:
 * Vacuum interaction: we neglect any effects of the background medium, such as plasma screening effects. This is reasonable for photon frequency much greater than the plasma frequency $$\nu_{\rm pe} \propto n_{\rm e}^{1/2}$$with $$n_\text{e}$$ the plasma electron density. Note that light waves are evanescent for $$\nu<\nu_{\rm pe}$$ and a significantly different approach would be needed.
 * Soft photons: $$h\nu\ll m_\text{e}v^2/2$$, that is, the photon energy is much less than the initial electron kinetic energy.

With these assumptions, two unitless parameters characterize the process: $$\eta_Z \equiv Z \bar e^2/\hbar v$$, which measures the strength of the electron-ion Coulomb interaction, and $$\eta_\nu \equiv h\nu/2m_\text{e}v^2$$, which measures the photon "softness" and we assume is always small (the choice of the factor 2 is for later convenience). In the limit $$\eta_Z\ll 1$$, the quantum-mechanical Born approximation gives: $$g_\text{ff,Born} = {\sqrt3 \over \pi}\ln{1\over\eta_\nu}$$

In the opposite limit $$\eta_Z\gg 1$$, the full quantum-mechanical result reduces to the purely classical result $$g_\text{ff,class} = {\sqrt3\over\pi}\left[\ln\left({1\over \eta_Z\eta_\nu}\right)- \gamma \right]$$ where $$\gamma\approx 0.577$$ is the Euler–Mascheroni constant. Note that $$1/\eta_Z\eta_\nu=m_\text{e}v^3/\pi Z\bar e^2\nu$$ which is a purely classical expression without the Planck constant $$h$$.

A semi-classical, heuristic way to understand the Gaunt factor is to write it as $$g_\text{ff} \approx \ln(b_\text{max}/b_\text{min})$$ where $$b_{\max}$$ and $$b_{\min}$$ are maximum and minimum "impact parameters" for the electron-ion collision, in the presence of the photon electric field. With our assumptions, $$b_{\rm max}=v/\nu$$: for larger impact parameters, the sinusoidal oscillation of the photon field provides "phase mixing" that strongly reduces the interaction. $$b_{\rm min}$$ is the larger of the quantum-mechanical de Broglie wavelength $$\approx h/m_\text{e} v$$ and the classical distance of closest approach $$\approx \bar e^2 / m_\text{e} v^2$$ where the electron-ion Coulomb potential energy is comparable to the electron's initial kinetic energy.

The above approximations generally apply as long as the argument of the logarithm is large, and break down when it is less than unity. Namely, these forms for the Gaunt factor become negative, which is unphysical. A rough approximation to the full calculations, with the appropriate Born and classical limits, is $$g_\text{ff} \approx \max\left[1, {\sqrt3\over\pi} \ln\left[{1\over \eta_\nu\max(1,e^\gamma\eta_Z)}\right] \right]$$

Thermal bremsstrahlung in a medium: emission and absorption
This section discusses bremsstrahlung emission and the inverse absorption process (called inverse bremsstrahlung) in a macroscopic medium. We start with the equation of radiative transfer, which applies to general processes and not just bremsstrahlung: $$\frac{1}{c} \partial_t I_\nu + \hat \mathbf n\cdot\nabla I_\nu = j_\nu-k_\nu I_\nu$$

$$I_\nu(t,\mathbf x)$$ is the radiation spectral intensity, or power per (area × solid angle in photon velocity space× photon frequency) summed over both polarizations. $$j_\nu$$ is the emissivity, analogous to $$j(v,\nu)$$defined above, and $$k_\nu$$ is the absorptivity. $$j_\nu$$ and $$k_\nu$$ are properties of the matter, not the radiation, and account for all the particles in the medium – not just a pair of one electron and one ion as in the prior section. If $$I_\nu$$ is uniform in space and time, then the left-hand side of the transfer equation is zero, and we find $$I_\nu={j_\nu \over k_\nu}$$

If the matter and radiation are also in thermal equilibrium at some temperature, then $$I_\nu$$ must be the blackbody spectrum: $$B_\nu(\nu, T_\text{e}) = \frac{2h\nu^3}{c^2}\frac{1}{e^{h\nu/k_\text{B}T_\text{e}} - 1}$$ Since $$j_\nu$$ and $$k_\nu$$ are independent of $$I_\nu$$, this means that $$j_\nu/k_\nu$$ must be the blackbody spectrum whenever the matter is in equilibrium at some temperature – regardless of the state of the radiation. This allows us to immediately know both $$j_\nu$$ and $$k_\nu$$ once one is known – for matter in equilibrium.

In plasma: approximate Classical Results
NOTE: this section currently gives formulas that apply in the Rayleigh–Jeans limit $$\hbar \omega \ll k_\text{B} T_\text{e}$$, and does not use a quantized (Planck) treatment of radiation. Thus a usual factor like $$\exp(-\hbar\omega/k_{\rm B}T_\text{e})$$ does not appear. The appearance of $$\hbar \omega / k_\text{B} T_\text{e}$$ in $$y$$ below is due to the quantum-mechanical treatment of collisions.

In a plasma, the free electrons continually collide with the ions, producing bremsstrahlung. A complete analysis requires accounting for both binary Coulomb collisions as well as collective (dielectric) behavior. A detailed treatment is given by Bekefi, while a simplified one is given by Ichimaru. In this section we follow Bekefi's dielectric treatment, with collisions included approximately via the cutoff wavenumber, $k_\text{max}$.

Consider a uniform plasma, with thermal electrons distributed according to the Maxwell–Boltzmann distribution with the temperature $$T_\text{e}$$. Following Bekefi, the power spectral density (power per angular frequency interval per volume, integrated over the whole $$4\pi$$ sr of solid angle, and in both polarizations) of the bremsstrahlung radiated, is calculated to be $$ {dP_\mathrm{Br} \over d\omega} = \frac{8\sqrt 2}{3\sqrt\pi} {\bar e^6 \over (m_\text{e} c^2)^{3/2}} \left[1-{\omega_{\rm p}^2 \over \omega^2}\right]^{1/2} {Z_i^2 n_i n_\text{e} \over (k_{\rm B} T_\text{e})^{1/2}} E_1(y), $$ where $$\omega_p \equiv (n_\text{e} e^2/\varepsilon_0m_\text{e})^{1/2}$$ is the electron plasma frequency, $$\omega$$ is the photon frequency, $$n_\text{e}, n_i$$ is the number density of electrons and ions, and other symbols are physical constants. The second bracketed factor is the index of refraction of a light wave in a plasma, and shows that emission is greatly suppressed for $$\omega < \omega_{\rm p}$$ (this is the cutoff condition for a light wave in a plasma; in this case the light wave is evanescent). This formula thus only applies for $$\omega>\omega_{\rm p}$$. This formula should be summed over ion species in a multi-species plasma.

The special function $$E_1$$ is defined in the exponential integral article, and the unitless quantity $$y$$ is $$y = \frac{1}{2} {\omega^2 m_\text{e} \over k_\text{max}^2 k_\text{B} T_\text{e}} $$

$$k_\text{max}$$ is a maximum or cutoff wavenumber, arising due to binary collisions, and can vary with ion species. Roughly, $$k_\text{max} = 1 / \lambda_\text{B}$$ when $$k_\text{B} T_\text{e} > Z_i^2 E_\text{h}$$ (typical in plasmas that are not too cold), where $$E_\text{h} \approx 27.2$$ eV is the Hartree energy, and $$\lambda_\text{B} = \hbar / (m_\text{e} k_\text{B} T_\text{e})^{1/2}$$ is the electron thermal de Broglie wavelength. Otherwise, $$k_\text{max} \propto 1/l_\text{C}$$ where $$l_\text{C}$$ is the classical Coulomb distance of closest approach.

For the usual case $$k_m = 1/\lambda_B$$, we find $$y = \frac{1}{2} \left[\frac{\hbar\omega}{k_\text{B} T_\text{e}}\right]^2. $$

The formula for $$dP_\mathrm{Br} / d\omega$$ is approximate, in that it neglects enhanced emission occurring for $$\omega$$ slightly above $\omega_\text{p}$.

In the limit $$y\ll 1$$, we can approximate $$E_1 $$ as $$E_1(y) \approx -\ln [y e^\gamma] + O(y) $$ where $$\gamma \approx 0.577$$ is the Euler–Mascheroni constant. The leading, logarithmic term is frequently used, and resembles the Coulomb logarithm that occurs in other collisional plasma calculations. For $$y > e^{-\gamma}$$ the log term is negative, and the approximation is clearly inadequate. Bekefi gives corrected expressions for the logarithmic term that match detailed binary-collision calculations.

The total emission power density, integrated over all frequencies, is $$\begin{align} P_\mathrm{Br} &= \int_{\omega_\text{p}}^\infty d\omega \frac{dP_\mathrm{Br}}{d\omega} = \frac{16}{3} \frac{\bar e^6}{m_\text{e}^2c^3} Z_i^2 n_i n_\text{e} k_\text{max} G(y_\text{p}) \\[1ex] G(y_p) &= \frac{1}{2\sqrt{\pi}} \int_{y_\text{p}}^\infty dy \, y^{-{1}/{2}} \left[1 - {y_\text{p} \over y}\right]^{1/2} E_1(y) \\[1ex] y_\text{p} &= y({\omega\!=\!\omega_\text{p}}) \end{align}$$
 * $$G(y_\text{p}=0) = 1$$ and decreases with $$y_\text{p}$$; it is always positive. For $$k_\text{max} = 1/\lambda_\text{B}$$, we find

$$P_\mathrm{Br} = {16 \over 3} {\bar e^6 \over (m_\text{e} c^2)^\frac{3}{2}\hbar} Z_i^2 n_i n_\text{e} (k_{\rm B} T_\text{e})^\frac{1}{2} G(y_{\rm p})$$

Note the appearance of $$\hbar$$ due to the quantum nature of $$\lambda_{\rm B}$$. In practical units, a commonly used version of this formula for $$G=1$$ is $$P_\mathrm{Br} [\mathrm{W/m^3}] = {Z_i^2 n_i n_\text{e} \over \left[7.69 \times 10^{18} \mathrm{m^{-3}}\right]^2} T_\text{e}[\mathrm{eV}]^\frac{1}{2}. $$

This formula is 1.59 times the one given above, with the difference due to details of binary collisions. Such ambiguity is often expressed by introducing Gaunt factor $$g_{\rm B}$$, e.g. in one finds $$\varepsilon_\text{ff} = 1.4\times 10^{-27} T^\frac{1}{2} n_\text{e} n_i Z^2 g_\text{B},\,$$ where everything is expressed in the CGS units.

Relativistic corrections
For very high temperatures there are relativistic corrections to this formula, that is, additional terms of the order of $k_\text{B} T_\text{e}/m_\text{e} c^2$.

Bremsstrahlung cooling
If the plasma is optically thin, the bremsstrahlung radiation leaves the plasma, carrying part of the internal plasma energy. This effect is known as the bremsstrahlung cooling. It is a type of radiative cooling. The energy carried away by bremsstrahlung is called bremsstrahlung losses and represents a type of radiative losses. One generally uses the term bremsstrahlung losses in the context when the plasma cooling is undesired, as e.g. in fusion plasmas.

Polarizational bremsstrahlung
Polarizational bremsstrahlung (sometimes referred to as "atomic bremsstrahlung") is the radiation emitted by the target's atomic electrons as the target atom is polarized by the Coulomb field of the incident charged particle. Polarizational bremsstrahlung contributions to the total bremsstrahlung spectrum have been observed in experiments involving relatively massive incident particles, resonance processes, and free atoms. However, there is still some debate as to whether or not there are significant polarizational bremsstrahlung contributions in experiments involving fast electrons incident on solid targets.

It is worth noting that the term "polarizational" is not meant to imply that the emitted bremsstrahlung is polarized. Also, the angular distribution of polarizational bremsstrahlung is theoretically quite different than ordinary bremsstrahlung.

X-ray tube

In an X-ray tube, electrons are accelerated in a vacuum by an electric field towards a piece of metal called the "target". X-rays are emitted as the electrons slow down (decelerate) in the metal. The output spectrum consists of a continuous spectrum of X-rays, with additional sharp peaks at certain energies. The continuous spectrum is due to bremsstrahlung, while the sharp peaks are characteristic X-rays associated with the atoms in the target. For this reason, bremsstrahlung in this context is also called continuous X-rays.

The shape of this continuum spectrum is approximately described by Kramers' law.

The formula for Kramers' law is usually given as the distribution of intensity (photon count) $$I$$ against the wavelength $$\lambda$$ of the emitted radiation: $$ I(\lambda) \, d\lambda = K \left( \frac{\lambda}{\lambda_{\min}} - 1 \right)\frac{d\lambda}{\lambda^2} $$

The constant $K$ is proportional to the atomic number of the target element, and $$\lambda_{\min}$$ is the minimum wavelength given by the Duane–Hunt law.

The spectrum has a sharp cutoff at $\lambda_{\min}$, which is due to the limited energy of the incoming electrons. For example, if an electron in the tube is accelerated through 60 kV, then it will acquire a kinetic energy of 60 keV, and when it strikes the target it can create X-rays with energy of at most 60 keV, by conservation of energy. (This upper limit corresponds to the electron coming to a stop by emitting just one X-ray photon. Usually the electron emits many photons, and each has an energy less than 60 keV.) A photon with energy of at most 60 keV has wavelength of at least $21 pm$, so the continuous X-ray spectrum has exactly that cutoff, as seen in the graph. More generally the formula for the low-wavelength cutoff, the Duane–Hunt law, is: $$\lambda_\min = \frac{h c}{e V} \approx \frac{1239.8}{V}\,\mathrm{pm/kV}$$ where $h$ is the Planck constant, $c$ is the speed of light, $V$ is the voltage that the electrons are accelerated through, $e$ is the elementary charge, and $pm$ is picometres.

Beta decay
Beta particle-emitting substances sometimes exhibit a weak radiation with continuous spectrum that is due to bremsstrahlung (see the "outer bremsstrahlung" below). In this context, bremsstrahlung is a type of "secondary radiation", in that it is produced as a result of stopping (or slowing) the primary radiation (beta particles). It is very similar to X-rays produced by bombarding metal targets with electrons in X-ray generators (as above) except that it is produced by high-speed electrons from beta radiation.

Inner and outer bremsstrahlung
The "inner" bremsstrahlung (also known as "internal bremsstrahlung") arises from the creation of the electron and its loss of energy (due to the strong electric field in the region of the nucleus undergoing decay) as it leaves the nucleus. Such radiation is a feature of beta decay in nuclei, but it is occasionally (less commonly) seen in the beta decay of free neutrons to protons, where it is created as the beta electron leaves the proton.

In electron and positron emission by beta decay the photon's energy comes from the electron-nucleon pair, with the spectrum of the bremsstrahlung decreasing continuously with increasing energy of the beta particle. In electron capture, the energy comes at the expense of the neutrino, and the spectrum is greatest at about one third of the normal neutrino energy, decreasing to zero electromagnetic energy at normal neutrino energy. Note that in the case of electron capture, bremsstrahlung is emitted even though no charged particle is emitted. Instead, the bremsstrahlung radiation may be thought of as being created as the captured electron is accelerated toward being absorbed. Such radiation may be at frequencies that are the same as soft gamma radiation, but it exhibits none of the sharp spectral lines of gamma decay, and thus is not technically gamma radiation.

The internal process is to be contrasted with the "outer" bremsstrahlung due to the impingement on the nucleus of electrons coming from the outside (i.e., emitted by another nucleus), as discussed above.

Radiation safety
In some cases, such as the decay of, the bremsstrahlung produced by shielding the beta radiation with the normally used dense materials (e.g. lead) is itself dangerous; in such cases, shielding must be accomplished with low density materials, such as Plexiglas (Lucite), plastic, wood, or water; as the atomic number is lower for these materials, the intensity of bremsstrahlung is significantly reduced, but a larger thickness of shielding is required to stop the electrons (beta radiation).

In astrophysics
The dominant luminous component in a cluster of galaxies is the 107 to 108 kelvin intracluster medium. The emission from the intracluster medium is characterized by thermal bremsstrahlung. This radiation is in the energy range of X-rays and can be easily observed with space-based telescopes such as Chandra X-ray Observatory, XMM-Newton, ROSAT, ASCA, EXOSAT, Suzaku, RHESSI and future missions like IXO and Astro-H.

Bremsstrahlung is also the dominant emission mechanism for H II regions at radio wavelengths.

In electric discharges
In electric discharges, for example as laboratory discharges between two electrodes or as lightning discharges between cloud and ground or within clouds, electrons produce Bremsstrahlung photons while scattering off air molecules. These photons become manifest in terrestrial gamma-ray flashes and are the source for beams of electrons, positrons, neutrons and protons. The appearance of Bremsstrahlung photons also influences the propagation and morphology of discharges in nitrogen–oxygen mixtures with low percentages of oxygen.

Quantum mechanical description
The complete quantum mechanical description was first performed by Bethe and Heitler. They assumed plane waves for electrons which scatter at the nucleus of an atom, and derived a cross section which relates the complete geometry of that process to the frequency of the emitted photon. The quadruply differential cross section, which shows a quantum mechanical symmetry to pair production, is
 * $$\begin{align}

d^4\sigma ={} &\frac{Z^2 \alpha_\text{fine}^3 \hbar^2}{(2\pi)^2}\frac{\left|\mathbf{p}_f\right|}{\left|\mathbf{p}_i\right|} \frac{d\omega}{\omega}\frac{d\Omega_i \, d\Omega_f \, d\Phi}{\left|\mathbf{q}\right|^4} \\ &{}\times \left[ \frac{\mathbf{p}_f^2\sin^2\Theta_f}{\left(E_f - c\left|\mathbf{p}_f\right| \cos\Theta_f\right)^2}\left(4E_i^2 - c^2\mathbf{q}^2\right) + \frac{\mathbf{p}_i^2\sin^2\Theta_i}{\left(E_i - c\left|\mathbf{p}_i\right| \cos\Theta_i\right)^2}\left(4E_f^2 - c^2\mathbf{q}^2\right) \right. \\               & {} \qquad+ 2\hbar^2\omega^2 \frac {\mathbf{p}_i^2 \sin^2\Theta_i + \mathbf{p}_f^2 \sin^2\Theta_f} {(E_f - c\left|\mathbf{p}_f\right| \cos\Theta_f)\left(E_i - c\left|\mathbf{p}_i\right| \cos\Theta_i\right)} \\ & {} \qquad- 2\left. \frac {\left|\mathbf{p}_i\right| \left|\mathbf{p}_f\right| \sin\Theta_i \sin\Theta_f \cos\Phi} {\left(E_f - c\left|\mathbf{p}_f\right| \cos\Theta_f\right)\left(E_i - c\left|\mathbf{p}_i\right|\cos\Theta_i\right)} \left(2E_i^2 + 2E_f^2 - c^2\mathbf{q}^2\right) \right], \end{align}$$ where $$Z$$ is the atomic number, $$\alpha_\text{fine}\approx 1/137$$ the fine-structure constant, $$\hbar$$ the reduced Planck constant and $$c$$ the speed of light. The kinetic energy $$E_{\text{kin},i/f}$$ of the electron in the initial and final state is connected to its total energy $$E_{i,f}$$ or its momenta $$\mathbf{p}_{i,f}$$ via $$ E_{i, f} = E_{\text{kin}, i/f} + m_\text{e} c^2 = \sqrt{m_\text{e}^2 c^4 + \mathbf{p}_{i, f}^2 c^2}, $$ where $$m_\text{e}$$ is the mass of an electron. Conservation of energy gives $$ E_f = E_i - \hbar\omega, $$ where $$ \hbar\omega $$ is the photon energy. The directions of the emitted photon and the scattered electron are given by $$\begin{align} \Theta_i &= \sphericalangle(\mathbf{p}_i, \mathbf{k}),\\ \Theta_f &= \sphericalangle(\mathbf{p}_f, \mathbf{k}),\\ \Phi &= \text{Angle between the planes } (\mathbf{p}_i, \mathbf{k}) \text{ and } (\mathbf{p}_f, \mathbf{k}), \end{align}$$ where $$\mathbf{k}$$ is the momentum of the photon.

The differentials are given as $$\begin{align} d\Omega_i &= \sin\Theta_i\ d\Theta_i,\\ d\Omega_f &= \sin\Theta_f\ d\Theta_f. \end{align}$$

The absolute value of the virtual photon between the nucleus and electron is
 * $$\begin{align}

-\mathbf{q}^2 ={} & -\left|\mathbf{p}_i\right|^2 - \left|\mathbf{p}_f\right|^2 - \left(\frac{\hbar}{c}\omega\right)^2 + 2\left|\mathbf{p}_i\right|\frac{\hbar}{c} \omega\cos\Theta_i - 2\left|\mathbf{p}_f\right|\frac{\hbar}{c} \omega\cos\Theta_f \\ & {} + 2\left|\mathbf{p}_i\right| \left|\mathbf{p}_f\right| \left(\cos\Theta_f\cos\Theta_i + \sin\Theta_f\sin\Theta_i\cos\Phi\right). \end{align}$$

The range of validity is given by the Born approximation $$ v \gg \frac{Zc}{137} $$ where this relation has to be fulfilled for the velocity $$ v $$ of the electron in the initial and final state.

For practical applications (e.g. in Monte Carlo codes) it can be interesting to focus on the relation between the frequency $$\omega$$ of the emitted photon and the angle between this photon and the incident electron. Köhn and Ebert integrated the quadruply differential cross section by Bethe and Heitler over $$\Phi$$ and $$\Theta_f$$ and obtained: $$ \frac{d^2\sigma (E_i, \omega, \Theta_i)}{d\omega \, d\Omega_i} = \sum\limits_{j=1}^6 I_j $$ with
 * $$\begin{align}

I_1 ={} &\frac{2\pi A}{\sqrt{\Delta_2^2 + 4p_i^2 p_f^2 \sin^2\Theta_i}} \ln\left(\frac              { \Delta_2^2 + 4p_i^2p_f^2\sin^2\Theta_i - \sqrt{\Delta_2^2 + 4p_i^2p_f^2\sin^2\Theta_i}\left(\Delta_1 + \Delta_2\right) + \Delta_1\Delta_2}               {-\Delta_2^2 - 4p_i^2p_f^2\sin^2\Theta_i - \sqrt{\Delta_2^2 + 4p_i^2p_f^2\sin^2\Theta_i}\left(\Delta_1 - \Delta_2\right) + \Delta_1\Delta_2}           \right) \\ & {} \times\left[ 1 +           \frac{c\Delta_2}{p_f\left(E_i - cp_i\cos\Theta_i\right)} - \frac{p_i^2 c^2 \sin^2\Theta_i}{\left(E_i - cp_i\cos\Theta_i\right)^2} - \frac{2\hbar^2\omega^2 p_f \Delta_2}{c\left(E_i - cp_i\cos\Theta_i\right)\left(\Delta_2^2 + 4p_i^2 p_f^2 \sin^2\Theta_i\right)} \right], \\ I_2 ={} &-\frac{2\pi Ac}{p_f\left(E_i - cp_i\cos\Theta_i\right)}\ln\left(\frac{E_f + p_fc}{E_f - p_fc}\right), \\ I_3 = {} & \frac{2\pi A}{\sqrt{\left(\Delta_2E_f + \Delta_1 p_f c\right)^4 + 4m^2 c^4 p_i^2 p_f^2 \sin^2\Theta_i}} \times \ln\left[\left(\left[E_f + p_fc\right]\right.\right. \\         & \left.\left[4p_i^2 p_f^2 \sin^2\Theta_i\left(E_f - p_f c\right) +              \left(\Delta_1 + \Delta_2\right)\left(\left[\Delta_2 E_f + \Delta_1 p_f c\right] - \sqrt{\left[\Delta_2 E_f + \Delta_1 p_f c\right]^2 + 4m^2 c^4 p_i^2 p_f^2 \sin^2\Theta_i}\right)\right]\right) \\ &\left[\left(E_f - p_f c\right)\left(4p_i^2 p_f^2 \sin^2\Theta_i\left[-E_f - p_f c\right]\right.\right. \\         & {} + \left.\left.\left(\Delta_1 - \Delta_2\right)\left(\left[\Delta_2 E_f + \Delta_1 p_f c\right] - \sqrt{\left(\Delta_2 E_f + \Delta_1 p_f c\right)^2 + 4m^2 c^4 p_i^2 p_f^2 \sin^2\Theta_i}\right]\right)\right]^{-1} \\         & {} \times \left[-\frac{              \left(\Delta_2^2 + 4p_i^2 p_f^2 \sin^2\Theta_i\right)\left(E_f^3 + E_f p_f^2 c^2\right) +              p_f c\left(2\left[\Delta_1^2 - 4p_i^2 p_f^2 \sin^2\Theta_i\right]E_f p_f c + \Delta_1 \Delta_2\left[3E_f^2 + p_f^2 c^2\right]\right)           }            {\left(\Delta_2E_f + \Delta_1 p_f c\right)^2 + 4m^2 c^4 p_i^2 p_f^2 \sin^2\Theta_i}        \right.\\          & {} -\frac{c\left(\Delta_2 E_f + \Delta_1 p_f c\right)}{p_f\left(E_i - cp_i \cos\Theta_i\right)} -              \frac{                  4E_i^2 p_f^2 \left(2\left[\Delta_2 E_f + \Delta_1 p_f c\right]^2 - 4m^2 c^4 p_i^2 p_f^2 \sin^2\Theta_i\right)\left(\Delta_1 E_f + \Delta_2 p_f c\right)               }                {\left(\left[\Delta_2 E_f + \Delta_1 p_f c\right]^2 + 4m^2 c^4 p_i^2 p_f^2 \sin^2\Theta_i\right)^2} \\          & {} + \left.\frac{              8p_i^2 p_f^2 m^2 c^4 \sin^2\Theta_i\left(E_i^2 + E_f^2\right) -              2\hbar^2\omega^2 p_i^2 \sin^2\Theta_i p_f c\left(\Delta_2 E_f + \Delta_1 p_f c\right) +              2\hbar^2 \omega^2 p_f m^2 c^3\left(\Delta_2 E_f + \Delta_1 p_f c\right)            }            {\left(E_i - cp_i\cos\Theta_i\right)\left(\left[\Delta_2 E_f + \Delta_1 p_f c\right]^2 + 4m^2 c^4 p_i^2 p_f^2 \sin^2\Theta_i\right)}\right], \\  I_4 ={} & {} -\frac              {4\pi A p_f c\left(\Delta_2 E_f + \Delta_1 p_f c\right)}              {\left(\Delta_2E_f + \Delta_1 p_f c\right)^2 + 4m^2 c^4 p_i^2 p_f^2 \sin^2\Theta_i} -            \frac {16\pi E_i^2 p_f^2 A\left(\Delta_2E_f + \Delta_1 p_f c\right)^2} {\left(\left[\Delta_2 E_f + \Delta_1 p_f c\right]^2 + 4m^2 c^4 p_i^2 p_f^2 \sin^2\Theta_i\right)^2}, \\ I_5 ={} & \frac {4\pi A}             { \left(-\Delta_2^2 + \Delta_1^2 - 4 p_i^2 p_f^2 \sin^2\Theta_i\right) \left(\left[\Delta_2 E_f + \Delta_1 p_f c\right]^2 + 4m^2 c^4 p_i^2 p_f^2 \sin^2\Theta_i\right) } \\         & {} \times\left[\frac{\hbar^2 \omega^2 p_f^2}{E_i - cp_i\cos\Theta_i}\right.\\ & {} \times\frac{ E_f\left(2\Delta_2^2\left[\Delta_2^2 - \Delta_1^2\right] + 8p_i^2 p_f^2 \sin^2\Theta_i\left[\Delta_2^2 + \Delta_1^2\right]\right) + p_f c\left(2\Delta_1\Delta_2\left[\Delta_2^2 - \Delta_1^2\right] + 16\Delta_1\Delta_2 p_i^2 p_f^2 \sin^2\Theta_i\right) }              {\Delta_2^2 + 4p_i^2 p_f^2 \sin^2\Theta_i} \\ & {} + \frac {2\hbar^2 \omega^2 p_i^2 \sin^2\Theta_i \left(2\Delta_1\Delta_2 p_f c + 2\Delta_2^2 E_f + 8p_i^2 p_f^2 \sin^2\Theta_i E_f\right)} {E_i - cp_i\cos\Theta_i} \\ & {} + \frac {2E_i^2 p_f^2 \left(                  2\left[\Delta_2^2 - \Delta_1^2\right]\left[\Delta_2 E_f + \Delta_1 p_f c\right]^2 +                   8p_i^2 p_f^2 \sin^2\Theta_i\left[\left(\Delta_1^2 + \Delta_2^2\right)\left(E_f^2 + p_f^2 c^2\right) + 4\Delta_1\Delta_2 E_f p_f c\right]                 \right) }              {\left(\Delta_2 E_f + \Delta_1 p_f c\right)^2 + 4m^2 c^4 p_i^2 p_f^2 \sin^2\Theta_i} \\ & {} + \left.\frac{8p_i^2 p_f^2 \sin^2\Theta_i\left(E_i^2 + E_f^2\right)\left(\Delta_2p_fc + \Delta_1 E_f\right)}{E_i - cp_i\cos\Theta_i}\right], \\ I_6 ={} & \frac{16\pi E_f^2 p_i^2 \sin^2\Theta_i A}{\left(E_i - cp_i\cos\Theta_i\right)^2 \left(-\Delta_2^2 + \Delta_1^2 - 4p_i^2 p_f^2 \sin^2\Theta_i\right)}, \end{align}$$ and
 * $$\begin{align}

A &= \frac{Z^2\alpha_\text{fine}^3}{(2\pi)^2} \frac{\left|\mathbf{p}_f\right|}{\left|\mathbf{p}_i\right|} \frac{\hbar^2}{\omega} \\ \Delta_1 &= -\mathbf{p}_i^2 - \mathbf{p}_f^2 - \left(\frac{\hbar}{c}\omega\right)^2 + 2\frac{\hbar}{c} \omega\left|\mathbf{p}_i\right|\cos\Theta_i, \\ \Delta_2 &= -2\frac{\hbar}{c}\omega\left|\mathbf{p}_f\right| + 2\left|\mathbf{p}_i\right|\left|\mathbf{p}_f\right|\cos\Theta_i. \end{align}$$

However, a much simpler expression for the same integral can be found in (Eq. 2BN) and in (Eq. 4.1).

An analysis of the doubly differential cross section above shows that electrons whose kinetic energy is larger than the rest energy (511 keV) emit photons in forward direction while electrons with a small energy emit photons isotropically.

Electron–electron bremsstrahlung
One mechanism, considered important for small atomic numbers $Z$, is the scattering of a free electron at the shell electrons of an atom or molecule. Since electron–electron bremsstrahlung is a function of $$Z$$ and the usual electron-nucleus bremsstrahlung is a function of $Z^2$, electron–electron bremsstrahlung is negligible for metals. For air, however, it plays an important role in the production of terrestrial gamma-ray flashes.

title: Bremsstrahlung


text:
Dicotyledon

The dicotyledons, also known as dicots (or, more rarely, dicotyls), are one of the two groups into which all the flowering plants (angiosperms) were formerly divided. The name refers to one of the typical characteristics of the group: namely, that the seed has two embryonic leaves or cotyledons. There are around 200,000 species within this group. The other group of flowering plants were called monocotyledons (or monocots), typically each having one cotyledon. Historically, these two groups formed the two divisions of the flowering plants.

Largely from the 1990s onwards, molecular phylogenetic research confirmed what had already been suspected: that dicotyledons are not a group made up of all the descendants of a common ancestor (i.e., they are not a monophyletic group). Rather, a number of lineages, such as the magnoliids and groups now collectively known as the basal angiosperms, diverged earlier than the monocots did; in other words, monocots evolved from within the dicots, as traditionally defined. The traditional dicots are thus a paraphyletic group.

The eudicots are the largest monophyletic group within the dicotyledons. They are distinguished from all other flowering plants by the structure of their pollen. Other dicotyledons and the monocotyledons have monosulcate pollen (or derived forms): grains with a single sulcus. Contrastingly, eudicots have tricolpate pollen (or derived forms): grains with three or more pores set in furrows called colpi.

Comparison with monocotyledons
Aside from cotyledon number, other broad differences have been noted between monocots and dicots, although these have proven to be differences primarily between monocots and eudicots. Many early-diverging dicot groups have monocot characteristics such as scattered vascular bundles, trimerous flowers, and non-tricolpate pollen. In addition, some monocots have dicot characteristics such as reticulated leaf veins.

Phylogeny
The consensus phylogenetic tree used in the APG IV system shows that the group traditionally treated as the dicots is paraphyletic to the monocots:

Historical
Traditionally, the dicots have been called the Dicotyledones (or Dicotyledoneae), at any rank. If treated as a class, as they are within the Cronquist system, they could be called the Magnoliopsida after the type genus Magnolia. In some schemes, the eudicots were either treated as a separate class, the Rosopsida (type genus Rosa), or as several separate classes. The remaining dicots (palaeodicots or basal angiosperms) may be kept in a single paraphyletic class, called Magnoliopsida, or further divided. Some botanists prefer to retain the dicotyledons as a valid class, arguing its practicality and that it makes evolutionary sense.

APG vs. Cronquist
The following lists show the orders in the Angiosperm Phylogeny Group APG IV system traditionally called dicots, together with the older Cronquist system.

Dahlgren and Thorne systems
Under the Dahlgren and Thorne systems, the subclass name Magnoliidae was used for the dicotyledons. This is also the case in some of the systems derived from the Cronquist system. These two systems are contrasted in the table below in terms of how each categorises by superorder; note that the sequence within each system has been altered in order to pair corresponding taxa

The Thorne system (1992) as depicted by Reveal is:

There exist variances between the superorders circumscribed from each system. Namely, although the systems share common names for many of the listed superorders, the specific list orders classified within each varies. For example, Thorne's Theanae corresponds to five distinct superorders under Dahlgren's system, only one of which is called Theanae.

title: Dicotyledon