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Wednesday, May 17, 2023

05-17-2023-0125 - mt Xinu, Inc. ; Apple_Public_Source_License (<=1980s est.)

From Wikipedia, the free encyclopedia
For the unrelated operating system with a similar name, see Xinu.
mt Xinu, Inc.
FoundedJuly 28, 1983; 39 years ago[1]
DefunctJune 26, 1995[1]
Fatedissolved
Headquarters
Berkeley, California
,
United States


mt Xinu (from the letters in "Unix™", reversed) was a software company founded in 1983 that produced two operating systems. Its slogan "We know Unix™ backwards and forwards" was an allusion to the company's name and abilities.[2]

mt Xinu offered several products:

  • mt Xinu was a commercially licensed version of the BSD Unix operating system for the DEC VAX. The initial version was based on 4.1cBSD; later versions were based on 4.2 and 4.3BSD.
  • more/BSD was mt Xinu's version of 4.3BSD-Tahoe for VAX and HP 9000, incorporating code from the University of Utah's HPBSD. It included NFS.
  • Mach386 was a hybrid of Mach 2.5/2.6 and 4.3BSD-Tahoe/Reno for 386 and 486-based IBM PC compatibles.

Apart from operating systems, mt Xinu also produced Apple-Unix interoperability software, including an AppleShare server for Unix.[3]

The company's principals were University of California, Berkeley computer science students and graduates, notably Bob Kridle, Alan Tobey, Ed Gould, and Vance Vaughan. Debbie Scherrer was a later contributor.

mt Xinu is also famous for its light-hearted Unix-themed calendars, including:

  • Command of the Month (1987–1988)
  • Lessons in Art (1989)
  • Platform of the Year (1990)

In 1991, a division of mt Xinu broke off to become Xinet.

Notes


  • California Business Search results for Mt Xinu (Entity Number C1148179).

  • Salus 1994

    1. "Mt Xinu ships Appleshare for HP workstations. InfoWorld, 10 September 1990, p. 51.

    References


    https://en.wikipedia.org/wiki/Mt_Xinu


    The Apple Public Source License (APSL) is the open-source and free software license under which Apple's Darwin operating system was released in 2000. A free and open-source software license was voluntarily adopted to further involve the community from which much of Darwin originated.

    The first version of the Apple Public Source License was approved by the Open Source Initiative (OSI).[5] Version 2.0, released July 29, 2003, is also approved as a free software license by the Free Software Foundation (FSF) which finds it acceptable for developers to work on projects that are already covered by this license. However, the FSF recommends that developers should not release new projects under this license, because the partial copyleft is not compatible with the GNU General Public License and allows linking with files released entirely as proprietary software.[4] The license does require that if any derivatives of the original source are released externally, their source should be made available; the Free Software Foundation compares this requirement to a similar one in its own GNU Affero General Public License.[4]

    Many software releases from Apple have now been relicensed under the more liberal Apache License, such as the Bonjour Zeroconf stack. However, most OS component source code remains under APSL.

    See also

    References


  • "Apple Public Source License (APSL)". The Big DFSG-compatible Licenses. Debian Project. Retrieved January 27, 2017.

  • "Apple Public Source License (APSL), version 2.x". Various Licenses and Comments about Them. Free Software Foundation. Archived from the original on July 16, 2009. Retrieved July 6, 2009.

  • "Various Licenses and Comments about Them - GNU Project - Free Software Foundation". Gnu.org. September 3, 1999. Retrieved May 13, 2022.

  • FSF website

    1. Raymond, Eric. "OSI clarifies the status of the APSL". Linux Weekly News. Retrieved February 14, 2013.

    External links


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    Category:Threshold temperatures Category Talk Read Edit View history Tools Help From Wikipedia, the free encyclopedia Wikimedia Commons has media related to Threshold temperatures. Category for critical temperatures of physical materials, at points of phase change. Pages in category "Threshold temperatures" The following 28 pages are in this category, out of 28 total. This list may not reflect recent changes. A Adiabatic flame temperature Autoignition temperature B Boiling point C Critical point (thermodynamics) Critical temperature D Dew point Doppler cooling limit Ductile-brittle transition temperature E Eutectic Eutectoid F Flash point Freezing point G Glass transition H Hagedorn temperature Heat deflection temperature Hydrocarbon dew point L Lambda point Liquidus M Melting point Minimum design metal temperature O Operating temperature Orders of magnitude (temperature) P Pour point R Relative thermal index S Slip melting point Solidus (chemistry) T Transition temperature Triple point Categories: Phase transitionsState functionsTemperature Hidden category: Commons category link from Wikidata https://en.wikipedia.org/wiki/Category:Threshold_temperatures The lambda point is the temperature at which normal fluid helium (helium I) makes the transition to superfluid helium II (approximately 2.17 K at 1 atmosphere). The lowest pressure at which He-I and He-II can coexist is the vapor−He-I−He-II triple point at 2.1768 K (−270.9732 °C) and 5.0418 kPa (0.049759 atm), which is the "saturated vapor pressure" at that temperature (pure helium gas in thermal equilibrium over the liquid surface, in a hermetic container).[1] The highest pressure at which He-I and He-II can coexist is the bcc−He-I−He-II triple point with a helium solid at 1.762 K (−271.388 °C), 29.725 atm (3,011.9 kPa).[2] The point's name derives from the graph (pictured) that results from plotting the specific heat capacity as a function of temperature (for a given pressure in the above range, in the example shown, at 1 atmosphere), which resembles the Greek letter lambda λ \lambda . The specific heat capacity has a sharp peak as the temperature approaches the lambda point. The tip of the peak is so sharp that a critical exponent characterizing the divergence of the heat capacity can be measured precisely only in zero gravity, to provide a uniform density over a substantial volume of fluid. Hence the heat capacity was measured within 2 nK below the transition in an experiment included in a Space Shuttle payload in 1992.[3] Unsolved problem in physics: Explain the discrepancy between the experimental and theoretical determinations of the heat capacity critical exponent α for the superfluid transition in helium-4.[4] (more unsolved problems in physics) Although the heat capacity has a peak, it does not tend towards infinity (contrary to what the graph may suggest), but has finite limiting values when approaching the transition from above and below.[3] The behavior of the heat capacity near the peak is described by the formula C ≈ A ± t − α + B ± {\displaystyle C\approx A_{\pm }t^{-\alpha }+B_{\pm }} where t = | 1 − T / T c | {\displaystyle t=|1-T/T_{c}|} is the reduced temperature, T c T_{c} is the Lambda point temperature, A ± , B ± {\displaystyle A_{\pm },B_{\pm }} are constants (different above and below the transition temperature), and α is the critical exponent: α = − 0.0127 ( 3 ) {\displaystyle \alpha =-0.0127(3)}.[3][5] Since this exponent is negative for the superfluid transition, specific heat remains finite.[6] The quoted experimental value of α is in a significant disagreement[7][4] with the most precise theoretical determinations[8][9][10] coming from high temperature expansion techniques, Monte Carlo methods and the conformal bootstrap. See also Lambda point refrigerator References Donnelly, Russell J.; Barenghi, Carlo F. (1998). "The Observed Properties of Liquid Helium at the Saturated Vapor Pressure". Journal of Physical and Chemical Reference Data. 27 (6): 1217–1274. Bibcode:1998JPCRD..27.1217D. doi:10.1063/1.556028. Hoffer, J. K.; Gardner, W. R.; Waterfield, C. G.; Phillips, N. E. (April 1976). "Thermodynamic properties of 4He. II. The bcc phase and the P-T and VT phase diagrams below 2 K". Journal of Low Temperature Physics. 23 (1): 63–102. Bibcode:1976JLTP...23...63H. doi:10.1007/BF00117245. S2CID 120473493. Lipa, J.A.; Swanson, D. R.; Nissen, J. A.; Chui, T. C. P.; Israelsson, U. E. (1996). "Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point". Physical Review Letters. 76 (6): 944–7. Bibcode:1996PhRvL..76..944L. doi:10.1103/PhysRevLett.76.944. hdl:2060/19950007794. PMID 10061591. S2CID 29876364. Rychkov, Slava (2020-01-31). "Conformal bootstrap and the λ-point specific heat experimental anomaly". Journal Club for Condensed Matter Physics. doi:10.36471/JCCM_January_2020_02. Lipa, J. A.; Nissen, J. A.; Stricker, D. A.; Swanson, D. R.; Chui, T. C. P. (2003-11-14). "Specific heat of liquid helium in zero gravity very near the lambda point". Physical Review B. 68 (17): 174518. arXiv:cond-mat/0310163. Bibcode:2003PhRvB..68q4518L. doi:10.1103/PhysRevB.68.174518. S2CID 55646571. For other phase transitions α \alpha may be negative (e.g. α ≈ + 0.1 {\displaystyle \alpha \approx +0.1} for the liquid-vapor critical point which has Ising critical exponents). For those phase transitions specific heat does tend to infinity. Vicari, Ettore (2008-03-21). "Critical phenomena and renormalization-group flow of multi-parameter Phi4 theories". Proceedings of the XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007). Regensburg, Germany: Sissa Medialab. 42: 023. doi:10.22323/1.042.0023. Campostrini, Massimo; Hasenbusch, Martin; Pelissetto, Andrea; Vicari, Ettore (2006-10-06). "Theoretical estimates of the critical exponents of the superfluid transition in $^{4}\mathrm{He}$ by lattice methods". Physical Review B. 74 (14): 144506. arXiv:cond-mat/0605083. doi:10.1103/PhysRevB.74.144506. S2CID 118924734. Hasenbusch, Martin (2019-12-26). "Monte Carlo study of an improved clock model in three dimensions". Physical Review B. 100 (22): 224517. arXiv:1910.05916. Bibcode:2019PhRvB.100v4517H. doi:10.1103/PhysRevB.100.224517. ISSN 2469-9950. S2CID 204509042. Chester, Shai M.; Landry, Walter; Liu, Junyu; Poland, David; Simmons-Duffin, David; Su, Ning; Vichi, Alessandro (2020). "Carving out OPE space and precise O(2) model critical exponents". Journal of High Energy Physics. 2020 (6): 142. arXiv:1912.03324. Bibcode:2020JHEP...06..142C. doi:10.1007/JHEP06(2020)142. S2CID 208910721. External links What is superfluidity? vte States of matter (list) State Solid Liquid Gas / Vapor Plasma Phase change - en.svg Low energy Bose–Einstein condensate Fermionic condensate Degenerate matter Quantum Hall Rydberg matter Rydberg polaron Strange matter Superfluid Supersolid Photonic molecule High energy QCD matter Lattice QCD Quark–gluon plasma Color-glass condensate Supercritical fluid Other states Colloid Glass Crystal Liquid crystal Time crystal Quantum spin liquid Exotic matter Programmable matter Dark matter Antimatter Magnetically ordered Antiferromagnet Ferrimagnet Ferromagnet String-net liquid Superglass Transitions Boiling Boiling point Condensation Critical line Critical point Crystallization Deposition Evaporation Flash evaporation Freezing Chemical ionization Ionization Lambda point Melting Melting point Recombination Regelation Saturated fluid Sublimation Supercooling Triple point Vaporization Vitrification Quantities Enthalpy of fusion Enthalpy of sublimation Enthalpy of vaporization Latent heat Latent internal energy Trouton's rule Volatility Concepts Baryonic matter Binodal Compressed fluid Cooling curve Equation of state Leidenfrost effect Macroscopic quantum phenomena Mpemba effect Order and disorder (physics) Spinodal Superconductivity Superheated vapor Superheating Thermo-dielectric effect Categories: Threshold temperaturesSuperfluidity https://en.wikipedia.org/wiki/Lambda_point From Wikipedia, the free encyclopedia Beyond the Standard Model CMS Higgs-event.jpg Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons Standard Model Evidence Theories Supersymmetry Quantum gravity Experiments vte In condensed matter physics, a string-net is an extended object whose collective behavior has been proposed as a physical mechanism for topological order by Michael A. Levin and Xiao-Gang Wen. A particular string-net model may involve only closed loops; or networks of oriented, labeled strings obeying branching rules given by some gauge group; or still more general networks.[1] Overview The string-net model is claimed to show the derivation of photons, electrons, and U(1) gauge charge, small (relative to the Planck mass) but nonzero masses, and suggestions that the leptons, quarks, and gluons can be modeled in the same way. In other words, string-net condensation provides a unified origin for photons and electrons (or gauge bosons and fermions). It can be viewed as an origin of light and electron (or gauge interactions and Fermi statistics). However, their model does not account for the chiral coupling between the fermions and the SU(2) gauge bosons in the standard model. For strings labeled by the positive integers, string-nets are the spin networks studied in loop quantum gravity. This has led to the proposal by Levin and Wen,[2] and Smolin, Markopoulou and Konopka[3] that loop quantum gravity's spin networks can give rise to the standard model of particle physics through this mechanism, along with fermi statistics and gauge interactions. To date, a rigorous derivation from LQG's spin networks to Levin and Wen's spin lattice has yet to be done, but the project to do so is called quantum graphity, and in a more recent paper, Tomasz Konopka, Fotini Markopoulou, Simone Severini argued that there are some similarities to spin networks (but not necessarily an exact equivalence) that gives rise to U(1) gauge charge and electrons in the string net mechanism.[4] Herbertsmithite may be an example of string-net matter.[5][6] Examples Z2 spin liquid Z2 spin liquid obtained using slave-particle approach may be the first theoretical example of string-net liquid.[7][8] The toric code The toric code is a two-dimensional spin-lattice that acts as a quantum error-correcting code. It is defined on a two-dimensional lattice with toric boundary conditions with a spin-1/2 on each link. It can be shown that the ground-state of the standard toric code Hamiltonian is an equal-weight superposition of closed-string states.[9] Such a ground-state is an example of a string-net condensate[10] which has the same topological order as the Z2 spin liquid above. References Levin, Michael A. & Xiao-Gang Wen (12 January 2005). "String-net condensation: A physical mechanism for topological phases". Physical Review B. 71 (45110): 21. arXiv:cond-mat/0404617. Bibcode:2005PhRvB..71d5110L. doi:10.1103/PhysRevB.71.045110. S2CID 51962817. Levin, Michael; Wen, Xiao-Gang (2005). "Photons and electrons as emergent phenomena". Rev. Mod. Phys. 77: 871–879 [878]. arXiv:cond-mat/0407140. Bibcode:2005RvMP...77..871L. doi:10.1103/RevModPhys.77.871. S2CID 117563047. "loop quantum gravity appears to be a string net condensation ..." Konopka, Tomasz; Markopoulou, Fotini; Smolin, Lee (2006). "Quantum Graphity". arXiv:hep-th/0611197. "We argue (but do not prove) that under certain conditions the spins in the system can arrange themselves in regular, lattice-like patterns at low temperatures." Konopka, Tomasz; Markopoulou, Fotini; Severini, Simone (May 2008). "Quantum graphity: A model of emergent locality". Phys. Rev. D. 77 (10): 19. arXiv:0801.0861. Bibcode:2008PhRvD..77j4029K. doi:10.1103/PhysRevD.77.104029. S2CID 6959359. "The characterization of the string-condensed ground state is difficult but its excitations are expected to be that of a U(1) gauge theory, ... The two main differences between this model and the original string-net condensation model proposed by Levin and Wen are that in the present case the background lattice is dynamical and has hexagonal rather than square plaquettes." Bowles, Claire. "Have researchers found a new state of matter?". Eureka Alert. Retrieved 29 January 2012. Merali, Zeeya (2007-03-17). "The universe is a string-net liquid". New Scientist. 193 (2595): 8–9. doi:10.1016/s0262-4079(07)60640-x. Retrieved 29 January 2012. Read, N.; Sachdev, Subir (1 March 1991). "Large-Nexpansion for frustrated quantum antiferromagnets". Physical Review Letters. American Physical Society (APS). 66 (13): 1773–1776. Bibcode:1991PhRvL..66.1773R. doi:10.1103/physrevlett.66.1773. ISSN 0031-9007. PMID 10043303. Xiao-Gang Wen, Mean Field Theory of Spin Liquid States with Finite Energy Gaps and Topological Orders, Phys. Rev. B44, 2664 (1991). Kitaev, Alexei, Y.; Chris Laumann (2009). "Topological phases and quantum computation". arXiv:0904.2771 [cond-mat.mes-hall]. Morimae, Tomoyuki (2012). "Quantum computational tensor network on string-net condensate". Physical Review A. 85 (6): 062328. arXiv:1012.1000. Bibcode:2012PhRvA..85f2328M. doi:10.1103/PhysRevA.85.062328. S2CID 118522495. vte States of matter (list) Categories: Quantum phasesCondensed matter physicsChemical engineeringPhases of matter https://en.wikipedia.org/wiki/String-net_liquid States of matter (list) State Solid Liquid Gas / Vapor Plasma Phase change - en.svg Low energy Bose–Einstein condensate Fermionic condensate Degenerate matter Quantum Hall Rydberg matter Rydberg polaron Strange matter Superfluid Supersolid Photonic molecule High energy QCD matter Lattice QCD Quark–gluon plasma Color-glass condensate Supercritical fluid Other states Colloid Glass Crystal Liquid crystal Time crystal Quantum spin liquid Exotic matter Programmable matter Dark matter Antimatter Magnetically ordered Antiferromagnet Ferrimagnet Ferromagnet String-net liquid Superglass Transitions Boiling Boiling point Condensation Critical line Critical point Crystallization Deposition Evaporation Flash evaporation Freezing Chemical ionization Ionization Lambda point Melting Melting point Recombination Regelation Saturated fluid Sublimation Supercooling Triple point Vaporization Vitrification Quantities Enthalpy of fusion Enthalpy of sublimation Enthalpy of vaporization Latent heat Latent internal energy Trouton's rule Volatility Concepts Baryonic matter Binodal Compressed fluid Cooling curve Equation of state Leidenfrost effect Macroscopic quantum phenomena Mpemba effect Order and disorder (physics) Spinodal Superconductivity Superheated vapor Superheating Thermo-dielectric effect Categories: Threshold temperaturesSuperfluidity https://en.wikipedia.org/wiki/Lambda_point The glass–liquid transition, or glass transition, is the gradual and reversible transition in amorphous materials (or in amorphous regions within semicrystalline materials) from a hard and relatively brittle "glassy" state into a viscous or rubbery state as the temperature is increased.[1][2] An amorphous solid that exhibits a glass transition is called a glass. The reverse transition, achieved by supercooling a viscous liquid into the glass state, is called vitrification. The glass-transition temperature Tg of a material characterizes the range of temperatures over which this glass transition occurs (as an experimental definition, typically marked as 100 s of relaxation time). It is always lower than the melting temperature, Tm, of the crystalline state of the material, if one exists. Hard plastics like polystyrene and poly(methyl methacrylate) are used well below their glass transition temperatures, i.e., when they are in their glassy state. Their Tg values are both at around 100 °C (212 °F). Rubber elastomers like polyisoprene and polyisobutylene are used above their Tg, that is, in the rubbery state, where they are soft and flexible; crosslinking prevents free flow of their molecules, thus endowing rubber with a set shape at room temperature (as opposed to a viscous liquid).[3] Despite the change in the physical properties of a material through its glass transition, the transition is not considered a phase transition; rather it is a phenomenon extending over a range of temperature and defined by one of several conventions.[2][4][5] Such conventions include a constant cooling rate (20 kelvins per minute (36 °F/min))[1] and a viscosity threshold of 1012 Pa·s, among others. Upon cooling or heating through this glass-transition range, the material also exhibits a smooth step in the thermal-expansion coefficient and in the specific heat, with the location of these effects again being dependent on the history of the material.[6] The question of whether some phase transition underlies the glass transition is a matter of ongoing research.[4][5][7][when?] IUPAC definition Glass transition (in polymer science): process in which a polymer melt changes on cooling to a polymer glass or a polymer glass changes on heating to a polymer melt.[8] Phenomena occurring at the glass transition of polymers are still subject to ongoing scientific investigation and debate. The glass transition presents features of a second-order transition since thermal studies often indicate that the molar Gibbs energies, molar enthalpies, and the molar volumes of the two phases, i.e., the melt and the glass, are equal, while the heat capacity and the expansivity are discontinuous. However, the glass transition is generally not regarded as a thermodynamic transition in view of the inherent difficulty in reaching equilibrium in a polymer glass or in a polymer melt at temperatures close to the glass-transition temperature. In the case of polymers, conformational changes of segments, typically consisting of 10–20 main-chain atoms, become infinitely slow below the glass transition temperature. In a partially crystalline polymer the glass transition occurs only in the amorphous parts of the material. The definition is different from that in ref.[9] The commonly used term “glass-rubber transition” for glass transition is not recommended.[8] Introduction The glass transition of a liquid to a solid-like state may occur with either cooling or compression.[10] The transition comprises a smooth increase in the viscosity of a material by as much as 17 orders of magnitude within a temperature range of 500 K without any pronounced change in material structure.[2][11] The consequence of this dramatic increase is a glass exhibiting solid-like mechanical properties on the timescale of practical observation.[clarification needed] This transition is in contrast to the freezing or crystallization transition, which is a first-order phase transition in the Ehrenfest classification and involves discontinuities in thermodynamic and dynamic properties such as volume, energy, and viscosity. In many materials that normally undergo a freezing transition, rapid cooling will avoid this phase transition and instead result in a glass transition at some lower temperature. Other materials, such as many polymers, lack a well defined crystalline state and easily form glasses, even upon very slow cooling or compression. The tendency for a material to form a glass while quenched is called glass forming ability. This ability depends on the composition of the material and can be predicted by the rigidity theory.[12] Below the transition temperature range, the glassy structure does not relax in accordance with the cooling rate used. The expansion coefficient for the glassy state is roughly equivalent to that of the crystalline solid. If slower cooling rates are used, the increased time for structural relaxation (or intermolecular rearrangement) to occur may result in a higher density glass product. Similarly, by annealing (and thus allowing for slow structural relaxation) the glass structure in time approaches an equilibrium density corresponding to the supercooled liquid at this same temperature. Tg is located at the intersection between the cooling curve (volume versus temperature) for the glassy state and the supercooled liquid.[2][13][14][15][16][17] The configuration of the glass in this temperature range changes slowly with time towards the equilibrium structure.[18] The principle of the minimization of the Gibbs free energy provides the thermodynamic driving force necessary for the eventual change. At somewhat higher temperatures than Tg, the structure corresponding to equilibrium at any temperature is achieved quite rapidly. In contrast, at considerably lower temperatures, the configuration of the glass remains sensibly stable over increasingly extended periods of time. Thus, the liquid-glass transition is not a transition between states of thermodynamic equilibrium. It is widely believed that the true equilibrium state is always crystalline. Glass is believed to exist in a kinetically locked state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon. Time and temperature are interchangeable quantities (to some extent) when dealing with glasses, a fact often expressed in the time–temperature superposition principle. On cooling a liquid, internal degrees of freedom successively fall out of equilibrium. However, there is a longstanding debate whether there is an underlying second-order phase transition in the hypothetical limit of infinitely long relaxation times.[clarification needed][6][19][20][21] In a more recent model of glass transition, the glass transition temperature corresponds to the temperature at which the largest openings between the vibrating elements in the liquid matrix become smaller than the smallest cross-sections of the elements or parts of them when the temperature is decreasing. As a result of the fluctuating input of thermal energy into the liquid matrix, the harmonics of the oscillations are constantly disturbed and temporary cavities ("free volume") are created between the elements, the number and size of which depend on the temperature. The glass transition temperature Tg0 defined in this way is a fixed material constant of the disordered (non-crystalline) state that is dependent only on the pressure. As a result of the increasing inertia of the molecular matrix when approaching Tg0, the setting of the thermal equilibrium is successively delayed, so that the usual measuring methods for determining the glass transition temperature in principle deliver Tg values that are too high. In principle, the slower the temperature change rate is set during the measurement, the closer the measured Tg value Tg0 approaches.[22] Techniques such as dynamic mechanical analysis can be used to measure the glass transition temperature.[23] Transition temperature Tg This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources in this section. Unsourced material may be challenged and removed. (July 2009) (Learn how and when to remove this template message) Determination of Tg by dilatometry. Measurement of Tg (the temperature at the point A) by differential scanning calorimetry Refer to the figure on the bottom right plotting the heat capacity as a function of temperature. In this context, Tg is the temperature corresponding to point A on the curve.[24] Different operational definitions of the glass transition temperature Tg are in use, and several of them are endorsed as accepted scientific standards. Nevertheless, all definitions are arbitrary, and all yield different numeric results: at best, values of Tg for a given substance agree within a few kelvins. One definition refers to the viscosity, fixing Tg at a value of 1013 poise (or 1012 Pa·s). As evidenced experimentally, this value is close to the annealing point of many glasses.[25] In contrast to viscosity, the thermal expansion, heat capacity, shear modulus, and many other properties of inorganic glasses show a relatively sudden change at the glass transition temperature. Any such step or kink can be used to define Tg. To make this definition reproducible, the cooling or heating rate must be specified. The most frequently used definition of Tg uses the energy release on heating in differential scanning calorimetry (DSC, see figure). Typically, the sample is first cooled with 10 K/min and then heated with that same speed. Yet another definition of Tg uses the kink in dilatometry (a.k.a. thermal expansion): refer to the figure on the top right. Here, heating rates of 3–5 K/min (5.4–9.0 °F/min) are common. The linear sections below and above Tg are colored green. Tg is the temperature at the intersection of the red regression lines.[24] Summarized below are Tg values characteristic of certain classes of materials. Polymers Material Tg (°C) Tg (°F) Commercial name Tire rubber −70 −94[26] Polyvinylidene fluoride (PVDF) −35 −31[27] Polypropylene (PP atactic) −20 −4[28] Polyvinyl fluoride (PVF) −20 −4[27] Polypropylene (PP isotactic) 0 32[28] Poly-3-hydroxybutyrate (PHB) 15 59[28] Poly(vinyl acetate) (PVAc) 30 86[28] Polychlorotrifluoroethylene (PCTFE) 45 113[27] Polyamide (PA) 47–60 117–140 Nylon-6,x Polylactic acid (PLA) 60–65 140–149 Polyethylene terephthalate (PET) 70 158[28] Poly(vinyl chloride) (PVC) 80 176[28] Poly(vinyl alcohol) (PVA) 85 185[28] Polystyrene (PS) 95 203[28] Poly(methyl methacrylate) (PMMA atactic) 105 221[28] Plexiglas, Perspex Acrylonitrile butadiene styrene (ABS) 105 221[29] Polytetrafluoroethylene (PTFE) 115 239[30] Teflon Poly(carbonate) (PC) 145 293[28] Lexan Polysulfone 185 365 Polynorbornene 215 419[28] Dry nylon-6 has a glass transition temperature of 47 °C (117 °F).[31] Nylon-6,6 in the dry state has a glass transition temperature of about 70 °C (158 °F).[32][33] Whereas polyethene has a glass transition range of −130 to −80 °C (−202 to −112 °F)[34] The above are only mean values, as the glass transition temperature depends on the cooling rate and molecular weight distribution and could be influenced by additives. For a semi-crystalline material, such as polyethene that is 60–80% crystalline at room temperature, the quoted glass transition refers to what happens to the amorphous part of the material upon cooling. Silicates and other covalent network glasses Material Tg (°C) Tg (°F) Chalcogenide GeSbTe 150 302[35] Chalcogenide AsGeSeTe 245 473 ZBLAN fluoride glass 235 455 Tellurium dioxide 280 536 Fluoroaluminate 400 752 Soda-lime glass 520–600 968–1,112 Fused quartz (approximate) 1,200 2,200[36] Kauzmann's paradox Entropy difference between crystal and undercooled melt As a liquid is supercooled, the difference in entropy between the liquid and solid phase decreases. By extrapolating the heat capacity of the supercooled liquid below its glass transition temperature, it is possible to calculate the temperature at which the difference in entropies becomes zero. This temperature has been named the Kauzmann temperature.[2] If a liquid could be supercooled below its Kauzmann temperature, and it did indeed display a lower entropy than the crystal phase, the consequences would be paradoxical. This Kauzmann paradox has been the subject of much debate and many publications since it was first put forward by Walter Kauzmann in 1948.[37][38] One resolution of the Kauzmann paradox is to say that there must be a phase transition before the entropy of the liquid decreases. In this scenario, the transition temperature is known as the calorimetric ideal glass transition temperature T0c. In this view, the glass transition is not merely a kinetic effect, i.e. merely the result of fast cooling of a melt, but there is an underlying thermodynamic basis for glass formation. The glass transition temperature: T g → T 0 c as d T d t → 0. T_{g}\to T_{{0c}}{\text{ as }}{\frac {dT}{dt}}\to 0. The Gibbs–DiMarzio model from 1958[39] specifically predicts that a supercooled liquid's configurational entropy disappears in the limit T → T K + {\displaystyle T\to T_{K}^{+}}, where the liquid's existence regime ends, its microstructure becomes identical to the crystal's, and their property curves intersect in a true second-order phase transition. This has never been experimentally verified due to the difficulty of realizing a slow enough cooling rate while avoiding accidental crystallization. The Adam–Gibbs model from 1965[40] suggested a resolution of the Kauzmann paradox according to which the relaxation time diverges at the Kauzmann temperature, implying that one can never equilibrate the metastable supercooled liquid here. A critical discussion of the Kauzmann paradox and the Adam–Gibbs model was given in 2009.[41] Data on several supercooled organic liquids do not confirm the Adam–Gibbs prediction of a diverging relaxation time at any finite temperature, e.g. the Kauzmann temperature.[42] Alternative resolutions There are at least three other possible resolutions to the Kauzmann paradox. It could be that the heat capacity of the supercooled liquid near the Kauzmann temperature smoothly decreases to a smaller value. It could also be that a first order phase transition to another liquid state occurs before the Kauzmann temperature with the heat capacity of this new state being less than that obtained by extrapolation from higher temperature. Finally, Kauzmann himself resolved the entropy paradox by postulating that all supercooled liquids must crystallize before the Kauzmann temperature is reached. In specific materials Silica, SiO2 Silica (the chemical compound SiO2) has a number of distinct crystalline forms in addition to the quartz structure. Nearly all of the crystalline forms involve tetrahedral SiO4 units linked together by shared vertices in different arrangements (stishovite, composed of linked SiO6 octahedra, is the main exception). Si-O bond lengths vary between the different crystal forms. For example, in α-quartz the bond length is 161 picometres (6.3×10−9 in), whereas in α-tridymite it ranges from 154–171 pm (6.1×10−9–6.7×10−9 in). The Si-O-Si bond angle also varies from 140° in α-tridymite to 144° in α-quartz to 180° in β-tridymite. Any deviations from these standard parameters constitute microstructural differences or variations that represent an approach to an amorphous, vitreous or glassy solid. The transition temperature Tg in silicates is related to the energy required to break and re-form covalent bonds in an amorphous (or random network) lattice of covalent bonds. The Tg is clearly influenced by the chemistry of the glass. For example, addition of elements such as B, Na, K or Ca to a silica glass, which have a valency less than 4, helps in breaking up the network structure, thus reducing the Tg. Alternatively, P, which has a valency of 5, helps to reinforce an ordered lattice, and thus increases the Tg.[43] Tg is directly proportional to bond strength, e.g. it depends on quasi-equilibrium thermodynamic parameters of the bonds e.g. on the enthalpy Hd and entropy Sd of configurons – broken bonds: Tg = Hd / [Sd + R ln[(1 − fc)/ fc] where R is the gas constant and fc is the percolation threshold. For strong melts such as SiO2 the percolation threshold in the above equation is the universal Scher–Zallen critical density in the 3-D space e.g. fc = 0.15, however for fragile materials the percolation thresholds are material-dependent and fc ≪ 1.[44] The enthalpy Hd and the entropy Sd of configurons – broken bonds can be found from available experimental data on viscosity.[45] Polymers In polymers the glass transition temperature, Tg, is often expressed as the temperature at which the Gibbs free energy is such that the activation energy for the cooperative movement of 50 or so elements of the polymer is exceeded[citation needed]. This allows molecular chains to slide past each other when a force is applied. From this definition, we can see that the introduction of relatively stiff chemical groups (such as benzene rings) will interfere with the flowing process and hence increase Tg.[46] The stiffness of thermoplastics decreases due to this effect (see figure.) When the glass temperature has been reached, the stiffness stays the same for a while, i.e., at or near E2, until the temperature exceeds Tm, and the material melts. This region is called the rubber plateau. In ironing, a fabric is heated through the glass-rubber transition. Coming from the low-temperature side, the shear modulus drops by many orders of magnitude at the glass transition temperature Tg. A molecular-level mathematical relation for the temperature-dependent shear modulus of the polymer glass on approaching Tg from below has been developed by Alessio Zaccone and Eugene Terentjev.[47] Even though the shear modulus does not really drop to zero (it drops down to the much lower value of the rubber plateau), upon setting the shear modulus to zero in the Zaccone–Terentjev formula, an expression for Tg is obtained which recovers the Flory–Fox equation, and also shows that Tg is inversely proportional to the thermal expansion coefficient in the glass state. This procedure provides yet another operational protocol to define the Tg of polymer glasses by identifying it with the temperature at which the shear modulus drops by many orders of magnitude down to the rubbery plateau. In ironing, a fabric is heated through this transition so that the polymer chains become mobile. The weight of the iron then imposes a preferred orientation. Tg can be significantly decreased by addition of plasticizers into the polymer matrix. Smaller molecules of plasticizer embed themselves between the polymer chains, increasing the spacing and free volume, and allowing them to move past one another even at lower temperatures. Addition of plasticizer can effectively take control over polymer chain dynamics and dominate the amounts of the associated free volume so that the increased mobility of polymer ends is not apparent.[48] The addition of nonreactive side groups to a polymer can also make the chains stand off from one another, reducing Tg. If a plastic with some desirable properties has a Tg that is too high, it can sometimes be combined with another in a copolymer or composite material with a Tg below the temperature of intended use. Note that some plastics are used at high temperatures, e.g., in automobile engines, and others at low temperatures.[28] Stiffness versus temperature In viscoelastic materials, the presence of liquid-like behavior depends on the properties of and so varies with rate of applied load, i.e., how quickly a force is applied. The silicone toy Silly Putty behaves quite differently depending on the time rate of applying a force: pull slowly and it flows, acting as a heavily viscous liquid; hit it with a hammer and it shatters, acting as a glass. On cooling, rubber undergoes a liquid-glass transition, which has also been called a rubber-glass transition. Mechanics of vitrification Main article: Vitrification Molecular motion in condensed matter can be represented by a Fourier series whose physical interpretation consists of a superposition of longitudinal and transverse waves of atomic displacement with varying directions and wavelengths. In monatomic systems, these waves are called density fluctuations. (In polyatomic systems, they may also include compositional fluctuations.)[49] Thus, thermal motion in liquids can be decomposed into elementary longitudinal vibrations (or acoustic phonons) while transverse vibrations (or shear waves) were originally described only in elastic solids exhibiting the highly ordered crystalline state of matter. In other words, simple liquids cannot support an applied force in the form of a shearing stress, and will yield mechanically via macroscopic plastic deformation (or viscous flow). Furthermore, the fact that a solid deforms locally while retaining its rigidity – while a liquid yields to macroscopic viscous flow in response to the application of an applied shearing force – is accepted by many as the mechanical distinction between the two.[50][51] The inadequacies of this conclusion, however, were pointed out by Frenkel in his revision of the kinetic theory of solids and the theory of elasticity in liquids. This revision follows directly from the continuous characteristic of the viscoelastic crossover from the liquid state into the solid one when the transition is not accompanied by crystallization—ergo the supercooled viscous liquid. Thus we see the intimate correlation between transverse acoustic phonons (or shear waves) and the onset of rigidity upon vitrification, as described by Bartenev in his mechanical description of the vitrification process.[52][53] This concept leads to defining the glass transition in terms of the vanishing or significant lowering of the low-frequency shear modulus, as shown quantitatively in the work of Zaccone and Terentjev[47] on the example of polymer glass. In fact, the shoving model stipulates that the activation energy of the relaxation time is proportional to the high-frequency plateau shear modulus,[2][54] a quantity that increases upon cooling thus explaining the ubiquitous non-Arrhenius temperature dependence of the relaxation time in glass-forming liquids. The velocities of longitudinal acoustic phonons in condensed matter are directly responsible for the thermal conductivity that levels out temperature differentials between compressed and expanded volume elements. Kittel proposed that the behavior of glasses is interpreted in terms of an approximately constant "mean free path" for lattice phonons, and that the value of the mean free path is of the order of magnitude of the scale of disorder in the molecular structure of a liquid or solid. The thermal phonon mean free paths or relaxation lengths of a number of glass formers have been plotted versus the glass transition temperature, indicating a linear relationship between the two. This has suggested a new criterion for glass formation based on the value of the phonon mean free path.[55] It has often been suggested that heat transport in dielectric solids occurs through elastic vibrations of the lattice, and that this transport is limited by elastic scattering of acoustic phonons by lattice defects (e.g. randomly spaced vacancies).[56] These predictions were confirmed by experiments on commercial glasses and glass ceramics, where mean free paths were apparently limited by "internal boundary scattering" to length scales of 10–100 micrometres (0.00039–0.00394 in).[57][58] The relationship between these transverse waves and the mechanism of vitrification has been described by several authors who proposed that the onset of correlations between such phonons results in an orientational ordering or "freezing" of local shear stresses in glass-forming liquids, thus yielding the glass transition.[59] Electronic structure The influence of thermal phonons and their interaction with electronic structure is a topic that was appropriately introduced in a discussion of the resistance of liquid metals. Lindemann's theory of melting is referenced,[60] and it is suggested that the drop in conductivity in going from the crystalline to the liquid state is due to the increased scattering of conduction electrons as a result of the increased amplitude of atomic vibration. Such theories of localization have been applied to transport in metallic glasses, where the mean free path of the electrons is very small (on the order of the interatomic spacing).[61][62] The formation of a non-crystalline form of a gold-silicon alloy by the method of splat quenching from the melt led to further considerations of the influence of electronic structure on glass forming ability, based on the properties of the metallic bond.[63][64][65][66][67] Other work indicates that the mobility of localized electrons is enhanced by the presence of dynamic phonon modes. One claim against such a model is that if chemical bonds are important, the nearly free electron models should not be applicable. However, if the model includes the buildup of a charge distribution between all pairs of atoms just like a chemical bond (e.g., silicon, when a band is just filled with electrons) then it should apply to solids.[68] Thus, if the electrical conductivity is low, the mean free path of the electrons is very short. The electrons will only be sensitive to the short-range order in the glass since they do not get a chance to scatter from atoms spaced at large distances. Since the short-range order is similar in glasses and crystals, the electronic energies should be similar in these two states. For alloys with lower resistivity and longer electronic mean free paths, the electrons could begin to sense[dubious – discuss] that there is disorder in the glass, and this would raise their energies and destabilize the glass with respect to crystallization. Thus, the glass formation tendencies of certain alloys may therefore be due in part to the fact that the electron mean free paths are very short, so that only the short-range order is ever important for the energy of the electrons. It has also been argued that glass formation in metallic systems is related to the "softness" of the interaction potential between unlike atoms. Some authors, emphasizing the strong similarities between the local structure of the glass and the corresponding crystal, suggest that chemical bonding helps to stabilize the amorphous structure.[69][70] Other authors have suggested that the electronic structure yields its influence on glass formation through the directional properties of bonds. Non-crystallinity is thus favored in elements with a large number of polymorphic forms and a high degree of bonding anisotropy. Crystallization becomes more unlikely as bonding anisotropy is increased from isotropic metallic to anisotropic metallic to covalent bonding, thus suggesting a relationship between the group number in the periodic table and the glass forming ability in elemental solids.[71] Testing for glass transition. Temperatures may have to be tested such as glass quartz around 2000 degrees Fahrenheit as shown above. Glass structure can be determined using infrared and Raman spectroscopy. IR rays are good mostly for silicate glasses and helps find water impurities. IR limited penetration to 1 to 25 micrometers. Electron microscopes and transmission electron microscopes can see structures to around 5 to 10 nanometers, however sample needs to be very smooth and have to interpret glass cluster variations due to electron interactions with differing terrain of glass at that scale. 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Polymers I Polymers II Archived 2010-01-11 at the Wayback Machine Angell: Aqueous media DoITPoMS Teaching and Learning Package- "The Glass Transition in Polymers" Glass Transition Temperature short overview vte Glass science topics Authority control: National Edit this at Wikidata Israel United States Categories: CryobiologyGlass engineering and scienceGlass physicsPhase transitionsPolymer chemistryRubber propertiesThreshold temperatures https://en.wikipedia.org/wiki/Glass_transition From Wikipedia, the free encyclopedia The autoignition temperature or self-ignition temperature, often called spontaneous ignition temperature or minimum ignition temperature (or shortly ignition temperature) and formerly also known as kindling point, of a substance is the lowest temperature in which it spontaneously ignites in a normal atmosphere without an external source of ignition, such as a flame or spark.[1] This temperature is required to supply the activation energy needed for combustion. The temperature at which a chemical ignites decreases as the pressure is increased. Substances which spontaneously ignite in a normal atmosphere at naturally ambient temperatures are termed pyrophoric. Autoignition temperatures of liquid chemicals are typically measured using a 500-millilitre (18 imp fl oz; 17 US fl oz) flask placed in a temperature-controlled oven in accordance with the procedure described in ASTM E659.[2] When measured for plastics, autoignition temperature can be also measured under elevated pressure and at 100% oxygen concentration. The resulting value is used as a predictor of viability for high-oxygen service. The main testing standard for this is ASTM G72.[3] Autoignition time equation The time t ig {\displaystyle t_{\text{ig}}} it takes for a material to reach its autoignition temperature T ig {\displaystyle T_{\text{ig}}} when exposed to a heat flux q ″ {\displaystyle q''} is given by the following equation:[4] t ig = π 4 k ρ c [ T ig − T 0 q ″ ] 2 , {\displaystyle t_{\text{ig}}={\frac {\pi }{4}}k\rho c\left[{\frac {T_{\text{ig}}-T_{0}}{q''}}\right]^{2},} where k = thermal conductivity, ρ = density, and c = specific heat capacity of the material of interest, T 0 T_{0} is the initial temperature of the material (or the temperature of the bulk material). Autoignition temperature of selected substances Temperatures vary widely in the literature and should only be used as estimates. Factors that may cause variation include partial pressure of oxygen, altitude, humidity, and amount of time required for ignition. Generally the autoignition temperature for hydrocarbon/air mixtures decreases with increasing molecular mass and increasing chain length. The autoignition temperature is also higher for branched-chain hydrocarbons than for straight-chain hydrocarbons.[5] Substance Autoignition[D] Note Barium 550 °C (1,022 °F) 550±90[1][C] Bismuth 735 °C (1,355 °F) 735±20[1][C] Butane 405 °C (761 °F) [6] Calcium 790 °C (1,450 °F) 790±10[1][C] Carbon disulfide 90 °C (194 °F) [7] Diesel or Jet A-1 210 °C (410 °F) [8] Diethyl ether 160 °C (320 °F) [9] Ethanol 365 °C (689 °F) [7] Gasoline (Petrol) 247–280 °C (477–536 °F) [7] Hydrogen 535 °C (995 °F) [10] Iron 1,315 °C (2,399 °F) 1315±20[1][C] Lead 850 °C (1,560 °F) 850±5[1][C] Leather / parchment 200–212 °C (392–414 °F) [8][11] Magnesium 635 °C (1,175 °F) 635±5[1][B][C] Magnesium 473 °C (883 °F) [7][B] Molybdenum 780 °C (1,440 °F) 780±5[1][C] Paper 218–246 °C (424–475 °F) [8][12] Phosphorus (white) 34 °C (93 °F) [7][A][B] Silane 21 °C (70 °F) [7] or below Strontium 1,075 °C (1,967 °F) 1075±120[1][C] Tin 940 °C (1,720 °F) 940±25[1][C] Triethylborane −20 °C (−4 °F) [7] A On contact with an organic substance, melts otherwise. B There are two distinct results in the published literature. Both are separately listed in this table. C At 1 atm. The ignition temperature depends on the air pressure. D Under standard conditions for pressure. See also Fire point Flash point Gas burner (for flame temperatures, combustion heat energy values and ignition temperatures) Spontaneous combustion References Laurendeau, N. M.; Glassman, I. (1971-04-01). "Ignition Temperatures of Metals in Oxygen Atmospheres". Combustion Science and Technology. 3 (2): 77–82. doi:10.1080/00102207108952274. E659 – 78 (Reapproved 2000), "Standard Test Method for Autoignition Temperature of Liquid Chemicals", ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959. S. Grynko, "Material Properties Explained" (2012), ISBN 1-4700-7991-7, p. 46. Principles of Fire Behavior. ISBN 0-8273-7732-0. 1998. Zabetakis, M. G. (1965), Flammability characteristics of combustible gases and vapours, U.S. Department of Mines, Bulletin 627. "Butane - Safety Properties". Wolfram|Alpha. Fuels and Chemicals - Autoignition Temperatures, engineeringtoolbox.com Cafe, Tony. "PHYSICAL CONSTANTS FOR INVESTIGATORS". tcforensic.com.au. TC Forensic P/L. Retrieved 11 February 2015. "Diethyl Ether - Safety Properties". Wolfram|Alpha. "Hydrogen – Autoignition Point". Wolfram|Alpha. "Flammability and flame retardancy of leather". leathermag.com. Leather International / Global Trade Media. Retrieved 11 February 2015. Tony Cafe. "Physical Constants for Investigators". Journal of Australian Fire Investigators. (Reproduced from "Firepoint" magazine) External links Analysis of Effective Thermal Properties of Thermally Thick Materials. vte Firelighting Campfire Bonfire Glossary Components Ember Fire triangle Firewood Spark Tinder Wood ash Wood fuel Topics Autoignition temperature Combustion Friction fire Minimum ignition energy Smouldering Early starters Burning glass (Solar Spark Lighter) Fire piston Fire plough Fire-saw Fire striker Flint Fire drill Hand drill Bow drill Pump drill Modern starters Match Black match Electric match Ferrocerium Lighter Blowtorch Other equipment Char cloth Feather stick Fire pan Fire pit Fire ring Matchbook Matchbox Punk Tinderbox Torch Chuckmuck Related articles Arson Control of fire by early humans Native American use of fire in ecosystems Outdoor cooking Firem'n Chit Pyrolysis Pyromania Survival skills Authority control: National Edit this at Wikidata Germany Categories: Chemical propertiesFireThreshold temperatures https://en.wikipedia.org/wiki/Autoignition_temperature From Wikipedia, the free encyclopedia (Redirected from Doppler cooling limit) Simplified principle of Doppler laser cooling: 1 A stationary atom sees the laser neither red- nor blue-shifted and does not absorb the photon. 2 An atom moving away from the laser sees it red-shifted and does not absorb the photon. 3.1 An atom moving towards the laser sees it blue-shifted and absorbs the photon, slowing the atom. 3.2 The photon excites the atom, moving an electron to a higher quantum state. 3.3 The atom re-emits a photon. As its direction is random, there is no net change in momentum over many photons. Doppler cooling is a mechanism that can be used to trap and slow the motion of atoms to cool a substance. The term is sometimes used synonymously with laser cooling, though laser cooling includes other techniques. History Doppler cooling was simultaneously proposed by two groups in 1975, the first being David J. Wineland and Hans Georg Dehmelt[1] and the second being Theodor W. Hänsch and Arthur Leonard Schawlow.[2] It was first demonstrated by Wineland, Drullinger, and Walls in 1978[3] and shortly afterwards by Neuhauser, Hohenstatt, Toschek and Dehmelt. One conceptually simple form of Doppler cooling is referred to as optical molasses, since the dissipative optical force resembles the viscous drag on a body moving through molasses. Steven Chu, Claude Cohen-Tannoudji and William D. Phillips were awarded the 1997 Nobel Prize in Physics for their work in laser cooling and atom trapping. Brief explanation Doppler cooling involves light with frequency tuned slightly below an electronic transition in an atom. Because the light is detuned to the "red" (i.e. at lower frequency) of the transition, the atoms will absorb more photons if they move towards the light source, due to the Doppler effect. Consider the simplest case of 1D motion on the x axis. Let the photon be traveling in the +x direction and the atom in the −x direction. In each absorption event, the atom loses a momentum equal to the momentum of the photon. The atom, which is now in the excited state, emits a photon spontaneously but randomly along +x or −x. Momentum is returned to the atom. If the photon was emitted along +x then there is no net change; however, if the photon was emitted along −x, then the atom is moving more slowly in either −x or +x. The net result of the absorption and emission process is a reduced speed of the atom, on the condition that its initial speed is larger than the recoil velocity from scattering a single photon. If the absorption and emission are repeated many times, the mean velocity, and therefore the kinetic energy of the atom, will be reduced. Since the temperature of an ensemble of atoms is a measure of the random internal kinetic energy, this is equivalent to cooling the atoms. The Doppler cooling limit is the minimum temperature achievable with Doppler cooling. Detailed explanation The vast majority of photons that come anywhere near a particular atom are almost[4] completely unaffected by that atom. The atom is almost completely transparent to most frequencies (colors) of photons. A few photons happen to "resonate" with the atom in a few very narrow bands of frequencies (a single color rather than a mixture like white light). When one of those photons comes close to the atom, the atom typically absorbs that photon (absorption spectrum) for a brief period of time, then emits an identical photon (emission spectrum) in some random, unpredictable direction. (Other sorts of interactions between atoms and photons exist, but are not relevant to this article.) The popular idea that lasers increase the thermal energy of matter is not the case when examining individual atoms. If a given atom is practically motionless (a "cold" atom), and the frequency of a laser focused upon it can be controlled, most frequencies do not affect the atom—it is invisible at those frequencies. There are only a few points of electromagnetic frequency that have any effect on that atom. At those frequencies, the atom can absorb a photon from the laser, while transitioning to an excited electronic state, and pick up the momentum of that photon. Since the atom now has the photon's momentum, the atom must begin to drift in the direction the photon was traveling. A short time later, the atom will spontaneously emit a photon in a random direction as it relaxes to a lower electronic state. If that photon is emitted in the direction of the original photon, the atom will give up its momentum to the photon and will become motionless again. If the photon is emitted in the opposite direction, the atom will have to provide momentum in that opposite direction, which means the atom will pick up even more momentum in the direction of the original photon (to conserve momentum), with double its original velocity. But usually the photon speeds away in some other direction, giving the atom at least some sideways thrust. Another way of changing frequencies is to change the positioning of the laser, for example, by using a monochromatic (single-color) laser that has a frequency that is a little below one of the "resonant" frequencies of this atom (at which frequency the laser will not directly affect the atom's state). If the laser were to be positioned so that it was moving towards the observed atoms, then the Doppler effect would raise its frequency. At one specific velocity, the frequency would be precisely correct for said atoms to begin absorbing photons. Something very similar happens in a laser cooling apparatus, except such devices start with a warm cloud of atoms moving in numerous directions at variable velocity. Starting with a laser frequency well below the resonant frequency, photons from any one laser pass right through the majority of atoms. However, atoms moving rapidly towards a particular laser catch the photons for that laser, slowing those atoms down until they become transparent again. (Atoms rapidly moving away from that laser are transparent to that laser's photons—but they are rapidly moving towards the laser directly opposite it). This utilization of a specific velocity to induce absorption is also seen in Mössbauer spectroscopy. On a graph of atom velocities (atoms moving rapidly to the right correspond with stationary dots far to the right, atoms moving rapidly to the left correspond with stationary dots far to the left), there is a narrow band on the left edge corresponding to the speed at which those atoms start absorbing photons from the left laser. Atoms in that band are the only ones that interact with the left laser. When a photon from the left laser slams into one of those atoms, it suddenly slows down an amount corresponding to the momentum of that photon (the dot would be redrawn some fixed "quantum" distance further to the right). If the atom releases the photon directly to the right, then the dot is redrawn that same distance to the left, putting it back in the narrow band of interaction. But usually the atom releases the photon in some other random direction, and the dot is redrawn that quantum distance in the opposite direction. Such an apparatus would be constructed with many lasers, corresponding to many boundary lines that completely surround that cloud of dots. As the laser frequency is increased, the boundary contracts, pushing all the dots on that graph towards zero velocity, the given definition of "cold". Limits Minimum temperature The Doppler temperature is the minimum temperature achievable with Doppler cooling. When a photon is absorbed by an atom counter-propagating to the light source, its velocity is decreased by momentum conservation. When the absorbed photon is spontaneously emitted by the excited atom, the atom receives a momentum kick in a random direction. The spontaneous emissions are isotropic and therefore these momentum kicks average to zero for the mean velocity. On the other hand, the mean squared velocity, ⟨ v 2 ⟩ \langle v^{2}\rangle , is not zero in the random process, and thus heat is supplied to the atom.[5] At equilibrium, the heating and cooling rates are equal, which sets a limit on the amount by which the atom can be cooled. As the transitions used for Doppler cooling have broad natural linewidths γ \gamma (measured in radians per second), this sets the lower limit to the temperature of the atoms after cooling to be[6] T D o p p l e r = ℏ γ / ( 2 k B ) , {\displaystyle T_{\mathrm {Doppler} }=\hbar \gamma /(2k_{\text{B}}),} where k B k_{\text{B}} is the Boltzmann constant and ℏ \hbar is the reduced Planck constant. This is usually much higher than the recoil temperature, which is the temperature associated with the momentum gained from the spontaneous emission of a photon. The Doppler limit has been verified with a gas of metastable helium.[7] Sub-Doppler cooling Main article: Sub-Doppler cooling Temperatures well below the Doppler limit have been achieved with various laser cooling methods, including Sisyphus cooling, evaporative cooling, and resolved sideband cooling. The theory of Doppler cooling assumes an atom with a simple two level structure, whereas most atomic species which are laser cooled have complicated hyperfine structure. Mechanisms such as Sisyphus cooling due to multiple ground states lead to temperatures lower than the Doppler limit. Maximum concentration The concentration must be minimal to prevent the absorption of the photons into the gas in the form of heat. This absorption happens when two atoms collide with each other while one of them has an excited electron. There is then a possibility of the excited electron dropping back to the ground state with its extra energy liberated in additional kinetic energy to the colliding atoms—which heats the atoms. This works against the cooling process and therefore limits the maximum concentration of gas that can be cooled using this method. Atomic structure Only certain atoms and ions have optical transitions amenable to laser cooling, since it is extremely difficult to generate the amounts of laser power needed at wavelengths much shorter than 300 nm. Furthermore, the more hyperfine structure an atom has, the more ways there are for it to emit a photon from the upper state and not return to its original state, putting it in a dark state and removing it from the cooling process. It is possible to use other lasers to optically pump those atoms back into the excited state and try again, but the more complex the hyperfine structure is, the more (narrow-band, frequency locked) lasers are required. Since frequency-locked lasers are both complex and expensive, atoms which need more than one extra repump laser are rarely cooled; the common rubidium magneto-optical trap, for example, requires one repump laser. This is also the reason why molecules are in general difficult to laser cool: in addition to hyperfine structure, molecules also have rovibronic couplings and so can also decay into excited rotational or vibrational states. However, laser cooling of molecules has been demonstrated, first with SrF molecules,[8] and subsequently with other diatomics such as CaF[9][10] and YO.[11] Configurations Counter-propagating sets of laser beams in all three Cartesian dimensions may be used to cool the three motional degrees of freedom of the atom. Common laser-cooling configurations include optical molasses, the magneto-optical trap, and the Zeeman slower. Atomic ions, trapped in an ion trap, can be cooled with a single laser beam as long as that beam has a component along all three motional degrees of freedom. This is in contrast to the six beams required to trap neutral atoms. The original laser cooling experiments were performed on ions in ion traps. (In theory, neutral atoms could be cooled with a single beam if they could be trapped in a deep trap, but in practice neutral traps are much shallower than ion traps and a single recoil event can be enough to kick a neutral atom out of the trap.) Applications One use for Doppler cooling is the optical molasses technique. This process itself forms a part of the magneto-optical trap but it can be used independently. Doppler cooling is also used in spectroscopy and metrology, where cooling allows narrower spectroscopic features. For example, all of the best atomic clock technologies involve Doppler cooling at some point. See also Magneto-optical trap Resolved sideband cooling References Wineland, D. J.; Dehmelt, H. (1975). "Proposed 1014 Δν < ν Laser Fluorescence Spectroscopy on Tl+ Mono-Ion Oscillator III" (PDF). Bulletin of the American Physical Society. 20: 637. Hänsch, T. W.; Shawlow, A. L. (1975). "Cooling of Gases by Laser Radiation". Optics Communications. 13 (1): 68. Bibcode:1975OptCo..13...68H. doi:10.1016/0030-4018(75)90159-5. Wineland, D. J.; Drullinger, R. E.; Walls, F. L. (1978). "Radiation-Pressure Cooling of Bound Resonant Absorbers". Physical Review Letters. 40 (25): 1639. Bibcode:1978PhRvL..40.1639W. doi:10.1103/PhysRevLett.40.1639. There are processes, such as Rayleigh and Raman scattering, by which atoms and molecules will scatter non-resonant photons; see, e.g., Hecht, E.; Zajac, A. (1974). Optics. Addison-Wesley. ISBN 978-0-201-02835-5. This type of scattering, however, is normally very weak in comparison to resonant absorption and emission (i.e., fluorescence). Lett, P. D.; Phillips, W. D.; Rolston, S. L.; Tanner, C. E.; Watts, R. N.; Westbrook, C. I. (1989). "Optical molasses". Journal of the Optical Society of America B. 6 (11): 2084–2107. Bibcode:1989JOSAB...6.2084L. doi:10.1364/JOSAB.6.002084. Letokhov, V. S.; Minogin, V. G.; Pavlik, B. D. (1977). "Cooling and capture of atoms and molecules by a resonant light field". Soviet Physics JETP. 45: 698. Bibcode:1977JETP...45..698L. Chang, R.; Hoendervanger, A. L.; Bouton, Q.; Fang, Y.; Klafka, T.; Audo, K.; Aspect, A.; Westbrook, C. I.; Clément, D. (2014). "Three-dimensional laser cooling at the Doppler limit". Physical Review A. 90 (6): 063407. arXiv:1409.2519. Bibcode:2014PhRvA..90f3407C. doi:10.1103/PhysRevA.90.063407. S2CID 55013080. Shuman, E. S.; Barry, J. F.; DeMille, D. (2010). "Laser cooling of a diatomic molecule". Nature. 467 (7317): 820–823. arXiv:1103.6004. Bibcode:2010Natur.467..820S. doi:10.1038/nature09443. PMID 20852614. S2CID 4430586. "Laser Cooling CaF". doylegroup.harvard.edu/. Doyle Group, Harvard University. Retrieved 9 November 2015. Zhelyazkova, V.; Cournol, A.; Wall, T. E.; Matsushima, A.; Hudson, J. J.; Hinds, E. A.; Tarbutt, M. R.; Sauer, B. E. (2014). "Laser cooling and slowing of CaF molecules". Physical Review A. 89 (5): 053416. arXiv:1308.0421. Bibcode:2014PhRvA..89e3416Z. doi:10.1103/PhysRevA.89.053416. S2CID 119285667. Hummon, M. T.; Yeo, M.; Stuhl, B. K.; Collopy, A. L.; Xia, Y.; Ye, J. (2013). "2D Magneto-Optical Trapping of Diatomic Molecules". Physical Review Letters. 110 (14): 143001. arXiv:1209.4069. Bibcode:2013PhRvL.110n3001H. doi:10.1103/PhysRevLett.110.143001. PMID 25166984. S2CID 13718902. Further reading Foot, C. J. (2005). Atomic Physics. Oxford University Press. pp. 182–213. ISBN 978-0-19-850696-6. Metcalf, H. J.; van der Straten, P. (1999). Laser Cooling and Trapping. Springer-Verlag. ISBN 978-0-387-98728-6. Phillips, W. D. (1997). "Laser Cooling and Trapping of Atoms" (PDF). Nobel Lecture. Nobel Foundation. pp. 199–237. vte Lasers Categories: Atomic physicsCooling technologyDoppler effects https://en.wikipedia.org/wiki/Doppler_cooling#Limits Ductile–brittle transition temperature Schematic appearance of round metal bars after tensile testing. (a) Brittle fracture (b) Ductile fracture (c) Completely ductile fracture Metals can undergo two different types of fractures: brittle fracture or ductile fracture. Failure propagation occurs faster in brittle materials due to the ability for ductile materials to undergo plastic deformation. Thus, ductile materials are able to sustain more stress due to their ability to absorb more energy prior to failure than brittle materials are. The plastic deformation results in the material following a modification of the Griffith equation, where the critical fracture stress increases due to the plastic work required to extend the crack adding to the work necessary to form the crack - work corresponding to the increase in surface energy that results from the formation of an addition crack surface.[26] The plastic deformation of ductile metals is important as it can be a sign of the potential failure of the metal. Yet, the point at which the material exhibits a ductile behavior versus a brittle behavior is not only dependent on the material itself but also on the temperature at which the stress is being applied to the material. The temperature where the material changes from brittle to ductile or vice versa is crucial for the design of load-bearing metallic products. The minimum temperature at which the metal transitions from a brittle behavior to a ductile behavior, or from a ductile behavior to a brittle behavior, is known as the ductile-brittle transition temperature (DBTT). Below the DBTT, the material will not be able to plastically deform, and the crack propagation rate increases rapidly leading to the material undergoing brittle failure rapidly. Furthermore, DBTT is important since, once a material is cooled below the DBTT, it has a much greater tendency to shatter on impact instead of bending or deforming (low temperature embrittlement). Thus, the DBTT indicates the temperature at which, as temperature decreases, a material's ability to deform in a ductile manner decreases and so the rate of crack propagation drastically increases. In other words, solids are very brittle at very low temperatures, and their toughness becomes much higher at elevated temperatures. For more general applications, it is preferred to have a lower DBTT to ensure the material has a wider ductility range. This ensures that sudden cracks are inhibited so that failures in the metal body are prevented. It has been determined that the more slip systems a material has, the wider the range of temperatures ductile behavior is exhibited at. This is due to the slip systems allowing for more motion of dislocations when a stress is applied to the material. Thus, in materials with a lower amount of slip systems, dislocations are often pinned by obstacles leading to strain hardening, which increases the materials strength which makes the material more brittle. For this reason, FCC (face centered cubic) structures are ductile over a wide range of temperatures, BCC (body centered cubic) structures are ductile only at high temperatures, and HCP (hexagonal closest packed) structures are often brittle over wide ranges of temperatures. This leads to each of these structures having different performances as they approach failure (fatigue, overload, and stress cracking) under various temperatures, and shows the importance of the DBTT in selecting the correct material for a specific application. For example, zamak 3 exhibits good ductility at room temperature but shatters when impacted at sub-zero temperatures. DBTT is a very important consideration in selecting materials that are subjected to mechanical stresses. A similar phenomenon, the glass transition temperature, occurs with glasses and polymers, although the mechanism is different in these amorphous materials. The DBTT is also dependent on the size of the grains within the metal, as typically smaller grain size leads to an increase in tensile strength, resulting in an increase in ductility and decrease in the DBTT. This increase in tensile strength is due to the smaller grain sizes resulting in grain boundary hardening occurring within the material, where the dislocations require a larger stress to cross the grain boundaries and continue to propagate throughout the material. It has been shown that by continuing to refine ferrite grains to reduce their size, from 40 microns down to 1.3 microns, that it is possible to eliminate the DBTT entirely so that a brittle fracture never occurs in ferritic steel (as the DBTT required would be below absolute zero).[27] In some materials, the transition is sharper than others and typically requires a temperature-sensitive deformation mechanism. For example, in materials with a body-centered cubic (bcc) lattice the DBTT is readily apparent, as the motion of screw dislocations is very temperature sensitive because the rearrangement of the dislocation core prior to slip requires thermal activation. This can be problematic for steels with a high ferrite content. This famously resulted in serious hull cracking in Liberty ships in colder waters during World War II, causing many sinkings. DBTT can also be influenced by external factors such as neutron radiation, which leads to an increase in internal lattice defects and a corresponding decrease in ductility and increase in DBTT. The most accurate method of measuring the DBTT of a material is by fracture testing. Typically four-point bend testing at a range of temperatures is performed on pre-cracked bars of polished material. Two fracture tests are typically utilized to determine the DBTT of specific metals: the Charpy V-Notch test and the Izod test. The Charpy V-notch test determines the impact energy absorption ability or toughness of the specimen by measuring the potential energy difference resulting from the collision between a mass on a free-falling pendulum and the machined V-shaped notch in the sample, resulting in the pendulum breaking through the sample. The DBTT is determined by repeating this test over a variety of temperatures and noting when the resulting fracture changes to a brittle behavior which occurs when the absorbed energy is dramatically decreased. The Izod test is essentially the same as the Charpy test, with the only differentiating factor being the placement of the sample; In the former the sample is placed vertically, while in the latter the sample is placed horizontally with respect to the bottom of the base. [28] For experiments conducted at higher temperatures, dislocation activity[clarification needed] increases. At a certain temperature, dislocations shield[clarification needed] the crack tip to such an extent that the applied deformation rate is not sufficient for the stress intensity at the crack-tip to reach the critical value for fracture (KiC). The temperature at which this occurs is the ductile–brittle transition temperature. If experiments are performed at a higher strain rate, more dislocation shielding is required to prevent brittle fracture, and the transition temperature is raised.[citation needed] See also Deformation Work hardening, which improves ductility in uniaxial tension by delaying the onset of instability Strength of materials References Brande, William Thomas (1853). A Dictionary of Science, Literature, and Art: Comprising the History, Description, and Scientific Principles of Every Branch of Human Knowledge : with the Derivation and Definition of All the Terms in General Use. Harper & Brothers. p. 369. Kalpakjian, Serope, 1928- (1984). Manufacturing processes for engineering materials. Reading, Mass.: Addison-Wesley. p. 30. ISBN 0-201-11690-1. OCLC 9783323. "Ductility - What is Ductile Material". Nuclear Power. Retrieved 2020-11-14. Budynas, Richard G. (2015). Shigley's Mechanical Engineering Design—10th ed. McGraw Hill. p. 233. ISBN 978-0-07-339820-4.. Chandler Roberts-Austen, William (1894). An Introduction to the Study of Metallurgy. London: C. Griffin. p. 16. Ductility and its effect on material failure. The Engineering Archive. (n.d.). https://theengineeringarchive.com/material-science/page-ductility-material-failure.html "Malleability - Malleable Materials". Nuclear Power. Archived from the original on 2020-09-25. Retrieved 2020-11-14. DOE FUNDAMENTALS HANDBOOK MATERIAL SCIENCE. Vol. 1, Module 2 – Properties of Metals. U.S. Department of Energy. January 1993. p. 25. Rich, Jack C. (1988). The Materials and Methods of Sculpture. Courier Dover Publications. p. 129. ISBN 978-0-486-25742-6.. Masuda, Hideki (2016). "Combined Transmission Electron Microscopy – In situ Observation of the Formation Process and Measurement of Physical Properties for Single Atomic-Sized Metallic Wires". In Janecek, Milos; Kral, Robert (eds.). Modern Electron Microscopy in Physical and Life Sciences. InTech. doi:10.5772/62288. ISBN 978-953-51-2252-4. S2CID 58893669. Vaccaro, John (2002) Materials handbook, Mc Graw-Hill handbooks, 15th ed. Schwartz, M. (2002) CRC encyclopedia of materials parts and finishes, 2nd ed. Lah, Che; Akmal, Nurul; Trigueros, Sonia (2019). "Synthesis and modelling of the mechanical properties of Ag, Au and Cu nanowires". Sci. Technol. Adv. Mater. 20 (1): 225–261. Bibcode:2019STAdM..20..225L. doi:10.1080/14686996.2019.1585145. PMC 6442207. PMID 30956731. Dieter, G. (1986) Mechanical Metallurgy, McGraw-Hill, ISBN 978-0-07-016893-0 "Ductility Review - Strength Mechanics of Materials - Engineers Edge". www.engineersedge.com. Retrieved 2020-07-14. Askeland, Donald R. (2016). "6-4 Properties Obtained from the Tensile Test". The science and engineering of materials. Wright, Wendelin J. (Seventh ed.). Boston, MA. p. 195. ISBN 978-1-305-07676-1. OCLC 903959750. Callister, William D. Jr. (2010). "6.6 Tensile Properties". Materials science and engineering : an introduction. Rethwisch, David G. (8th ed.). Hoboken, NJ. p. 166. ISBN 978-0-470-41997-7. OCLC 401168960. Matic, P (1988). "The Relation of Tensile Specimen Size and Geometry Effects to Unique Constitutive Parameters for Ductile Materials". Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences. 417 (1853): 309–333. Bibcode:1988RSPSA.417..309M. doi:10.1098/rspa.1988.0063. S2CID 43033448. Havner, K (2004). "On the Onset of Necking in the Tensile Test". International Journal of Plasticity. 20 (4–5): 965–978. doi:10.1016/j.ijplas.2003.05.004. Kim, H (2005). "Finite Element Analysis of the Onset of Necking and the Post-Necking Behaviour During Uniaxial Tensile Testing". Materials Transactions. 46 (10): 2159–2163. doi:10.2320/matertrans.46.2159. Joun, M (2007). "Finite Element Analysis of Tensile Testing with Emphasis on Necking". Computational Materials Science. 41 (1): 63–69. doi:10.1016/j.commatsci.2007.03.002. Osovski, S (2013). "Dynamic Tensile Necking: Influence of Specimen Geometry and Boundary Conditions". Mechanics of Materials. 62: 1–13. doi:10.1016/j.mechmat.2013.03.002. hdl:10016/17020. Choung, J (2008). "Study on True Stress Correction from Tensile Tests". Journal of Mechanical Science and Technology. 22 (6): 1039–1051. doi:10.1007/s12206-008-0302-3. S2CID 108776720. Ho, H (2019). "Modelling Tensile Tests on High Strength S690 Steel Materials Undergoing Large Deformations". Engineering Structures. 192: 305–322. doi:10.1016/j.engstruct.2019.04.057. S2CID 182744244. Samuel, E (2008). "Inter-Relation between True Stress at the Onset of Necking and True Uniform Strain in Steels - a Manifestation of Onset to Plastic Instability". Materials Science and Engineering A-Structural Materials Properties Microstructure and Processing. 480 (1–2): 506–509. doi:10.1016/j.msea.2007.07.074. "FRACTURE OF MATERIALS" (PDF). U.S. Naval Academy. Archived (PDF) from the original on 2022-10-09. Retrieved 2 July 2022. Qiu, Hai; Hanamura, Toshihiro; Torizuka, Shiro (2014). "Influence of Grain Size on the Ductile Fracture Toughness of Ferritic Steel". ISIJ International. 54 (8): 1958–1964. doi:10.2355/isijinternational.54.1958. "Ductile-Brittle Transition Temperature and Impact Energy Tests - Yena Engineering". 18 November 2020. External links Look up ductility in Wiktionary, the free dictionary. Look up malleability in Wiktionary, the free dictionary. Ductility definition at engineersedge.com DoITPoMS Teaching and Learning Package- "The Ductile-Brittle Transition Categories: Continuum mechanicsDeformation (mechanics) https://en.wikipedia.org/wiki/Ductility#Ductile%E2%80%93brittle_transition_temperature MDMT is one of the design conditions for pressure vessels engineering calculations, design and manufacturing according to the ASME Boilers and Pressure Vessels Code. Each pressure vessel that conforms to the ASME code has its own MDMT, and this temperature is stamped on the vessel nameplate. The precise definition can sometimes be a little elaborate, but in simple terms the MDMT is a temperature arbitrarily selected by the user of type of fluid and the temperature range the vessel is going to handle. The so-called arbitrary MDMT must be lower than or equal to the CET (which is an environmental or "process" property, see below) and must be higher than or equal to the (MDMT)M (which is a material property). Critical exposure temperature (CET) is the lowest anticipated temperature to which the vessel will be subjected, taking into consideration lowest operating temperature, operational upsets, autorefrigeration, atmospheric temperature, and any other sources of cooling. In some cases it may be the lowest temperature at which significant stresses will occur and not the lowest possible temperature. (MDMT)M is the lowest temperature permitted according to the metallurgy of the vessel fabrication materials and the thickness of the vessel component, that is, according to the low temperature embrittlement range and the charpy impact test requirements per temperature and thickness, for each one of the vessel's components. References ASME, Boilers and Pressure Vessels Code Dennis R. Moss, Pressure Vessel Design Manual, 1997 (2nd ed.) Stub icon This article about a mechanical engineering topic is a stub. You can help Wikipedia by expanding it. Categories: Pressure vesselsThreshold temperaturesMechanical engineering stubs https://en.wikipedia.org/wiki/Minimum_design_metal_temperature From Wikipedia, the free encyclopedia Ethanol burning with its spectrum depicted In the study of combustion, the adiabatic flame temperature is the temperature reached by a flame under ideal conditions. It is an upper bound of the temperature that is reached in actual processes. There are two types adiabatic flame temperature: constant volume and constant pressure, depending on how the process is completed. The constant volume adiabatic flame temperature is the temperature that results from a complete combustion process that occurs without any work, heat transfer or changes in kinetic or potential energy. Its temperature is higher than in the constant pressure process because no energy is utilized to change the volume of the system (i.e., generate work). Common flames Propane Iso-Octane (2,2,4-Trimethylpentane) In daily life, the vast majority of flames one encounters are those caused by rapid oxidation of hydrocarbons in materials such as wood, wax, fat, plastics, propane, and gasoline. The constant-pressure adiabatic flame temperature of such substances in air is in a relatively narrow range around 1950 °C. This is mostly because the heat of combustion of these compounds is roughly proportional to the amount of oxygen consumed, which proportionally increases the amount of air that has to be heated, so the effect of a larger heat of combustion on the flame temperature is offset. Incomplete reaction at higher temperature further curtails the effect of a larger heat of combustion. Because most combustion processes that happen naturally occur in the open air, there is nothing that confines the gas to a particular volume like the cylinder in an engine. As a result, these substances will burn at a constant pressure, which allows the gas to expand during the process. Common flame temperatures Assuming initial atmospheric conditions (1 bar and 20 °C), the following table[1] lists the flame temperature for various fuels under constant pressure conditions. The temperatures mentioned here are for a stoichiometric fuel-oxidizer mixture (i.e. equivalence ratio φ = 1). Note that these are theoretical, not actual, flame temperatures produced by a flame that loses no heat. The closest will be the hottest part of a flame, where the combustion reaction is most efficient. This also assumes complete combustion (e.g. perfectly balanced, non-smoky, usually bluish flame). Several values in the table significantly disagree with the literature[1] or predictions by online calculators. Adiabatic flame temperature (constant pressure) of common fuels Fuel Oxidizer T ad {\displaystyle T_{\text{ad}}} (°C) (°F) Acetylene (C2H2) Air 2500 4532 Oxygen 3480 6296 Butane (C4H10) Air 2231 4074[2] Cyanogen (C2N2) Oxygen 4525 8177 Dicyanoacetylene (C4N2) Oxygen 4990 9010 Ethane (C2H6) Air 1955 3551 Ethanol (C2H5OH) Air 2082 3779[3] Gasoline Air 2138 3880[3] Hydrogen (H2) Air 2254 4089[3] Magnesium (Mg) Air 1982 3600[4] Methane (CH4) Air 1963 3565[5] Methanol (CH3OH) Air 1949 3540[5] Naphtha Air 2533 4591[2] Natural gas Air 1960 3562[6] Pentane (C5H12) Air 1977 3591[5] Propane (C3H8) Air 1980 3596[7] Methylacetylene (CH3CCH) Air 2010 3650 Oxygen 2927 5301 Toluene (C7H8) Air 2071 3760[5] Wood Air 1980 3596 Kerosene Air 2093[8] 3801 Light fuel oil Air 2104[8] 3820 Medium fuel oil Air 2101[8] 3815 Heavy fuel oil Air 2102[8] 3817 Bituminous Coal Air 2172[8] 3943 Anthracite Air 2180[8] 3957 Oxygen ≈3500[9] ≈6332 Aluminium Oxygen 3732 6750[5] Lithium Oxygen 2438 4420[5] Phosphorus (white) Oxygen 2969 5376[5] Zirconium Oxygen 4005 7241[5] Thermodynamics First law of thermodynamics for a closed reacting system From the first law of thermodynamics for a closed reacting system we have R Q P − R W P = U P − U R {}_{R}Q_{P}-{}_{R}W_{P}=U_{P}-U_{R} where, R Q P {}_{R}Q_{P} and R W P {}_{R}W_{P} are the heat and work transferred from the system to the surroundings during the process, respectively, and U R U_{R} and U P U_{P} are the internal energy of the reactants and products, respectively. In the constant volume adiabatic flame temperature case, the volume of the system is held constant and hence there is no work occurring: R W P = ∫ R P p d V = 0 {}_{R}W_{P}=\int \limits _{R}^{P}{pdV}=0 There is also no heat transfer because the process is defined to be adiabatic: R Q P = 0 {}_{R}Q_{P}=0. As a result, the internal energy of the products is equal to the internal energy of the reactants: U P = U R U_{P}=U_{R}. Because this is a closed system, the mass of the products and reactants is constant and the first law can be written on a mass basis, U P = U R ⇒ m P u P = m R u R ⇒ u P = u R U_{P}=U_{R}\Rightarrow m_{P}u_{P}=m_{R}u_{R}\Rightarrow u_{P}=u_{R}. Enthalpy versus temperature diagram illustrating closed system calculation In the case of the constant pressure adiabatic flame temperature, the pressure of the system is held constant, which results in the following equation for the work: R W P = ∫ R P p d V = p ( V P − V R ) {}_{R}W_{P}=\int \limits _{R}^{P}{pdV}=p\left({V_{P}-V_{R}}\right) Again there is no heat transfer occurring because the process is defined to be adiabatic: R Q P = 0 {}_{R}Q_{P}=0. From the first law, we find that, − p ( V P − V R ) = U P − U R ⇒ U P + p V P = U R + p V R -p\left({V_{P}-V_{R}}\right)=U_{P}-U_{R}\Rightarrow U_{P}+pV_{P}=U_{R}+pV_{R} Recalling the definition of enthalpy we obtain H P = H R H_{P}=H_{R}. Because this is a closed system, the mass of the products and reactants is the same and the first law can be written on a mass basis: H P = H R ⇒ m P h P = m R h R ⇒ h P = h R H_{P}=H_{R}\Rightarrow m_{P}h_{P}=m_{R}h_{R}\Rightarrow h_{P}=h_{R}. We see that the adiabatic flame temperature of the constant pressure process is lower than that of the constant volume process. This is because some of the energy released during combustion goes, as work, into changing the volume of the control system. Adiabatic flame temperatures and pressures as a function of ratio of air to iso-octane. A ratio of 1 corresponds to the stoichiometric ratio Constant volume flame temperature of a number of fuels, with air If we make the assumption that combustion goes to completion (i.e. forming only CO 2 and H 2O), we can calculate the adiabatic flame temperature by hand either at stoichiometric conditions or lean of stoichiometry (excess air). This is because there are enough variables and molar equations to balance the left and right hand sides, C α H β O γ N δ + ( a O 2 + b N 2 ) → ν 1 C O 2 + ν 2 H 2 O + ν 3 N 2 + ν 4 O 2 {{\rm {{C}}}}_{\alpha }{{\rm {{H}}}}_{\beta }{{\rm {{O}}}}_{\gamma }{{\rm {{N}}}}_{\delta }+\left({a{{\rm {{O}}}}_{{{\rm {{2}}}}}+b{{\rm {{N}}}}_{{{\rm {{2}}}}}}\right)\to \nu _{1}{{\rm {{CO}}}}_{{{\rm {{2}}}}}+\nu _{2}{{\rm {{H}}}}_{{{\rm {{2}}}}}{{\rm {{O}}}}+\nu _{3}{{\rm {{N}}}}_{{{\rm {{2}}}}}+\nu _{4}{{\rm {{O}}}}_{{{\rm {{2}}}}} Rich of stoichiometry there are not enough variables because combustion cannot go to completion with at least CO and H 2 needed for the molar balance (these are the most common products of incomplete combustion), C α H β O γ N δ + ( a O 2 + b N 2 ) → ν 1 C O 2 + ν 2 H 2 O + ν 3 N 2 + ν 5 C O + ν 6 H 2 {{\rm {{C}}}}_{\alpha }{{\rm {{H}}}}_{\beta }{{\rm {{O}}}}_{\gamma }{{\rm {{N}}}}_{\delta }+\left({a{{\rm {{O}}}}_{{{\rm {{2}}}}}+b{{\rm {{N}}}}_{{{\rm {{2}}}}}}\right)\to \nu _{1}{{\rm {{CO}}}}_{{{\rm {{2}}}}}+\nu _{2}{{\rm {{H}}}}_{{{\rm {{2}}}}}{{\rm {{O}}}}+\nu _{3}{{\rm {{N}}}}_{{{\rm {{2}}}}}+\nu _{5}{{\rm {{CO}}}}+\nu _{6}{{\rm {{H}}}}_{{{\rm {{2}}}}} However, if we include the water gas shift reaction, C O 2 + H 2 ⇔ C O + H 2 O {{\rm {{CO}}}}_{{{\rm {{2}}}}}+H_{2}\Leftrightarrow {{\rm {{CO}}}}+{{\rm {{H}}}}_{{{\rm {{2}}}}}{{\rm {{O}}}} and use the equilibrium constant for this reaction, we will have enough variables to complete the calculation. Different fuels with different levels of energy and molar constituents will have different adiabatic flame temperatures. Constant pressure flame temperature of a number of fuels, with air Nitromethane versus isooctane flame temperature and pressure We can see by the following figure why nitromethane (CH3NO2) is often used as a power boost for cars. Since each molecule of nitromethane contains an oxidant with relatively high-energy bonds between nitrogen and oxygen, it can burn much hotter than hydrocarbons or oxygen-containing methanol. This is analogous to adding pure oxygen, which also raises the adiabatic flame temperature. This in turn allows it to build up more pressure during a constant volume process. The higher the pressure, the more force upon the piston creating more work and more power in the engine. It stays relatively hot rich of stoichiometry because it contains its own oxidant. However, continual running of an engine on nitromethane will eventually melt the piston and/or cylinder because of this higher temperature. Effects of dissociation on adiabatic flame temperature In real world applications, complete combustion does not typically occur. Chemistry dictates that dissociation and kinetics will change the composition of the products. There are a number of programs available that can calculate the adiabatic flame temperature taking into account dissociation through equilibrium constants (Stanjan, NASA CEA, AFTP). The following figure illustrates that the effects of dissociation tend to lower the adiabatic flame temperature. This result can be explained through Le Chatelier's principle. See also Flame speed References See under "Tables" in the external references below. Libal, Angela (27 April 2018). "What Temperatures Do Lighters Burn At?". Leaf Group Ltd. / Leaf Group Media. Sciencing. Flame Temperature Analysis and NOx Emissions for Different Fuels "How hot does magnesium burn? | Reference.com". Archived from the original on 2017-09-17. Retrieved 2017-09-17. CRC Handbook of Chemistry and Physics, 96th Edition, p. 15-51 "North American Combustion Handbook, Volume 1, 3rd edition, North American Mfg Co., 1986". Archived from the original on 2011-07-16. Retrieved 2009-12-09. "Archived copy" (PDF). Archived from the original (PDF) on 2015-09-24. Retrieved 2013-05-19. Power Point Presentation: Flame Temperature, Hsin Chu, Department of Environmental Engineering, National Cheng Kung University, Taiwan Analysis of oxy-fuel combustion power cycle utilizing a pressurized coal combustor by Jongsup Hong et al., MIT, which cites IPCC Special Report on Carbon Dioxide Capture and Storage (PDF). Intergovernmental Panel on Climate Change. 2005. p. 122.. But the IPCC report actually gives a much less precise statement: "The direct combustion of fuel and oxygen has been practised for many years in the metallurgical and glass industries where burners operate at near stoichiometric conditions with flame temperatures of up to 3500°C." The temperature may depend on pressure, because at lower pressure there will be more dissociation of the combustion products, implying a lower adiabatic temperature. External links General information Babrauskas, Vytenis (2006-02-25). "Temperatures in flames and fires". Fire Science and Technology Inc. Archived from the original on 12 January 2008. Retrieved 2008-01-27. Computation of adiabatic flame temperature Adiabatic flame temperature Tables "Adiabatic Flame Temperature". The Engineering Toolbox. Archived from the original on 28 January 2008. Retrieved 2008-01-27. adiabatic flame temperature of hydrogen, methane, propane and octane with oxygen or air as oxidizers "Flame Temperatures for some Common Gases". The Engineering Toolbox. Archived from the original on 7 January 2008. Retrieved 2008-01-27. Temperature of a blue flame and common materials Calculators Online adiabatic flame temperature calculator using Cantera Adiabatic flame temperature program Gaseq, program for performing chemical equilibrium calculations. Flame Temperature Calculator - Constant pressure bipropellant adiabatic combustion Adiabatic Flame Temperature calculator Categories: CombustionTemperatureThreshold temperatures https://en.wikipedia.org/wiki/Adiabatic_flame_temperature Category:State functions Category Talk Read Edit View history Tools Help From Wikipedia, the free encyclopedia Wikimedia Commons has media related to State functions. The main article for this category is State function. Subcategories This category has the following 3 subcategories, out of 3 total. T Thermodynamic entropy‎ (1 C, 41 P) Thermodynamic free energy‎ (9 P) Threshold temperatures‎ (28 P) Pages in category "State functions" The following 15 pages are in this category, out of 15 total. This list may not reflect recent changes. State function E Enthalpy Entropy Entropy (order and disorder) Exergy F Fugacity G Gibbs free energy H Helmholtz free energy I Internal energy P Particle number Pressure T Temperature Thermodynamic free energy Thermodynamic temperature V Volume (thermodynamics) Categories: Thermodynamic propertiesContinuum mechanics Hidden category: Commons category link from Wikidata https://en.wikipedia.org/wiki/Category:State_functions From Wikipedia, the free encyclopedia (Redirected from Eutectoid) "Eutectic" redirects here. For the sports mascot, see St. Louis College of Pharmacy § Mascot. A phase diagram for a fictitious binary chemical mixture (with the two components denoted by A and B) used to depict the eutectic composition, temperature, and point. (L denotes the liquid state.) A eutectic system or eutectic mixture (/juːˈtɛktɪk/ yoo-TEK-tik)[1] is a homogeneous mixture that has a melting point lower than those of the constituents.[2] The lowest possible melting point over all of the mixing ratios of the constituents is called the eutectic temperature. On a phase diagram, the eutectic temperature is seen as the eutectic point (see plot on the right).[3] Non-eutectic mixture ratios would have different melting temperatures for their different constituents, since one component's lattice will melt at a lower temperature than the other's. Conversely, as a non-eutectic mixture cools down, each of its components would solidify (form a lattice) at a different temperature, until the entire mass is solid. Not all binary alloys have eutectic points, since the valence electrons of the component species are not always compatible,[clarification needed] in any mixing ratio, to form a new type of joint crystal lattice. For example, in the silver-gold system the melt temperature (liquidus) and freeze temperature (solidus) "meet at the pure element endpoints of the atomic ratio axis while slightly separating in the mixture region of this axis".[4] The term eutectic was coined in 1884 by British physicist and chemist Frederick Guthrie (1833–1886). The word originates from the Greek εὐ- (eû 'well') and τῆξῐς (têxis 'melting').[2] Eutectic phase transition Four eutectic structures: A) lamellar B) rod-like C) globular D) acicular. The eutectic solidification is defined as follows:[5] Liquid → cooling eutectic temperature α solid solution + β solid solution \text{Liquid} \xrightarrow[\text{cooling}]{\text{eutectic temperature}} \alpha \,\, \text{solid solution} + \beta \,\, \text{solid solution} This type of reaction is an invariant reaction, because it is in thermal equilibrium; another way to define this is the change in Gibbs free energy equals zero. Tangibly, this means the liquid and two solid solutions all coexist at the same time and are in chemical equilibrium. There is also a thermal arrest for the duration of the change of phase during which the temperature of the system does not change.[5] The resulting solid macrostructure from a eutectic reaction depends on a few factors, with the most important factor being how the two solid solutions nucleate and grow. The most common structure is a lamellar structure, but other possible structures include rodlike, globular, and acicular.[6] Non-eutectic compositions Compositions of eutectic systems that are not at the eutectic point can be classified as hypoeutectic or hypereutectic. Hypoeutectic compositions are those with a smaller percent composition of species β and a greater composition of species α than the eutectic composition (E) while hypereutectic solutions are characterized as those with a higher composition of species β and a lower composition of species α than the eutectic composition. As the temperature of a non-eutectic composition is lowered the liquid mixture will precipitate one component of the mixture before the other. In a hypereutectic solution, there will be a proeutectoid phase of species β whereas a hypoeutectic solution will have a proeutectic α phase.[5] Types Alloys Eutectic alloys have two or more materials and have a eutectic composition. When a non-eutectic alloy solidifies, its components solidify at different temperatures, exhibiting a plastic melting range. Conversely, when a well-mixed, eutectic alloy melts, it does so at a single, sharp temperature. The various phase transformations that occur during the solidification of a particular alloy composition can be understood by drawing a vertical line from the liquid phase to the solid phase on the phase diagram for that alloy. Some uses include: NEMA Eutectic Alloy Overload Relays for electrical protection of 3-phase motors for pumps, fans, conveyors, and other factory process equipment.[7] Eutectic alloys for soldering, both traditional alloys composed of lead (Pb) and tin (Sn), sometimes with additional silver (Ag) or gold (Au) — especially Sn63Pb37 and Sn62Pb36Ag2 alloy formula for electronics - and newer lead-free soldering alloys, in particular ones composed of tin (Sn), silver (Ag), and copper (Cu) such as Sn96.5Ag3.5. Casting alloys, such as aluminium-silicon and cast iron (at the composition of 4.3% carbon in iron producing an austenite-cementite eutectic) Silicon chips are bonded to gold-plated substrates through a silicon-gold eutectic by the application of ultrasonic energy to the chip. See eutectic bonding. Brazing, where diffusion can remove alloying elements from the joint, so that eutectic melting is only possible early in the brazing process Temperature response, e.g., Wood's metal and Field's metal for fire sprinklers Non-toxic mercury replacements, such as galinstan Experimental glassy metals, with extremely high strength and corrosion resistance Eutectic alloys of sodium and potassium (NaK) that are liquid at room temperature and used as coolant in experimental fast neutron nuclear reactors. Others Solid–liquid phase change of ethanol–water mixtures Sodium chloride and water form a eutectic mixture whose eutectic point is −21.2 °C[8] and 23.3% salt by mass.[9] The eutectic nature of salt and water is exploited when salt is spread on roads to aid snow removal, or mixed with ice to produce low temperatures (for example, in traditional ice cream making). Ethanol–water has an unusually biased eutectic point, i.e. it is close to pure ethanol, which sets the maximum proof obtainable by fractional freezing. "Solar salt", 60% NaNO3 and 40% KNO3, forms a eutectic molten salt mixture which is used for thermal energy storage in concentrated solar power plants.[10] To reduce the eutectic melting point in the solar molten salts, calcium nitrate is used in the following proportion: 42% Ca(NO3)2, 43% KNO3, and 15% NaNO3. Lidocaine and prilocaine—both are solids at room temperature—form a eutectic that is an oil with a 16 °C (61 °F) melting point that is used in eutectic mixture of local anesthetic (EMLA) preparations. Menthol and camphor, both solids at room temperature, form a eutectic that is a liquid at room temperature in the following proportions: 8:2, 7:3, 6:4, and 5:5. Both substances are common ingredients in pharmacy extemporaneous preparations.[11] Minerals may form eutectic mixtures in igneous rocks, giving rise to characteristic intergrowth textures exhibited, for example, by granophyre.[12] Some inks are eutectic mixtures, allowing inkjet printers to operate at lower temperatures.[13] Choline chloride produces eutectic mixtures with many natural products such as citric acid, malic acid and sugars. These liquid mixtures can be used, for example, to obtain antioxidant and antidiabetic extracts from natural products.[14] Strengthening Mechanisms Alloys The primary strengthening mechanism of the eutectic structure in metals is composite strengthening (See strengthening mechanisms of materials). This deformation mechanism works through load transfer between the two constituent phases where the more compliant phase transfers stress to the stiffer phase[15]. By taking advantage of the strength of the stiff phase and the ductility of the compliant phase, the overall toughness of the material increases. As the composition is varied to either hypoeutectic or hypereutectic formations, the load transfer mechanism becomes more complex as there is now load transfer between the eutectic phase and the secondary phase as well as the load transfer within the eutectic phase itself. A second tunable strengthening mechanism of eutectic structures is the spacing of the secondary phase. By changing the spacing of the secondary phase, the fraction of contact between the two phases through shared phase boundaries is also changed. By decreasing the spacing of the eutectic phase, creating a fine eutectic structure, more surface area is shared between the two constituent phases resulting in more effective load transfer[16]. On the micro-scale, the additional boundary area acts as a barrier to dislocations further strengthening the material. As a result of this strengthening mechanism, coarse eutectic structures tend to be less stiff but more ductile while fine eutectic structures are stiffer but more brittle[16]. The spacing of the eutectic phase can be controlled during processing as it is directly related to the cooling rate during solidification of the eutectic structure. For example, for a simple lamellar eutectic structure, the minimal lamellae spacing is[17]: λ ∗ = 2 γ V m T E Δ H ∗ Δ T 0 {\displaystyle \lambda ^{*}={\frac {2\gamma V_{m}T_{E}}{\Delta H*\Delta T_{0}}}} Where is γ \gamma is the surface energy of the two-phase boundary, V m V_{m} is the molar volume of the eutectic phase, T E T_{E} is the solidification temperature of the eutectic phase, Δ H \Delta H is the enthalpy of formation of the eutectic phase, and Δ T 0 {\displaystyle \Delta T_{0}} is the undercooling of the material. So, by altering the undercooling, and by extension the cooling rate, the minimal achievable spacing of the secondar phase is controlled. Strengthening metallic eutectic phases to resist deformation at high temperatures (see creep deformation) is more convoluted as the primary deformation mechanism changes depending on the level of stress applied. At high temperatures where deformation is dominated by dislocation movement, the strengthening from load transfer and secondary phase spacing remain as they continue to resist dislocation motion. At lower strains where Nabarro-Herring creep is dominant, the shape and size of the eutectic phase structure plays a significant role in material deformation as it affects the available boundary area for vacancy diffusion to occur[18]. Other critical points Iron–carbon phase diagram, showing the eutectoid transformation between austenite (γ) and pearlite. Eutectoid When the solution above the transformation point is solid, rather than liquid, an analogous eutectoid transformation can occur. For instance, in the iron-carbon system, the austenite phase can undergo a eutectoid transformation to produce ferrite and cementite, often in lamellar structures such as pearlite and bainite. This eutectoid point occurs at 723 °C (1,333 °F) and 0.76 wt% carbon.[19] Peritectoid A peritectoid transformation is a type of isothermal reversible reaction that has two solid phases reacting with each other upon cooling of a binary, ternary, ..., n-ary alloy to create a completely different and single solid phase.[20] The reaction plays a key role in the order and decomposition of quasicrystalline phases in several alloy types.[21] A similar structural transition is also predicted for rotating columnar crystals. Peritectic Gold–aluminium phase diagram Peritectic transformations are also similar to eutectic reactions. Here, a liquid and solid phase of fixed proportions react at a fixed temperature to yield a single solid phase. Since the solid product forms at the interface between the two reactants, it can form a diffusion barrier and generally causes such reactions to proceed much more slowly than eutectic or eutectoid transformations. Because of this, when a peritectic composition solidifies it does not show the lamellar structure that is found with eutectic solidification. Such a transformation exists in the iron-carbon system, as seen near the upper-left corner of the figure. It resembles an inverted eutectic, with the δ phase combining with the liquid to produce pure austenite at 1,495 °C (2,723 °F) and 0.17% carbon. At the peritectic decomposition temperature the compound, rather than melting, decomposes into another solid compound and a liquid. The proportion of each is determined by the lever rule. In the Al-Au phase diagram, for example, it can be seen that only two of the phases melt congruently, AuAl2 and Au2Al , while the rest peritectically decompose. Eutectic calculation The composition and temperature of a eutectic can be calculated from enthalpy and entropy of fusion of each components.[22] The Gibbs free energy G depends on its own differential: G = H − T S ⇒ { H = G + T S ( ∂ G ∂ T ) P = − S ⇒ H = G − T ( ∂ G ∂ T ) P . {\displaystyle G=H-TS\Rightarrow {\begin{cases}H=G+TS\\\left({\frac {\partial G}{\partial T}}\right)_{P}=-S\end{cases}}\Rightarrow H=G-T\left({\frac {\partial G}{\partial T}}\right)_{P}.} Thus, the G/T derivative at constant pressure is calculated by the following equation: ( ∂ G / T ∂ T ) P = 1 T ( ∂ G ∂ T ) P − 1 T 2 G = − 1 T 2 ( G − T ( ∂ G ∂ T ) P ) = − H T 2 . {\displaystyle \left({\frac {\partial G/T}{\partial T}}\right)_{P}={\frac {1}{T}}\left({\frac {\partial G}{\partial T}}\right)_{P}-{\frac {1}{T^{2}}}G=-{\frac {1}{T^{2}}}\left(G-T\left({\frac {\partial G}{\partial T}}\right)_{P}\right)=-{\frac {H}{T^{2}}}.} The chemical potential μ i \mu _{i} is calculated if we assume that the activity is equal to the concentration: μ i = μ i ∘ + R T ln ⁡ a i a ≈ μ i ∘ + R T ln ⁡ x i . {\displaystyle \mu _{i}=\mu _{i}^{\circ }+RT\ln {\frac {a_{i}}{a}}\approx \mu _{i}^{\circ }+RT\ln x_{i}.} At the equilibrium, μ i = 0 {\displaystyle \mu _{i}=0}, thus μ i ∘ \mu_i^\circ is obtained as μ i = μ i ∘ + R T ln ⁡ x i = 0 ⇒ μ i ∘ = − R T ln ⁡ x i . {\displaystyle \mu _{i}=\mu _{i}^{\circ }+RT\ln x_{i}=0\Rightarrow \mu _{i}^{\circ }=-RT\ln x_{i}.} Using[clarification needed] and integrating gives ( ∂ μ i / T ∂ T ) P = ∂ ∂ T ( R ln ⁡ x i ) ⇒ R ln ⁡ x i = − H i ∘ T + K . {\displaystyle \left({\frac {\partial \mu _{i}/T}{\partial T}}\right)_{P}={\frac {\partial }{\partial T}}\left(R\ln x_{i}\right)\Rightarrow R\ln x_{i}=-{\frac {H_{i}^{\circ }}{T}}+K.} The integration constant K may be determined for a pure component with a melting temperature T ∘ T^\circ and an enthalpy of fusion H ∘ H^\circ: x i = 1 ⇒ T = T i ∘ ⇒ K = H i ∘ T i ∘ . {\displaystyle x_{i}=1\Rightarrow T=T_{i}^{\circ }\Rightarrow K={\frac {H_{i}^{\circ }}{T_{i}^{\circ }}}.} We obtain a relation that determines the molar fraction as a function of the temperature for each component: R ln ⁡ x i = − H i ∘ T + H i ∘ T i ∘ . {\displaystyle R\ln x_{i}=-{\frac {H_{i}^{\circ }}{T}}+{\frac {H_{i}^{\circ }}{T_{i}^{\circ }}}.} The mixture of n components is described by the system { ln ⁡ x i + H i ∘ R T − H i ∘ R T i ∘ = 0 , ∑ i = 1 n x i = 1. {\displaystyle {\begin{cases}\ln x_{i}+{\frac {H_{i}^{\circ }}{RT}}-{\frac {H_{i}^{\circ }}{RT_{i}^{\circ }}}=0,\\\sum \limits _{i=1}^{n}x_{i}=1.\end{cases}}} { ∀ i < n ⇒ ln ⁡ x i + H i ∘ R T − H i ∘ R T i ∘ = 0 , ln ⁡ ( 1 − ∑ i = 1 n − 1 x i ) + H n ∘ R T − H n ∘ R T n ∘ = 0 , {\displaystyle {\begin{cases}\forall i

     

     Battle of a French ship of the line and two galleys of the Barbary corsairs

    Battle of a French ship of the line and two galleys of the Barbary corsairs


    https://en.wikipedia.org/wiki/Barbary_pirates#/media/File:Th%C3%A9odore_Gudin-Combat_d'un_vaisseau_fran%C3%A7ais_et_de_deux_gal%C3%A8res_barbaresques_mg_5061.jpg

    https://en.wikipedia.org/wiki/Valencia


    https://en.wikipedia.org/wiki/Spain


    https://en.wikipedia.org/wiki/Fall_of_the_Western_Roman_Empire


    https://en.wikipedia.org/wiki/Visigothic_Kingdom


    https://en.wikipedia.org/wiki/Hispania


    https://en.wikipedia.org/wiki/Galicia_(Spain)


    https://en.wikipedia.org/wiki/Atlantic_Europe


    https://en.wikipedia.org/wiki/Bell_Beaker_culture


    https://en.wikipedia.org/wiki/Maghreb


    https://en.wikipedia.org/wiki/Barbary_Coast


    https://en.wikipedia.org/wiki/Tunisian_navy_(1705%E2%80%931881)


    https://en.wikipedia.org/wiki/Bronze_Age_Europe


    https://en.wikipedia.org/wiki/Bronze_Age_in_Romania


    https://en.wikipedia.org/wiki/Inverted_bell


    https://en.wikipedia.org/wiki/Corinthian_order


    https://en.wikipedia.org/wiki/Trajan


    https://en.wikipedia.org/wiki/Haplogroup_R1b


    (Redirected from Haplogroup R1b (Y-DNA))
    "M343" redirects here. For the state highway in Michigan, see M-343 (Michigan highway).
    Haplogroup R1b
    Possible time of originProbably soon after R1, possibly between 18,000-14,000 BC[1]
    Possible place of originWestern Asia, North Eurasia or Eastern Europe[2]
    AncestorR1
    Descendants
    • R1b1a (L754, PF6269, YSC0000022)
    • R1b2 (PH155)
    Defining mutationsM343

    Haplogroup R1b (R-M343), previously known as Hg1 and Eu18, is a human Y-chromosome haplogroup.

    It is the most frequently occurring paternal lineage in Western Europe, as well as some parts of Russia (e.g. the Bashkirs) and pockets of Central Africa (e.g. parts of Chad and among the Chadic-speaking minority ethnic groups of Cameroon). The clade is also present at lower frequencies throughout Eastern Europe, Western Asia, as well as parts of North Africa, South Asia and Central Asia. 

    https://en.wikipedia.org/wiki/Haplogroup_R1b

     

    https://en.wikipedia.org/wiki/Samara

     

    https://en.wikipedia.org/wiki/Novokuybyshevsk

     

    https://en.wikipedia.org/wiki/Russia

     

    Main articles: Haplogroup P-P295 and Structure of Y-DNA Haplogroup K
    https://en.wikipedia.org/wiki/Haplogroup_R1b
     
    Analysis of ancient Y-DNA from the remains from early Neolithic Central and North European Linear Pottery culture settlements have not yet found males belonging to haplogroup R1b-M269.[30][31] Olalde et al. (2017) trace the spread of haplogroup R1b-M269 in western Europe, particularly Britain, to the spread of the Beaker culture, with a sudden appearance of many R1b-M269 haplogroups in Western Europe ca. 5000–4500 years BP during the early Bronze Age.[32] In the 2016 Nature article "The genetic history of Ice Age Europe".[33]
    https://en.wikipedia.org/wiki/Haplogroup_R1b
     

    Internal structure of R1b

    Names such as R1b, R1b1 and so on are phylogenetic (i.e. "family tree") names which make clear their place within the branching of haplogroups, or the phylogenetic tree. An alternative way of naming the same haplogroups and subclades refers to their defining SNP mutations: for example, R-M343 is equivalent to R1b.[34] Phylogenetic names change with new discoveries and SNP-based names are consequently reclassified within the phylogenetic tree. In some cases, an SNP is found to be unreliable as a defining mutation and an SNP-based name is removed completely. For example, before 2005, R1b was synonymous with R-P25, which was later reclassified as R1b1; in 2016, R-P25 was removed completely as a defining SNP, due to a significant rate of back-mutation.[35] (Below is the basic outline of R1b according to the ISOGG Tree as it stood on January 30, 2017.[36])

    Basic phylogenetic tree for R1b

     M343/PF6242 

    R-M343* (R1b*). No cases have been reported.


     L278 
    PH155

    R-PH155 (R1b2) has been found in individuals from Albania, Bahrain, Bhutan, China, Germany, India, Italy, Singapore, Tajikistan, Turkey, the UK, and the USA.


    L754/PF6269/YSC0000022
    V88

    R-V88 (R1b1b): the most common forms of R1b found among males native to Sub-Saharan Africa, also found rarely elsewhere.


    L389/PF6531
     V1636

    R-V1636 (R1b1a2) is rare, but has been found in China,[37][38] Bulgaria, Belarus, Southern Finland, Turkey, Iraq, Lebanon, Kuwait, Qatar, Saudi Arabia, Russia (including a Tomsk Tatar), Italy (including one from the Province of Salerno), Puerto Rico, the Dominican Republic, Canada, Germany, Valais, Israel, and Armenia.[39][40]


     P297/PF6398 
     M73 

    Subclades of R-M73 (R1b1a1a) are rare overall, with most cases being observed in the Caucasus, Siberia, Central Asia, and Mongolia.


     M269/PF6517 

    Subclades of R-M269 (R1b1a1b; previously R1b1a1a2) are now extremely common throughout Western Europe, but are also found at lower levels in many other parts of Western Eurasia and the Mediterranean.







    https://en.wikipedia.org/wiki/Haplogroup_R1b




    https://en.wikipedia.org/wiki/Epigravettian
    https://en.wikipedia.org/wiki/Solutrean
    https://en.wikipedia.org/wiki/Magdalenian


     https://en.wikipedia.org/wiki/Upper_Paleolithic
     
     

     2000 1900 1500 0 -1500 -3000 3000 6000 9000 -10000 -20000 -100000 -1m -3m -6m -b

    5b 5quint exp

    1cent -1cent inf unk unc n/a -inf 0

    universe age unk earth age unk est.


    The Neanderthals continued to use Mousterian stone tool technology and possibly Châtelperronian technology. These tools disappeared from the archeological record at around the same time the Neanderthals themselves disappeared from the fossil record, about 40,000 cal BP.[6] 

    https://en.wikipedia.org/wiki/Upper_Paleolithic

    The peopling of Australia most likely took place before c. 60 ka. Europe was peopled after c. 45 ka. Anatomically modern humans are known to have expanded northward into Siberia as far as the 58th parallel by about 45 ka (Ust'-Ishim man). The Upper Paleolithic is divided by the Last Glacial Maximum (LGM), from about 25 to 15 ka. The peopling of the Americas occurred during this time, with East and Central Asia populations reaching the Bering land bridge after about 35 ka, and expanding into the Americas by about 15 ka. In Western Eurasia, the Paleolithic eases into the so-called Epipaleolithic or Mesolithic from the end of the LGM, beginning 15 ka. The Holocene glacial retreat begins 11.7 ka (10th millennium BC), falling well into the Old World Epipaleolithic, and marking the beginning of the earliest forms of farming in the Fertile Crescent. 

    https://en.wikipedia.org/wiki/Upper_Paleolithic

    Magdalenian
    Homo Sapiens in Europe - magdalenian distribution map-fr.svg
    Geographical rangeWestern Europe
    PeriodUpper Paleolithic
    Mesolithic
    Datesc. 17,000 – c. 12,000 BP[a][is this date calibrated?]
    Type siteAbri de la Madeleine
    Major sitesCave of Altamira, Kents Cavern, Lascaux
    Preceded bySolutrean
    Followed byAzilian, Ahrensburg culture

    Magdalenian cave painting

    https://en.wikipedia.org/wiki/Magdalenian

     

    Chronology

    The culture spans from approximately 17,000 to 12,000 BP,[is this date calibrated?] toward the end of the most recent ice age. Magdalenian tool culture is characterised by regular blade industries struck from carinated cores.

    The Magdalenian epoch is divided into six phases generally agreed to have chronological significance (Magdalenian I through VI, I being the earliest and VI being the latest). The earliest phases are recognised by the varying proportion of blades and specific varieties of scrapers, the middle phases marked by the emergence of a microlithic component (particularly the distinctive denticulated microliths), and the later phases by the presence of uniserial (phase 5) and biserial 'harpoons' (phase 6) made of bone, antler and ivory.[3]

    Magdalenian people dwelt in tents such as this one of Pincevent (France) that dates to 12,000 years ago.[4]

    Debate continues about the nature of the earliest Magdalenian assemblages, and it remains questionable whether the Badegoulian culture is the earliest phase of Magdalenian culture. Similarly, finds from the forest of Beauregard near Paris have been suggested as belonging to the earliest Magdalenian.[5] The earliest Magdalenian sites are in France. The Epigravettian is a similar culture appearing at the same time. Its known range extends from southeast France to the western shores of the Volga River, Russia, with many sites in Italy.

    The later phases of Magdalenian culture are contemporaneous with the human re-settlement of north-western Europe after the Last Glacial Maximum during the Late Glacial Maximum.[6][7] As hunter gatherers, Magdalenians did not re-settle permanently in northwest Europe, instead following herds and seasons.

    By the end of the Magdalenian epoch, lithic technology shows a pronounced trend toward increased microlithisation. The bone harpoons and points have the most distinctive chronological markers within the typological sequence. As well as flint tools, Magdalenians are known for their elaborate worked bone, antler and ivory that served both functional and aesthetic purposes, including perforated batons.

    The sea shells and fossils found in Magdalenian sites may be sourced to relatively precise areas and have been used to support hypotheses of Magdalenian hunter-gatherer seasonal ranges, and perhaps trade routes.

    In northern Spain and south-west France this tool culture was superseded by the Azilian culture. In northern Europe it was followed by variants of the Tjongerian techno-complex. It has been suggested that key Late-glacial sites in south-western Britain may be attributed to Magdalenian culture, including Kent's Cavern.

    Art

    Antler carving, France, 15,000 BC

    Bones, reindeer antlers and animal teeth display crude pictures carved or etched on them of seals, fish, reindeer, mammoths and other creatures.

    The best of Magdalenian artworks are a mammoth engraved on a fragment of its own ivory;[dubious – discuss] a dagger of reindeer antler, with a handle in form of a reindeer; a cave-bear cut on a flat piece of schist; a seal on a bear's tooth; a fish drawn on a reindeer antler; and a complete picture, also on reindeer antler, showing horses, an aurochs, trees, and a snake biting a man's leg. The man is naked, which, together with the snake, suggests a warm climate in spite of the presence of the reindeer.

    In the Tuc d'Audoubert cave, an 18-inch clay statue of two bison sculpted in relief was discovered in the deepest room, now known as the Room of the Bisons.[8]

    Examples of Magdalenian portable art include batons, figurines, and intricately engraved projectile points, as well as items of personal adornment including sea shells, perforated carnivore teeth (presumably necklaces), and fossils.

    Cave sites such as Lascaux contain the best known examples of Magdalenian cave art. The site of Altamira in Spain, with its extensive and varied forms of Magdalenian mobiliary art has been suggested to be an agglomeration site where groups of Magdalenian hunter-gatherers congregated.[9]

    Gallery

    Treatment of the dead

    Some skulls were cleaned of soft tissues, then had the facial regions removed, with the remaining brain case retouched, possibly to make the broken edges more regular. This manipulation suggests the shaping of skulls to produce skull cups.[10]

    Genetics

    The genes of seven Magdalenians, the El Miron Cluster in Iberia, have shown close relationship to a population who had lived in Northern Europe some 20,000 years previously. The analyses suggested that 70-80% of the ancestry of these individuals was from the population represented by Goyet Q116-1, associated with the Aurignacian culture of about 35,000 BP, from the Goyet Caves in modern Belgium.[11]

    The three samples of Y-DNA included two samples of haplogroup I and one sample of HIJK. All samples of mtDNA belonged to U, including five samples of U8b and one sample of U5b.

    https://en.wikipedia.org/wiki/Magdalenian


    From Wikipedia, the free encyclopedia
    Magdalenian
    Homo Sapiens in Europe - magdalenian distribution map-fr.svg
    Geographical rangeWestern Europe
    PeriodUpper Paleolithic
    Mesolithic
    Datesc. 17,000 – c. 12,000 BP[a][is this date calibrated?]
    Type siteAbri de la Madeleine
    Major sitesCave of Altamira, Kents Cavern, Lascaux
    Preceded bySolutrean
    Followed byAzilian, Ahrensburg culture
    See also: Prehistoric Europe

    The Magdalenian cultures (also Madelenian; French: Magdalénien) are later cultures of the Upper Paleolithic and Mesolithic in western Europe. They date from around 17,000 to 12,000 years ago.[a][is this date calibrated?] It is named after the type site of La Madeleine, a rock shelter located in the Vézère valley, commune of Tursac, in France's Dordogne department.

    Édouard Lartet and Henry Christy originally termed the period L'âge du renne (the Age of the Reindeer). They conducted the first systematic excavations of the type site, publishing in 1875. The Magdalenian epoch is associated with reindeer hunters, although Magdalenian sites contain extensive evidence for the hunting of red deer, horses, and other large mammals present in Europe toward the end of the last glacial period. The culture was geographically widespread, and later Magdalenian sites stretched from Portugal in the west to Poland in the east, and as far north as France, the Channel Islands, England, and Wales. It is the third epoch of Gabriel de Mortillet's cave chronology system, corresponding roughly to the Late Pleistocene. Besides La Madeleine, the chief stations of the epoch are Les Eyzies, Laugerie-Basse, and Gorges d'Enfer in the Dordogne; Grotte du Placard in Charente and others in south-west France.

    Period biology

    Magdalenian cave painting

    The Magdalenian epoch is represented by numerous sites, whose contents show progress in arts and culture. It was characterized by a cold and dry climate, humans in association with the reindeer, and the extinction of the mammoth. The use of bone and ivory as implements, begun in the preceding Solutrean epoch, increased, making the period essentially a bone period. Bone instruments are quite varied: spear-points, harpoon-heads, borers, hooks and needles.[citation needed]

    The fauna of the Magdalenian epoch seems to have included tigers and other tropical species along with reindeer, arctic foxes, arctic hares, and other polar creatures. Magdalenian humans appear to have been of short stature, dolichocephalic, with a low retreating forehead and prominent brow ridges.[citation needed]

    Chronology

    The culture spans from approximately 17,000 to 12,000 BP,[is this date calibrated?] toward the end of the most recent ice age. Magdalenian tool culture is characterised by regular blade industries struck from carinated cores.

    The Magdalenian epoch is divided into six phases generally agreed to have chronological significance (Magdalenian I through VI, I being the earliest and VI being the latest). The earliest phases are recognised by the varying proportion of blades and specific varieties of scrapers, the middle phases marked by the emergence of a microlithic component (particularly the distinctive denticulated microliths), and the later phases by the presence of uniserial (phase 5) and biserial 'harpoons' (phase 6) made of bone, antler and ivory.[3]

    Magdalenian people dwelt in tents such as this one of Pincevent (France) that dates to 12,000 years ago.[4]

    Debate continues about the nature of the earliest Magdalenian assemblages, and it remains questionable whether the Badegoulian culture is the earliest phase of Magdalenian culture. Similarly, finds from the forest of Beauregard near Paris have been suggested as belonging to the earliest Magdalenian.[5] The earliest Magdalenian sites are in France. The Epigravettian is a similar culture appearing at the same time. Its known range extends from southeast France to the western shores of the Volga River, Russia, with many sites in Italy.

    The later phases of Magdalenian culture are contemporaneous with the human re-settlement of north-western Europe after the Last Glacial Maximum during the Late Glacial Maximum.[6][7] As hunter gatherers, Magdalenians did not re-settle permanently in northwest Europe, instead following herds and seasons.

    By the end of the Magdalenian epoch, lithic technology shows a pronounced trend toward increased microlithisation. The bone harpoons and points have the most distinctive chronological markers within the typological sequence. As well as flint tools, Magdalenians are known for their elaborate worked bone, antler and ivory that served both functional and aesthetic purposes, including perforated batons.

    The sea shells and fossils found in Magdalenian sites may be sourced to relatively precise areas and have been used to support hypotheses of Magdalenian hunter-gatherer seasonal ranges, and perhaps trade routes.

    In northern Spain and south-west France this tool culture was superseded by the Azilian culture. In northern Europe it was followed by variants of the Tjongerian techno-complex. It has been suggested that key Late-glacial sites in south-western Britain may be attributed to Magdalenian culture, including Kent's Cavern.

    Art

    Antler carving, France, 15,000 BC

    Bones, reindeer antlers and animal teeth display crude pictures carved or etched on them of seals, fish, reindeer, mammoths and other creatures.

    The best of Magdalenian artworks are a mammoth engraved on a fragment of its own ivory;[dubious – discuss] a dagger of reindeer antler, with a handle in form of a reindeer; a cave-bear cut on a flat piece of schist; a seal on a bear's tooth; a fish drawn on a reindeer antler; and a complete picture, also on reindeer antler, showing horses, an aurochs, trees, and a snake biting a man's leg. The man is naked, which, together with the snake, suggests a warm climate in spite of the presence of the reindeer.

    In the Tuc d'Audoubert cave, an 18-inch clay statue of two bison sculpted in relief was discovered in the deepest room, now known as the Room of the Bisons.[8]

    Examples of Magdalenian portable art include batons, figurines, and intricately engraved projectile points, as well as items of personal adornment including sea shells, perforated carnivore teeth (presumably necklaces), and fossils.

    Cave sites such as Lascaux contain the best known examples of Magdalenian cave art. The site of Altamira in Spain, with its extensive and varied forms of Magdalenian mobiliary art has been suggested to be an agglomeration site where groups of Magdalenian hunter-gatherers congregated.[9]

    Gallery

    Treatment of the dead

    Some skulls were cleaned of soft tissues, then had the facial regions removed, with the remaining brain case retouched, possibly to make the broken edges more regular. This manipulation suggests the shaping of skulls to produce skull cups.[10]

    Genetics

    The genes of seven Magdalenians, the El Miron Cluster in Iberia, have shown close relationship to a population who had lived in Northern Europe some 20,000 years previously. The analyses suggested that 70-80% of the ancestry of these individuals was from the population represented by Goyet Q116-1, associated with the Aurignacian culture of about 35,000 BP, from the Goyet Caves in modern Belgium.[11]

    The three samples of Y-DNA included two samples of haplogroup I and one sample of HIJK. All samples of mtDNA belonged to U, including five samples of U8b and one sample of U5b.

    See also

    Preceded by Magdalenian
    17,000–9,000 BP     		Succeeded by
    The Paleolithic
    ↑ Pliocene (before Homo)

    Lower Paleolithic
     (c. 3.3 Ma – 300 ka)

    Middle Paleolithic
     (c. 300–50 ka)

    Upper Paleolithic
     (c. 50–12 ka)

    Fertile Crescent:

    Europe:

    Africa:

    Siberia:

    ↓ Mesolithic

    References

    Notes


    1. Dates given vary somewhat.[1][2]

    Footnotes


  • "The Magdalenian". Les Eyzies Tourist Info. Retrieved 2019-09-28.

  • Enloe 2001.

  • de Sonneville-Bordes & Perrot 1956.

  • "Pincevent; a prehistoric site museum". UNESCO.

  • Hemingway 1980.

  • Housley et al. 1997.

  • Charles 1996.

  • <Madeleine Muzdakis> (January 26, 2021). "15,000-Year-Old Bison Sculptures Are Perfectly Preserved in a French Cave". My Modern Met. Retrieved January 29, 2021.

  • Conkey et al. 1980.

  • Bello, Silvia M.; Parfitt, Simon A.; Stringer, Chris B.; Petraglia, Michael (16 February 2011). "Earliest Directly-Dated Human Skull-Cups". PLOS ONE. 6 (2): e17026. Bibcode:2011PLoSO...617026B. doi:10.1371/journal.pone.0017026. PMC 3040189. PMID 21359211.

    1. Fu et al. 2016.

    Bibliography

    External links

    Wikimedia Commons has media related to Magdalenian.

    Farming
    Food processing
    Hunting
    Projectile points
    Systems
    Toolmaking
    Other tools


     

     https://en.wikipedia.org/wiki/Magdalenian

     Knapping is the shaping of flint, chert, obsidian, or other conchoidal fracturing stone through the process of lithic reduction to manufacture stone tools, strikers for flintlock firearms, or to produce flat-faced stones for building or facing walls, and flushwork decoration. The original Germanic term knopp meant to strike, shape, or work, so it could theoretically have referred equally well to making statues or dice. Modern usage is more specific, referring almost exclusively to the hand-tool pressure-flaking process pictured. It is distinguished from the more general verb "chip" (to break up into small pieces, or unintentionally break off a piece of something) and is different from "carve" (removing only part of a face), and "cleave" (breaking along a natural plane). 

    https://en.wikipedia.org/wiki/Knapping

     

    Flint jewelry was known in the prehistoric, protodynastic, and early dynastic periods of ancient Egypt. Ancient Egyptians skillfully made bracelets[1][2] and armlets[3][4] out of flint.

    The flint came from locations that include Giza and Upper Egypt.[5] The exact technique used to form rings is not known, but there are several theories based on the examples that have been found in graves and workshops.

    Flint bracelets can be found in collections such as those in the Cairo Museum of Egyptian Antiquities,[6] the Fitzwilliam Museum,[7] the Pitt Rivers Museum,[8] the Metropolitan Museum of Art,[9] and the Brooklyn Museum.[10]

    See also

    References

     

  • Graves-Brown, Carolyn (2010). "AB29 Flint bracelet". Egypt Centre. Swansea University. Archived from the original on 19 March 2012. Retrieved 11 June 2012.

  • Capart, Jean (2010). Primitive Art in Egypt. Forgotten Books. pp. 49–51. ISBN 9781451000009.

  • Petrie, W. M. Flinders (2003). Arts and Crafts of Ancient Egypt. p. 81. ISBN 9780766128347.

  • "Notes and News: The Burnt House at Siitagroi During the summer of 1968 and 1969". Antiquity. 44 (174): 131–148. June 1970. ISSN 0003-598X. OCLC 1481624.(subscription required)

  • Pawlik, Alfred F. (13–17 September 1999). "The Lithic industry of the Pharaonic site Kom al-Ahmar in Middle Egypt and its relationship to the flint mines of the Wadi al-Sheikh" (PDF). In Weisgerber, Gerd (ed.). Stone Age – Mining Age. Proceedings of the VIII International Flint Symposium. Bochum, Germany. pp. 240–206. Archived from the original (PDF) on 11 June 2007. Retrieved 11 June 2012.

  • Thomas, Ernest S. (December 2006). "Short Guide to the Chief Exhibits of the Cairo Museum of Antiquities (Electronic Edition)". Rice University. Retrieved 11 June 2012.

  • "Flint bracelet". Fitzwilliam Museum. University of Cambridge. Archived from the original on 16 January 2014. Retrieved 11 June 2012.

  • Asbury, Beth. "Rethinking Pitt-Rivers". Pitt Rivers Museum. University of Oxford. Retrieved 11 June 2012.

  • "Flint bracelet". Metropolitan Museum of Art. Retrieved 11 June 2012.

    1. "Flint bracelet". Brooklyn Museum. Retrieved 11 June 2012.


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