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| {{Redirect|Eutectic|the sports mascot|St. Louis College of Pharmacy#Mascot}}
| | Name: Glenna Blake<br>My age: 25<br>Country: Netherlands<br>Town: Giessenburg <br>Post code: 3381 Db<br>Address: Liesveld 54<br><br>Also visit my homepage - [http://hemorrhoidtreatmentfix.com/prolapsed-hemorrhoid prolapsed internal hemorrhoids] |
| [[File:Eutectic system phase diagram.svg|thumb|350px|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.)]]
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| A '''eutectic system''' is a [[mixture]] of chemical compounds or elements that have a single [[chemical composition]] that [[solidification|solidifies]] at a lower temperature than any other composition made up of the same ingredients. This composition is known as the ''eutectic composition'' and the temperature at which it solidifies is known as the ''eutectic temperature''.
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| On a [[phase diagram]] the [[Intersection (set theory)|intersection]] of the eutectic temperature and the eutectic composition gives the ''eutectic point''.<ref>{{harvnb|Smith|Hashemi|2006|pp=326–327}}.</ref> Non-eutectic mixtures will display solidification of one component of the mixture before the other. Not all [[binary alloy]]s have a eutectic point; for example, in the silver-gold system the melt temperature ([[liquidus]]) and freeze temperature ([[solidus (chemistry)|solidus]]) both increase [[Monotonic function|monotonically]] as the mix changes from pure silver to pure gold.<ref>http://www.crct.polymtl.ca/fact/phase_diagram.php?file=Ag-Au.jpg&dir=SGTE</ref>
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| ==Eutectic reaction==
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| [[File:Various eutectic structures.png|thumb|Four eutectic structures: A) lamellar B) rod-like C) globular D) acicular.]]
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| The eutectic reaction is defined as follows:<ref name="smith327">{{harvnb|Smith|Hashemi|2006|p=327}}.</ref>
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| :<math>\text{Liquid} \xrightarrow[\text{cooling}]{\text{eutectic temperature}} \alpha \,\, \text{solid solution} + \beta \,\, \text{solid solution}</math> | |
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| This type of reaction is an [[invariant reaction]], because it is in [[thermal equilibrium]]; another way to define this is the [[Gibbs free energy]] equals zero. Tangibly, this means the liquid and two [[solid solution]]s 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.<ref name="smith327"/>
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| The resulting solid [[macrostructure]] from a eutectic reaction depends on a few factors. The most important factor is 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 (crystal habit)|acicular]].<ref>{{harvnb|Smith|Hashemi|2006|pp=332–333}}.</ref>
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| ==Non-eutectic compositions==
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| Compositions of eutectic systems that are not the eutectic composition are called either ''hypoeutectic'' or ''hypereutectic''. Hypoeutectic compositions are those to the left of the eutectic composition while hypereutectic compositions are those to the right. As the temperature of a non-eutectic composition is lowered the liquid mixture will precipitate one component of the mixture before the other.<ref name="smith327"/>
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| ==Types==
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| ===Alloys===
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| Eutectic [[alloy]]s 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.
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| Some uses include:
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| *Eutectic alloys for [[soldering]], composed of [[tin]] (Sn), [[lead]] (Pb) and sometimes [[silver]] (Ag) or [[gold]] (Au) — especially [[Solder#Solder alloys|Sn{{sub|63}}Pb{{sub|37}}]] alloy formula for electronics
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| *Casting alloys, such as [[aluminium]]-[[silicon]] and [[cast iron]] (at the composition of 4.3% carbon in iron producing an [[austenite]]-[[cementite]] eutectic)
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| *[[Silicon chip]]s are bonded to gold-plated substrates through a silicon-gold eutectic by the application of [[ultrasound|ultrasonic]] energy to the chip. See [[eutectic bonding]].
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| *[[Brazing]], where diffusion can remove alloying elements from the joint, so that eutectic melting is only possible early in the brazing process
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| *Temperature response, e.g., [[Wood's metal]] and [[Field's metal]] for [[fire sprinkler]]s
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| *Non-toxic [[Mercury (element)|mercury]] replacements, such as [[galinstan]]
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| *Experimental [[amorphous metal|glassy metals]], with extremely high strength and [[corrosion]] resistance
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| *Eutectic alloys of [[sodium]] and [[potassium]] ([[NaK]]) that are liquid at room temperature and used as [[coolant]] in experimental [[Fast neutron reactor|fast neutron nuclear reactor]]s.
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| ===Others===
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| * [[Sodium chloride]] and [[water]] form a eutectic mixture whose eutectic point is −21.2˚C<ref>{{cite web | last = Muldrew | first = Ken | coauthors = Locksley E. McGann | year = 1997 | url = http://www.ucalgary.ca/~kmuldrew/cryo_course/cryo_chap6_1.html | title = Phase Diagrams | work = Cryobiology—A Short Course | publisher = University of Calgary | accessdate = 2006-04-29}}</ref> and 23.3% salt by mass.<ref>{{cite web | last = Senese | first = Fred | year = 1999 | url = http://antoine.frostburg.edu/chem/senese/101/solutions/faq/saltwater-ice-volume.shtml | title = Does salt water expand as much as fresh water does when it freezes? | work = Solutions: Frequently asked questions | publisher = Department of Chemistry, Frostburg State University | accessdate = 2006-04-29}}</ref> 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).
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| * Ethanol–water has an unusually biased{{huh|date=November 2013}} eutectic point. [[File:Phase diagram ethanol water s l en.svg|thumb|Solid-liquid phase change of ethanol water mixtures]]
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| * "Solar salt", 60% NaNO<sub>3</sub> and 40% KNO<sub>3</sub>, forms a eutectic molten salt mixture which is used for [[thermal energy storage]] in [[concentrated solar power]] plants.<ref>{{cite web|title=Molten salts properties|url=http://www.archimedesolarenergy.com/molten_salt.htm|work=Archimede Solar Plant Specs}}</ref> To reduce the eutectic melting point in the solar molten salts [[calcium nitrate]] is used in the following proportion: 42% Ca(NO<sub>3</sub>)<sub>2</sub>, 43% KNO<sub>3,</sub> and 15% NaNO<sub>3</sub>.
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| * [[Lidocaine]] and [[prilocaine|prilocaine—]]<nowiki/>both are solids at room temperature—form a eutectic that is an oil with a {{convert|16|C|abbr=on}} melting point that is used in [[eutectic mixture of local anesthetic]] (EMLA) preparations.
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| * [[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.{{clarification needed|date=November 2013}}{{citation needed|date=November 2013}}
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| * [[Mineral]]s may form eutectic mixtures in [[igneous]] rocks, giving rise to characteristic [[Rock microstructure#Graphic and other intergrowth textures|intergrowth textures]] exhibited by [[granophyre]].<ref>{{cite web | last = Fichter | first = Lynn S. | year = 2000 | url = http://csmres.jmu.edu/geollab/Fichter/IgnRx/Phasdgrm.html | title = Igneous Phase Diagrams | work = Igneous Rocks | publisher = James Madison University | accessdate = 2006-04-29}}</ref>
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| * Some inks are eutectic mixtures, allowing [[inkjet printer]]s to operate at lower temperatures.<ref>{{cite web | last = Davies | first = Nicholas A. | coauthors = Beatrice M. Nicholas | year = 1992 | url = http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=/netahtml/search-bool.html&r=1&f=G&l=50&co1=AND&d=ptxt&s1=5298062.WKU.&OS=PN/5298062&RS=PN/5298062 | title = Eutectic compositions for hot melt jet inks | work = US Patent & Trademark Office, Patent Full Text and Image Database | publisher = United States Patent and Trademark Office | accessdate = 2006-04-29}}</ref>
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| == Other critical points==
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| ===Eutectoid===
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| [[File:Steel pd.svg|thumb|right|300px|Iron-carbon phase diagram, showing the eutectoid transformation between austenite (γ) and pearlite.]]
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| 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 (iron)|ferrite]] and cementite, often in lamellar structures such as [[pearlite]] and [[bainite]]. This eutectoid point occurs at {{convert|727|C|abbr=on}} and about 0.76% carbon.<ref>[http://www.sv.vt.edu/classes/MSE2094_NoteBook/96ClassProj/examples/kimcon.html Iron-Iron Carbide Phase Diagram Example<!-- Bot generated title -->]</ref>
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| ===Peritectoid===
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| A ''peritectoid'' transformation is a type of [[isothermal]] [[reversible reaction]] that have two solid [[Phase (matter)|phase]]s reacting with each other upon cooling of a binary, ternary, ..., <math>n\!</math> [[alloy]] to create a completely different and single solid phase.<ref name="Gold Book PAC,1994,66,588">IUPAC Compendium of Chemical Terminology, Electronic version. [http://goldbook.iupac.org/P04501.html "Peritectoid Reaction"] Retrieved May 22, 2007.</ref> The reaction plays a key role in the order and [[decomposition]] of [[quasicrystalline]] phases in several alloy types.<ref>Numerical Model of Peritectoid Transformation. [http://doc.tms.org/ezMerchant/prodtms.nsf/ProductLookupItemID/MMTA-9910-2563/$FILE/MMTA-9910-2563F.pdf?OpenElement Peritectoid Transformation] Retrieved May 22, 2007. {{Dead link|date=October 2013}}</ref>
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| ===Peritectic===
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| 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.
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| 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 {{convert|1495|C|abbr=on}} and 0.17% carbon.
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| [[File:Phasendiagramm Gold-Aluminium.svg|right|300px|thumb|Gold-aluminium [[phase diagram]] (German). Top axis title reads "Weight-percent Gold", lower axis title reads "Atomic-percent Gold"]]
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| Peritectic decomposition. Up to this point in the discussion transformations have been addressed from the point of view of cooling. They also can be discussed noting the changes that occur to some solid [[chemical compounds]] as they are heated. Rather than melting, at the peritectic decomposition temperature, the compound decomposes into another solid compound and a liquid. The proportion of each is determined by the [[lever rule]]. The vocabulary changes slightly. Just as the cooling of water, which leads to [[ice]], is termed [[freezing]], the warming of ice leads to [[melting]]. In the [[Gold-aluminium intermetallic|Al-Au]] phase diagram, for example, it can be seen that only two of the phases melt congruently, [[Gold-aluminium intermetallic|AuAl<sub>2</sub>]] and [[Gold-aluminium intermetallic|Au<sub>2</sub>Al]]. The rest peritectically decompose.
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| ==Eutectic calculation==
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| The composition and temperature of a eutectic can be calculated from enthalpy and entropy of fusion of each components.<ref>International Journal of Modern Physics C, Vol. 15, No. 5. (2004), pp. 675-687</ref>
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| The free Gibbs enthalpy G depends
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| on its own differential by Eq.
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| <math>
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| G = H - TS \Rightarrow {\left\{
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| \begin{array}{l}
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| H = G + TS \\
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| \\
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| {\left( {\frac{\partial G}{\partial T}} \right)_P = - S}
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| \end{array}
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| \right.}
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| \Rightarrow H = G - T\left( {\frac{\partial G}{\partial T}}
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| \right)_P .
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| </math>
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| Thus, the G/T derivative at constant pressure is calculated by
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| equation Eq.
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| <math>
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| \left( {\frac{\partial G / T}{\partial T}} \right)_P
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| =
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| \frac{1}{T}\left( {\frac{\partial G}{\partial T}} \right)_P - \frac{1}{T^{2}}G
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| =
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| - \frac{1}{T^{2}}\left( {G - T\left({\frac{\partial G}{\partial T}} \right)_P
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| } \right)
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| = - \frac{H}{T^{2}}
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| </math>
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| The chemical potential <math>\mu _{i}</math> is calculated if we assume the activity is equal to the
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| concentration we suppose the activity equal to the concentration.
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| <math>
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| \mu _i = \mu _i^\circ + RT\ln \frac{a_i}{a} \approx \mu _i^\circ +
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| RT\ln x_i
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| </math>
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| At the equilibrium, <math>\mu_i =0</math>, thus <math>\mu_i^\circ</math> is obtained by:
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| <math>
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| \mu _i = \mu _i^\circ + RT\ln x_i = 0 \Rightarrow \mu _i^\circ = -
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| RT\ln x_i.
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| </math>
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| Using and integrating gives Eq.
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| <math>\begin{array}{l}
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| \left( {\frac{\partial \mu _i / T}{\partial T}} \right)_P = \frac{\partial
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| }{\partial T}\left( {R\ln x_i } \right) \Rightarrow R\ln x_i = -
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| \frac{H_i
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| ^\circ }{T} + K \\
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| \\
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| \end{array}
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| </math>
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| The integration constant K may be determined for a pure
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| component with a melting temperature <math>T^\circ</math> and an enthalpy of
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| fusion <math>H^\circ</math> Eq.
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| <math>
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| x_i = 1 \Rightarrow T = T_i^\circ \Rightarrow K = \frac{H_i^\circ
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| }{T_i^\circ }
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| </math>
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| We obtain a relation that determines
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| the molar fraction as a function of the temperature for each
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| component.
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| <math>
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| R\ln x_i = - \frac{H_i ^\circ }{T} + \frac{H_i^\circ }{T_i^\circ }
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| </math>
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| The mixture of n components is described by the system
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| <math>
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| \begin{array}{l}
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| \left\{ {{\begin{array}{*{20}c}
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| {\ln x_i + \frac{H_i ^\circ }{RT} - \frac{H_i^\circ }{RT_i^\circ } =
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| 0} \\
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| {\sum\limits_{i = 1}^n {x_i = 1} } \\
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| \end{array} }} \right. \\
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| \\
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| \end{array}
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| </math>
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| <math>
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| \begin{array}{l}
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| \left\{ {{\begin{array}{*{20}c}
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| {\forall i < n \Rightarrow \ln x_i + \frac{H_i ^\circ }{RT} -
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| \frac{H_i^\circ }{RT_i^\circ } = 0} \\
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| {\ln \left( {1 - \sum\limits_{i = 1}^{n - 1} {x_i } } \right) +
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| \frac{H_n
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| ^\circ }{RT} - \frac{H_n^\circ }{RT_n^\circ } = 0} \\
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| \end{array} }} \right. \\
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| \\
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| \end{array}
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| </math>
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| that can be solved by
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| <math>
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| \begin{array}{c}
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| \left[ {{\begin{array}{*{20}c}
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| {\Delta x_1 } \\
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| {\Delta x_2 } \\
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| {\Delta x_3 } \\
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| \vdots \\
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| {\Delta x_{n - 1} } \\
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| {\Delta T} \\
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| \end{array} }} \right] = \left[ {{\begin{array}{*{20}c}
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| {1 / x_1 } & 0 & 0 & 0 & 0 & { - \frac{H_1^\circ }{RT^{2}}} \\
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| 0 & {1 / x_2 } & 0 & 0 & 0 & { - \frac{H_2^\circ }{RT^{2}}} \\
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| 0 & 0 & {1 / x_3 } & 0 & 0 & { - \frac{H_3^\circ }{RT^{2}}} \\
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| 0 & 0 & 0 & \ddots & 0 & { - \frac{H_4^\circ }{RT^{2}}} \\
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| 0 & 0 & 0 & 0 & {1 / x_{n - 1} } & { - \frac{H_{n - 1}^\circ }{RT^{2}}}
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| \\
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| {\frac{ - 1}{1 - \sum\limits_{1 = 1}^{n - 1} {x_i } }} & {\frac{ - 1}{1 -
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| \sum\limits_{1 = 1}^{n - 1} {x_i } }} & {\frac{ - 1}{1 -
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| \sum\limits_{1 = 1}^{n - 1} {x_i } }} & {\frac{ - 1}{1 -
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| \sum\limits_{1 = 1}^{n - 1} {x_i } }} & {\frac{ - 1}{1 -
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| \sum\limits_{1 = 1}^{n - 1} {x_i } }} & { -
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| \frac{H_n^\circ }{RT^{2}}} \\
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| \end{array} }} \right]^{ - 1}
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| .\left[ {{\begin{array}{*{20}c}
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| {\ln x_1 + \frac{H_1 ^\circ }{RT} - \frac{H_1^\circ }{RT_1^\circ }}
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| \\
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| {\ln x_2 + \frac{H_2 ^\circ }{RT} - \frac{H_2^\circ }{RT_2^\circ }}
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| \\
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| {\ln x_3 + \frac{H_3 ^\circ }{RT} - \frac{H_3^\circ }{RT_3^\circ }}
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| \\
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| \vdots \\
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| {\ln x_{n - 1} + \frac{H_{n - 1} ^\circ }{RT} - \frac{H_{n - 1}^\circ
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| }{RT_{n - 1i}^\circ }} \\
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| {\ln \left( {1 - \sum\limits_{i = 1}^{n - 1} {x_i } } \right) + \frac{H_n
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| ^\circ }{RT} - \frac{H_n^\circ }{RT_n^\circ }} \\
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| \end{array} }} \right]
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| \end{array}
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| </math>
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| ==See also==
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| *[[Azeotrope]], constant boiling mixture
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| *[[Freezing-point depression]]
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| ==References==
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| {{Reflist}}
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| ===Bibliography===
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| *{{Citation | last = Smith | first = William F. | last2 = Hashemi | first2 = Javad | title = Foundations of Materials Science and Engineering | edition = 4th | year = 2006 | publisher = McGraw-Hill | isbn = 0-07-295358-6 | postscript =.}}
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| ==Further reading==
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| {{Wiktionary|eutectic}}
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| *{{cite book
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| | last = Askeland
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| | first = Donald R.
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| | coauthors = Pradeep P. Phule
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| | year = 2005
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| | title = The Science and Engineering of Materials
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| | publisher = Thomson-Engineering
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| | isbn = 0-534-55396-6
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| }}
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| *{{cite book
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| | last = Easterling
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| | first = Edward
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| | year = 1992
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| | title = Phase Transformations in Metals and Alloys
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| | publisher = CRC
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| | isbn = 0-7487-5741-4
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| }}
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| *{{cite book
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| | last = Mortimer
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| | first = Robert G.
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| | year = 2000
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| | title = Physical Chemistry
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| | publisher = Academic Press
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| | isbn = 0-12-508345-9
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| }}
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| *{{cite book
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| | last = Reed-Hill
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| | first = R.E.
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| | authorlink =
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| | coauthors = Reza Abbaschian
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| | year = 1992
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| | title = Physical Metallurgy Principles
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| | publisher =Thomson-Engineering
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| | isbn = 0-534-92173-6
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| }}
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| *{{cite web
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| | last = Sadoway
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| | first = Donald
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| | year = 2004
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| | url = http://ocw.mit.edu/NR/rdonlyres/Materials-Science-and-Engineering/3-091Fall-2004/6ECFB930-9D59-4DD5-A872-FE48002587B0/0/notes_10.pdf
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| | title = Phase Equilibria and Phase Diagrams
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| | format = pdf
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| | work = 3.091 Introduction to Solid State Chemistry, Fall 2004
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| | publisher = MIT Open Courseware
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| | accessdate = 2006-04-12
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| | authorlink = Donald Sadoway
| |
| |archiveurl = http://web.archive.org/web/20051020162911/http://ocw.mit.edu/NR/rdonlyres/Materials-Science-and-Engineering/3-091Fall-2004/6ECFB930-9D59-4DD5-A872-FE48002587B0/0/notes_10.pdf <!-- Bot retrieved archive --> |archivedate = 2005-10-20}}
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| [[Category:Metallurgy]]
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| [[Category:Geochemistry]]
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| [[Category:Phase transitions]]
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