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{{redirect|Eutectic|the sports mascot|St. Louis College of Pharmacy#Mascot}}
[[File:Eutectic system phase diagram.svg|thumb|upright=1.4|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''' ({{IPAc-en|j|uː|ˈ|t|ɛ|k|t|ɪ|k}} {{respell|yoo|TEK|tik}})<ref>{{MerriamWebsterDictionary|eutectic}}</ref> from the Greek "εύ" (eu = well) and "τήξις" (tēxis = melting) is a homogeneous mixture of substances that melts or solidifies at a single temperature that is lower than the melting point of either of the constituents.<ref>{{Cite journal|last=Guthrie|first=F.|date=1884|title=On Eutexia|url=https://zenodo.org/record/2390124/files/article.pdf|journal=Physical Society|volume=|pages=462–482|via=}}</ref>

The eutectic temperature is the lowest possible melting temperature over all of the mixing ratios for the involved component species.

Upon heating any other mixture ratio, and reaching the eutectic temperature – see the adjacent [[phase diagram]] – one component's lattice will melt first, while the temperature of the mixture has to further increase for (all) the other component lattice(s) to melt.   Conversely, as a non-eutectic mixture cools down, each mixture's component will solidify (form its lattice) at a distinct temperature, until all material is solid.

The coordinates defining a ''eutectic point'' on a [[phase diagram]] are the ''eutectic percentage ratio'' (on the [[Phase diagram|atomic/molecular ratio]] [[Abscissa|axis]] of the diagram) and the ''eutectic temperature'' (on the [[temperature]] [[Ordinate|axis]] of the diagram).<ref>{{harvnb|Smith|Hashemi|2006|pp=326–327}}</ref>

Not all [[binary alloy]]s have eutectic points because the [[valence electron]]s of the component species are not always compatible,{{clarify|compatible electrons?|date=November 2014}} 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 (chemistry)|solidus]]) "meet at the pure element endpoints of the atomic ratio axis while slightly separating in the mixture region of this axis".<ref>{{cite web|url=http://www.crct.polymtl.ca/fact/phase_diagram.php?file=Ag-Au.jpg&dir=SGTE2007|title=Collection of Phase Diagrams|website=www.crct.polymtl.ca}}</ref>

The term {{em|eutectic}} was coined in 1884 by British physicist and chemist [[Frederick Guthrie]] (1833–1886).<ref>Guthrie, Frederick (1884) "On eutexia", ''Philosophical Magazine'', 5th series, '''17''' :  462–482.  [https://babel.hathitrust.org/cgi/pt?id=mdp.39015024088166;view=1up;seq=480 From p. 462:]  "The main argument of the present communication hinges upon the existence of compound bodies, whose chief characteristic is the lowness of their temperatures of fusion.  This property of the bodies may be called Eutexia †, the bodies possessing it eutectic bodies or eutectics (''εύ τήκειν'')."</ref>

==Eutectic phase transition==
[[File:Various eutectic structures.png|thumb|Four eutectic structures: A) lamellar B) rod-like C) globular D) acicular.]]

The eutectic solidification is defined as follows:<ref name="smith327">{{harvnb|Smith|Hashemi|2006|p=327}}.</ref>

:<math>\text{Liquid} \xrightarrow[\text{cooling}]{\text{eutectic temperature}} \alpha \,\, \text{solid solution} + \beta \,\, \text{solid solution}</math>

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 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"/>

The resulting solid [[wikt:macrostructure|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>

==Non-eutectic compositions==
Compositions of eutectic systems that are not at the eutectic composition 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.<ref name="smith327"/>

==Types==

===Alloys===
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.

Some uses include:
*NEMA Eutectic Alloy Overload Relays for [[power-system protection|electrical protection]] of 3-phase motors for pumps, fans, conveyors, and other factory process equipment.<ref>{{cite web |url= http://www.industrial-electronics.com/output_devices_amplifiers_valves_relays_variable-frequency_drives_stepper_motors_servomotors/Operation_Overloads.html |title= Operation of the Overloads |accessdate= 2015-08-05 }}</ref>
*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
*Casting alloys, such as [[Silumin|aluminium-silicon]] and [[cast iron]] (at the composition of 4.3% carbon in iron producing an [[austenite]]-[[cementite]] eutectic)
*[[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]].
*[[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 sprinkler]]s
*Non-toxic [[Mercury (element)|mercury]] replacements, such as [[galinstan]]
*Experimental [[amorphous metal|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 reactor|fast neutron nuclear reactor]]s.

===Others===
[[File:Phase diagram ethanol water s l en.svg|thumb|upright=1.3|Solid–liquid phase change of ethanol–water mixtures]]
* [[Sodium chloride]] and [[water]] form a eutectic mixture whose eutectic point is −21.2&nbsp;°C<ref>{{cite web | last = Muldrew | first = Ken |author2=Locksley E. McGann | year = 1997 | url = https://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).
* 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% 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>.
* [[Lidocaine]] and [[prilocaine]]—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.
* [[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.<ref>{{Cite journal |last=Phaechamud |first=Thawatchai |last2=Tuntarawongsa |first2=Sarun |last3=Charoensuksai |first3=Purin |date=October 2016 |title=Evaporation Behavior and Characterization of Eutectic Solvent and Ibuprofen Eutectic Solution |journal=AAPS PharmSciTech |volume=17 |issue=5 |pages=1213–1220 |doi=10.1208/s12249-015-0459-x |issn=1530-9932 |pmid=26669887}}</ref>
* [[Mineral]]s may form eutectic mixtures in [[igneous]] rocks, giving rise to characteristic [[Rock microstructure#Graphic and other intergrowth textures|intergrowth textures]] exhibited, for example, 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>
* Some inks are eutectic mixtures, allowing [[inkjet printer]]s to operate at lower temperatures.<ref>{{cite web | last = Davies | first = Nicholas A. |author2=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>

== Other critical points==
[[File:Iron carbon phase diagram.svg|thumb|upright=1.75|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 [[Allotropes of 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>{{cite web|url=http://www.sv.vt.edu/classes/MSE2094_NoteBook/96ClassProj/examples/kimcon.html|title=Iron-Iron Carbide Phase Diagram Example<!-- Bot generated title -->|url-status=dead|archiveurl=https://web.archive.org/web/20080216023642/http://www.sv.vt.edu/classes/MSE2094_NoteBook/96ClassProj/examples/kimcon.html|archivedate=2008-02-16}}</ref>

===Peritectoid===
A ''peritectoid'' transformation is a type of [[isothermal]] [[reversible reaction]] that has two solid [[Phase (matter)|phase]]s reacting with each other upon cooling of a binary, ternary, ..., <math>n\!</math>-ary [[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/$FILE/MMTA-9910-2563F.pdf?OpenElement Peritectoid Transformation] Retrieved May 22, 2007.  {{webarchive |url=https://web.archive.org/web/20070928024906/http://doc.tms.org/ezMerchant/prodtms.nsf/ProductLookupItemID/MMTA-9910-2563/$FILE/MMTA-9910-2563F.pdf?OpenElement |date=September 28, 2007 }}</ref>

===Peritectic===
[[File:Phasendiagramm Gold-Aluminium.svg|upright=1.25|thumb|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 {{convert|1495|C|abbr=on}} 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 [[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]] , 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.<ref>International Journal of Modern Physics C, Vol. 15, No. 5. (2004), pp. 675–687.</ref>

The Gibbs free energy ''G'' depends on its own differential:
: <math>
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.
</math>

Thus, the ''G''/''T'' derivative at constant pressure is calculated by the following equation:
: <math>
    \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}.
</math>

The chemical potential <math>\mu_i</math> is calculated if we assume that the activity is equal to the concentration:
: <math>
\mu_i = \mu_i^\circ + RT\ln \frac{a_i}{a} \approx \mu_i^\circ + RT\ln x_i.
</math>

At the equilibrium, <math>\mu_i = 0</math>, thus <math>\mu_i^\circ</math> is obtained as
: <math>
\mu _i = \mu _i^\circ + RT\ln x_i = 0 \Rightarrow \mu_i^\circ = -RT\ln x_i.
</math>

Using{{what?|date=January 2019}} and integrating gives
: <math>
 \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.
</math>

The integration constant ''K'' may be determined for a pure component with a melting temperature <math>T^\circ</math> and an enthalpy of fusion <math>H^\circ</math>:
: <math>
x_i = 1 \Rightarrow T = T_i^\circ \Rightarrow K = \frac{H_i^\circ}{T_i^\circ}.
</math>

We obtain a relation that determines the molar fraction as a function of the temperature for each component:
: <math>
R\ln x_i = -\frac{H_i^\circ}{T} + \frac{H_i^\circ}{T_i^\circ}.
</math>

The mixture of ''n'' components is described by the system
: <math>
\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}
</math>
: <math>
\begin{cases}
 \forall i < n \Rightarrow \ln x_i + \frac{H_i^\circ}{RT} - \frac{H_i^\circ}{RT_i^\circ} = 0, \\
 \ln \left(1 - \sum\limits_{i = 1}^{n - 1} x_i\right) + \frac{H_n^\circ}{RT} - \frac{H_n^\circ}{RT_n^\circ} = 0, 
\end{cases}
</math>

which can be solved by
: <math>
\begin{array}{c}
\left[ {{\begin{array}{*{20}c}
 {\Delta x_1 } \\
 {\Delta x_2 } \\
 {\Delta x_3 } \\
 \vdots \\
 {\Delta x_{n - 1} } \\
 {\Delta T} \\
\end{array} }} \right] = \left[ {{\begin{array}{*{20}c}
 {1 / x_1 } & 0 & 0 & 0 & 0 & { - \frac{H_1^\circ }{RT^{2}}} \\
 0 & {1 / x_2 } & 0 & 0 & 0 & { - \frac{H_2^\circ }{RT^{2}}} \\
 0 & 0 & {1 / x_3 } & 0 & 0 & { - \frac{H_3^\circ }{RT^{2}}} \\
 \vdots & \ddots & \ddots & \ddots & \ddots & { \vdots} \\
 0 & 0 & 0 & 0 & {1 / x_{n - 1} } & { - \frac{H_{n - 1}^\circ }{RT^{2}}}
\\
 {\frac{ - 1}{1 - \sum\limits_{i = 1}^{n - 1} {x_i } }} & {\frac{ - 1}{1 -
\sum\limits_{i = 1}^{n - 1} {x_i } }} & {\frac{ - 1}{1 -
\sum\limits_{i = 1}^{n - 1} {x_i } }} & {\frac{ - 1}{1 -
\sum\limits_{i = 1}^{n - 1} {x_i } }} & {\frac{ - 1}{1 -
\sum\limits_{i = 1}^{n - 1} {x_i } }} & { -
\frac{H_n^\circ }{RT^{2}}} \\
\end{array} }} \right]^{ - 1}

.\left[ {{\begin{array}{*{20}c}
 {\ln x_1 + \frac{H_1 ^\circ }{RT} - \frac{H_1^\circ }{RT_1^\circ }}
\\
 {\ln x_2 + \frac{H_2 ^\circ }{RT} - \frac{H_2^\circ }{RT_2^\circ }}
\\
 {\ln x_3 + \frac{H_3 ^\circ }{RT} - \frac{H_3^\circ }{RT_3^\circ }}
\\
 \vdots \\
 {\ln x_{n - 1} + \frac{H_{n - 1} ^\circ }{RT} - \frac{H_{n - 1}^\circ
}{RT_{n - 1}^\circ }} \\
 {\ln \left( {1 - \sum\limits_{i = 1}^{n - 1} {x_i } } \right) + \frac{H_n
^\circ }{RT} - \frac{H_n^\circ }{RT_n^\circ }} \\
\end{array} }} \right]
 \end{array}
</math>

==See also==
*[[Azeotrope]], or constant boiling mixture
*[[Freezing-point depression]]

==References==
{{Reflist}}

===Bibliography===
*{{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 = 978-0-07-295358-9 | postscript =.}}

==Further reading==
{{Wiktionary|eutectic}}

*{{cite book
 | last = Askeland
 | first = Donald R.
 |author2=Pradeep P. Phule
 | year = 2005
 | title = The Science and Engineering of Materials
 | publisher = Thomson-Engineering
 | isbn = 978-0-534-55396-8
}}
*{{cite book
 | last = Easterling
 | first = Edward
 | year = 1992
 | title = Phase Transformations in Metals and Alloys
 | publisher = CRC
 | isbn = 978-0-7487-5741-1
}}
*{{cite book
 | last = Mortimer
 | first = Robert G.
 | year = 2000
 | title = Physical Chemistry
 | publisher = Academic Press
 | isbn = 978-0-12-508345-4
}}
*{{cite book
 | last = Reed-Hill
 | first = R. E.
 | authorlink =
 |author2=Reza Abbaschian
 | year = 1992
 | title = Physical Metallurgy Principles
 | publisher =Thomson-Engineering
 | isbn = 978-0-534-92173-6
| author2-link = Reza Abbaschian
 }}
*{{cite web
 |last=Sadoway 
 |first=Donald 
 |year=2004 
 |url=http://ocw.mit.edu/NR/rdonlyres/Materials-Science-and-Engineering/3-091Fall-2004/6ECFB930-9D59-4DD5-A872-FE48002587B0/0/notes_10.pdf 
 |title=Phase Equilibria and Phase Diagrams 
 |work=3.091 Introduction to Solid State Chemistry, Fall 2004 
 |publisher=MIT Open Courseware 
 |accessdate=2006-04-12 
 |authorlink=Donald Sadoway 
 |archiveurl=https://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 
 |archivedate=2005-10-20 
 |url-status=dead 
}}

{{Chemical solutions}}

[[Category:Materials science]]
[[Category:Chemistry]]
[[Category:Phase transitions]]