Eutectic system
A eutectic system (US dict: )^{[1]} from the Greek "ευ" (eu = easy) and "Τήξις" (tecsis = melting) describes a homogeneous solid mix of atomic and/or chemical species, to form a joint superlattice, by striking a unique atomic percentage ratio between the components — as each pure component has its own distinct bulk lattice arrangement. It is only in this atomic/molecular ratio that the eutectic system melts as a whole, at a specific temperature (the eutectic temperature) the superlattice releasing at once all its components into a liquid mixture. 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 phase diagram to the right — 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 noneutectic mixture cools down, each mixture's component will solidify (form its lattice) at a distinct temperature, until all material is solid.
The coordinates defining an eutectic point on a phase diagram are the eutectic percentage ratio (on the atomic/molecular ratio axis of the diagram) and the eutectic temperature (on the temperature axis of the diagram).^{[2]}
Not all binary alloys have eutectic points because the valence electrons of the component species are not always compatible, in any mixing ratio, to form a new type of joint crystal lattice. For example, in the silvergold 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".^{[3]}
Contents
 Eutectic reaction 1
 Noneutectic compositions 2

Types 3
 Alloys 3.1
 Others 3.2

Other critical points 4
 Eutectoid 4.1
 Peritectoid 4.2
 Peritectic 4.3
 Eutectic calculation 5
 See also 6

References 7
 Bibliography 7.1
 Further reading 8
Eutectic reaction
The eutectic reaction is defined as follows:^{[4]}
 \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 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.^{[4]}
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.^{[5]}
Noneutectic 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 noneutectic 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.^{[4]}
Types
Alloys
Eutectic alloys have two or more materials and have a eutectic composition. When a noneutectic alloy solidifies, its components solidify at different temperatures, exhibiting a plastic melting range. Conversely, when a wellmixed, 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 3phase motors for pumps, fans, conveyors, and other factory process equipment.^{[6]}
 Eutectic alloys for soldering, composed of tin (Sn), lead (Pb) and sometimes silver (Ag) or gold (Au) — especially Sn_{63}Pb_{37} alloy formula for electronics
 Casting alloys, such as aluminiumsilicon and cast iron (at the composition of 4.3% carbon in iron producing an austenitecementite eutectic)
 Silicon chips are bonded to goldplated substrates through a silicongold 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
 Nontoxic 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
 Sodium chloride and water form a eutectic mixture whose eutectic point is −21.2˚C^{[7]} and 23.3% salt by mass.^{[8]} 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 distillation (see azeotrope).
 "Solar salt", 60% NaNO_{3} and 40% KNO_{3}, forms a eutectic molten salt mixture which is used for thermal energy storage in concentrated solar power plants.^{[9]} To reduce the eutectic melting point in the solar molten salts calcium nitrate is used in the following proportion: 42% Ca(NO_{3})_{2}, 43% KNO_{3,} and 15% NaNO_{3}.
 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.
 Minerals may form eutectic mixtures in igneous rocks, giving rise to characteristic intergrowth textures exhibited, for example, by granophyre.^{[10]}
 Some inks are eutectic mixtures, allowing inkjet printers to operate at lower temperatures.^{[11]}
Other critical points
Eutectoid
When the solution above the transformation point is solid, rather than liquid, an analogous eutectoid transformation can occur. For instance, in the ironcarbon 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 727 °C (1,341 °F) and about 0.76% carbon.^{[12]}
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\! alloy to create a completely different and single solid phase.^{[13]} The reaction plays a key role in the order and decomposition of quasicrystalline phases in several alloy types.^{[14]}
Peritectic
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 ironcarbon system, as seen near the upperleft 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.
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 AlAu phase diagram, for example, it can be seen that only two of the phases melt congruently, AuAl_{2} and Au_{2}Al. 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.^{[15]}
The Gibbs free energy, G, depends on its own differential
G = H  TS \Rightarrow {\left\{ \begin{array}{l} H = G + TS \\ \\ {\left( {\frac{\partial G}{\partial T}} \right)_P =  S} \end{array} \right.} \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
\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 \mu _{i} is calculated if we assume the activity is equal to the concentration.
\mu _i = \mu _i^\circ + RT\ln \frac{a_i}{a} \approx \mu _i^\circ + RT\ln x_i
At the equilibrium, \mu_i =0, thus \mu_i^\circ is obtained by:
\mu _i = \mu _i^\circ + RT\ln x_i = 0 \Rightarrow \mu _i^\circ =  RT\ln x_i.
Using and integrating gives
\begin{array}{l} \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 \\ \\ \end{array}
The integration constant K may be determined for a pure component with a melting temperature T^\circ and an enthalpy of fusion H^\circ Eq.
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 =  \frac{H_i ^\circ }{T} + \frac{H_i^\circ }{T_i^\circ }
The mixture of n components is described by the system
\begin{array}{l} \left\{ \right. \\ \\ \end{array} \begin{array}{l} \left\{ \right. \\ \\ \end{array}
that can be solved by
\begin{array}{c} \left[ \right] = \left[ } \\ 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}}} \\ 0 & 0 & 0 & \ddots & 0 & {  \frac{H_4^\circ }{RT^{2}}} \\ 0 & 0 & 0 & 0 & {1 / x_{n  1} } & {  \frac{H_{n  1}^\circ }{RT^{2}}} \\ {\frac{  1}{1  \sum\limits_{1 = 1}^{n  1} {x_i } }} & {\frac{  1}{1  \sum\limits_{1 = 1}^{n  1} {x_i } }} & {\frac{  1}{1  \sum\limits_{1 = 1}^{n  1} {x_i } }} & {\frac{  1}{1  \sum\limits_{1 = 1}^{n  1} {x_i } }} & {\frac{  1}{1  \sum\limits_{1 = 1}^{n  1} {x_i } }} & {  \frac{H_n^\circ }{RT^{2}}} \\ \end{array} }} \right]^{  1} .\left[ \\ {\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  1i}^\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}
See also
 Azeotrope, constant boiling mixture
 Freezingpoint depression
References
 ^ MerriamWebster Dictionary eutectic
 ^ Smith & Hashemi 2006, pp. 326–327
 ^ http://www.crct.polymtl.ca/fact/phase_diagram.php?file=AgAu.jpg&dir=SGTE
 ^ ^{a} ^{b} ^{c} Smith & Hashemi 2006, p. 327.
 ^ Smith & Hashemi 2006, pp. 332–333.
 ^ "Operation of the Overloads". Retrieved 20150805.
 ^ Muldrew, Ken; Locksley E. McGann (1997). "Phase Diagrams". Cryobiology—A Short Course. University of Calgary. Retrieved 20060429.
 ^ Senese, Fred (1999). "Does salt water expand as much as fresh water does when it freezes?". Solutions: Frequently asked questions. Department of Chemistry, Frostburg State University. Retrieved 20060429.
 ^ "Molten salts properties". Archimede Solar Plant Specs.
 ^ Fichter, Lynn S. (2000). "Igneous Phase Diagrams". Igneous Rocks. James Madison University. Retrieved 20060429.
 ^ Davies, Nicholas A.; Beatrice M. Nicholas (1992). "Eutectic compositions for hot melt jet inks". US Patent & Trademark Office, Patent Full Text and Image Database. United States Patent and Trademark Office. Retrieved 20060429.
 ^ IronIron Carbide Phase Diagram Example
 ^ IUPAC Compendium of Chemical Terminology, Electronic version. "Peritectoid Reaction" Retrieved May 22, 2007.
 ^ Numerical Model of Peritectoid Transformation. Peritectoid Transformation Retrieved May 22, 2007. Archived September 28, 2007 at the Wayback Machine
 ^ International Journal of Modern Physics C, Vol. 15, No. 5. (2004), pp. 675687
Bibliography
 Smith, William F.; Hashemi, Javad (2006), Foundations of Materials Science and Engineering (4th ed.), McGrawHill,
Further reading
 Askeland, Donald R.; Pradeep P. Phule (2005). The Science and Engineering of Materials. ThomsonEngineering.
 Easterling, Edward (1992). Phase Transformations in Metals and Alloys. CRC.
 Mortimer, Robert G. (2000). Physical Chemistry. Academic Press.
 ReedHill, R.E.; Reza Abbaschian (1992). Physical Metallurgy Principles. ThomsonEngineering.