Eutectic system

A eutectic system ( ) from the Greek "εύ" (eu = well) and "τήξις" (tēxis = melting) is an homogeneous mixture of substances that melts or solidifies at a single temperature that is lower than the melting point of any of the constituents. This temperature is known as the "eutectic temperature", and is the lowest possible melting temperature over all of the mixing ratios for the involved component species. On a phase diagram, the eutectic temperature is seen as the "eutectic point" (see plot on the right).
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, 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".
The term was coined in 1884 by British physicist and chemist Frederick Guthrie (1833–1886).
Eutectic phase transition.
The eutectic solidification is defined as follows:
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.
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.
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.
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:
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 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 and about 0.8% carbon.
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, ..., formula_2-ary alloy to create a completely different and single solid phase. The reaction plays a key role in the order and decomposition of quasicrystalline phases in several alloy types. A similar structural transition is also predicted for rotating columnar crystals.
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 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 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.
The Gibbs free energy "G" depends on its own differential:
Thus, the "G"/"T" derivative at constant pressure is calculated by the following equation:
The chemical potential formula_5 is calculated if we assume that the activity is equal to the concentration:
At the equilibrium, formula_7, thus formula_8 is obtained as
Using and integrating gives
The integration constant "K" may be determined for a pure component with a melting temperature formula_11 and an enthalpy of fusion formula_12:
We obtain a relation that determines the molar fraction as a function of the temperature for each component:
The mixture of "n" components is described by the system
which can be solved by