Eutectic system



A eutectic system or eutectic mixture is a homogeneous mixture that has a melting point lower than those of the constituents. 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).

Non-eutectic mixture ratios 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 solidifies into 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".

In the real world, eutectic properties can be used to advantage in such processes as eutectic bonding, where silicon chips are bonded to gold-plated substrates with ultrasound, and eutectic alloys prove valuable in such diverse applications as soldering, brazing, metal casting, electrical protection, fire sprinkler systems, and nontoxic mercury substitutes. By managing phase transformation during solidification, a suitable eutectic alloy can be made stronger than any of its individual components, a valuable property in an extreme application such as the hypereutectic cast aluminum pistons used in the high-revving 550 hp twin-turbo intercooled DOHC Cadillac Blackwing V8 introduced in 2018.

The term was coined in 1884 by British physicist and chemist Frederick Guthrie (1833–1886). The word originates.

Eutectic phase transition


The eutectic solidification is defined as follows:


 * $$\text{Liquid} \quad \xrightarrow[\text{cooling}]{\text{eutectic} \atop \text{temperature}} \quad \alpha \text{ solid solution} \ + \ \beta \text{ solid solution}$$

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 phase change 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 point can be classified as hypoeutectic or hypereutectic:


 * Hypoeutectic compositions are those with a greater composition of species α and a smaller percent composition of species β than the eutectic composition (E)


 * Hypereutectic compositions 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.

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 for eutectic alloys include:
 * NEMA Eutectic Alloy Overload Relays for electrical protection of 3-phase motors for pumps, fans, conveyors, and other factory process equipment.
 * Eutectic alloys for soldering, both traditional alloys composed of lead (Pb) and tin (Sn), sometimes with additional silver (Ag) or gold (Au) — especially Sn$63$Pb$37$ and Sn$62$Pb$36$Ag$2$ alloy formula for electronics - and newer lead-free soldering alloys, in particular ones composed of tin (Sn), silver (Ag), and copper (Cu) such as Sn$96.5$Ag$3.5$.
 * 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 eutectic bonded to gold-plated substrates through a silicon-gold eutectic by the application of ultrasonic energy to the chip.
 * 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

 * Sodium chloride and water form a eutectic mixture whose eutectic point is −21.2 °C and 23.3% salt by mass. 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. 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 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.
 * Some inks are eutectic mixtures, allowing inkjet printers to operate at lower temperatures.
 * 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.

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. 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 a 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. 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. 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:

$$\lambda^*=\frac{2\gamma V_m T_E }{\Delta H * \Delta T_0}$$

Where  is $$\gamma$$ is the surface energy of the two-phase boundary, $$V_m$$ is the molar volume of the eutectic phase, $$T_E$$  is the solidification temperature of the eutectic phase, $$\Delta H$$ is the enthalpy of formation of the eutectic phase, and $$\Delta T_0$$ is the undercooling of the material. So, by altering the undercooling, and by extension the cooling rate, the minimal achievable spacing of the secondary 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.

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 and 0.76 wt% 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, ..., n-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 1495 C 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:

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:

\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 that 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 as

\mu _i = \mu _i^\circ + RT\ln x_i = 0 \Rightarrow \mu_i^\circ = -RT\ln x_i. $$

Using and integrating gives

\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 $$T^\circ$$ and an enthalpy of fusion $$H^\circ$$:

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{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} $$

\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} $$

which can be solved by

\begin{array}{c} \left[ \right] = \left[  \right]^{ - 1}

.\left[ \right] \end{array} $$