Phase equilibria eutectic point

Figure 4.14 A very simplified melting diagram of the Fe-C system where a stationary metastable phase can form during the catalytic graphitization of amorphous carbon. FesC (cementite) and Fe2C are stoichiometric iron carbides. A is the equilibrium eutectic point (T = 1420 K, x = 0.173), and B is the stationary oversaturated state (T = 920 K).

At the eutectic point the three phases are in equilibrium. The compositions of the two new phases are given by the ends of the line through the eutectic point. 

Both liquid and vapor phases are totally miscible. Conventional vapor/liquid equilibrium. Neither phase is pure. Separation factors are moderate and decrease as purity increases. Ultrahigh purity is difficult to achieve. No theoretical limit on recovery. Liquid phases are totally miscible solid phases are not. Eutectic system. Solid phase is pure, except at eutectic point. Partition coefficients are very high (theoretically, they can be infinite). Ultrahigh purity is easy to achieve. Recovery is limited by eutectic composition. 

Eutectic point (Tc) A single point on a temperature concentration phase (or state) diagram for a binary solution (e.g., water and sugars or salts) where the solution can exist in equilibrium with both crystalline solute and crystalline solvent. Under equilibrium conditions, cooling at Te results in simultaneous crystallization of solvent and solute in constant proportion and at constant temperature until maximum solidification has occurred (based on Fennema, 1996). 

For the niobium-copper system different phase diagrams of the simple eutectic type (with the eutectic point very close to Cu) have been proposed, either with an S-shaped near horizontal liquidus line or with a monotectic equilibrium. It was stated that the presence of about 0.3 at.% O can induce the monotectic reaction to occur, whereas if a lesser amount of oxygen is present no immiscibility gap is observed in the liquid. 

In the liquid state sulfur and selenium are known to mix in all proportions. The provisional phase diagram shows an eutectic point at 40 mol-% of selenium (m.p. 105 °C). Mixtures with lower selenium content should show freezing points between 105 and 118 °C while those with higher selenium content are expected to have their freezing points at considerably higher temperatures. In practice equilibrium crystallization of the melt is hindered by supercooling and therefore only the melting points can be studied. 

We now consider the eutectic point e. If the temperature is just above die eutectic temperature, it is a single liquid phase that is present. If the temperature is just below the eutectic temperature, however, two solid phases, solid A and solid B, are present. At the eutectic point, therefore, all three phases, i.e., solid A, solid B and liquid, coexist in equilibrium. We may thus write a reaction which occurs at the eutectic point ... 

In a two component system, three phases exist in equilibrium at the eutectic point. 

The nature of alloys. Homogeneous and heterogeneous alloys. Solid solutions, intermetallic compounds. The phase rule, P - - P = C 2 number of phases, variance, number of components of a system in equilibrium triple point. Phase diagrams of binary systems eutectic mixture eutectic point. The systems As-Pb, Pb-Sn, Ag-Au, Ag-Sr. 

The line Kk corresponds to the three phase system solution + solid A + sohd B this is a divariant system but when p is fixed the representative points for the solution lie on a line. The three lines k K, k K and k K meet at K which is the ternary eutectic point at which the four phases, liquid, solid A, solid B and solid C are in equilibrium. This system is monovariant, but at a given pressure there is only one point representing this state, namely K. 

The constant pressure diagram for this system is shown schematically in fig. 21.14. The boiling point of the mixture is independent of composition as shown by the horizontal dotted line at except when the second component disappears when, of course, the boiling point rises abruptly to that of the pure component T or T ), The line T E gives the composition of the vapour in equilibrium with pure liquid 1 as a function of temperature. The equilibrium temperature is lower than the boiling point of 1 as its partial pressure in the vapour phase is lower than total pressure. Similarly T E gives the composition of T mixed vapour in equilibrium with p liquid 2. At the eutectic point we have co-existence of the two liquid phases and vapour. The lines T E and T E are given by equations like (18.23) and (18.23 ). 

The individual curves or straight lines in the phase diagrams, which are denoted as boundary lines, represent the equilibrium between two phases. In a phase diagram of the binary system, the plane above both the boundary lines has the highest degree of freedom possible, i.e. v = 2. On the boundary lines, the degrees of freedom decreases to v = 1 and in the eutectic point, where the boundary lines meet, the degree of freedom is equal to zero. 

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