Invariant eutectic point

Two other monovariant curves extend from the invariant eutectic point in the direction of higher (L-Sa-Sb equilibrium) and lower (G-Sa-Sb) pressures are the curves of liquid... 

Figure 2.40. Phase diagram of the Mg-Cu alloy system. For the alloys marked (1) (at 5 at.% Cu) and (2) (at 20 at.% Cu), the DTA curves are shown on the right. Notice that, on cooling, a sharp thermal effect due to the invariant eutectic transformation is observed. At higher temperature the crossing of the liquidus curves is detected. (The coordinates of the eutectic point are 485°C and 14.5 at.% Cu.)...

These two theorems are general and include as particular cases the theorems established in chap. XVIII, 6 and in chap. XXIII. They do not however apply to mono variant or invariant systems. Thus the eutectic point, which is certainly an indifferent point, does not represent, mathematically, an extreme value of or p for it is the point of intersection of two curves each of which refers to a two-phase system e.g. solution + ice or solution-f salt) under constant pressure. Only at the eutectic do three phases (solution + salt + ice) coexist. A mono variant three-phase system does not have an isobaric curve. 

The results of our investigation of the Ti-comer of the Ti-Zr-Si system (Fig.8) show that the above three-phase fields form by invariant eutectic equilibrium. The coordinates of the invariant point E were determined to be 1330°C and 78Ti-l IZr-l ISi (Fig.8a). In the solid state the three-phase field a+ 3+S2 was found with the temperature decreasing when the Zr concentration increases. 

It may be pointed out that when the solid components exist in polymorphic forms, the cooling curve will show a line of constant temperature, similar to Fd (Fig. 34) at the transition point. In this case, however, the liquid will not completely solidify, and only a change in the solid phase will take place. When this change is complete, the temperature will again fall until the eutectic point (or other point corresponding to an invariant system) is reached. 

At the cryohydric point, therefore, we are not dealing with a single solid phase, but with two solid phases, ice and salt and, as we have already learned, the constancy of temperature and composition at the cryohydric or eutectic point is due to the fact that we are dealing with an invariant system. 

The cryohydric or eutectic point is thus clearly seen to be the point of intersection of the solubility curve of the salt and the freezing-point curve of water. At this point, also, the curves of the univariant systems ice—salt— vapour and ice—salt —solution intersect. The cryohydric point is therefore a quadruple point, and represents an invariant system. 

Concentration-Temperature Diagram.—In this diagram the temperatures are taken as the abscissae, and the composition of the solution, expressed in atoms of chlorine to one atom of iodine, is represented by the ordinates. In the diagram, A represents the melting-point of pure iodine, 114°. If chlorine is added to the system, a solution of chlorine in liquid iodine is obtained, and the temperature at which solid iodine is in equilibrium with the liquid solution will be all the lower the greater the concentration of the chlorine. We therefore obtain the curve ABF, which represents the composition of the solution with which solid iodine is in equilibrium at different temperatures. This curve can be followed down to 0°, but at temperatures below 7 9 (B) it represents metastable equilibria. At B iodine monochloride can be formed, and if present the system becomes invariant B is therefore a quadruple point at which the four phases, iodine, iodine monochloride, solution, and vapour, can co-exist. Continued withdrawal of heat at this point will therefore lead to the complete solidification of the solution to a mixture or conglomerate of iodine and iodine monochloride, while the temperature remains constant during the process. B is the eutectic point for iodine and iodine monochloride. 

Corresponding to the point Q/the melting-point of pure iodine, there is the point C, which represents the vapour pressure of iodine at its melting-point. At this point three curves cut i, the sublimation curve of iodine 2, the vaporisation curve of fused iodine 3, CiB, the vapour-pressure curve of the saturated solutions in equilibrium with solid iodine. Starting, therefore, with the system solid iodine— liquid iodine, addition of chlorine will cause the temperature of equilibrium to fall continuously, while the vapour pressure will first increase, pass through a maximum and then fall continuously until the eutectic point, B (Bjl), is reached. At this point the system is invariant, and the pressure will therefore remain constant until all the iodine has disappeared. As the concentration of the chlorine increases in the manner represented by the curve B/H, the pressure of the vapour also increases as represented by the curve Bj/iHi. At the eutectic point for iodine monochloride and iodine trichloride, the pressure again remains constant until all the monochloridc has disappeared. As the concentration of the solution passes along the curve HF, the pressure... 

Pressure-Temperature Dia am. —If sulphur dioxide is passed into water at 0°, a solution will be formed and the temperature at which ice can exist in equilibrium with this solution will fall more and more as the concentration of the sulphur dioxide increases. At — 2 6°, however, an eutectic point is reached at which solid hydrate separates out, and the system becomes invariant. The curve AB (Fig. 86), therefore, represents the pressure of the system ice—solution II.— vapour, and B represents the temperature and pressure at which the invariant system ice—hydrate—solution II.— vapour can exist. At this point the temperature is — 2-6°, and the pressure 21-2 cm. If heat is withdrawn from this system, the solution will ultimately solidify to a mixture of ice and hydrate, and there wull be obtained the univariant system ice— hydrate— vapour. The vapour pressure of this system has been determined down to a tern- p perature of — 9 5 , at which temperature the pressure amounts to 15 cm. The pressures for this system are represented by the curve BC. 

The invariance of the system at the eutectic point allows eutectic mixtures to be used as constant temperature baths. Suppose solid sodium chloride is mixed with ice at 0 °C in a vacuum flask. The composition point moves from 0% NaCl to some positive value. However, at this composition the freezing point of ice is below 0 °C hence, some ice melts. Since the system is in an insulated flask, the melting of the ice reduces the temperature of the mixture. If sufficient NaCl has been added, the temperature will drop to the eutectic temperature, —21.1 °C. At the eutectic temperature, ice, solid salt, and saturated solution can coexist in equilibrium. The temperature remains at the eutectic temperature until the remainder of the ice is melted by the heat that leaks slowly into the flask. 

A different type of system in which solid solutions appear is shown in Fig. 15.18. This system has a transition point rather than a eutectic point. Any point on the line abc describes an invariant system in which a, p, and melt of composition c coexist. The temperature of abc is the transition temperature. If the point lies between a and b, cooling... 

The eutectic point is therefore analogous to a triple point in a one-component system and, like a triple point, it is also an invariant point. The three phases can be in equilibrium only at one temperature and composition, at a fixed pressure (see Section SI.5). The reaction that occurs on cooling or heating through a eutectic point is called an invariant reaction. A cooling curve shows a horizontal break on passing through a eutectic. 

There are three invariant points in the iron-carbon diagram (Figures 4.16 and 4.17). A eutectic point is found at 4.30 wt% carbon and 1148 °C. At a eutectic point, a liquid transforms to two solids on cooling ... 

A eutectic point on a binary phase diagram is (a) An invariant point... 

The binary eutectics are represented by points A (31.5 °C 72.5 per cent O, 27.5 per cent M), B (33.5 °C 75.5 per cent O, 24.5 per cent M) and C (61.5 °C 54.8 per cent M, 45.2 per cent P). Curve AD within the prism represents the effect of the addition of the component P to the 0-M binary eutectic A. Similarly, curves BD and CD denote the lowering of the freezing points of the binary eutectics B and C, respectively, on the addition of the third component. Point D, which indicates the lowest temperature at which solid and liquid phases can coexist in equilibrium in this system, is a ternary eutectic point (21.5 °C 57.7 per cent O, 23.2 per cent M, 19.1 per cent P). At this temperature and concentration the liquid freezes invariantly to form a solid mixture of the three components. The section of the space model above the freezing point surfaces formed by the liquidus curves represents the homogeneous liquid phase. The section below these surfaces down to a temperature represented by point D denotes solid and liquid phases in equilibium. Below this temperature the section of the model represents a completely solidified system. 

At any point along the liquidus curves TA-eAB and Te-eAB, there exist two phases-either solid A -i- melt, or solid B -i- melt Consequently, the degree of freedom F is 1 that is, either the temperature or the composition can be altered without changing the number of phases present (univariant equilibrium). At the eutectic point Oab the two solid phases A and B are in equilibrium with the melt Thus, the number of phases is P = 3, and F = 0, since any variation of the temperature or the composition will invariably displace the system from point Oab at which two solubility (liquidus) curves intersect (invariant equilibrium). 

According to Gibbs condensed phase rule, at the ternary eutectic points four phases coexist (G = 3, P = 4, F = 0) three solid phases and one Hquid melt phase. For example, at the ternary eutecHc point Ei the two ternary phases X and Z, the binary phase A2C, and the melt (not shown in projection) coexist. By definition, this point is invariant (F = 0) to changes in temperature and/or composition, as each departure from its values will displace the system from point Ej. A composition anywhere along a phase boundary Hnes is subject to a univariant equUibrium (F = 1), since it is possible to alter either the temperature or the concentration of one of the two components without leaving the boundary line between two... 

As temperature is increased, the liquid free energy curve drops because of the —TAS term in the free energy, and encoimters the mutual tangent line at T. At this temperature, three phases can coexist, a liquid plus the two solid phases. The Gibbs phase rule tells us that, at constant pressure, we have no additional degrees of freedom therefore, there is only one composition and temperature for which this situation can occur. We call this particular combination of temperature and composition the eutectic point. This particular temperature is called the eutectic temperature and the composition is called the eutectic composition. Since temperature and composition are fixed at this particular point, it is called an invariant point. At this invariant point we say a eutectic reaction occurs. We will encounter other invariant points characterized by different invariant reactions. 

When a second component is added to a pure material, the freezing point is often lowered. This is evident in the lowered liquidus curves for both end members. This diagram shows a eutectic point, k. It is an invariant point, as... 

Below the equilibrium lines, but above the eutectic temperature, a liquid and solid are in equilibrium. Under line ac, solid benzene, and liquid Li, whose composition is given by line ac, are present. Under line be, the phases present are solid 1,4-dimethylbenzene and liquid Li, whose composition is given by line be. Below point c, solid benzene and solid 1,4-dimethylbenzene are present. In the two phase regions, one degree of freedom is present. Thus, specifying T fixes the composition of the liquid, or specifying X2 fixes the temperature.cc Finally, at point c (the eutectic) three phases (solid benzene, solid 1,4-dimethylbenzene, and liquid with x2 = vi.e) are present. This is an invariant point, since no degrees of freedom are present. 

P8.4 The (solid + liquid) phase diagram for (.Yin-C6Hi4 + y2c-C6Hi2) has a eutectic at T = 170.59 K and y2 = 0.3317. A solid phase transition occurs in c-CftH at T— 186.12 K, resulting in a second invariant point in the phase diagram at this temperature and. y2 — 0.6115, where liquid and the two solid forms of c-C6H12 are in equilibrium. A fit of the experimental... 

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