Equilibrium—continued diagram

Fig. 2.35 shows the equilibrium phase diagram of the system In-Pb (continuous lines) together with a metastable diagram. The procedure adopted in the determination of this phase diagram is briefly described here it may be useful as an example... 

Figure 2.36. Au-Sb system. The continuous line represents the (equilibrium) phase diagram containing the peritectic melting AuSb2 compound and a eutectic equilibrium (Es). Dotted lines represent equilibria (and phases) which may be observed on rapid cooling. The sequence of phases (C, AuSb2, it) detected in fast-quenched alloys and their composition ranges are shown in the...

Fig. 3.8. Backscattered electron image of the transition zone between cobalt and silicon after annealing at 800°C for 230400 s (64 h) in vacuum.264 The microstructure reveals all the phases available on the equilibrium phase diagram of the Co-Si binary system. A continuous crack is seen between Co and C02SL Photograph kindly provided by Dr. A.A. Kodentsov. Reprinted with permission from Elsevier Science.

Equation (3-31) relates the interfacial concentrations to each other. So, it is valid only at that point on the equilibrium-distribution curve which represents the local interfacial compositions. For the purpose of locating that point, rewrite equation (3-31) as a continuous relation between the variables in the equilibrium-distribution diagram, namely xA and yA ... 

Microporous framework solids are synthesised via solvent-mediated crystallisations from mixtures of reactive precursors. The reaction pathway is controlled by kinetic as well as thermodynamic considerations so that equilibrium phase diagrams, so relevant in the high-temperature preparation of ceramics, are not useful here. Rather, synthetic routes have been developed empirically via a major synthetic effort that continues today. The continuing industrial and academic interest in these materials provides a powerful incentive to understand the principles underlying their formation through the processes of gel formation and evolution, nucleation and crystal growth. 

The general case of two compounds forming a continuous series of solid solutions may now be considered. The components are completely miscible in the sohd state and also in the hquid state. Three different types of curves are known. The most important is that in which the freezing points (or melting points) of all mixtures lie between the freezing points (or melting points) of the pure components. The equilibrium diagram is shown in Fig. 7, 76, 1. The hquidus curve portrays the composition of the hquid phase in equihbrium with sohd, the composition of... 

Figure 3.35. Information flow diagram for the continuous equilibrium extraction stage.

Figure 4. Evolution of the (N2/N1) ratio in a reservoir in the two cases of closed system evolution (as a function of t/T2, where t is the time since fractionation), or in an open-system, steady-state reservoir (the steady-state (N2/N1) ratio is plotted as a function of x/ T2, where x is the residence time of the magma in the reservoir). Initial fractionation results in an arbitrarily chosen ratio of 2, which is kept constant for the iirfluent magma in the continuously replenished reservoir. The diagram shows that radioactive equilibrium is reached sooner in a closed system evolution. It also illustrates the fact that the radioactive parent-daughter pair should be chosen such as T2 is commensmate with the residence time of the magma in the reservoir (e.g., x/ T2 between 0.1 and 10). If T2 is much longer than the residence time x, then the (N2/N1) ratio will remain close to the initial value (here 2). If T2 is much shorter than x, equilibrium will be nearly established in the reservoir.

Figure 2.31. Schematic representation of the P/T equilibria in a simple two-component system (forming continuous solid and liquid solutions). In (a) a perspective view of the P-T-X diagram is shown in (b) its projection on the P/T plane. Notice the two single-component systems represented, for instance, for the component B by the three lines SB/G (sublimation line of B representing the gas/so lid equilibrium), SB/LB (melting equilibrium of B) and the boiling line LB/G. The solid solution is indicated by a. Notice in (a) the isobaric and isothermal sections of the diagrams (compare with Fig. 2.1).

Figure 2.35. In-Pb diagram. The equilibrium diagram is shown (continuous line) together with a metastable solidus (dotted line).

The pressure-temperature-composition diagram presented by Morey is shown in Fig. 8. The vapor pressure of pure water (on the P-T projection) terminates at the critical point (647 K, 220 bar). The continuous curve represents saturated solutions of NaCl in water, i.e., there is a three-phase equilibrium of gas-solution-solid NaCl. The gas-phase pressure maximizes over 400 bar at around 950 K. Olander and Liander s data for a 25 wt. % NaCl solution are shown, and T-X and P X projections given. At the pressure maximum, the solution phase contains almost 80% NaCl. 

An exceptional case of a very different type is provided by helium [15], for which the third law is valid despite the fact that He remains a liquid at 0 K. A phase diagram for helium is shown in Figure 11.5. In this case, in contrast to other substances, the solid-liquid equilibrium line at high pressures does not continue downward at low pressures until it meets the hquid-vapor pressure curve to intersect at a triple point. Rather, the sohd-hquid equilibrium line takes an unusual turn toward the horizontal as the temperature drops to near 2 K. This change is caused by a surprising... 

Using specific metal combinations, electrodeposited alloys can be made to exhibit hardening as a result of heat treatment subsequent to deposition. This, it should be noted, causes solid precipitation. When alloys such as Cu-Ag, Cu-Pb, and Cu-Ni are coelectrodeposited within the limits of diffusion currents, equilibrium solutions or supersaturated solid solutions are in evidence, as observed by x-rays. The actual type of deposit can, for instance, be determined by the work value of nucleus formation under the overpotential conditions of the more electronegative metal. When the metals are codeposited at low polarization values, formation of solid solutions or of supersaturated solid solutions results. This is so even when the metals are not mutually soluble in the solid state according to the phase diagram. Codeposition at high polarization values, on the other hand, results, as a rule, in two-phase alloys even with systems capable of forming a continuous series of solid solutions. 

For a number of applications, particularly those associated with conditions of continuous cooling or heating, equilibrium is clearly never approached and calculations must be modified to take kinetic factors into account. For example, solidification rarely occurs via equilibrium, amorphous phases are formed by a variety of non-equilibrium processing routes and in solid-state transformations in low-alloy steels much work is done to understand time-temperature-transformation diagrams which are non-equilibrium in nature. The next chapter shows how CALPHAD methods can be extended to such cases. 

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