Interpretation of Phase Diagrams

For a binary system of known composition and temperature at eqnilibrium, at least three kinds of information are available (1) the phases that are present, (2) the compositions of these phases, and (3) the percentages or fractions of the phases. The procedures for making these determinations will be demonstrated using the copper-nickel system. 

For an alloy having composition and temperature located in a two-phase region, the situation is more comphcated. In all two-phase regions (and in two-phase regions only), one may imagine a series of horizontal lines, one at every temperatnre each of these is known as a tie line, or sometimes as an isotherm. These tie lines extend across the two-phase region and terminate at the phase bonndary lines on either side. To compute the equilibrium concentrations of the two phases, the following procedure is used  

A tie line is constructed across the two-phase region at the temperature of the alloy. 

The intersections of the tie line and the phase boundaries on either side are noted. 

Perpendiculars are dropped from these intersections to the horizontal composition 

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Today, partly by the accumulation of empirical knowledge and partly by the interpretation of phase diagrams, we can deal with the fusion of oxide mixtures by deliberate planning. However, science is a long way from managing such designs by purely intellectual methods. 

The melting point of high cristoballte is 1996 i 5 K, while the metastable melting point of high quartz is 1696 A gH is the difference between Aj,H for liquid and high cristoballte at T. Values ranging from 1.8 to 3.6 kcal mol been derived from various interpretations of phase diagrams (1 ). 

A similar interpretation of phase diagrams has been recently proposed by Safran and Turkevich (18). These authors have considered the effects of interaction and curvature on the stability of microemulsions. They suggest that unstabilities of spherical microemulsion droplets lead the system to separate with water in order to prevent micellar growth above a limit radius R. Taking into account interactions with a phenomenologic treatment, they show that phase separation due to interaction is also possible and they found a critical radius Rc. If Rc is greater than R a water phase is formed and if Rc is lower than R phase separation gives rise to two micellar phases with a critical point. This theoretical treatment reflects very well the behavior we observe but it is not in full accordance with our experimental results. The main difference is that when interactions are not preponderant the phase separation does not occur with a water phase but with a lamellar phase. 

Figure 13-18 Some interpretations of phase diagrams, (a) The phase diagram of water. Phase relationships at various points in this diagram are described in the text, (b) Two paths by which a gas can be liquefied. (1) Below the critical temperature. Compressing the sample at constant temperature is represented by the vertical line WZ. Where this line crosses the vapor pressure curve AC, the gas liquefies at that set of conditions, two distinct phases, gas and liquid, are present in equilibrium with each other. These two phases have different properties, for example, different densities. Raising the pressure further results in a completely liquid sample at point Z. (2) Above the critical temperature. Suppose that we instead first warm the gas at constant pressure from W to X, a temperature above its critical temperamre. Then, holding the temperamre constant, we increase the pressure to point Y. Along this path, the sample increases smoothly in density, with no sharp transition between phases. From Y, we then decrease the temperature to reach final point Z, where the sample is clearly a liquid.

Phase diagrams for multicomponent mixtures possess additional degrees of freedom and are inherently multidimensional. In practice, construction and interpretation of phase diagrams of multicomponent mixtures are similar to, and based on, those of binary mixtures. " " The phase behavior of multicomponent mixtures can also be depicted as sections in PTxiX2-space, keeping one or more of the variables constant. A widely used section for ternary mixtures is an equilateral triangle composition diagram at fixed pressure and temperature (Fig. 7). 

Required Knowledge (1) The states of matter. (2) The interpretation of phase diagrams. 

Phase diagrams have been experimentally determined for many ceramic systems. For binary or two-component phase diagrams, it is frequently the case that the two components are compounds that share a common element, often oxygen. These diagrams may have configurations similar to those for metal-metal systems, and they are interpreted in the same way. For a review of the interpretation of phase diagrams, the reader is referred to Section 9.8. 

Figure 7,8 Gibbs free energy curves and T-X phase relations for an intermediate compound (C), totally immiscible with pure components. Column 1 Gibbs free energy relations leading to formation of two eutectic minima separated by a thermal barrier. Column 2 energy relations of a peritectic reaction (incongruent melting). To facilitate interpretation of phase stability fields, pure crystals of components 1 and 2 coexisting with crystals C are labeled y and y", respectively, in T-X diagrams same notation identifies mechanical mixtures 2-C and C-1 in G-X plots.

To interpret the phase diagram in Fig. 7.1 quantitatively, we must return to Eq. (7.3) and more fully define the chemical potential. For ideal gases, the chemical potential can be rigorously derived from statistical mechanics. A useful definition of the ideal-gas chemical potential for O2 is... 

The reader should be able to construct and interpret the phase diagram in Fig. 3.15.6 on a similar basis. This situation arises mainly when the melting points of pure A and B differ considerably. Diagrams of this type are classified as... 

The mutual solubility of ozone and oxygen at —183° and —195.5° C. has been determined by measuring the magnetic susceptibility and vapor pressure (4) of solutions, and a critical solution temperature of —180° C is indicated. The vapor pressure-composition data, combined with vapor pressure data for liquid ozone (1), were used to interpret the phase diagram of the system ( ). Measurements of the density and viscosity of solutions and the surface tension of liquid ozone are reported. 

Pseudoternary phase diagrams of the water-dodecane-SDS-pentanol and water-dodecane-SDS-hexanol systems have been investigated in detail. A great variety of new domains has been evidenced in the oil rich part of these diagrams including, one-, two-, three- and four-phase liquid regions. An interpretation of these diagrams is proposed it is shown that interactions between water domains play an important role in microemulsion stability. 

The diffusion path method has been used to interpret nonequilibrium phenomena in metallurgical and ceramic systems (10-11) and to explain diffusion-related spontaneous emulsification in simple ternary fluid systems having no surfactants (12). It has recently been applied to surfactant systems such as those studied here including the necessary extension to incorporate initial mixtures which are stable dispersions instead of single thermodynamic phases (13). The details of these calculations will be reported elsewhere. Here we simply present a series of phase diagrams to show that the observed number and type of intermediate phases formed and the occurrence of spontaneous emulsification in these systems can be predicted by the use of diffusion paths. 

The previous sections dealt with various types of phase diagrams and their interpretations. What has been glossed over, however, is what determines their shape. In principle, the answer is simple the phase or combination of phases for which the free energy of the system is lowest is by definition the equilibrium state. However, to say that a phase transformation occurs because it lowers the free energy of the system is a tautology, since it would not be observed otherwise — thermodynamics forbids it. The more... 

It is usual for phase diagrams to contain several features solid solutions, compound formation, eutectic points, transition points, and the like. Once the interpretation of the individual features is understood, the interpretation of complex diagrams poses no difficulty. 

P.W. Brown, 1999, Interpreting Ternary Phase Diagrams , Journal of Materials Education 21 203. 

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