Phase Equlibria

Phase Stability

Gibbs Phase Rule

Types of Phase Diagrams

Unary Phase Diagram

As we progress to multi-component systems, it will be useful to discuss binary- and ternary systems in the context of specific materials. The Fe-C (metallic) phase diagram is a classic example of a binary system, and the Al_{2}O_{3}-CaO-SiO_{2} ternary phase diagram is probably the most widely-utilized ceramic phase diagram known. Thermodynamics of polymeric systems encompasses much more than simply phase equilibria. Aspects of solution thermodynamics, chain conformations and phase separation are dealt with in a separate chapter on polymers. Finally, thermodynamic properties of composite systems are discussed.

Metals and Alloys: Phase Equlibria

Ceramics and Glasses: Phase Equilibria and Densification

Polymers: Phase Separation and Solution Thermodynamics

Composites: Bond Formation and Interphase Adhesion

Here, is the latent heat of fusion (or melting, or crystallization, as the case may be) and the latent heat of vaporization. We will return to phase transformations later, but let's now see why these phases form in the first place and why each one is stable over such a wide range of temperatures.

= enthalpy

= entropy

Any system is said to be in equilibrium if there are no unbalanced forces within the system, *i.e.*, . If the free energy is less than zero, a phase can spontaneously transform to another phase; *e.g.*, solid to liquid. This type of transformation is said to be "thermodynamically favorable." If the free energy is greater than zero, a phase transformation will *not* occur spontaneously. Keep in mind that the free energy condition is a thermodynamic one only; it does not describe the rate at which transformations from one phase to another may take place, even if they are thermodynamically favorable. Phase transformations are rate-dependent, and as such are discussed in the appropriate chapters on kinetics.

This is a very important relationship. It describes the

The number of components, *C*, is fairly straightforward. If I mix oil and water, I have two components. If I put some tin into molten lead, I have two components. Water is an example of a one-component system. If I put salt in water, I once again have two components. You might argue that when I dissolve salt in water I have only one component: salt water. What I have is one *phase*; there are still two components. What if I put in too much salt? It begins to precipitate out and I get two phases, but in both instances I have two components: the salt and the water.

As you can see in the saltwater example, the number of phases, *P*, is something that is not always known. Sometimes this is the quantity we desire, but more often than not, we can determine the number of phases in a system by inspecting the system, either visually or with a microscope. If we keep in mind that a phase is a homogeneous region of matter, we can usually identify how many of these regions are present. Remember that these regions need not be continuous. Bubbles in a liquid represent only two phases, even though the bubbles are separated from each other by the liquid.

The number of noncompositional variables, *N*, is simply the process variables we wish to consider other than composition. Usually, these are temperature and pressure, so that *N*=2, but for condensed systems; *e.g.*, two solids, the effect of pressure is often times negligible, so that *N* can also be 1.

The degrees of freedom, *F*, are difficult to conceptualize. They don't have any physical significance, that is, they don't represent a certain phase, or a process variable. Just as with the other variable in the Gibbs Phase Rule, though, they count the number of something. You can think of the degrees of freedom as counting whatever is left from adding and subtracting the other variables (*C*, *N* and *P*). If *F*=0, we say the system is *invariant*. Similarly, we can have *monovariant*, *divariant* or *trivariant* systems for *F*=1, 2 or 3, respectively.

Often times, we wish to determine the degrees of freedom. We know how many components we have, we know how many process variables (noncompositional variables) we wish to vary, and we sometimes know how many phases we have. By determining F, we find out how many of the process variables can be changed independently without affecting the number of phases present. The best way to strengthen your grasp on this concept is to forge ahead with phase diagrams. As the complexity of the diagrams increases, you should see why it is important to know the degrees of freedom for a given system.

- number of phases present
- composition of each phase
- quantity of each phase

= intensive variable;

e.g.,

e.g.,

e.g.,

As in any phase diagram, lines indicate phase boundaries, which are transition regions where both phases coexist, that is, both phases are in thermodynamic equilibrium. The critical point is where two phases have exactly the same density and are indistinguishable. The triple point is where all three phases coexist at equilibrium (P=3, F=0). At the critical point, you can't change any variable without losing a phase. The region above the critical point is called the "supercritical" region. Supercritical fluids like CO_{2} (it's nearly impossible to distinquish between liquid and vapor at this point, so we call it a "fluid") are technologically important for separation and extraction purposes.

- Smith, J.M. and H.C. Van Ness, "Introduction to Chemical Engineering Thermodynamics," 4th Edition, McGraw-Hill, 1987

Problems

This ends the introduction to the thermodynamics of phase equilibria. As stated at the beginning of this section, phase equilbria is best described further in the context of specific materials. If you want the complete description of phase equilibria and phase transitions, follow the sequence of chapters given below.

Metals and Alloys: Phase Equlibria

Ceramics and Glasses: Phase Equilibria and Densification

Polymers: Phase Separation and Solution Thermodynamics

Composites: Bond Formation and Interphase Adhesion

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