PHASE DIAGRAMS (EQUILIBRIUM DIAGRAMS) FOR METALLIC SYSTEMS

Before beginning this task it must be noted that various rules must be observed to ensure correctness of the diagrams. These rules are derived from Gibbs' formulations developed over 100 years ago, the most important of which is the Gibbs phase rule.

The construction of phase diagrams is based on the Gibbs phase rule, which is expressed in equation form as

where P is the number of phases in equilibrium; F is the variance or number of degrees of freedom, or the number of variables such as pressure, temperature, or composition that can be varied without affecting the number of phases in equilibrium; and C is the number of components (elements, compounds, or solutions) in a particular system. The number "2" in the equation stands for temperature and pressure, the two variables that can be allowed to change.

The phase diagram for water is plotted in Figure 5-9, with the pressure as ordinate and the temperature as abscissa. This is a unary phase diagram, meaning that it consists of one component - in this instance, water (H20). The series of curves in the diagram show the division between the three phases in which water can exist depending on temperature and pressure conditions.

Point A in the liquid region is defined by a certain combination of pressure and temperature. The number of components (C) at this point is 1, a unary diagram. The number of phases (P) is 1 because only liquid water exists in this region. The phase rule tells us that the number of degrees of freedom is

The "2" means that, within the limits of the liquid phase, the pressure, temperature, or both can be changed and the phase would still be liquid. No phase changes occur and equilibrium is maintained.

Point B is on the fusion curve (T-F), the boundary between the liquid and solid phases of water. The number of components has not changed and therefore C = 1. The number of phases is P = 2 because anywhere along this curve, liquid and solid phases of water coexist in equilibrium. Using the phase rule to find the number of variables that can be changed without changing any phases in equilibrium, we have

This single degree of freedom means that if the pressure is changed, the temperature must also be changed to stay anywhere on that boundary line. We can no longer change either the pressure or the temperature independently and stay on the boundary line where liquid and solid phases of water coexist in equilibrium.

Point T, at the intersection of the three curves, is known as the triple point of water. Here the three phases of water coexist. The phase rule tells us that the number of degrees of freedom for this position on the phase diagram is

Zero degrees of freedom means that we cannot change pressure or temperature. If we did, the three phases would no longer coexist in equilibrium. It also means that the pressure and temperature are fixed for this condition to exist. The word invariant is also used to describe this particular point.

Point V, which is known as a critical point, means that no matter how high the temperature and pressure rise beyond this point, the vapor phase will never change to a liquid.

Materials science deals primarily with the solid and liquid phases of materials. Second, the pressure variable has only a small effect on materials. Third, metallic phase diagrams are usually limited to showing the interactions between only two components and thus are known as binary diagrams. For example, the iron - iron carbide diagram or the phase diagram for brass has only two components, copper and zinc. Consequently, phase diagrams deal with temperature changes versus changes in the composition of materials. This means that the phase rule can be simplified as follows:

We may now wish to know what the actual composition of the two-phase region (Figure 5-10) is for a particular alloy at a specific temperature. Figure 5-10(a) shows a typical phase diagram for two metallic elements, and Figure 5-10(b) shows ceramic materials that are completely soluble in each other in both liquid and solid phases. The vertical axis at the left represents a pure metal A with a melting point of T.. The vertical axis at the right represents metal B and has a melting temperature less than metal A. The upper curved line of the cigar shaped L + S region is the liquidus and the lower line is the solidus. The pure metals and any composition of the two are in the liquid (melt) phase upon heating above the liquidus. Upon cooling to the solidus, they solidify. When an alloy is at a temperature above the solidus but below the liquidus, it exists as part liquid and part solid in a two- phase region labeled L + S. Figure 5-11, for comparison purposes, is a hypothetical phase diagram for two metals that are completely insoluble in each other, both in the liquid and solid phases.
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