Ternary Phase Diagrams

Phase diagrams have been constructed for the case of one component ( $P$- $T$ diagrams for a pure material), and for two component systems ( $T$- $X_B$ diagrams drawn at constant pressure). Each time a new component is added, another intensive variable must be held constant if the phase diagram is to be drawn in two-dimensions.

For ternary systems, there are three components. Let the three components be denoted by $R$, $G$, and $B$. Because, $X_R + X_G + X_B = 1$, the system can be represented by two components, say $X_R$, and $X_G$, and the phase diagram could be represented in the following coordinate system:

Figure 31-1: Possible way to draw a ternary phase diagram at constant pressure. It would be difficult to interpret such diagrams.

Question: what is the maximum number of phases that can be in equilibrium at one point in Figure 31-1?

It may be possible to represent such a diagram in two dimensions by taking slices at constant composition, for instance:

Figure 31-2: Pseudo-binary slices of a ternary phase diagram at constant pressure. The figure on the left is a true binary phase diagram and has the same corresponding rules for the degrees of freedom.

Ternary phase diagrams are traditionally drawn at constant pressure and temperature--and the following scheme is used to represent all three components:

Figure 31-3: Representation of three components at constant pressure and temperature. Each triangle vertex corresponds to a pure component. Each triangle side corresponds to: 1) a system with none of the component from the opposite vertex; 2) a binary alloy with none of the third component represented by the opposite vertex.

For example, a ternary phase diagram may look something like this:

Figure 31-4: An example of a ternary phase diagram. Three phase regions become triangles where the limiting composition of each co-existing phase is given by the vertices of the triangle. The sides of the triangle are the limits of the tie-lines from an abutting two phase region. The lever rule in three phase region is graphically illustrated by the weighted phase fractions distributed about the average composition.

Figure 31-5: Example of a simple ternary phase diagram at constant $P$ and $T$.