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Ternary Phase Diagrams

Phase diagrams have been constructed for the case of one component ( \bgroup\color{blue}$ P$\egroup- \bgroup\color{blue}$ T$\egroup diagrams for a pure material), and for two component systems ( \bgroup\color{blue}$ T$\egroup- \bgroup\color{blue}$ X_B$\egroup 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 \bgroup\color{blue}$ R$\egroup, \bgroup\color{blue}$ G$\egroup, and \bgroup\color{blue}$ B$\egroup. Because, \bgroup\color{blue}$ X_R + X_G + X_B = 1$\egroup, the system can be represented by two components, say \bgroup\color{blue}$ X_R$\egroup, and \bgroup\color{blue}$ X_G$\egroup, 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.
\begin{figure}\resizebox{6in}{!}
{\epsfig{file=figures/22-7A.eps}}
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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.
\begin{figure}\resizebox{6in}{!}
{\epsfig{file=figures/22-7B.eps}}
\end{figure}

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.
\begin{figure}\resizebox{6in}{!}
{\epsfig{file=figures/22-8A.eps}}
\end{figure}

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.
\begin{figure}\resizebox{6in}{!}
{\epsfig{file=figures/22-8B.eps}}
\end{figure}

Figure 31-5: Example of a simple ternary phase diagram at constant $ P$ and $ T$.
\begin{figure}\resizebox{6in}{!}
{\epsfig{file=figures/ternary-example.eps}}
\end{figure}


next up previous
Next: Solution Free Energies that Up: Lecture_31_web Previous: Lecture_31_web
W. Craig Carter 2002-12-03