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Phase diagrams have been constructed for the case
of one component (

diagrams for a pure material),
and for two component systems (

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
twodimensions.
For ternary systems, there are three components. Let
the three components be denoted by
,
, and
.
Because,
, the system can be
represented by two components, say
, and
, and
the phase diagram could be represented in the following
coordinate system:
Figure 311:
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 311?
It may be possible to represent such a diagram in two dimensions
by taking slices at constant composition, for instance:
Figure 312:
Pseudobinary 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 temperatureand the following scheme is used to represent all
three components:
Figure 313:
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 314:
An example of a ternary phase diagram.
Three phase regions become triangles where the limiting
composition of each coexisting phase is given by the
vertices of the triangle.
The sides of the triangle are the limits of the tielines 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 315:
Example of a simple ternary phase diagram
at constant and .

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W. Craig Carter
20021203