 ```Phases Diagrams Of Ceramics
Third Stage
A straight line connecting the points representing the compositions of the
crystals in the ternary system is called a binary join. A join connecting the
compositions of the primary crystals of two areas having a common
boundary line is called an Alkemade line. The use of Alkemade lines
simplifies the analysis and interpretation of ternary phase relations. The
following example should help to clarify the distinction between joins and
In the system shown in fig.(35), there is an intermediate binary
compound BC which has a primary phase field labeled bc. The line A-BC is
a join connecting the compositions of the primary crystals of two areas
having a common boundary line, ED, and therefore, the line A-BC is an
Alkemade line. Lines AC, AB, B-BC, and BC-C are also Alkemade lines.
Line BC, although a join, does not fulfil1 the condition of the common
boundary line because areas c and b are not adjacent; consequently, BC is
Fig (35) Join BC is not an Alkemade line.
1
Phases Diagrams Of Ceramics
Third Stage
The Alkemade theorem states that the intersection of a boundary line (or
line extended) represents a temperature maximum on that boundary line and
permits one to analyze with respect to temperature the direction of slope of
boundary lines.
In fig.(36) the slopes of the boundary lines for the system A-B-C have
been determined by applying the Alkemade theorem. Three boundary lines
slope to a common junction at E and at D. These points are eutectic points.
Fig. (36) Application of the Alkemade theorem to determine slopes of
boundary lines.
2-4-2 Composition Triangles:
Alkemade lines divide a ternary diagram into composition triangles. In
the diagram of fig.(35), triangles A-BC-B and A-BC-C are composition
triangles. A composition triangle is always made up of three Alkemade lines.
2
Phases Diagrams Of Ceramics
Third Stage
It should be noted that Alkemade lines never cross one another.
Example: For fig. (37), label primary phase fields and construct Alkemade
lines.
Fig. (37) Ternary systems for example.
3
```