Compositions in Ternary Diagrams

All compositions, e.g., bulk compositions, liquid compositions, compositions of solid phases, on ternary diagrams are expressed in terms of the three end member components which define the system. These three components are located a the apices of the triangle.

Each apex on the triangle representing the ternary system represents 100% of the component at that apex. The side of the triangle, directly opposite the apex, represents 0% of the apex component. Compositions of points which lie along the outside edge of the triangle are simply a mixture of the two components at each end of the tie line, with 0% of the third component.

1. Method 1 - Triangular Grid
   In this method a grid is constructed on the diagram. This grid is most commonly set up representing a 10% incremental increase in the components. To determine the composition of a point within the triangular area of the diagram a series of three lines are drawn through the point of intersest, with each line parallel to a side of the triangle. With these lines in place the percentage of each component in the compostion of the point can readliy be determined.
   
2. Method 2 - Two Line Method
   In this method only two lines are drawn, through the point of interest, parallel to any two sides of the triangle. The intersection of these two lines with the third side divides this side into three line segments. The lengths of the individual line segments are proportional to the relative amounts of the three components.

The two methods outlined above assumed an equilateral triangle, however both methods can be applied when dealing with a non-equilateral or scalene triangle in nature.

Determining Compositions

To determine the composition of a point lying inside the triangular diagram, a series of three lines through the point of interest, with each line parallel to a side of the triangle are drawn, as shown on the above image.

With these lines in place the composition of each point in terms of the end member components can be read directly from the diagram.

1. Point E has a composition of 36% A, 43% B and 21% C.
2. Point 1 has a composition of 19% A, 30% B and , 51% C.
3. Point 2 has a composition of 45% A, 23% B and 32%C.
4. Point e₃ has a composition of 60% A, 0% B and 40% C.