A ternary diagram is a specialized graphical tool used to visualize the relative proportions of three distinct variables within a system. These variables, often representing chemical, mineral, or material components, must collectively sum to a constant value, typically normalized to 100%. This type of plot is useful for analyzing compositional data because it allows three dimensions of information to be displayed simultaneously on a two-dimensional surface. Scientists and engineers across disciplines, including geology, materials science, and physical chemistry, employ ternary diagrams to understand complex mixtures.
The Geometric Structure of the Diagram
The fundamental framework of a ternary diagram is an equilateral triangle, necessary to represent the three variables that total 100%. Each of the three corners, or vertices, is dedicated to a single component, representing 100% of that component and 0% of the others. The side opposite a component’s vertex represents the 0% baseline for that component. The percentage of any component increases uniformly as one moves across the triangle from its 0% baseline toward its 100% vertex. The triangle’s interior is typically gridded with lines corresponding to equal percentage increments for all three variables.
Interpreting Individual Component Values
Reading the percentage of a single component involves tracing a path parallel to its 0% baseline (the side opposite its vertex). The component’s percentage is constant along these parallel lines, increasing as they approach the 100% vertex.
For Component A, you trace lines parallel to the side opposite the A vertex. For Component B (lower-left), the scale lines run parallel to the right edge of the triangle, and for Component C (lower-right), you follow lines parallel to the left side. This oblique reading technique, where the reference lines are oriented differently for each component, is the most challenging aspect of using the diagram. The consistent rule is always to read the value by tracking the line that is parallel to the component’s 0% base.
Plotting and Locating Data Points
Locating a specific data point requires finding the single intersection where the three component percentages meet. Consider a sample composition, such as 40% A, 30% B, and 30% C. First, trace the line corresponding to 40% of Component A, running parallel to the A-opposite side.
Next, locate the line for 30% of Component B, running parallel to the B-opposite side. The point where the A and B lines cross is the exact location of the sample. Because the three variables are dependent, the line for Component C will automatically pass through this intersection point.
This automatic convergence serves as a built-in verification mechanism. If the three percentage lines meet at a single point, it confirms that the component values sum to 100%. This method ensures that any composition satisfying the constant-sum rule has a unique location within the triangle.
Practical Applications and Data Interpretation
Once multiple data points are plotted, the true utility of the ternary diagram becomes apparent through the interpretation of data clustering. In fields like soil science, the diagram is partitioned into distinct compositional fields, such as “sand,” “silt,” and “clay” mixtures. Boundaries define soil texture classes, and a cluster of points within a field classifies those samples as having similar properties.
In materials science and metallurgy, ternary diagrams are often used as phase diagrams to map regions of stability for different phases in a three-component alloy system. The position of a point indicates the material’s composition, and the field it falls into dictates its physical state or crystalline structure. Interpreting the location of a point relative to these predefined fields provides rapid insight into the material’s likely behavior or properties.