# How do I use ternary diagrams?Depicting ratios of three variables in the Earth sciences

## An introduction to using ternary diagrams

Ternary diagrams, also known as triangular diagrams or ternary plots, are graphical representations used to visualize data that consists of three components. They allow you to represent the relative proportions or percentages of the three components within a sample or system. These diagrams are valuable to Earth scientists when examining and classifying rocks, sediments, geochemical data, and other important Earth science data. These plots are not restricted to scientific data, one can use ternary plots on any three component system.

Let's think about a system with end-members chocolate, milk, and sugar like the image to the left. Where do your tastes lie on this ternary diagram? Do you like unsweetened chocolate that trends more toward the chocolate part of the triangle? Maybe you're a fan of chocolate milk, which is mostly chocolate and milk with a little bit of sugar? Don't like milk or chocolate? Pixie sticks (essentially pure sugar) might be for you. You can get a feel for the relative abundances of chocolate, milk, and sugar in each confection. Earth scientists use these principles of relative abundances to examine data from natural systems

## When do I use ternary diagrams?

Many Earth science data sets can be simplified down to three components to create an easy way to classify or name minerals, rocks, and landforms. Additionally, geochemical data are commonly plotted on ternary diagrams to examine relative concentrations with respect to three components. Many subdisciplines in Earth science have developed standardize ternary plots for defining classifications of plotted data sets. The figure below shows some examples from the fields of soil science, petrology, and geomorphology. When large data sets are plotted on ternary diagrams, the data can be evaluated to determine if trends of enrichment or depletion of individual components are present in the system.

## How do I plot data on a ternary diagram?

You are tasked with identifying the texture of a soil. Soil texture only includes the mineral components of soil. Following textural analysis, you find that the 50.0 g sample contains 18.5 g sand, 21.5 g silt, and 10.0 g clay.  Use the textural triangle to plot the texture of the soil sample and name the associated texture. Keep in mind that soil contains air, water, and organic matter in addition to the mineral components important to textural analysis.

Here are some steps to follow when plotting data on a ternary diagram:

The apex of a triangle is one of the corners. Apices is the plural form of apex.

Step 1: Identify the three components of interest (the apices of the ternary diagram) and the data associated with the components

Normalizing data means getting it on a "level playing field" so that numbers can be compared.  With ternary diagrams, we normalize to the three end members to find relative percentages of each of the three components.

Step 2. Normalize the data into percentages of each component. Add the values for each of the three components (excluding any excess data), then divide the value for one component by the total value and multiply by 100. Repeat for the other two components. The three calculated values must add up to 100%.

A/((A+B+C)) " * " 100 = A%

B/((A+B+C)) " * " 100 = B%

C/((A+B+C)) " * " 100 = C%

A% + B% + C% = 100%

Step 3. Orient yourself to the specific ternary diagram. In addition to the end members, you also need to notice what way the numbering on the axes goes - it can be clockwise or counterclockwise!

Step 4: Plot the normalized data as a single point. Remember all 3 normalized values must add up to 100%!

Let's start by figuring out the lines on this plot. The group of lines associated with an end member component are parallel (do not intersect) to the opposite side of the triangle.  In the figure below, each component has 10 lines and 1 apex associated with each component. All the purple lines are for component A, blue lines for component B, and orange lines for component C. If your sample plots at apex A, then it consists of 100% of component A.  If your sample plots on the line furthest away from the A apex, then 0% of your sample is component A. When you plot all your normalized values for each component, you will have three lines that cross each other at a single point -- this is why your normalized data MUST add up to 100%!

To plot your data, start with one of the three components and find that component corner on the ternary. Find your normalized value on the lines parallel to the opposite side and draw a line parallel to the lines. Repeat for the other two components - you should have a 3 lines that intersect at a point.

Step 5: Identify category, if applicable to the specific ternary diagram

## How do I read a ternary diagram?

Sometimes you might have data already plotted and need to extract the component compositions from the ternary diagram. Here is an example of that case:

Petrologists will plot rocks on diagrams with respect to their mineral abundance to determine the rock type. There may be many minerals in the rock, however, only three end-member compositions are needed to plot most rock types. Depending on rock composition, different ternary diagrams could be applicable for a specific rock.

If you have a coarse-grained (phaneritic/plutonic) igneous rock that is dominated by olivine and pyroxenes, the ultramafic igneous ternary diagram to the right would be most applicable. Answer the following questions with respect to the red dot plotted on the ultramafic diagram.

Step 1: Identify the three components of interest on the ternary diagram.

Step 2: Understand the relative abundances.

Step 3: Determine each component abundance.

Step 4: Checking you work.

## Where do you use ternary diagrams in Earth science?

• Plotting geochemical components to determine trends with respect to spatial or temporal data sets
• Petrology - classification of igneous rock types (QPM, clastic rocks, etc.)
• Mineralogy -  pyroxene and feldspar classification
• Water Quality - cation and anion variation diagrams
• Soils - soil texture classification
• Geomorphology - dune morphology, delta morphology , hydraulic geometry
• Climatology - Holdridge life zones

## Next steps

Two format options we can choose from