Ternary plots are frequently used by a number of natural science fields, including inorganic chemistry, soil science, mineralogy, and petrology. In this post we’ll show you how to adjust ternary graphs to be rescaled to show a particular region of interest. Because all three axes are tied in the strict relationship where values x+y+z always equal 1, different shapes, including rhombuses, diamonds, and trapezoids, can often be creating by only manually adjusting the range of two of these axes. You can follow along with this tutorial with this OPJ.
In the above figure we see a ternary graph with some randomly generated X-Y-Z data that has been normalized based on the XYZ sum rule. Let’s say we want to change our graph so it only focuses on the highlighted area. However, the values for the points on these axes may not seem intuitive at first, so how would one approach this?
In this color-coded version of the graph we can clearly see which grid lines correspond with which Cartesian coordinates. Another easy way of determining which values correspond with which points is by using the Screen Reader tool (the icon on the left side of the screen, below the Scale In/Scale Out tools) to read coordinates at a given point, even those without plotted data.
Once we know our coordinates we can determine the ranges of our region of interest. While there are 3 ranges that define this, in this instance, we will only need to adjust two of them, x and y, and z will adjust automatically. First double click on an axis line to open the axis dialog, and after setting x and y from 0.125 to 0.5 in their respective “scale” nodes, we’ll click Apply. The resulting graph should look something like this-
Note: If the resulting graph has scatter points showing outside the graph axes, you can hide those by choosing Format: Layer, then clicking on the Display/Speed tab to the right side of Plot Details and checking the Clip Data to Frame box.
A similar principal applies to creating a diamond shaped ROI.
After determining our necessary ranges we’ll adjust our x and z ranges from 0.125 to 0.5. With these two adjustments, our y-range will change automatically.
After clicking apply, the resulting graph will appear like so-
And lastly let’s assume we want to make a trapezoidal graph.
Unlike a diamond or rhombus shaped region of interest, which both share the same geometry, a trapezoid will require adjustments for all 3 axes in the axis dialog.
After adjusting x and z from 0 to 0.625, and y from 0 to 0.375, we see the resulting section shown here-
This covers the basics of setting the axis scale of a ternary graph in Origin. Ternary graphs can also be rescaled to smaller triangular ranges by giving all three axes equal ranges. Or use the Scale-In tool ( ) on Tools toolbar to click and drag a region of interest over your graph, then fine tune x, y and z axis scale in Axis dialog.