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Geology is the Way

Interactive: how to use a ternary plot

Ternary plots or ternary diagrams are triangular representations of the compositions of objects that can be expressed by mixtures of three components. In geology they are widely used to show the composition of rocks and minerals, in function of the mineral content, proportion of end-members, or even chemical composition. Many rock classification schemes are also based on ternary plots. Beyond geology, their use is very common also in metallurgy, chemistry, and other sciences.

Empty ternary plot. Credits to Smith609 (wikipedia.org)

Anatomy of a ternary plot
Ternary plots are graphical representations mixtures of any three components, typically expresses as % and whose sum must be 100%. Each apex represent a specific component. In this example, let’s say you have a rock which is composed of a mixture of the minerals A, B, and C. Each apex corresponds to 100% of the component written on the vertex. The percentage of this component is 0% on the side, opposite to the apex. In between, the percentage of that component increases – in this case by 10% – on each line parallel to the side, approaching the vertex. Let’s consider, for example, A, the top apex of the diagram: the percentage of A is 100% at the apex and 0% on the opposite side, at the bottom of the diagram. The content of A progressively increases from 0 to 100% approaching the top apex, following the red arrow. Each horizontal line, parallel to the bottom side and perpendicular to the red arrow, represents a 10% increase in the content of A: 10%, 20%, 30%…. and so on.

Apices B and C work the same way as A but we must be careful because their scale bar (green and blue arrows) are rotated by 120°, and this may cause confusion when we are at our first approach to this kind of diagrams. In any case, B and C are 100% at their respective apices and 0% on the opposite sides. Starting from the lower left apex B, the content of B decreases obliquely approaching the opposite side, to the right. This decrement is highlighted by the lines which dip to the right and are parallel to that side, each corresponding to a 10% decrease. Same story for C, but in this case the lines inclided to the left are those that represent the percentage of C (parallel, indeed, to the side opposite to C). My practical advice is, in case we fear to get confused, to physically rotate the diagram or tilt your head, so that the vertex you are working with is at the top.

Interactive: Let's practice with lines!

The diagram on the right is interactive and allows to visualize the lines that correspond to a specific percentage of a component, highlighted with different colors. Gently hover the mouse on the image to visualize them. As you can see, each line corresponds to a specific percentage of a component and, if we approach an apex starting from the opposite side, we may notice how that percentage progressively increases from 0 to 100%. Try it!

image/svg+xml 100% C 100% A 100% B 90% A 90% A 80% A 80% A 70% A 70% A 60% A 60% A 50% A 50% A 40% A 40% A 30% A 30% A 20% A 20% A 10% A 10% A 0% A 0% A 0% C 10% C 30% C 40% C 70% C 80% C 90% C 20% C 0% B 10% B 20% B 30% B 40% B 50% B 60% B 70% B 80% B 90% B 60% C 50% C

Now let’s mix!
Technically speaking, each line represents the locus of the points where the percentage of a said component is constant. Since the sum A + B + C = 100%, the three lines must intersect in a single point. Special cases occur when (1) a component is missing (e.g. A = 0%, B = 30%, C = 70%), in which case the composition lies on a point to the side where that component is 0%, or (2) when there is a single component (e.g. A = 100%), and in this case the composition corresponds to the apex of that component (in this case A). In all other situations, lines must cross in a single point within the diagram. Here on the right you can see an example of a mix of 50% A, 20% B e 30% C. As you can see, the three lines intersect in a single point, corresponding to the composition of our rock.

TERNARY PLOT EXAMPLE

Interactive ternary plot
Sometimes things are more difficult to explain and relatively simple to visualize. The interactive diagram below shows how the percentage of A, B, and C, varies for each point of the ternary plot: just hover the mouse on intersection points and you will see. Let’s see if you can find the following points BEFORE hovering the mouse:

B = 100%
A = 80%, C = 20%
A = 50%, B = 50%
A= 10%, B = 70%, C = 20%
A = 60%, B = 10%, C = 30%
A = 20%, B = 10%, C = 80%
A = 10%, B = 80%, C = 10%
A = 30%, B = 30%, C = 40%

Come on! Try it!

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